diff --git a/benchmarks/README.md b/benchmarks/README.md
new file mode 100644
index 0000000..32544e7
--- /dev/null
+++ b/benchmarks/README.md
@@ -0,0 +1,19 @@
+# Benchmark Tests
+
+This directory contains a series of benchmark tests designed to evaluate performance. The test files are located in the `src/basic` and `src/model` folders, specifically:
+
+- `basic` folder: Contains tests for basic matrix operations, event-driven CSR matrix operations and jitconn matrix operations.
+- `model` folder: Contains tests for complex models, such as `test_COBA.py` and `test_MultipleArea.py`.
+
+
+To run these tests, ensure all necessary dependencies are installed. You can install the dependencies using the following command:
+
+```bash
+pip install -r requirements.txt
+```
+
+or if you are using a CUDA-enabled GPU, you can install the dependencies using the following command:
+
+```bash
+pip install -r requirements_cuda.txt
+```
diff --git a/benchmarks/analysis/basic/matvec/internal benchmarks/csrmv_cpu.csv b/benchmarks/analysis/basic/matvec/internal benchmarks/csrmv_cpu.csv
new file mode 100644
index 0000000..ef61a20
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/internal benchmarks/csrmv_cpu.csv	
@@ -0,0 +1,197 @@
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diff --git a/benchmarks/analysis/basic/matvec/internal benchmarks/csrmv_gpu.csv b/benchmarks/analysis/basic/matvec/internal benchmarks/csrmv_gpu.csv
new file mode 100644
index 0000000..58e6a37
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/internal benchmarks/csrmv_gpu.csv	
@@ -0,0 +1,197 @@
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diff --git a/benchmarks/analysis/basic/matvec/internal benchmarks/csrmv_grad_cpu.csv b/benchmarks/analysis/basic/matvec/internal benchmarks/csrmv_grad_cpu.csv
new file mode 100644
index 0000000..19a6630
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/internal benchmarks/csrmv_grad_cpu.csv	
@@ -0,0 +1,197 @@
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diff --git a/benchmarks/analysis/basic/matvec/internal benchmarks/csrmv_grad_gpu.csv b/benchmarks/analysis/basic/matvec/internal benchmarks/csrmv_grad_gpu.csv
new file mode 100644
index 0000000..93b459f
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/internal benchmarks/csrmv_grad_gpu.csv	
@@ -0,0 +1,197 @@
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diff --git a/benchmarks/analysis/basic/matvec/internal benchmarks/event_csr_matvec_vs_csr_matvec.py b/benchmarks/analysis/basic/matvec/internal benchmarks/event_csr_matvec_vs_csr_matvec.py
new file mode 100644
index 0000000..5d2a75d
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/internal benchmarks/event_csr_matvec_vs_csr_matvec.py	
@@ -0,0 +1,144 @@
+import pandas as pd
+import numpy as np
+import seaborn as sns
+import matplotlib.pyplot as plt
+import os
+
+current_path = os.path.dirname(os.path.abspath(__file__))
+
+csrmv_cpu = f"{current_path}/csrmv_cpu.csv"
+csrmv_gpu = f"{current_path}/csrmv_gpu.csv"
+event_csrmv_cpu = f"{current_path}/event_csrmv_cpu.csv"
+event_csrmv_gpu = f"{current_path}/event_csrmv_gpu.csv"
+csrmv_grad_cpu = f"{current_path}/csrmv_grad_cpu.csv"
+csrmv_grad_gpu = f"{current_path}/csrmv_grad_gpu.csv"
+event_csrmv_grad_cpu = f"{current_path}/event_csrmv_grad_cpu.csv"
+event_csrmv_grad_gpu = f"{current_path}/event_csrmv_grad_gpu.csv"
+
+# 去除一组列中的异常值
+def remove_row_outliers(df, column_prefix, threshold=1.5):
+    time_columns = [col for col in df.columns if col.startswith(column_prefix)]
+    
+    for index, row in df.iterrows():
+        time_values = row[time_columns]
+        mean = time_values.mean()
+        # 计算每个值与该行其他值的均值的差异
+        deviation = time_values.sub(time_values.mean())
+        abs_deviation = np.abs(deviation)
+        # 标记那些与均值差异过大的值为异常值
+        outliers = abs_deviation > (abs_deviation.mean() + threshold * abs_deviation.std())
+        df.loc[index, time_columns] = time_values.mask(outliers, np.nan)
+
+    return df
+
+# 重新计算speedup
+# Function to calculate the mean taichi aot time and speedup
+def calculate_speedup(base_df, event_df):
+    # Calculating mean taichi aot time for both datasets
+    taichi_aot_time_columns = [col for col in base_df.columns if col.startswith('taichi aot time')]
+    base_df['taichi aot time mean'] = base_df[taichi_aot_time_columns].mean(axis=1)
+    event_df['taichi aot time mean'] = event_df[taichi_aot_time_columns].mean(axis=1)
+
+    # Merging the datasets on shape[0], shape[1], values type, and transpose
+    merged_df = pd.merge(base_df[['shape[0]', 'shape[1]', 'values type', 'transpose', 'taichi aot time mean']],
+                         event_df[['shape[0]', 'shape[1]', 'values type', 'transpose', 'taichi aot time mean']],
+                         on=['shape[0]', 'shape[1]', 'values type', 'transpose'],
+                         suffixes=('', '_event'))
+
+    # Calculating speedup
+    merged_df['speedup'] = np.where(merged_df['taichi aot time mean_event'] < merged_df['taichi aot time mean'],
+                                    1 - (merged_df['taichi aot time mean'] / merged_df['taichi aot time mean_event']),
+                                    (merged_df['taichi aot time mean_event'] / merged_df['taichi aot time mean']) - 1)
+
+    return merged_df
+
+# 计算这行的taichi aot time mean
+def calculate_taichi_mean(df):
+    taichi_aot_time_columns = [col for col in df.columns if col.startswith('taichi aot time')]
+    df['taichi aot time mean'] = df[taichi_aot_time_columns].mean(axis=1)
+    return df
+
+def drop_columns(df):
+    df.drop(columns=['backend'], inplace=True)
+    df.drop(columns=['events type'], inplace=True)
+    df.drop(columns=['s'], inplace=True)
+    df.drop(columns=['p'], inplace=True)
+    return df
+
+# Function to plot speedup heatmaps for different values type and transpose combinations
+def plot_speedup_heatmaps(df, backend, filename):
+    plt.figure(figsize=(14, 14))  # Adjusting figure size for multiple subplots
+
+    # Creating subplots for each combination of values type and transpose
+    for i, (values_type, transpose) in enumerate([(vt, tr) for vt in df['values type'].unique() for tr in df['transpose'].unique()]):
+        plt.subplot(2, 2, i + 1)
+
+        # Filtering data and creating a pivot table for the heatmap
+        filtered_df = df[(df['values type'] == values_type) & (df['transpose'] == transpose)]
+        heatmap_data = filtered_df.pivot_table(index='shape[0]', columns='shape[1]', values='speedup', aggfunc='mean')
+
+        # Creating the heatmap
+        sns.heatmap(heatmap_data, annot=True, fmt=".2f", cmap='YlGnBu')
+        plt.title(f'values type: {values_type}, transpose: {transpose}')
+        plt.xlabel('shape[1]')
+        plt.ylabel('shape[0]')
+
+    # Adding an overall title with adjusted position
+    plt.suptitle(f'{backend}csrmv speedup over event_csrmv)\n' + \
+                 'speedup = event avg time / common avg time - 1 if common faster than event\n' + \
+                 'speedup = 1 - common avg time / event avg time if common slower than event', fontsize=16)
+
+    # Adjust layout to make room for the title
+    plt.tight_layout(rect=[0, 0, 1, 0.95])
+    plt.savefig(filename)
+    # plt.show()
+
+# 读取合并csrmv_cpu.csv 和 event_csrmv_cpu.csv, csrmv_gpu.csv 和 event_csrmv_gpu.csv
+# 只看values 和 transpose
+csrmv_cpu_df = pd.read_csv(csrmv_cpu)
+event_csrmv_cpu_df = pd.read_csv(event_csrmv_cpu)
+csrmv_gpu_df = pd.read_csv(csrmv_gpu)
+event_csrmv_gpu_df = pd.read_csv(event_csrmv_gpu)
+csrmv_grad_cpu_df = pd.read_csv(csrmv_grad_cpu)
+event_csrmv_grad_cpu_df = pd.read_csv(event_csrmv_grad_cpu)
+csrmv_grad_gpu_df = pd.read_csv(csrmv_grad_gpu)
+event_csrmv_grad_gpu_df = pd.read_csv(event_csrmv_grad_gpu)
+
+csrmv_cpu_df = drop_columns(csrmv_cpu_df)
+event_csrmv_cpu_df = drop_columns(event_csrmv_cpu_df)
+csrmv_gpu_df = drop_columns(csrmv_gpu_df)
+event_csrmv_gpu_df = drop_columns(event_csrmv_gpu_df)
+csrmv_grad_cpu_df = drop_columns(csrmv_grad_cpu_df)
+event_csrmv_grad_cpu_df = drop_columns(event_csrmv_grad_cpu_df)
+csrmv_grad_gpu_df = drop_columns(csrmv_grad_gpu_df)
+event_csrmv_grad_gpu_df = drop_columns(event_csrmv_grad_gpu_df)
+
+csrmv_cpu_df = remove_row_outliers(csrmv_cpu_df, "taichi aot time")
+event_csrmv_cpu_df = remove_row_outliers(event_csrmv_cpu_df, "taichi aot time")
+csrmv_gpu_df = remove_row_outliers(csrmv_gpu_df, "taichi aot time")
+event_csrmv_gpu_df = remove_row_outliers(event_csrmv_gpu_df, "taichi aot time")
+csrmv_grad_cpu_df= remove_row_outliers(csrmv_grad_cpu_df, "taichi aot time")
+event_csrmv_grad_cpu_df= remove_row_outliers(event_csrmv_grad_cpu_df, "taichi aot time")
+csrmv_grad_gpu_df= remove_row_outliers(csrmv_grad_gpu_df, "taichi aot time")
+event_csrmv_grad_gpu_df= remove_row_outliers(event_csrmv_grad_gpu_df, "taichi aot time")
+
+# csrmv_cpu_df = remove_row_outliers(csrmv_cpu_df, "brainpy time")
+# event_csrmv_cpu_df = remove_row_outliers(event_csrmv_cpu_df, "brainpy time")
+# csrmv_gpu_df = remove_row_outliers(csrmv_gpu_df, "brainpy time")
+# event_csrmv_gpu_df = remove_row_outliers(event_csrmv_gpu_df, "brainpy time")
+# csrmv_grad_cpu_df= remove_row_outliers(csrmv_grad_cpu_df, "brainpy time")
+# event_csrmv_grad_cpu_df= remove_row_outliers(event_csrmv_grad_cpu_df, "brainpy time")
+# csrmv_grad_gpu_df= remove_row_outliers(csrmv_grad_gpu_df, "brainpy time")
+# event_csrmv_grad_gpu_df= remove_row_outliers(event_csrmv_grad_gpu_df, "brainpy time")
+
+speedup_cpu = calculate_speedup(csrmv_cpu_df, event_csrmv_cpu_df)
+speedup_gpu = calculate_speedup(csrmv_gpu_df, event_csrmv_gpu_df)
+speedup_grad_cpu = calculate_speedup(csrmv_grad_cpu_df, event_csrmv_grad_cpu_df)
+speedup_grad_gpu = calculate_speedup(csrmv_grad_gpu_df, event_csrmv_grad_gpu_df)
+
+# Plotting heatmaps for each dataset
+plot_speedup_heatmaps(speedup_cpu, '[CPU] ', f'{current_path}/figure1/cpu.png')
+plot_speedup_heatmaps(speedup_gpu, '[GPU] ', f'{current_path}/figure1/gpu.png')
+plot_speedup_heatmaps(speedup_grad_cpu, '[CPU] Grad ', f'{current_path}/figure1/grad_cpu.png')
+plot_speedup_heatmaps(speedup_grad_gpu, '[GPU] Grad ', f'{current_path}/figure1/grad_gpu.png')
+
diff --git a/benchmarks/analysis/basic/matvec/internal benchmarks/event_csrmv_cpu.csv b/benchmarks/analysis/basic/matvec/internal benchmarks/event_csrmv_cpu.csv
new file mode 100644
index 0000000..6ec5619
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/internal benchmarks/event_csrmv_cpu.csv	
@@ -0,0 +1,393 @@
+s,p,shape[0],shape[1],backend,values type,events type,transpose,taichi aot time1(ms),taichi aot time2(ms),taichi aot time3(ms),taichi aot time4(ms),taichi aot time5(ms),taichi aot time6(ms),taichi aot time7(ms),taichi aot time8(ms),taichi aot time9(ms),taichi aot time10(ms),brainpy time1(ms),brainpy time2(ms),brainpy time3(ms),brainpy time4(ms),brainpy time5(ms),brainpy time6(ms),brainpy time7(ms),brainpy time8(ms),brainpy time9(ms),brainpy time10(ms)
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diff --git a/benchmarks/analysis/basic/matvec/internal benchmarks/event_csrmv_gpu.csv b/benchmarks/analysis/basic/matvec/internal benchmarks/event_csrmv_gpu.csv
new file mode 100644
index 0000000..ebd568a
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/internal benchmarks/event_csrmv_gpu.csv	
@@ -0,0 +1,393 @@
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diff --git a/benchmarks/analysis/basic/matvec/internal benchmarks/event_csrmv_grad_cpu.csv b/benchmarks/analysis/basic/matvec/internal benchmarks/event_csrmv_grad_cpu.csv
new file mode 100644
index 0000000..0ee7aff
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/internal benchmarks/event_csrmv_grad_cpu.csv	
@@ -0,0 +1,393 @@
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diff --git a/benchmarks/analysis/basic/matvec/internal benchmarks/event_csrmv_grad_gpu.csv b/benchmarks/analysis/basic/matvec/internal benchmarks/event_csrmv_grad_gpu.csv
new file mode 100644
index 0000000..79824cf
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/internal benchmarks/event_csrmv_grad_gpu.csv	
@@ -0,0 +1,393 @@
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+"(50000, 50000)",0.5,50000,50000,gpu,homo,bool,False,2.8030872344970703,2.5031566619873047,2.4580955505371094,2.5086402893066406,2.498626708984375,2.485990524291992,2.4411678314208984,2.875089645385742,2.6886463165283203,2.6824474334716797,3.6008358001708984,3.6737918853759766,3.592967987060547,3.7648677825927734,3.673553466796875,3.6873817443847656,3.7348270416259766,3.6885738372802734,3.742218017578125,3.751993179321289
+"(50000, 50000)",0.5,50000,50000,gpu,homo,float,True,1.985788345336914,2.177000045776367,1.985311508178711,2.0055770874023438,1.9636154174804688,1.9752979278564453,1.9621849060058594,1.9757747650146484,1.9307136535644531,2.1729469299316406,3.710031509399414,3.226757049560547,3.2393932342529297,3.2722949981689453,3.1845569610595703,3.6420822143554688,3.0891895294189453,3.1919479370117188,3.287792205810547,3.2668113708496094
+"(50000, 50000)",0.5,50000,50000,gpu,homo,float,False,2.621173858642578,2.6912689208984375,2.571582794189453,2.5589466094970703,2.5475025177001953,2.8717517852783203,2.694368362426758,2.6602745056152344,2.710580825805664,2.663135528564453,3.640413284301758,3.6039352416992188,3.9467811584472656,3.651142120361328,3.716707229614258,3.6830902099609375,3.812074661254883,4.15492057800293,3.8843154907226562,3.878355026245117
+"(50000, 50000)",0.5,50000,50000,gpu,heter,bool,True,2.302885055541992,2.079010009765625,2.075672149658203,2.0644664764404297,2.0627975463867188,2.0856857299804688,1.9977092742919922,2.0525455474853516,2.315044403076172,2.0079612731933594,2.2859573364257812,2.2912025451660156,2.2902488708496094,2.3050308227539062,2.2308826446533203,2.157449722290039,2.3093223571777344,2.269744873046875,2.3119449615478516,2.315044403076172
+"(50000, 50000)",0.5,50000,50000,gpu,heter,bool,False,2.6552677154541016,2.623319625854492,2.9566287994384766,2.6836395263671875,2.631664276123047,2.635955810546875,2.665996551513672,2.6497840881347656,2.958536148071289,2.6891231536865234,2.4766921997070312,2.596616744995117,2.6695728302001953,2.6030540466308594,2.5985240936279297,2.636432647705078,2.8908252716064453,2.6390552520751953,2.6390552520751953,2.61688232421875
+"(50000, 50000)",0.5,50000,50000,gpu,heter,float,True,2.1889209747314453,2.104043960571289,2.1562576293945312,2.0880699157714844,2.1674633026123047,2.0856857299804688,2.1562576293945312,2.4080276489257812,2.192258834838867,2.288341522216797,2.3822784423828125,2.4106502532958984,2.3360252380371094,2.294301986694336,2.387523651123047,2.260923385620117,2.297639846801758,2.492189407348633,2.389669418334961,2.4254322052001953
+"(50000, 50000)",0.5,50000,50000,gpu,heter,float,False,2.658367156982422,2.651214599609375,2.5997161865234375,2.64739990234375,2.6395320892333984,3.328561782836914,2.919435501098633,2.9070377349853516,2.935647964477539,2.905130386352539,2.5725364685058594,2.5606155395507812,2.8159618377685547,2.6416778564453125,2.6390552520751953,2.5420188903808594,2.820253372192383,2.825021743774414,2.797365188598633,2.9268264770507812
diff --git a/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn csr_matvec_vs_csr_matvec.py b/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn csr_matvec_vs_csr_matvec.py
new file mode 100644
index 0000000..3313364
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn csr_matvec_vs_csr_matvec.py	
@@ -0,0 +1,132 @@
+import pandas as pd
+import numpy as np
+import seaborn as sns
+import matplotlib.pyplot as plt
+import os
+
+current_path = os.path.dirname(os.path.abspath(__file__))
+
+jitconn_matvec_cpu = f"{current_path}/jitconn_matvec_cpu.csv"
+jitconn_matvec_gpu = f"{current_path}/jitconn_matvec_gpu.csv"
+csrmv_cpu = f"{current_path}/csrmv_cpu.csv"
+csrmv_gpu = f"{current_path}/csrmv_gpu.csv"
+jitconn_matvec_grad_cpu = f"{current_path}/jitconn_matvec_grad_cpu.csv"
+jitconn_matvec_grad_gpu = f"{current_path}/jitconn_matvec_grad_gpu.csv"
+csrmv_grad_cpu = f"{current_path}/csrmv_grad_cpu.csv"
+csrmv_grad_gpu = f"{current_path}/csrmv_grad_gpu.csv"
+
+# 去除一组列中的异常值
+def remove_row_outliers(df, column_prefix, threshold=1.5):
+    time_columns = [col for col in df.columns if col.startswith(column_prefix)]
+    
+    for index, row in df.iterrows():
+        time_values = row[time_columns]
+        mean = time_values.mean()
+        # 计算每个值与该行其他值的均值的差异
+        deviation = time_values.sub(time_values.mean())
+        abs_deviation = np.abs(deviation)
+        # 标记那些与均值差异过大的值为异常值
+        outliers = abs_deviation > (abs_deviation.mean() + threshold * abs_deviation.std())
+        df.loc[index, time_columns] = time_values.mask(outliers, np.nan)
+
+    return df
+
+# 重新计算speedup
+# Function to calculate the mean taichi aot time and speedup
+def calculate_speedup(base_df, event_df):
+    # Calculating mean taichi aot time for both datasets
+    taichi_aot_time_columns = [col for col in base_df.columns if col.startswith('taichi aot time')]
+    base_df['taichi aot time mean'] = base_df[taichi_aot_time_columns].mean(axis=1)
+    event_df['taichi aot time mean'] = event_df[taichi_aot_time_columns].mean(axis=1)
+
+    # Merging the datasets on shape[0], shape[1], values type, and transpose
+    merged_df = pd.merge(base_df[['shape[0]', 'shape[1]', 'transpose', 'taichi aot time mean']],
+                         event_df[['shape[0]', 'shape[1]', 'transpose', 'taichi aot time mean']],
+                         on=['shape[0]', 'shape[1]', 'transpose'],
+                         suffixes=('', '_event'))
+
+    # Calculating speedup
+    merged_df['speedup'] = np.where(merged_df['taichi aot time mean_event'] < merged_df['taichi aot time mean'],
+                                    merged_df['taichi aot time mean_event'] / merged_df['taichi aot time mean'] - 1,
+                                    1 - merged_df['taichi aot time mean'] / merged_df['taichi aot time mean_event'])
+
+    return merged_df
+
+# 计算这行的taichi aot time mean
+def calculate_taichi_mean(df):
+    taichi_aot_time_columns = [col for col in df.columns if col.startswith('taichi aot time')]
+    df['taichi aot time mean'] = df[taichi_aot_time_columns].mean(axis=1)
+    return df
+
+def drop_columns(df):
+    df.drop(columns=['backend'], inplace=True)
+    return df
+
+# Function to plot speedup heatmaps for different values type and transpose combinations
+def plot_speedup_heatmaps(df, backend, filename):
+    plt.figure(figsize=(14, 14))  # Adjusting figure size for multiple subplots
+
+    # Creating subplots for each combination of values type and transpose
+    for i, transpose in enumerate([tr  for tr in df['transpose'].unique()]):
+        plt.subplot(2, 1, i + 1)
+
+        # Filtering data and creating a pivot table for the heatmap
+        filtered_df = df[(df['transpose'] == transpose)]
+        heatmap_data = filtered_df.pivot_table(index='shape[0]', columns='shape[1]', values='speedup', aggfunc='mean')
+
+        # Creating the heatmap
+        sns.heatmap(heatmap_data, annot=True, fmt=".2f", cmap='YlGnBu')
+        plt.title(f'transpose: {transpose}')
+        plt.xlabel('shape[1]')
+        plt.ylabel('shape[0]')
+
+    # Adding an overall title with adjusted position
+    plt.suptitle(f'{backend} jitconn matvec speedup over csrmv)\n' + \
+                 'speedup = common csrmv avg time / jitconn avg time - 1 if jitconn faster than common csrmv\n' + \
+                 'speedup = 1 - jitconn avg time / common csrmv avg time if jitconn slower than common csrmv', fontsize=16)
+
+    # Adjust layout to make room for the title
+    plt.tight_layout(rect=[0, 0, 1, 0.95])
+    plt.savefig(filename)
+    # plt.show()
+
+# 读取合并csrmv_cpu.csv 和 event_csrmv_cpu.csv, csrmv_gpu.csv 和 event_csrmv_gpu.csv
+# 只看values 和 transpose
+jitconn_matvec_cpu_df = pd.read_csv(jitconn_matvec_cpu)
+csrmv_cpu_df = pd.read_csv(csrmv_cpu)
+jitconn_matvec_gpu_df = pd.read_csv(jitconn_matvec_gpu)
+csrmv_gpu_df = pd.read_csv(csrmv_gpu)
+jitconn_matvec_grad_cpu_df = pd.read_csv(jitconn_matvec_grad_cpu)
+csrmv_grad_cpu_df = pd.read_csv(csrmv_grad_cpu)
+jitconn_matvec_grad_gpu_df = pd.read_csv(jitconn_matvec_grad_gpu)
+csrmv_grad_gpu_df = pd.read_csv(csrmv_grad_gpu)
+
+jitconn_matvec_cpu_df = drop_columns(jitconn_matvec_cpu_df)
+csrmv_cpu_df = drop_columns(csrmv_cpu_df)
+jitconn_matvec_gpu_df = drop_columns(jitconn_matvec_gpu_df)
+csrmv_gpu_df = drop_columns(csrmv_gpu_df)
+jitconn_matvec_grad_cpu_df = drop_columns(jitconn_matvec_grad_cpu_df)
+csrmv_grad_cpu_df = drop_columns(csrmv_grad_cpu_df)
+jitconn_matvec_grad_gpu_df = drop_columns(jitconn_matvec_grad_gpu_df)
+csrmv_grad_gpu_df = drop_columns(csrmv_grad_gpu_df)
+
+jitconn_matvec_cpu_df = remove_row_outliers(jitconn_matvec_cpu_df, "taichi aot time")
+csrmv_cpu_df = remove_row_outliers(csrmv_cpu_df, "taichi aot time")
+jitconn_matvec_gpu_df = remove_row_outliers(jitconn_matvec_gpu_df, "taichi aot time")
+csrmv_gpu_df = remove_row_outliers(csrmv_gpu_df, "taichi aot time")
+jitconn_matvec_grad_cpu_df= remove_row_outliers(jitconn_matvec_grad_cpu_df, "taichi aot time")
+csrmv_grad_cpu_df= remove_row_outliers(csrmv_grad_cpu_df, "taichi aot time")
+jitconn_matvec_grad_gpu_df= remove_row_outliers(jitconn_matvec_grad_gpu_df, "taichi aot time")
+csrmv_grad_gpu_df= remove_row_outliers(csrmv_grad_gpu_df, "taichi aot time")
+
+speedup_cpu = calculate_speedup(jitconn_matvec_cpu_df, csrmv_cpu_df)
+speedup_gpu = calculate_speedup(jitconn_matvec_gpu_df, csrmv_gpu_df)
+speedup_grad_cpu = calculate_speedup(jitconn_matvec_grad_cpu_df, csrmv_grad_cpu_df)
+speedup_grad_gpu = calculate_speedup(jitconn_matvec_grad_gpu_df, csrmv_grad_gpu_df)
+
+# Plotting heatmaps for each dataset
+plot_speedup_heatmaps(speedup_cpu, '[CPU] ', f'{current_path}/figure3/cpu.png')
+plot_speedup_heatmaps(speedup_gpu, '[GPU] ', f'{current_path}/figure3/gpu.png')
+plot_speedup_heatmaps(speedup_grad_cpu, '[CPU] Grad ', f'{current_path}/figure3/grad_cpu.png')
+plot_speedup_heatmaps(speedup_grad_gpu, '[GPU] Grad ', f'{current_path}/figure3/grad_gpu.png')
+
diff --git a/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn event_csr_matvec_vs_csr_matvec.py b/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn event_csr_matvec_vs_csr_matvec.py
new file mode 100644
index 0000000..ea0771d
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn event_csr_matvec_vs_csr_matvec.py	
@@ -0,0 +1,132 @@
+import pandas as pd
+import numpy as np
+import seaborn as sns
+import matplotlib.pyplot as plt
+import os
+
+current_path = os.path.dirname(os.path.abspath(__file__))
+
+jitconn_event_matvec_cpu = f"{current_path}/jitconn_event_matvec_cpu.csv"
+jitconn_event_matvec_gpu = f"{current_path}/jitconn_event_matvec_gpu.csv"
+event_csrmv_cpu = f"{current_path}/event_csrmv_cpu.csv"
+event_csrmv_gpu = f"{current_path}/event_csrmv_gpu.csv"
+jitconn_event_matvec_grad_cpu = f"{current_path}/jitconn_event_matvec_grad_cpu.csv"
+jitconn_event_matvec_grad_gpu = f"{current_path}/jitconn_event_matvec_grad_gpu.csv"
+event_csrmv_grad_cpu = f"{current_path}/event_csrmv_grad_cpu.csv"
+event_csrmv_grad_gpu = f"{current_path}/event_csrmv_grad_gpu.csv"
+
+# 去除一组列中的异常值
+def remove_row_outliers(df, column_prefix, threshold=1.5):
+    time_columns = [col for col in df.columns if col.startswith(column_prefix)]
+    
+    for index, row in df.iterrows():
+        time_values = row[time_columns]
+        mean = time_values.mean()
+        # 计算每个值与该行其他值的均值的差异
+        deviation = time_values.sub(time_values.mean())
+        abs_deviation = np.abs(deviation)
+        # 标记那些与均值差异过大的值为异常值
+        outliers = abs_deviation > (abs_deviation.mean() + threshold * abs_deviation.std())
+        df.loc[index, time_columns] = time_values.mask(outliers, np.nan)
+
+    return df
+
+# 重新计算speedup
+# Function to calculate the mean taichi aot time and speedup
+def calculate_speedup(base_df, event_df):
+    # Calculating mean taichi aot time for both datasets
+    taichi_aot_time_columns = [col for col in base_df.columns if col.startswith('taichi aot time')]
+    base_df['taichi aot time mean'] = base_df[taichi_aot_time_columns].mean(axis=1)
+    event_df['taichi aot time mean'] = event_df[taichi_aot_time_columns].mean(axis=1)
+
+    # Merging the datasets on shape[0], shape[1], values type, and transpose
+    merged_df = pd.merge(base_df[['shape[0]', 'shape[1]', 'transpose', 'taichi aot time mean']],
+                         event_df[['shape[0]', 'shape[1]', 'transpose', 'taichi aot time mean']],
+                         on=['shape[0]', 'shape[1]', 'transpose'],
+                         suffixes=('', '_event'))
+
+    # Calculating speedup
+    merged_df['speedup'] = np.where(merged_df['taichi aot time mean_event'] < merged_df['taichi aot time mean'],
+                                    merged_df['taichi aot time mean_event'] / merged_df['taichi aot time mean'] - 1,
+                                    1 - merged_df['taichi aot time mean'] / merged_df['taichi aot time mean_event'])
+
+    return merged_df
+
+# 计算这行的taichi aot time mean
+def calculate_taichi_mean(df):
+    taichi_aot_time_columns = [col for col in df.columns if col.startswith('taichi aot time')]
+    df['taichi aot time mean'] = df[taichi_aot_time_columns].mean(axis=1)
+    return df
+
+def drop_columns(df):
+    df.drop(columns=['backend'], inplace=True)
+    return df
+
+# Function to plot speedup heatmaps for different values type and transpose combinations
+def plot_speedup_heatmaps(df, backend, filename):
+    plt.figure(figsize=(14, 14))  # Adjusting figure size for multiple subplots
+
+    # Creating subplots for each combination of values type and transpose
+    for i, transpose in enumerate([tr  for tr in df['transpose'].unique()]):
+        plt.subplot(2, 1, i + 1)
+
+        # Filtering data and creating a pivot table for the heatmap
+        filtered_df = df[(df['transpose'] == transpose)]
+        heatmap_data = filtered_df.pivot_table(index='shape[0]', columns='shape[1]', values='speedup', aggfunc='mean')
+
+        # Creating the heatmap
+        sns.heatmap(heatmap_data, annot=True, fmt=".2f", cmap='YlGnBu')
+        plt.title(f'transpose: {transpose}')
+        plt.xlabel('shape[1]')
+        plt.ylabel('shape[0]')
+
+    # Adding an overall title with adjusted position
+    plt.suptitle(f'{backend} jitconn event matvec speedup over event_csrmv)\n' + \
+                 'speedup = event avg time / jitconn event avg time - 1 if jitconn event faster than event\n' + \
+                 'speedup = 1 - jitconn event avg time / event avg time if jitconn event slower than event', fontsize=16)
+
+    # Adjust layout to make room for the title
+    plt.tight_layout(rect=[0, 0, 1, 0.95])
+    plt.savefig(filename)
+    # plt.show()
+
+# 读取合并csrmv_cpu.csv 和 event_csrmv_cpu.csv, csrmv_gpu.csv 和 event_csrmv_gpu.csv
+# 只看values 和 transpose
+jitconn_event_matvec_cpu_df = pd.read_csv(jitconn_event_matvec_cpu)
+event_csrmv_cpu_df = pd.read_csv(event_csrmv_cpu)
+jitconn_event_matvec_gpu_df = pd.read_csv(jitconn_event_matvec_gpu)
+event_csrmv_gpu_df = pd.read_csv(event_csrmv_gpu)
+jitconn_event_matvec_grad_cpu_df = pd.read_csv(jitconn_event_matvec_grad_cpu)
+event_csrmv_grad_cpu_df = pd.read_csv(event_csrmv_grad_cpu)
+jitconn_event_matvec_grad_gpu_df = pd.read_csv(jitconn_event_matvec_grad_gpu)
+event_csrmv_grad_gpu_df = pd.read_csv(event_csrmv_grad_gpu)
+
+jitconn_event_matvec_cpu_df = drop_columns(jitconn_event_matvec_cpu_df)
+event_csrmv_cpu_df = drop_columns(event_csrmv_cpu_df)
+jitconn_event_matvec_gpu_df = drop_columns(jitconn_event_matvec_gpu_df)
+event_csrmv_gpu_df = drop_columns(event_csrmv_gpu_df)
+jitconn_event_matvec_grad_cpu_df = drop_columns(jitconn_event_matvec_grad_cpu_df)
+event_csrmv_grad_cpu_df = drop_columns(event_csrmv_grad_cpu_df)
+jitconn_event_matvec_grad_gpu_df = drop_columns(jitconn_event_matvec_grad_gpu_df)
+event_csrmv_grad_gpu_df = drop_columns(event_csrmv_grad_gpu_df)
+
+jitconn_event_matvec_cpu_df = remove_row_outliers(jitconn_event_matvec_cpu_df, "taichi aot time")
+event_csrmv_cpu_df = remove_row_outliers(event_csrmv_cpu_df, "taichi aot time")
+jitconn_event_matvec_gpu_df = remove_row_outliers(jitconn_event_matvec_gpu_df, "taichi aot time")
+event_csrmv_gpu_df = remove_row_outliers(event_csrmv_gpu_df, "taichi aot time")
+jitconn_event_matvec_grad_cpu_df= remove_row_outliers(jitconn_event_matvec_grad_cpu_df, "taichi aot time")
+event_csrmv_grad_cpu_df= remove_row_outliers(event_csrmv_grad_cpu_df, "taichi aot time")
+jitconn_event_matvec_grad_gpu_df= remove_row_outliers(jitconn_event_matvec_grad_gpu_df, "taichi aot time")
+event_csrmv_grad_gpu_df= remove_row_outliers(event_csrmv_grad_gpu_df, "taichi aot time")
+
+speedup_cpu = calculate_speedup(jitconn_event_matvec_cpu_df, event_csrmv_cpu_df)
+speedup_gpu = calculate_speedup(jitconn_event_matvec_gpu_df, event_csrmv_gpu_df)
+speedup_grad_cpu = calculate_speedup(jitconn_event_matvec_grad_cpu_df, event_csrmv_grad_cpu_df)
+speedup_grad_gpu = calculate_speedup(jitconn_event_matvec_grad_gpu_df, event_csrmv_grad_gpu_df)
+
+# Plotting heatmaps for each dataset
+plot_speedup_heatmaps(speedup_cpu, '[CPU] ', f'{current_path}/figure2/cpu.png')
+plot_speedup_heatmaps(speedup_gpu, '[GPU] ', f'{current_path}/figure2/gpu.png')
+plot_speedup_heatmaps(speedup_grad_cpu, '[CPU] Grad ', f'{current_path}/figure2/grad_cpu.png')
+plot_speedup_heatmaps(speedup_grad_gpu, '[GPU] Grad ', f'{current_path}/figure2/grad_gpu.png')
+
diff --git a/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn_event_matvec_cpu.csv b/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn_event_matvec_cpu.csv
new file mode 100644
index 0000000..e90fa22
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn_event_matvec_cpu.csv	
@@ -0,0 +1,1177 @@
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diff --git a/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn_event_matvec_gpu.csv b/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn_event_matvec_gpu.csv
new file mode 100644
index 0000000..bbab75c
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn_event_matvec_gpu.csv	
@@ -0,0 +1,1177 @@
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diff --git a/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn_event_matvec_grad_cpu.csv b/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn_event_matvec_grad_cpu.csv
new file mode 100644
index 0000000..e0ff9ef
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn_event_matvec_grad_cpu.csv	
@@ -0,0 +1,1177 @@
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diff --git a/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn_event_matvec_grad_gpu.csv b/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn_event_matvec_grad_gpu.csv
new file mode 100644
index 0000000..487a01d
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn_event_matvec_grad_gpu.csv	
@@ -0,0 +1,1177 @@
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diff --git a/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn_matvec_cpu.csv b/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn_matvec_cpu.csv
new file mode 100644
index 0000000..85ed98f
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn_matvec_cpu.csv	
@@ -0,0 +1,589 @@
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diff --git a/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn_matvec_gpu.csv b/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn_matvec_gpu.csv
new file mode 100644
index 0000000..ec822d2
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn_matvec_gpu.csv	
@@ -0,0 +1,589 @@
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diff --git a/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn_matvec_grad_cpu.csv b/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn_matvec_grad_cpu.csv
new file mode 100644
index 0000000..ef7dab7
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn_matvec_grad_cpu.csv	
@@ -0,0 +1,589 @@
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diff --git a/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn_matvec_grad_gpu.csv b/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn_matvec_grad_gpu.csv
new file mode 100644
index 0000000..6c6cecf
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/internal benchmarks/jitconn_matvec_grad_gpu.csv	
@@ -0,0 +1,589 @@
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diff --git a/benchmarks/analysis/basic/matvec/test_results/csr matvec/analysis cpu.py b/benchmarks/analysis/basic/matvec/test_results/csr matvec/analysis cpu.py
new file mode 100644
index 0000000..90287b5
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/test_results/csr matvec/analysis cpu.py	
@@ -0,0 +1,72 @@
+import pandas as pd
+import numpy as np
+import seaborn as sns
+import matplotlib.pyplot as plt
+
+combined_csv_path = "csr matvec/csrmv_cpu.csv"
+
+# 去除一组列中的异常值
+def remove_row_outliers(df, column_prefix, threshold=1.5):
+    time_columns = [col for col in df.columns if col.startswith(column_prefix)]
+    
+    for index, row in df.iterrows():
+        time_values = row[time_columns]
+        mean = time_values.mean()
+        # 计算每个值与该行其他值的均值的差异
+        deviation = time_values.sub(time_values.mean())
+        abs_deviation = np.abs(deviation)
+        # 标记那些与均值差异过大的值为异常值
+        outliers = abs_deviation > (abs_deviation.mean() + threshold * abs_deviation.std())
+        df.loc[index, time_columns] = time_values.mask(outliers, np.nan)
+
+    return df
+
+# 重新计算speedup
+def calculate_speedup(df):
+    # 计算每行taichi aot time与brainpy time的均值
+    taichi_aot_time_columns = [col for col in df.columns if col.startswith('taichi aot time')]
+    brainpy_time_columns = [col for col in df.columns if col.startswith('brainpy time')]
+    df['taichi aot time mean'] = df[taichi_aot_time_columns].mean(axis=1)
+    df['brainpy time mean'] = df[brainpy_time_columns].mean(axis=1)
+    # 计算speedup
+    df['speedup'] = np.where(df['brainpy time mean'] < df['taichi aot time mean'], 1 - (df['taichi aot time mean'] / df['brainpy time mean']), (df['brainpy time mean'] / df['taichi aot time mean']) - 1)
+    return df
+
+# Load the combined dataset
+combined_df = pd.read_csv(combined_csv_path)
+combined_df.drop(columns=['backend'], inplace=True)
+combined_df.drop(columns=['events type'], inplace=True)
+combined_df.drop(columns=['s'], inplace=True)
+combined_df.drop(columns=['p'], inplace=True)
+combined_df = remove_row_outliers(combined_df, "taichi aot time")
+combined_df = remove_row_outliers(combined_df, "brainpy time")
+combined_df = calculate_speedup(combined_df)
+
+# Averaging the speedup values for each combination of 's', 'p', 'backend', 'values type', and 'events type'
+avg_speedup_df = combined_df.groupby(['values type', 'transpose', 'shape[0]', 'shape[1]']).mean().reset_index()
+
+# Setting up the plots for heatmaps based on different backends, values types, and events types
+plt.figure(figsize=(14, 14))  # Adjusting figure size for eight subplots
+
+# Creating subplots for each combination of backend, values type, and events type
+for i, (values_type, transpose) in enumerate([(v, t)  for v in avg_speedup_df['values type'].unique() for t in avg_speedup_df['transpose'].unique()]):
+    plt.subplot(2, 2, i + 1)
+
+    # Filtering data and creating a pivot table for the heatmap
+    filtered_df = avg_speedup_df[(avg_speedup_df['values type'] == values_type) & (avg_speedup_df['transpose'] == transpose)]
+    heatmap_data = filtered_df.pivot(index="shape[0]", columns="shape[1]", values="speedup")
+
+    # Creating the heatmap
+    sns.heatmap(heatmap_data, annot=True, fmt=".2f", cmap='YlGnBu')
+    plt.title(f'values type: {values_type}, transpose: {transpose}')
+    plt.xlabel('shape[0]')
+    plt.ylabel('shape[1]')
+
+# Adding an overall title with adjusted position
+plt.suptitle('[CPU] csr matvec taichi speedup over brainpylib\n'
+             'speedup = (brainpylib time / taichi aot time) - 1', fontsize=16)
+
+# Adjust layout to make room for the title
+plt.tight_layout(rect=[0, 0, 1, 0.95])
+plt.savefig('csr matvec/csrmv cpu.png')
+# plt.show()
diff --git a/benchmarks/analysis/basic/matvec/test_results/csr matvec/analysis gpu.py b/benchmarks/analysis/basic/matvec/test_results/csr matvec/analysis gpu.py
new file mode 100644
index 0000000..19a7dc7
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/test_results/csr matvec/analysis gpu.py	
@@ -0,0 +1,70 @@
+import pandas as pd
+import numpy as np
+import seaborn as sns
+import matplotlib.pyplot as plt
+
+combined_csv_path = "csr matvec/csrmv_gpu.csv"
+
+def remove_row_outliers(df, column_prefix, threshold=1.5):
+    time_columns = [col for col in df.columns if col.startswith(column_prefix)]
+    
+    for index, row in df.iterrows():
+        time_values = row[time_columns]
+        mean = time_values.mean()
+        # 计算每个值与该行其他值的均值的差异
+        deviation = time_values.sub(time_values.mean())
+        abs_deviation = np.abs(deviation)
+        # 标记那些与均值差异过大的值为异常值
+        outliers = abs_deviation > (abs_deviation.mean() + threshold * abs_deviation.std())
+        df.loc[index, time_columns] = time_values.mask(outliers, np.nan)
+
+    return df
+
+# 重新计算speedup
+def calculate_speedup(df):
+    # 计算每行taichi aot time与brainpy time的均值
+    taichi_aot_time_columns = [col for col in df.columns if col.startswith('taichi aot time')]
+    brainpy_time_columns = [col for col in df.columns if col.startswith('brainpy time')]
+    df['taichi aot time mean'] = df[taichi_aot_time_columns].mean(axis=1)
+    df['brainpy time mean'] = df[brainpy_time_columns].mean(axis=1)
+    # 计算speedup
+    df['speedup'] = np.where(df['brainpy time mean'] < df['taichi aot time mean'], 1 - (df['taichi aot time mean'] / df['brainpy time mean']), (df['brainpy time mean'] / df['taichi aot time mean']) - 1)
+    return df
+
+# Load the combined dataset
+combined_df = pd.read_csv(combined_csv_path)
+combined_df.drop(columns=['backend'], inplace=True)
+combined_df.drop(columns=['events type'], inplace=True)
+combined_df.drop(columns=['s'], inplace=True)
+combined_df = remove_row_outliers(combined_df, "taichi aot time")
+combined_df = remove_row_outliers(combined_df, "brainpy time")
+combined_df = calculate_speedup(combined_df)
+
+# Averaging the speedup values for each combination of 's', 'p', 'backend', 'values type', and 'events type'
+avg_speedup_df = combined_df.groupby(['values type', 'transpose', 'shape[0]', 'shape[1]']).mean().reset_index()
+
+# Setting up the plots for heatmaps based on different backends, values types, and events types
+plt.figure(figsize=(14, 14))  # Adjusting figure size for eight subplots
+
+# Creating subplots for each combination of backend, values type, and events type
+for i, (values_type, transpose) in enumerate([(v, t)  for v in avg_speedup_df['values type'].unique() for t in avg_speedup_df['transpose'].unique()]):
+    plt.subplot(2, 2, i + 1)
+
+    # Filtering data and creating a pivot table for the heatmap
+    filtered_df = avg_speedup_df[(avg_speedup_df['values type'] == values_type) & (avg_speedup_df['transpose'] == transpose)]
+    heatmap_data = filtered_df.pivot(index="shape[0]", columns="shape[1]", values="speedup")
+
+    # Creating the heatmap
+    sns.heatmap(heatmap_data, annot=True, fmt=".2f", cmap='YlGnBu')
+    plt.title(f'values type: {values_type}, transpose: {transpose}')
+    plt.xlabel('shape[0]')
+    plt.ylabel('shape[1]')
+
+# Adding an overall title with adjusted position
+plt.suptitle('[GPU] csr matvec taichi speedup over brainpylib method: cusparse\n'
+             'speedup = (brainpylib time / taichi aot time) - 1', fontsize=16)
+
+# Adjust layout to make room for the title
+plt.tight_layout(rect=[0, 0, 1, 0.95])
+plt.savefig('csr matvec/csrmv gpu.png')
+# plt.show()
diff --git a/benchmarks/analysis/basic/matvec/test_results/csr matvec/barchart_cpu.py b/benchmarks/analysis/basic/matvec/test_results/csr matvec/barchart_cpu.py
new file mode 100644
index 0000000..ec95a02
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/test_results/csr matvec/barchart_cpu.py	
@@ -0,0 +1,48 @@
+import matplotlib.pyplot as plt
+import pandas as pd
+import numpy as np
+
+# 去除一组列中的异常值
+def remove_row_outliers(df, column_prefix, threshold=1.5):
+    time_columns = [col for col in df.columns if col.startswith(column_prefix)]
+    
+    for index, row in df.iterrows():
+        time_values = row[time_columns]
+        mean = time_values.mean()
+        # 计算每个值与该行其他值的均值的差异
+        deviation = time_values.sub(time_values.mean())
+        abs_deviation = np.abs(deviation)
+        # 标记那些与均值差异过大的值为异常值
+        outliers = abs_deviation > (abs_deviation.mean() + threshold * abs_deviation.std())
+        df.loc[index, time_columns] = time_values.mask(outliers, np.nan)
+
+    return df
+
+# 重新计算speedup
+def calculate_speedup(df):
+    # 计算每行taichi aot time与brainpy time的均值
+    taichi_aot_time_columns = [col for col in df.columns if col.startswith('taichi aot time')]
+    brainpy_time_columns = [col for col in df.columns if col.startswith('brainpy time')]
+    df['taichi aot time mean'] = df[taichi_aot_time_columns].mean(axis=1)
+    df['brainpy time mean'] = df[brainpy_time_columns].mean(axis=1)
+    # 计算speedup
+    df['speedup'] = np.where(df['brainpy time mean'] < df['taichi aot time mean'], 1 - (df['taichi aot time mean'] / df['brainpy time mean']), (df['brainpy time mean'] / df['taichi aot time mean']) - 1)
+    return df
+
+# Load the combined dataset
+combined_df = pd.read_csv("csr matvec/csrmv_cpu.csv")
+combined_df.drop(columns=['backend'], inplace=True)
+combined_df.drop(columns=['events type'], inplace=True)
+combined_df.drop(columns=['s'], inplace=True)
+combined_df.drop(columns=['p'], inplace=True)
+combined_df = remove_row_outliers(combined_df, "taichi aot time")
+combined_df = remove_row_outliers(combined_df, "brainpy time")
+combined_df = calculate_speedup(combined_df)
+
+plt.hist(combined_df['speedup'], bins=50)
+plt.xlabel('Speedup')
+plt.ylabel('Frequency')
+plt.title('[CPU] csr matvec taichi speedup over brainpylib' + '\n' +
+          'speedup = (brainpylib time / taichi aot time) - 1')
+plt.savefig('csr matvec/csrmv cpu dist.png')
+
diff --git a/benchmarks/analysis/basic/matvec/test_results/csr matvec/barchart_gpu.py b/benchmarks/analysis/basic/matvec/test_results/csr matvec/barchart_gpu.py
new file mode 100644
index 0000000..d8f738f
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/test_results/csr matvec/barchart_gpu.py	
@@ -0,0 +1,47 @@
+import matplotlib.pyplot as plt
+import pandas as pd
+import numpy as np
+
+# 去除一组列中的异常值
+def remove_row_outliers(df, column_prefix, threshold=1.5):
+    time_columns = [col for col in df.columns if col.startswith(column_prefix)]
+    
+    for index, row in df.iterrows():
+        time_values = row[time_columns]
+        mean = time_values.mean()
+        # 计算每个值与该行其他值的均值的差异
+        deviation = time_values.sub(time_values.mean())
+        abs_deviation = np.abs(deviation)
+        # 标记那些与均值差异过大的值为异常值
+        outliers = abs_deviation > (abs_deviation.mean() + threshold * abs_deviation.std())
+        df.loc[index, time_columns] = time_values.mask(outliers, np.nan)
+
+    return df
+
+# 重新计算speedup
+def calculate_speedup(df):
+    # 计算每行taichi aot time与brainpy time的均值
+    taichi_aot_time_columns = [col for col in df.columns if col.startswith('taichi aot time')]
+    brainpy_time_columns = [col for col in df.columns if col.startswith('brainpy time')]
+    df['taichi aot time mean'] = df[taichi_aot_time_columns].mean(axis=1)
+    df['brainpy time mean'] = df[brainpy_time_columns].mean(axis=1)
+    # 计算speedup
+    df['speedup'] = np.where(df['brainpy time mean'] < df['taichi aot time mean'], 1 - (df['taichi aot time mean'] / df['brainpy time mean']), (df['brainpy time mean'] / df['taichi aot time mean']) - 1)
+    return df
+
+# Load the combined dataset
+combined_df = pd.read_csv("csr matvec/csrmv_gpu.csv")
+combined_df.drop(columns=['backend'], inplace=True)
+combined_df.drop(columns=['events type'], inplace=True)
+combined_df.drop(columns=['s'], inplace=True)
+combined_df.drop(columns=['p'], inplace=True)
+combined_df = remove_row_outliers(combined_df, "taichi aot time")
+combined_df = remove_row_outliers(combined_df, "brainpy time")
+combined_df = calculate_speedup(combined_df)
+
+plt.hist(combined_df['speedup'], bins=50)
+plt.xlabel('Speedup')
+plt.ylabel('Frequency')
+plt.title('[GPU] csr matvec taichi speedup over brainpylib' + '\n' +
+          'speedup = (brainpylib time / taichi aot time) - 1')
+plt.savefig('csr matvec/csrmv gpu dist.png')
\ No newline at end of file
diff --git a/benchmarks/analysis/basic/matvec/test_results/csr matvec/csrmv_cpu.csv b/benchmarks/analysis/basic/matvec/test_results/csr matvec/csrmv_cpu.csv
new file mode 100644
index 0000000..ef61a20
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/test_results/csr matvec/csrmv_cpu.csv	
@@ -0,0 +1,197 @@
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diff --git a/benchmarks/analysis/basic/matvec/test_results/csr matvec/csrmv_gpu.csv b/benchmarks/analysis/basic/matvec/test_results/csr matvec/csrmv_gpu.csv
new file mode 100644
index 0000000..58e6a37
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/test_results/csr matvec/csrmv_gpu.csv	
@@ -0,0 +1,197 @@
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diff --git a/benchmarks/analysis/basic/matvec/test_results/event csr matvec/analysis cpu.py b/benchmarks/analysis/basic/matvec/test_results/event csr matvec/analysis cpu.py
new file mode 100644
index 0000000..a419a97
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/test_results/event csr matvec/analysis cpu.py	
@@ -0,0 +1,70 @@
+import pandas as pd
+import numpy as np
+import seaborn as sns
+import matplotlib.pyplot as plt
+
+combined_csv_path = "event csr matvec/event_csrmv_cpu.csv"
+
+# 去除一组列中的异常值
+def remove_row_outliers(df, column_prefix, threshold=1.5):
+    time_columns = [col for col in df.columns if col.startswith(column_prefix)]
+    
+    for index, row in df.iterrows():
+        time_values = row[time_columns]
+        mean = time_values.mean()
+        # 计算每个值与该行其他值的均值的差异
+        deviation = time_values.sub(time_values.mean())
+        abs_deviation = np.abs(deviation)
+        # 标记那些与均值差异过大的值为异常值
+        outliers = abs_deviation > (abs_deviation.mean() + threshold * abs_deviation.std())
+        df.loc[index, time_columns] = time_values.mask(outliers, np.nan)
+
+    return df
+
+# 重新计算speedup
+def calculate_speedup(df):
+    # 计算每行taichi aot time与brainpy time的均值
+    taichi_aot_time_columns = [col for col in df.columns if col.startswith('taichi aot time')]
+    brainpy_time_columns = [col for col in df.columns if col.startswith('brainpy time')]
+    df['taichi aot time mean'] = df[taichi_aot_time_columns].mean(axis=1)
+    df['brainpy time mean'] = df[brainpy_time_columns].mean(axis=1)
+    # 计算speedup
+    df['speedup'] = np.where(df['brainpy time mean'] < df['taichi aot time mean'], 1 - (df['taichi aot time mean'] / df['brainpy time mean']), (df['brainpy time mean'] / df['taichi aot time mean']) - 1)
+    return df
+
+# Load the combined dataset
+combined_df = pd.read_csv(combined_csv_path)
+combined_df.drop(columns=['backend'], inplace=True)
+combined_df.drop(columns=['s'], inplace=True)
+combined_df = remove_row_outliers(combined_df, "taichi aot time")
+combined_df = remove_row_outliers(combined_df, "brainpy time")
+combined_df = calculate_speedup(combined_df)
+
+# Averaging the speedup values for each combination of 's', 'p', 'backend', 'values type', and 'events type'
+avg_speedup_df = combined_df.groupby(['values type', 'events type', 'transpose', 'shape[0]', 'shape[1]']).mean().reset_index()
+
+# Setting up the plots for heatmaps based on different backends, values types, and events types
+plt.figure(figsize=(14, 20))  # Adjusting figure size for eight subplots
+
+# Creating subplots for each combination of backend, values type, and events type
+for i, (values_type, events_type, transpose) in enumerate([(v, e, t)  for v in avg_speedup_df['values type'].unique() for e in avg_speedup_df['events type'].unique() for t in avg_speedup_df['transpose'].unique()]):
+    plt.subplot(4, 2, i + 1)
+
+    # Filtering data and creating a pivot table for the heatmap
+    filtered_df = avg_speedup_df[(avg_speedup_df['values type'] == values_type) & (avg_speedup_df['events type'] == events_type) & (avg_speedup_df['transpose'] == transpose)]
+    heatmap_data = filtered_df.pivot(index="shape[0]", columns="shape[1]", values="speedup")
+
+    # Creating the heatmap
+    sns.heatmap(heatmap_data, annot=True, fmt=".2f", cmap='YlGnBu')
+    plt.title(f'values type: {values_type}, events type: {events_type}, transpose: {transpose}')
+    plt.xlabel('shape[0]')
+    plt.ylabel('shape[1]')
+
+# Adding an overall title with adjusted position
+plt.suptitle('[CPU] event csr matvec taichi speedup over brainpylib\n'
+             'speedup = (brainpylib time / taichi aot time) - 1', fontsize=16)
+
+# Adjust layout to make room for the title
+plt.tight_layout(rect=[0, 0, 1, 0.95])
+plt.savefig('event csr matvec/event csrmv cpu.png')
+# plt.show()
diff --git a/benchmarks/analysis/basic/matvec/test_results/event csr matvec/analysis gpu.py b/benchmarks/analysis/basic/matvec/test_results/event csr matvec/analysis gpu.py
new file mode 100644
index 0000000..4d51f29
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/test_results/event csr matvec/analysis gpu.py	
@@ -0,0 +1,70 @@
+import pandas as pd
+import numpy as np
+import seaborn as sns
+import matplotlib.pyplot as plt
+
+combined_csv_path = "event csr matvec/event_csrmv_gpu.csv"
+
+# 去除一组列中的异常值
+def remove_row_outliers(df, column_prefix, threshold=1.5):
+    time_columns = [col for col in df.columns if col.startswith(column_prefix)]
+    
+    for index, row in df.iterrows():
+        time_values = row[time_columns]
+        mean = time_values.mean()
+        # 计算每个值与该行其他值的均值的差异
+        deviation = time_values.sub(time_values.mean())
+        abs_deviation = np.abs(deviation)
+        # 标记那些与均值差异过大的值为异常值
+        outliers = abs_deviation > (abs_deviation.mean() + threshold * abs_deviation.std())
+        df.loc[index, time_columns] = time_values.mask(outliers, np.nan)
+
+    return df
+
+# 重新计算speedup
+def calculate_speedup(df):
+    # 计算每行taichi aot time与brainpy time的均值
+    taichi_aot_time_columns = [col for col in df.columns if col.startswith('taichi aot time')]
+    brainpy_time_columns = [col for col in df.columns if col.startswith('brainpy time')]
+    df['taichi aot time mean'] = df[taichi_aot_time_columns].mean(axis=1)
+    df['brainpy time mean'] = df[brainpy_time_columns].mean(axis=1)
+    # 计算speedup
+    df['speedup'] = np.where(df['brainpy time mean'] < df['taichi aot time mean'], 1 - (df['taichi aot time mean'] / df['brainpy time mean']), (df['brainpy time mean'] / df['taichi aot time mean']) - 1)
+    return df
+
+# Load the combined dataset
+combined_df = pd.read_csv(combined_csv_path)
+combined_df.drop(columns=['backend'], inplace=True)
+combined_df.drop(columns=['s'], inplace=True)
+combined_df = remove_row_outliers(combined_df, "taichi aot time")
+combined_df = remove_row_outliers(combined_df, "brainpy time")
+combined_df = calculate_speedup(combined_df)
+
+# Averaging the speedup values for each combination of 's', 'p', 'backend', 'values type', and 'events type'
+avg_speedup_df = combined_df.groupby(['values type', 'events type', 'transpose', 'shape[0]', 'shape[1]']).mean().reset_index()
+
+# Setting up the plots for heatmaps based on different backends, values types, and events types
+plt.figure(figsize=(14, 20))  # Adjusting figure size for eight subplots
+
+# Creating subplots for each combination of backend, values type, and events type
+for i, (values_type, events_type, transpose) in enumerate([(v, e, t)  for v in avg_speedup_df['values type'].unique() for e in avg_speedup_df['events type'].unique() for t in avg_speedup_df['transpose'].unique()]):
+    plt.subplot(4, 2, i + 1)
+
+    # Filtering data and creating a pivot table for the heatmap
+    filtered_df = avg_speedup_df[(avg_speedup_df['values type'] == values_type) & (avg_speedup_df['events type'] == events_type) & (avg_speedup_df['transpose'] == transpose)]
+    heatmap_data = filtered_df.pivot(index="shape[0]", columns="shape[1]", values="speedup")
+
+    # Creating the heatmap
+    sns.heatmap(heatmap_data, annot=True, fmt=".2f", cmap='YlGnBu')
+    plt.title(f'values type: {values_type}, events type: {events_type}, transpose: {transpose}')
+    plt.xlabel('shape[0]')
+    plt.ylabel('shape[1]')
+
+# Adding an overall title with adjusted position
+plt.suptitle('[GPU] event csr matvec taichi speedup over brainpylib\n'
+             'speedup = (brainpylib time / taichi aot time) - 1', fontsize=16)
+
+# Adjust layout to make room for the title
+plt.tight_layout(rect=[0, 0, 1, 0.95])
+plt.savefig('event csr matvec/event csrmv gpu.png')
+# plt.show()
diff --git a/benchmarks/analysis/basic/matvec/test_results/event csr matvec/barchart_cpu.py b/benchmarks/analysis/basic/matvec/test_results/event csr matvec/barchart_cpu.py
new file mode 100644
index 0000000..767f53d
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/test_results/event csr matvec/barchart_cpu.py	
@@ -0,0 +1,48 @@
+import matplotlib.pyplot as plt
+import pandas as pd
+import numpy as np
+
+# 去除一组列中的异常值
+def remove_row_outliers(df, column_prefix, threshold=1.5):
+    time_columns = [col for col in df.columns if col.startswith(column_prefix)]
+    
+    for index, row in df.iterrows():
+        time_values = row[time_columns]
+        mean = time_values.mean()
+        # 计算每个值与该行其他值的均值的差异
+        deviation = time_values.sub(time_values.mean())
+        abs_deviation = np.abs(deviation)
+        # 标记那些与均值差异过大的值为异常值
+        outliers = abs_deviation > (abs_deviation.mean() + threshold * abs_deviation.std())
+        df.loc[index, time_columns] = time_values.mask(outliers, np.nan)
+
+    return df
+
+# 重新计算speedup
+def calculate_speedup(df):
+    # 计算每行taichi aot time与brainpy time的均值
+    taichi_aot_time_columns = [col for col in df.columns if col.startswith('taichi aot time')]
+    brainpy_time_columns = [col for col in df.columns if col.startswith('brainpy time')]
+    df['taichi aot time mean'] = df[taichi_aot_time_columns].mean(axis=1)
+    df['brainpy time mean'] = df[brainpy_time_columns].mean(axis=1)
+    # 计算speedup
+    df['speedup'] = np.where(df['brainpy time mean'] < df['taichi aot time mean'], 1 - (df['taichi aot time mean'] / df['brainpy time mean']), (df['brainpy time mean'] / df['taichi aot time mean']) - 1)
+    return df
+
+# Load the combined dataset
+combined_df = pd.read_csv("event csr matvec/event_csrmv_cpu.csv")
+combined_df.drop(columns=['backend'], inplace=True)
+combined_df.drop(columns=['events type'], inplace=True)
+combined_df.drop(columns=['s'], inplace=True)
+combined_df.drop(columns=['p'], inplace=True)
+combined_df = remove_row_outliers(combined_df, "taichi aot time")
+combined_df = remove_row_outliers(combined_df, "brainpy time")
+combined_df = calculate_speedup(combined_df)
+
+plt.hist(combined_df['speedup'], bins=50)
+plt.xlabel('Speedup')
+plt.ylabel('Frequency')
+plt.title('[CPU] event csr matvec taichi speedup over brainpylib' + '\n' +
+          'speedup = (brainpylib time / taichi aot time) - 1')
+plt.savefig('event csr matvec/event csrmv cpu dist.png')
+
diff --git a/benchmarks/analysis/basic/matvec/test_results/event csr matvec/barchart_gpu.py b/benchmarks/analysis/basic/matvec/test_results/event csr matvec/barchart_gpu.py
new file mode 100644
index 0000000..2c0a1bb
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/test_results/event csr matvec/barchart_gpu.py	
@@ -0,0 +1,48 @@
+import matplotlib.pyplot as plt
+import pandas as pd
+import numpy as np
+
+# 去除一组列中的异常值
+def remove_row_outliers(df, column_prefix, threshold=1.5):
+    time_columns = [col for col in df.columns if col.startswith(column_prefix)]
+    
+    for index, row in df.iterrows():
+        time_values = row[time_columns]
+        mean = time_values.mean()
+        # 计算每个值与该行其他值的均值的差异
+        deviation = time_values.sub(time_values.mean())
+        abs_deviation = np.abs(deviation)
+        # 标记那些与均值差异过大的值为异常值
+        outliers = abs_deviation > (abs_deviation.mean() + threshold * abs_deviation.std())
+        df.loc[index, time_columns] = time_values.mask(outliers, np.nan)
+
+    return df
+
+# 重新计算speedup
+def calculate_speedup(df):
+    # 计算每行taichi aot time与brainpy time的均值
+    taichi_aot_time_columns = [col for col in df.columns if col.startswith('taichi aot time')]
+    brainpy_time_columns = [col for col in df.columns if col.startswith('brainpy time')]
+    df['taichi aot time mean'] = df[taichi_aot_time_columns].mean(axis=1)
+    df['brainpy time mean'] = df[brainpy_time_columns].mean(axis=1)
+    # 计算speedup
+    df['speedup'] = np.where(df['brainpy time mean'] < df['taichi aot time mean'], 1 - (df['taichi aot time mean'] / df['brainpy time mean']), (df['brainpy time mean'] / df['taichi aot time mean']) - 1)
+    return df
+
+# Load the combined dataset
+combined_df = pd.read_csv("event csr matvec/event_csrmv_gpu.csv")
+combined_df.drop(columns=['backend'], inplace=True)
+combined_df.drop(columns=['events type'], inplace=True)
+combined_df.drop(columns=['s'], inplace=True)
+combined_df.drop(columns=['p'], inplace=True)
+combined_df = remove_row_outliers(combined_df, "taichi aot time")
+combined_df = remove_row_outliers(combined_df, "brainpy time")
+combined_df = calculate_speedup(combined_df)
+
+plt.hist(combined_df['speedup'], bins=50)
+plt.xlabel('Speedup')
+plt.ylabel('Frequency')
+plt.title('[GPU] event csr matvec taichi speedup over brainpylib' + '\n' +
+          'speedup = (brainpylib time / taichi aot time) - 1')
+plt.savefig('event csr matvec/event csrmv gpu dist.png')
+
diff --git a/benchmarks/analysis/basic/matvec/test_results/event csr matvec/event_csrmv_cpu.csv b/benchmarks/analysis/basic/matvec/test_results/event csr matvec/event_csrmv_cpu.csv
new file mode 100644
index 0000000..6ec5619
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/test_results/event csr matvec/event_csrmv_cpu.csv	
@@ -0,0 +1,393 @@
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diff --git a/benchmarks/analysis/basic/matvec/test_results/event csr matvec/event_csrmv_gpu.csv b/benchmarks/analysis/basic/matvec/test_results/event csr matvec/event_csrmv_gpu.csv
new file mode 100644
index 0000000..ebd568a
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/test_results/event csr matvec/event_csrmv_gpu.csv	
@@ -0,0 +1,393 @@
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+"(50000, 50000)",0.5,50000,50000,gpu,heter,bool,False,1.8317699432373047,1.8429756164550781,1.9011497497558594,1.8315315246582031,2.048492431640625,1.760244369506836,1.7380714416503906,1.8644332885742188,1.7714500427246094,1.7349720001220703,1.619577407836914,1.619100570678711,1.5516281127929688,1.6210079193115234,1.615285873413086,1.6329288482666016,1.6674995422363281,1.5790462493896484,2.0558834075927734,1.5659332275390625
+"(50000, 50000)",0.5,50000,50000,gpu,heter,float,True,0.4897117614746094,0.48923492431640625,0.4878044128417969,0.4782676696777344,0.4813671112060547,0.4699230194091797,0.4811286926269531,0.4711151123046875,0.47659873962402344,0.4699230194091797,0.5011558532714844,0.49996376037597656,0.5042552947998047,0.5276203155517578,0.5233287811279297,0.8902549743652344,0.5104541778564453,0.5016326904296875,0.499725341796875,0.5028247833251953
+"(50000, 50000)",0.5,50000,50000,gpu,heter,float,False,1.9931793212890625,1.93023681640625,1.9903182983398438,1.9545555114746094,1.9876956939697266,1.9392967224121094,1.9423961639404297,2.1784305572509766,1.9931793212890625,1.93023681640625,2.390623092651367,1.997232437133789,1.9779205322265625,1.9867420196533203,1.9881725311279297,1.99127197265625,2.0911693572998047,2.0134449005126953,2.2766590118408203,1.9996166229248047
diff --git a/benchmarks/analysis/basic/matvec/test_results/jitconn event matvec/analysis cpu.py b/benchmarks/analysis/basic/matvec/test_results/jitconn event matvec/analysis cpu.py
new file mode 100644
index 0000000..2a30325
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/test_results/jitconn event matvec/analysis cpu.py	
@@ -0,0 +1,70 @@
+import pandas as pd
+import numpy as np
+import seaborn as sns
+import matplotlib.pyplot as plt
+
+combined_csv_path = "jitconn event matvec/jitconn_event_matvec_cpu.csv"
+
+# 去除一组列中的异常值
+def remove_row_outliers(df, column_prefix, threshold=1.5):
+    time_columns = [col for col in df.columns if col.startswith(column_prefix)]
+    
+    for index, row in df.iterrows():
+        time_values = row[time_columns]
+        mean = time_values.mean()
+        # 计算每个值与该行其他值的均值的差异
+        deviation = time_values.sub(time_values.mean())
+        abs_deviation = np.abs(deviation)
+        # 标记那些与均值差异过大的值为异常值
+        outliers = abs_deviation > (abs_deviation.mean() + threshold * abs_deviation.std())
+        df.loc[index, time_columns] = time_values.mask(outliers, np.nan)
+
+    return df
+
+# 重新计算speedup
+def calculate_speedup(df):
+    # 计算每行taichi aot time与brainpy time的均值
+    taichi_aot_time_columns = [col for col in df.columns if col.startswith('taichi aot time')]
+    brainpy_time_columns = [col for col in df.columns if col.startswith('brainpy time')]
+    df['taichi aot time mean'] = df[taichi_aot_time_columns].mean(axis=1)
+    df['brainpy time mean'] = df[brainpy_time_columns].mean(axis=1)
+    # 计算speedup
+    df['speedup'] = np.where(df['brainpy time mean'] < df['taichi aot time mean'], 1 - (df['taichi aot time mean'] / df['brainpy time mean']), (df['brainpy time mean'] / df['taichi aot time mean']) - 1)
+    return df
+# Load the combined dataset
+
+combined_df = pd.read_csv(combined_csv_path)
+combined_df.drop(columns=['backend'], inplace=True)
+combined_df = remove_row_outliers(combined_df, "taichi aot time")
+combined_df = remove_row_outliers(combined_df, "brainpy time")
+combined_df = calculate_speedup(combined_df)
+
+# Averaging the speedup values for each combination of 's', 'p', 'backend', 'values type', and 'events type'
+avg_speedup_df = combined_df.groupby(['type', 'transpose', 'outdim_parallel', 'bool_event', 'shape[0]', 'shape[1]']).mean().reset_index()
+
+# Setting up the plots for heatmaps based on different backends, values types, and events types
+plt.figure(figsize=(24, 22))  # Adjusting figure size for eight subplots
+
+# Creating subplots for each combination of backend, values type, and events type
+for i, (_type, transpose, bool_event, outdim_parallel) in enumerate([(_t, t, b, o)  for _t in avg_speedup_df['type'].unique() for t in avg_speedup_df['transpose'].unique() for b in avg_speedup_df['bool_event'].unique() for o in avg_speedup_df['outdim_parallel'].unique()]):
+    plt.subplot(6, 4, i + 1)
+
+    # Filtering data and creating a pivot table for the heatmap
+    filtered_df = avg_speedup_df[(avg_speedup_df['type'] == _type) & (avg_speedup_df['transpose'] == transpose) & (avg_speedup_df['bool_event'] == bool_event) & (avg_speedup_df['outdim_parallel'] == outdim_parallel)]
+    heatmap_data = filtered_df.pivot(index="shape[0]", columns="shape[1]", values="speedup")
+
+    # Creating the heatmap
+    sns.heatmap(heatmap_data, annot=True, fmt=".2f", cmap='YlGnBu')
+    plt.title(f'type: {_type}, transpose: {transpose}\n'
+              f'bool_event: {bool_event}, outdim_parallel: {outdim_parallel}')
+    plt.xlabel('shape[0]')
+    plt.ylabel('shape[1]')
+
+# Adding an overall title with adjusted position
+plt.suptitle('[CPU] jitconn event matvec taichi speedup over brainpylib\n'
+             'speedup = (brainpylib time / taichi aot time) - 1', fontsize=16)
+
+# Adjust layout to make room for the title
+plt.tight_layout(rect=[0, 0, 1, 0.95])
+plt.savefig('jitconn event matvec/jitconn_event_matvec_cpu.png')
+# plt.show()
diff --git a/benchmarks/analysis/basic/matvec/test_results/jitconn event matvec/analysis gpu.py b/benchmarks/analysis/basic/matvec/test_results/jitconn event matvec/analysis gpu.py
new file mode 100644
index 0000000..826af44
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/test_results/jitconn event matvec/analysis gpu.py	
@@ -0,0 +1,70 @@
+import pandas as pd
+import numpy as np
+import seaborn as sns
+import matplotlib.pyplot as plt
+
+combined_csv_path = "jitconn event matvec/jitconn_event_matvec_gpu.csv"
+
+# 去除一组列中的异常值
+def remove_row_outliers(df, column_prefix, threshold=1.5):
+    time_columns = [col for col in df.columns if col.startswith(column_prefix)]
+    
+    for index, row in df.iterrows():
+        time_values = row[time_columns]
+        mean = time_values.mean()
+        # 计算每个值与该行其他值的均值的差异
+        deviation = time_values.sub(time_values.mean())
+        abs_deviation = np.abs(deviation)
+        # 标记那些与均值差异过大的值为异常值
+        outliers = abs_deviation > (abs_deviation.mean() + threshold * abs_deviation.std())
+        df.loc[index, time_columns] = time_values.mask(outliers, np.nan)
+
+    return df
+
+# 重新计算speedup
+def calculate_speedup(df):
+    # 计算每行taichi aot time与brainpy time的均值
+    taichi_aot_time_columns = [col for col in df.columns if col.startswith('taichi aot time')]
+    brainpy_time_columns = [col for col in df.columns if col.startswith('brainpy time')]
+    df['taichi aot time mean'] = df[taichi_aot_time_columns].mean(axis=1)
+    df['brainpy time mean'] = df[brainpy_time_columns].mean(axis=1)
+    # 计算speedup
+    df['speedup'] = np.where(df['brainpy time mean'] < df['taichi aot time mean'], 1 - (df['taichi aot time mean'] / df['brainpy time mean']), (df['brainpy time mean'] / df['taichi aot time mean']) - 1)
+    return df
+# Load the combined dataset
+
+combined_df = pd.read_csv(combined_csv_path)
+combined_df.drop(columns=['backend'], inplace=True)
+combined_df = remove_row_outliers(combined_df, "taichi aot time")
+combined_df = remove_row_outliers(combined_df, "brainpy time")
+combined_df = calculate_speedup(combined_df)
+
+# Averaging the speedup values for each combination of 's', 'p', 'backend', 'values type', and 'events type'
+avg_speedup_df = combined_df.groupby(['type', 'transpose', 'outdim_parallel', 'bool_event', 'shape[0]', 'shape[1]']).mean().reset_index()
+
+# Setting up the plots for heatmaps based on different backends, values types, and events types
+plt.figure(figsize=(24, 22))  # Adjusting figure size for eight subplots
+
+# Creating subplots for each combination of backend, values type, and events type
+for i, (_type, transpose, bool_event, outdim_parallel) in enumerate([(_t, t, b, o)  for _t in avg_speedup_df['type'].unique() for t in avg_speedup_df['transpose'].unique() for b in avg_speedup_df['bool_event'].unique() for o in avg_speedup_df['outdim_parallel'].unique()]):
+    plt.subplot(6, 4, i + 1)
+
+    # Filtering data and creating a pivot table for the heatmap
+    filtered_df = avg_speedup_df[(avg_speedup_df['type'] == _type) & (avg_speedup_df['transpose'] == transpose) & (avg_speedup_df['bool_event'] == bool_event) & (avg_speedup_df['outdim_parallel'] == outdim_parallel)]
+    heatmap_data = filtered_df.pivot(index="shape[0]", columns="shape[1]", values="speedup")
+
+    # Creating the heatmap
+    sns.heatmap(heatmap_data, annot=True, fmt=".2f", cmap='YlGnBu')
+    plt.title(f'type: {_type}, transpose: {transpose}\n'
+              f'bool_event: {bool_event}, outdim_parallel: {outdim_parallel}')
+    plt.xlabel('shape[0]')
+    plt.ylabel('shape[1]')
+
+# Adding an overall title with adjusted position
+plt.suptitle('[GPU] jitconn event matvec taichi speedup over brainpylib\n'
+             'speedup = (brainpylib time / taichi aot time) - 1', fontsize=16)
+
+# Adjust layout to make room for the title
+plt.tight_layout(rect=[0, 0, 1, 0.95])
+plt.savefig('jitconn event matvec/jitconn_event_matvec_gpu.png')
+# plt.show()
diff --git a/benchmarks/analysis/basic/matvec/test_results/jitconn event matvec/barchart_cpu.py b/benchmarks/analysis/basic/matvec/test_results/jitconn event matvec/barchart_cpu.py
new file mode 100644
index 0000000..0b810f8
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/test_results/jitconn event matvec/barchart_cpu.py	
@@ -0,0 +1,45 @@
+import matplotlib.pyplot as plt
+import pandas as pd
+import numpy as np
+
+# 去除一组列中的异常值
+def remove_row_outliers(df, column_prefix, threshold=1.5):
+    time_columns = [col for col in df.columns if col.startswith(column_prefix)]
+    
+    for index, row in df.iterrows():
+        time_values = row[time_columns]
+        mean = time_values.mean()
+        # 计算每个值与该行其他值的均值的差异
+        deviation = time_values.sub(time_values.mean())
+        abs_deviation = np.abs(deviation)
+        # 标记那些与均值差异过大的值为异常值
+        outliers = abs_deviation > (abs_deviation.mean() + threshold * abs_deviation.std())
+        df.loc[index, time_columns] = time_values.mask(outliers, np.nan)
+
+    return df
+
+# 重新计算speedup
+def calculate_speedup(df):
+    # 计算每行taichi aot time与brainpy time的均值
+    taichi_aot_time_columns = [col for col in df.columns if col.startswith('taichi aot time')]
+    brainpy_time_columns = [col for col in df.columns if col.startswith('brainpy time')]
+    df['taichi aot time mean'] = df[taichi_aot_time_columns].mean(axis=1)
+    df['brainpy time mean'] = df[brainpy_time_columns].mean(axis=1)
+    # 计算speedup
+    df['speedup'] = np.where(df['brainpy time mean'] < df['taichi aot time mean'], 1 - (df['taichi aot time mean'] / df['brainpy time mean']), (df['brainpy time mean'] / df['taichi aot time mean']) - 1)
+    return df
+
+# Load the combined dataset
+combined_df = pd.read_csv("jitconn event matvec/jitconn_event_matvec_cpu.csv")
+combined_df.drop(columns=['backend'], inplace=True)
+combined_df = remove_row_outliers(combined_df, "taichi aot time")
+combined_df = remove_row_outliers(combined_df, "brainpy time")
+combined_df = calculate_speedup(combined_df)
+
+plt.hist(combined_df['speedup'], bins=50)
+plt.xlabel('Speedup')
+plt.ylabel('Frequency')
+plt.title('[CPU] jitconn event matvec taichi speedup over brainpylib' + '\n' +
+          'speedup = (brainpylib time / taichi aot time) - 1')
+plt.savefig('jitconn event matvec/jitconn_event_matvec_cpu_dist.png')
+
diff --git a/benchmarks/analysis/basic/matvec/test_results/jitconn event matvec/barchart_gpu.py b/benchmarks/analysis/basic/matvec/test_results/jitconn event matvec/barchart_gpu.py
new file mode 100644
index 0000000..0515580
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/test_results/jitconn event matvec/barchart_gpu.py	
@@ -0,0 +1,45 @@
+import matplotlib.pyplot as plt
+import pandas as pd
+import numpy as np
+
+# 去除一组列中的异常值
+def remove_row_outliers(df, column_prefix, threshold=1.5):
+    time_columns = [col for col in df.columns if col.startswith(column_prefix)]
+    
+    for index, row in df.iterrows():
+        time_values = row[time_columns]
+        mean = time_values.mean()
+        # 计算每个值与该行其他值的均值的差异
+        deviation = time_values.sub(time_values.mean())
+        abs_deviation = np.abs(deviation)
+        # 标记那些与均值差异过大的值为异常值
+        outliers = abs_deviation > (abs_deviation.mean() + threshold * abs_deviation.std())
+        df.loc[index, time_columns] = time_values.mask(outliers, np.nan)
+
+    return df
+
+# 重新计算speedup
+def calculate_speedup(df):
+    # 计算每行taichi aot time与brainpy time的均值
+    taichi_aot_time_columns = [col for col in df.columns if col.startswith('taichi aot time')]
+    brainpy_time_columns = [col for col in df.columns if col.startswith('brainpy time')]
+    df['taichi aot time mean'] = df[taichi_aot_time_columns].mean(axis=1)
+    df['brainpy time mean'] = df[brainpy_time_columns].mean(axis=1)
+    # 计算speedup
+    df['speedup'] = np.where(df['brainpy time mean'] < df['taichi aot time mean'], 1 - (df['taichi aot time mean'] / df['brainpy time mean']), (df['brainpy time mean'] / df['taichi aot time mean']) - 1)
+    return df
+
+# Load the combined dataset
+combined_df = pd.read_csv("jitconn event matvec/jitconn_event_matvec_gpu.csv")
+combined_df.drop(columns=['backend'], inplace=True)
+combined_df = remove_row_outliers(combined_df, "taichi aot time")
+combined_df = remove_row_outliers(combined_df, "brainpy time")
+combined_df = calculate_speedup(combined_df)
+
+plt.hist(combined_df['speedup'], bins=50)
+plt.xlabel('Speedup')
+plt.ylabel('Frequency')
+plt.title('[GPU] jitconn event matvec taichi speedup over brainpylib' + '\n' +
+          'speedup = (brainpylib time / taichi aot time) - 1')
+plt.savefig('jitconn event matvec/jitconn_event_matvec_gpu_dist.png')
+
diff --git a/benchmarks/analysis/basic/matvec/test_results/jitconn event matvec/jitconn_event_matvec_cpu.csv b/benchmarks/analysis/basic/matvec/test_results/jitconn event matvec/jitconn_event_matvec_cpu.csv
new file mode 100644
index 0000000..958ee7b
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/test_results/jitconn event matvec/jitconn_event_matvec_cpu.csv	
@@ -0,0 +1,589 @@
+shape[0],shape[1],backend,type,transpose,outdim_parallel,bool_event,taichi aot time1(ms),taichi aot time2(ms),taichi aot time3(ms),taichi aot time4(ms),taichi aot time5(ms),taichi aot time6(ms),taichi aot time7(ms),taichi aot time8(ms),taichi aot time9(ms),taichi aot time10(ms),brainpy time1(ms),brainpy time2(ms),brainpy time3(ms),brainpy time4(ms),brainpy time5(ms),brainpy time6(ms),brainpy time7(ms),brainpy time8(ms),brainpy time9(ms),brainpy time10(ms)
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diff --git a/benchmarks/analysis/basic/matvec/test_results/jitconn event matvec/jitconn_event_matvec_gpu.csv b/benchmarks/analysis/basic/matvec/test_results/jitconn event matvec/jitconn_event_matvec_gpu.csv
new file mode 100644
index 0000000..ff6fed0
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/test_results/jitconn event matvec/jitconn_event_matvec_gpu.csv	
@@ -0,0 +1,589 @@
+shape[0],shape[1],backend,type,transpose,outdim_parallel,bool_event,taichi aot time1(ms),taichi aot time2(ms),taichi aot time3(ms),taichi aot time4(ms),taichi aot time5(ms),taichi aot time6(ms),taichi aot time7(ms),taichi aot time8(ms),taichi aot time9(ms),taichi aot time10(ms),brainpy time1(ms),brainpy time2(ms),brainpy time3(ms),brainpy time4(ms),brainpy time5(ms),brainpy time6(ms),brainpy time7(ms),brainpy time8(ms),brainpy time9(ms),brainpy time10(ms)
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diff --git a/benchmarks/analysis/basic/matvec/test_results/jitconn matvec/analysis cpu.py b/benchmarks/analysis/basic/matvec/test_results/jitconn matvec/analysis cpu.py
new file mode 100644
index 0000000..8e8f235
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/test_results/jitconn matvec/analysis cpu.py	
@@ -0,0 +1,69 @@
+import pandas as pd
+import numpy as np
+import seaborn as sns
+import matplotlib.pyplot as plt
+
+combined_csv_path = "jitconn matvec/jitconn_matvec_cpu.csv"
+
+# 去除一组列中的异常值
+def remove_row_outliers(df, column_prefix, threshold=1.5):
+    time_columns = [col for col in df.columns if col.startswith(column_prefix)]
+    
+    for index, row in df.iterrows():
+        time_values = row[time_columns]
+        mean = time_values.mean()
+        # 计算每个值与该行其他值的均值的差异
+        deviation = time_values.sub(time_values.mean())
+        abs_deviation = np.abs(deviation)
+        # 标记那些与均值差异过大的值为异常值
+        outliers = abs_deviation > (abs_deviation.mean() + threshold * abs_deviation.std())
+        df.loc[index, time_columns] = time_values.mask(outliers, np.nan)
+
+    return df
+
+# 重新计算speedup
+def calculate_speedup(df):
+    # Calculate the mean of 'taichi aot time' and 'brainpy time' for each row
+    taichi_aot_time_columns = [col for col in df.columns if col.startswith('taichi aot time')]
+    brainpy_time_columns = [col for col in df.columns if col.startswith('brainpy time')]
+    df['taichi aot time mean'] = df[taichi_aot_time_columns].mean(axis=1)
+    df['brainpy time mean'] = df[brainpy_time_columns].mean(axis=1)
+    # Calculate speedup, if 'brainpy time' is smaller than 'taichi aot time', speedup is negative
+    df['speedup'] = np.where(df['brainpy time mean'] < df['taichi aot time mean'], 1 - (df['taichi aot time mean'] / df['brainpy time mean']), (df['brainpy time mean'] / df['taichi aot time mean']) - 1)
+    return df
+
+# Load the combined dataset
+combined_df = pd.read_csv(combined_csv_path)
+combined_df.drop(columns=['backend'], inplace=True)
+combined_df = remove_row_outliers(combined_df, "taichi aot time")
+combined_df = remove_row_outliers(combined_df, "brainpy time")
+combined_df = calculate_speedup(combined_df)
+
+# Averaging the speedup values for each combination of 's', 'p', 'backend', 'values type', and 'events type'
+avg_speedup_df = combined_df.groupby(['type', 'transpose', 'outdim_parallel', 'shape[0]', 'shape[1]']).mean().reset_index()
+
+# Setting up the plots for heatmaps based on different backends, values types, and events types
+plt.figure(figsize=(22, 18))  # Adjusting figure size for eight subplots
+
+# Creating subplots for each combination of backend, values type, and events type
+for i, (_type, transpose, outdim_parallel) in enumerate([(_t, t, o)  for _t in avg_speedup_df['type'].unique() for t in avg_speedup_df['transpose'].unique() for o in avg_speedup_df['outdim_parallel'].unique()]):
+    plt.subplot(3, 4, i + 1)
+
+    # Filtering data and creating a pivot table for the heatmap
+    filtered_df = avg_speedup_df[(avg_speedup_df['type'] == _type) & (avg_speedup_df['transpose'] == transpose) & (avg_speedup_df['outdim_parallel'] == outdim_parallel)]
+    heatmap_data = filtered_df.pivot(index="shape[0]", columns="shape[1]", values="speedup")
+
+    # Creating the heatmap
+    sns.heatmap(heatmap_data, annot=True, fmt=".2f", cmap='YlGnBu')
+    plt.title(f'type: {_type}, transpose: {transpose}, outdim_parallel: {outdim_parallel}')
+    plt.xlabel('shape[0]')
+    plt.ylabel('shape[1]')
+
+# Adding an overall title with adjusted position
+plt.suptitle('[CPU] jitconn matvec taichi speedup over brainpylib\n'
+             'speedup = (brainpylib time / taichi aot time) - 1', fontsize=16)
+
+# Adjust layout to make room for the title
+plt.tight_layout(rect=[0, 0, 1, 0.95])
+plt.savefig('jitconn matvec/jitconn_matvec_cpu.png')
+# plt.show()
diff --git a/benchmarks/analysis/basic/matvec/test_results/jitconn matvec/analysis gpu.py b/benchmarks/analysis/basic/matvec/test_results/jitconn matvec/analysis gpu.py
new file mode 100644
index 0000000..51b9018
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/test_results/jitconn matvec/analysis gpu.py	
@@ -0,0 +1,69 @@
+import pandas as pd
+import numpy as np
+import seaborn as sns
+import matplotlib.pyplot as plt
+
+combined_csv_path = "jitconn matvec/jitconn_matvec_gpu.csv"
+
+# 去除一组列中的异常值
+def remove_row_outliers(df, column_prefix, threshold=1.5):
+    time_columns = [col for col in df.columns if col.startswith(column_prefix)]
+    
+    for index, row in df.iterrows():
+        time_values = row[time_columns]
+        mean = time_values.mean()
+        # 计算每个值与该行其他值的均值的差异
+        deviation = time_values.sub(time_values.mean())
+        abs_deviation = np.abs(deviation)
+        # 标记那些与均值差异过大的值为异常值
+        outliers = abs_deviation > (abs_deviation.mean() + threshold * abs_deviation.std())
+        df.loc[index, time_columns] = time_values.mask(outliers, np.nan)
+
+    return df
+
+# 重新计算speedup
+def calculate_speedup(df):
+    # 计算每行taichi aot time与brainpy time的均值
+    taichi_aot_time_columns = [col for col in df.columns if col.startswith('taichi aot time')]
+    brainpy_time_columns = [col for col in df.columns if col.startswith('brainpy time')]
+    df['taichi aot time mean'] = df[taichi_aot_time_columns].mean(axis=1)
+    df['brainpy time mean'] = df[brainpy_time_columns].mean(axis=1)
+    # 计算speedup
+    df['speedup'] = np.where(df['brainpy time mean'] < df['taichi aot time mean'], 1 - (df['taichi aot time mean'] / df['brainpy time mean']), (df['brainpy time mean'] / df['taichi aot time mean']) - 1)
+    return df
+# Load the combined dataset
+
+combined_df = pd.read_csv(combined_csv_path)
+combined_df.drop(columns=['backend'], inplace=True)
+combined_df = remove_row_outliers(combined_df, "taichi aot time")
+combined_df = remove_row_outliers(combined_df, "brainpy time")
+combined_df = calculate_speedup(combined_df)
+
+# Averaging the speedup values for each combination of 's', 'p', 'backend', 'values type', and 'events type'
+avg_speedup_df = combined_df.groupby(['type', 'transpose', 'outdim_parallel', 'shape[0]', 'shape[1]']).mean().reset_index()
+
+# Setting up the plots for heatmaps based on different backends, values types, and events types
+plt.figure(figsize=(22, 18))  # Adjusting figure size for eight subplots
+
+# Creating subplots for each combination of backend, values type, and events type
+for i, (_type, transpose, outdim_parallel) in enumerate([(_t, t, o)  for _t in avg_speedup_df['type'].unique() for t in avg_speedup_df['transpose'].unique() for o in avg_speedup_df['outdim_parallel'].unique()]):
+    plt.subplot(3, 4, i + 1)
+
+    # Filtering data and creating a pivot table for the heatmap
+    filtered_df = avg_speedup_df[(avg_speedup_df['type'] == _type) & (avg_speedup_df['transpose'] == transpose) & (avg_speedup_df['outdim_parallel'] == outdim_parallel)]
+    heatmap_data = filtered_df.pivot(index="shape[0]", columns="shape[1]", values="speedup")
+
+    # Creating the heatmap
+    sns.heatmap(heatmap_data, annot=True, fmt=".2f", cmap='YlGnBu')
+    plt.title(f'type: {_type}, transpose: {transpose}, outdim_parallel: {outdim_parallel}')
+    plt.xlabel('shape[0]')
+    plt.ylabel('shape[1]')
+
+# Adding an overall title with adjusted position
+plt.suptitle('[GPU] jitconn matvec taichi speedup over brainpylib\n'
+             'speedup = (brainpylib time / taichi aot time) - 1', fontsize=16)
+
+# Adjust layout to make room for the title
+plt.tight_layout(rect=[0, 0, 1, 0.95])
+plt.savefig('jitconn matvec\jitconn_matvec_gpu.png')
+# plt.show()
diff --git a/benchmarks/analysis/basic/matvec/test_results/jitconn matvec/barchart_cpu.py b/benchmarks/analysis/basic/matvec/test_results/jitconn matvec/barchart_cpu.py
new file mode 100644
index 0000000..ee6820b
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/test_results/jitconn matvec/barchart_cpu.py	
@@ -0,0 +1,53 @@
+import matplotlib.pyplot as plt
+import pandas as pd
+import numpy as np
+import os
+import seaborn as sns
+from matplotlib.font_manager import FontProperties
+
+font = FontProperties(fname='C:\\Windows\\Fonts\\msyh.ttc')
+
+def remove_row_outliers(df, column_prefix, threshold=1.5):
+    time_columns = [col for col in df.columns if col.startswith(column_prefix)]
+    
+    for index, row in df.iterrows():
+        time_values = row[time_columns]
+        mean = time_values.mean()
+        # 计算每个值与该行其他值的均值的差异
+        deviation = time_values.sub(time_values.mean())
+        abs_deviation = np.abs(deviation)
+        # 标记那些与均值差异过大的值为异常值
+        outliers = abs_deviation > (abs_deviation.mean() + threshold * abs_deviation.std())
+        df.loc[index, time_columns] = time_values.mask(outliers, np.nan)
+
+    return df
+
+# 重新计算speedup
+def calculate_speedup(df):
+    # 计算每行taichi aot time与brainpy time的均值
+    taichi_aot_time_columns = [col for col in df.columns if col.startswith('taichi aot time')]
+    brainpy_time_columns = [col for col in df.columns if col.startswith('brainpy time')]
+    df['taichi aot time mean'] = df[taichi_aot_time_columns].mean(axis=1)
+    df['brainpy time mean'] = df[brainpy_time_columns].mean(axis=1)
+    # 计算speedup
+    df['speedup'] = np.where(df['brainpy time mean'] < df['taichi aot time mean'], 1 - (df['taichi aot time mean'] / df['brainpy time mean']), (df['brainpy time mean'] / df['taichi aot time mean']) - 1)
+    return df
+
+# Load the combined dataset
+PATH = os.path.dirname(os.path.abspath(__file__))
+combined_df = pd.read_csv(os.path.join(PATH, 'jitconn_matvec_cpu.csv'))
+combined_df.drop(columns=['backend'], inplace=True)
+combined_df = remove_row_outliers(combined_df, "taichi aot time")
+combined_df = remove_row_outliers(combined_df, "brainpy time")
+combined_df = calculate_speedup(combined_df)
+
+sns.set(style="whitegrid")
+sns.histplot(combined_df['speedup'], bins=25, kde=True, color='darkorange')
+# plt.hist(combined_df['speedup'], bins=50, density=True)
+
+plt.xlabel('加速比', fontsize=16, fontproperties=font)
+plt.ylabel('频次', fontsize=16, fontproperties=font)
+# plt.title('[CPU] jitconn matvec taichi speedup over brainpylib')
+plt.savefig(os.path.join(PATH, 'jitconn_matvec_cpu_dist.png'))
+
+
diff --git a/benchmarks/analysis/basic/matvec/test_results/jitconn matvec/barchart_gpu.py b/benchmarks/analysis/basic/matvec/test_results/jitconn matvec/barchart_gpu.py
new file mode 100644
index 0000000..639ea0e
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/test_results/jitconn matvec/barchart_gpu.py	
@@ -0,0 +1,54 @@
+import matplotlib.pyplot as plt
+import pandas as pd
+import numpy as np
+import os
+import seaborn as sns
+from matplotlib.font_manager import FontProperties
+
+font = FontProperties(fname='C:\\Windows\\Fonts\\msyh.ttc')
+
+# 去除一组列中的异常值
+def remove_row_outliers(df, column_prefix, threshold=1.5):
+    time_columns = [col for col in df.columns if col.startswith(column_prefix)]
+    
+    for index, row in df.iterrows():
+        time_values = row[time_columns]
+        mean = time_values.mean()
+        # 计算每个值与该行其他值的均值的差异
+        deviation = time_values.sub(time_values.mean())
+        abs_deviation = np.abs(deviation)
+        # 标记那些与均值差异过大的值为异常值
+        outliers = abs_deviation > (abs_deviation.mean() + threshold * abs_deviation.std())
+        df.loc[index, time_columns] = time_values.mask(outliers, np.nan)
+
+    return df
+
+# 重新计算speedup
+def calculate_speedup(df):
+    # 计算每行taichi aot time与brainpy time的均值
+    taichi_aot_time_columns = [col for col in df.columns if col.startswith('taichi aot time')]
+    brainpy_time_columns = [col for col in df.columns if col.startswith('brainpy time')]
+    df['taichi aot time mean'] = df[taichi_aot_time_columns].mean(axis=1)
+    df['brainpy time mean'] = df[brainpy_time_columns].mean(axis=1)
+    # 计算speedup
+    df['speedup'] = np.where(df['brainpy time mean'] < df['taichi aot time mean'], 1 - (df['taichi aot time mean'] / df['brainpy time mean']), (df['brainpy time mean'] / df['taichi aot time mean']) - 1)
+    return df
+
+# Load the combined dataset
+PATH = os.path.dirname(os.path.abspath(__file__))
+combined_df = pd.read_csv(os.path.join(PATH, 'jitconn_matvec_gpu.csv'))
+combined_df.drop(columns=['backend'], inplace=True)
+combined_df = remove_row_outliers(combined_df, "taichi aot time")
+combined_df = remove_row_outliers(combined_df, "brainpy time")
+combined_df = calculate_speedup(combined_df)
+
+
+sns.set(style="whitegrid")
+sns.histplot(combined_df['speedup'], bins=25, kde=True, color='darkorange')
+# plt.hist(combined_df['speedup'], bins=50, density=True)
+plt.xlabel('加速比', fontsize=16, fontproperties=font)
+plt.ylabel('频次', fontsize=16, fontproperties=font)
+# plt.title('[GPU] jitconn matvec taichi speedup over origin brainpy')
+plt.savefig(os.path.join(PATH, 'jitconn_matvec_gpu_dist.png'))
+
+
diff --git a/benchmarks/analysis/basic/matvec/test_results/jitconn matvec/jitconn_matvec_cpu.csv b/benchmarks/analysis/basic/matvec/test_results/jitconn matvec/jitconn_matvec_cpu.csv
new file mode 100644
index 0000000..85ed98f
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/test_results/jitconn matvec/jitconn_matvec_cpu.csv	
@@ -0,0 +1,589 @@
+shape[0],shape[1],backend,type,transpose,outdim_parallel,bool_event,taichi aot time1(ms),taichi aot time2(ms),taichi aot time3(ms),taichi aot time4(ms),taichi aot time5(ms),taichi aot time6(ms),taichi aot time7(ms),taichi aot time8(ms),taichi aot time9(ms),taichi aot time10(ms),brainpy time1(ms),brainpy time2(ms),brainpy time3(ms),brainpy time4(ms),brainpy time5(ms),brainpy time6(ms),brainpy time7(ms),brainpy time8(ms),brainpy time9(ms),brainpy time10(ms)
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diff --git a/benchmarks/analysis/basic/matvec/test_results/jitconn matvec/jitconn_matvec_gpu.csv b/benchmarks/analysis/basic/matvec/test_results/jitconn matvec/jitconn_matvec_gpu.csv
new file mode 100644
index 0000000..ec822d2
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/test_results/jitconn matvec/jitconn_matvec_gpu.csv	
@@ -0,0 +1,589 @@
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+50000,50000,cpu,normal,False,True,False,1.4805793762207031,1.7681121826171875,1.5096664428710938,1.786947250366211,1.6243457794189453,1.4841556549072266,1.4510154724121094,1.4045238494873047,1.4798641204833984,1.524209976196289,1.0912418365478516,1.0356903076171875,1.0175704956054688,1.0788440704345703,1.0943412780761719,1.1432170867919922,1.1191368103027344,1.4302730560302734,1.108407974243164,1.0499954223632812
+50000,50000,cpu,normal,True,False,False,3.076314926147461,2.939462661743164,2.9897689819335938,3.220081329345703,2.9344558715820312,2.815723419189453,2.8040409088134766,2.6857852935791016,2.862215042114258,3.1342506408691406,5.888700485229492,5.400180816650391,5.530118942260742,5.863428115844727,5.306005477905273,5.273342132568359,5.850553512573242,5.392551422119141,5.45954704284668,5.741596221923828
+50000,50000,cpu,normal,False,False,False,3.1075477600097656,2.7425289154052734,2.748250961303711,2.936840057373047,3.4623146057128906,3.016948699951172,3.1883716583251953,2.994060516357422,3.129243850708008,3.435373306274414,5.332231521606445,5.271673202514648,5.354642868041992,5.280017852783203,5.356073379516602,5.265474319458008,5.82575798034668,5.097627639770508,5.312204360961914,5.749702453613281
diff --git a/benchmarks/analysis/basic/matvec/test_results/test.bat b/benchmarks/analysis/basic/matvec/test_results/test.bat
new file mode 100644
index 0000000..6bb5fe5
--- /dev/null
+++ b/benchmarks/analysis/basic/matvec/test_results/test.bat
@@ -0,0 +1,17 @@
+@REM python "csr matvec\analysis cpu.py"
+@REM python "csr matvec\analysis gpu.py"
+@REM python "csr matvec\barchart_cpu.py"
+@REM python "csr matvec\barchart_gpu.py"
+@REM python "event csr matvec\analysis cpu.py"
+@REM python "event csr matvec\analysis gpu.py"
+@REM python "event csr matvec\barchart_cpu.py"
+@REM python "event csr matvec\barchart_gpu.py"
+python "jitconn event matvec\analysis cpu.py"
+python "jitconn event matvec\analysis gpu.py"
+python "jitconn event matvec\barchart_cpu.py"
+python "jitconn event matvec\barchart_gpu.py"
+python "jitconn matvec\analysis cpu.py"
+python "jitconn matvec\analysis gpu.py"
+python "jitconn matvec\barchart_cpu.py"
+python "jitconn matvec\barchart_gpu.py"
+
diff --git a/benchmarks/analysis/basic/test_results/analysis_distribution.py b/benchmarks/analysis/basic/test_results/analysis_distribution.py
new file mode 100644
index 0000000..358bb3d
--- /dev/null
+++ b/benchmarks/analysis/basic/test_results/analysis_distribution.py
@@ -0,0 +1,103 @@
+import matplotlib.pyplot as plt
+import pandas as pd
+import numpy as np
+import os
+
+# 去除一组列中的异常值
+def remove_row_outliers(df, column_prefix, threshold=1.5):
+    time_columns = [col for col in df.columns if col.startswith(column_prefix)]
+    
+    for index, row in df.iterrows():
+        time_values = row[time_columns]
+        mean = time_values.mean()
+        # 计算每个值与该行其他值的均值的差异
+        deviation = time_values.sub(time_values.mean())
+        abs_deviation = np.abs(deviation)
+        # 标记那些与均值差异过大的值为异常值
+        outliers = abs_deviation > (abs_deviation.mean() + threshold * abs_deviation.std())
+        df.loc[index, time_columns] = time_values.mask(outliers, np.nan)
+
+    return df
+
+# 重新计算speedup
+def calculate_speedup(df):
+    # 计算每行taichi aot time与brainpy time的均值
+    taichi_aot_time_columns = [col for col in df.columns if col.startswith('taichi aot time')]
+    brainpy_time_columns = [col for col in df.columns if col.startswith('brainpy time')]
+    df['taichi aot time mean'] = df[taichi_aot_time_columns].mean(axis=1)
+    df['brainpy time mean'] = df[brainpy_time_columns].mean(axis=1)
+    # 计算speedup
+    df['speedup'] = np.where(df['brainpy time mean'] < df['taichi aot time mean'], 1 - (df['taichi aot time mean'] / df['brainpy time mean']), (df['brainpy time mean'] / df['taichi aot time mean']) - 1)
+    return df
+
+def process_target_df(path):
+    # Load the combined dataset
+    combined_df = pd.read_csv(path)
+    combined_df.drop(columns=['backend'], inplace=True)
+    try:
+        combined_df.drop(columns=['events type'], inplace=True)
+        combined_df.drop(columns=['s'], inplace=True)
+        combined_df.drop(columns=['p'], inplace=True)
+    except:
+        pass
+    combined_df = remove_row_outliers(combined_df, "taichi aot time")
+    combined_df = remove_row_outliers(combined_df, "brainpy time")
+    combined_df = calculate_speedup(combined_df)
+    return combined_df
+
+def plot_stacked_histograms_with_fixed_bins(case_dict, root_path, num_bins=40):
+    fig, axs = plt.subplots(2, 1, figsize=(12, 10))  # 创建两个子图
+    colors = ['blue', 'green', 'red', 'cyan']  # 定义每个案例的颜色
+
+    for i, (device, cases) in enumerate(case_dict.items()):
+        all_speedups = []  # 收集所有speedup值以计算共享的bins范围
+        for case_name, file_path in cases.items():
+            data_path = os.path.join(root_path, file_path)
+            df = process_target_df(data_path)  # 加载和处理数据
+            all_speedups.extend(df['speedup'].values)  # 添加到速度提升列表
+
+        # 基于当前设备的所有speedup值计算bins
+        min_speedup, max_speedup = min(all_speedups), max(all_speedups)
+        bins = np.linspace(min_speedup, max_speedup, num_bins + 1)
+        bottom = np.zeros(len(bins)-1)  # 初始化底部累积值
+
+        for j, (case_name, file_path) in enumerate(cases.items()):
+            data_path = os.path.join(root_path, file_path)
+            df = process_target_df(data_path)  # 再次加载和处理数据
+            # 计算当前案例的直方图
+            counts, _ = np.histogram(df['speedup'], bins=bins, density=True)
+            
+            # 绘制柱状图
+            axs[i].bar(bins[:-1] + np.diff(bins)/2, counts, width=np.diff(bins), bottom=bottom, color=colors[j], label=case_name, alpha=0.75)
+            bottom += counts  # 更新底部累积值，为下一个案例做准备
+
+        axs[i].set_title(f'{device} backend')
+        axs[i].set_xlabel('Speedup')
+        axs[i].set_ylabel('Density')
+        axs[i].legend()
+
+    plt.tight_layout()
+    # plt.show()
+    plt.savefig(os.path.join(root_path, 'stacked_histograms.png'))
+
+
+
+
+# Load the combined dataset
+PATH = os.path.dirname(os.path.abspath(__file__))
+case_dict = {
+    'CPU': {
+        'csr matvec': os.path.join(PATH, 'csr matvec', 'csrmv_cpu.csv'),
+        'event csr matvec': os.path.join(PATH, 'event csr matvec', 'event_csrmv_cpu.csv'),
+        'jitconn matvec': os.path.join(PATH, 'jitconn matvec', 'jitconn_matvec_cpu.csv'),
+        'jitconn event matvec': os.path.join(PATH, 'jitconn event matvec', 'jitconn_event_matvec_cpu.csv'),
+    },
+    'GPU': {
+        'csr matvec': os.path.join(PATH, 'csr matvec', 'csrmv_gpu.csv'),
+        'event csr matvec': os.path.join(PATH, 'event csr matvec', 'event_csrmv_gpu.csv'),
+        'jitconn matvec': os.path.join(PATH, 'jitconn matvec', 'jitconn_matvec_gpu.csv'),
+        'jitconn event matvec': os.path.join(PATH, 'jitconn event matvec', 'jitconn_event_matvec_gpu.csv'),
+    },
+}
+
+plot_stacked_histograms_with_fixed_bins(case_dict, PATH)
\ No newline at end of file
diff --git a/benchmarks/analysis/model/COBA results/analysis_COBA.py b/benchmarks/analysis/model/COBA results/analysis_COBA.py
new file mode 100644
index 0000000..3c22372
--- /dev/null
+++ b/benchmarks/analysis/model/COBA results/analysis_COBA.py	
@@ -0,0 +1,70 @@
+import pandas as pd
+import numpy as np
+import seaborn as sns
+import matplotlib.pyplot as plt
+import os
+
+PATH = os.path.dirname(os.path.abspath(__file__))
+
+# Function to remove outliers for brainpylib and taichi execution times
+def remove_outliers(df, prefix):
+    time_columns = [col for col in df.columns if col.startswith(prefix)]
+    for index, row in df.iterrows():
+        time_values = row[time_columns]
+        mean = time_values.mean()
+        deviation = time_values.sub(mean)
+        abs_deviation = abs(deviation)
+        outliers = abs_deviation > (abs_deviation.mean() + 1.5 * abs_deviation.std())
+        df.loc[index, time_columns] = time_values.mask(outliers, np.nan)
+    return df
+
+# Calculate mean execution times and speedup
+def calculate_means_and_speedup(df):
+    brainpylib_columns = [col for col in df.columns if col.startswith('brainpylib_time')]
+    taichi_columns = [col for col in df.columns if col.startswith('taichi_time')]
+    df['brainpylib_mean'] = df[brainpylib_columns].mean(axis=1)
+    df['taichi_mean'] = df[taichi_columns].mean(axis=1)
+    df['speedup'] = np.where(df['taichi_mean'] > df['brainpylib_mean'],
+                            1 - (df['taichi_mean'] / df['brainpylib_mean']),
+                            (df['brainpylib_mean'] / df['taichi_mean']) - 1)
+    return df
+
+def main(benchmark_df):
+    # Applying the functions
+    benchmark_df = remove_outliers(benchmark_df, 'brainpylib_time')
+    benchmark_df = remove_outliers(benchmark_df, 'taichi_time')
+    benchmark_df = calculate_means_and_speedup(benchmark_df)
+    DEVICE = benchmark_df['device'].unique()[0]
+    benchmark_df = benchmark_df.drop('device', axis=1)
+
+    # Aggregating speedup values
+    agg_speedup_df = benchmark_df.groupby(['comm_type', 'post_num', 'conn_num']).mean().reset_index()
+
+    # Unique communication types for creating separate heatmaps
+    comm_types = agg_speedup_df['comm_type'].unique()
+
+    # Setting up the plots
+    plt.figure(figsize=(20, 20))
+
+    for i, comm_type in enumerate(comm_types):
+        plt.subplot(2, 2, i + 1)
+        filtered_df = agg_speedup_df[agg_speedup_df['comm_type'] == comm_type]
+        heatmap_data = filtered_df.pivot(index='post_num', columns='conn_num', values='speedup')
+        
+        sns.heatmap(heatmap_data, annot=True, fmt=".2f", cmap='YlGnBu', annot_kws={"size": 24})
+        plt.title(f'[{DEVICE}]COBA network Comm Type: {comm_type}\n' + \
+                'speedup = brainpylib time / taichi time - 1 if taichi faster than brainpylib\n' + \
+                'speedup = 1 - taichi time / brainpylib time if taichi slower than brainpylib')
+        plt.xlabel('Conn Num')
+        plt.ylabel('Post Num')
+
+    plt.tight_layout()
+    plt.savefig(f'{PATH}/benchmark_COBA_{DEVICE}_heatmap.png')
+
+# Load the dataset
+benchmark_path = f"{PATH}/benchmark_COBA_cpu2.csv"
+benchmark_df = pd.read_csv(benchmark_path)
+main(benchmark_df)
+benchmark_path = f"{PATH}/benchmark_COBA_gpu2.csv"
+benchmark_df = pd.read_csv(benchmark_path)
+main(benchmark_df)
\ No newline at end of file
diff --git a/benchmarks/analysis/model/COBA results/analysis_COBA_barchart.py b/benchmarks/analysis/model/COBA results/analysis_COBA_barchart.py
new file mode 100644
index 0000000..5a1f6a8
--- /dev/null
+++ b/benchmarks/analysis/model/COBA results/analysis_COBA_barchart.py	
@@ -0,0 +1,97 @@
+import pandas as pd
+import numpy as np
+import seaborn as sns
+import matplotlib.pyplot as plt
+import os
+
+PATH = os.path.dirname(os.path.abspath(__file__))
+
+# Function to remove outliers for brainpylib and taichi execution times
+def remove_outliers(df, prefix):
+    time_columns = [col for col in df.columns if col.startswith(prefix)]
+    for index, row in df.iterrows():
+        time_values = row[time_columns]
+        mean = time_values.mean()
+        deviation = time_values.sub(mean)
+        abs_deviation = abs(deviation)
+        outliers = abs_deviation > (abs_deviation.mean() + 1.5 * abs_deviation.std())
+        df.loc[index, time_columns] = time_values.mask(outliers, np.nan)
+    return df
+
+# Calculate mean execution times and speedup
+def calculate_means_and_speedup(df):
+    brainpylib_columns = [col for col in df.columns if col.startswith('brainpylib_time')]
+    taichi_columns = [col for col in df.columns if col.startswith('taichi_time')]
+    df['brainpylib_mean'] = df[brainpylib_columns].mean(axis=1)
+    df['taichi_mean'] = df[taichi_columns].mean(axis=1)
+    df['speedup'] = np.where(df['taichi_mean'] > df['brainpylib_mean'],
+                            1 - (df['taichi_mean'] / df['brainpylib_mean']),
+                            (df['brainpylib_mean'] / df['taichi_mean']) - 1)
+    return df
+
+
+def process_target_df(path):
+    # Load the combined dataset
+    benchmark_df = pd.read_csv(path)
+    # Applying the functions
+    benchmark_df = remove_outliers(benchmark_df, 'brainpylib_time')
+    benchmark_df = remove_outliers(benchmark_df, 'taichi_time')
+    benchmark_df = calculate_means_and_speedup(benchmark_df)
+    DEVICE = benchmark_df['device'].unique()[0]
+    benchmark_df = benchmark_df.drop('device', axis=1)
+
+    # Aggregating speedup values
+    agg_speedup_df = benchmark_df.groupby(['comm_type', 'post_num', 'conn_num']).mean().reset_index()
+
+    return agg_speedup_df
+
+def plot_stacked_histograms_with_fixed_bins(root_path, num_bins=40):
+    plt.figure(figsize=(12, 10))  # 调整为单个图形
+    colors = ['blue', 'green', 'red', 'cyan']  # 定义每个案例的颜色
+
+    cpu_path = os.path.join(root_path, 'benchmark_COBA_cpu.csv')
+    gpu_path = os.path.join(root_path, 'benchmark_COBA_gpu.csv')
+    cpu_df = process_target_df(cpu_path)
+    gpu_df = process_target_df(gpu_path)
+    devices_df = {'CPU': cpu_df, 'GPU': gpu_df}
+
+    # 为CPU和GPU绘制不同的图
+    for i, (device, df) in enumerate(devices_df.items()):
+        plt.subplot(2, 1, i + 1)  # 创建子图
+        bottom = np.zeros(num_bins)  # 重置底部数组
+
+        # 按comm_type分组绘制
+        for j, comm_type in enumerate(df['comm_type'].unique()):
+            comm_df = df[df['comm_type'] == comm_type]
+            counts, bins = np.histogram(comm_df['speedup'], bins=num_bins, range=(df['speedup'].min(), df['speedup'].max()), density=True)
+            plt.bar(bins[:-1], counts, width=(bins[1] - bins[0]), bottom=bottom, color=colors[j], alpha=0.7, label=comm_type)
+            bottom += counts  # 更新底部以堆叠下一组
+
+        plt.title(f'COBA network [{device}]')
+        plt.xlabel('Speedup')
+        plt.ylabel('Density')
+        plt.legend(title='Comm Type')
+
+    plt.tight_layout()
+    plt.savefig(f'{root_path}/benchmark_COBA_speedup_stacked.png')
+    plt.show()
+
+
+
+# Load the dataset
+PATH = os.path.dirname(os.path.abspath(__file__))
+case_dict = {
+    'CPU': [
+        # 'EventCSRLinear',
+        'EventJitFPHomoLinear',
+        # 'EventJitFPUniformLinear',
+        # 'EventJitFPNormalLinear',
+    ],
+    'GPU': [
+        # 'EventCSRLinear',
+        'EventJitFPHomoLinear',
+        # 'EventJitFPUniformLinear',
+        # 'EventJitFPNormalLinear',
+    ],
+}
+plot_stacked_histograms_with_fixed_bins(PATH)
diff --git a/benchmarks/analysis/model/COBA results/analysis_COBA_normal_barchart.py b/benchmarks/analysis/model/COBA results/analysis_COBA_normal_barchart.py
new file mode 100644
index 0000000..024c30e
--- /dev/null
+++ b/benchmarks/analysis/model/COBA results/analysis_COBA_normal_barchart.py	
@@ -0,0 +1,59 @@
+import matplotlib.pyplot as plt
+import pandas as pd
+import numpy as np
+import os
+import seaborn as sns
+from matplotlib.font_manager import FontProperties
+
+font = FontProperties(fname='C:\\Windows\\Fonts\\msyh.ttc')
+
+# 去除一组列中的异常值
+def remove_row_outliers(df, column_prefix, threshold=1.5):
+    time_columns = [col for col in df.columns if col.startswith(column_prefix)]
+    
+    for index, row in df.iterrows():
+        time_values = row[time_columns]
+        mean = time_values.mean()
+        # 计算每个值与该行其他值的均值的差异
+        deviation = time_values.sub(time_values.mean())
+        abs_deviation = np.abs(deviation)
+        # 标记那些与均值差异过大的值为异常值
+        outliers = abs_deviation > (abs_deviation.mean() + threshold * abs_deviation.std())
+        df.loc[index, time_columns] = time_values.mask(outliers, np.nan)
+
+    return df
+
+# 重新计算speedup
+def calculate_speedup(df):
+    # 计算每行taichi aot time与brainpy time的均值
+    taichi_aot_time_columns = [col for col in df.columns if col.startswith('taichi_time')]
+    brainpy_time_columns = [col for col in df.columns if col.startswith('brainpylib_time')]
+    df['taichi aot time mean'] = df[taichi_aot_time_columns].mean(axis=1)
+    df['brainpy time mean'] = df[brainpy_time_columns].mean(axis=1)
+    # 计算speedup
+    df['speedup'] = np.where(df['brainpy time mean'] < df['taichi aot time mean'], 1 - (df['taichi aot time mean'] / df['brainpy time mean']), (df['brainpy time mean'] / df['taichi aot time mean']) - 1)
+    return df
+
+# Load the combined dataset
+PATH = os.path.dirname(os.path.abspath(__file__))
+combined_df = pd.read_csv(os.path.join(PATH, 'benchmark_COBA_cpu.csv'))
+# combined_df.drop(columns=['backend'], inplace=True)
+combined_df = remove_row_outliers(combined_df, "taichi aot time")
+combined_df = remove_row_outliers(combined_df, "brainpy time")
+combined_df = calculate_speedup(combined_df)
+# 只选取comm_type为EventJitFPHomoLinear
+combined_df = combined_df[combined_df['comm_type'] == 'EventJitFPNormalLinear']
+combined_df = combined_df[combined_df['conn_num'] == 80]
+
+# print(combined_df)
+
+plt.figure(figsize=(10, 6))  # 调整图形大小
+sns.lineplot(x=combined_df['post_num'], y=combined_df['speedup'], marker='o', linestyle='-', color='darkorange', linewidth=2.5)
+plt.xlabel('神经元个数', fontsize=16, fontproperties=font)
+plt.ylabel('加速比', fontsize=16, fontproperties=font)
+# plt.title('[CPU] COBA EI network speedup over origin brainpy op', fontsize=18)
+plt.grid(True, which='both', linestyle='--', linewidth=0.5)  # 显示网格
+plt.savefig(os.path.join(PATH, 'benchmark_COBA_linechart_cpu.png'))
+# plt.show()
+
+
diff --git a/benchmarks/analysis/model/COBA results/analysis_COBA_spks.py b/benchmarks/analysis/model/COBA results/analysis_COBA_spks.py
new file mode 100644
index 0000000..ba91d35
--- /dev/null
+++ b/benchmarks/analysis/model/COBA results/analysis_COBA_spks.py	
@@ -0,0 +1,26 @@
+import pandas as pd
+import matplotlib.pyplot as plt
+import os
+import seaborn as sns
+import numpy as np
+
+PATH = os.path.dirname(os.path.abspath(__file__))
+
+# Load the data from CSV file
+data = pd.read_csv(os.path.join(PATH, 'benchmark_COBA_spks_cpu.csv'))
+# Calculate the absolute difference between brainpylib_spk and taichi_spk
+data['abs_diff'] = np.abs(data['brainpylib_spk'] - data['taichi_spk'])
+
+# Apply a non-linear (logarithmic) transformation to the 'post_num' column
+data['post_num_log'] = np.log10(data['post_num'])
+
+# Plotting with a regression line to show the trend
+plt.figure(figsize=(12, 6))
+sns.regplot(x='post_num_log', y='abs_diff', data=data, scatter=True, color='skyblue')
+# plt.title('Trend of Absolute Difference of Spikes with Regression (CPU)')
+plt.xlabel('Log10 of Total Neurons')
+plt.ylabel('Absolute Difference of Spikes per Neuron per Second')
+plt.ylim(0, None)  # Set the lower limit of y-axis to 0
+# plt.grid(True)
+plt.savefig(os.path.join(PATH, 'benchmark_COBA_spks_cpu.png'))
+plt.show()
\ No newline at end of file
diff --git a/benchmarks/analysis/model/COBA results/benchmark_COBA_cpu.csv b/benchmarks/analysis/model/COBA results/benchmark_COBA_cpu.csv
new file mode 100644
index 0000000..c601661
--- /dev/null
+++ b/benchmarks/analysis/model/COBA results/benchmark_COBA_cpu.csv	
@@ -0,0 +1,13 @@
+post_num,conn_num,comm_type,device,brainpylib_time1,brainpylib_time2,brainpylib_time3,brainpylib_time4,brainpylib_time5,brainpylib_time6,brainpylib_time7,brainpylib_time8,brainpylib_time9,brainpylib_time10,taichi_time1,taichi_time2,taichi_time3,taichi_time4,taichi_time5,taichi_time6,taichi_time7,taichi_time8,taichi_time9,taichi_time10
+400,80,EventJitFPNormalLinear,cpu,160.96997261047363,163.98382186889648,163.85197639465332,163.71822357177734,162.0919704437256,161.39674186706543,160.19201278686523,160.4163646697998,161.89122200012207,160.46595573425293,181.48088455200195,181.47540092468262,181.0600757598877,182.68108367919922,181.38766288757324,242.37370491027832,205.51156997680664,178.00545692443848,228.27911376953125,214.25247192382812
+800,80,EventJitFPNormalLinear,cpu,174.68690872192383,187.84689903259277,187.41655349731445,223.46162796020508,192.7318572998047,188.2331371307373,187.74652481079102,167.62757301330566,190.1390552520752,189.90540504455566,218.24336051940918,209.96904373168945,247.01166152954102,201.0514736175537,222.08213806152344,208.1923484802246,213.7436866760254,203.02557945251465,224.26676750183105,235.1834774017334
+1600,80,EventJitFPNormalLinear,cpu,210.51311492919922,211.8840217590332,188.09175491333008,207.52215385437012,209.90657806396484,209.0444564819336,198.58026504516602,285.1295471191406,210.82377433776855,212.23187446594238,216.63999557495117,210.3879451751709,210.77299118041992,216.0353660583496,231.92763328552246,217.30732917785645,208.3108425140381,208.20975303649902,217.2873020172119,215.99149703979492
+3200,80,EventJitFPNormalLinear,cpu,237.9586696624756,256.11400604248047,251.04713439941406,278.6679267883301,255.3870677947998,254.9281120300293,335.951566696167,253.32927703857422,237.10942268371582,254.0130615234375,224.47824478149414,228.67107391357422,222.0299243927002,229.6590805053711,212.21518516540527,222.69868850708008,223.3569622039795,217.88811683654785,226.15337371826172,198.1949806213379
+6400,80,EventJitFPNormalLinear,cpu,354.8469543457031,348.0198383331299,344.79260444641113,348.9513397216797,327.79812812805176,351.2415885925293,453.047513961792,353.2745838165283,329.0753364562988,355.7624816894531,255.75661659240723,226.60589218139648,222.49650955200195,229.30288314819336,233.32786560058594,257.65371322631836,243.18957328796387,219.52390670776367,236.8607521057129,231.30369186401367
+12800,80,EventJitFPNormalLinear,cpu,538.7852191925049,538.8321876525879,517.9896354675293,551.6452789306641,548.774003982544,516.0872936248779,558.1607818603516,550.8236885070801,513.2966041564941,515.9540176391602,366.12892150878906,231.92334175109863,229.14457321166992,252.94017791748047,223.30737113952637,246.17457389831543,244.82250213623047,224.0605354309082,228.9893627166748,212.48531341552734
+25600,80,EventJitFPNormalLinear,cpu,872.1559047698975,911.4937782287598,922.6400852203369,895.4815864562988,893.7103748321533,897.2029685974121,920.8102226257324,901.4368057250977,948.8134384155273,899.7750282287598,262.4173164367676,252.70533561706543,269.5791721343994,255.78665733337402,265.11216163635254,242.811918258667,389.89949226379395,258.4688663482666,254.52947616577148,254.744291305542
+51200,80,EventJitFPNormalLinear,cpu,1694.0693855285645,1621.8159198760986,1734.8582744598389,1693.960428237915,1662.1885299682617,1610.3579998016357,1656.7039489746094,1611.2608909606934,1656.3975811004639,1654.7210216522217,328.8989067077637,324.3732452392578,308.6099624633789,318.8014030456543,329.0390968322754,351.1490821838379,293.717622756958,319.57387924194336,313.0652904510498,311.5103244781494
+100000,80,EventJitFPNormalLinear,cpu,2919.220209121704,2925.20809173584,3119.706153869629,2941.241502761841,2935.343027114868,2932.901620864868,2933.8808059692383,2943.2263374328613,2902.801513671875,2923.5544204711914,307.59477615356445,319.9424743652344,320.50633430480957,308.2001209259033,307.8455924987793,307.9347610473633,324.57566261291504,308.5949420928955,314.4867420196533,313.7054443359375
+200000,80,EventJitFPNormalLinear,cpu,5781.855344772339,5711.039781570435,5720.657825469971,5743.339538574219,5758.7339878082275,5764.442443847656,5731.518983840942,5772.5770473480225,5875.596284866333,5782.744884490967,536.3578796386719,488.08813095092773,447.14832305908203,447.89934158325195,447.50070571899414,588.6516571044922,444.03791427612305,492.08831787109375,463.9921188354492,468.4431552886963
+400000,80,EventJitFPNormalLinear,cpu,11406.693458557129,11463.652610778809,11335.768938064575,11327.718734741211,11334.57350730896,11338.078022003174,11307.35993385315,11338.592052459717,11332.566738128662,11358.972787857056,709.4035148620605,736.3247871398926,729.2377948760986,697.6583003997803,684.0634346008301,681.3712120056152,690.8729076385498,700.2103328704834,677.4790287017822,672.919750213623
+800000,80,EventJitFPNormalLinear,cpu,22577.19659805298,22561.086893081665,22529.523849487305,22437.955379486084,22764.678955078125,22440.315008163452,22468.382835388184,22431.846141815186,22639.31393623352,22489.261865615845,1181.5659999847412,1158.522129058838,1197.1487998962402,1205.7430744171143,1153.594970703125,1184.3750476837158,1171.1905002593994,1211.423635482788,1220.9784984588623,1172.5356578826904
diff --git a/benchmarks/analysis/model/COBA results/benchmark_COBA_cpu2.csv b/benchmarks/analysis/model/COBA results/benchmark_COBA_cpu2.csv
new file mode 100644
index 0000000..e3f7778
--- /dev/null
+++ b/benchmarks/analysis/model/COBA results/benchmark_COBA_cpu2.csv	
@@ -0,0 +1,81 @@
+post_num,conn_num,comm_type,device,brainpylib_time1,brainpylib_time2,brainpylib_time3,brainpylib_time4,brainpylib_time5,brainpylib_time6,brainpylib_time7,brainpylib_time8,brainpylib_time9,brainpylib_time10,taichi_time1,taichi_time2,taichi_time3,taichi_time4,taichi_time5,taichi_time6,taichi_time7,taichi_time8,taichi_time9,taichi_time10
+400,20,EventCSRLinear,cpu,347.7926254272461,418.92147064208984,340.49010276794434,360.567569732666,325.01935958862305,418.3840751647949,336.95483207702637,316.4248466491699,427.384614944458,334.46741104125977,156.89730644226074,159.5900058746338,157.37676620483398,153.49531173706055,158.83135795593262,155.76457977294922,163.00344467163086,142.25387573242188,162.0171070098877,157.50384330749512
+400,20,EventJitFPHomoLinear,cpu,186.02705001831055,147.66740798950195,239.90607261657715,148.40340614318848,143.67318153381348,145.68281173706055,147.75586128234863,143.13268661499023,146.37279510498047,144.09255981445312,155.7157039642334,156.75616264343262,151.39341354370117,153.25164794921875,151.7465114593506,199.28669929504395,155.39860725402832,171.31972312927246,157.99880027770996,157.90033340454102
+400,20,EventJitFPUniformLinear,cpu,153.8534164428711,151.58629417419434,234.80749130249023,145.9786891937256,148.59867095947266,150.67028999328613,151.3512134552002,151.8728733062744,146.16799354553223,152.82392501831055,178.05719375610352,190.16003608703613,159.39927101135254,176.5592098236084,176.57947540283203,180.43231964111328,158.0357551574707,192.39544868469238,155.9443473815918,158.02550315856934
+400,20,EventJitFPNormalLinear,cpu,151.3528823852539,150.1922607421875,151.5064239501953,150.3129005432129,151.11422538757324,150.787353515625,146.3186740875244,254.71782684326172,151.9756317138672,151.29971504211426,158.68425369262695,158.921480178833,164.60561752319336,161.52071952819824,178.14064025878906,161.59987449645996,158.4475040435791,162.25647926330566,162.16254234313965,159.10935401916504
+400,40,EventCSRLinear,cpu,328.4430503845215,447.767972946167,335.74771881103516,332.5684070587158,321.1047649383545,319.4618225097656,456.38442039489746,313.32850456237793,318.1898593902588,315.7522678375244,141.81995391845703,141.72697067260742,140.48147201538086,141.96515083312988,146.05951309204102,141.67189598083496,141.07203483581543,140.7935619354248,142.8241729736328,138.01264762878418
+400,40,EventJitFPHomoLinear,cpu,281.86774253845215,170.1502799987793,166.26548767089844,167.2995090484619,149.66177940368652,167.18626022338867,180.01747131347656,172.82700538635254,167.10710525512695,167.38605499267578,170.7451343536377,159.70420837402344,159.70563888549805,158.5831642150879,209.3505859375,167.55104064941406,170.84932327270508,154.77824211120605,173.54154586791992,183.52270126342773
+400,40,EventJitFPUniformLinear,cpu,164.6883487701416,168.83540153503418,151.07035636901855,153.52988243103027,168.55454444885254,171.38910293579102,150.79998970031738,168.43438148498535,270.4765796661377,150.6030559539795,160.6583595275879,191.99037551879883,183.3195686340332,175.96888542175293,160.90941429138184,162.58955001831055,181.85758590698242,160.1557731628418,160.5699062347412,182.76429176330566
+400,40,EventJitFPNormalLinear,cpu,179.5024871826172,157.2103500366211,185.7459545135498,169.8167324066162,168.90692710876465,154.30498123168945,159.3008041381836,165.30799865722656,171.31471633911133,172.63555526733398,164.2906665802002,183.10141563415527,171.60868644714355,159.44886207580566,164.83759880065918,158.33735466003418,162.43600845336914,159.51895713806152,161.7262363433838,154.9999713897705
+400,80,EventCSRLinear,cpu,314.53990936279297,321.0628032684326,319.0195560455322,313.42220306396484,316.9863224029541,487.73837089538574,316.68567657470703,323.11177253723145,313.3659362792969,322.6006031036377,150.85840225219727,142.71807670593262,138.50116729736328,140.39897918701172,140.73610305786133,141.2026882171631,142.36950874328613,141.54767990112305,316.8015480041504,139.45627212524414
+400,80,EventJitFPHomoLinear,cpu,153.04255485534668,169.06213760375977,168.36309432983398,150.43950080871582,170.14408111572266,171.84138298034668,147.8111743927002,165.91978073120117,153.4121036529541,146.3949680328369,155.7021141052246,170.1829433441162,195.46985626220703,194.37432289123535,190.66095352172852,170.7291603088379,150.25854110717773,173.70128631591797,177.39105224609375,172.41716384887695
+400,80,EventJitFPUniformLinear,cpu,166.14913940429688,161.2985134124756,175.15850067138672,174.09443855285645,154.7846794128418,169.10886764526367,170.6223487854004,153.00774574279785,189.24379348754883,157.17720985412598,158.49685668945312,201.39122009277344,176.01943016052246,178.45845222473145,159.30676460266113,174.93247985839844,182.81912803649902,336.2231254577637,189.9242401123047,191.9574737548828
+400,80,EventJitFPNormalLinear,cpu,178.71499061584473,174.52716827392578,172.50418663024902,187.8347396850586,160.04347801208496,202.61645317077637,166.3663387298584,156.91065788269043,186.29956245422363,196.0165500640869,162.4162197113037,181.29301071166992,178.97820472717285,173.6452579498291,177.61588096618652,175.5979061126709,182.46841430664062,160.54248809814453,176.18060111999512,175.98533630371094
+400,100,EventCSRLinear,cpu,316.6515827178955,511.0282897949219,312.5486373901367,324.5856761932373,318.6841011047363,324.69868659973145,318.12524795532227,317.60191917419434,318.65406036376953,548.3312606811523,138.64994049072266,141.4649486541748,140.41590690612793,141.6783332824707,143.56374740600586,141.8132781982422,141.95871353149414,140.78497886657715,142.00496673583984,144.46687698364258
+400,100,EventJitFPHomoLinear,cpu,153.25307846069336,152.8615951538086,151.04055404663086,151.1225700378418,145.82490921020508,153.1221866607666,150.04825592041016,151.43513679504395,150.7430076599121,145.51568031311035,157.3331356048584,151.11255645751953,156.8589210510254,151.21126174926758,153.52368354797363,150.63118934631348,155.41958808898926,152.6317596435547,154.6473503112793,172.38426208496094
+400,100,EventJitFPUniformLinear,cpu,159.45076942443848,158.50138664245605,160.1088047027588,157.69505500793457,157.4106216430664,156.73041343688965,159.50703620910645,157.85813331604004,152.59456634521484,156.83412551879883,174.27325248718262,182.88016319274902,177.77371406555176,163.8927459716797,200.4990577697754,397.05944061279297,162.10103034973145,194.67759132385254,203.97377014160156,158.0655574798584
+400,100,EventJitFPNormalLinear,cpu,164.77394104003906,159.48939323425293,164.76941108703613,179.7928810119629,158.25581550598145,159.83319282531738,179.0752410888672,179.03733253479004,166.21875762939453,166.4905548095703,215.48962593078613,175.53377151489258,161.07916831970215,163.39731216430664,195.2674388885498,183.15625190734863,200.86336135864258,163.21420669555664,159.24406051635742,196.1231231689453
+4000,20,EventCSRLinear,cpu,334.3369960784912,339.1413688659668,579.9598693847656,334.7511291503906,336.9777202606201,337.05997467041016,332.7343463897705,332.521915435791,331.8166732788086,314.8012161254883,157.6850414276123,157.85479545593262,161.76700592041016,160.9814167022705,158.21027755737305,157.7436923980713,158.75506401062012,149.61934089660645,144.32597160339355,157.93275833129883
+4000,20,EventJitFPHomoLinear,cpu,170.28045654296875,458.4317207336426,162.95170783996582,176.66888236999512,176.72967910766602,160.01081466674805,174.7457981109619,180.38105964660645,179.4416904449463,161.80658340454102,203.25303077697754,191.9403076171875,194.02670860290527,157.65380859375,191.44916534423828,173.60949516296387,192.29698181152344,155.93791007995605,179.09622192382812,171.74220085144043
+4000,20,EventJitFPUniformLinear,cpu,181.82635307312012,186.0795021057129,183.02178382873535,169.7983741760254,185.8525276184082,184.07702445983887,171.38051986694336,176.35440826416016,169.78788375854492,165.39335250854492,182.01971054077148,162.34374046325684,181.5812587738037,157.5796604156494,176.01776123046875,164.86358642578125,219.27571296691895,162.6739501953125,181.37335777282715,164.41679000854492
+4000,20,EventJitFPNormalLinear,cpu,193.9220428466797,179.58402633666992,195.4975128173828,194.98729705810547,194.50736045837402,181.1215877532959,177.89864540100098,194.99444961547852,178.95197868347168,177.2160530090332,201.8892765045166,197.89791107177734,161.30876541137695,185.133695602417,460.23058891296387,182.5389862060547,196.52223587036133,197.24512100219727,184.25703048706055,198.56023788452148
+4000,40,EventCSRLinear,cpu,342.2565460205078,335.5977535247803,338.106632232666,333.44030380249023,338.90414237976074,336.44723892211914,340.05165100097656,655.057430267334,312.76607513427734,337.3422622680664,160.49480438232422,151.82137489318848,158.74242782592773,157.67979621887207,160.49957275390625,142.49920845031738,139.79148864746094,160.4897975921631,161.39507293701172,159.99984741210938
+4000,40,EventJitFPHomoLinear,cpu,175.08769035339355,192.6443576812744,185.1365566253662,171.79250717163086,191.6518211364746,178.37047576904297,192.72541999816895,197.80683517456055,174.88384246826172,177.4439811706543,160.56561470031738,161.52715682983398,156.8007469177246,173.23946952819824,155.26676177978516,191.99061393737793,155.17616271972656,157.35960006713867,174.05295372009277,158.81085395812988
+4000,40,EventJitFPUniformLinear,cpu,213.33980560302734,183.14528465270996,202.925443649292,202.72302627563477,205.80792427062988,192.9624080657959,202.49629020690918,201.17831230163574,221.20928764343262,189.6815299987793,162.46414184570312,162.59241104125977,178.4985065460205,181.8222999572754,163.94376754760742,203.4323215484619,202.13627815246582,161.17405891418457,217.85283088684082,195.08886337280273
+4000,40,EventJitFPNormalLinear,cpu,212.5701904296875,217.79346466064453,535.3691577911377,222.72491455078125,208.14275741577148,222.57113456726074,220.7331657409668,207.3676586151123,223.6616611480713,223.0374813079834,179.93950843811035,179.4302463531494,180.17268180847168,162.7652645111084,179.4147491455078,163.7575626373291,179.37493324279785,203.12952995300293,179.3045997619629,180.18126487731934
+4000,80,EventCSRLinear,cpu,351.55653953552246,348.3619689941406,358.95538330078125,339.2040729522705,339.5371437072754,370.60093879699707,709.4740867614746,341.0515785217285,352.73265838623047,343.7519073486328,157.1483612060547,158.87022018432617,183.8219165802002,181.55717849731445,183.62140655517578,163.6815071105957,160.50291061401367,161.391019821167,157.55057334899902,159.32965278625488
+4000,80,EventJitFPHomoLinear,cpu,221.17877006530762,200.93703269958496,223.62971305847168,217.76604652404785,206.76255226135254,218.89257431030273,255.26022911071777,202.43453979492188,218.796968460083,219.29121017456055,176.76377296447754,155.75909614562988,215.15631675720215,195.4214572906494,192.9788589477539,154.8616886138916,159.4552993774414,175.35853385925293,172.42908477783203,173.62141609191895
+4000,80,EventJitFPUniformLinear,cpu,257.5268745422363,240.05889892578125,235.1822853088379,238.2223606109619,237.07962036132812,238.5580539703369,215.76786041259766,223.2375144958496,235.97002029418945,234.8306179046631,196.67577743530273,177.75774002075195,214.310884475708,214.50567245483398,184.0951442718506,177.37817764282227,201.7529010772705,195.1746940612793,180.20367622375488,161.04531288146973
+4000,80,EventJitFPNormalLinear,cpu,280.3950309753418,633.195161819458,260.7119083404541,277.84037590026855,277.82320976257324,278.12671661376953,280.05170822143555,263.2410526275635,273.9534378051758,263.9119625091553,162.63461112976074,166.69487953186035,181.77175521850586,187.47496604919434,199.46670532226562,181.08415603637695,162.57381439208984,163.63930702209473,160.74585914611816,168.81775856018066
+4000,100,EventCSRLinear,cpu,335.81995964050293,336.4710807800293,321.63500785827637,334.6529006958008,321.7592239379883,342.4496650695801,336.5769386291504,337.10408210754395,728.9233207702637,323.43435287475586,158.08415412902832,161.6380214691162,180.27162551879883,184.33785438537598,187.36577033996582,142.43698120117188,160.2940559387207,158.14781188964844,159.10816192626953,154.82044219970703
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+4000,100,EventJitFPNormalLinear,cpu,288.68651390075684,304.2263984680176,309.24534797668457,285.84909439086914,307.94453620910645,302.548885345459,303.7116527557373,294.09193992614746,312.4048709869385,288.70534896850586,183.81190299987793,224.44820404052734,213.95039558410645,586.0717296600342,178.5123348236084,206.03322982788086,188.5051727294922,179.89683151245117,180.9685230255127,165.03047943115234
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+4000000,20,EventJitFPNormalLinear,cpu,28833.25958251953,29178.29203605652,28933.218479156494,28851.6047000885,28691.073656082153,28758.530616760254,28739.754676818848,28677.356719970703,28842.222452163696,28647.88293838501,473.1900691986084,593.2085514068604,512.6669406890869,451.7805576324463,445.5385208129883,429.57210540771484,480.1983833312988,467.7736759185791,440.8714771270752,441.7717456817627
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+4000000,40,EventJitFPHomoLinear,cpu,28069.449186325073,27886.1243724823,27536.673545837402,27636.22212409973,27454.87666130066,27331.61473274231,27494.812965393066,27532.155513763428,27456.008672714233,27521.018266677856,522.0868587493896,486.2699508666992,441.2217140197754,475.8565425872803,457.6985836029053,522.1612453460693,497.18546867370605,455.30080795288086,448.08220863342285,416.54443740844727
+4000000,40,EventJitFPUniformLinear,cpu,36919.69895362854,36553.49040031433,36411.74030303955,36291.84174537659,36197.20482826233,35994.441986083984,36032.08088874817,35943.43447685242,35942.75212287903,36033.99348258972,546.6344356536865,590.7251834869385,472.6078510284424,1385.7667446136475,449.7864246368408,427.7076721191406,446.03419303894043,431.7588806152344,431.64873123168945,507.5075626373291
+4000000,40,EventJitFPNormalLinear,cpu,57314.92805480957,56745.04041671753,56270.84755897522,56235.56160926819,56180.66906929016,56167.72818565369,56238.415479660034,56067.86036491394,56290.117263793945,56105.252504348755,617.3462867736816,577.1431922912598,525.4836082458496,495.41711807250977,441.7989253997803,469.8970317840576,432.82532691955566,436.04183197021484,478.1217575073242,498.2011318206787
+4000000,80,EventCSRLinear,cpu,1038.896083831787,744.3234920501709,690.2463436126709,667.6650047302246,634.1962814331055,669.7430610656738,626.7402172088623,644.3040370941162,690.0053024291992,677.2735118865967,840.1679992675781,564.3014907836914,495.1317310333252,491.49274826049805,451.41029357910156,462.43739128112793,464.58935737609863,464.0624523162842,474.2100238800049,489.84718322753906
+4000000,80,EventJitFPHomoLinear,cpu,54699.74088668823,53805.47094345093,53642.53735542297,53467.51356124878,53361.92989349365,53539.96467590332,53368.425369262695,53436.15937232971,53846.15516662598,53644.071102142334,592.5815105438232,519.1617012023926,445.39880752563477,468.4278964996338,457.3168754577637,435.2250099182129,430.7887554168701,435.19091606140137,431.1995506286621,439.5453929901123
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+4000000,80,EventJitFPNormalLinear,cpu,112461.70663833618,111467.83590316772,111409.78074073792,111047.99199104309,111195.64485549927,111403.6226272583,111088.00601959229,111264.6701335907,111223.135471344,111206.47525787354,709.9075317382812,606.4767837524414,499.81212615966797,471.10962867736816,1453.2856941223145,470.36004066467285,447.5364685058594,504.9464702606201,480.81064224243164,473.65736961364746
+4000000,100,EventCSRLinear,cpu,1042.1838760375977,747.6012706756592,670.478105545044,655.6832790374756,628.371000289917,666.8875217437744,636.3496780395508,640.1898860931396,695.061206817627,654.9673080444336,862.0049953460693,597.7156162261963,498.93641471862793,451.31659507751465,455.3370475769043,458.88710021972656,461.35663986206055,467.2722816467285,486.27686500549316,479.917049407959
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diff --git a/benchmarks/analysis/model/COBA results/benchmark_COBA_gpu.csv b/benchmarks/analysis/model/COBA results/benchmark_COBA_gpu.csv
new file mode 100644
index 0000000..c26a4ac
--- /dev/null
+++ b/benchmarks/analysis/model/COBA results/benchmark_COBA_gpu.csv	
@@ -0,0 +1,13 @@
+post_num,conn_num,comm_type,device,brainpylib_time1,brainpylib_time2,brainpylib_time3,brainpylib_time4,brainpylib_time5,brainpylib_time6,brainpylib_time7,brainpylib_time8,brainpylib_time9,brainpylib_time10,taichi_time1,taichi_time2,taichi_time3,taichi_time4,taichi_time5,taichi_time6,taichi_time7,taichi_time8,taichi_time9,taichi_time10
+400,80,EventJitFPNormalLinear,gpu,217.67067909240723,216.78948402404785,214.04027938842773,193.8493251800537,185.43386459350586,188.4467601776123,180.9558868408203,184.05580520629883,185.5638027191162,186.62071228027344,201.13229751586914,200.78229904174805,197.52979278564453,254.7297477722168,201.6448974609375,245.99123001098633,229.2482852935791,198.93312454223633,204.54096794128418,198.31252098083496
+800,80,EventJitFPNormalLinear,gpu,190.59228897094727,192.10004806518555,189.61191177368164,183.11667442321777,189.80932235717773,190.12999534606934,189.9247169494629,190.40155410766602,190.65380096435547,254.0891170501709,210.2642059326172,220.4873561859131,203.57346534729004,202.22735404968262,203.45306396484375,205.8572769165039,206.1440944671631,199.78618621826172,203.22656631469727,204.6184539794922
+1600,80,EventJitFPNormalLinear,gpu,202.83126831054688,198.81796836853027,191.25890731811523,199.75757598876953,199.25665855407715,261.7778778076172,200.6244659423828,194.79608535766602,210.58249473571777,211.29941940307617,222.75161743164062,223.92559051513672,216.02630615234375,212.73136138916016,221.44818305969238,208.418607711792,211.59791946411133,212.21017837524414,211.00544929504395,209.78498458862305
+3200,80,EventJitFPNormalLinear,gpu,206.787109375,215.8205509185791,206.41517639160156,223.0217456817627,288.85340690612793,203.25160026550293,211.4548683166504,202.89921760559082,208.0075740814209,208.81223678588867,214.04671669006348,219.27499771118164,225.84199905395508,218.4746265411377,220.83568572998047,225.75139999389648,211.8074893951416,219.79451179504395,212.65625953674316,216.9342041015625
+6400,80,EventJitFPNormalLinear,gpu,223.52075576782227,210.4775905609131,208.6660861968994,206.2699794769287,306.29611015319824,213.30881118774414,208.9371681213379,187.22939491271973,187.9563331604004,215.0254249572754,215.49630165100098,239.44330215454102,224.74241256713867,226.14288330078125,225.2175807952881,219.3610668182373,239.8815155029297,215.27719497680664,231.1551570892334,227.2796630859375
+12800,80,EventJitFPNormalLinear,gpu,216.94493293762207,223.61254692077637,187.22152709960938,234.13681983947754,232.0702075958252,254.68134880065918,217.65732765197754,332.3230743408203,231.31155967712402,223.46019744873047,250.17142295837402,224.87115859985352,266.77632331848145,266.91555976867676,232.1913242340088,247.65777587890625,246.47188186645508,279.6781063079834,257.7357292175293,228.79576683044434
+25600,80,EventJitFPNormalLinear,gpu,250.88095664978027,247.72000312805176,223.3579158782959,255.22971153259277,248.63529205322266,261.41953468322754,230.7753562927246,211.97986602783203,219.57039833068848,244.82226371765137,236.38319969177246,260.6780529022217,348.07682037353516,276.0903835296631,269.7412967681885,236.77682876586914,279.44445610046387,294.8625087738037,286.5469455718994,292.2804355621338
+51200,80,EventJitFPNormalLinear,gpu,284.60001945495605,292.8457260131836,293.05410385131836,291.72205924987793,269.0999507904053,247.0724582672119,272.92847633361816,283.39147567749023,248.95405769348145,284.96503829956055,303.01976203918457,310.09697914123535,310.92047691345215,301.9297122955322,327.9564380645752,292.86742210388184,314.00394439697266,332.4236869812012,317.5830841064453,310.3177547454834
+100000,80,EventJitFPNormalLinear,gpu,192.59095191955566,201.88212394714355,199.48458671569824,197.99137115478516,193.10975074768066,195.35207748413086,197.0367431640625,197.19314575195312,193.88914108276367,202.8791904449463,260.4043483734131,247.68424034118652,244.71282958984375,257.39288330078125,245.98336219787598,256.76655769348145,241.40310287475586,263.2014751434326,243.9749240875244,241.0900592803955
+200000,80,EventJitFPNormalLinear,gpu,241.07074737548828,242.5711154937744,239.09831047058105,221.87018394470215,293.11561584472656,239.67504501342773,234.2844009399414,240.78655242919922,244.0943717956543,232.7444553375244,424.32403564453125,269.1760063171387,259.57560539245605,264.4064426422119,271.8937397003174,286.33832931518555,269.1686153411865,268.749475479126,267.655611038208,269.76823806762695
+400000,80,EventJitFPNormalLinear,gpu,244.0347671508789,238.7986183166504,233.7479591369629,238.52086067199707,240.50045013427734,242.27643013000488,239.01915550231934,246.60110473632812,238.8131618499756,232.2535514831543,324.91326332092285,324.56421852111816,322.9351043701172,322.42393493652344,325.7174491882324,337.82482147216797,335.76488494873047,326.43747329711914,329.68950271606445,329.2527198791504
+800000,80,EventJitFPNormalLinear,gpu,301.6948699951172,328.3581733703613,494.7850704193115,314.2673969268799,368.36934089660645,309.1142177581787,354.8698425292969,325.1519203186035,351.1927127838135,312.3452663421631,471.250057220459,462.0852470397949,436.82098388671875,454.4506072998047,432.79576301574707,458.00018310546875,454.82873916625977,430.2699565887451,439.1796588897705,464.04123306274414
diff --git a/benchmarks/analysis/model/COBA results/benchmark_COBA_gpu2.csv b/benchmarks/analysis/model/COBA results/benchmark_COBA_gpu2.csv
new file mode 100644
index 0000000..0e208b6
--- /dev/null
+++ b/benchmarks/analysis/model/COBA results/benchmark_COBA_gpu2.csv	
@@ -0,0 +1,81 @@
+post_num,conn_num,comm_type,device,brainpylib_time1,brainpylib_time2,brainpylib_time3,brainpylib_time4,brainpylib_time5,brainpylib_time6,brainpylib_time7,brainpylib_time8,brainpylib_time9,brainpylib_time10,taichi_time1,taichi_time2,taichi_time3,taichi_time4,taichi_time5,taichi_time6,taichi_time7,taichi_time8,taichi_time9,taichi_time10
+400,20,EventCSRLinear,gpu,180.77373504638672,170.96519470214844,198.26054573059082,190.23919105529785,185.52112579345703,200.6056308746338,185.5325698852539,198.02546501159668,243.39747428894043,193.39513778686523,229.170560836792,207.6241970062256,221.3592529296875,236.59133911132812,227.1738052368164,195.9531307220459,212.7823829650879,196.9316005706787,266.0336494445801,195.23072242736816
+400,20,EventJitFPHomoLinear,gpu,227.25462913513184,185.60361862182617,198.8980770111084,200.5300521850586,217.41461753845215,181.0317039489746,196.42066955566406,217.22936630249023,227.09274291992188,205.92546463012695,187.43062019348145,203.5965919494629,189.9123191833496,190.14883041381836,216.02249145507812,226.81617736816406,231.3368320465088,262.79401779174805,239.46595191955566,218.26577186584473
+400,20,EventJitFPUniformLinear,gpu,186.32054328918457,186.99121475219727,186.25879287719727,182.56735801696777,179.5198917388916,192.40999221801758,185.23383140563965,190.04559516906738,180.79233169555664,275.2196788787842,195.24812698364258,196.49386405944824,193.50886344909668,199.52750205993652,272.51482009887695,222.08237648010254,198.85492324829102,193.70198249816895,199.5701789855957,200.35696029663086
+400,20,EventJitFPNormalLinear,gpu,182.905912399292,186.5689754486084,275.723934173584,234.32207107543945,187.41345405578613,218.40500831604004,182.81841278076172,184.25464630126953,186.70940399169922,184.10968780517578,198.41265678405762,192.08860397338867,195.08981704711914,195.4975128173828,289.4158363342285,198.4415054321289,197.90911674499512,187.71791458129883,195.66631317138672,200.20627975463867
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+400,40,EventJitFPHomoLinear,gpu,184.39745903015137,182.16991424560547,180.04584312438965,182.72018432617188,182.65819549560547,250.4441738128662,181.2751293182373,180.5410385131836,182.9967498779297,183.81905555725098,197.9663372039795,186.93852424621582,192.46935844421387,192.16179847717285,195.16444206237793,195.74356079101562,191.99252128601074,258.1627368927002,194.1511631011963,214.89477157592773
+400,40,EventJitFPUniformLinear,gpu,201.1103630065918,201.45487785339355,227.03218460083008,199.13458824157715,238.79456520080566,298.34818840026855,199.5236873626709,183.8700771331787,184.56435203552246,200.58679580688477,204.67114448547363,212.26239204406738,217.44942665100098,197.73077964782715,216.9651985168457,199.81050491333008,203.03654670715332,193.95112991333008,204.00404930114746,245.88608741760254
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+400,80,EventCSRLinear,gpu,192.87657737731934,238.22879791259766,194.09418106079102,181.66351318359375,272.0599174499512,188.65013122558594,170.85957527160645,186.36536598205566,205.67703247070312,172.60146141052246,207.37576484680176,189.3022060394287,197.81041145324707,222.1207618713379,175.6114959716797,183.95042419433594,259.66453552246094,222.84293174743652,204.32734489440918,218.4884548187256
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+400000,40,EventCSRLinear,gpu,229.85601425170898,305.3863048553467,227.7066707611084,217.83852577209473,229.00104522705078,226.98402404785156,223.2966423034668,214.4167423248291,226.51338577270508,207.0446014404297,216.19796752929688,304.25500869750977,219.68865394592285,215.9252166748047,239.45999145507812,209.28001403808594,205.29508590698242,236.69958114624023,206.3751220703125,207.69977569580078
+400000,40,EventJitFPHomoLinear,gpu,218.28937530517578,206.10547065734863,202.5439739227295,205.0797939300537,202.0103931427002,228.78265380859375,218.2753086090088,207.59344100952148,223.5715389251709,203.33123207092285,205.13582229614258,210.08706092834473,216.60208702087402,212.39328384399414,214.4486904144287,209.20419692993164,209.8867893218994,227.07676887512207,216.64166450500488,211.26604080200195
+400000,40,EventJitFPUniformLinear,gpu,215.79647064208984,201.56168937683105,206.72202110290527,210.60705184936523,208.0056667327881,208.6167335510254,206.10642433166504,212.33153343200684,216.95780754089355,207.49330520629883,248.8076686859131,327.9097080230713,256.53791427612305,219.65646743774414,225.71301460266113,231.69279098510742,220.94297409057617,220.1690673828125,242.44403839111328,236.62376403808594
+400000,40,EventJitFPNormalLinear,gpu,234.0219020843506,219.12670135498047,229.71463203430176,239.62116241455078,217.79465675354004,229.10046577453613,308.1188201904297,253.40652465820312,242.6152229309082,211.9314670562744,310.7271194458008,256.3345432281494,247.58505821228027,214.1280174255371,239.2423152923584,346.72093391418457,260.21385192871094,244.0176010131836,231.3535213470459,231.2781810760498
+400000,80,EventCSRLinear,gpu,281.1307907104492,218.34492683410645,214.07771110534668,223.80661964416504,246.66309356689453,237.5185489654541,236.27376556396484,205.33108711242676,220.92390060424805,218.9643383026123,283.12063217163086,203.57489585876465,202.0862102508545,270.7083225250244,210.03961563110352,204.9415111541748,225.60858726501465,231.35924339294434,231.04596138000488,223.923921585083
+400000,80,EventJitFPHomoLinear,gpu,308.60090255737305,235.23473739624023,250.3223419189453,216.3681983947754,252.63237953186035,343.80030632019043,224.69115257263184,208.5418701171875,883.7277889251709,237.75577545166016,232.41376876831055,247.8482723236084,231.0640811920166,268.2938575744629,329.1480541229248,238.3100986480713,242.29907989501953,214.44988250732422,214.83922004699707,224.32780265808105
+400000,80,EventJitFPUniformLinear,gpu,237.15662956237793,331.3016891479492,218.74332427978516,239.60161209106445,214.90144729614258,220.17621994018555,223.58202934265137,223.9832878112793,218.93739700317383,257.89880752563477,232.0270538330078,254.5337677001953,254.08530235290527,250.16474723815918,232.57040977478027,248.94952774047852,311.1231327056885,237.01715469360352,249.6039867401123,215.27910232543945
+400000,80,EventJitFPNormalLinear,gpu,218.57738494873047,209.90872383117676,231.58693313598633,301.15246772766113,227.83875465393066,229.0656566619873,240.18597602844238,230.8495044708252,262.7601623535156,229.8436164855957,268.5117721557617,218.7023162841797,244.1723346710205,232.30576515197754,260.30945777893066,309.94439125061035,224.14588928222656,251.05547904968262,213.38844299316406,248.91996383666992
+400000,100,EventCSRLinear,gpu,194.41604614257812,199.42331314086914,189.09239768981934,199.21231269836426,205.49440383911133,194.39363479614258,192.28053092956543,226.1066436767578,194.9620246887207,191.7097568511963,198.4388828277588,200.80041885375977,216.5243625640869,195.54567337036133,207.21030235290527,245.26739120483398,219.80690956115723,240.21410942077637,225.65865516662598,257.74621963500977
+400000,100,EventJitFPHomoLinear,gpu,264.44268226623535,234.71832275390625,232.46097564697266,208.15491676330566,212.0382785797119,203.7038803100586,207.80158042907715,207.01122283935547,209.37871932983398,217.9408073425293,219.50507164001465,220.07489204406738,233.95037651062012,219.3458080291748,218.80793571472168,223.1600284576416,227.09274291992188,241.6985034942627,234.4813346862793,239.18914794921875
+400000,100,EventJitFPUniformLinear,gpu,231.5678596496582,222.0747470855713,219.56944465637207,253.65900993347168,233.7017059326172,225.88062286376953,224.64585304260254,325.37126541137695,214.12324905395508,213.8206958770752,254.4388771057129,316.7140483856201,246.25778198242188,227.1890640258789,239.5017147064209,244.10295486450195,338.51122856140137,236.54818534851074,225.07667541503906,253.29089164733887
+400000,100,EventJitFPNormalLinear,gpu,285.25805473327637,237.0142936706543,240.93389511108398,215.5141830444336,272.52817153930664,221.24457359313965,196.40064239501953,236.22751235961914,226.61256790161133,216.27068519592285,926.1467456817627,264.63842391967773,341.4278030395508,246.94347381591797,260.0131034851074,220.15833854675293,246.43921852111816,308.7501525878906,231.37855529785156,218.74332427978516
+4000000,20,EventCSRLinear,gpu,314.9740695953369,295.05228996276855,334.52916145324707,299.62730407714844,324.80883598327637,319.87547874450684,300.03952980041504,294.9409484863281,314.32366371154785,349.7140407562256,315.4933452606201,317.54016876220703,320.05906105041504,320.2016353607178,287.6436710357666,304.40568923950195,314.7289752960205,320.18542289733887,335.25657653808594,296.43774032592773
+4000000,20,EventJitFPHomoLinear,gpu,273.1821537017822,285.0170135498047,247.70569801330566,335.0682258605957,246.73986434936523,246.81448936462402,246.06990814208984,266.8027877807617,330.90806007385254,259.65046882629395,308.4900379180908,341.6309356689453,325.4871368408203,332.78656005859375,316.558837890625,339.97583389282227,321.0713863372803,297.943115234375,313.48633766174316,332.4697017669678
+4000000,20,EventJitFPUniformLinear,gpu,287.80269622802734,304.54373359680176,297.58739471435547,286.3049507141113,288.0520820617676,356.342077255249,298.3517646789551,336.2410068511963,263.75675201416016,332.4882984161377,392.7593231201172,315.67978858947754,331.9675922393799,302.5190830230713,342.5877094268799,301.1758327484131,351.05323791503906,311.3236427307129,357.2850227355957,299.9393939971924
+4000000,20,EventJitFPNormalLinear,gpu,267.4059867858887,255.3863525390625,273.77796173095703,268.72992515563965,301.21564865112305,269.31095123291016,324.33032989501953,281.7363739013672,365.4458522796631,282.29689598083496,299.4377613067627,300.78601837158203,318.80831718444824,313.45057487487793,307.8007698059082,314.65673446655273,332.4611186981201,326.9927501678467,310.5335235595703,307.9814910888672
+4000000,40,EventCSRLinear,gpu,311.7787837982178,331.221342086792,295.70841789245605,348.18124771118164,296.82111740112305,340.99364280700684,294.4211959838867,352.6132106781006,277.41432189941406,359.72142219543457,334.14196968078613,296.0190773010254,345.9336757659912,309.0839385986328,342.73648262023926,291.2108898162842,350.1157760620117,304.25477027893066,339.02430534362793,297.4743843078613
+4000000,40,EventJitFPHomoLinear,gpu,255.61118125915527,320.9269046783447,255.50317764282227,326.8091678619385,255.79357147216797,262.9880905151367,255.58066368103027,259.1891288757324,330.96957206726074,257.33017921447754,301.5174865722656,351.3166904449463,306.6065311431885,338.6857509613037,311.13576889038086,345.45040130615234,301.5027046203613,357.2423458099365,306.67972564697266,331.44235610961914
+4000000,40,EventJitFPUniformLinear,gpu,257.21216201782227,261.0318660736084,321.4278221130371,275.24805068969727,370.44501304626465,303.90286445617676,338.5205268859863,301.116943359375,352.9064655303955,301.7897605895996,341.42327308654785,334.12837982177734,297.6851463317871,1110.9437942504883,390.0313377380371,324.19562339782715,333.9574337005615,316.6089057922363,339.6944999694824,315.2480125427246
+4000000,40,EventJitFPNormalLinear,gpu,278.29813957214355,354.7194004058838,286.44418716430664,364.7005558013916,263.15855979919434,321.2876319885254,263.5185718536377,265.3923034667969,252.01892852783203,274.9960422515869,321.0453987121582,326.3428211212158,328.1419277191162,327.3019790649414,321.69580459594727,329.90336418151855,327.0387649536133,342.5884246826172,332.81826972961426,301.9375801086426
+4000000,80,EventCSRLinear,gpu,371.44923210144043,300.22382736206055,338.362455368042,314.88823890686035,340.6403064727783,318.7258243560791,321.9754695892334,331.3405513763428,320.28698921203613,321.09951972961426,317.2750473022461,336.8222713470459,318.3326721191406,323.1682777404785,298.1090545654297,305.2387237548828,298.4120845794678,310.49489974975586,303.1942844390869,339.4773006439209
+4000000,80,EventJitFPHomoLinear,gpu,268.7397003173828,271.72231674194336,330.02424240112305,271.4118957519531,309.6346855163574,276.09825134277344,269.4363594055176,271.19922637939453,270.89691162109375,267.3463821411133,343.1985378265381,343.1053161621094,309.77439880371094,322.6451873779297,340.9590721130371,321.5973377227783,317.8367614746094,305.9847354888916,333.89925956726074,338.00482749938965
+4000000,80,EventJitFPUniformLinear,gpu,328.51481437683105,299.9541759490967,311.80524826049805,262.23015785217285,295.5942153930664,315.6392574310303,276.17835998535156,372.377872467041,276.18908882141113,322.8490352630615,392.55738258361816,312.6561641693115,327.10957527160645,310.5194568634033,340.5642509460449,322.5669860839844,333.40907096862793,327.162504196167,334.93757247924805,314.2125606536865
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+4000000,100,EventCSRLinear,gpu,360.3508472442627,350.46863555908203,428.36761474609375,328.04369926452637,347.7439880371094,355.73673248291016,324.0060806274414,314.1202926635742,319.6587562561035,311.0334873199463,288.87462615966797,291.4402484893799,296.675443649292,301.44190788269043,295.76683044433594,384.68360900878906,289.37721252441406,363.9848232269287,310.0557327270508,336.96818351745605
+4000000,100,EventJitFPHomoLinear,gpu,272.6597785949707,276.15976333618164,350.77738761901855,274.70993995666504,314.1143321990967,268.5227394104004,268.6483860015869,255.77950477600098,271.8229293823242,299.8185157775879,331.10594749450684,331.4707279205322,338.5775089263916,384.9179744720459,324.89991188049316,336.1637592315674,326.7347812652588,414.78586196899414,361.51719093322754,387.74967193603516
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+4000000,100,EventJitFPNormalLinear,gpu,303.2417297363281,281.3730239868164,280.0946235656738,354.83312606811523,300.69684982299805,351.44996643066406,311.65313720703125,337.25500106811523,307.6746463775635,341.724157333374,372.0674514770508,338.8686180114746,334.89465713500977,322.53360748291016,326.50017738342285,329.5607566833496,332.3698043823242,317.25597381591797,321.0129737854004,319.41962242126465
diff --git a/benchmarks/analysis/model/COBA results/benchmark_COBA_spks_cpu.csv b/benchmarks/analysis/model/COBA results/benchmark_COBA_spks_cpu.csv
new file mode 100644
index 0000000..316fb91
--- /dev/null
+++ b/benchmarks/analysis/model/COBA results/benchmark_COBA_spks_cpu.csv	
@@ -0,0 +1,12 @@
+post_num,conn_num,comm_type,device,brainpylib_spk,taichi_spk
+200,80,EventJitFPHomoLinear,cpu,2.53,1.25
+400,80,EventJitFPHomoLinear,cpu,2.495,2.905
+800,80,EventJitFPHomoLinear,cpu,2.62,3.535
+1600,80,EventJitFPHomoLinear,cpu,2.9175,3.22875
+3200,80,EventJitFPHomoLinear,cpu,2.716875,3.11375
+6400,80,EventJitFPHomoLinear,cpu,3.0475,3.42875
+12800,80,EventJitFPHomoLinear,cpu,3.13125,3.4248438
+25600,80,EventJitFPHomoLinear,cpu,3.104453,3.4130468
+51200,80,EventJitFPHomoLinear,cpu,3.1396484,3.4102345
+100000,80,EventJitFPHomoLinear,cpu,3.09538,3.33186
+200000,80,EventJitFPHomoLinear,cpu,3.16811,3.44457
diff --git a/benchmarks/analysis/model/COBA results/benchmark_COBA_spks_gpu.csv b/benchmarks/analysis/model/COBA results/benchmark_COBA_spks_gpu.csv
new file mode 100644
index 0000000..c569c24
--- /dev/null
+++ b/benchmarks/analysis/model/COBA results/benchmark_COBA_spks_gpu.csv	
@@ -0,0 +1,12 @@
+post_num,conn_num,comm_type,device,brainpylib_spk,taichi_spk
+200,80,EventJitFPHomoLinear,gpu,2.24,3.22
+400,80,EventJitFPHomoLinear,gpu,2.35,2.305
+800,80,EventJitFPHomoLinear,gpu,2.995,3.2124999
+1600,80,EventJitFPHomoLinear,gpu,3.1499999,3.0237498
+3200,80,EventJitFPHomoLinear,gpu,3.01625,2.9681249
+6400,80,EventJitFPHomoLinear,gpu,3.0853124,3.1768749
+12800,80,EventJitFPHomoLinear,gpu,3.0839062,3.4031248
+25600,80,EventJitFPHomoLinear,gpu,3.0870311,3.3578906
+51200,80,EventJitFPHomoLinear,gpu,3.0295312,3.3873827
+100000,80,EventJitFPHomoLinear,gpu,3.08552,3.29154
+200000,80,EventJitFPHomoLinear,gpu,3.0284,3.3159099
diff --git a/benchmarks/analysis/model/COBA results/benchmark_COBA_spks_gpu.xlsx b/benchmarks/analysis/model/COBA results/benchmark_COBA_spks_gpu.xlsx
new file mode 100644
index 0000000..8f4b445
Binary files /dev/null and b/benchmarks/analysis/model/COBA results/benchmark_COBA_spks_gpu.xlsx differ
diff --git a/benchmarks/analysis/model/COBA results/benchmark_MultipleArea_spks_gpu.xlsx b/benchmarks/analysis/model/COBA results/benchmark_MultipleArea_spks_gpu.xlsx
new file mode 100644
index 0000000..eada3e6
Binary files /dev/null and b/benchmarks/analysis/model/COBA results/benchmark_MultipleArea_spks_gpu.xlsx differ
diff --git a/benchmarks/analysis/model/Multiple Area results/analysis_MultipleArea.py b/benchmarks/analysis/model/Multiple Area results/analysis_MultipleArea.py
new file mode 100644
index 0000000..9832e4d
--- /dev/null
+++ b/benchmarks/analysis/model/Multiple Area results/analysis_MultipleArea.py	
@@ -0,0 +1,74 @@
+import pandas as pd
+import numpy as np
+import seaborn as sns
+import matplotlib.pyplot as plt
+import os
+
+PATH = os.path.dirname(os.path.abspath(__file__))
+
+
+# Function to remove outliers for brainpylib and taichi execution times
+def remove_outliers(df, prefix):
+    time_columns = [col for col in df.columns if col.startswith(prefix)]
+    for index, row in df.iterrows():
+        time_values = row[time_columns]
+        mean = time_values.mean()
+        deviation = time_values.sub(mean)
+        abs_deviation = abs(deviation)
+        outliers = abs_deviation > (abs_deviation.mean() + 1.5 * abs_deviation.std())
+        df.loc[index, time_columns] = time_values.mask(outliers, np.nan)
+    return df
+
+
+# Calculate mean execution times and speedup
+def calculate_means_and_speedup(df):
+    brainpylib_columns = [col for col in df.columns if col.startswith('brainpylib_time')]
+    taichi_columns = [col for col in df.columns if col.startswith('taichi_time')]
+    df['brainpylib_mean'] = df[brainpylib_columns].mean(axis=1)
+    df['taichi_mean'] = df[taichi_columns].mean(axis=1)
+    df['speedup'] = np.where(df['taichi_mean'] > df['brainpylib_mean'],
+                             1 - (df['taichi_mean'] / df['brainpylib_mean']),
+                             (df['brainpylib_mean'] / df['taichi_mean']) - 1)
+    return df
+
+
+def main(benchmark_df):
+    # Applying the functions
+    benchmark_df = remove_outliers(benchmark_df, 'brainpylib_time')
+    benchmark_df = remove_outliers(benchmark_df, 'taichi_time')
+    benchmark_df = calculate_means_and_speedup(benchmark_df)
+    DEVICE = benchmark_df['device'].unique()[0]
+    benchmark_df = benchmark_df.drop('device', axis=1)
+
+    # Aggregating speedup values
+    agg_speedup_df = benchmark_df.groupby(['syn_func_type', 'neuron_num', 'conn_num']).mean().reset_index()
+
+    # Unique communication types for creating separate heatmaps
+    syn_func_types = agg_speedup_df['syn_func_type'].unique()
+
+    # Setting up the plots
+    plt.figure(figsize=(20, 20))
+
+    for i, syn_func_type in enumerate(syn_func_types):
+        plt.subplot(2, 2, i + 1)
+        filtered_df = agg_speedup_df[agg_speedup_df['syn_func_type'] == syn_func_type]
+        heatmap_data = filtered_df.pivot(index='neuron_num', columns='conn_num', values='speedup')
+
+        sns.heatmap(heatmap_data, annot=True, fmt=".2f", cmap='YlGnBu', annot_kws={"size": 24})
+        plt.title(f'[{DEVICE}]Multi area network Comm Type: {syn_func_type}\n' + \
+                  'speedup = brainpylib time / taichi time - 1 if taichi faster than brainpylib\n' + \
+                  'speedup = 1 - taichi time / brainpylib time if taichi slower than brainpylib')
+        plt.xlabel('Conn Num')
+        plt.ylabel('Neuron Num')
+
+    plt.tight_layout()
+    plt.savefig(f'{PATH}/benchmark__MultipleArea_{DEVICE}_heatmap.png')
+
+
+# Load the dataset
+benchmark_path = f"{PATH}/benchmark_MultipleArea_cpu.csv"
+benchmark_df = pd.read_csv(benchmark_path)
+main(benchmark_df)
+benchmark_path = f"{PATH}/benchmark_MultipleArea_gpu.csv"
+benchmark_df = pd.read_csv(benchmark_path)
+main(benchmark_df)
\ No newline at end of file
diff --git a/benchmarks/analysis/model/Multiple Area results/analysis_MultipleArea_homo_barchart.py b/benchmarks/analysis/model/Multiple Area results/analysis_MultipleArea_homo_barchart.py
new file mode 100644
index 0000000..914b42c
--- /dev/null
+++ b/benchmarks/analysis/model/Multiple Area results/analysis_MultipleArea_homo_barchart.py	
@@ -0,0 +1,59 @@
+import matplotlib.pyplot as plt
+import pandas as pd
+import numpy as np
+import os
+import seaborn as sns
+from matplotlib.font_manager import FontProperties
+
+font = FontProperties(fname='C:\\Windows\\Fonts\\msyh.ttc')
+
+# 去除一组列中的异常值
+def remove_row_outliers(df, column_prefix, threshold=1.5):
+    time_columns = [col for col in df.columns if col.startswith(column_prefix)]
+    
+    for index, row in df.iterrows():
+        time_values = row[time_columns]
+        mean = time_values.mean()
+        # 计算每个值与该行其他值的均值的差异
+        deviation = time_values.sub(time_values.mean())
+        abs_deviation = np.abs(deviation)
+        # 标记那些与均值差异过大的值为异常值
+        outliers = abs_deviation > (abs_deviation.mean() + threshold * abs_deviation.std())
+        df.loc[index, time_columns] = time_values.mask(outliers, np.nan)
+
+    return df
+
+# 重新计算speedup
+def calculate_speedup(df):
+    # 计算每行taichi aot time与brainpy time的均值
+    taichi_aot_time_columns = [col for col in df.columns if col.startswith('taichi_time')]
+    brainpy_time_columns = [col for col in df.columns if col.startswith('brainpylib_time')]
+    df['taichi aot time mean'] = df[taichi_aot_time_columns].mean(axis=1)
+    df['brainpy time mean'] = df[brainpy_time_columns].mean(axis=1)
+    # 计算speedup
+    df['speedup'] = np.where(df['brainpy time mean'] < df['taichi aot time mean'], 1 - (df['taichi aot time mean'] / df['brainpy time mean']), (df['brainpy time mean'] / df['taichi aot time mean']) - 1)
+    return df
+
+# Load the combined dataset
+PATH = os.path.dirname(os.path.abspath(__file__))
+combined_df = pd.read_csv(os.path.join(PATH, 'benchmark_MultipleArea_gpu.csv'))
+# combined_df.drop(columns=['backend'], inplace=True)
+combined_df = remove_row_outliers(combined_df, "taichi aot time")
+combined_df = remove_row_outliers(combined_df, "brainpy time")
+combined_df = calculate_speedup(combined_df)
+# 只选取comm_type为EventJitFPHomoLinear
+combined_df = combined_df[combined_df['syn_func_type'] == 'event_mv_prob_homo']
+combined_df = combined_df[combined_df['conn_num'] == 80]
+
+# print(combined_df)
+
+plt.figure(figsize=(10, 6))  # 调整图形大小
+sns.lineplot(x=combined_df['neuron_num'], y=combined_df['speedup'], marker='o', linestyle='-', color='darkorange', linewidth=2.5)
+plt.xlabel('神经元个数', fontsize=16, fontproperties=font)
+plt.ylabel('加速比', fontsize=16, fontproperties=font)
+# plt.title('[CPU] Multiple Area network speedup over origin brainpy op', fontsize=18)
+plt.grid(True)  # 显示网格
+plt.savefig(os.path.join(PATH, 'benchmark_MultipleArea_linechart_gpu.png'))
+# plt.show()
+
+
diff --git a/benchmarks/analysis/model/Multiple Area results/benchmark_MultipleArea_cpu.csv b/benchmarks/analysis/model/Multiple Area results/benchmark_MultipleArea_cpu.csv
new file mode 100644
index 0000000..53690ca
--- /dev/null
+++ b/benchmarks/analysis/model/Multiple Area results/benchmark_MultipleArea_cpu.csv	
@@ -0,0 +1,17 @@
+neuron_num,conn_num,syn_func_type,device,brainpylib_time1,brainpylib_time2,brainpylib_time3,brainpylib_time4,brainpylib_time5,brainpylib_time6,brainpylib_time7,brainpylib_time8,brainpylib_time9,brainpylib_time10,taichi_time1,taichi_time2,taichi_time3,taichi_time4,taichi_time5,taichi_time6,taichi_time7,taichi_time8,taichi_time9,taichi_time10
+400,20,event_mv_prob_homo,cpu,5320.09244,5298.760653,5261.881351,5386.330843,5268.09144,5284.725428,5280.577183,5476.103306,5266.391516,5270.550728,2923.835993,2846.207619,2833.133221,3060.726166,2854.762554,2864.91251,2871.534348,2867.85841,2878.942966,2867.083073
+400,40,event_mv_prob_homo,cpu,6102.053165,6370.962858,6146.04187,6375.769615,6369.595766,6128.163099,6398.961544,6078.85766,6456.188679,6438.052177,2982.048273,2926.072598,3039.696693,3038.121223,2986.246109,2774.986506,2956.939936,2946.209908,2777.033567,3025.351763
+400,80,event_mv_prob_homo,cpu,7849.857092,8345.089674,7837.632179,7868.107319,8372.108221,7772.301912,8387.889624,7857.409477,7861.587286,8466.136932,2789.082527,3007.338762,3025.847435,2755.603552,3089.376688,2802.808523,3080.138445,2741.533041,3113.970757,2798.70224
+400,100,event_mv_prob_homo,cpu,9450.073004,8786.75127,8832.87096,9517.216682,8861.433029,8788.664579,9512.123585,8830.234051,8887.856722,8856.782198,2778.038025,3101.743937,2761.056185,3192.33036,2818.915129,3154.206991,2778.687,3172.785044,2768.222332,3200.985193
+2000,20,event_mv_prob_homo,cpu,10180.52649,9460.271597,9426.660538,9381.123304,10437.62827,9261.743069,9293.121099,9302.006483,10304.15869,9310.164928,2857.232809,3403.56636,2841.917753,3339.203358,2846.178532,2913.407087,3346.580267,2874.168158,2857.472181,3466.297388
+2000,40,event_mv_prob_homo,cpu,14828.66096,13767.66467,13825.66428,13869.93694,13871.20676,14881.60849,13853.55854,13882.16758,13815.41228,13891.79778,2893.532276,3368.492126,2833.408833,3428.082228,2884.333849,2838.856459,2846.339941,3569.788694,2856.797218,2903.918505
+2000,80,event_mv_prob_homo,cpu,22782.03273,22870.02683,22855.3772,22831.30646,22878.12138,24143.55016,23000.71096,22841.89796,23022.74275,22942.11316,2842.271328,2850.68655,3481.729269,2859.132528,2861.854315,2862.40077,3544.389963,2906.280279,2991.344213,3618.81423
+2000,100,event_mv_prob_homo,cpu,27274.73712,27329.51665,28774.5502,27394.20104,27679.7843,27488.87086,27374.96853,27419.5652,28891.34049,27616.91475,2850.430489,2858.147621,3582.837343,2874.961138,2943.628073,2855.905771,3618.551016,2854.799271,2931.392193,3026.417732
+20000,20,event_mv_prob_homo,cpu,54998.60835,56203.51458,55155.55882,55241.87016,55148.87309,55249.90106,55297.20402,55358.19411,56875.53787,55398.3171,3206.662655,3156.676531,3977.317095,3276.796579,3167.846918,3168.477297,3190.993071,4161.873579,3402.873278,3319.668531
+20000,40,event_mv_prob_homo,cpu,99636.72018,99561.51915,101968.6644,100025.4569,100122.5393,100433.4424,100338.6056,100598.804,100940.4099,100980.3019,4043.170691,3266.072989,3210.56509,3254.617691,3193.814993,4062.630415,3292.419195,3337.968588,3416.754484,4365.555286
+20000,80,event_mv_prob_homo,cpu,189750.3152,190223.4373,190311.9094,190676.4436,190957.83,193480.4265,191729.6481,192255.7721,192013.9606,191849.9422,3193.478584,3187.992334,3230.459213,4146.084785,3189.015627,3225.276947,3227.953196,3420.581102,4521.155119,3605.683088
+20000,100,event_mv_prob_homo,cpu,234531.9102,234854.2635,238271.1678,236026.0019,235688.1781,235852.833,236579.6351,237201.694,237097.3186,237706.5146,3215.920687,3162.595272,4283.617735,3210.680008,3237.701178,3173.654079,3358.522892,3520.175219,4679.183006,3713.667631
+200000,20,event_mv_prob_homo,cpu,512275.357,511785.7099,512971.2567,511707.7079,513940.8758,514585.0391,516247.6735,516882.3886,516362.4446,515996.7556,5671.805382,5705.989599,6782.857895,5629.230022,5595.428705,5642.111301,5762.625456,5839.789629,7257.294178,6427.206755
+200000,40,event_mv_prob_homo,cpu,962637.6698,960847.6758,964300.3139,965336.9873,966105.9308,967388.0758,970536.706,974415.8425,972677.1748,972981.59,5573.898077,5552.32811,5621.579409,6696.351767,5506.146431,5556.497574,5594.604254,5879.435778,6465.978146,7996.859074
+200000,80,event_mv_prob_homo,cpu,566795.4404,566608.9172,566843.9989,566787.6008,565969.1348,566704.1562,567101.2981,567714.1318,567699.8138,568025.1191,5499.38941,5441.596746,5528.663635,5530.964136,6762.066841,5534.946442,5668.459654,6205.40452,7181.733608,8140.119791
+200000,100,event_mv_prob_homo,cpu,702580.5631,702753.9413,702931.8953,703220.8757,703795.4051,703186.0437,703508.1973,703194.0668,705449.4426,705461.4458,6969.969273,5629.896402,5667.449713,5685.665607,5793.05625,5707.055569,5894.05632,8054.272175,7590.444803,8690.71126
diff --git a/benchmarks/analysis/model/Multiple Area results/benchmark_MultipleArea_gpu.csv b/benchmarks/analysis/model/Multiple Area results/benchmark_MultipleArea_gpu.csv
new file mode 100644
index 0000000..616ead5
--- /dev/null
+++ b/benchmarks/analysis/model/Multiple Area results/benchmark_MultipleArea_gpu.csv	
@@ -0,0 +1,17 @@
+neuron_num,conn_num,syn_func_type,device,brainpylib_time1,brainpylib_time2,brainpylib_time3,brainpylib_time4,brainpylib_time5,brainpylib_time6,brainpylib_time7,brainpylib_time8,brainpylib_time9,brainpylib_time10,taichi_time1,taichi_time2,taichi_time3,taichi_time4,taichi_time5,taichi_time6,taichi_time7,taichi_time8,taichi_time9,taichi_time10
+400,20,event_mv_prob_homo,gpu,5225.788593,5248.739958,5281.020164,5356.081724,5194.756985,5130.764723,5206.002951,5220.570803,5368.921995,5245.995998,2988.225937,2803.512096,2639.175892,2841.075897,2695.433378,2743.739128,2711.382866,2783.400297,2726.024151,2731.174469
+400,40,event_mv_prob_homo,gpu,5331.706762,5466.321707,5074.504137,5446.493864,5412.169695,5117.430449,5467.240572,5192.729473,5586.794853,5132.650375,2804.477453,2786.421299,2774.957418,2748.043776,2569.314003,2817.370415,2825.714111,2821.123838,2608.34074,2784.522057
+400,80,event_mv_prob_homo,gpu,5137.099981,5621.876717,5158.361435,5178.043365,5652.561426,5179.442883,5721.498013,5211.066246,5156.998396,5809.758425,2732.997656,2895.892859,2582.412481,2878.422737,2867.451668,2628.942966,2870.758057,2594.787359,2967.459202,2713.845968
+400,100,event_mv_prob_homo,gpu,5159.072161,5162.688971,5211.242199,5882.608652,5176.633835,5161.213398,5988.92045,5292.003393,5186.958075,6013.464212,2647.527933,2902.929306,2576.241255,2944.647789,2594.871521,2957.994938,2562.972546,3034.98292,2587.608814,3031.41427
+2000,20,event_mv_prob_homo,gpu,5035.104036,5068.686962,5123.366594,6004.686832,5157.875538,5057.668924,5107.382298,6024.97673,5286.473989,5159.739971,2570.845604,3060.300589,2560.367584,3071.783304,2672.683954,2602.151871,3090.597153,2595.441341,2628.655195,3105.814219
+2000,40,event_mv_prob_homo,gpu,6113.401651,5162.857771,5117.12575,5161.980867,6255.856991,5162.735224,5178.324699,5157.694101,5204.548359,6267.880917,3131.955385,2599.047184,2656.648159,3153.191566,2572.120667,2629.455328,3197.260141,2601.000309,2638.398409,3204.082251
+2000,80,event_mv_prob_homo,gpu,5206.852198,5184.469461,5237.735987,5217.684984,6455.245256,5249.902487,5236.986876,5198.282719,5216.538429,5219.142914,2690.881491,2588.576555,3221.496582,2689.310551,2608.34527,3233.947515,2614.217758,2645.102262,2557.004929,3284.113169
+2000,100,event_mv_prob_homo,gpu,5233.712673,6662.431002,5264.905453,5260.61511,5245.330095,5339.635134,5477.787971,6715.729237,5279.00362,5299.650431,2684.35955,3377.104044,2654.477596,2665.858507,2580.581188,3405.245304,2627.017021,2608.865023,2647.441387,3405.772924
+20000,20,event_mv_prob_homo,gpu,5109.594822,5124.227285,5071.169138,5075.152636,5109.781742,5155.590057,6782.439232,5171.597481,5121.687889,5080.947638,2585.692167,2599.056005,3393.801451,2611.367702,2605.940819,2663.303137,3426.917076,2603.841066,2599.776983,2646.802902
+20000,40,event_mv_prob_homo,gpu,6870.853901,5196.27285,5179.847956,5255.484581,5332.738876,5189.063787,5119.814396,5145.489454,6968.67013,5133.377075,3448.118925,2593.331575,2619.646072,2670.207739,3458.892584,2622.168541,2613.295078,2588.120222,2625.531435,3474.826574
+20000,80,event_mv_prob_homo,gpu,5250.054121,5274.657965,5277.2789,7222.079515,5288.225889,5269.620657,5280.060053,5279.959917,5316.82539,5340.78598,2578.747272,2635.437727,3594.285965,2652.739286,2627.231836,2606.610537,2574.881792,3588.382006,2635.725975,2650.26021
+20000,100,event_mv_prob_homo,gpu,5312.38842,5321.16127,5274.114132,5484.419346,5321.036577,5329.850674,5316.152811,5310.187817,5285.223484,7474.493027,2608.267069,3635.898352,2602.170944,2650.74563,2560.703754,2597.735405,2602.103949,3646.585941,2609.36594,2601.499081
+200000,20,event_mv_prob_homo,gpu,5486.63044,5573.32468,5447.728634,5612.046242,5543.540001,5485.932112,5513.92293,7867.495775,5499.745607,5647.913218,2700.843811,3859.992981,2884.974957,2869.605064,2652.793169,2695.958376,2720.035553,3788.316488,2679.11911,2667.832136
+200000,40,event_mv_prob_homo,gpu,5704.92816,5808.07066,5704.146624,5765.314341,5746.998787,5721.133709,5746.482372,8269.215107,5758.587122,5748.302221,2688.74836,2770.340204,4255.34749,3030.006409,2685.783148,2715.818644,2693.838596,2678.348303,3977.509499,2716.60924
+200000,80,event_mv_prob_homo,gpu,5920.151949,5959.203243,5986.8958,5976.567984,5987.99777,6002.91872,5982.886553,6031.452656,8754.291773,5987.105608,2642.485619,2874.575138,3382.770777,4650.416851,2721.915722,2686.686754,2732.921362,2650.930643,2671.117783,2674.759865
+200000,100,event_mv_prob_homo,gpu,6025.264025,6095.170975,6095.050812,6160.686731,6080.094576,6060.666323,6019.967794,6058.868647,6099.057674,6100.421667,2731.099367,2857.214689,3609.241962,3502.672672,2710.209608,4145.43128,2691.901684,2772.157431,2703.720808,2713.130474
diff --git a/benchmarks/analysis/model/Multiple Area results/benchmark_MultipleArea_spks_cpu.csv b/benchmarks/analysis/model/Multiple Area results/benchmark_MultipleArea_spks_cpu.csv
new file mode 100644
index 0000000..ff4101b
--- /dev/null
+++ b/benchmarks/analysis/model/Multiple Area results/benchmark_MultipleArea_spks_cpu.csv	
@@ -0,0 +1,10 @@
+neuron_num,conn_num,syn_func_type,device,brainpylib_e_spk,brainpylib_i_spk,taichi_e_spk,taichi_i_spk
+200,80,event_mv_prob_homo,cpu,146.66667,193.33334,142.22223,233.33334
+400,80,event_mv_prob_homo,cpu,116.666664,193.33334,124.44444,190.0
+800,80,event_mv_prob_homo,cpu,115.55556,198.33334,125.0,203.33334
+1600,80,event_mv_prob_homo,cpu,124.44444,211.66666,118.05556,221.66666
+3200,80,event_mv_prob_homo,cpu,129.30556,188.75,130.69444,203.33334
+6400,80,event_mv_prob_homo,cpu,132.15277,194.79166,127.708336,193.54166
+12800,80,event_mv_prob_homo,cpu,126.31944,202.8125,127.8125,198.125
+25600,80,event_mv_prob_homo,cpu,126.16319,199.7396,129.1493,199.6875
+51200,80,event_mv_prob_homo,cpu,126.28473,201.40625,126.49306,201.17188
diff --git a/benchmarks/analysis/model/Multiple Area results/benchmark_MultipleArea_spks_gpu.csv b/benchmarks/analysis/model/Multiple Area results/benchmark_MultipleArea_spks_gpu.csv
new file mode 100644
index 0000000..b08693a
--- /dev/null
+++ b/benchmarks/analysis/model/Multiple Area results/benchmark_MultipleArea_spks_gpu.csv	
@@ -0,0 +1,10 @@
+neuron_num,conn_num,syn_func_type,device,brainpylib_e_spk,brainpylib_i_spk,taichi_e_spk,taichi_i_spk
+200,80,event_mv_prob_homo,gpu,485.3333,916.0,462.66666,928.0
+400,80,event_mv_prob_homo,gpu,449.66666,967.0,463.66666,942.0
+800,80,event_mv_prob_homo,gpu,457.99997,978.5,457.8333,948.0
+1600,80,event_mv_prob_homo,gpu,465.8333,954.0,459.41666,960.5
+3200,80,event_mv_prob_homo,gpu,465.66666,953.25,463.12497,940.25
+6400,80,event_mv_prob_homo,gpu,464.12497,937.75,468.18747,950.4375
+12800,80,event_mv_prob_homo,gpu,465.56247,952.3125,463.93747,941.1875
+25600,80,event_mv_prob_homo,gpu,462.49997,954.2656,462.33853,948.71875
+51200,80,event_mv_prob_homo,gpu,464.36978,945.97656,466.58072,949.2969
diff --git a/benchmarks/analysis/model/Multiple Area results/benchmark_MultipleArea_spks_gpu.xlsx b/benchmarks/analysis/model/Multiple Area results/benchmark_MultipleArea_spks_gpu.xlsx
new file mode 100644
index 0000000..0640f03
--- /dev/null
+++ b/benchmarks/analysis/model/Multiple Area results/benchmark_MultipleArea_spks_gpu.xlsx	
@@ -0,0 +1,17 @@
+neuron_num,conn_num,syn_func_type,device,brainpylib_time1,brainpylib_time2,brainpylib_time3,brainpylib_time4,brainpylib_time5,brainpylib_time6,brainpylib_time7,brainpylib_time8,brainpylib_time9,brainpylib_time10,taichi_time1,taichi_time2,taichi_time3,taichi_time4,taichi_time5,taichi_time6,taichi_time7,taichi_time8,taichi_time9,taichi_time10
+400,20,event_mv_prob_homo,gpu,5225.788593292236,5248.739957809448,5281.020164489746,5356.08172416687,5194.756984710693,5130.764722824097,5206.002950668335,5220.570802688599,5368.921995162964,5245.995998382568,2840.640068054199,2924.7496128082275,2911.5209579467773,2931.5075874328613,2760.2884769439697,2979.6042442321777,3006.3092708587646,2765.7999992370605,3221.2281227111816,2941.9023990631104
+400,40,event_mv_prob_homo,gpu,5331.706762313843,5466.321706771851,5074.504137039185,5446.493864059448,5412.169694900513,5117.4304485321045,5467.240571975708,5192.729473114014,5586.794853210449,5132.650375366211,2768.5046195983887,3123.474359512329,2746.1793422698975,3119.1043853759766,2719.6083068847656,3183.4800243377686,2737.81418800354,3148.721218109131,2738.910436630249,2746.4077472686768
+400,80,event_mv_prob_homo,gpu,5137.099981307983,5621.8767166137695,5158.361434936523,5178.043365478516,5652.56142616272,5179.442882537842,5721.498012542725,5211.066246032715,5156.9983959198,5809.758424758911,2773.9365100860596,3325.9406089782715,2794.856309890747,2764.8487091064453,3358.729362487793,2701.3771533966064,2720.9537029266357,3357.842206954956,2752.7873516082764,2718.535900115967
+400,100,event_mv_prob_homo,gpu,5159.072160720825,5162.688970565796,5211.242198944092,5882.608652114868,5176.633834838867,5161.213397979736,5988.920450210571,5292.003393173218,5186.958074569702,6013.4642124176025,2742.539405822754,2760.516405105591,3581.23779296875,2732.9800128936768,2785.722494125366,2704.6916484832764,3546.4649200439453,2735.804557800293,2698.8067626953125,2732.2490215301514
+2000,20,event_mv_prob_homo,gpu,5035.104036331177,5068.686962127686,5123.366594314575,6004.6868324279785,5157.875537872314,5057.668924331665,5107.382297515869,6024.97673034668,5286.473989486694,5159.739971160889,2815.4988288879395,3741.7731285095215,2783.991575241089,2756.480932235718,2773.073196411133,2697.2718238830566,3732.052803039551,2678.271770477295,2738.4042739868164,2780.4336547851562
+2000,40,event_mv_prob_homo,gpu,6113.401651382446,5162.8577709198,5117.125749588013,5161.980867385864,6255.856990814209,5162.735223770142,5178.3246994018555,5157.694101333618,5204.548358917236,6267.880916595459,2827.4190425872803,2775.7866382598877,2774.376630783081,2763.470411300659,3932.3112964630127,2752.937078475952,2779.6432971954346,2722.6510047912598,2721.2307453155518,2724.8430252075195
+2000,80,event_mv_prob_homo,gpu,5206.852197647095,5184.46946144104,5237.735986709595,5217.684984207153,6455.24525642395,5249.9024868011475,5236.986875534058,5198.282718658447,5216.538429260254,5219.142913818359,2770.3490257263184,2716.423988342285,2779.653310775757,2766.946315765381,2743.5989379882812,4085.0069522857666,2769.04296875,2727.140426635742,2819.460868835449,2734.645366668701
+2000,100,event_mv_prob_homo,gpu,5233.712673187256,6662.431001663208,5264.9054527282715,5260.615110397339,5245.330095291138,5339.635133743286,5477.787971496582,6715.729236602783,5279.003620147705,5299.650430679321,2771.986246109009,2737.0829582214355,2777.7740955352783,4238.395929336548,2819.639205932617,2792.672634124756,2710.01935005188,2723.083734512329,2759.138584136963,2723.6952781677246
+20000,20,event_mv_prob_homo,gpu,5109.594821929932,5124.227285385132,5071.169137954712,5075.152635574341,5109.781742095947,5155.590057373047,6782.439231872559,5171.597480773926,5121.687889099121,5080.947637557983,2768.4829235076904,2804.6579360961914,2732.4817180633545,4489.212512969971,2699.646472930908,2757.366418838501,2737.015962600708,2736.555337905884,2746.8795776367188,2750.6155967712402
+20000,40,event_mv_prob_homo,gpu,6870.853900909424,5196.272850036621,5179.847955703735,5255.484580993652,5332.738876342773,5189.063787460327,5119.814395904541,5145.489454269409,6968.670129776001,5133.3770751953125,2730.6206226348877,2758.795738220215,2772.143602371216,2765.8252716064453,2767.0681476593018,4639.579772949219,2739.851236343384,2781.384229660034,2758.7318420410156,2735.1627349853516
+20000,80,event_mv_prob_homo,gpu,5250.054121017456,5274.657964706421,5277.278900146484,7222.079515457153,5288.225889205933,5269.620656967163,5280.060052871704,5279.959917068481,5316.825389862061,5340.785980224609,2760.009765625,4774.209260940552,2763.4291648864746,2783.85329246521,2728.2872200012207,2761.165142059326,2748.3818531036377,2734.5385551452637,2680.896520614624,2720.0629711151123
+20000,100,event_mv_prob_homo,gpu,5312.3884201049805,5321.161270141602,5274.11413192749,5484.419345855713,5321.036577224731,5329.850673675537,5316.152811050415,5310.187816619873,5285.223484039307,7474.493026733398,2811.8736743927,2780.400037765503,2780.6036472320557,2727.7398109436035,2694.3678855895996,2701.8353939056396,2712.817907333374,2726.9599437713623,4945.3184604644775,2755.4831504821777
+200000,20,event_mv_prob_homo,gpu,5486.630439758301,5573.324680328369,5447.728633880615,5612.046241760254,5543.540000915527,5485.932111740112,5513.922929763794,7867.495775222778,5499.745607376099,5647.913217544556,2887.5577449798584,2959.2208862304688,3005.4397583007812,2964.8044109344482,2881.890296936035,2929.9890995025635,2927.363395690918,5339.345693588257,2937.0241165161133,2925.084114074707
+200000,40,event_mv_prob_homo,gpu,5704.928159713745,5808.070659637451,5704.14662361145,5765.314340591431,5746.9987869262695,5721.133708953857,5746.482372283936,8269.215106964111,5758.587121963501,5748.302221298218,2930.31907081604,2901.646137237549,3073.148727416992,3034.167766571045,2860.145092010498,2864.661693572998,2880.96284866333,2900.2866744995117,5550.427675247192,2891.0281658172607
+200000,80,event_mv_prob_homo,gpu,5920.151948928833,5959.203243255615,5986.895799636841,5976.567983627319,5987.997770309448,6002.918720245361,5982.886552810669,6031.452655792236,8754.291772842407,5987.10560798645,2880.10311126709,3027.24552154541,3220.5355167388916,3222.4478721618652,2912.2531414031982,2879.6353340148926,2884.650707244873,2915.6272411346436,2882.5862407684326,2894.4296836853027
+200000,100,event_mv_prob_homo,gpu,6025.264024734497,6095.170974731445,6095.050811767578,6160.686731338501,6080.094575881958,6060.66632270813,6019.967794418335,6058.868646621704,6099.057674407959,6100.421667098999,5854.90608215332,3041.9886112213135,3316.0011768341064,3293.5538291931152,2917.0920848846436,2891.8728828430176,2902.7891159057617,2908.7133407592773,2897.25661277771,2901.3142585754395
diff --git a/benchmarks/requirements.txt b/benchmarks/requirements.txt
new file mode 100644
index 0000000..07ab7d5
--- /dev/null
+++ b/benchmarks/requirements.txt
@@ -0,0 +1,8 @@
+jax[cpu]==0.4.14
+brainpy==2.4.6.post5
+taichi==1.7.0
+brainpylib==0.2.6
+pandas
+matplotlib
+seaborn
+numpy==1.26.4
\ No newline at end of file
diff --git a/benchmarks/requirements_cuda.txt b/benchmarks/requirements_cuda.txt
new file mode 100644
index 0000000..a4380fe
--- /dev/null
+++ b/benchmarks/requirements_cuda.txt
@@ -0,0 +1,9 @@
+-f https://storage.googleapis.com/jax-releases/jax_cuda_releases.html
+jax[cuda12_pip]==0.4.14 
+brainpy==2.4.6.post5
+taichi==1.7.0
+brainpylib-cu12x==0.2.6
+pandas
+matplotlib
+seaborn
+numpy==1.26.4
\ No newline at end of file
diff --git a/benchmarks/src/basic/csrmv_taichi_VS_csrmv.py b/benchmarks/src/basic/csrmv_taichi_VS_csrmv.py
new file mode 100644
index 0000000..c502ecb
--- /dev/null
+++ b/benchmarks/src/basic/csrmv_taichi_VS_csrmv.py
@@ -0,0 +1,252 @@
+# from jax_taichi import jax_taichi_call
+
+import time
+from functools import partial
+import os
+
+import brainpy as bp
+import brainpy.math as bm
+import jax
+import jax.numpy as jnp
+import numpy as np
+import pandas as pd
+import taichi as ti
+
+
+bm.set_platform('gpu')
+
+
+s = [1000, 5000, 10000, 15000, 20000, 25000, 30000]
+p = [0.1, 0.2, 0.3, 0.4, 0.5]
+
+shape = [
+        1000, 
+        2500, 
+        5000, 
+        10000, 
+        25000, 
+        37500, 
+        50000
+]
+
+values_type = [
+               'homo', 
+               'heter'
+              ]
+events_type = ['float']
+transpose = [
+             True, 
+             False
+             ]
+method = 'cusparse'
+
+ITERATION = 100
+if bm.get_platform() == 'cpu':
+  ITERATION = 10
+
+print(bm.get_platform())
+
+@partial(jax.jit, static_argnums=(4, 5))
+def csrmv_taichi(weight, indices, indptr, vector, shape, transpose):
+  r = 0
+  for i in range(ITERATION):
+    r += bm.sparse.csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose)[0]
+  return r
+  
+@partial(jax.jit, static_argnums=(4, 5))
+def csrmv(weight, indices, indptr, vector, shape, transpose):
+  r = 0
+  for i in range(ITERATION):
+    r += bm.sparse.csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose)
+  return r
+
+def test_sparse_csrmv(shape, values_type, events_type, transpose):
+  rng = bm.random.RandomState(seed=1234)
+  indices, indptr = bp.conn.FixedProb(0.05, seed=1234, allow_multi_conn=True)(*shape).require('pre2post')
+  vector = rng.random(shape[0] if transpose else shape[1]) < 0.1
+  weight = 1.
+  
+
+  if events_type == 'float':
+    vector = vector.astype(bm.float32)
+  if values_type == 'heter':
+    heter_data = bm.ones(indices.shape) * weight
+    weight = heter_data
+
+  result = jax.block_until_ready(csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  result = jax.block_until_ready(csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  result = jax.block_until_ready(csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  result = jax.block_until_ready(csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  result = jax.block_until_ready(csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+
+  time0 = time.time()
+  result = jax.block_until_ready(csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time1 = time.time()
+
+  time2 = time.time()
+  result = jax.block_until_ready(csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time3 = time.time()
+
+  time4 = time.time()
+  result = jax.block_until_ready(csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time5 = time.time()
+
+  time6 = time.time()
+  result = jax.block_until_ready(csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time7 = time.time()
+
+  time8 = time.time()
+  result = jax.block_until_ready(csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time9 = time.time()
+  
+  time10 = time.time()
+  result = jax.block_until_ready(csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time11 = time.time()
+  
+  time12 = time.time()
+  result = jax.block_until_ready(csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time13 = time.time()
+  
+  time14 = time.time()
+  result = jax.block_until_ready(csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time15 = time.time()
+  
+  time16 = time.time()
+  result = jax.block_until_ready(csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time17 = time.time()
+  
+  time18 = time.time()
+  result = jax.block_until_ready(csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time19 = time.time()
+  
+
+  result = jax.block_until_ready(csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  result = jax.block_until_ready(csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  result = jax.block_until_ready(csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  result = jax.block_until_ready(csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  result = jax.block_until_ready(csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+
+  time20 = time.time()
+  result = jax.block_until_ready(csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time21 = time.time()
+
+  time22 = time.time()
+  result = jax.block_until_ready(csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time23 = time.time()
+
+  time24 = time.time()
+  result = jax.block_until_ready(csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time25 = time.time()
+
+  time26 = time.time()
+  result = jax.block_until_ready(csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time27 = time.time()
+
+  time28 = time.time()
+  result = jax.block_until_ready(csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time29 = time.time()
+  
+  time30 = time.time()
+  result = jax.block_until_ready(csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time31 = time.time()
+  
+  time32 = time.time()
+  result = jax.block_until_ready(csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time33 = time.time()
+  
+  time34 = time.time()
+  result = jax.block_until_ready(csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time35 = time.time()
+  
+  time36 = time.time()
+  result = jax.block_until_ready(csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time37 = time.time()
+  
+  time38 = time.time()
+  result = jax.block_until_ready(csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time39 = time.time()
+
+  taichi_aot_time1 = (time1 - time0) * 1000
+  taichi_aot_time2 = (time3 - time2) * 1000
+  taichi_aot_time3 = (time5 - time4) * 1000
+  taichi_aot_time4 = (time7 - time6) * 1000
+  taichi_aot_time5 = (time9 - time8) * 1000
+  taichi_aot_time6 = (time11 - time10) * 1000
+  taichi_aot_time7 = (time13 - time12) * 1000
+  taichi_aot_time8 = (time15 - time14) * 1000
+  taichi_aot_time9 = (time17 - time16) * 1000
+  taichi_aot_time10 = (time19 - time18) * 1000
+  brainpy_time1 = (time21 - time20) * 1000
+  brainpy_time2 = (time23 - time22) * 1000
+  brainpy_time3 = (time25 - time24) * 1000
+  brainpy_time4 = (time27 - time26) * 1000
+  brainpy_time5 = (time29 - time28) * 1000
+  brainpy_time6 = (time31 - time30) * 1000
+  brainpy_time7 = (time33 - time32) * 1000
+  brainpy_time8 = (time35 - time34) * 1000
+  brainpy_time9 = (time37 - time36) * 1000
+  brainpy_time10 = (time39 - time38) * 1000
+  print('shape: ', shape, 'values_type: ', values_type, 'events_type: ', events_type, 'transpose: ', transpose)
+  print('taichi_aot_1: ', taichi_aot_time1, 'ms')
+  print('taichi_aot_3: ', taichi_aot_time3, 'ms')
+  print('taichi_aot_5: ', taichi_aot_time5, 'ms')
+  print('taichi_aot_7: ', taichi_aot_time7, 'ms')
+  print('taichi_aot_9: ', taichi_aot_time9, 'ms')
+  print('brainpylib_1: ', brainpy_time1, 'ms')
+  print('brainpylib_3: ', brainpy_time3, 'ms')
+  print('brainpylib_5: ', brainpy_time5, 'ms')
+  print('brainpylib_7: ', brainpy_time7, 'ms')
+  print('brainpylib_9: ', brainpy_time9, 'ms')
+
+
+  return taichi_aot_time1, taichi_aot_time2, taichi_aot_time3, taichi_aot_time4, taichi_aot_time5,\
+      taichi_aot_time6, taichi_aot_time7, taichi_aot_time8, taichi_aot_time9, taichi_aot_time10,\
+      brainpy_time1, brainpy_time2, brainpy_time3, brainpy_time4, brainpy_time5, \
+      brainpy_time6, brainpy_time7, brainpy_time8, brainpy_time9, brainpy_time10
+
+
+PATH = os.path.dirname(os.path.abspath(__file__))
+
+# init dataframe
+df = pd.DataFrame(columns=['s', 'p', 'shape[0]', 'shape[1]', 'backend', 'values type', 'events type', 'transpose',
+                           'taichi aot time1(ms)', 'taichi aot time2(ms)', 'taichi aot time3(ms)', 'taichi aot time4(ms)', 'taichi aot time5(ms)',
+                           'taichi aot time6(ms)', 'taichi aot time7(ms)', 'taichi aot time8(ms)', 'taichi aot time9(ms)', 'taichi aot time10(ms)',
+                           'brainpy time1(ms)', 'brainpy time2(ms)', 'brainpy time3(ms)', 'brainpy time4(ms)', 'brainpy time5(ms)',
+                           'brainpy time6(ms)', 'brainpy time7(ms)', 'brainpy time8(ms)', 'brainpy time9(ms)', 'brainpy time10(ms)'])
+
+### RECTANGULAR MATRIX
+if (bm.get_platform() == 'cpu'):
+  for shape1 in shape:
+    for shape2 in shape:
+      for _values_type in values_type:
+          for _events_type in events_type:
+            for _transpose in transpose:
+              taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,\
+                taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,\
+                  brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, \
+                  brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10 = test_sparse_csrmv((shape1, shape2), _values_type, _events_type, _transpose)
+              # append to dataframe
+              df.loc[df.shape[0]] = [(shape1, shape2), 0.5 , shape1, shape2, 'cpu', _values_type, _events_type, _transpose,
+                                    taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,
+                                    taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,
+                                    brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, 
+                                    brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10]
+  df.to_csv(f'{PATH}/csrmv_cpu.csv', index=False)
+
+if (bm.get_platform() == 'gpu'):
+  for shape1 in shape:
+    for shape2 in shape:
+      for _values_type in values_type:
+          for _events_type in events_type:
+            for _transpose in transpose:
+              taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,\
+                taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,\
+                  brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, \
+                  brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10 = test_sparse_csrmv((shape1, shape2), _values_type, _events_type, _transpose)
+              # append to dataframe
+              df.loc[df.shape[0]] = [(shape1, shape2), 0.5 , shape1, shape2, 'gpu', _values_type, _events_type, _transpose,
+                                    taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,
+                                    taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,
+                                    brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, 
+                                    brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10]
+  df.to_csv(f'{PATH}/csrmv_gpu.csv', index=False)
diff --git a/benchmarks/src/basic/csrmv_taichi_VS_csrmv_grad.py b/benchmarks/src/basic/csrmv_taichi_VS_csrmv_grad.py
new file mode 100644
index 0000000..d902c93
--- /dev/null
+++ b/benchmarks/src/basic/csrmv_taichi_VS_csrmv_grad.py
@@ -0,0 +1,273 @@
+# from jax_taichi import jax_taichi_call
+
+import time
+from functools import partial
+import os
+
+import brainpy as bp
+import brainpy.math as bm
+import jax
+import jax.numpy as jnp
+import numpy as np
+import pandas as pd
+import taichi as ti
+
+bm.set_platform('cpu')
+
+s = [1000, 
+     5000, 
+     10000, 
+     15000, 
+     20000, 
+     25000, 
+     30000]
+p = [0.1, 0.2, 0.3, 0.4, 0.5]
+
+shape = [
+        1000, 
+        2500, 
+        5000, 
+        10000, 
+        25000, 
+        37500, 
+        50000
+]
+
+values_type = [
+               'homo', 
+               'heter'
+              ]
+events_type = ['float']
+transpose = [
+             True, 
+             False
+             ]
+method = 'cusparse'
+
+ITERATION = 100
+if bm.get_platform() == 'cpu':
+  ITERATION = 10
+
+print(bm.get_platform())
+
+def sum_op(op):
+  def func(*args, **kwargs):
+    r = op(*args, **kwargs)
+    return r.sum()
+
+  return func
+
+
+def sum_op2(op):
+  def func(*args, **kwargs):
+    r = op(*args, **kwargs)[0]
+    return r.sum()
+
+  return func
+
+@partial(jax.jit, static_argnums=(4, 5))
+def csrmv_taichi_grad(weight, indices, indptr, vector, shape, transpose):
+  r = 0
+  for i in range(ITERATION):
+    r += jax.grad(sum_op2(bm.sparse.csrmv_taichi), argnums=3)(
+      weight, indices, indptr, vector.astype(float), shape=shape, transpose=transpose)
+  return r
+
+@partial(jax.jit, static_argnums=(4, 5))
+def csrmv_grad(weight, indices, indptr, vector, shape, transpose):
+  r = 0
+  for i in range(ITERATION):
+    r += jax.grad(sum_op(bm.sparse.csrmv), argnums=3)(
+    weight, indices, indptr, vector.astype(float), shape=shape, transpose=transpose)
+  return r
+
+def test_sparse_csrmv(shape, values_type, events_type, transpose):
+  rng = bm.random.RandomState(seed=1234)
+  indices, indptr = bp.conn.FixedProb(0.05, seed=1234, allow_multi_conn=True)(*shape).require('pre2post')
+  vector = rng.random(shape[0] if transpose else shape[1]) < 0.1
+  weight = 1.
+  
+
+  if events_type == 'float':
+    vector = vector.astype(bm.float32)
+  if values_type == 'heter':
+    heter_data = bm.ones(indices.shape) * weight
+    weight = heter_data
+
+  result = jax.block_until_ready(csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  result = jax.block_until_ready(csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  result = jax.block_until_ready(csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  result = jax.block_until_ready(csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  result = jax.block_until_ready(csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+
+  time0 = time.time()
+  result = jax.block_until_ready(csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time1 = time.time()
+
+  time2 = time.time()
+  result = jax.block_until_ready(csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time3 = time.time()
+
+  time4 = time.time()
+  result = jax.block_until_ready(csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time5 = time.time()
+
+  time6 = time.time()
+  result = jax.block_until_ready(csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time7 = time.time()
+
+  time8 = time.time()
+  result = jax.block_until_ready(csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time9 = time.time()
+  
+  time10 = time.time()
+  result = jax.block_until_ready(csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time11 = time.time()
+  
+  time12 = time.time()
+  result = jax.block_until_ready(csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time13 = time.time()
+  
+  time14 = time.time()
+  result = jax.block_until_ready(csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time15 = time.time()
+  
+  time16 = time.time()
+  result = jax.block_until_ready(csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time17 = time.time()
+  
+  time18 = time.time()
+  result = jax.block_until_ready(csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time19 = time.time()
+  
+
+  result = jax.block_until_ready(csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  result = jax.block_until_ready(csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  result = jax.block_until_ready(csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  result = jax.block_until_ready(csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  result = jax.block_until_ready(csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+
+  time20 = time.time()
+  result = jax.block_until_ready(csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time21 = time.time()
+
+  time22 = time.time()
+  result = jax.block_until_ready(csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time23 = time.time()
+
+  time24 = time.time()
+  result = jax.block_until_ready(csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time25 = time.time()
+
+  time26 = time.time()
+  result = jax.block_until_ready(csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time27 = time.time()
+
+  time28 = time.time()
+  result = jax.block_until_ready(csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time29 = time.time()
+  
+  time30 = time.time()
+  result = jax.block_until_ready(csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time31 = time.time()
+  
+  time32 = time.time()
+  result = jax.block_until_ready(csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time33 = time.time()
+  
+  time34 = time.time()
+  result = jax.block_until_ready(csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time35 = time.time()
+  
+  time36 = time.time()
+  result = jax.block_until_ready(csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time37 = time.time()
+  
+  time38 = time.time()
+  result = jax.block_until_ready(csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time39 = time.time()
+
+  taichi_aot_time1 = (time1 - time0) * 1000
+  taichi_aot_time2 = (time3 - time2) * 1000
+  taichi_aot_time3 = (time5 - time4) * 1000
+  taichi_aot_time4 = (time7 - time6) * 1000
+  taichi_aot_time5 = (time9 - time8) * 1000
+  taichi_aot_time6 = (time11 - time10) * 1000
+  taichi_aot_time7 = (time13 - time12) * 1000
+  taichi_aot_time8 = (time15 - time14) * 1000
+  taichi_aot_time9 = (time17 - time16) * 1000
+  taichi_aot_time10 = (time19 - time18) * 1000
+  brainpy_time1 = (time21 - time20) * 1000
+  brainpy_time2 = (time23 - time22) * 1000
+  brainpy_time3 = (time25 - time24) * 1000
+  brainpy_time4 = (time27 - time26) * 1000
+  brainpy_time5 = (time29 - time28) * 1000
+  brainpy_time6 = (time31 - time30) * 1000
+  brainpy_time7 = (time33 - time32) * 1000
+  brainpy_time8 = (time35 - time34) * 1000
+  brainpy_time9 = (time37 - time36) * 1000
+  brainpy_time10 = (time39 - time38) * 1000
+  print('shape: ', shape, 'values_type: ', values_type, 'events_type: ', events_type, 'transpose: ', transpose)
+  print('taichi_aot_1: ', taichi_aot_time1, 'ms')
+  print('taichi_aot_3: ', taichi_aot_time3, 'ms')
+  print('taichi_aot_5: ', taichi_aot_time5, 'ms')
+  print('taichi_aot_7: ', taichi_aot_time7, 'ms')
+  print('taichi_aot_9: ', taichi_aot_time9, 'ms')
+  print('brainpylib_1: ', brainpy_time1, 'ms')
+  print('brainpylib_3: ', brainpy_time3, 'ms')
+  print('brainpylib_5: ', brainpy_time5, 'ms')
+  print('brainpylib_7: ', brainpy_time7, 'ms')
+  print('brainpylib_9: ', brainpy_time9, 'ms')
+
+
+  return taichi_aot_time1, taichi_aot_time2, taichi_aot_time3, taichi_aot_time4, taichi_aot_time5,\
+      taichi_aot_time6, taichi_aot_time7, taichi_aot_time8, taichi_aot_time9, taichi_aot_time10,\
+      brainpy_time1, brainpy_time2, brainpy_time3, brainpy_time4, brainpy_time5, \
+      brainpy_time6, brainpy_time7, brainpy_time8, brainpy_time9, brainpy_time10
+
+PATH = os.path.dirname(os.path.abspath(__file__))
+
+# init dataframe
+df = pd.DataFrame(columns=['s', 'p', 'shape[0]', 'shape[1]', 'backend', 'values type', 'events type', 'transpose',
+                           'taichi aot time1(ms)', 'taichi aot time2(ms)', 'taichi aot time3(ms)', 'taichi aot time4(ms)', 'taichi aot time5(ms)',
+                           'taichi aot time6(ms)', 'taichi aot time7(ms)', 'taichi aot time8(ms)', 'taichi aot time9(ms)', 'taichi aot time10(ms)',
+                           'brainpy time1(ms)', 'brainpy time2(ms)', 'brainpy time3(ms)', 'brainpy time4(ms)', 'brainpy time5(ms)',
+                           'brainpy time6(ms)', 'brainpy time7(ms)', 'brainpy time8(ms)', 'brainpy time9(ms)', 'brainpy time10(ms)'])
+
+
+### RECTANGULAR MATRIX
+if (bm.get_platform() == 'cpu'):
+  for shape1 in shape:
+    for shape2 in shape:
+      for _values_type in values_type:
+          for _events_type in events_type:
+            for _transpose in transpose:
+              taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,\
+                taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,\
+                  brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, \
+                  brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10 = test_sparse_csrmv((shape1, shape2), _values_type, _events_type, _transpose)
+              # append to dataframe
+              df.loc[df.shape[0]] = [(shape1, shape2), 0.5 , shape1, shape2, 'cpu', _values_type, _events_type, _transpose,
+                                    taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,
+                                    taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,
+                                    brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, 
+                                    brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10]
+  df.to_csv(f'{PATH}/csrmv_grad_cpu.csv', index=False)
+
+if (bm.get_platform() == 'gpu'):
+  for shape1 in shape:
+    for shape2 in shape:
+      for _values_type in values_type:
+          for _events_type in events_type:
+            for _transpose in transpose:
+              taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,\
+                taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,\
+                  brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, \
+                  brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10 = test_sparse_csrmv((shape1, shape2), _values_type, _events_type, _transpose)
+              # append to dataframe
+              df.loc[df.shape[0]] = [(shape1, shape2), 0.5 , shape1, shape2, 'gpu', _values_type, _events_type, _transpose,
+                                    taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,
+                                    taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,
+                                    brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, 
+                                    brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10]
+  df.to_csv(f'{PATH}/csrmv_grad_gpu.csv', index=False)
diff --git a/benchmarks/src/basic/event_csr_matmat_VS_csr_matmat.py b/benchmarks/src/basic/event_csr_matmat_VS_csr_matmat.py
new file mode 100644
index 0000000..872c69e
--- /dev/null
+++ b/benchmarks/src/basic/event_csr_matmat_VS_csr_matmat.py
@@ -0,0 +1,285 @@
+# from jax_taichi import jax_taichi_call
+
+import time
+from functools import partial
+import os
+
+import brainpy as bp
+import brainpy.math as bm
+import jax
+import jax.numpy as jnp
+import numpy as np
+import pandas as pd
+import taichi as ti
+
+bm.set_platform('cpu')
+
+size = [
+  (100, 100, 100),
+  (100, 1000, 100),
+  (1000, 1000, 100),
+  (1000, 1000, 1000),
+  (100, 10000, 100),
+  (10000, 100, 1000),
+  (1000, 100, 10000),
+  (10000, 10000, 1000),
+  (10000, 1000, 10000),
+  (10000, 10000, 10000),
+  (20000, 20000, 20000),
+]
+
+values_type = [
+  'heter',
+  'homo',
+]
+events_type = ['bool',
+               'float',
+               ]
+transpose = [
+  # True,
+  False
+]
+
+ITERATION = 100
+if bm.get_platform() == 'cpu':
+  ITERATION = 10
+
+print(bm.get_platform())
+
+
+@partial(jax.jit, static_argnums=(4, 5))
+def csrmm(weight, indices, indptr, matrix, shape, transpose):
+  r = 0
+  for i in range(ITERATION):
+    r += bm.sparse.csrmm(weight, indices, indptr, matrix, shape=shape, transpose=transpose)
+  return r
+
+
+@partial(jax.jit, static_argnums=(4, 5))
+def event_csrmm(weight, indices, indptr, matrix, shape, transpose):
+  r = 0
+  for i in range(ITERATION):
+    r += bm.event.csrmm(weight, indices, indptr, matrix, shape=shape, transpose=transpose)
+  return r
+
+
+def test_sparse_csrmm(shape, values_type, events_type, transpose):
+  rng = bm.random.RandomState(seed=1234)
+  matrix1_shape = (shape[1], shape[0]) if transpose else (shape[0], shape[1])
+  matrix2_shape = (shape[1], shape[2])
+  indices, indptr = bp.conn.FixedProb(0.05, seed=1234, allow_multi_conn=True)(*matrix1_shape).require('pre2post')
+  matrix = rng.random(matrix2_shape)
+  matrix = bm.as_jax(matrix)
+  weight = 1.
+
+  if events_type == 'float':
+    matrix = matrix.astype(bm.float32)
+  if values_type == 'heter':
+    heter_data = bm.ones(indices.shape) * weight
+    weight = heter_data
+
+  result = jax.block_until_ready(csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  result = jax.block_until_ready(csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  result = jax.block_until_ready(csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  result = jax.block_until_ready(csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  result = jax.block_until_ready(csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+
+  time0 = time.time()
+  result = jax.block_until_ready(csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  time1 = time.time()
+
+  time2 = time.time()
+  result = jax.block_until_ready(csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  time3 = time.time()
+
+  time4 = time.time()
+  result = jax.block_until_ready(csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  time5 = time.time()
+
+  time6 = time.time()
+  result = jax.block_until_ready(csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  time7 = time.time()
+
+  time8 = time.time()
+  result = jax.block_until_ready(csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  time9 = time.time()
+
+  time10 = time.time()
+  result = jax.block_until_ready(csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  time11 = time.time()
+
+  time12 = time.time()
+  result = jax.block_until_ready(csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  time13 = time.time()
+
+  time14 = time.time()
+  result = jax.block_until_ready(csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  time15 = time.time()
+
+  time16 = time.time()
+  result = jax.block_until_ready(csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  time17 = time.time()
+
+  time18 = time.time()
+  result = jax.block_until_ready(csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  time19 = time.time()
+
+  result1 = result
+
+  result = jax.block_until_ready(event_csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  result = jax.block_until_ready(event_csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  result = jax.block_until_ready(event_csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  result = jax.block_until_ready(event_csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  result = jax.block_until_ready(event_csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+
+  time20 = time.time()
+  result = jax.block_until_ready(event_csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  time21 = time.time()
+
+  result2 = result
+
+  time22 = time.time()
+  result = jax.block_until_ready(event_csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  time23 = time.time()
+
+  time24 = time.time()
+  result = jax.block_until_ready(event_csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  time25 = time.time()
+
+  time26 = time.time()
+  result = jax.block_until_ready(event_csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  time27 = time.time()
+
+  time28 = time.time()
+  result = jax.block_until_ready(event_csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  time29 = time.time()
+
+  time30 = time.time()
+  result = jax.block_until_ready(event_csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  time31 = time.time()
+
+  time32 = time.time()
+  result = jax.block_until_ready(event_csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  time33 = time.time()
+
+  time34 = time.time()
+  result = jax.block_until_ready(event_csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  time35 = time.time()
+
+  time36 = time.time()
+  result = jax.block_until_ready(event_csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  time37 = time.time()
+
+  time38 = time.time()
+  result = jax.block_until_ready(event_csrmm(weight, indices, indptr, matrix, shape=matrix1_shape, transpose=transpose))
+  time39 = time.time()
+
+  csrmm_time1 = (time1 - time0) * 1000
+  csrmm_time2 = (time3 - time2) * 1000
+  csrmm_time3 = (time5 - time4) * 1000
+  csrmm_time4 = (time7 - time6) * 1000
+  csrmm_time5 = (time9 - time8) * 1000
+  csrmm_time6 = (time11 - time10) * 1000
+  csrmm_time7 = (time13 - time12) * 1000
+  csrmm_time8 = (time15 - time14) * 1000
+  csrmm_time9 = (time17 - time16) * 1000
+  csrmm_time10 = (time19 - time18) * 1000
+  event_csrmm_time1 = (time21 - time20) * 1000
+  event_csrmm_time2 = (time23 - time22) * 1000
+  event_csrmm_time3 = (time25 - time24) * 1000
+  event_csrmm_time4 = (time27 - time26) * 1000
+  event_csrmm_time5 = (time29 - time28) * 1000
+  event_csrmm_time6 = (time31 - time30) * 1000
+  event_csrmm_time7 = (time33 - time32) * 1000
+  event_csrmm_time8 = (time35 - time34) * 1000
+  event_csrmm_time9 = (time37 - time36) * 1000
+  event_csrmm_time10 = (time39 - time38) * 1000
+  print('shape: ', shape, 'values_type: ', values_type, 'events_type: ', events_type, 'transpose: ', transpose)
+  print('csrmm_1: ', csrmm_time1, 'ms')
+  print('csrmm_3: ', csrmm_time3, 'ms')
+  print('csrmm_5: ', csrmm_time5, 'ms')
+  print('csrmm_7: ', csrmm_time7, 'ms')
+  print('csrmm_9: ', csrmm_time9, 'ms')
+  print('event_csrmm_1: ', event_csrmm_time1, 'ms')
+  print('event_csrmm_3: ', event_csrmm_time3, 'ms')
+  print('event_csrmm_5: ', event_csrmm_time5, 'ms')
+  print('event_csrmm_7: ', event_csrmm_time7, 'ms')
+  print('event_csrmm_9: ', event_csrmm_time9, 'ms')
+
+  r = bm.allclose(result1, result2)
+  if not r:
+    print('result1: ', result1)
+    print('result2: ', result2)
+
+  return csrmm_time1, csrmm_time2, csrmm_time3, csrmm_time4, csrmm_time5, \
+    csrmm_time6, csrmm_time7, csrmm_time8, csrmm_time9, csrmm_time10, \
+    event_csrmm_time1, event_csrmm_time2, event_csrmm_time3, event_csrmm_time4, event_csrmm_time5, \
+    event_csrmm_time6, event_csrmm_time7, event_csrmm_time8, event_csrmm_time9, event_csrmm_time10
+
+
+PATH = os.path.dirname(os.path.abspath(__file__))
+
+# init dataframe
+df = pd.DataFrame(
+  columns=['shape', 'p', 'shape[0]', 'shape[1]', 'shape[2]', 'backend', 'values type', 'events type', 'transpose',
+           'csrmm time1(ms)', 'csrmm time2(ms)', 'csrmm time3(ms)', 'csrmm time4(ms)',
+           'csrmm time5(ms)',
+           'csrmm time6(ms)', 'csrmm time7(ms)', 'csrmm time8(ms)', 'csrmm time9(ms)',
+           'csrmm time10(ms)',
+           'event_csrmm time1(ms)', 'event_csrmm time2(ms)', 'event_csrmm time3(ms)', 'event_csrmm time4(ms)',
+           'event_csrmm time5(ms)',
+           'event_csrmm time6(ms)', 'event_csrmm time7(ms)', 'event_csrmm time8(ms)', 'event_csrmm time9(ms)',
+           'event_csrmm time10(ms)'])
+
+### RECTANGULAR MATRIX
+if (bm.get_platform() == 'cpu'):
+  for shape in size:
+    for _values_type in values_type:
+      for _events_type in events_type:
+        for _transpose in transpose:
+          csrmm_time_1, csrmm_time_2, csrmm_time_3, csrmm_time_4, csrmm_time_5, \
+            csrmm_time_6, csrmm_time_7, csrmm_time_8, csrmm_time_9, csrmm_time_10, \
+            event_csrmm_time_1, event_csrmm_time_2, event_csrmm_time_3, event_csrmm_time_4, event_csrmm_time_5, \
+            event_csrmm_time_6, event_csrmm_time_7, event_csrmm_time_8, event_csrmm_time_9, event_csrmm_time_10 = test_sparse_csrmm(
+            shape,
+            _values_type,
+            _events_type,
+            _transpose)
+          # append to dataframe
+          df.loc[df.shape[0]] = [shape, 0.05, shape[0], shape[1], shape[2], 'cpu', _values_type, _events_type,
+                                 _transpose,
+                                 csrmm_time_1, csrmm_time_2, csrmm_time_3, csrmm_time_4,
+                                 csrmm_time_5,
+                                 csrmm_time_6, csrmm_time_7, csrmm_time_8, csrmm_time_9,
+                                 csrmm_time_10,
+                                 event_csrmm_time_1, event_csrmm_time_2, event_csrmm_time_3, event_csrmm_time_4,
+                                 event_csrmm_time_5,
+                                 event_csrmm_time_6, event_csrmm_time_7, event_csrmm_time_8, event_csrmm_time_9,
+                                 event_csrmm_time_10]
+          df.to_csv(f'{PATH}/csrmm_cpu.csv', index=False)
+
+if (bm.get_platform() == 'gpu'):
+  for shape in size:
+    for _values_type in values_type:
+      for _events_type in events_type:
+        for _transpose in transpose:
+          csrmm_time_1, csrmm_time_2, csrmm_time_3, csrmm_time_4, csrmm_time_5, \
+            csrmm_time_6, csrmm_time_7, csrmm_time_8, csrmm_time_9, csrmm_time_10, \
+            event_csrmm_time_1, event_csrmm_time_2, event_csrmm_time_3, event_csrmm_time_4, event_csrmm_time_5, \
+            event_csrmm_time_6, event_csrmm_time_7, event_csrmm_time_8, event_csrmm_time_9, event_csrmm_time_10 = test_sparse_csrmm(
+            shape,
+            _values_type,
+            _events_type,
+            _transpose)
+          # append to dataframe
+          df.loc[df.shape[0]] = [shape, 0.05, shape[0], shape[1], shape[2], 'gpu', _values_type, _events_type,
+                                 _transpose,
+                                 csrmm_time_1, csrmm_time_2, csrmm_time_3, csrmm_time_4,
+                                 csrmm_time_5,
+                                 csrmm_time_6, csrmm_time_7, csrmm_time_8, csrmm_time_9,
+                                 csrmm_time_10,
+                                 event_csrmm_time_1, event_csrmm_time_2, event_csrmm_time_3, event_csrmm_time_4,
+                                 event_csrmm_time_5,
+                                 event_csrmm_time_6, event_csrmm_time_7, event_csrmm_time_8, event_csrmm_time_9,
+                                 event_csrmm_time_10]
+          df.to_csv(f'{PATH}/csrmm_gpu.csv', index=False)
diff --git a/benchmarks/src/basic/event_csrmv_taichi_VS_event_csrmv.py b/benchmarks/src/basic/event_csrmv_taichi_VS_event_csrmv.py
new file mode 100644
index 0000000..3ac1e0e
--- /dev/null
+++ b/benchmarks/src/basic/event_csrmv_taichi_VS_event_csrmv.py
@@ -0,0 +1,254 @@
+# from jax_taichi import jax_taichi_call
+
+import time
+from functools import partial
+import os
+
+import brainpy as bp
+import brainpy.math as bm
+import jax
+import jax.numpy as jnp
+import numpy as np
+import pandas as pd
+import taichi as ti
+
+bm.set_platform('cpu')
+
+s = [1000, 5000, 10000, 20000, 25000, 30000]
+p = [0.1, 0.2, 0.3, 0.4, 0.5]
+
+shape = [
+        1000, 
+        2500, 
+        5000, 
+        10000, 
+        25000, 
+        37500, 
+        50000
+]
+
+
+
+values_type = [
+               'homo', 
+               'heter'
+               ]
+events_type = [
+               'bool', 
+               'float',
+               ]
+transpose = [
+             True, 
+             False
+            ]
+
+ITERATION = 100
+if bm.get_platform() == 'cpu':
+  ITERATION = 10
+
+print(bm.get_platform())
+
+@partial(jax.jit, static_argnums=(4, 5))
+def event_csrmv_taichi(weight, indices, indptr, vector, shape, transpose):
+  r = 0
+  for i in range(ITERATION):
+    r += bm.event.csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose)[0]
+  return r
+
+@partial(jax.jit, static_argnums=(4, 5))
+def event_csrmv(weight, indices, indptr, vector, shape, transpose):
+  r = 0
+  for i in range(ITERATION):
+    r += bm.event.csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose)
+  return r
+
+def test_event_csrmv(shape, values_type, events_type, transpose):
+  rng = bm.random.RandomState(seed=1234)
+  indices, indptr = bp.conn.FixedProb(0.05, seed=1234, allow_multi_conn=True)(*shape).require('pre2post')
+  vector = rng.random(shape[0] if transpose else shape[1]) < 0.1
+  weight = 1.
+  
+
+  if events_type == 'float':
+    vector = vector.astype(bm.float32)
+  if values_type == 'heter':
+    heter_data = bm.ones(indices.shape) * weight
+    weight = heter_data
+
+  jax.block_until_ready(event_csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  jax.block_until_ready(event_csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  jax.block_until_ready(event_csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  jax.block_until_ready(event_csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  jax.block_until_ready(event_csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+
+  time0 = time.time()
+  jax.block_until_ready(event_csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time1 = time.time()
+
+  time2 = time.time()
+  jax.block_until_ready(event_csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time3 = time.time()
+
+  time4 = time.time()
+  jax.block_until_ready(event_csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time5 = time.time()
+
+  time6 = time.time()
+  jax.block_until_ready(event_csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time7 = time.time()
+
+  time8 = time.time()
+  jax.block_until_ready(event_csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time9 = time.time()
+  
+  time10 = time.time()
+  jax.block_until_ready(event_csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time11 = time.time()
+  
+  time12 = time.time()
+  jax.block_until_ready(event_csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time13 = time.time()
+  
+  time14 = time.time()
+  jax.block_until_ready(event_csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time15 = time.time()
+  
+  time16 = time.time()
+  jax.block_until_ready(event_csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time17 = time.time()
+  
+  time18 = time.time()
+  jax.block_until_ready(event_csrmv_taichi(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time19 = time.time()
+  
+
+  jax.block_until_ready(event_csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  jax.block_until_ready(event_csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  jax.block_until_ready(event_csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  jax.block_until_ready(event_csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  jax.block_until_ready(event_csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+
+  time20 = time.time()
+  jax.block_until_ready(event_csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time21 = time.time()
+
+  time22 = time.time()
+  jax.block_until_ready(event_csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time23 = time.time()
+
+  time24 = time.time()
+  jax.block_until_ready(event_csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time25 = time.time()
+
+  time26 = time.time()
+  jax.block_until_ready(event_csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time27 = time.time()
+
+  time28 = time.time()
+  jax.block_until_ready(event_csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time29 = time.time()
+  
+  time30 = time.time()
+  jax.block_until_ready(event_csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time31 = time.time()
+  
+  time32 = time.time()
+  jax.block_until_ready(event_csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time33 = time.time()
+  
+  time34 = time.time()
+  jax.block_until_ready(event_csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time35 = time.time()
+  
+  time36 = time.time()
+  jax.block_until_ready(event_csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time37 = time.time()
+  
+  time38 = time.time()
+  jax.block_until_ready(event_csrmv(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time39 = time.time()
+
+  taichi_aot_time1 = (time1 - time0) * 1000
+  taichi_aot_time2 = (time3 - time2) * 1000
+  taichi_aot_time3 = (time5 - time4) * 1000
+  taichi_aot_time4 = (time7 - time6) * 1000
+  taichi_aot_time5 = (time9 - time8) * 1000
+  taichi_aot_time6 = (time11 - time10) * 1000
+  taichi_aot_time7 = (time13 - time12) * 1000
+  taichi_aot_time8 = (time15 - time14) * 1000
+  taichi_aot_time9 = (time17 - time16) * 1000
+  taichi_aot_time10 = (time19 - time18) * 1000
+  brainpy_time1 = (time21 - time20) * 1000
+  brainpy_time2 = (time23 - time22) * 1000
+  brainpy_time3 = (time25 - time24) * 1000
+  brainpy_time4 = (time27 - time26) * 1000
+  brainpy_time5 = (time29 - time28) * 1000
+  brainpy_time6 = (time31 - time30) * 1000
+  brainpy_time7 = (time33 - time32) * 1000
+  brainpy_time8 = (time35 - time34) * 1000
+  brainpy_time9 = (time37 - time36) * 1000
+  brainpy_time10 = (time39 - time38) * 1000
+  print('shape: ', shape, 'values_type: ', values_type, 'events_type: ', events_type, 'transpose: ', transpose)
+  print('taichi_aot_1: ', taichi_aot_time1, 'ms')
+  print('taichi_aot_3: ', taichi_aot_time3, 'ms')
+  print('taichi_aot_5: ', taichi_aot_time5, 'ms')
+  print('taichi_aot_7: ', taichi_aot_time7, 'ms')
+  print('taichi_aot_9: ', taichi_aot_time9, 'ms')
+  print('brainpylib_1: ', brainpy_time1, 'ms')
+  print('brainpylib_3: ', brainpy_time3, 'ms')
+  print('brainpylib_5: ', brainpy_time5, 'ms')
+  print('brainpylib_7: ', brainpy_time7, 'ms')
+  print('brainpylib_9: ', brainpy_time9, 'ms')
+
+  # assert(jnp.allclose(result1[0], result2))
+
+  return taichi_aot_time1, taichi_aot_time2, taichi_aot_time3, taichi_aot_time4, taichi_aot_time5,\
+      taichi_aot_time6, taichi_aot_time7, taichi_aot_time8, taichi_aot_time9, taichi_aot_time10,\
+      brainpy_time1, brainpy_time2, brainpy_time3, brainpy_time4, brainpy_time5, \
+      brainpy_time6, brainpy_time7, brainpy_time8, brainpy_time9, brainpy_time10
+
+PATH = os.path.dirname(os.path.abspath(__file__))
+
+# init dataframe
+df = pd.DataFrame(columns=['s', 'p', 'shape[0]', 'shape[1]', 'backend', 'values type', 'events type', 'transpose',
+                           'taichi aot time1(ms)', 'taichi aot time2(ms)', 'taichi aot time3(ms)', 'taichi aot time4(ms)', 'taichi aot time5(ms)',
+                           'taichi aot time6(ms)', 'taichi aot time7(ms)', 'taichi aot time8(ms)', 'taichi aot time9(ms)', 'taichi aot time10(ms)',
+                           'brainpy time1(ms)', 'brainpy time2(ms)', 'brainpy time3(ms)', 'brainpy time4(ms)', 'brainpy time5(ms)',
+                           'brainpy time6(ms)', 'brainpy time7(ms)', 'brainpy time8(ms)', 'brainpy time9(ms)', 'brainpy time10(ms)'])
+
+### RECTANGULAR MATRIX
+if (bm.get_platform() == 'cpu'):
+  for shape1 in shape:
+    for shape2 in shape:
+      for _values_type in values_type:
+          for _events_type in events_type:
+            for _transpose in transpose:
+              taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,\
+                taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,\
+                  brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, \
+                  brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10 = test_event_csrmv((shape1, shape2), _values_type, _events_type, _transpose)
+              # append to dataframe
+              df.loc[df.shape[0]] = [(shape1, shape2), 0.5 , shape1, shape2, 'cpu', _values_type, _events_type, _transpose,
+                                    taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,
+                                    taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,
+                                    brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, 
+                                    brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10]
+  df.to_csv(f'{PATH}/event_csrmv_cpu.csv', index=False)
+
+if (bm.get_platform() == 'gpu'):
+  for shape1 in shape:
+    for shape2 in shape:
+      for _values_type in values_type:
+          for _events_type in events_type:
+            for _transpose in transpose:
+              taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,\
+                taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,\
+                  brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, \
+                  brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10 = test_event_csrmv((shape1, shape2), _values_type, _events_type, _transpose)
+              # append to dataframe
+              df.loc[df.shape[0]] = [(shape1, shape2), 0.5 , shape1, shape2, 'gpu', _values_type, _events_type, _transpose,
+                                    taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,
+                                    taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,
+                                    brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, 
+                                    brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10]
+  df.to_csv(f'{PATH}/event_csrmv_gpu.csv', index=False)
diff --git a/benchmarks/src/basic/event_csrmv_taichi_VS_event_csrmv_grad.py b/benchmarks/src/basic/event_csrmv_taichi_VS_event_csrmv_grad.py
new file mode 100644
index 0000000..98793e6
--- /dev/null
+++ b/benchmarks/src/basic/event_csrmv_taichi_VS_event_csrmv_grad.py
@@ -0,0 +1,271 @@
+# from jax_taichi import jax_taichi_call
+
+import time
+from functools import partial
+import os
+
+import brainpy as bp
+import brainpy.math as bm
+import jax
+import jax.numpy as jnp
+import numpy as np
+import pandas as pd
+import taichi as ti
+
+bm.set_platform('cpu')
+
+s = [1000, 5000, 10000, 20000, 25000, 30000]
+p = [0.1, 0.2, 0.3, 0.4, 0.5]
+
+shape = [
+        1000, 
+        2500, 
+        5000, 
+        10000, 
+        25000, 
+        37500, 
+        50000
+]
+
+
+
+values_type = [
+               'homo', 
+               'heter'
+               ]
+events_type = [
+               'bool', 
+               'float',
+               ]
+transpose = [
+             True, 
+             False
+            ]
+
+ITERATION = 100
+if bm.get_platform() == 'cpu':
+  ITERATION = 10
+
+print(bm.get_platform())
+
+def sum_op(op):
+  def func(*args, **kwargs):
+    r = op(*args, **kwargs)
+    return r.sum()
+
+  return func
+
+
+def sum_op2(op):
+  def func(*args, **kwargs):
+    r = op(*args, **kwargs)[0]
+    return r.sum()
+
+  return func
+
+@partial(jax.jit, static_argnums=(4, 5))
+def event_csrmv_taichi_grad(weight, indices, indptr, vector, shape, transpose):
+  r = 0
+  for i in range(ITERATION):
+    r += jax.grad(sum_op2(bm.event.csrmv_taichi), argnums=3)(
+      weight, indices, indptr, vector.astype(float), shape=shape, transpose=transpose)
+  return r
+
+@partial(jax.jit, static_argnums=(4, 5))
+def event_csrmv_grad(weight, indices, indptr, vector, shape, transpose):
+  r = 0
+  for i in range(ITERATION):
+    r += jax.grad(sum_op(bm.event.csrmv), argnums=3)(
+      weight, indices, indptr, vector.astype(float), shape=shape, transpose=transpose)
+  return r
+
+
+def test_event_csrmv(shape, values_type, events_type, transpose):
+  rng = bm.random.RandomState(seed=1234)
+  indices, indptr = bp.conn.FixedProb(0.05, seed=1234, allow_multi_conn=True)(*shape).require('pre2post')
+  vector = rng.random(shape[0] if transpose else shape[1]) < 0.1
+  weight = 1.
+  
+
+  if events_type == 'float':
+    vector = vector.astype(bm.float32)
+  if values_type == 'heter':
+    heter_data = bm.ones(indices.shape) * weight
+    weight = heter_data
+
+  result = jax.block_until_ready(event_csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  result = jax.block_until_ready(event_csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  result = jax.block_until_ready(event_csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  result = jax.block_until_ready(event_csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  result = jax.block_until_ready(event_csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+
+  time0 = time.time()
+  result = jax.block_until_ready(event_csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time1 = time.time()
+
+  time2 = time.time()
+  result = jax.block_until_ready(event_csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time3 = time.time()
+
+  time4 = time.time()
+  result = jax.block_until_ready(event_csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time5 = time.time()
+
+  time6 = time.time()
+  result = jax.block_until_ready(event_csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time7 = time.time()
+
+  time8 = time.time()
+  result = jax.block_until_ready(event_csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time9 = time.time()
+  
+  time10 = time.time()
+  result = jax.block_until_ready(event_csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time11 = time.time()
+  
+  time12 = time.time()
+  result = jax.block_until_ready(event_csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time13 = time.time()
+  
+  time14 = time.time()
+  result = jax.block_until_ready(event_csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time15 = time.time()
+  
+  time16 = time.time()
+  result = jax.block_until_ready(event_csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time17 = time.time()
+  
+  time18 = time.time()
+  result = jax.block_until_ready(event_csrmv_taichi_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time19 = time.time()
+  
+
+  result = jax.block_until_ready(event_csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  result = jax.block_until_ready(event_csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  result = jax.block_until_ready(event_csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  result = jax.block_until_ready(event_csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  result = jax.block_until_ready(event_csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+
+  time20 = time.time()
+  result = jax.block_until_ready(event_csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time21 = time.time()
+
+  time22 = time.time()
+  result = jax.block_until_ready(event_csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time23 = time.time()
+
+  time24 = time.time()
+  result = jax.block_until_ready(event_csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time25 = time.time()
+
+  time26 = time.time()
+  result = jax.block_until_ready(event_csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time27 = time.time()
+
+  time28 = time.time()
+  result = jax.block_until_ready(event_csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time29 = time.time()
+  
+  time30 = time.time()
+  result = jax.block_until_ready(event_csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time31 = time.time()
+  
+  time32 = time.time()
+  result = jax.block_until_ready(event_csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time33 = time.time()
+  
+  time34 = time.time()
+  result = jax.block_until_ready(event_csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time35 = time.time()
+  
+  time36 = time.time()
+  result = jax.block_until_ready(event_csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time37 = time.time()
+  
+  time38 = time.time()
+  result = jax.block_until_ready(event_csrmv_grad(weight, indices, indptr, vector, shape=shape, transpose=transpose))
+  time39 = time.time()
+
+  taichi_aot_time1 = (time1 - time0) * 1000
+  taichi_aot_time2 = (time3 - time2) * 1000
+  taichi_aot_time3 = (time5 - time4) * 1000
+  taichi_aot_time4 = (time7 - time6) * 1000
+  taichi_aot_time5 = (time9 - time8) * 1000
+  taichi_aot_time6 = (time11 - time10) * 1000
+  taichi_aot_time7 = (time13 - time12) * 1000
+  taichi_aot_time8 = (time15 - time14) * 1000
+  taichi_aot_time9 = (time17 - time16) * 1000
+  taichi_aot_time10 = (time19 - time18) * 1000
+  brainpy_time1 = (time21 - time20) * 1000
+  brainpy_time2 = (time23 - time22) * 1000
+  brainpy_time3 = (time25 - time24) * 1000
+  brainpy_time4 = (time27 - time26) * 1000
+  brainpy_time5 = (time29 - time28) * 1000
+  brainpy_time6 = (time31 - time30) * 1000
+  brainpy_time7 = (time33 - time32) * 1000
+  brainpy_time8 = (time35 - time34) * 1000
+  brainpy_time9 = (time37 - time36) * 1000
+  brainpy_time10 = (time39 - time38) * 1000
+  print('shape: ', shape, 'values_type: ', values_type, 'events_type: ', events_type, 'transpose: ', transpose)
+  print('taichi_aot_1: ', taichi_aot_time1, 'ms')
+  print('taichi_aot_3: ', taichi_aot_time3, 'ms')
+  print('taichi_aot_5: ', taichi_aot_time5, 'ms')
+  print('taichi_aot_7: ', taichi_aot_time7, 'ms')
+  print('taichi_aot_9: ', taichi_aot_time9, 'ms')
+  print('brainpylib_1: ', brainpy_time1, 'ms')
+  print('brainpylib_3: ', brainpy_time3, 'ms')
+  print('brainpylib_5: ', brainpy_time5, 'ms')
+  print('brainpylib_7: ', brainpy_time7, 'ms')
+  print('brainpylib_9: ', brainpy_time9, 'ms')
+
+
+  return taichi_aot_time1, taichi_aot_time2, taichi_aot_time3, taichi_aot_time4, taichi_aot_time5,\
+      taichi_aot_time6, taichi_aot_time7, taichi_aot_time8, taichi_aot_time9, taichi_aot_time10,\
+      brainpy_time1, brainpy_time2, brainpy_time3, brainpy_time4, brainpy_time5, \
+      brainpy_time6, brainpy_time7, brainpy_time8, brainpy_time9, brainpy_time10
+
+PATH = os.path.dirname(os.path.abspath(__file__))
+
+# init dataframe
+df = pd.DataFrame(columns=['s', 'p', 'shape[0]', 'shape[1]', 'backend', 'values type', 'events type', 'transpose',
+                           'taichi aot time1(ms)', 'taichi aot time2(ms)', 'taichi aot time3(ms)', 'taichi aot time4(ms)', 'taichi aot time5(ms)',
+                           'taichi aot time6(ms)', 'taichi aot time7(ms)', 'taichi aot time8(ms)', 'taichi aot time9(ms)', 'taichi aot time10(ms)',
+                           'brainpy time1(ms)', 'brainpy time2(ms)', 'brainpy time3(ms)', 'brainpy time4(ms)', 'brainpy time5(ms)',
+                           'brainpy time6(ms)', 'brainpy time7(ms)', 'brainpy time8(ms)', 'brainpy time9(ms)', 'brainpy time10(ms)'])
+
+### RECTANGULAR MATRIX
+if (bm.get_platform() == 'cpu'):
+  for shape1 in shape:
+    for shape2 in shape:
+      for _values_type in values_type:
+          for _events_type in events_type:
+            for _transpose in transpose:
+              taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,\
+                taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,\
+                  brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, \
+                  brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10 = test_event_csrmv((shape1, shape2), _values_type, _events_type, _transpose)
+              # append to dataframe
+              df.loc[df.shape[0]] = [(shape1, shape2), 0.5 , shape1, shape2, 'cpu', _values_type, _events_type, _transpose,
+                                    taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,
+                                    taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,
+                                    brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, 
+                                    brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10]
+  df.to_csv(f'{PATH}/event_csrmv_grad_cpu.csv', index=False)
+
+if (bm.get_platform() == 'gpu'):
+  for shape1 in shape:
+    for shape2 in shape:
+      for _values_type in values_type:
+          for _events_type in events_type:
+            for _transpose in transpose:
+              taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,\
+                taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,\
+                  brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, \
+                  brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10 = test_event_csrmv((shape1, shape2), _values_type, _events_type, _transpose)
+              # append to dataframe
+              df.loc[df.shape[0]] = [(shape1, shape2), 0.5 , shape1, shape2, 'gpu', _values_type, _events_type, _transpose,
+                                    taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,
+                                    taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,
+                                    brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, 
+                                    brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10]
+  df.to_csv(f'{PATH}/event_csrmv_grad_gpu.csv', index=False)
diff --git a/benchmarks/src/basic/jitconn_event_matvec_taichi_VS_jitconn_event_matvec.py b/benchmarks/src/basic/jitconn_event_matvec_taichi_VS_jitconn_event_matvec.py
new file mode 100644
index 0000000..21a2466
--- /dev/null
+++ b/benchmarks/src/basic/jitconn_event_matvec_taichi_VS_jitconn_event_matvec.py
@@ -0,0 +1,573 @@
+# from jax_taichi import jax_taichi_call
+
+import time
+from functools import partial
+import os
+
+import brainpy as bp
+import brainpy.math as bm
+import jax
+import jax.numpy as jnp
+import numpy as np
+import pandas as pd
+import taichi as ti
+
+bm.set_platform('cpu')
+
+seed = 1234
+
+shape = [
+        1000, 
+        2500, 
+        5000, 
+        10000, 
+        25000, 
+        37500, 
+        50000
+        ]
+types = [
+       'homo', 
+       'uniform',
+       'normal'
+       ]
+transpose = [
+            True, 
+            False
+            ]
+outdim_parallel = [
+                  True,
+                  False,
+                  ]
+bool_event = [
+             True,
+             False
+             ]
+conn_prob = 0.05
+homo_data = 1.
+w_low = 0.
+w_high = 1.
+w_mu = 0.
+w_sigma = 0.1
+
+ITERATION = 100
+if bm.get_platform() == 'cpu':
+  ITERATION = 10
+
+print(bm.get_platform())
+
+@partial(jax.jit, static_argnums=(4, 5, 6))
+def jitconn_event_matvec_homo_taichi(vector, homo_data, conn_prob, seed, shape, transpose, outdim_parallel):
+  r = 0
+  for i in range(ITERATION):
+    r += bm.jitconn.event_mv_prob_homo_taichi(vector, homo_data, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel)[0]
+  return r
+
+@partial(jax.jit, static_argnums=(4, 5, 6))
+def jitconn_event_matvec_homo(vector, homo_data, conn_prob, seed, shape, transpose, outdim_parallel):
+  r = 0
+  for i in range(ITERATION):
+    r += bm.jitconn.event_mv_prob_homo(vector, homo_data, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel)[0]
+  return r
+
+@partial(jax.jit, static_argnums=(5, 6, 7))
+def jitconn_event_matvec_uniform_taichi(vector, w_low, w_high, conn_prob, seed, shape, transpose, outdim_parallel):
+  r = 0
+  for i in range(ITERATION):
+    r += bm.jitconn.event_mv_prob_uniform_taichi(vector, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel)
+  return r
+
+@partial(jax.jit, static_argnums=(5, 6, 7))
+def jitconn_event_matvec_uniform(vector, w_low, w_high, conn_prob, seed, shape, transpose, outdim_parallel):
+  r = 0
+  for i in range(ITERATION):
+    r += bm.jitconn.event_mv_prob_uniform(vector, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel)
+  return r
+
+@partial(jax.jit, static_argnums=(5, 6, 7))
+def jitconn_event_matvec_normal_taichi(vector, w_mu, w_sigma, conn_prob, seed, shape, transpose, outdim_parallel):
+  r = 0
+  for i in range(ITERATION):
+    r += bm.jitconn.event_mv_prob_normal_taichi(vector, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel)
+  return r
+
+@partial(jax.jit, static_argnums=(5, 6, 7))
+def jitconn_event_matvec_normal(vector, w_mu, w_sigma, conn_prob, seed, shape, transpose, outdim_parallel):
+  r = 0
+  for i in range(ITERATION):
+    r += bm.jitconn.event_mv_prob_normal(vector, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel)
+  return r
+  
+  
+def test_jitconn_matvec_homo(shape, transpose, outdim_parallel, bool_event):
+  rng = bm.random.RandomState(seed=seed)
+  events = bm.as_jax(rng.random(shape[0] if transpose else shape[1])) < 0.1
+  if not bool_event:
+    events = events.astype(float)
+
+  # groundtruth = bm.as_jax(events, dtype=float) @ bm.as_jax(dense)
+
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+
+  time0 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time1 = time.time()
+
+  time2 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time3 = time.time()
+
+  time4 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time5 = time.time()
+
+  time6 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time7 = time.time()
+
+  time8 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time9 = time.time()
+  
+  time10 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time11 = time.time()
+  
+  time12 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time13 = time.time()
+  
+  time14 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time15 = time.time()
+  
+  time16 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time17 = time.time()
+  
+  time18 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time19 = time.time()
+  
+
+  result = jax.block_until_ready(jitconn_event_matvec_homo(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_homo(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_homo(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_homo(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_homo(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+
+  time20 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time21 = time.time()
+
+  time22 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time23 = time.time()
+
+  time24 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time25 = time.time()
+
+  time26 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time27 = time.time()
+
+  time28 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time29 = time.time()
+  
+  time30 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time31 = time.time()
+  
+  time32 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time33 = time.time()
+  
+  time34 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time35 = time.time()
+  
+  time36 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time37 = time.time()
+  
+  time38 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time39 = time.time()
+
+  taichi_aot_time1 = (time1 - time0) * 1000
+  taichi_aot_time2 = (time3 - time2) * 1000
+  taichi_aot_time3 = (time5 - time4) * 1000
+  taichi_aot_time4 = (time7 - time6) * 1000
+  taichi_aot_time5 = (time9 - time8) * 1000
+  taichi_aot_time6 = (time11 - time10) * 1000
+  taichi_aot_time7 = (time13 - time12) * 1000
+  taichi_aot_time8 = (time15 - time14) * 1000
+  taichi_aot_time9 = (time17 - time16) * 1000
+  taichi_aot_time10 = (time19 - time18) * 1000
+  brainpy_time1 = (time21 - time20) * 1000
+  brainpy_time2 = (time23 - time22) * 1000
+  brainpy_time3 = (time25 - time24) * 1000
+  brainpy_time4 = (time27 - time26) * 1000
+  brainpy_time5 = (time29 - time28) * 1000
+  brainpy_time6 = (time31 - time30) * 1000
+  brainpy_time7 = (time33 - time32) * 1000
+  brainpy_time8 = (time35 - time34) * 1000
+  brainpy_time9 = (time37 - time36) * 1000
+  brainpy_time10 = (time39 - time38) * 1000
+  print('taichi_aot_1: ', taichi_aot_time1, 'ms')
+  print('taichi_aot_3: ', taichi_aot_time3, 'ms')
+  print('taichi_aot_5: ', taichi_aot_time5, 'ms')
+  print('taichi_aot_7: ', taichi_aot_time7, 'ms')
+  print('taichi_aot_9: ', taichi_aot_time9, 'ms')
+  print('brainpylib_1: ', brainpy_time1, 'ms')
+  print('brainpylib_3: ', brainpy_time3, 'ms')
+  print('brainpylib_5: ', brainpy_time5, 'ms')
+  print('brainpylib_7: ', brainpy_time7, 'ms')
+  print('brainpylib_9: ', brainpy_time9, 'ms')
+
+
+  return taichi_aot_time1, taichi_aot_time2, taichi_aot_time3, taichi_aot_time4, taichi_aot_time5,\
+      taichi_aot_time6, taichi_aot_time7, taichi_aot_time8, taichi_aot_time9, taichi_aot_time10,\
+      brainpy_time1, brainpy_time2, brainpy_time3, brainpy_time4, brainpy_time5, \
+      brainpy_time6, brainpy_time7, brainpy_time8, brainpy_time9, brainpy_time10
+      
+def test_jitconn_matvec_uniform(shape, transpose, outdim_parallel, bool_event):
+  rng = bm.random.RandomState(seed=seed)
+  events = bm.as_jax(rng.random(shape[0] if transpose else shape[1])) < 0.1
+  if not bool_event:
+      events = events.astype(float)
+
+  # groundtruth = bm.as_jax(vector, dtype=float) @ bm.as_jax(dense)
+
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+
+  time0 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time1 = time.time()
+
+  time2 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time3 = time.time()
+
+  time4 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time5 = time.time()
+
+  time6 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time7 = time.time()
+
+  time8 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time9 = time.time()
+  
+  time10 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time11 = time.time()
+  
+  time12 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time13 = time.time()
+  
+  time14 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time15 = time.time()
+  
+  time16 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time17 = time.time()
+  
+  time18 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time19 = time.time()
+  
+
+  result = jax.block_until_ready(jitconn_event_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+
+  time20 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time21 = time.time()
+
+  time22 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time23 = time.time()
+
+  time24 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time25 = time.time()
+
+  time26 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time27 = time.time()
+
+  time28 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time29 = time.time()
+  
+  time30 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time31 = time.time()
+  
+  time32 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time33 = time.time()
+  
+  time34 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time35 = time.time()
+  
+  time36 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time37 = time.time()
+  
+  time38 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time39 = time.time()
+
+  taichi_aot_time1 = (time1 - time0) * 1000
+  taichi_aot_time2 = (time3 - time2) * 1000
+  taichi_aot_time3 = (time5 - time4) * 1000
+  taichi_aot_time4 = (time7 - time6) * 1000
+  taichi_aot_time5 = (time9 - time8) * 1000
+  taichi_aot_time6 = (time11 - time10) * 1000
+  taichi_aot_time7 = (time13 - time12) * 1000
+  taichi_aot_time8 = (time15 - time14) * 1000
+  taichi_aot_time9 = (time17 - time16) * 1000
+  taichi_aot_time10 = (time19 - time18) * 1000
+  brainpy_time1 = (time21 - time20) * 1000
+  brainpy_time2 = (time23 - time22) * 1000
+  brainpy_time3 = (time25 - time24) * 1000
+  brainpy_time4 = (time27 - time26) * 1000
+  brainpy_time5 = (time29 - time28) * 1000
+  brainpy_time6 = (time31 - time30) * 1000
+  brainpy_time7 = (time33 - time32) * 1000
+  brainpy_time8 = (time35 - time34) * 1000
+  brainpy_time9 = (time37 - time36) * 1000
+  brainpy_time10 = (time39 - time38) * 1000
+  print('taichi_aot_1: ', taichi_aot_time1, 'ms')
+  print('taichi_aot_3: ', taichi_aot_time3, 'ms')
+  print('taichi_aot_5: ', taichi_aot_time5, 'ms')
+  print('taichi_aot_7: ', taichi_aot_time7, 'ms')
+  print('taichi_aot_9: ', taichi_aot_time9, 'ms')
+  print('brainpylib_1: ', brainpy_time1, 'ms')
+  print('brainpylib_3: ', brainpy_time3, 'ms')
+  print('brainpylib_5: ', brainpy_time5, 'ms')
+  print('brainpylib_7: ', brainpy_time7, 'ms')
+  print('brainpylib_9: ', brainpy_time9, 'ms')
+
+
+  return taichi_aot_time1, taichi_aot_time2, taichi_aot_time3, taichi_aot_time4, taichi_aot_time5,\
+      taichi_aot_time6, taichi_aot_time7, taichi_aot_time8, taichi_aot_time9, taichi_aot_time10,\
+      brainpy_time1, brainpy_time2, brainpy_time3, brainpy_time4, brainpy_time5, \
+      brainpy_time6, brainpy_time7, brainpy_time8, brainpy_time9, brainpy_time10
+
+def test_jitconn_matvec_normal(shape, transpose, outdim_parallel, bool_event):
+  rng = bm.random.RandomState(seed=seed)
+  events = bm.as_jax(rng.random(shape[0] if transpose else shape[1])) < 0.1
+  if not bool_event:
+      events = events.astype(float)
+  # groundtruth = bm.as_jax(vector, dtype=float) @ bm.as_jax(dense)
+
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+
+  time0 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time1 = time.time()
+
+  time2 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time3 = time.time()
+
+  time4 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time5 = time.time()
+
+  time6 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time7 = time.time()
+
+  time8 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time9 = time.time()
+  
+  time10 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time11 = time.time()
+  
+  time12 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time13 = time.time()
+  
+  time14 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time15 = time.time()
+  
+  time16 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time17 = time.time()
+  
+  time18 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time19 = time.time()
+  
+
+  result = jax.block_until_ready(jitconn_event_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+
+  time20 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time21 = time.time()
+
+  time22 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time23 = time.time()
+
+  time24 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time25 = time.time()
+
+  time26 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time27 = time.time()
+
+  time28 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time29 = time.time()
+  
+  time30 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time31 = time.time()
+  
+  time32 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time33 = time.time()
+  
+  time34 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time35 = time.time()
+  
+  time36 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time37 = time.time()
+  
+  time38 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time39 = time.time()
+
+  taichi_aot_time1 = (time1 - time0) * 1000
+  taichi_aot_time2 = (time3 - time2) * 1000
+  taichi_aot_time3 = (time5 - time4) * 1000
+  taichi_aot_time4 = (time7 - time6) * 1000
+  taichi_aot_time5 = (time9 - time8) * 1000
+  taichi_aot_time6 = (time11 - time10) * 1000
+  taichi_aot_time7 = (time13 - time12) * 1000
+  taichi_aot_time8 = (time15 - time14) * 1000
+  taichi_aot_time9 = (time17 - time16) * 1000
+  taichi_aot_time10 = (time19 - time18) * 1000
+  brainpy_time1 = (time21 - time20) * 1000
+  brainpy_time2 = (time23 - time22) * 1000
+  brainpy_time3 = (time25 - time24) * 1000
+  brainpy_time4 = (time27 - time26) * 1000
+  brainpy_time5 = (time29 - time28) * 1000
+  brainpy_time6 = (time31 - time30) * 1000
+  brainpy_time7 = (time33 - time32) * 1000
+  brainpy_time8 = (time35 - time34) * 1000
+  brainpy_time9 = (time37 - time36) * 1000
+  brainpy_time10 = (time39 - time38) * 1000
+  print('taichi_aot_1: ', taichi_aot_time1, 'ms')
+  print('taichi_aot_3: ', taichi_aot_time3, 'ms')
+  print('taichi_aot_5: ', taichi_aot_time5, 'ms')
+  print('taichi_aot_7: ', taichi_aot_time7, 'ms')
+  print('taichi_aot_9: ', taichi_aot_time9, 'ms')
+  print('brainpylib_1: ', brainpy_time1, 'ms')
+  print('brainpylib_3: ', brainpy_time3, 'ms')
+  print('brainpylib_5: ', brainpy_time5, 'ms')
+  print('brainpylib_7: ', brainpy_time7, 'ms')
+  print('brainpylib_9: ', brainpy_time9, 'ms')
+
+
+  return taichi_aot_time1, taichi_aot_time2, taichi_aot_time3, taichi_aot_time4, taichi_aot_time5,\
+      taichi_aot_time6, taichi_aot_time7, taichi_aot_time8, taichi_aot_time9, taichi_aot_time10,\
+      brainpy_time1, brainpy_time2, brainpy_time3, brainpy_time4, brainpy_time5, \
+      brainpy_time6, brainpy_time7, brainpy_time8, brainpy_time9, brainpy_time10
+
+
+def test_jitconn_matvec(shape, _type, transpose, outdim_parallel, bool_event):
+  print('shape: ', shape, ' type: ', _type, ' transpose: ', transpose, ' outdim_parallel: ', outdim_parallel)
+  if _type == 'homo':
+    return test_jitconn_matvec_homo(shape, transpose, outdim_parallel, bool_event)
+  elif _type == 'uniform':
+    return test_jitconn_matvec_uniform(shape, transpose, outdim_parallel, bool_event)
+  elif _type == 'normal':
+    return test_jitconn_matvec_normal(shape, transpose, outdim_parallel, bool_event)
+  else:
+    raise ValueError
+
+
+PATH = os.path.dirname(os.path.abspath(__file__))
+
+# init dataframe
+df = pd.DataFrame(columns=['shape[0]', 'shape[1]', 'backend', 'type', 'transpose', 'outdim_parallel', 'bool_event',
+                            'taichi aot time1(ms)', 'taichi aot time2(ms)', 'taichi aot time3(ms)', 'taichi aot time4(ms)', 'taichi aot time5(ms)',
+                           'taichi aot time6(ms)', 'taichi aot time7(ms)', 'taichi aot time8(ms)', 'taichi aot time9(ms)', 'taichi aot time10(ms)',
+                           'brainpy time1(ms)', 'brainpy time2(ms)', 'brainpy time3(ms)', 'brainpy time4(ms)', 'brainpy time5(ms)',
+                           'brainpy time6(ms)', 'brainpy time7(ms)', 'brainpy time8(ms)', 'brainpy time9(ms)', 'brainpy time10(ms)'])
+
+### RECTANGULAR MATRIX
+if (bm.get_platform() == 'cpu'):
+  for shape1 in shape:
+    for shape2 in shape:
+      for _type in types:
+        for _outdim_parallel in outdim_parallel:
+          for _transpose in transpose:
+            for _bool_event in bool_event:
+              taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,\
+                taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,\
+                  brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, \
+                  brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10 = test_jitconn_matvec((shape1, shape2), _type, _transpose, _outdim_parallel, _bool_event)
+              # append to dataframe
+              df.loc[df.shape[0]] = [shape1, shape2, 'cpu', _type, _transpose, _outdim_parallel, _bool_event,
+                                  taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,
+                                    taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,
+                                    brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, 
+                                    brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10]
+  df.to_csv(f'{PATH}/jitconn_event_matvec_cpu.csv', index=False)
+
+if (bm.get_platform() == 'gpu'):
+  for shape1 in shape:
+    for shape2 in shape:
+      for _type in types:
+        for _outdim_parallel in outdim_parallel:
+          for _transpose in transpose:
+            for _bool_event in bool_event:
+              taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,\
+                taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,\
+                  brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, \
+                  brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10 = test_jitconn_matvec((shape1, shape2), _type, _transpose, _outdim_parallel, _bool_event)
+              # append to dataframe
+              df.loc[df.shape[0]] = [shape1, shape2, 'gpu', _type, _transpose, _outdim_parallel, _bool_event,
+                                  taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,
+                                    taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,
+                                    brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, 
+                                    brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10]
+  df.to_csv(f'{PATH}/jitconn_event_matvec_gpu.csv', index=False)
diff --git a/benchmarks/src/basic/jitconn_event_matvec_taichi_VS_jitconn_event_matvec_grad.py b/benchmarks/src/basic/jitconn_event_matvec_taichi_VS_jitconn_event_matvec_grad.py
new file mode 100644
index 0000000..ff4f01a
--- /dev/null
+++ b/benchmarks/src/basic/jitconn_event_matvec_taichi_VS_jitconn_event_matvec_grad.py
@@ -0,0 +1,589 @@
+# from jax_taichi import jax_taichi_call
+
+import time
+from functools import partial
+import os
+
+import brainpy as bp
+import brainpy.math as bm
+import jax
+import jax.numpy as jnp
+import numpy as np
+import pandas as pd
+import taichi as ti
+
+bm.set_platform('cpu')
+# bm.disable_gpu_memory_preallocation()
+
+seed = 1234
+
+shape = [
+        1000, 
+        2500, 
+        5000, 
+        10000, 
+        25000, 
+        37500, 
+        50000
+        ]
+types = [
+       'homo', 
+       'uniform',
+       'normal'
+       ]
+transpose = [
+            True, 
+            False
+            ]
+outdim_parallel = [
+                  True,
+                  False,
+                  ]
+bool_event = [
+             True,
+             False
+             ]
+conn_prob = 0.05
+homo_data = 1.
+w_low = 0.
+w_high = 1.
+w_mu = 0.
+w_sigma = 0.1
+
+print(bm.get_platform())
+
+def sum_op(op):
+  def func(*args, **kwargs):
+    r = op(*args, **kwargs)[0]
+    return r.sum()
+
+  return func
+
+ITERATION = 100
+if bm.get_platform() == 'cpu':
+  ITERATION = 10
+
+@partial(jax.jit, static_argnums=(4, 5, 6))
+def jitconn_event_matvec_homo_taichi_grad(vector, homo_data, conn_prob, seed, shape, transpose, outdim_parallel):
+  r = 0
+  for i in range(ITERATION):
+    r +=jax.grad(sum_op(bm.jitconn.event_mv_prob_homo_taichi), argnums=0)(
+      vector.astype(float), homo_data, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel
+    )
+  return r
+  
+@partial(jax.jit, static_argnums=(4, 5, 6))
+def jitconn_event_matvec_homo_grad(vector, homo_data, conn_prob, seed, shape, transpose, outdim_parallel):
+  r = 0
+  for i in range(ITERATION):
+    r += jax.grad(sum_op(bm.jitconn.event_mv_prob_homo), argnums=0)(
+      vector.astype(float), homo_data, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel
+    )
+  return r
+  
+@partial(jax.jit, static_argnums=(5, 6, 7))
+def jitconn_event_matvec_uniform_taichi_grad(vector, w_low, w_high, conn_prob, seed, shape, transpose, outdim_parallel):
+  r = 0
+  for i in range(ITERATION):
+    r += jax.grad(sum_op(bm.jitconn.event_mv_prob_uniform_taichi), argnums=0)(
+      vector.astype(float), w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel
+    )
+  return r
+  
+@partial(jax.jit, static_argnums=(5, 6, 7))
+def jitconn_event_matvec_uniform_grad(vector, w_low, w_high, conn_prob, seed, shape, transpose, outdim_parallel):
+  r = 0
+  for i in range(ITERATION):
+    r += jax.grad(sum_op(bm.jitconn.event_mv_prob_uniform), argnums=0)(
+      vector.astype(float), w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel
+    )
+  return r
+  
+@partial(jax.jit, static_argnums=(5, 6, 7))
+def jitconn_event_matvec_normal_taichi_grad(vector, w_mu, w_sigma, conn_prob, seed, shape, transpose, outdim_parallel):
+  r = 0
+  for i in range(ITERATION):
+    r += jax.grad(sum_op(bm.jitconn.event_mv_prob_normal_taichi), argnums=0)(
+      vector.astype(float), w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel
+    )
+  return r
+  
+@partial(jax.jit, static_argnums=(5, 6, 7))
+def jitconn_event_matvec_normal_grad(vector, w_mu, w_sigma, conn_prob, seed, shape, transpose, outdim_parallel):
+  r = 0
+  for i in range(ITERATION):
+    r += jax.grad(sum_op(bm.jitconn.event_mv_prob_normal), argnums=0)(
+      vector.astype(float), w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel
+    )
+  return r
+
+def test_jitconn_matvec_homo(shape, transpose, outdim_parallel, bool_event):
+  rng = bm.random.RandomState(seed=seed)
+  events = bm.as_jax(rng.random(shape[0] if transpose else shape[1])) < 0.1
+  if not bool_event:
+      events = events.astype(float)
+  # groundtruth = bm.as_jax(vector, dtype=float) @ bm.as_jax(dense)
+
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+
+  time0 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time1 = time.time()
+
+  time2 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time3 = time.time()
+
+  time4 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time5 = time.time()
+
+  time6 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time7 = time.time()
+
+  time8 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time9 = time.time()
+  
+  time10 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time11 = time.time()
+  
+  time12 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time13 = time.time()
+  
+  time14 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time15 = time.time()
+  
+  time16 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time17 = time.time()
+  
+  time18 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_taichi_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time19 = time.time()
+  
+
+  result = jax.block_until_ready(jitconn_event_matvec_homo_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_homo_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_homo_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_homo_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_homo_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+
+  time20 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time21 = time.time()
+
+  time22 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time23 = time.time()
+
+  time24 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time25 = time.time()
+
+  time26 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time27 = time.time()
+
+  time28 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time29 = time.time()
+  
+  time30 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time31 = time.time()
+  
+  time32 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time33 = time.time()
+  
+  time34 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time35 = time.time()
+  
+  time36 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time37 = time.time()
+  
+  time38 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_homo_grad(events, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time39 = time.time()
+
+  taichi_aot_time1 = (time1 - time0) * 1000
+  taichi_aot_time2 = (time3 - time2) * 1000
+  taichi_aot_time3 = (time5 - time4) * 1000
+  taichi_aot_time4 = (time7 - time6) * 1000
+  taichi_aot_time5 = (time9 - time8) * 1000
+  taichi_aot_time6 = (time11 - time10) * 1000
+  taichi_aot_time7 = (time13 - time12) * 1000
+  taichi_aot_time8 = (time15 - time14) * 1000
+  taichi_aot_time9 = (time17 - time16) * 1000
+  taichi_aot_time10 = (time19 - time18) * 1000
+  brainpy_time1 = (time21 - time20) * 1000
+  brainpy_time2 = (time23 - time22) * 1000
+  brainpy_time3 = (time25 - time24) * 1000
+  brainpy_time4 = (time27 - time26) * 1000
+  brainpy_time5 = (time29 - time28) * 1000
+  brainpy_time6 = (time31 - time30) * 1000
+  brainpy_time7 = (time33 - time32) * 1000
+  brainpy_time8 = (time35 - time34) * 1000
+  brainpy_time9 = (time37 - time36) * 1000
+  brainpy_time10 = (time39 - time38) * 1000
+  print('taichi_aot_1: ', taichi_aot_time1, 'ms')
+  print('taichi_aot_3: ', taichi_aot_time3, 'ms')
+  print('taichi_aot_5: ', taichi_aot_time5, 'ms')
+  print('taichi_aot_7: ', taichi_aot_time7, 'ms')
+  print('taichi_aot_9: ', taichi_aot_time9, 'ms')
+  print('brainpylib_1: ', brainpy_time1, 'ms')
+  print('brainpylib_3: ', brainpy_time3, 'ms')
+  print('brainpylib_5: ', brainpy_time5, 'ms')
+  print('brainpylib_7: ', brainpy_time7, 'ms')
+  print('brainpylib_9: ', brainpy_time9, 'ms')
+
+
+  return taichi_aot_time1, taichi_aot_time2, taichi_aot_time3, taichi_aot_time4, taichi_aot_time5,\
+      taichi_aot_time6, taichi_aot_time7, taichi_aot_time8, taichi_aot_time9, taichi_aot_time10,\
+      brainpy_time1, brainpy_time2, brainpy_time3, brainpy_time4, brainpy_time5, \
+      brainpy_time6, brainpy_time7, brainpy_time8, brainpy_time9, brainpy_time10
+
+def test_jitconn_matvec_uniform(shape, transpose, outdim_parallel, bool_event):
+  rng = bm.random.RandomState(seed=seed)
+  events = bm.as_jax(rng.random(shape[0] if transpose else shape[1])) < 0.1
+  if not bool_event:
+      events = events.astype(float)
+  # groundtruth = bm.as_jax(vector, dtype=float) @ bm.as_jax(dense)
+
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+
+  time0 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time1 = time.time()
+
+  time2 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time3 = time.time()
+
+  time4 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time5 = time.time()
+
+  time6 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time7 = time.time()
+
+  time8 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time9 = time.time()
+  
+  time10 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time11 = time.time()
+  
+  time12 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time13 = time.time()
+  
+  time14 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time15 = time.time()
+  
+  time16 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time17 = time.time()
+  
+  time18 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time19 = time.time()
+  
+
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+
+  time20 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time21 = time.time()
+
+  time22 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time23 = time.time()
+
+  time24 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time25 = time.time()
+
+  time26 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time27 = time.time()
+
+  time28 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time29 = time.time()
+  
+  time30 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time31 = time.time()
+  
+  time32 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time33 = time.time()
+  
+  time34 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time35 = time.time()
+  
+  time36 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time37 = time.time()
+  
+  time38 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time39 = time.time()
+
+  taichi_aot_time1 = (time1 - time0) * 1000
+  taichi_aot_time2 = (time3 - time2) * 1000
+  taichi_aot_time3 = (time5 - time4) * 1000
+  taichi_aot_time4 = (time7 - time6) * 1000
+  taichi_aot_time5 = (time9 - time8) * 1000
+  taichi_aot_time6 = (time11 - time10) * 1000
+  taichi_aot_time7 = (time13 - time12) * 1000
+  taichi_aot_time8 = (time15 - time14) * 1000
+  taichi_aot_time9 = (time17 - time16) * 1000
+  taichi_aot_time10 = (time19 - time18) * 1000
+  brainpy_time1 = (time21 - time20) * 1000
+  brainpy_time2 = (time23 - time22) * 1000
+  brainpy_time3 = (time25 - time24) * 1000
+  brainpy_time4 = (time27 - time26) * 1000
+  brainpy_time5 = (time29 - time28) * 1000
+  brainpy_time6 = (time31 - time30) * 1000
+  brainpy_time7 = (time33 - time32) * 1000
+  brainpy_time8 = (time35 - time34) * 1000
+  brainpy_time9 = (time37 - time36) * 1000
+  brainpy_time10 = (time39 - time38) * 1000
+  print('taichi_aot_1: ', taichi_aot_time1, 'ms')
+  print('taichi_aot_3: ', taichi_aot_time3, 'ms')
+  print('taichi_aot_5: ', taichi_aot_time5, 'ms')
+  print('taichi_aot_7: ', taichi_aot_time7, 'ms')
+  print('taichi_aot_9: ', taichi_aot_time9, 'ms')
+  print('brainpylib_1: ', brainpy_time1, 'ms')
+  print('brainpylib_3: ', brainpy_time3, 'ms')
+  print('brainpylib_5: ', brainpy_time5, 'ms')
+  print('brainpylib_7: ', brainpy_time7, 'ms')
+  print('brainpylib_9: ', brainpy_time9, 'ms')
+
+
+  return taichi_aot_time1, taichi_aot_time2, taichi_aot_time3, taichi_aot_time4, taichi_aot_time5,\
+      taichi_aot_time6, taichi_aot_time7, taichi_aot_time8, taichi_aot_time9, taichi_aot_time10,\
+      brainpy_time1, brainpy_time2, brainpy_time3, brainpy_time4, brainpy_time5, \
+      brainpy_time6, brainpy_time7, brainpy_time8, brainpy_time9, brainpy_time10
+
+def test_jitconn_matvec_normal(shape, transpose, outdim_parallel, bool_event):
+  rng = bm.random.RandomState(seed=seed)
+  events = bm.as_jax(rng.random(shape[0] if transpose else shape[1])) < 0.1
+  if not bool_event:
+      events = events.astype(float)
+  # groundtruth = bm.as_jax(vector, dtype=float) @ bm.as_jax(dense)
+
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+
+  time0 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time1 = time.time()
+
+  time2 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time3 = time.time()
+
+  time4 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time5 = time.time()
+
+  time6 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time7 = time.time()
+
+  time8 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time9 = time.time()
+  
+  time10 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time11 = time.time()
+  
+  time12 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time13 = time.time()
+  
+  time14 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time15 = time.time()
+  
+  time16 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time17 = time.time()
+  
+  time18 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time19 = time.time()
+  
+
+  result = jax.block_until_ready(jitconn_event_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_event_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+
+  time20 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time21 = time.time()
+
+  time22 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time23 = time.time()
+
+  time24 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time25 = time.time()
+
+  time26 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time27 = time.time()
+
+  time28 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time29 = time.time()
+  
+  time30 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time31 = time.time()
+  
+  time32 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time33 = time.time()
+  
+  time34 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time35 = time.time()
+  
+  time36 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time37 = time.time()
+  
+  time38 = time.time()
+  result = jax.block_until_ready(jitconn_event_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time39 = time.time()
+
+  taichi_aot_time1 = (time1 - time0) * 1000
+  taichi_aot_time2 = (time3 - time2) * 1000
+  taichi_aot_time3 = (time5 - time4) * 1000
+  taichi_aot_time4 = (time7 - time6) * 1000
+  taichi_aot_time5 = (time9 - time8) * 1000
+  taichi_aot_time6 = (time11 - time10) * 1000
+  taichi_aot_time7 = (time13 - time12) * 1000
+  taichi_aot_time8 = (time15 - time14) * 1000
+  taichi_aot_time9 = (time17 - time16) * 1000
+  taichi_aot_time10 = (time19 - time18) * 1000
+  brainpy_time1 = (time21 - time20) * 1000
+  brainpy_time2 = (time23 - time22) * 1000
+  brainpy_time3 = (time25 - time24) * 1000
+  brainpy_time4 = (time27 - time26) * 1000
+  brainpy_time5 = (time29 - time28) * 1000
+  brainpy_time6 = (time31 - time30) * 1000
+  brainpy_time7 = (time33 - time32) * 1000
+  brainpy_time8 = (time35 - time34) * 1000
+  brainpy_time9 = (time37 - time36) * 1000
+  brainpy_time10 = (time39 - time38) * 1000
+  print('taichi_aot_1: ', taichi_aot_time1, 'ms')
+  print('taichi_aot_3: ', taichi_aot_time3, 'ms')
+  print('taichi_aot_5: ', taichi_aot_time5, 'ms')
+  print('taichi_aot_7: ', taichi_aot_time7, 'ms')
+  print('taichi_aot_9: ', taichi_aot_time9, 'ms')
+  print('brainpylib_1: ', brainpy_time1, 'ms')
+  print('brainpylib_3: ', brainpy_time3, 'ms')
+  print('brainpylib_5: ', brainpy_time5, 'ms')
+  print('brainpylib_7: ', brainpy_time7, 'ms')
+  print('brainpylib_9: ', brainpy_time9, 'ms')
+
+
+  return taichi_aot_time1, taichi_aot_time2, taichi_aot_time3, taichi_aot_time4, taichi_aot_time5,\
+      taichi_aot_time6, taichi_aot_time7, taichi_aot_time8, taichi_aot_time9, taichi_aot_time10,\
+      brainpy_time1, brainpy_time2, brainpy_time3, brainpy_time4, brainpy_time5, \
+      brainpy_time6, brainpy_time7, brainpy_time8, brainpy_time9, brainpy_time10
+
+def test_jitconn_matvec(shape, _type, transpose, outdim_parallel, bool_event):
+  print('shape: ', shape, ' type: ', _type, ' transpose: ', transpose, ' outdim_parallel: ', outdim_parallel)
+  if _type == 'homo':
+    return test_jitconn_matvec_homo(shape, transpose, outdim_parallel, bool_event)
+  elif _type == 'uniform':
+    return test_jitconn_matvec_uniform(shape, transpose, outdim_parallel, bool_event)
+  elif _type == 'normal':
+    return test_jitconn_matvec_normal(shape, transpose, outdim_parallel, bool_event)
+  else:
+    raise ValueError
+
+PATH = os.path.dirname(os.path.abspath(__file__))
+
+# init dataframe
+df = pd.DataFrame(columns=['shape[0]', 'shape[1]', 'backend', 'type', 'transpose', 'outdim_parallel', 'bool_event',
+                            'taichi aot time1(ms)', 'taichi aot time2(ms)', 'taichi aot time3(ms)', 'taichi aot time4(ms)', 'taichi aot time5(ms)',
+                           'taichi aot time6(ms)', 'taichi aot time7(ms)', 'taichi aot time8(ms)', 'taichi aot time9(ms)', 'taichi aot time10(ms)',
+                           'brainpy time1(ms)', 'brainpy time2(ms)', 'brainpy time3(ms)', 'brainpy time4(ms)', 'brainpy time5(ms)',
+                           'brainpy time6(ms)', 'brainpy time7(ms)', 'brainpy time8(ms)', 'brainpy time9(ms)', 'brainpy time10(ms)'])
+
+
+### RECTANGULAR MATRIX
+if (bm.get_platform() == 'cpu'):
+  for shape1 in shape:
+    for shape2 in shape:
+      for _type in types:
+        for _outdim_parallel in outdim_parallel:
+          for _transpose in transpose:
+            for _bool_event in bool_event:
+              taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,\
+                taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,\
+                  brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, \
+                  brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10 = test_jitconn_matvec((shape1, shape2), _type, _transpose, _outdim_parallel, _bool_event)
+              # append to dataframe
+              df.loc[df.shape[0]] = [shape1, shape2, 'cpu', _type, _transpose, _outdim_parallel, _bool_event,
+                                  taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,
+                                    taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,
+                                    brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, 
+                                    brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10]
+  df.to_csv(f'{PATH}/jitconn_event_matvec_grad_cpu.csv', index=False)
+
+if (bm.get_platform() == 'gpu'):
+  for shape1 in shape:
+    for shape2 in shape:
+      for _type in types:
+        for _outdim_parallel in outdim_parallel:
+          for _transpose in transpose:
+            for _bool_event in bool_event:
+              taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,\
+                taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,\
+                  brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, \
+                  brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10 = test_jitconn_matvec((shape1, shape2), _type, _transpose, _outdim_parallel, _bool_event)
+              # append to dataframe
+              df.loc[df.shape[0]] = [shape1, shape2, 'gpu', _type, _transpose, _outdim_parallel, _bool_event,
+                                  taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,
+                                    taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,
+                                    brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, 
+                                    brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10]
+  df.to_csv(f'{PATH}/jitconn_event_matvec_grad_gpu.csv', index=False)
diff --git a/benchmarks/src/basic/jitconn_matvec_taichi_VS_jitconn_matvec.py b/benchmarks/src/basic/jitconn_matvec_taichi_VS_jitconn_matvec.py
new file mode 100644
index 0000000..14a19ae
--- /dev/null
+++ b/benchmarks/src/basic/jitconn_matvec_taichi_VS_jitconn_matvec.py
@@ -0,0 +1,560 @@
+# from jax_taichi import jax_taichi_call
+
+import time
+from functools import partial
+import os
+
+import brainpy as bp
+import brainpy.math as bm
+import jax
+import jax.numpy as jnp
+import numpy as np
+import pandas as pd
+import taichi as ti
+
+bm.set_platform('gpu')
+
+seed = 1234
+
+shape = [
+        1000, 
+        2500, 
+        5000, 
+        10000, 
+        25000, 
+        37500, 
+        50000
+        ]
+types = [
+       'homo', 
+       'uniform',
+       'normal'
+       ]
+transpose = [
+            True, 
+            False
+            ]
+outdim_parallel = [
+                  True,
+                  False,
+                  ]
+bool_event = False
+conn_prob = 0.05
+homo_data = 1.
+w_low = 0.
+w_high = 1.
+w_mu = 0.
+w_sigma = 0.1
+
+ITERATION = 100
+if bm.get_platform() == 'cpu':
+  ITERATION = 10
+
+print(bm.get_platform())
+
+@partial(jax.jit, static_argnums=(4, 5, 6))
+def jitconn_matvec_homo_taichi(vector, homo_data, conn_prob, seed, shape, transpose, outdim_parallel):
+  r = 0
+  for i in range(ITERATION):
+    r += bm.jitconn.mv_prob_homo_taichi(vector, homo_data, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel)
+  return r
+  
+@partial(jax.jit, static_argnums=(4, 5, 6))
+def jitconn_matvec_homo(vector, homo_data, conn_prob, seed, shape, transpose, outdim_parallel):
+  r = 0
+  for i in range(ITERATION):
+    r += bm.jitconn.mv_prob_homo(vector, homo_data, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel)
+  return r
+  
+@partial(jax.jit, static_argnums=(5, 6, 7))
+def jitconn_matvec_uniform_taichi(vector, w_low, w_high, conn_prob, seed, shape, transpose, outdim_parallel):
+  r = 0
+  for i in range(ITERATION):
+    r += bm.jitconn.mv_prob_uniform_taichi(vector, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel)
+  return r
+  
+@partial(jax.jit, static_argnums=(5, 6, 7))
+def jitconn_matvec_uniform(vector, w_low, w_high, conn_prob, seed, shape, transpose, outdim_parallel):
+  r = 0
+  for i in range(ITERATION):
+    r += bm.jitconn.mv_prob_uniform(vector, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel)
+  return r
+  
+@partial(jax.jit, static_argnums=(5, 6, 7))
+def jitconn_matvec_normal_taichi(vector, w_mu, w_sigma, conn_prob, seed, shape, transpose, outdim_parallel):
+  r = 0
+  for i in range(ITERATION):
+    r += bm.jitconn.mv_prob_normal_taichi(vector, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel)
+  return r
+  
+@partial(jax.jit, static_argnums=(5, 6, 7))
+def jitconn_matvec_normal(vector, w_mu, w_sigma, conn_prob, seed, shape, transpose, outdim_parallel):
+  r = 0
+  for i in range(ITERATION):
+    r += bm.jitconn.mv_prob_normal(vector, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel)
+  return r
+
+def test_jitconn_matvec_homo(shape, transpose, outdim_parallel):
+  rng = bm.random.RandomState(seed=seed)
+  vector = bm.as_jax(rng.random(shape[0] if transpose else shape[1]))
+
+  # groundtruth = bm.as_jax(vector, dtype=float) @ bm.as_jax(dense)
+
+  result = jax.block_until_ready(jitconn_matvec_homo_taichi(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_matvec_homo_taichi(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_matvec_homo_taichi(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_matvec_homo_taichi(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_matvec_homo_taichi(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+
+  time0 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_homo_taichi(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time1 = time.time()
+
+  time2 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_homo_taichi(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time3 = time.time()
+
+  time4 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_homo_taichi(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time5 = time.time()
+
+  time6 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_homo_taichi(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time7 = time.time()
+
+  time8 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_homo_taichi(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time9 = time.time()
+  
+  time10 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_homo_taichi(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time11 = time.time()
+  
+  time12 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_homo_taichi(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time13 = time.time()
+  
+  time14 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_homo_taichi(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time15 = time.time()
+  
+  time16 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_homo_taichi(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time17 = time.time()
+  
+  time18 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_homo_taichi(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time19 = time.time()
+  
+
+  result = jax.block_until_ready(jitconn_matvec_homo(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_matvec_homo(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_matvec_homo(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_matvec_homo(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_matvec_homo(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+
+  time20 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_homo(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time21 = time.time()
+
+  time22 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_homo(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time23 = time.time()
+
+  time24 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_homo(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time25 = time.time()
+
+  time26 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_homo(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time27 = time.time()
+
+  time28 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_homo(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time29 = time.time()
+  
+  time30 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_homo(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time31 = time.time()
+  
+  time32 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_homo(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time33 = time.time()
+  
+  time34 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_homo(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time35 = time.time()
+  
+  time36 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_homo(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time37 = time.time()
+  
+  time38 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_homo(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time39 = time.time()
+
+  taichi_aot_time1 = (time1 - time0) * 1000
+  taichi_aot_time2 = (time3 - time2) * 1000
+  taichi_aot_time3 = (time5 - time4) * 1000
+  taichi_aot_time4 = (time7 - time6) * 1000
+  taichi_aot_time5 = (time9 - time8) * 1000
+  taichi_aot_time6 = (time11 - time10) * 1000
+  taichi_aot_time7 = (time13 - time12) * 1000
+  taichi_aot_time8 = (time15 - time14) * 1000
+  taichi_aot_time9 = (time17 - time16) * 1000
+  taichi_aot_time10 = (time19 - time18) * 1000
+  brainpy_time1 = (time21 - time20) * 1000
+  brainpy_time2 = (time23 - time22) * 1000
+  brainpy_time3 = (time25 - time24) * 1000
+  brainpy_time4 = (time27 - time26) * 1000
+  brainpy_time5 = (time29 - time28) * 1000
+  brainpy_time6 = (time31 - time30) * 1000
+  brainpy_time7 = (time33 - time32) * 1000
+  brainpy_time8 = (time35 - time34) * 1000
+  brainpy_time9 = (time37 - time36) * 1000
+  brainpy_time10 = (time39 - time38) * 1000
+  print('taichi_aot_1: ', taichi_aot_time1, 'ms')
+  print('taichi_aot_3: ', taichi_aot_time3, 'ms')
+  print('taichi_aot_5: ', taichi_aot_time5, 'ms')
+  print('taichi_aot_7: ', taichi_aot_time7, 'ms')
+  print('taichi_aot_9: ', taichi_aot_time9, 'ms')
+  print('brainpylib_1: ', brainpy_time1, 'ms')
+  print('brainpylib_3: ', brainpy_time3, 'ms')
+  print('brainpylib_5: ', brainpy_time5, 'ms')
+  print('brainpylib_7: ', brainpy_time7, 'ms')
+  print('brainpylib_9: ', brainpy_time9, 'ms')
+
+
+  return taichi_aot_time1, taichi_aot_time2, taichi_aot_time3, taichi_aot_time4, taichi_aot_time5,\
+      taichi_aot_time6, taichi_aot_time7, taichi_aot_time8, taichi_aot_time9, taichi_aot_time10,\
+      brainpy_time1, brainpy_time2, brainpy_time3, brainpy_time4, brainpy_time5, \
+      brainpy_time6, brainpy_time7, brainpy_time8, brainpy_time9, brainpy_time10
+
+def test_jitconn_matvec_uniform(shape, transpose, outdim_parallel):
+  rng = bm.random.RandomState(seed=seed)
+  events = bm.as_jax(rng.random(shape[0] if transpose else shape[1]))
+
+  # groundtruth = bm.as_jax(vector, dtype=float) @ bm.as_jax(dense)
+
+  result1 = jax.block_until_ready(jitconn_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+
+  time0 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time1 = time.time()
+
+  time2 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time3 = time.time()
+
+  time4 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time5 = time.time()
+
+  time6 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time7 = time.time()
+
+  time8 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time9 = time.time()
+  
+  time10 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time11 = time.time()
+  
+  time12 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time13 = time.time()
+  
+  time14 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time15 = time.time()
+  
+  time16 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time17 = time.time()
+  
+  time18 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_uniform_taichi(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time19 = time.time()
+  
+
+  result = jax.block_until_ready(jitconn_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+
+  time20 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time21 = time.time()
+
+  time22 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time23 = time.time()
+
+  time24 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time25 = time.time()
+
+  time26 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time27 = time.time()
+
+  time28 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time29 = time.time()
+  
+  time30 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time31 = time.time()
+  
+  time32 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time33 = time.time()
+  
+  time34 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time35 = time.time()
+  
+  time36 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time37 = time.time()
+  
+  time38 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_uniform(events, w_low, w_high, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time39 = time.time()
+
+  taichi_aot_time1 = (time1 - time0) * 1000
+  taichi_aot_time2 = (time3 - time2) * 1000
+  taichi_aot_time3 = (time5 - time4) * 1000
+  taichi_aot_time4 = (time7 - time6) * 1000
+  taichi_aot_time5 = (time9 - time8) * 1000
+  taichi_aot_time6 = (time11 - time10) * 1000
+  taichi_aot_time7 = (time13 - time12) * 1000
+  taichi_aot_time8 = (time15 - time14) * 1000
+  taichi_aot_time9 = (time17 - time16) * 1000
+  taichi_aot_time10 = (time19 - time18) * 1000
+  brainpy_time1 = (time21 - time20) * 1000
+  brainpy_time2 = (time23 - time22) * 1000
+  brainpy_time3 = (time25 - time24) * 1000
+  brainpy_time4 = (time27 - time26) * 1000
+  brainpy_time5 = (time29 - time28) * 1000
+  brainpy_time6 = (time31 - time30) * 1000
+  brainpy_time7 = (time33 - time32) * 1000
+  brainpy_time8 = (time35 - time34) * 1000
+  brainpy_time9 = (time37 - time36) * 1000
+  brainpy_time10 = (time39 - time38) * 1000
+  print('taichi_aot_1: ', taichi_aot_time1, 'ms')
+  print('taichi_aot_3: ', taichi_aot_time3, 'ms')
+  print('taichi_aot_5: ', taichi_aot_time5, 'ms')
+  print('taichi_aot_7: ', taichi_aot_time7, 'ms')
+  print('taichi_aot_9: ', taichi_aot_time9, 'ms')
+  print('brainpylib_1: ', brainpy_time1, 'ms')
+  print('brainpylib_3: ', brainpy_time3, 'ms')
+  print('brainpylib_5: ', brainpy_time5, 'ms')
+  print('brainpylib_7: ', brainpy_time7, 'ms')
+  print('brainpylib_9: ', brainpy_time9, 'ms')
+
+
+  return taichi_aot_time1, taichi_aot_time2, taichi_aot_time3, taichi_aot_time4, taichi_aot_time5,\
+      taichi_aot_time6, taichi_aot_time7, taichi_aot_time8, taichi_aot_time9, taichi_aot_time10,\
+      brainpy_time1, brainpy_time2, brainpy_time3, brainpy_time4, brainpy_time5, \
+      brainpy_time6, brainpy_time7, brainpy_time8, brainpy_time9, brainpy_time10
+
+def test_jitconn_matvec_normal(shape, transpose, outdim_parallel):
+  rng = bm.random.RandomState(seed=seed)
+  events = bm.as_jax(rng.random(shape[0] if transpose else shape[1]))
+
+  # groundtruth = bm.as_jax(vector, dtype=float) @ bm.as_jax(dense)
+
+  result = jax.block_until_ready(jitconn_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+
+  time0 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time1 = time.time()
+
+  time2 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time3 = time.time()
+
+  time4 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time5 = time.time()
+
+  time6 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time7 = time.time()
+
+  time8 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time9 = time.time()
+  
+  time10 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time11 = time.time()
+  
+  time12 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time13 = time.time()
+  
+  time14 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time15 = time.time()
+  
+  time16 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time17 = time.time()
+  
+  time18 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_normal_taichi(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time19 = time.time()
+  
+
+  result = jax.block_until_ready(jitconn_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  result = jax.block_until_ready(jitconn_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+
+  time20 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time21 = time.time()
+
+  time22 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time23 = time.time()
+
+  time24 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time25 = time.time()
+
+  time26 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time27 = time.time()
+
+  time28 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time29 = time.time()
+  
+  time30 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time31 = time.time()
+  
+  time32 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time33 = time.time()
+  
+  time34 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time35 = time.time()
+  
+  time36 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time37 = time.time()
+  
+  time38 = time.time()
+  result = jax.block_until_ready(jitconn_matvec_normal(events, w_mu, w_sigma, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time39 = time.time()
+
+  taichi_aot_time1 = (time1 - time0) * 1000
+  taichi_aot_time2 = (time3 - time2) * 1000
+  taichi_aot_time3 = (time5 - time4) * 1000
+  taichi_aot_time4 = (time7 - time6) * 1000
+  taichi_aot_time5 = (time9 - time8) * 1000
+  taichi_aot_time6 = (time11 - time10) * 1000
+  taichi_aot_time7 = (time13 - time12) * 1000
+  taichi_aot_time8 = (time15 - time14) * 1000
+  taichi_aot_time9 = (time17 - time16) * 1000
+  taichi_aot_time10 = (time19 - time18) * 1000
+  brainpy_time1 = (time21 - time20) * 1000
+  brainpy_time2 = (time23 - time22) * 1000
+  brainpy_time3 = (time25 - time24) * 1000
+  brainpy_time4 = (time27 - time26) * 1000
+  brainpy_time5 = (time29 - time28) * 1000
+  brainpy_time6 = (time31 - time30) * 1000
+  brainpy_time7 = (time33 - time32) * 1000
+  brainpy_time8 = (time35 - time34) * 1000
+  brainpy_time9 = (time37 - time36) * 1000
+  brainpy_time10 = (time39 - time38) * 1000
+  print('taichi_aot_1: ', taichi_aot_time1, 'ms')
+  print('taichi_aot_3: ', taichi_aot_time3, 'ms')
+  print('taichi_aot_5: ', taichi_aot_time5, 'ms')
+  print('taichi_aot_7: ', taichi_aot_time7, 'ms')
+  print('taichi_aot_9: ', taichi_aot_time9, 'ms')
+  print('brainpylib_1: ', brainpy_time1, 'ms')
+  print('brainpylib_3: ', brainpy_time3, 'ms')
+  print('brainpylib_5: ', brainpy_time5, 'ms')
+  print('brainpylib_7: ', brainpy_time7, 'ms')
+  print('brainpylib_9: ', brainpy_time9, 'ms')
+
+
+  return taichi_aot_time1, taichi_aot_time2, taichi_aot_time3, taichi_aot_time4, taichi_aot_time5,\
+      taichi_aot_time6, taichi_aot_time7, taichi_aot_time8, taichi_aot_time9, taichi_aot_time10,\
+      brainpy_time1, brainpy_time2, brainpy_time3, brainpy_time4, brainpy_time5, \
+      brainpy_time6, brainpy_time7, brainpy_time8, brainpy_time9, brainpy_time10
+
+def test_jitconn_matvec(shape, _type, transpose, outdim_parallel):
+  print('shape: ', shape, ' type: ', _type, ' transpose: ', transpose, ' outdim_parallel: ', outdim_parallel)
+  if _type == 'homo':
+    return test_jitconn_matvec_homo(shape, transpose, outdim_parallel)
+  elif _type == 'uniform':
+    return test_jitconn_matvec_uniform(shape, transpose, outdim_parallel)
+  elif _type == 'normal':
+    return test_jitconn_matvec_normal(shape, transpose, outdim_parallel)
+  else:
+    raise ValueError
+
+PATH = os.path.dirname(os.path.abspath(__file__))
+
+# init dataframe
+df = pd.DataFrame(columns=['shape[0]', 'shape[1]', 'backend', 'type', 'transpose', 'outdim_parallel', 'bool_event',
+                            'taichi aot time1(ms)', 'taichi aot time2(ms)', 'taichi aot time3(ms)', 'taichi aot time4(ms)', 'taichi aot time5(ms)',
+                           'taichi aot time6(ms)', 'taichi aot time7(ms)', 'taichi aot time8(ms)', 'taichi aot time9(ms)', 'taichi aot time10(ms)',
+                           'brainpy time1(ms)', 'brainpy time2(ms)', 'brainpy time3(ms)', 'brainpy time4(ms)', 'brainpy time5(ms)',
+                           'brainpy time6(ms)', 'brainpy time7(ms)', 'brainpy time8(ms)', 'brainpy time9(ms)', 'brainpy time10(ms)'])
+
+### RECTANGULAR MATRIX
+if (bm.get_platform() == 'cpu'):
+  for shape1 in shape:
+    for shape2 in shape:
+      for _type in types:
+        for _outdim_parallel in outdim_parallel:
+          for _transpose in transpose:
+            taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,\
+                taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,\
+                  brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, \
+                  brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10 = test_jitconn_matvec((shape1, shape2), _type, _transpose, _outdim_parallel)
+            # append to dataframe
+            df.loc[df.shape[0]] = [shape1, shape2, 'cpu', _type, _transpose, _outdim_parallel, bool_event,
+                                  taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,
+                                    taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,
+                                    brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, 
+                                    brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10]
+  df.to_csv(f'{PATH}/jitconn_matvec_cpu.csv', index=False)
+
+if (bm.get_platform() == 'gpu'):
+  for shape1 in shape:
+    for shape2 in shape:
+      for _type in types:
+        for _outdim_parallel in outdim_parallel:
+          for _transpose in transpose:
+            taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,\
+                taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,\
+                  brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, \
+                  brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10 = test_jitconn_matvec((shape1, shape2), _type, _transpose, _outdim_parallel)
+            # append to dataframe
+            df.loc[df.shape[0]] = [shape1, shape2, 'cpu', _type, _transpose, _outdim_parallel, bool_event,
+                                  taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,
+                                    taichi_aot_time_6, taichi_aot_time_7, taichi_aot_time_8, taichi_aot_time_9, taichi_aot_time_10,
+                                    brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, 
+                                    brainpy_time_6, brainpy_time_7, brainpy_time_8, brainpy_time_9, brainpy_time_10]
+  df.to_csv(f'{PATH}/jitconn_matvec_gpu.csv', index=False)
diff --git a/benchmarks/src/basic/jitconn_matvec_taichi_VS_jitconn_matvec_grad.py b/benchmarks/src/basic/jitconn_matvec_taichi_VS_jitconn_matvec_grad.py
new file mode 100644
index 0000000..165c9b1
--- /dev/null
+++ b/benchmarks/src/basic/jitconn_matvec_taichi_VS_jitconn_matvec_grad.py
@@ -0,0 +1,736 @@
+# from jax_taichi import jax_taichi_call
+
+import time
+from functools import partial
+import os
+
+import brainpy as bp
+import brainpy.math as bm
+import jax
+import jax.numpy as jnp
+import numpy as np
+import pandas as pd
+import taichi as ti
+
+bm.set_platform('cpu')
+
+seed = 1234
+
+shape = [
+        1000, 
+        2500, 
+        5000, 
+        10000, 
+        25000, 
+        37500, 
+        50000
+        ]
+bool_event = False
+types = [
+       'homo', 
+       'uniform',
+       'normal'
+       ]
+transpose = [
+            True, 
+            False
+            ]
+outdim_parallel = [
+                  True,
+                  False,
+                  ]
+conn_prob = 0.05
+homo_data = 1.
+w_low = 0.
+w_high = 1.
+w_mu = 0.
+w_sigma = 0.1
+
+ITERATION = 100
+if bm.get_platform() == 'cpu':
+  ITERATION = 10
+
+print(bm.get_platform())
+
+def sum_op(op):
+  def func(*args, **kwargs):
+    r = op(*args, **kwargs)[0]
+    return r.sum()
+
+  return func
+
+@partial(jax.jit, static_argnums=(4, 5, 6))
+def jitconn_matvec_homo_taichi_grad(vector, homo_data, conn_prob, seed, shape, transpose, outdim_parallel):
+  r = 0
+  for i in range(ITERATION):
+    r += jax.grad(sum_op(bm.jitconn.mv_prob_homo_taichi), argnums=0)(
+      vector, homo_data, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel
+    )
+  return r
+  
+@partial(jax.jit, static_argnums=(4, 5, 6))
+def jitconn_matvec_homo_grad(vector, homo_data, conn_prob, seed, shape, transpose, outdim_parallel):
+  r = 0
+  for i in range(ITERATION):
+    r += jax.grad(sum_op(bm.jitconn.mv_prob_homo), argnums=0)(
+      vector, homo_data, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel
+    )
+  return r
+  
+@partial(jax.jit, static_argnums=(5, 6, 7))
+def jitconn_matvec_uniform_taichi_grad(vector, w_low, w_high, conn_prob, seed, shape, transpose, outdim_parallel):
+  r = 0
+  for i in range(ITERATION):
+    r += jax.grad(sum_op(bm.jitconn.mv_prob_uniform_taichi), argnums=0)(
+      vector, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel
+    )
+  return r
+  
+@partial(jax.jit, static_argnums=(5, 6, 7))
+def jitconn_matvec_uniform_grad(vector, w_low, w_high, conn_prob, seed, shape, transpose, outdim_parallel):
+  r = 0
+  for i in range(ITERATION):
+    r += jax.grad(sum_op(bm.jitconn.mv_prob_uniform), argnums=0)(
+      vector, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel
+    )
+  return r
+  
+@partial(jax.jit, static_argnums=(5, 6, 7))
+def jitconn_matvec_normal_taichi_grad(vector, w_mu, w_sigma, conn_prob, seed, shape, transpose, outdim_parallel):
+  r = 0
+  for i in range(ITERATION):
+    r += jax.grad(sum_op(bm.jitconn.mv_prob_normal_taichi), argnums=0)(
+      vector, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel
+    )
+  return r
+  
+@partial(jax.jit, static_argnums=(5, 6, 7))
+def jitconn_matvec_normal_grad(vector, w_mu, w_sigma, conn_prob, seed, shape, transpose, outdim_parallel):
+  r = 0
+  for i in range(ITERATION):
+    r += jax.grad(sum_op(bm.jitconn.mv_prob_normal), argnums=0)(
+      vector, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel
+    )
+  return r
+
+def test_jitconn_matvec_homo_cpu(shape, transpose, outdim_parallel):
+  rng = bm.random.RandomState(seed=seed)
+  vector = bm.as_jax(rng.random(shape[0] if transpose else shape[1]))
+
+  # groundtruth = bm.as_jax(vector, dtype=float) @ bm.as_jax(dense)
+
+  result1 = jax.block_until_ready(jitconn_matvec_homo_taichi_grad(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  # time.sleep(2)
+
+  time0 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_homo_taichi_grad(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time1 = time.time()
+  # time.sleep(2)
+
+  time2 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_homo_taichi_grad(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time3 = time.time()
+  # time.sleep(2)
+
+  time4 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_homo_taichi_grad(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time5 = time.time()
+  # time.sleep(2)
+
+  time6 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_homo_taichi_grad(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time7 = time.time()
+
+  time8 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_homo_taichi_grad(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time9 = time.time()
+
+  result2 = jax.block_until_ready(jitconn_matvec_homo_grad(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+
+  time12 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_homo_grad(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time13 = time.time()
+  # time.sleep(2)
+
+  time14 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_homo_grad(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time15 = time.time()
+  # time.sleep(2)
+
+  time16 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_homo_grad(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time17 = time.time()
+  # time.sleep(2)
+
+  time18 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_homo_grad(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time19 = time.time()
+
+  time20 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_homo_grad(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time21 = time.time()
+
+  taichi_aot_time1 = (time1 - time0) * 1000
+  taichi_aot_time2 = (time3 - time2) * 1000
+  taichi_aot_time3 = (time5 - time4) * 1000
+  taichi_aot_time4 = (time7 - time6) * 1000
+  taichi_aot_time5 = (time9 - time8) * 1000
+  brainpy_time1 = (time13 - time12) * 1000
+  brainpy_time2 = (time15 - time14) * 1000
+  brainpy_time3 = (time17 - time16) * 1000
+  brainpy_time4 = (time19 - time18) * 1000
+  brainpy_time5 = (time21 - time20) * 1000
+
+  print('taichi_aot_1: ', taichi_aot_time1, 'ms')
+  print('taichi_aot_2: ', taichi_aot_time2, 'ms')
+  print('taichi_aot_3: ', taichi_aot_time3, 'ms')
+  print('taichi_aot_4: ', taichi_aot_time4, 'ms')
+  print('taichi_aot_5: ', taichi_aot_time5, 'ms')
+  print('brainpylib_cpu_1: ', brainpy_time1, 'ms')
+  print('brainpylib_cpu_2: ', brainpy_time2, 'ms')
+  print('brainpylib_cpu_3: ', brainpy_time3, 'ms')
+  print('brainpylib_cpu_4: ', brainpy_time4, 'ms')
+  print('brainpylib_cpu_5: ', brainpy_time5, 'ms')
+  # assert(jnp.allclose(result1[0], result2))
+
+  speedup = (brainpy_time1 + brainpy_time2 + brainpy_time3 + brainpy_time4 + brainpy_time5) / \
+            (taichi_aot_time1 + taichi_aot_time2 + taichi_aot_time3 + taichi_aot_time4 + taichi_aot_time5) - 1
+
+  return taichi_aot_time1, taichi_aot_time2, taichi_aot_time3, taichi_aot_time4, taichi_aot_time5,\
+      brainpy_time1, brainpy_time2, brainpy_time3, brainpy_time4, brainpy_time5, speedup
+
+def test_jitconn_matvec_uniform_cpu(shape, transpose, outdim_parallel):
+  rng = bm.random.RandomState(seed=seed)
+  events = bm.as_jax(rng.random(shape[0] if transpose else shape[1]))
+
+  # groundtruth = bm.as_jax(vector, dtype=float) @ bm.as_jax(dense)
+
+  result1 = jax.block_until_ready(jitconn_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  # time.sleep(2)
+
+  time0 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time1 = time.time()
+  # time.sleep(2)
+
+  time2 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time3 = time.time()
+  # time.sleep(2)
+
+  time4 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time5 = time.time()
+  # time.sleep(2)
+
+  time6 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time7 = time.time()
+
+  time8 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time9 = time.time()
+
+  result2 = jax.block_until_ready(jitconn_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+#   print(result1[0])
+#   print(result2)
+#   print(groundtruth - result1[0])
+#   print(groundtruth - result2)
+  
+  # print(result1[0] - result2)
+  # print(bm.allclose(groundtruth, result1[0]))
+  # print(bm.allclose(groundtruth, result2))
+  # assert bm.allclose(result1[0], result2)
+
+  time12 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time13 = time.time()
+  # time.sleep(2)
+
+  time14 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time15 = time.time()
+  # time.sleep(2)
+
+  time16 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time17 = time.time()
+  # time.sleep(2)
+
+  time18 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time19 = time.time()
+
+  time20 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time21 = time.time()
+
+  taichi_aot_time1 = (time1 - time0) * 1000
+  taichi_aot_time2 = (time3 - time2) * 1000
+  taichi_aot_time3 = (time5 - time4) * 1000
+  taichi_aot_time4 = (time7 - time6) * 1000
+  taichi_aot_time5 = (time9 - time8) * 1000
+  brainpy_time1 = (time13 - time12) * 1000
+  brainpy_time2 = (time15 - time14) * 1000
+  brainpy_time3 = (time17 - time16) * 1000
+  brainpy_time4 = (time19 - time18) * 1000
+  brainpy_time5 = (time21 - time20) * 1000
+
+  print('taichi_aot_1: ', taichi_aot_time1, 'ms')
+  print('taichi_aot_2: ', taichi_aot_time2, 'ms')
+  print('taichi_aot_3: ', taichi_aot_time3, 'ms')
+  print('taichi_aot_4: ', taichi_aot_time4, 'ms')
+  print('taichi_aot_5: ', taichi_aot_time5, 'ms')
+  print('brainpylib_cpu_1: ', brainpy_time1, 'ms')
+  print('brainpylib_cpu_2: ', brainpy_time2, 'ms')
+  print('brainpylib_cpu_3: ', brainpy_time3, 'ms')
+  print('brainpylib_cpu_4: ', brainpy_time4, 'ms')
+  print('brainpylib_cpu_5: ', brainpy_time5, 'ms')
+  # assert(jnp.allclose(result1[0], result2))
+
+  speedup = (brainpy_time1 + brainpy_time2 + brainpy_time3 + brainpy_time4 + brainpy_time5) / \
+            (taichi_aot_time1 + taichi_aot_time2 + taichi_aot_time3 + taichi_aot_time4 + taichi_aot_time5) - 1
+
+  return taichi_aot_time1, taichi_aot_time2, taichi_aot_time3, taichi_aot_time4, taichi_aot_time5,\
+      brainpy_time1, brainpy_time2, brainpy_time3, brainpy_time4, brainpy_time5, speedup
+
+def test_jitconn_matvec_normal_cpu(shape, transpose, outdim_parallel):
+  rng = bm.random.RandomState(seed=seed)
+  events = bm.as_jax(rng.random(shape[0] if transpose else shape[1]))
+
+  # groundtruth = bm.as_jax(vector, dtype=float) @ bm.as_jax(dense)
+
+  result1 = jax.block_until_ready(jitconn_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  # time.sleep(2)
+
+  time0 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time1 = time.time()
+  # time.sleep(2)
+
+  time2 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time3 = time.time()
+  # time.sleep(2)
+
+  time4 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time5 = time.time()
+  # time.sleep(2)
+
+  time6 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time7 = time.time()
+
+  time8 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time9 = time.time()
+
+  result2 = jax.block_until_ready(jitconn_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+#   print(result1[0])
+#   print(result2)
+#   print(groundtruth - result1[0])
+#   print(groundtruth - result2)
+  
+  # print(result1[0] - result2)
+  # print(bm.allclose(groundtruth, result1[0]))
+  # print(bm.allclose(groundtruth, result2))
+  # assert bm.allclose(result1[0], result2)
+
+  time12 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time13 = time.time()
+  # time.sleep(2)
+
+  time14 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time15 = time.time()
+  # time.sleep(2)
+
+  time16 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time17 = time.time()
+  # time.sleep(2)
+
+  time18 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time19 = time.time()
+
+  time20 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time21 = time.time()
+
+  taichi_aot_time1 = (time1 - time0) * 1000
+  taichi_aot_time2 = (time3 - time2) * 1000
+  taichi_aot_time3 = (time5 - time4) * 1000
+  taichi_aot_time4 = (time7 - time6) * 1000
+  taichi_aot_time5 = (time9 - time8) * 1000
+  brainpy_time1 = (time13 - time12) * 1000
+  brainpy_time2 = (time15 - time14) * 1000
+  brainpy_time3 = (time17 - time16) * 1000
+  brainpy_time4 = (time19 - time18) * 1000
+  brainpy_time5 = (time21 - time20) * 1000
+
+  print('taichi_aot_1: ', taichi_aot_time1, 'ms')
+  print('taichi_aot_2: ', taichi_aot_time2, 'ms')
+  print('taichi_aot_3: ', taichi_aot_time3, 'ms')
+  print('taichi_aot_4: ', taichi_aot_time4, 'ms')
+  print('taichi_aot_5: ', taichi_aot_time5, 'ms')
+  print('brainpylib_cpu_1: ', brainpy_time1, 'ms')
+  print('brainpylib_cpu_2: ', brainpy_time2, 'ms')
+  print('brainpylib_cpu_3: ', brainpy_time3, 'ms')
+  print('brainpylib_cpu_4: ', brainpy_time4, 'ms')
+  print('brainpylib_cpu_5: ', brainpy_time5, 'ms')
+  # assert(jnp.allclose(result1[0], result2))
+
+  speedup = (brainpy_time1 + brainpy_time2 + brainpy_time3 + brainpy_time4 + brainpy_time5) / \
+            (taichi_aot_time1 + taichi_aot_time2 + taichi_aot_time3 + taichi_aot_time4 + taichi_aot_time5) - 1
+
+  return taichi_aot_time1, taichi_aot_time2, taichi_aot_time3, taichi_aot_time4, taichi_aot_time5,\
+      brainpy_time1, brainpy_time2, brainpy_time3, brainpy_time4, brainpy_time5, speedup
+
+def test_jitconn_matvec_homo_gpu(shape, transpose, outdim_parallel):
+  rng = bm.random.RandomState(seed=seed)
+  vector = bm.as_jax(rng.random(shape[0] if transpose else shape[1]))
+
+  # groundtruth = bm.as_jax(vector, dtype=float) @ bm.as_jax(dense)
+
+  result1 = jax.block_until_ready(jitconn_matvec_homo_taichi_grad(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  # time.sleep(2)
+
+  time0 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_homo_taichi_grad(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time1 = time.time()
+  # time.sleep(2)
+
+  time2 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_homo_taichi_grad(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time3 = time.time()
+  # time.sleep(2)
+
+  time4 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_homo_taichi_grad(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time5 = time.time()
+  # time.sleep(2)
+
+  time6 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_homo_taichi_grad(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time7 = time.time()
+
+  time8 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_homo_taichi_grad(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time9 = time.time()
+
+  result2 = jax.block_until_ready(jitconn_matvec_homo_grad(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+#   print(result1[0])
+#   print(result2)
+#   print(groundtruth - result1[0])
+#   print(groundtruth - result2)
+  
+  # print(result1[0] - result2)
+  # print(bm.allclose(groundtruth, result1[0]))
+  # print(bm.allclose(groundtruth, result2))
+  # assert bm.allclose(result1[0], result2)
+
+  time12 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_homo_grad(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time13 = time.time()
+  # time.sleep(2)
+
+  time14 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_homo_grad(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time15 = time.time()
+  # time.sleep(2)
+
+  time16 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_homo_grad(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time17 = time.time()
+  # time.sleep(2)
+
+  time18 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_homo_grad(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time19 = time.time()
+
+  time20 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_homo_grad(vector, homo_data, conn_prob, seed, shape=shape, outdim_parallel=outdim_parallel, transpose=transpose))
+  time21 = time.time()
+
+  taichi_aot_time1 = (time1 - time0) * 1000
+  taichi_aot_time2 = (time3 - time2) * 1000
+  taichi_aot_time3 = (time5 - time4) * 1000
+  taichi_aot_time4 = (time7 - time6) * 1000
+  taichi_aot_time5 = (time9 - time8) * 1000
+  brainpy_time1 = (time13 - time12) * 1000
+  brainpy_time2 = (time15 - time14) * 1000
+  brainpy_time3 = (time17 - time16) * 1000
+  brainpy_time4 = (time19 - time18) * 1000
+  brainpy_time5 = (time21 - time20) * 1000
+
+  print('taichi_aot_1: ', taichi_aot_time1, 'ms')
+  print('taichi_aot_2: ', taichi_aot_time2, 'ms')
+  print('taichi_aot_3: ', taichi_aot_time3, 'ms')
+  print('taichi_aot_4: ', taichi_aot_time4, 'ms')
+  print('taichi_aot_5: ', taichi_aot_time5, 'ms')
+  print('brainpylib_1: ', brainpy_time1, 'ms')
+  print('brainpylib_2: ', brainpy_time2, 'ms')
+  print('brainpylib_3: ', brainpy_time3, 'ms')
+  print('brainpylib_4: ', brainpy_time4, 'ms')
+  print('brainpylib_5: ', brainpy_time5, 'ms')
+  # assert(jnp.allclose(result1[0], result2))
+
+  speedup = (brainpy_time1 + brainpy_time2 + brainpy_time3 + brainpy_time4 + brainpy_time5) / \
+            (taichi_aot_time1 + taichi_aot_time2 + taichi_aot_time3 + taichi_aot_time4 + taichi_aot_time5) - 1
+
+  return taichi_aot_time1, taichi_aot_time2, taichi_aot_time3, taichi_aot_time4, taichi_aot_time5,\
+      brainpy_time1, brainpy_time2, brainpy_time3, brainpy_time4, brainpy_time5, speedup
+
+def test_jitconn_matvec_uniform_gpu(shape, transpose, outdim_parallel):
+  rng = bm.random.RandomState(seed=seed)
+  events = bm.as_jax(rng.random(shape[0] if transpose else shape[1]))
+
+  # groundtruth = bm.as_jax(vector, dtype=float) @ bm.as_jax(dense)
+
+  result1 = jax.block_until_ready(jitconn_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  # time.sleep(2)
+
+  time0 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time1 = time.time()
+  # time.sleep(2)
+
+  time2 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time3 = time.time()
+  # time.sleep(2)
+
+  time4 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time5 = time.time()
+  # time.sleep(2)
+
+  time6 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time7 = time.time()
+
+  time8 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_uniform_taichi_grad(events, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time9 = time.time()
+
+  result2 = jax.block_until_ready(jitconn_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+#   print(result1[0])
+#   print(result2)
+#   print(groundtruth - result1[0])
+#   print(groundtruth - result2)
+  
+  # print(result1[0] - result2)
+  # print(bm.allclose(groundtruth, result1[0]))
+  # print(bm.allclose(groundtruth, result2))
+  # assert bm.allclose(result1[0], result2)
+
+  time12 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time13 = time.time()
+  # time.sleep(2)
+
+  time14 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time15 = time.time()
+  # time.sleep(2)
+
+  time16 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time17 = time.time()
+  # time.sleep(2)
+
+  time18 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time19 = time.time()
+
+  time20 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_uniform_grad(events, w_low, w_high, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time21 = time.time()
+
+  taichi_aot_time1 = (time1 - time0) * 1000
+  taichi_aot_time2 = (time3 - time2) * 1000
+  taichi_aot_time3 = (time5 - time4) * 1000
+  taichi_aot_time4 = (time7 - time6) * 1000
+  taichi_aot_time5 = (time9 - time8) * 1000
+  brainpy_time1 = (time13 - time12) * 1000
+  brainpy_time2 = (time15 - time14) * 1000
+  brainpy_time3 = (time17 - time16) * 1000
+  brainpy_time4 = (time19 - time18) * 1000
+  brainpy_time5 = (time21 - time20) * 1000
+
+  print('taichi_aot_1: ', taichi_aot_time1, 'ms')
+  print('taichi_aot_2: ', taichi_aot_time2, 'ms')
+  print('taichi_aot_3: ', taichi_aot_time3, 'ms')
+  print('taichi_aot_4: ', taichi_aot_time4, 'ms')
+  print('taichi_aot_5: ', taichi_aot_time5, 'ms')
+  print('brainpylib_1: ', brainpy_time1, 'ms')
+  print('brainpylib_2: ', brainpy_time2, 'ms')
+  print('brainpylib_3: ', brainpy_time3, 'ms')
+  print('brainpylib_4: ', brainpy_time4, 'ms')
+  print('brainpylib_5: ', brainpy_time5, 'ms')
+  # assert(jnp.allclose(result1[0], result2))
+
+  speedup = (brainpy_time1 + brainpy_time2 + brainpy_time3 + brainpy_time4 + brainpy_time5) / \
+            (taichi_aot_time1 + taichi_aot_time2 + taichi_aot_time3 + taichi_aot_time4 + taichi_aot_time5) - 1
+
+  return taichi_aot_time1, taichi_aot_time2, taichi_aot_time3, taichi_aot_time4, taichi_aot_time5,\
+      brainpy_time1, brainpy_time2, brainpy_time3, brainpy_time4, brainpy_time5, speedup
+
+def test_jitconn_matvec_normal_gpu(shape, transpose, outdim_parallel):
+  rng = bm.random.RandomState(seed=seed)
+  events = bm.as_jax(rng.random(shape[0] if transpose else shape[1]))
+
+  # groundtruth = bm.as_jax(vector, dtype=float) @ bm.as_jax(dense)
+
+  result1 = jax.block_until_ready(jitconn_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  # time.sleep(2)
+
+  time0 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time1 = time.time()
+  # time.sleep(2)
+
+  time2 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time3 = time.time()
+  # time.sleep(2)
+
+  time4 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time5 = time.time()
+  # time.sleep(2)
+
+  time6 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time7 = time.time()
+
+  time8 = time.time()
+  result1 = jax.block_until_ready(jitconn_matvec_normal_taichi_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time9 = time.time()
+
+  result2 = jax.block_until_ready(jitconn_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+#   print(result1[0])
+#   print(result2)
+#   print(groundtruth - result1[0])
+#   print(groundtruth - result2)
+  
+  # print(result1[0] - result2)
+  # print(bm.allclose(groundtruth, result1[0]))
+  # print(bm.allclose(groundtruth, result2))
+  # assert bm.allclose(result1[0], result2)
+
+  time12 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time13 = time.time()
+  # time.sleep(2)
+
+  time14 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time15 = time.time()
+  # time.sleep(2)
+
+  time16 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time17 = time.time()
+  # time.sleep(2)
+
+  time18 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time19 = time.time()
+
+  time20 = time.time()
+  result2 = jax.block_until_ready(jitconn_matvec_normal_grad(events, w_mu, w_sigma, conn_prob, seed, shape=shape, transpose=transpose, outdim_parallel=outdim_parallel))
+  time21 = time.time()
+
+  taichi_aot_time1 = (time1 - time0) * 1000
+  taichi_aot_time2 = (time3 - time2) * 1000
+  taichi_aot_time3 = (time5 - time4) * 1000
+  taichi_aot_time4 = (time7 - time6) * 1000
+  taichi_aot_time5 = (time9 - time8) * 1000
+  brainpy_time1 = (time13 - time12) * 1000
+  brainpy_time2 = (time15 - time14) * 1000
+  brainpy_time3 = (time17 - time16) * 1000
+  brainpy_time4 = (time19 - time18) * 1000
+  brainpy_time5 = (time21 - time20) * 1000
+
+  print('taichi_aot_1: ', taichi_aot_time1, 'ms')
+  print('taichi_aot_2: ', taichi_aot_time2, 'ms')
+  print('taichi_aot_3: ', taichi_aot_time3, 'ms')
+  print('taichi_aot_4: ', taichi_aot_time4, 'ms')
+  print('taichi_aot_5: ', taichi_aot_time5, 'ms')
+  print('brainpylib_1: ', brainpy_time1, 'ms')
+  print('brainpylib_2: ', brainpy_time2, 'ms')
+  print('brainpylib_3: ', brainpy_time3, 'ms')
+  print('brainpylib_4: ', brainpy_time4, 'ms')
+  print('brainpylib_5: ', brainpy_time5, 'ms')
+  # assert(jnp.allclose(result1[0], result2))
+
+  speedup = (brainpy_time1 + brainpy_time2 + brainpy_time3 + brainpy_time4 + brainpy_time5) / \
+            (taichi_aot_time1 + taichi_aot_time2 + taichi_aot_time3 + taichi_aot_time4 + taichi_aot_time5) - 1
+
+  return taichi_aot_time1, taichi_aot_time2, taichi_aot_time3, taichi_aot_time4, taichi_aot_time5,\
+      brainpy_time1, brainpy_time2, brainpy_time3, brainpy_time4, brainpy_time5, speedup
+
+
+def test_jitconn_matvec_cpu(shape, _type, transpose, outdim_parallel):
+  print('shape: ', shape, ' type: ', _type, ' transpose: ', transpose, ' outdim_parallel: ', outdim_parallel)
+  if _type == 'homo':
+    return test_jitconn_matvec_homo_cpu(shape, transpose, outdim_parallel)
+  elif _type == 'uniform':
+    return test_jitconn_matvec_uniform_cpu(shape, transpose, outdim_parallel)
+  elif _type == 'normal':
+    return test_jitconn_matvec_normal_cpu(shape, transpose, outdim_parallel)
+  else:
+    raise ValueError
+
+
+def test_jitconn_matvec_gpu(shape, _type, transpose, outdim_parallel):
+  print('shape: ', shape, ' type: ', _type, ' transpose: ', transpose, ' outdim_parallel: ', outdim_parallel)
+  if _type == 'homo':
+    return test_jitconn_matvec_homo_gpu(shape, transpose, outdim_parallel)
+  elif _type == 'uniform':
+    return test_jitconn_matvec_uniform_gpu(shape, transpose, outdim_parallel)
+  elif _type == 'normal':
+    return test_jitconn_matvec_normal_gpu(shape, transpose, outdim_parallel)
+  else:
+    raise ValueError
+
+PATH = os.path.dirname(os.path.abspath(__file__))
+
+# init dataframe
+df = pd.DataFrame(columns=['shape[0]', 'shape[1]', 'backend', 'type', 'transpose', 'outdim_parallel',
+                           'taichi aot time1(ms)', 'taichi aot time2(ms)', 'taichi aot time3(ms)', 'taichi aot time4(ms)', 'taichi aot time5(ms)',
+                           'brainpy time1(ms)', 'brainpy time2(ms)', 'brainpy time3(ms)', 'brainpy time4(ms)', 'brainpy time5(ms)',
+                           'speedup'])
+
+### RECTANGULAR MATRIX
+if (bm.get_platform() == 'cpu'):
+  for shape1 in shape:
+    for shape2 in shape:
+      for _type in types:
+        for _outdim_parallel in outdim_parallel:
+          for _transpose in transpose:
+            taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,\
+                brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, speedup = test_jitconn_matvec_cpu((shape1, shape2), _type, _transpose, _outdim_parallel)
+            # append to dataframe
+            df.loc[df.shape[0]] = [shape1, shape2, 'cpu', _type, _transpose, _outdim_parallel,
+                                  taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,
+                                  brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, speedup]
+  df.to_csv(f'{PATH}/jitconn_matvec_grad_cpu.csv', index=False)
+
+if (bm.get_platform() == 'gpu'):
+  for shape1 in shape:
+    for shape2 in shape:
+      for _type in types:
+        for _outdim_parallel in outdim_parallel:
+          for _transpose in transpose:
+            taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,\
+                brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, speedup = test_jitconn_matvec_gpu((shape1, shape2), _type, _transpose, _outdim_parallel)
+            # append to dataframe
+            df.loc[df.shape[0]] = [shape1, shape2, 'gpu', _type, _transpose, _outdim_parallel,
+                                  taichi_aot_time_1, taichi_aot_time_2, taichi_aot_time_3, taichi_aot_time_4, taichi_aot_time_5,
+                                  brainpy_time_1, brainpy_time_2, brainpy_time_3, brainpy_time_4, brainpy_time_5, speedup]
+  df.to_csv(f'{PATH}/jitconn_matvec_grad_gpu.csv', index=False)
diff --git a/benchmarks/src/model/Matlab/README.md b/benchmarks/src/model/Matlab/README.md
new file mode 100644
index 0000000..9b1bf76
--- /dev/null
+++ b/benchmarks/src/model/Matlab/README.md
@@ -0,0 +1,3 @@
+Matlab original codes and files
+
+The codes are also available on https://github.com/xjwanglab/JoglekarEtAl2018_Neuron
diff --git a/benchmarks/src/model/Matlab/caret2/badcons_4pt5.mat b/benchmarks/src/model/Matlab/caret2/badcons_4pt5.mat
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diff --git a/benchmarks/src/model/Matlab/caret2/grate.mat b/benchmarks/src/model/Matlab/caret2/grate.mat
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diff --git a/benchmarks/src/model/Matlab/caret2/nofbgoodcons_5pt5.mat b/benchmarks/src/model/Matlab/caret2/nofbgoodcons_5pt5.mat
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diff --git a/benchmarks/src/model/Matlab/efelenMatpython.mat b/benchmarks/src/model/Matlab/efelenMatpython.mat
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diff --git a/benchmarks/src/model/Matlab/hierValspython.mat b/benchmarks/src/model/Matlab/hierValspython.mat
new file mode 100644
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diff --git a/benchmarks/src/model/Matlab/rishimodel_generatefigs_rate.m b/benchmarks/src/model/Matlab/rishimodel_generatefigs_rate.m
new file mode 100644
index 0000000..34c4ea4
--- /dev/null
+++ b/benchmarks/src/model/Matlab/rishimodel_generatefigs_rate.m
@@ -0,0 +1,1778 @@
+clear all; 
+%this is to generate figures for the rate models in joglekar et al neuron
+%2018
+load subgraphData.mat %loading fln and hierarchy data. 
+
+netwParams=struct('nNodes',nNodes,'alpha',0.68);
+
+netwParams.hier=hierVals/max(hierVals);%hierarchy normalized. 
+betaE = .066 ; betaI = .351 ; %Hz/pA
+
+muEE = 33.7 ; muIE = 25.3; omegaEE = 24.3 ; omegaEI = 19.7 ;  netwParams.alpha=.68;omegaIE = 12.2 ; omegaII = 12.5 ; 
+%omegaEI = 25.2 ; muEE = 51.5;
+cv(1,1:3) = [0.4660, 0.6740, 0.1880]; cv(2,1:3) = [0.4940,0.1840,0.5560];%color scheme.
+
+%various cases below plot figures in neuron paper. 
+
+caseval = 0; %normal fln values (not removing fb, symmetrizing fln matrix etc.) %netwParams.alpha=0
+%caseval = 1; flnMat = tril(flnMat);  %removing fb worsens propagation 
+%caseval = -1; netwParams.alpha=0;  %no hierarchy 
+%caseval = 2; flnMat = (flnMat+flnMat')/2; netwParams.alpha=.6;%symmetrizing fln matrix -- using arithmetic mean. 
+%caseval = 3; flnMat = sqrt(flnMat.*flnMat'); %symmetrizing fln -- geometric mean. 
+%caseval = 4; %change threshold and connection density .. measure propagation ratio
+%caseval = 5; nofb=0;%plot how muEE changes and activity in 24c blows up or too low 
+%flnMat = tril(flnMat); %to test case5 w/out fb. % other tests: nofb=1; flnMat = tril(flnMat);%netwParams.alpha=0;
+%caseval = 6; %histogram showing few strong connections vs all flns. 
+%caseval = 7; %for figure about balanced amp. in local circuit  
+%caseval = 8; %for figure about either blowup or badprop in 24c vs V1. along with input to V1. 
+%caseval = 9; %jorge's mejias sci advances figure 
+%caseval = 10; %jorge's mejias sci advances figure
+%caseval = 11; %compare max rate control case / no fb / symmetrized fln with arithmetic / geometric mean. 
+%caseval = 12; %caret figs. for brain. 
+%caseval = 13; %jorge mejias science advances -- fig oscillations. 
+%caseval = 14 ; %contour plot large scale system  
+%caseval = -2; flnMat = (flnMat+flnMat')/2; netwParams.alpha=0; 
+%caseval = -3; flnMat = (flnMat+flnMat')/2; netwParams.alpha=0; 
+%caseval = 15; %burkhalter result implement in supplementary. vary muIE
+
+%%%%%%%%%%%% pulse to V1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%basic network setup below
+
+localParams.bgInh=zeros(netwParams.nNodes,1);%background inhibitory
+localParams.tauE=2e-2; localParams.tauI=1e-2; % time constants
+tParams.nSteps=5e4;tParams.dt=2e-4;
+tSteps=(1:tParams.nSteps)*tParams.dt;
+toplotstart=round(1.75/tParams.dt);toplotend=round(5/tParams.dt);
+%input to v1
+inpArea='V1'; inpType='whiteNoise'; areaInput.idx=areaMap(inpArea);nNodes=29;
+currParams.desiredSs=[10*ones(nNodes,1); 35*ones(nNodes,1)]; 
+localParams.noiseStd=0;  % No local noise here for pulse input to V1
+
+lw = 1; fsize=7;fsizelab=7;msize=7; poster = 0;
+
+%poster=1;
+if poster==1
+    fsize=10;fsizelab=10;msize=10;
+end
+
+if caseval < 4  
+    for count=1:2
+        if count==1
+            omegaEI = 19.7 ; muEE = 33.7 ; %weak GBA
+        else
+            omegaEI = 25.2 ; muEE = 51.5;%strong GBA
+        end
+        
+        localParams.ee=betaE*omegaEE*(1+netwParams.alpha*netwParams.hier);
+        localParams.ie=betaI*omegaIE*(1+netwParams.alpha*netwParams.hier);
+        localParams.ei=-betaE*omegaEI; 
+        localParams.ii=-betaI*omegaII;         
+             
+        ldParams.ee=betaE*muEE*(1+netwParams.alpha*netwParams.hier);
+        ldParams.ie=betaI*muIE*(1+netwParams.alpha*netwParams.hier);     
+        
+        if caseval == -3
+          localParams.ee=betaE*omegaEE*(1+.68*netwParams.hier); %note eta = .68 as in chaudhuri 2015 neuron
+          localParams.ie=betaI*omegaIE*(1+.68*netwParams.hier);
+        end    
+       
+        ldConns.ee= bsxfun(@times,flnMat,ldParams.ee);
+        ldConns.ie= bsxfun(@times,flnMat,ldParams.ie);
+
+        
+%         %if caseval == 15
+%             burkmat = zeros(nNodes, nNodes);
+%             mf = .1;  %vary mf. 
+%             %burkhalter like scaling of long range E to I. 
+%             for r = 1:nNodes 
+%                 for s = 1:nNodes
+%                     burkmat(r,s) = max(0,netwParams.hier(r,1) - netwParams.hier(s,1));
+% %                    burkmat(r,s) = netwParams.hier(r,1) - netwParams.hier(s,1);
+%                 end ;
+%             end;
+%             burkmat = 1 + mf*burkmat;
+%             ldConns.ie = bsxfun(@times,ldConns.ie,burkmat);
+%         %end
+        
+        
+        nNodes=size(ldConns.ee,1);%29 nodes. 
+        %build local and long range connections. 
+        wEe=diag(-1+localParams.ee)+ldConns.ee;
+        wEi=localParams.ei*eye(nNodes);%these ws would be 29x29 identity matrices. 
+        wIe=diag(localParams.ie)+ldConns.ie;
+        wIi=(-1+localParams.ii)*eye(nNodes);%compare this to eqn 4 - where does -1 come from??
+
+        A = [wEe/localParams.tauE wEi/localParams.tauE;...
+            wIe/localParams.tauI wIi/localParams.tauI];
+
+        currParams.A=A; 
+
+        B=currParams.A;%B=params.A;
+                B(1:nNodes,:)=B(1:nNodes,:)*localParams.tauE;
+                B((nNodes+1):end,:)=B((nNodes+1):end,:)*localParams.tauI;
+                currs=-B*currParams.desiredSs; %currs=-B*params.desiredSs;
+
+        localParams.bgExc=currs(1:nNodes); localParams.bgInh=currs((nNodes+1):end);
+        bgCurr=[localParams.bgExc; localParams.bgInh];%bg = background
+
+        combMat=A;
+        combMat(1:nNodes,:)=combMat(1:nNodes,:)*localParams.tauE;
+        combMat((nNodes+1):end,:)=combMat((nNodes+1):end,:)*localParams.tauI;
+        sstate=-combMat\bgCurr;%which is -bgCurr/combMat %this is steady state. 
+
+        netwParams.initConds.exc=sstate(1:nNodes); netwParams.initConds.inh=sstate((nNodes+1):end);
+
+        if (caseval==0 || caseval == -1)
+            if (count == 1)
+                %inputs set in various cases to set firing rate to 100 Hz. 
+            inpParams=struct('tStart',2,'tEnd',2.25,'ampl',22.05*1.9);
+            else
+            inpParams=struct('tStart',2,'tEnd',2.25,'ampl',11.54*1.9);    
+            end
+        end
+        if caseval==1
+            if (count == 1)
+            inpParams=struct('tStart',2,'tEnd',2.25,'ampl',22.68*1.9);
+            else
+            inpParams=struct('tStart',2,'tEnd',2.25,'ampl',37.8*1.9);    
+            end
+        end
+        if caseval==2
+            if (count == 1)
+            inpParams=struct('tStart',2,'tEnd',2.25,'ampl',22.07*1.9);
+            else
+            inpParams=struct('tStart',2,'tEnd',2.25,'ampl',11.18*1.9);    
+            end
+        end
+        if caseval==3
+            if (count == 1)
+            inpParams=struct('tStart',2,'tEnd',2.25,'ampl',22.07*1.9);
+            else
+            inpParams=struct('tStart',2,'tEnd',2.25,'ampl',13.63*1.9);    
+            end
+        end
+        
+        if caseval== -2 || caseval== -3
+            if (count == 1)
+            inpParams=struct('tStart',2,'tEnd',2.25,'ampl',22.07*1.9);
+            else
+            inpParams=struct('tStart',2,'tEnd',2.25,'ampl',13.63*1.9);    
+            end
+        end
+        
+        areaInput.inp=zeros(tParams.nSteps,1);
+        areaInput.inp(round(inpParams.tStart/tParams.dt):round(inpParams.tEnd/tParams.dt))=inpParams.ampl;
+
+
+        if (count == 1)
+            popRatesbad=runNetworkAreaInputNEW(tParams,localParams,netwParams,ldConns,areaInput,'threshLinear');
+            maxpeakbad=zeros(nNodes,1);
+            for r=1:nNodes
+            maxpeakbad(r,1)=max(popRatesbad.exc(r,(toplotstart:toplotend))-popRatesbad.exc(r,toplotstart));
+            end
+        else
+            popRatesgood=runNetworkAreaInputNEW(tParams,localParams,netwParams,ldConns,areaInput,'threshLinear');
+            maxpeakgood=zeros(nNodes,1);
+            for r=1:nNodes
+            maxpeakgood(r,1)=max(popRatesgood.exc(r,(toplotstart:toplotend))-popRatesgood.exc(r,toplotstart));
+            end
+        end    
+
+        if (caseval==0 || caseval==1 || caseval==2 || caseval == -1 || caseval == -2 || caseval == -3)
+            if (count == 1)
+            s=1000;%weak gba
+            else
+            s=100;%strong gba 
+            end
+        end
+        if caseval==3
+            if (count == 1)
+            s=10000;%weak gba
+            else
+            s=100;%strong gba 
+            end
+        end
+        
+        lw=1;
+        x1 = -98.25; x2 = -96; cv(1,1:3) = [0.4660, 0.6740, 0.1880]; cv(2,1:3) = [0.4940,0.1840,0.5560];
+
+        hFig = figure();
+        if count == 1
+          set(hFig,'units', 'centimeters', 'Position', [0 0 5.7 6],'PaperUnits','centimeters','PaperPosition',[.1 -.4 5.7 6],'PaperSize',[6. 5.8])          
+        else
+          set(hFig,'units', 'centimeters', 'Position', [0 0 5.7 6],'PaperUnits','centimeters','PaperPosition',[.1 -.4 5.7 6],'PaperSize',[6. 5.8])  
+        end
+
+        if count ==1 
+            maxpeak = maxpeakbad;
+        else
+            maxpeak = maxpeakgood;
+        end
+        
+        if count == 1
+            subplot(9,1,1);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(1,(toplotstart:toplotend))-popRatesbad.exc(1,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'xcolor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(1,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 140]);%ylabel('V1','FontSize', 18)
+            hold on;plot(tSteps(round(inpParams.tStart/tParams.dt):round(inpParams.tEnd/tParams.dt))-100,135*ones(size(tSteps(round(inpParams.tStart/tParams.dt):round(inpParams.tEnd/tParams.dt)))),'k');
+
+            if poster == 0
+               annotation('textbox', [0.42,0.9,0.1,0.1],'String', 'Weak GBA','FontSize',fsizelab,'LineStyle','None');
+               annotation('textbox', [0.23,0.88,0.1,0.1],'String', '250 ms','FontSize',fsizelab,'LineStyle','None');
+            end
+            
+            subplot(9,1,2);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(3,(toplotstart:toplotend))-popRatesbad.exc(3,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'xcolor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(3,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(3,1)]);%ylabel('V4')
+            subplot(9,1,3);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(6,(toplotstart:toplotend))-popRatesbad.exc(6,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(6,1))/s, 'Yticklabel',round(s*maxpeak(6,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(6,1)]);
+            subplot(9,1,4);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(8,(toplotstart:toplotend))-popRatesbad.exc(8,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(8,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(8,1)]);%ylabel('8l')
+            subplot(9,1,5);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(9,(toplotstart:toplotend))-popRatesbad.exc(9,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(9,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(9,1)]);%ylabel('TEO')
+            subplot(9,1,6);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(13,(toplotstart:toplotend))-popRatesbad.exc(13,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(13,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(13,1)]);%ylabel('7A')
+            subplot(9,1,7);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(17,(toplotstart:toplotend))-popRatesbad.exc(17,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(17,1))/s,'Yticklabel',round(s*maxpeak(17,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(17,1)]);%ylabel('9/46D')
+            subplot(9,1,8);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(19,(toplotstart:toplotend))-popRatesbad.exc(19,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(19,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(19,1)]);%ylabel('TEpd')
+            subplot(9,1,9);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(29,(toplotstart:toplotend))-popRatesbad.exc(29,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(29,1))/s,'Yticklabel',round(s*maxpeak(29,1))/s,'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(29,1)]);
+        else
+            
+            subplot(9,1,1);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(1,(toplotstart:toplotend))-popRatesbad.exc(1,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(1,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 140]);%ylabel('V1','FontSize', 18)
+              if poster == 0
+                 annotation('textbox', [0.42,0.9,0.1,0.1],'String', 'Strong GBA','FontSize',fsizelab,'LineStyle','None');
+                 annotation('textbox', [0.21,0.88,0.1,0.1],'String', '250 ms','FontSize',fsizelab,'LineStyle','None');
+              end
+              hold on;subplot(9,1,1);plot(tSteps(toplotstart:toplotend)-100,popRatesgood.exc(1,(toplotstart:toplotend))-popRatesgood.exc(1,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(1,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 140]);%ylabel('V1','FontSize', 18)
+              hold on;plot(tSteps(round(inpParams.tStart/tParams.dt):round(inpParams.tEnd/tParams.dt))-100,135*ones(size(tSteps(round(inpParams.tStart/tParams.dt):round(inpParams.tEnd/tParams.dt)))),'k');
+              
+            subplot(9,1,2);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(3,(toplotstart:toplotend))-popRatesbad.exc(3,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(3,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(3,1)]);%ylabel('V4')
+              hold on;subplot(9,1,2);plot(tSteps(toplotstart:toplotend)-100,popRatesgood.exc(3,(toplotstart:toplotend))-popRatesgood.exc(3,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(3,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(3,1)]);%ylabel('V4')
+            subplot(9,1,3);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(6,(toplotstart:toplotend))-popRatesbad.exc(6,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(6,1))/s, 'Yticklabel',round(s*maxpeak(6,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(6,1)]);
+              hold on;subplot(9,1,3);plot(tSteps(toplotstart:toplotend)-100,popRatesgood.exc(6,(toplotstart:toplotend))-popRatesgood.exc(6,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(6,1))/s, 'Yticklabel',round(s*maxpeak(6,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(6,1)]);
+            subplot(9,1,4);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(8,(toplotstart:toplotend))-popRatesbad.exc(8,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(8,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(8,1)]);%ylabel('8l')
+              hold on;subplot(9,1,4);plot(tSteps(toplotstart:toplotend)-100,popRatesgood.exc(8,(toplotstart:toplotend))-popRatesgood.exc(8,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(8,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(8,1)]);%ylabel('8l')
+            subplot(9,1,5);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(9,(toplotstart:toplotend))-popRatesbad.exc(9,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(9,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(9,1)]);%ylabel('TEO')
+              hold on;subplot(9,1,5);plot(tSteps(toplotstart:toplotend)-100,popRatesgood.exc(9,(toplotstart:toplotend))-popRatesgood.exc(9,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(9,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(9,1)]);%ylabel('TEO')
+            subplot(9,1,6);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(13,(toplotstart:toplotend))-popRatesbad.exc(13,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(13,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(13,1)]);%ylabel('7A')
+              hold on;subplot(9,1,6);plot(tSteps(toplotstart:toplotend)-100,popRatesgood.exc(13,(toplotstart:toplotend))-popRatesgood.exc(13,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(13,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(13,1)]);%ylabel('7A')
+            subplot(9,1,7);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(17,(toplotstart:toplotend))-popRatesbad.exc(17,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(17,1))/s,'Yticklabel',round(s*maxpeak(17,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(17,1)]);%ylabel('9/46D')
+              hold on;subplot(9,1,7);plot(tSteps(toplotstart:toplotend)-100,popRatesgood.exc(17,(toplotstart:toplotend))-popRatesgood.exc(17,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(17,1))/s,'Yticklabel',round(s*maxpeak(17,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(17,1)]);%ylabel('9/46D')
+            subplot(9,1,8);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(19,(toplotstart:toplotend))-popRatesbad.exc(19,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(19,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(19,1)]);%ylabel('TEpd')
+              hold on;subplot(9,1,8);plot(tSteps(toplotstart:toplotend)-100,popRatesgood.exc(19,(toplotstart:toplotend))-popRatesgood.exc(19,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(19,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(19,1)]);%ylabel('TEpd')
+            subplot(9,1,9);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(29,(toplotstart:toplotend))-popRatesbad.exc(29,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(29,1))/s,'Yticklabel',round(s*maxpeak(29,1))/s,'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(29,1)]);            
+              hold on;subplot(9,1,9);plot(tSteps(toplotstart:toplotend)-100,popRatesgood.exc(29,(toplotstart:toplotend))-popRatesgood.exc(29,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(29,1))/s,'Yticklabel',round(s*maxpeak(29,1))/s,'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(29,1)]);            
+        end
+        
+        h = xlabel('Time (s)','FontSize', fsize);set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [.01, 0.4, -0.9]);%
+        set(gca,'Xtick',-98.:2:-96);set(gca,'XTickLabel',['0';'2']);%timept = [' ';'0';' ';' ';' ';' ';' ';' ';' ';'2'];set(gca,'XTickLabel',timept);
+        set(gca,'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(29,1))/s);%ylabel('18c')
+        
+        if count == 2
+            xv = .89;%0.87
+            annotation('textbox', [xv,0.83,0.1,0.1],'String', 'V1','FontSize',fsizelab,'LineStyle','None');
+            annotation('textbox', [xv,0.735,0.1,0.1],'String', 'V4','FontSize',fsizelab,'LineStyle','None');
+            annotation('textbox', [xv,0.645,0.1,0.1],'String', '8m','FontSize',fsizelab,'LineStyle','None');
+            annotation('textbox', [xv,0.55,0.1,0.1],'String', '8l','FontSize',fsizelab,'LineStyle','None');
+            annotation('textbox', [xv,0.445,0.1,0.1],'String', 'TEO','FontSize',fsizelab,'LineStyle','None');
+            annotation('textbox', [xv,0.353,0.1,0.1],'String', '7A','FontSize',fsizelab,'LineStyle','None');
+            annotation('textbox', [xv,0.265,0.1,0.1],'String', '9/46d','FontSize',fsizelab,'LineStyle','None');
+            annotation('textbox', [xv,0.173,0.1,0.1],'String', 'TEpd','FontSize',fsizelab,'LineStyle','None');
+            annotation('textbox', [xv,0.08,0.1,0.1],'String', '24c','FontSize',fsizelab,'LineStyle','None');
+        end
+        
+        if (caseval==0 || caseval==1 || caseval==2 || caseval==-1)
+            if (count==1)
+             h = ylabel('Change in firing rate (Hz)','FontSize', fsize);set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [-.01, 6.2, -0.9]);%bad
+            
+            end
+        end
+        if caseval==3
+            if (count==1)
+             h = ylabel('Change in firing rate (Hz)','FontSize', fsize);set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [-.01, 6.3, -0.9]);%bad
+            else
+             h = ylabel('Change in firing rate (Hz)','FontSize', fsize);set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [-.04, 6.3, -0.9]);%good
+            end
+        end
+      
+        %%%%%%%%%%%%%%%%%for peak firing rate figures across various areas %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+        nodelen=1:29;nodelen=nodelen';
+        if (count==1)
+            hFig2 = figure();
+            set(hFig2,'units', 'centimeters', 'Position', [0 0 8 6],'PaperUnits','centimeters','PaperPosition',[.1 .1 8 6],'PaperSize',[8.2 6.2]) 
+       %     set(hFig2,'units', 'centimeters', 'Position', [0 0 8 8],'PaperUnits','centimeters','PaperPosition',[.1 .1 8 8],'PaperSize',[8.2 8.2]) 
+            semilogy(nodelen,100*(maxpeakbad)/maxpeakbad(1,1),'.-','LineWidth',lw,'MarkerSize',fsizelab, 'Color',[0.4660, 0.6740, 0.1880]); 
+            if caseval==1
+            hold on; semilogy(6:2:8,100*(maxpeakbad(6:2:8,1))/maxpeakbad(1,1),':','LineWidth',lw,'MarkerSize',fsizelab,'Color',[0.4660, 0.6740, 0.1880]);
+            hold on; semilogy(9:2:11,100*(maxpeakbad(9:2:11,1))/maxpeakbad(1,1),':','LineWidth',lw,'MarkerSize',fsizelab,'Color',[0.4660, 0.6740, 0.1880]);
+            set(gca,'Ytick',logspace(-6,2,3),'YTickLabel',['10^{-6}';'10^{-2}';'10^{2} ']);
+            else
+            set(gca,'Ytick',logspace(-4,2,4),'YTickLabel',['10^{-4}';'10^{-2}';'10^{0} ';'10^{2} ']);
+            end
+        else
+            hFig2 = figure();
+            set(hFig2,'units', 'centimeters', 'Position', [0 0 7.5 3.8],'PaperUnits','centimeters','PaperPosition',[.05 .01 7.5 3.8],'PaperSize',[7. 3.8]) ;
+            semilogy(nodelen-1,100*(maxpeakbad)/maxpeakbad(1,1),'.-','LineWidth',lw,'MarkerSize',fsizelab,'Color',[0.4660, 0.6740, 0.1880]);hold on;
+            semilogy(nodelen-1,100*(maxpeakgood)/maxpeakgood(1,1),'.-','LineWidth',lw,'MarkerSize',fsizelab,'Color',[0.4940,0.1840,0.5560]);        
+            if caseval==1   
+            hold on; semilogy((6:2:8)-1,100*(maxpeakbad(6:2:8,1))/maxpeakbad(1,1),':','LineWidth',lw,'MarkerSize',fsizelab,'Color',[0.4660, 0.6740, 0.1880]);
+            hold on; semilogy((9:2:11)-1,100*(maxpeakbad(9:2:11,1))/maxpeakbad(1,1),':','LineWidth',lw,'MarkerSize',fsizelab,'Color',[0.4660, 0.6740, 0.1880]);
+            hold on; semilogy((6:2:8)-1,100*(maxpeakgood(6:2:8,1))/maxpeakgood(1,1),':','LineWidth',lw,'MarkerSize',fsizelab,'Color',[0.4940,0.1840,0.5560]);
+            hold on; semilogy((9:2:11)-1,100*(maxpeakgood(9:2:11,1))/maxpeakgood(1,1),':','LineWidth',lw,'MarkerSize',fsizelab,'Color',[0.4940,0.1840,0.5560]);
+            set(gca,'Ytick',logspace(-6,2,3),'YTickLabel',['10^{-6}';'10^{-2}';'10^{2} '],'ylim',[1e-8 1e2]);
+            else
+            set(gca,'Ytick',logspace(-4,2,4),'YTickLabel',['10^{-4}';'10^{-2}';'10^{0} ';'10^{2} ']);
+            legend({'weak GBA','strong GBA'},'Position',[0.7 0.87 0.1 0.1],'Box','off','FontSize',fsize);  
+            end
+        end
+        xlabel('Areas','FontSize',fsize);
+        set(gca,'FontSize',fsizelab);
+        set(gca,'Xtick',0:1:28,'box','off');
+        areapt = ['  V1 ';'  V2 ';'  V4 ';'  DP ';'  MT ';'  8m ';'  5  ';'  8l ';' TEO ';'  2  ';'  F1 ';' STPc';'  7A ';' 46d ';'  10 ';'9/46v';'9/46d';'  F5 ';' TEpd';' PBr ';' 7m  ';' 7B  ';'  F2 ';' STPi';' PROm';' F7  ';' 8B  ';' STPr';' 24c ']; %timept = ['';'0';'';'';'1';'';'';'2'];
+        set(gca,'XTickLabel',areapt);
+        ax = gca;ax.XTickLabelRotation = 90; 
+        h = ylabel('Maximum firing rate (Hz)','FontSize',fsize);%set(h, 'Units', 'Normalized');
+        pos = get(h, 'Position');set(h, 'Position', pos + [-.02, -.06, -0.9]);%
+        
+        if count == 2
+            if caseval == 0
+                maxpeakbad_control = maxpeakbad; maxpeakgood_control = maxpeakgood;
+                %save('maxpeakbad_control.mat','maxpeakbad_control'); save('maxpeakgood_control.mat','maxpeakgood_control');
+            end
+            if caseval == 1
+                maxpeakbad_nofb= maxpeakbad; maxpeakgood_nofb = maxpeakgood;
+                %save('maxpeakbad_nofb.mat','maxpeakbad_nofb'); save('maxpeakgood_nofb.mat','maxpeakgood_nofb');
+            end
+            if caseval == 2
+                maxpeakbad_arimean = maxpeakbad; maxpeakgood_arimean = maxpeakgood;
+                %save('maxpeakbad_arimean.mat','maxpeakbad_arimean'); save('maxpeakgood_arimean.mat','maxpeakgood_arimean');
+            end
+            if caseval == 3
+                maxpeakbad_geomean = maxpeakbad; maxpeakgood_geomean = maxpeakgood;
+                %save('maxpeakbad_geomean.mat','maxpeakbad_geomean'); save('maxpeakgood_geomean.mat','maxpeakgood_geomean');
+            end
+            if caseval == -1
+                maxpeakbad_nohier = maxpeakbad; maxpeakgood_nohier = maxpeakgood;
+                %save('maxpeakbad_nohier.mat','maxpeakbad_nohier'); save('maxpeakgood_nohier.mat','maxpeakgood_nohier');
+            end
+   
+            if caseval == -2 %new after revision. this and below case -3. 
+                maxpeakbad_arimeannohier = maxpeakbad; maxpeakgood_arimeannohier = maxpeakgood;
+                %save('maxpeakbad_arimeannohier.mat','maxpeakbad_arimeannohier'); save('maxpeakgood_arimeannohier.mat','maxpeakgood_arimeannohier');
+            end
+            if caseval == -3
+                maxpeakbad_arimeanlochier = maxpeakbad; maxpeakgood_arimeanlochier = maxpeakgood;
+                %save('maxpeakbad_arimeanlochier.mat','maxpeakbad_arimeanlochier'); save('maxpeakgood_arimeanlochier.mat','maxpeakgood_arimeanlochier');
+            end
+         
+        end
+        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+        if (caseval==0)
+            if count == 1
+                % saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 2E', 'pdf')                
+
+            else
+                 %saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 2G', 'pdf')
+            end
+        end
+        if (caseval==1)
+            if count == 1
+             %   saveas(hFig2, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/supp fig 1 nofbbadmaxrate', 'pdf');
+            else
+              %   saveas(hFig2, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/supp fig 1 nofbgoodmaxrate', 'pdf')
+            end
+        end
+        if (caseval==2)
+            if count == 1
+              %   saveas(hFig2, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/supp fig 2 symflnarmeanbadmaxrate', 'pdf')
+            else
+             %   saveas(hFig2, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/supp fig 2 symflnarmeangoodmaxrate', 'pdf')
+            end
+        end
+        if (caseval==3)
+            if count == 1
+%                 saveas(hFig2, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/supp fig 3 symflngeomeanbadmaxrate', 'pdf')
+            else
+%                 saveas(hFig2, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/supp fig 3 symflngeomeangoodmaxrate', 'pdf')
+            end
+        end
+  
+    end
+end
+
+%%%%%%%%%%for figure with threshold and removing weak connections. %%%%%%
+if caseval == 4
+
+ binsize=15;%no of divisions for conn strength calculation. 
+ thresvec = logspace(-5,-2,binsize)'; 
+ frac=zeros(binsize,1);peakratio = zeros(binsize,2);
+ inpParams=struct('tStart',2,'tEnd',2.25,'ampl',21.5*1.951);
+ areaInput.inp=zeros(tParams.nSteps,1);
+ areaInput.inp(round(inpParams.tStart/tParams.dt):round(inpParams.tEnd/tParams.dt))=inpParams.ampl;
+for u=1:length(thresvec) %run loop... 
+  thres = thresvec(u);
+  clear flnMatloop; flnMatloop = flnMat;
+ 
+frac(u,1) = numel(flnMat( flnMat(:)>thresvec(u)  ))/8.12;%--area to area only. on x axis.% figure; plot(thresvec,frac)
+ 
+for flnrow=1:length(flnMat)
+  for flncol=1:length(flnMat)
+ if(flnMat(flnrow,flncol)<thres)
+    flnMatloop(flnrow,flncol) = 0;
+ end
+  end
+end
+
+ for uu = 1:2 %orig vs reg 1.
+         
+    if (uu==1)
+     clear A popRates; muEE = 33.7 ; omegaEI = 19.7 ; 
+    else
+     clear A popRates; muEE = 51.5; omegaEI = 25.2 ; 
+    end
+
+    localParams.bgInh=zeros(netwParams.nNodes,1);%background inhibitory        
+    localParams.ee=betaE*omegaEE*(1+netwParams.alpha*netwParams.hier);
+    localParams.ie=betaI*omegaIE*(1+netwParams.alpha*netwParams.hier);
+    localParams.ei=-betaE*omegaEI; 
+    localParams.ii=-betaI*omegaII;         
+    ldParams.ee=betaE*muEE*(1+netwParams.alpha*netwParams.hier);
+    ldParams.ie=betaI*muIE*(1+netwParams.alpha*netwParams.hier);
+    ldConns.ee= bsxfun(@times,flnMatloop,ldParams.ee);
+    ldConns.ie= bsxfun(@times,flnMatloop,ldParams.ie);
+
+    wEe=diag(-1+localParams.ee)+ldConns.ee;
+    wEi=localParams.ei*eye(nNodes);%these ws would be 29x29 identity matrices. 
+    wIe=diag(localParams.ie)+ldConns.ie;
+    wIi=(-1+localParams.ii)*eye(nNodes);
+    A = [wEe/localParams.tauE wEi/localParams.tauE;...
+        wIe/localParams.tauI wIi/localParams.tauI];
+
+    currParams.A=A; 
+    B=currParams.A;
+    B(1:nNodes,:)=B(1:nNodes,:)*localParams.tauE;
+    B((nNodes+1):end,:)=B((nNodes+1):end,:)*localParams.tauI;
+    currs=-B*currParams.desiredSs; 
+
+    localParams.bgExc=currs(1:nNodes); localParams.bgInh=currs((nNodes+1):end);
+    bgCurr=[localParams.bgExc; localParams.bgInh];%bg = background
+    combMat=A;
+    combMat(1:nNodes,:)=combMat(1:nNodes,:)*localParams.tauE;
+    combMat((nNodes+1):end,:)=combMat((nNodes+1):end,:)*localParams.tauI;
+    sstate=-combMat\bgCurr;%which is -bgCurr/combMat
+    netwParams.initConds.exc=sstate(1:nNodes); netwParams.initConds.inh=sstate((nNodes+1):end);
+ 
+    popRates=runNetworkAreaInputNEW(tParams,localParams,netwParams,ldConns,areaInput,'threshLinear');
+
+    maxpeak=zeros(nNodes,1);
+    for r=1:nNodes
+    maxpeak(r,1)=max(popRates.exc(r,(toplotstart:toplotend))-popRates.exc(r,toplotstart));
+    end
+    peakratio(u,uu) = maxpeak(29,1)/maxpeak(1,1);
+    
+    
+  if u == 12
+     %plot -  threshold, connection density 
+        lw=1;
+        x1 = -98.25; x2 = -96; cv(1,1:3) = [0.4660, 0.6740, 0.1880]; cv(2,1:3) = [0.4940,0.1840,0.5560];
+
+        if uu == 1
+            count = uu;
+            popRatesbad = popRates;
+            hFig = figure();
+            s=1000;
+            set(hFig,'units', 'centimeters', 'Position', [0 0 5.7 8],'PaperUnits','centimeters','PaperPosition',[.1 -.4 5.7 8],'PaperSize',[6. 7.6]) 
+            subplot(9,1,1);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(1,(toplotstart:toplotend))-popRatesbad.exc(1,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'xcolor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(1,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(1,1)]);%ylabel('V1','FontSize', 18)
+            hold on;plot(tSteps(round(inpParams.tStart/tParams.dt):round(inpParams.tEnd/tParams.dt))-100,123*ones(size(tSteps(round(inpParams.tStart/tParams.dt):round(inpParams.tEnd/tParams.dt)))),'k');
+               annotation('textbox', [0.45,0.9,0.1,0.1],'String', 'weak GBA','FontSize',fsizelab,'LineStyle','None');
+               annotation('textbox', [0.23,0.865,0.1,0.1],'String', '250 ms','FontSize',fsizelab,'LineStyle','None');
+            subplot(9,1,2);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(3,(toplotstart:toplotend))-popRatesbad.exc(3,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'xcolor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(3,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(3,1)]);%ylabel('V4')
+            subplot(9,1,3);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(6,(toplotstart:toplotend))-popRatesbad.exc(6,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(6,1))/s, 'Yticklabel',round(s*maxpeak(6,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(6,1)]);
+            subplot(9,1,4);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(8,(toplotstart:toplotend))-popRatesbad.exc(8,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(8,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(8,1)]);%ylabel('8l')
+            subplot(9,1,5);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(9,(toplotstart:toplotend))-popRatesbad.exc(9,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(9,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(9,1)]);%ylabel('TEO')
+            subplot(9,1,6);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(13,(toplotstart:toplotend))-popRatesbad.exc(13,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(13,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(13,1)]);%ylabel('7A')
+            subplot(9,1,7);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(17,(toplotstart:toplotend))-popRatesbad.exc(17,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(17,1))/s,'Yticklabel',round(s*maxpeak(17,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(17,1)]);%ylabel('9/46D')
+            subplot(9,1,8);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(19,(toplotstart:toplotend))-popRatesbad.exc(19,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(19,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(19,1)]);%ylabel('TEpd')
+            subplot(9,1,9);plot(tSteps(toplotstart:toplotend)-100,popRatesbad.exc(29,(toplotstart:toplotend))-popRatesbad.exc(29,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(29,1))/s,'Yticklabel',round(s*maxpeak(29,1))/s,'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(29,1)]);
+    
+        else
+             s=100;
+             count = uu;
+             popRatesgood = popRates;
+             hFig = figure();
+             set(hFig,'units', 'centimeters', 'Position', [0 0 5.7 8],'PaperUnits','centimeters','PaperPosition',[.1 -.4 5.7 8],'PaperSize',[6. 7.6])  
+             subplot(9,1,1);plot(tSteps(toplotstart:toplotend)-100,popRatesgood.exc(1,(toplotstart:toplotend))-popRatesgood.exc(1,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(1,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(1,1)]);%ylabel('V1','FontSize', 18)
+                 annotation('textbox', [0.45,0.9,0.1,0.1],'String', 'strong GBA','FontSize',fsizelab,'LineStyle','None');
+                 annotation('textbox', [0.21,0.88,0.1,0.1],'String', '250 ms','FontSize',fsizelab,'LineStyle','None');
+              hold on;subplot(9,1,2);plot(tSteps(toplotstart:toplotend)-100,popRatesgood.exc(3,(toplotstart:toplotend))-popRatesgood.exc(3,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(3,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(3,1)]);%ylabel('V4')
+              hold on;subplot(9,1,3);plot(tSteps(toplotstart:toplotend)-100,popRatesgood.exc(6,(toplotstart:toplotend))-popRatesgood.exc(6,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(6,1))/s, 'Yticklabel',round(s*maxpeak(6,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(6,1)]);
+              hold on;subplot(9,1,4);plot(tSteps(toplotstart:toplotend)-100,popRatesgood.exc(8,(toplotstart:toplotend))-popRatesgood.exc(8,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(8,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(8,1)]);%ylabel('8l')
+              hold on;subplot(9,1,5);plot(tSteps(toplotstart:toplotend)-100,popRatesgood.exc(9,(toplotstart:toplotend))-popRatesgood.exc(9,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(9,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(9,1)]);%ylabel('TEO')
+              hold on;subplot(9,1,6);plot(tSteps(toplotstart:toplotend)-100,popRatesgood.exc(13,(toplotstart:toplotend))-popRatesgood.exc(13,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(13,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(13,1)]);%ylabel('7A')
+              hold on;subplot(9,1,7);plot(tSteps(toplotstart:toplotend)-100,popRatesgood.exc(17,(toplotstart:toplotend))-popRatesgood.exc(17,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(17,1))/s,'Yticklabel',round(s*maxpeak(17,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(17,1)]);%ylabel('9/46D')
+              hold on;subplot(9,1,8);plot(tSteps(toplotstart:toplotend)-100,popRatesgood.exc(19,(toplotstart:toplotend))-popRatesgood.exc(19,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(19,1))/s,'Xtick',[],'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(19,1)]);%ylabel('TEpd')
+              hold on;subplot(9,1,9);plot(tSteps(toplotstart:toplotend)-100,popRatesgood.exc(29,(toplotstart:toplotend))-popRatesgood.exc(29,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(count,:));set(gca,'XColor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(29,1))/s,'Yticklabel',round(s*maxpeak(29,1))/s,'XLim',[x1 x2],'YLim',[0 1.2*maxpeak(29,1)]);            
+        end     
+        h = xlabel('Time (s)','FontSize', fsize);set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [.01, 0.4, -0.9]);%
+        set(gca,'Xtick',-98.:2:-96);set(gca,'XTickLabel',['0';'2']);%timept = [' ';'0';' ';' ';' ';' ';' ';' ';' ';'2'];set(gca,'XTickLabel',timept);
+        set(gca,'FontSize',fsizelab,'box','off','Ytick',round(s*maxpeak(29,1))/s);%ylabel('18c')     
+        if uu == 2
+          %  annotation('textbox', [0.89,0.83,0.1,0.1],'String', 'Input','FontSize',fsizelab,'LineStyle','None');
+            annotation('textbox', [0.87,0.83,0.1,0.1],'String', 'V1','FontSize',fsizelab,'LineStyle','None');
+            annotation('textbox', [0.87,0.725,0.1,0.1],'String', 'V4','FontSize',fsizelab,'LineStyle','None');
+            annotation('textbox', [0.87,0.645,0.1,0.1],'String', '8m','FontSize',fsizelab,'LineStyle','None');
+            annotation('textbox', [0.87,0.54,0.1,0.1],'String', '8l','FontSize',fsizelab,'LineStyle','None');
+            annotation('textbox', [0.87,0.445,0.1,0.1],'String', 'TEO','FontSize',fsizelab,'LineStyle','None');
+            annotation('textbox', [0.87,0.353,0.1,0.1],'String', '7A','FontSize',fsizelab,'LineStyle','None');
+            annotation('textbox', [0.87,0.265,0.1,0.1],'String', '9/46d','FontSize',fsizelab,'LineStyle','None');
+            annotation('textbox', [0.87,0.163,0.1,0.1],'String', 'TEpd','FontSize',fsizelab,'LineStyle','None');
+            annotation('textbox', [0.87,0.08,0.1,0.1],'String', '24c','FontSize',fsizelab,'LineStyle','None');
+        end
+        if uu == 1
+        h = ylabel('Change in firing rate (Hz)','FontSize', fsize);set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [-.01, 6.2, -0.9]);%bad
+        end
+%        if uu == 1
+%                 saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/supp fig 4 conndens 26percent bad', 'pdf');
+%        else
+%                 saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/supp fig 4 conndens 26percent good', 'pdf');
+%        end
+
+  end  
+    
+    
+    
+  end
+end  
+
+hFig = figure();
+    set(hFig,'units', 'centimeters', 'Position', [0 0 4.3 4],'PaperUnits','centimeters','PaperPosition',[.05 .2 4.3 4],'PaperSize',[4.8 4.5])  
+
+semilogy(frac,peakratio(:,1),'.-','LineWidth',lw,'MarkerSize',msize,'Color',cv(1,:));hold on; 
+semilogy(frac,peakratio(:,2),'.-','LineWidth',lw,'MarkerSize',msize,'Color',cv(2,:));%legend('Original','New','FontSize', 24,'fontweight','bold');set(gca,'FontSize',fsize)
+%hold on; semilogy(frac(12),peakratio(12,2),'vk','LineWidth',lw,'MarkerSize',msize-2,'Color','k');%ADDED
+%hold on; semilogy(frac(12),peakratio(12,2),'vk','LineWidth',lw,'MarkerSize',msize-2,'Color','k');%ADDED
+set(gca,'FontSize',fsizelab,'box','off');
+set(gca,'Xtick',15:15:60,'XTickLabel',['15';'30';'45';'60'],'xlim',[15 65]);
+set(gca,'ylim',[.99999*1e-5 2*1e-2],'Ytick',logspace(-5,-2,4),'YTickLabel',['10^{-5}';'10^{-4}';'10^{-3}';'10^{-2}'],'YMinorTick','off');
+h = xlabel('Connection density','FontSize', fsize);%set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [-.0, -0.01, -0.9]);
+h = ylabel('Propagation ratio','FontSize', fsize);%set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [-.01, 0., -0.9]);
+%legend('control','strong GBA')
+    legend({'weak GBA','strong GBA'},'Position',[0.75 0.21 0.1 0.1],'Box','off','FontSize',fsize);         
+
+hFig2 = figure(); 
+set(hFig2,'units', 'centimeters', 'Position', [0 0 4 4],'PaperUnits','centimeters','PaperPosition',[.1 .1 4 4],'PaperSize',[4.2 4.2])   
+semilogx(thresvec,frac,'.-','LineWidth',lw,'MarkerSize',fsizelab);
+%hold on;semilogx(thresvec(12),frac(12),'v','LineWidth',lw,'MarkerSize',fsizelab-4);%ADDED
+xlabel('Threshold','FontSize',fsize);
+set(gca,'FontSize',fsizelab,'box','off');
+set(gca,'Xtick',logspace(-5,-2,4),'XTickLabel',['10^{-5}';'10^{-4}';'10^{-3}';'10^{-2}'],'xlim',[.99999*1e-5 2*1e-2],'XMinorTick','off');
+set(gca,'Ytick',15:15:65,'YTickLabel',['15';'30';'45';'60'],'ylim',[15 65]);
+h = ylabel('Connection density','FontSize', fsize);set(h, 'Units', 'Normalized');%pos = get(h, 'Position');set(h, 'Position', pos + [-.03, 0., -0.9]);
+
+
+%saveas(hFig2, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/supp fig 4B', 'pdf');
+
+end
+
+%%%%%%%%%%%%%%%%change muEE - show bad prop or blowup %%%%%%%%%%%%%%%%%%%%%
+
+if caseval == 5
+    inpParams=struct('tStart',2,'tEnd',2.25,'ampl',22.05*1.9);
+    areaInput.inp=zeros(tParams.nSteps,1);
+    areaInput.inp(round(inpParams.tStart/tParams.dt):round(inpParams.tEnd/tParams.dt))=inpParams.ampl;
+    %muEErange = 21:2:51;
+    muEErange = 20:2:50;
+    muEErange = 28:2:42;omegaEI = 19.7; %final
+    
+    muEErange = 28:2:42;omegaEI = 19.7;%testing only. 
+    
+    prop24c = zeros(length(muEErange),2);
+    condA2 = zeros(length(muEErange),1); propV1 = zeros(length(muEErange),1); condA1 = zeros(length(muEErange),1); condA3 = zeros(length(muEErange),1);maxeig = zeros(length(muEErange),1);
+    
+    for uu = 1:2 %orig vs regime.
+
+     for muval=1:length(muEErange)
+        muEE = muEErange(muval); clear A popRates;
+        if (uu==2) 
+          omegaEI = 19.7 + (muEE-33.7)*55/178; %%%%%%now changing omegaEI too. 
+        end   
+        
+        localParams.bgInh=zeros(netwParams.nNodes,1);%background inhibitory
+        localParams.ee=betaE*omegaEE*(1+netwParams.alpha*netwParams.hier);%rsc*2.29119*(1+netwParams.alpha*netwParams.hier);
+        localParams.ie=betaI*omegaIE*(1+netwParams.alpha*netwParams.hier);%rsc*6.09552*(1+netwParams.alpha*netwParams.hier);
+        localParams.ei=-betaE*omegaEI; %-1.29954;
+        localParams.ii=-betaI*omegaII; %-4.40204;        
+        ldParams.ee=betaE*muEE*(1+netwParams.alpha*netwParams.hier);%rsc*2.29119*(1+netwParams.alpha*netwParams.hier);
+        ldParams.ie=betaI*muIE*(1+netwParams.alpha*netwParams.hier);%rsc*6.09552*(1+netwParams.alpha*netwParams.hier);
+        ldConns.ee= bsxfun(@times,flnMat,ldParams.ee);
+        ldConns.ie= bsxfun(@times,flnMat,ldParams.ie);
+        wEe=diag(-1+localParams.ee)+ldConns.ee;
+        wEi=localParams.ei*eye(nNodes);%these ws would be 29x29 identity matrices. 
+        wIe=diag(localParams.ie)+ldConns.ie;
+        wIi=(-1+localParams.ii)*eye(nNodes);%compare this to eqn 4 - where does -1 come from??
+        A = [wEe/localParams.tauE wEi/localParams.tauE;...
+            wIe/localParams.tauI wIi/localParams.tauI];
+        currParams.A=A; 
+        B=currParams.A;%B=params.A;
+        B(1:nNodes,:)=B(1:nNodes,:)*localParams.tauE;
+        B((nNodes+1):end,:)=B((nNodes+1):end,:)*localParams.tauI;
+        currs=-B*currParams.desiredSs; %currs=-B*params.desiredSs;
+        localParams.bgExc=currs(1:nNodes); localParams.bgInh=currs((nNodes+1):end);
+        bgCurr=[localParams.bgExc; localParams.bgInh];%bg = background
+        combMat=A;
+        combMat(1:nNodes,:)=combMat(1:nNodes,:)*localParams.tauE;
+        combMat((nNodes+1):end,:)=combMat((nNodes+1):end,:)*localParams.tauI;
+        sstate=-combMat\bgCurr;%which is -bgCurr/combMat%this is steady state. 
+        netwParams.initConds.exc=sstate(1:nNodes); netwParams.initConds.inh=sstate((nNodes+1):end);
+        popRates=runNetworkAreaInputNEW(tParams,localParams,netwParams,ldConns,areaInput,'threshLinear'); 
+        maxpeak=zeros(nNodes,1);
+        for r=1:nNodes
+        maxpeak(r,1)=max(popRates.exc(r,(toplotstart:toplotend))-popRates.exc(r,toplotstart));
+        end
+        nodelen=1:29;nodelen=nodelen';
+        prop24c(muval,uu) = maxpeak(nNodes,1);
+        if (prop24c(muval,uu)>500)
+        prop24c(muval,uu) = 500;
+        end
+        
+        if uu==1
+            [vcond,wcond]=sortEig(A);maxeig(muval,1)=max(real(wcond));
+            disp(max(real(wcond)));
+        else    
+            condA2(muval,1) = sqrt( sum(svd(A).^2) - sum(abs(eig(A)).^2) ); propV1(muval,1) = maxpeak(1,1);
+            [vcond,wcond]=sortEig(A);condA1(muval,1) = cond(vcond); condA3(muval,1) = norm(A*A' - A'*A,'fro');
+        end
+        %propv1(muval,uu) = maxpeak(1,1);if (propv1(muval,uu)>500)propv1(muval,uu) = 500;end
+        disp([muEE,uu]);
+     end        
+    end
+    cv(1,1:3) = [0.4660, 0.6740, 0.1880]; cv(2,1:3) = [0.4940,0.1840,0.5560];
+    hFig = figure(); 
+    if nofb == 0 
+        set(hFig,'units', 'centimeters', 'Position', [0 0 3.6 4],'PaperUnits','centimeters','PaperPosition',[.1 .1 3.2 4],'PaperSize',[3.6 4.]) ;
+        %set(hFig,'units', 'centimeters', 'Position', [0 0 4 3.5],'PaperUnits','centimeters','PaperPosition',[.1 .1 4 3.5],'PaperSize',[3.8 3.5]);%for xjtalk             
+    else
+        set(hFig,'units', 'centimeters', 'Position', [0 0 3. 4],'PaperUnits','centimeters','PaperPosition',[-.2 .1 2.6 4],'PaperSize',[2.7 4]) ;
+    end
+    fsize = 7; msize = 7; 
+    semilogy(muEErange,prop24c(:,1),'.-','LineWidth',lw,'MarkerSize',msize, 'Color',cv(1,:));set(gca,'FontSize',fsizelab,'box','off');
+    h = xlabel('Global E to E coupling','FontSize', fsize);%set(h, 'Units', 'Normalized');%pos = get(h, 'Position');set(h, 'Position', pos + [-.0, -0.01, -0.9]);
+    %hold on; semilogy(muEErange(4),prop24c(4,1),'x','LineWidth',lw,'MarkerSize',msize, 'Color',cv(1,:));
+    %hold on; semilogy(muEErange(5),prop24c(5,1),'o','LineWidth',lw,'MarkerSize',msize, 'Color',cv(1,:));
+    
+    %xlabel({'line 1';'line2'});
+    %xlabel({'Global coupling';'Global coupling'},'FontSize', fsize);
+  
+    %set(gca,'Xtick',30:5:40,'XTickLabel',['30';'35';'40'],'xlim',[28. 42]);
+    %set(gca,'Ytick',logspace(-6,3,4),'YTickLabel',['10^{-6}';'10^{-3}';'10^{0} ';'10^{3} '],'ylim',[1e-6, 1e3]);
+    set(gca,'Ytick',logspace(-8,4,4),'YTickLabel',['10^{-8}';'10^{-4}';'10^{0} ';'10^{4} '],'ylim',[1e-8, 1e4]);
+    set(gca,'Xtick',20:10:50,'XTickLabel',['20';'30';'40';'50'],'xlim',[20. 50]);
+    
+    if nofb==0
+        h = ylabel('Maximum rate in 24c (Hz)','FontSize', fsize);%set(h, 'Units', 'Normalized');%pos = get(h, 'Position');set(h, 'Position', pos + [-.02, 0., -0.9]);
+    else
+        set(gca,'ycolor',get(gcf,'color') ) ;     
+    end
+    %saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 1 24cblowup', 'pdf')
+    %saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 1C ', 'pdf')
+    
+    %saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 1 24c no fb slowblowup', 'pdf')
+    %saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 1C nofb', 'pdf')
+    
+    %saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/suppfig8_nohier', 'pdf')
+    %saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/xj columbia talk/main fig 2I only green', 'pdf');
+
+    hFig = figure();  fsize = 7; msize = 7;
+        set(hFig,'units', 'centimeters', 'Position', [0 0 4 3.5],'PaperUnits','centimeters','PaperPosition',[.1 .1 4 3.5],'PaperSize',[3.8 3.5])
+    semilogy(muEErange,prop24c(:,1),'.-','LineWidth',lw,'MarkerSize',msize,'Color',cv(1,:));set(gca,'FontSize',fsizelab,'box','off');
+    hold on; semilogy(muEErange,prop24c(:,2),'.-','LineWidth',lw,'MarkerSize',msize,'Color',cv(2,:));set(gca,'box','off');
+    h = xlabel('Global E to E coupling','FontSize', fsize);set(h, 'Units', 'Normalized');%pos = get(h, 'Position');set(h, 'Position', pos + [-.0, -0.01, -0.9]);
+    h = ylabel('Maximum rate in 24c (Hz)','FontSize', fsize);set(h, 'Units', 'Normalized');%pos = get(h, 'Position');set(h, 'Position', pos + [-.02, 0., -0.9]);
+    set(gca,'Xtick',20:10:50,'XTickLabel',['20';'30';'40';'50'],'xlim',[20 52]);
+    %legend({'increase \mu_{EE}', 'increase \mu_{EE}, \omega_{EI}'},'Position',[0.58 0.2 0.1 0.1],'Box','off','FontSize',7);
+    set(gca,'Ytick',logspace(-8,4,4),'YTickLabel',['10^{-8}';'10^{-4}';'10^{0} ';'10^{4} '],'ylim',[1e-8, 1e4]);
+    %saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 3 24cgoodandbad', 'pdf');
+    %saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 2I', 'pdf');
+
+    
+    hFig = figure();set(hFig,'units', 'centimeters', 'Position', [0 0 4 4],'PaperUnits','centimeters','PaperPosition',[.1 .1 4 4],'PaperSize',[4. 4.])
+    semilogx(prop24c(:,2),condA2,'.-','LineWidth',lw,'MarkerSize',msize,'Color',cv(2,:));set(gca,'FontSize',fsizelab,'box','off');
+    h = xlabel('Maximum rate in 24c (Hz)', 'FontSize',fsize);set(h, 'Units', 'Normalized');
+    h = ylabel('Nonnormality measure','FontSize', fsize);set(h, 'Units', 'Normalized');
+    set(gca,'Xtick',logspace(-7,1,3),'XTickLabel',['10^{-7}';'10^{-3}';'10^{1} '],'xlim',[1e-7 1e1]);
+    set(gca,'Ytick',4500:150:4650,'YTickLabel',['4500';'4650'],'ylim',[4500, 4650]);
+    %saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/supp fig nonnormality', 'pdf');
+
+    
+    %%%%%%%%%%% brain figure %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
+    load('2012_12_10_data_sorted_coordinates.mat');
+    fsize = 6; msize = 6; 
+    crds=coord.sortCrdList;
+    %hFig2 = figure(); set(hFig2,'units', 'centimeters', 'Position', [0 0 8.7 6.4],'PaperUnits','centimeters','PaperPosition',[.0 .0 8.7 6.4],'PaperSize',[8.7 6.4]) 
+    hFig2 = figure(); set(hFig2,'units', 'centimeters', 'Position', [0 0 6.4 4.6],'PaperUnits','centimeters','PaperPosition',[.0 .0 6.4 4.6],'PaperSize',[6.4 4.6]) 
+    
+    axes1 = axes('Parent',hFig2); hold on;
+    plot3(crds(:,1),crds(:,2),crds(:,3),'.','MarkerSize',msize,'Color',[0 0 0]);
+    
+    % Now start to fill in the strong connections Symmetrize, for now
+    symmConns=(flnMat+flnMat')/2; 
+    thresh=5e-3;
+    lnWt=@(x) log10(x/thresh)/log10(1/thresh);
+    % Can set various thresholds for what gets plotted and scale the weights in various ways
+    for i=1:nNodes
+        for j=1:(i-1)
+            if(symmConns(i,j)>thresh)
+                lineToPlot=[crds(i,:); crds(j,:)];
+                plot3(lineToPlot(:,1),lineToPlot(:,2),lineToPlot(:,3),'LineWidth',(.1*lnWt(symmConns(i,j))),'Color', [0.9290    0.6940    0.1250]);
+            end
+        end
+    end
+    view(axes1,[106 18]); 
+    labels=areaList;
+    xc=crds(:,1); yc=crds(:,2); zc=crds(:,3); text(xc,yc,zc,labels,'FontSize',fsize);
+    plot3(crds(:,1),crds(:,2),crds(:,3),'.','MarkerSize',msize,'Color',[0 0 0]);
+    set(gca,'xlim',[min(crds(:,1)) max(crds(:,1))],'ylim',[min(crds(:,2)) max(crds(:,2))],'zlim',[min(crds(:,3)) max(crds(:,3))]);axis off;
+ %   saveas(hFig2, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 3 brain', 'pdf')
+   % saveas(hFig2, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 1A', 'pdf')
+
+    hFig2 = figure(); set(hFig2,'units', 'centimeters', 'Position', [0 0 8.7 6.4],'PaperUnits','centimeters','PaperPosition',[.0 .0 8.7 6.4],'PaperSize',[8.7 6.4]) 
+    axes1 = axes('Parent',hFig2); hold on;
+    plot3(crds(:,1),crds(:,2),crds(:,3),'.','MarkerSize',msize,'Color',[0 0 0]);
+    for i=1:nNodes
+        for j=1:(i-1)
+            if(symmConns(i,j)>thresh)
+                lineToPlot=[crds(i,:); crds(j,:)];
+                plot3(lineToPlot(:,1),lineToPlot(:,2),lineToPlot(:,3),'LineWidth',(.1*lnWt(symmConns(i,j))),'Color', [0.9290    0.6940    0.1250]);
+            end
+        end
+    end
+    view(axes1,[106 18]); 
+    xc=crds(:,1); yc=crds(:,2); zc=crds(:,3);% text(xc,yc,zc,labels,'FontSize',fsize);
+    plot3(crds(:,1),crds(:,2),crds(:,3),'.','MarkerSize',msize,'Color',[0 0 0]);
+    set(gca,'xlim',[min(crds(:,1)) max(crds(:,1))],'ylim',[min(crds(:,2)) max(crds(:,2))],'zlim',[min(crds(:,3)) max(crds(:,3))]);axis off;
+%    saveas(hFig2, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 3 brainsmall', 'pdf')
+
+    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+    
+    
+end
+
+if caseval == 6
+    fsize=8;fsizelab=8;msize=8;
+    
+    ventarea = [1:3,9,19];flnMatpos=zeros(500,1);
+    count=0;
+    for i=1:29 
+        for j=1:29 
+            if(flnMat(i,j)>0) 
+                count=count+1;flnMatpos(count,1) = flnMat(i,j);
+            end; 
+        end;
+    end;
+    flnMatpos=flnMatpos(1:count,1);
+    
+    count=0;flnMatvisven=zeros(500,1);
+    for i = 1:length(ventarea) 
+        for j = 1:length(ventarea) 
+            if(flnMat(ventarea(i),ventarea(j))>0) 
+                count=count+1;
+                flnMatvisven(count,1)=(flnMat(ventarea(i),ventarea(j)));
+                disp([i, j, flnMatvisven(count,1)]);
+            end; 
+        end;
+    end;
+    flnMatvisven = flnMatvisven(1:count,1);
+    
+hFig = figure(); set(hFig,'units', 'centimeters', 'Position', [0 0 4 3],'PaperUnits','centimeters','PaperPosition',[.1 .1 4 3],'PaperSize',[4.1 3.1]) 
+hist(flnMatpos,logspace(-6,0,13));set(gca,'xscale','log');h = findobj(gca,'Type','patch');
+set(h,'FaceColor',[0.4940    0.1840    0.5560],'EdgeColor','w','FaceAlpha',0.35,'LineWidth',0.2);
+%h = findobj(gca,'Type','line');set(h,'Marker','none'); 
+hold on;
+hist(flnMatvisven,logspace(-6,0,13));
+h = findobj(gca,'Type','line');set(h,'Marker','none'); 
+%h = findobj(gca,'Type','patch');%set(h,'EdgeAlpha',0.8);
+set(gca,'FontSize',fsizelab,'box','off');
+set(gca,'xlim',[1e-6 3],'Xtick',logspace(-6,0,4),'XTickLabel',['10^{-6}';'10^{-4}';'10^{-2}';'10^{0} ']);
+set(gca,'ylim',[0 70],'Ytick',0:20:60,'YTickLabel',['0 ';'20';'40';'60']);
+ylabel('FLN counts','FontSize', fsize);%set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [-.01, -0.0, -0.9]);
+[counts,~]=hist(flnMatpos,logspace(-6,0,13));[countsvv,~]=hist(flnMatvisven,logspace(-6,0,13));
+disp(sum(countsvv(10:13))/sum(counts(10:13)));
+
+%saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 5 histfln', 'pdf')
+
+    hFig = figure(); 
+    %set(hFig,'units', 'centimeters', 'Position', [0 0 4 2.5],'PaperUnits','centimeters','PaperPosition',[.1 .1 4 2.5],'PaperSize',[4.1 2.6])
+set(hFig,'units', 'centimeters', 'Position', [0 0 4.2 2.5],'PaperUnits','centimeters','PaperPosition',[.1 .1 4.2 2.5],'PaperSize',[4.3 2.6])
+
+hist(flnMatpos,logspace(-6,1,15));set(gca,'xscale','log');h = findobj(gca,'Type','patch');
+%set(h,'FaceColor',[0.4940    0.1840    0.5560],'EdgeColor','w','FaceAlpha',0.35,'LineWidth',0.2);
+set(h,'FaceColor',[0.4940    0.1840    0.5560],'FaceAlpha',0.35,'LineWidth',0.2);
+h = findobj(gca,'Type','line');set(h,'Marker','none'); h = findobj(gca,'Type','patch');%set(h,'EdgeAlpha',0.8);
+set(gca,'FontSize',fsizelab,'box','off');
+set(gca,'xlim',[1e-6 3],'Xtick',logspace(-6,0,4),'XTickLabel',['10^{-6}';'10^{-4}';'10^{-2}';'10^{0} ']);
+set(gca,'ylim',[0 70],'Ytick',0:20:60,'YTickLabel',['0 ';'20';'40';'60']);
+ylabel('FLN counts','FontSize', fsize);%set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [-.01, -0.0, -0.9]);
+[counts,~]=hist(flnMatpos,logspace(-6,0,13));
+disp(sum(~(10:13))/sum(counts(10:13)));
+%saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 5 histfln1', 'pdf')
+saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 4F', 'pdf')
+
+    hFig = figure(); 
+    %set(hFig,'units', 'centimeters', 'Position', [0 0 4 2.5],'PaperUnits','centimeters','PaperPosition',[.1 .1 4 2.5],'PaperSize',[4.1 2.9]) 
+    set(hFig,'units', 'centimeters', 'Position', [0 0 4.2 2.5],'PaperUnits','centimeters','PaperPosition',[.1 .1 4.2 2.5],'PaperSize',[4.3 2.9]) 
+    %hist(flnMatvisven,logspace(-4,1,11));
+hist(flnMatvisven,logspace(-6,1,15));
+set(gca,'xscale','log');h = findobj(gca,'Type','patch');
+set(h,'FaceColor',[0.4940    0.1840    0.5560],'FaceAlpha',0.75,'LineWidth',0.2);
+h = findobj(gca,'Type','line');set(h,'Marker','none'); 
+%h = findobj(gca,'Type','patch');%set(h,'EdgeAlpha',0.8);
+set(gca,'FontSize',fsizelab,'box','off');
+    set(gca,'xlim',[1e-6 3],'Xtick',logspace(-6,0,4),'XTickLabel',['10^{-6}';'10^{-4}';'10^{-2}';'10^{0} ']);%['10^{-6}';'10^{-4}';'10^{-2}';'10^{0} ']);'XTickLabel',[]
+    set(gca,'ylim',[0 5],'Ytick',0:5:5,'YTickLabel',['0 ';'5 ']);
+h = ylabel('FLNs: ventral stream','FontSize', fsize);%set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [-.01, -0.0, -0.9]);
+
+[countsvv,centersvv]=hist(flnMatvisven,logspace(-4,1,11));
+%disp(sum(countsvv(10:13))/sum(counts(10:13)));
+%saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 5 histfln2', 'pdf')
+saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 4G', 'pdf')
+
+%all vs feedback
+flnMatfb=zeros(500,1);
+    count=0;
+    for i=1:29 
+        for j=i:29 
+            if(flnMat(i,j)>0) 
+                count=count+1;flnMatfb(count,1) = flnMat(i,j);
+            end; 
+        end;
+    end;
+flnMatfb=flnMatfb(1:count,1);
+hFig = figure(); set(hFig,'units', 'centimeters', 'Position', [0 0 4 3],'PaperUnits','centimeters','PaperPosition',[.1 .1 4 3],'PaperSize',[4.1 3.1]) 
+hist(flnMatpos,logspace(-6,1,15));set(gca,'xscale','log');h = findobj(gca,'Type','patch');
+set(h,'FaceColor',[0.4940    0.1840    0.5560],'EdgeColor','w','FaceAlpha',0.35,'LineWidth',0.2);
+%h = findobj(gca,'Type','line');set(h,'Marker','none'); 
+hold on;
+hist(flnMatfb,logspace(-6,1,15));
+h = findobj(gca,'Type','line');set(h,'Marker','none'); 
+%h = findobj(gca,'Type','patch');%set(h,'EdgeAlpha',0.8);
+set(gca,'FontSize',fsizelab,'box','off');
+set(gca,'xlim',[1e-6 3],'Xtick',logspace(-6,0,4),'XTickLabel',['10^{-6}';'10^{-4}';'10^{-2}';'10^{0} ']);
+set(gca,'ylim',[0 70],'Ytick',0:20:60,'YTickLabel',['0 ';'20';'40';'60']);
+ylabel('FLN counts','FontSize', fsize);%set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [-.01, -0.0, -0.9]);
+[counts,~]=hist(flnMatpos,logspace(-6,0,13));[countsvv,~]=hist(flnMatfb,logspace(-6,0,13));
+disp(sum(countsvv)/sum(counts)); %.5093
+%saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig fb fln', 'pdf')
+        
+
+%one-directional. 
+count=0;flnMatonedir=zeros(500,1);
+    for i = 1:29 
+        for j = 1:i 
+            if( (flnMat(i,j)*flnMat(j,i)==0) && (flnMat(i,j) + flnMat(j,i) > 0) )
+                count=count+1;
+                flnMatonedir(count,1)= max( flnMat(i,j) , flnMat(j,i) );
+            end; 
+        end;
+    end;
+flnMatonedir = flnMatonedir(1:count,1);
+
+hFig = figure(); set(hFig,'units', 'centimeters', 'Position', [0 0 4 3],'PaperUnits','centimeters','PaperPosition',[.1 .1 4 3],'PaperSize',[4.1 3.1]) 
+hist(flnMatpos,logspace(-6,1,15));set(gca,'xscale','log');h = findobj(gca,'Type','patch');
+set(h,'FaceColor',[0.4940    0.1840    0.5560],'EdgeColor','w','FaceAlpha',0.35,'LineWidth',0.2);
+%h = findobj(gca,'Type','line');set(h,'Marker','none'); 
+hold on;
+hist(flnMatonedir,logspace(-6,1,15));
+h = findobj(gca,'Type','line');set(h,'Marker','none'); 
+%h = findobj(gca,'Type','patch');%set(h,'EdgeAlpha',0.8);
+set(gca,'FontSize',fsizelab,'box','off');
+set(gca,'xlim',[1e-6 3],'Xtick',logspace(-6,0,4),'XTickLabel',['10^{-6}';'10^{-4}';'10^{-2}';'10^{0} ']);
+set(gca,'ylim',[0 70],'Ytick',0:20:60,'YTickLabel',['0 ';'20';'40';'60']);
+ylabel('FLN counts','FontSize', fsize);%set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [-.01, -0.0, -0.9]);
+[counts,~]=hist(flnMatpos,logspace(-6,0,13));[countsvv,~]=hist(flnMatonedir,logspace(-6,0,13));
+disp(sum(countsvv)/sum(counts)); %.2015
+%saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig fln one dir', 'pdf')
+
+flnMatthres=zeros(500,1); thres = .0023;
+    count=0;
+    for i=1:29 
+        for j=1:29 
+            if(flnMat(i,j)>thres) 
+                count=count+1;flnMatthres(count,1) = flnMat(i,j);
+                if (i==2 && j == 1)
+                    disp('here')
+                end
+            end; 
+        end;
+    end;
+flnMatthres=flnMatthres(1:count,1);
+hFig = figure(); set(hFig,'units', 'centimeters', 'Position', [0 0 4 3],'PaperUnits','centimeters','PaperPosition',[.1 .1 4 3],'PaperSize',[4.1 3.1]) 
+hist(flnMatpos,logspace(-6,1,15));set(gca,'xscale','log');h = findobj(gca,'Type','patch');
+set(h,'FaceColor',[0.4940    0.1840    0.5560],'EdgeColor','w','FaceAlpha',0.35,'LineWidth',0.2);
+%h = findobj(gca,'Type','line');set(h,'Marker','none'); 
+hold on;
+hist(flnMatthres,logspace(-6,1,15));
+h = findobj(gca,'Type','line');set(h,'Marker','none'); 
+%h = findobj(gca,'Type','patch');%set(h,'EdgeAlpha',0.8);
+set(gca,'FontSize',fsizelab,'box','off');
+set(gca,'xlim',[1e-6 3],'Xtick',logspace(-6,0,4),'XTickLabel',['10^{-6}';'10^{-4}';'10^{-2}';'10^{0} ']);
+set(gca,'ylim',[0 70],'Ytick',0:20:60,'YTickLabel',['0 ';'20';'40';'60']);
+ylabel('FLN counts','FontSize', fsize);%set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [-.01, -0.0, -0.9]);
+[counts,~]=hist(flnMatpos,logspace(-6,0,13));[countsvv,~]=hist(flnMatthres,logspace(-6,0,13));
+disp(sum(countsvv)/sum(counts)); %
+%saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig thres fln', 'pdf')
+
+end
+
+if caseval == 7
+    
+    wmillerEErange = 4.:.025:6.5; wmillerEIrange = 4.5:.025:7.;%for fig. 
+
+
+    wmillerorig=4 + 2/7; kmillerorig=1.1;
+    wmillerorigtoplot=4.45; kmillerorigtoplot=4.7/wmillerorigtoplot;
+
+    taue=.02; 
+    taumatrix = [1/taue;1/taue];  
+    tmpzero = zeros(2,1);
+    maxamplocal = zeros(length(wmillerEIrange),length(wmillerEErange));
+    eigA = zeros(length(wmillerEIrange),length(wmillerEErange));
+
+    tstep = .0001; tmax=2;
+    trange = 0:tstep:tmax;
+    init = [1;0];
+    state_m=zeros(2,length(trange));state_m(1:2,1) = init;
+
+    wexctoinh = wmillerorig; winhself = wmillerorig*kmillerorig;
+
+%     for s=1:length(wmillerEErange)   %comment to make run faster - save
+%     values
+%     %data for contour. 
+%          for ss=1:length(wmillerEIrange)
+%             disp([s, ss]);
+% 
+%       wmiller = wmillerEErange(s); wkmiller=wmillerEIrange(ss); 
+% 
+%       wexcself = wmiller; 
+%       winhtoexc = wkmiller; 
+% 
+%       A = [(wexcself-1) -winhtoexc; wexctoinh (-winhself-1)];
+%       A = bsxfun(@times, A,taumatrix);
+% 
+%     for time=1:length(trange)-1
+%     state_m(1:2,time+1) = max(state_m(1:2,time)+ tstep*A*state_m(1:2,time), tmpzero);
+%     end
+%     [~,wcond]=eig(A);
+%     eigA(ss,s) = max(real(diag(wcond)));
+% 
+%     if (eigA(ss,s)<0)
+%     maxamplocal(ss,s) = max(state_m(1,:)); 
+%     end;
+%         end
+%     end 
+
+    
+    hFig = figure(); fsizelab = 7; fsize=7;mksize = 4;
+    %set(hFig,'units', 'centimeters', 'Position', [0 0 7. 4.],'PaperUnits','centimeters','PaperPosition',[.1 .1 7. 4.],'PaperSize',[6.7 4.]) 
+    %save('maxampsaved','maxampsaved')   
+    set(hFig,'units', 'centimeters', 'Position', [0 0 7. 4.],'PaperUnits','centimeters','PaperPosition',[.1 .1 7. 4.],'PaperSize',[7 4.3]) 
+    load maxampsaved; maxamplocal = maxampsaved; 
+    for i = 1:101; for j = 1:101; if maxamplocal(i,j) ==0;  maxamplocal(i,j)=-5; end;end;end; %revision added.    
+    ax=gca; pos=get(gca,'pos');
+    [C,h] = contourf(wmillerEErange,wmillerEIrange,maxamplocal,20);%,'Position',[pos(1)+pos(3)+.1 pos(2) .1 pos(4)]);    
+    xlabel('Local E to E coupling','FontSize', fsize); ylabel('Local I to E coupling','FontSize', fsize);
+    annotation('textbox', [0.4,0.25,0.1,0.1],'Color','w','String', 'unstable','FontSize',fsizelab,'LineStyle','None');
+    shading flat;set(h,'LineColor','none');h = colorbar;ylabel(h, 'Maximum firing rate in E (Hz)','FontSize',fsizelab);
+    set(h,'Ticks',[0,4,8]);%colorbar('Ticks',[0,1,2,3]);  
+    x1=get(gca,'position');x=get(h,'Position');x(3)=0.03;set(h,'Position',x);set(gca,'position',x1);
+    set(gca,'FontSize',fsizelab);
+    set(gca,'Xtick',4:1:6,'XTickLabel',['4';'5';'6']); set(gca,'Ytick',4.5:1:6.5,'YTickLabel',['4.5';'5.5';'6.5']);
+    %h = xlabel('Local E to E coupling','FontSize', fsize);set(h, 'Units', 'Normalized');
+    %h = ylabel('Local I to E coupling','FontSize', fsize);set(h, 'Units', 'Normalized');%pos = get(h, 'Position');set(h, 'Position', pos + [-.01, -0.0, -0.9]);
+    wkmillerorigtoplot = wmillerorigtoplot*kmillerorigtoplot; wmillernew = 6; wkmillernew = 6.7; 
+    %hold on; plot(wmillerorigtoplot, wkmillerorigtoplot, 'v','LineWidth',.1,'MarkerEdgeColor',cv(1,:),'MarkerFaceColor',cv(1,:),'Markersize',mksize);
+    %hold on;plot(wmillernew,wkmillernew,'v','LineWidth',0.1,'MarkerEdgeColor',cv(2,:),'MarkerFaceColor',cv(2,:),'Markersize',mksize);
+    hold on; plot(wmillerorigtoplot, wkmillerorigtoplot, 'x','LineWidth',.1,'MarkerEdgeColor',cv(1,:),'MarkerFaceColor',cv(1,:),'Markersize',mksize);
+    hold on;plot(wmillernew,wkmillernew,'x','LineWidth',.1,'MarkerEdgeColor',cv(2,:),'MarkerFaceColor',cv(2,:),'Markersize',mksize);
+    %caxis([0.5 9.3]); set colorvar limit manually 
+    colormap(hot); %revision    
+    %saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 2 contour', 'pdf');
+    %saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 2C', 'pdf');
+
+    tmax=.6;trange=0:tstep:tmax;
+    for count=1:2
+        if count==1
+          
+          wmiller =  wmillerorigtoplot; wkmiller = wmillerorigtoplot*kmillerorigtoplot;wkmillerboundary=4.62;
+        else      
+          wmiller = 6; wkmiller = 6.7; wkmillerboundary=6.668; 
+        end
+        
+        wexcself = wmiller; 
+        winhtoexc = wkmiller;
+        winhtoexc_bound = wkmillerboundary;
+
+        A = [(wexcself-1) -winhtoexc; wexctoinh (-winhself-1)];
+        A = bsxfun(@times, A,taumatrix);
+
+        Abound = [(wexcself-1) -winhtoexc_bound; wexctoinh (-winhself-1)];
+        Abound = bsxfun(@times, Abound,taumatrix);
+        
+        state_m=zeros(2,length(trange));state_m(1:2,1) = init;
+        state_mbound=zeros(2,length(trange));state_mbound(1:2,1) = init;
+        
+        for time=1:length(trange)-1
+        state_m(1:2,time+1) = max ( state_m(1:2,time) + tstep*A*state_m(1:2,time) , tmpzero);
+        state_mbound(1:2,time+1) = max ( state_mbound(1:2,time) + tstep*Abound*state_mbound(1:2,time) , tmpzero);
+        end
+        
+        if count==1
+            lw = 1; fsizelab = 7; fsize=7;msize=7;
+            state_m_old = state_m; state_mbound_old = state_mbound;
+            hFig = figure();set(hFig,'units', 'centimeters', 'Position', [0 0 3.6 2.5],'PaperUnits','centimeters','PaperPosition',[.1 .1 3.6 2.5],'PaperSize',[3.8 2.8]);
+            plot(trange,state_m(1,:),'g','LineWidth',lw,'MarkerSize',msize,'Color',cv(1,:));% ,'Color',[0.4660    0.6740    0.1880]);,'Color',[0.4940    0.1840    0.5560]
+        else
+        hold on;plot(trange,state_m(1,:),'m','LineWidth',lw,'MarkerSize',msize,'Color',cv(2,:)); grid off;set(gca,'FontSize',fsizelab,'box','off');            
+        h = xlabel('Time (s)','FontSize', fsize);set(h, 'Units', 'Normalized');%pos = get(h, 'Position');set(h, 'Position', pos + [-.0, -0.01, -0.9]);
+        h = ylabel('Excitatory rate (Hz)','FontSize', fsize);set(h, 'Units', 'Normalized');%pos = get(h, 'Position');set(h, 'Position', pos + [-.02, 0., -0.9]);
+        set(gca,'Xtick',0:.2:.6,'XTickLabel',['0  ';'0.2';'0.4';'0.6']);%,'xlim',[20 52]);
+        set(gca,'Ytick',0:2:6,'YTickLabel',['0';'2';'4';'6']);
+        legend({'weak LBA','strong LBA'},'Position',[0.61 0.89 0.1 0.1],'Box','off','FontSize',fsize);         
+%        saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 2 BA', 'pdf')
+ %       saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 2B', 'pdf')
+
+        hFig = figure();set(hFig,'units', 'centimeters', 'Position', [0 0 4 4],'PaperUnits','centimeters','PaperPosition',[.2 .2 4 4],'PaperSize',[4.2 4.2]);
+        plot(trange,state_m_old(1,:),'Color',cv(1,:),'LineWidth',lw,'MarkerSize',msize); hold on; 
+        plot(trange,state_m(1,:),'Color',cv(2,:),'LineWidth',lw,'MarkerSize',msize); hold on; 
+        plot(trange,state_mbound_old(1,:),'-.','Color',cv(1,:),'LineWidth',lw,'MarkerSize',msize);hold on;                 
+        plot(trange,state_mbound(1,:),'-.','Color',cv(2,:),'LineWidth',lw,'MarkerSize',msize);
+        grid off;set(gca,'FontSize',fsizelab,'box','off');            
+        h = xlabel('Time (s)','FontSize', fsize);set(h, 'Units', 'Normalized');%pos = get(h, 'Position');set(h, 'Position', pos + [-.0, -0.01, -0.9]);
+        h = ylabel('Excitatory rate (Hz)','FontSize', fsize);set(h, 'Units', 'Normalized');%pos = get(h, 'Position');set(h, 'Position', pos + [-.02, 0., -0.9]);
+        %set(gca,'Xtick',0:.1:.2,'XTickLabel',['0  ';'0.1';'0.2']);%,'xlim',[20 52]);
+        set(gca,'Xtick',0:.2:.6,'XTickLabel',['0  ';'0.2';'0.4';'0.6']);%,'xlim',[20 52]);
+        set(gca,'Ytick',0:2:6,'YTickLabel',['0';'2';'4';'6']);
+        %saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 2 BAnearedge good', 'pdf')
+%        saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/supp fig 5 BAnearedge', 'pdf');
+        end
+    end
+end
+
+if caseval == 8
+   
+    inpParams=struct('tStart',2,'tEnd',2.25,'ampl',21.8*1.9);%,22.05*1.9);
+    areaInput.inp=zeros(tParams.nSteps,1);
+    areaInput.inp(round(inpParams.tStart/tParams.dt):round(inpParams.tEnd/tParams.dt))=inpParams.ampl;
+    muEErange = 34:2:36;omegaEI = 19.7;
+    prop24c = zeros(length(muEErange),2);
+
+     for muval=1:length(muEErange)
+        muEE = muEErange(muval); clear A popRates;
+ 
+        localParams.bgInh=zeros(netwParams.nNodes,1);%background inhibitory
+        localParams.ee=betaE*omegaEE*(1+netwParams.alpha*netwParams.hier);
+        localParams.ie=betaI*omegaIE*(1+netwParams.alpha*netwParams.hier);
+        localParams.ei=-betaE*omegaEI; 
+        localParams.ii=-betaI*omegaII;         
+        ldParams.ee=betaE*muEE*(1+netwParams.alpha*netwParams.hier);
+        ldParams.ie=betaI*muIE*(1+netwParams.alpha*netwParams.hier);
+        ldConns.ee= bsxfun(@times,flnMat,ldParams.ee);
+        ldConns.ie= bsxfun(@times,flnMat,ldParams.ie);
+        wEe=diag(-1+localParams.ee)+ldConns.ee;
+        wEi=localParams.ei*eye(nNodes);%these ws would be 29x29 identity matrices. 
+        wIe=diag(localParams.ie)+ldConns.ie;
+        wIi=(-1+localParams.ii)*eye(nNodes);
+        A = [wEe/localParams.tauE wEi/localParams.tauE;...
+            wIe/localParams.tauI wIi/localParams.tauI];
+        currParams.A=A; 
+        B=currParams.A;%B=params.A;
+        B(1:nNodes,:)=B(1:nNodes,:)*localParams.tauE;
+        B((nNodes+1):end,:)=B((nNodes+1):end,:)*localParams.tauI;
+        currs=-B*currParams.desiredSs; 
+        localParams.bgExc=currs(1:nNodes); localParams.bgInh=currs((nNodes+1):end);
+        bgCurr=[localParams.bgExc; localParams.bgInh];%bg = background
+        combMat=A;
+        combMat(1:nNodes,:)=combMat(1:nNodes,:)*localParams.tauE;
+        combMat((nNodes+1):end,:)=combMat((nNodes+1):end,:)*localParams.tauI;
+        sstate=-combMat\bgCurr;%which is -bgCurr/combMat%this is steady state. 
+        netwParams.initConds.exc=sstate(1:nNodes); netwParams.initConds.inh=sstate((nNodes+1):end);
+        popRates=runNetworkAreaInputNEW(tParams,localParams,netwParams,ldConns,areaInput,'threshLinear'); 
+        maxpeak=zeros(nNodes,1);
+        for r=1:nNodes
+        maxpeak(r,1)=max(popRates.exc(r,(toplotstart:toplotend))-popRates.exc(r,toplotstart));
+        end
+        nodelen=1:29;nodelen=nodelen';disp(muEE);
+        
+        x1 = -98.25; 
+        x2 = -95.5;
+        s=1000;
+        a = max(popRates.exc(29,(toplotstart:toplotstart+16000))-popRates.exc(29,toplotstart));
+        b = max(popRates.exc(1,(toplotstart:toplotstart+16000))-popRates.exc(1,toplotstart));
+        if muval==1
+            hFig = figure();set(hFig,'units', 'centimeters', 'Position', [0 0 4 4],'PaperUnits','centimeters','PaperPosition',[.1 .1 3.5 4],'PaperSize',[3.7 4.1]);
+        else
+             hFig = figure();set(hFig,'units', 'centimeters', 'Position', [0 0 3.4 4],'PaperUnits','centimeters','PaperPosition',[-.2 .1 3.1 4],'PaperSize',[3. 4.1]);
+
+        end
+ %       plot(tSteps(toplotstart:toplotend)-100,popRates.exc(1,(toplotstart:toplotend))-popRates.exc(1,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab);set(gca,'FontSize',fsizelab,'box','off','Xtick',[],'XLim',[x1 x2]);%ylabel('V1','FontSize', 18)
+ %       hold on;plot(tSteps(toplotstart:toplotend)-100,popRates.exc(29,(toplotstart:toplotend))-popRates.exc(29,toplotstart),'LineWidth',lw,'MarkerSize',fsizelab);set(gca,'FontSize',fsizelab,'box','off','XLim',[x1 x2]);
+        popratesv1notzero = max(1e-2,popRates.exc(1,(toplotstart:toplotend))-popRates.exc(1,toplotstart));
+        poprates24cnotzero = max(1e-2,popRates.exc(29,(toplotstart:toplotend))-popRates.exc(29,toplotstart));
+        semilogy(tSteps(toplotstart:toplotend)-100,popratesv1notzero,'LineWidth',lw,'MarkerSize',fsizelab,'color',[65 182 196]/255);%cv(1,:)*.8);
+        set(gca,'FontSize',fsizelab,'box','off','Xtick',[],'XLim',[x1 x2]);%ylabel('V1','FontSize', 18)
+        hold on;semilogy(tSteps(toplotstart:toplotend)-100,poprates24cnotzero,'LineWidth',lw,'MarkerSize',fsizelab,'color',[0 109 44]/255);%cv(1,:)*(1/.8));
+        set(gca,'FontSize',fsizelab,'box','off','XLim',[x1 x2]);
+
+        h = xlabel('Time (s)','FontSize', fsize);
+        set(gca,'Xtick',-98.:2:-96);set(gca,'XTickLabel',['0';'2']);
+        if muval==1
+            c = 1.2*max(a,b); set(gca,'Ytick',[round(s*maxpeak(29,1))/s,round(s*maxpeak(1,1))/s]);set(gca,'YTickLabel',[round(s*maxpeak(29,1))/s,round(s*maxpeak(1,1))/s],'YLim',[1e-2 5*c]);
+            ylim1 = 5*c;
+            set(gca,'Ytick',logspace(-2,2,3),'YTickLabel',['10^{-2}';'10^{0} ';'10^{2} ']);
+            hold on; plot(tSteps(round(inpParams.tStart/tParams.dt):round(inpParams.tEnd/tParams.dt))-100,1.6*c*ones(size(tSteps(round(inpParams.tStart/tParams.dt):round(inpParams.tEnd/tParams.dt)))),'k');
+            %%legend('V1','24c');
+            
+            annotation('textbox', [0.38,0.55,0.1,0.1],'String', 'V1','FontSize',fsizelab,'LineStyle','None');
+            annotation('textbox', [0.47,0.22,0.1,0.1],'String', '24c','FontSize',fsizelab,'LineStyle','None');
+            h = ylabel('Change in firing rate (Hz)','FontSize', fsize);%set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [-.01, 6.2, -0.9]);%bad
+            set(gca,'FontSize',fsizelab,'box','off');annotation('textbox', [0.25,0.85,0.1,0.1],'String', '250 ms','FontSize',fsizelab,'LineStyle','None');
+        else
+            c = 300; %set(gca,'Ytick',[round(s*maxpeak(1,1))/s,round(s*maxpeak(29,1))/s]);
+            %set(gca,'YTickLabel',[round(s*maxpeak(1,1))/s,round(s*maxpeak(29,1))/s],'YLim',[1e-2 800]);%300]);
+            set(gca,'YTickLabel',[],'YLim',[1e-2 ylim1]);%800]);
+            %set(gca,'Ytick',logspace(-2,2,3),'YTickLabel',['10^{-2}';'10^{0} ';'10^{2} ']);
+            hold on; plot(tSteps(round(inpParams.tStart/tParams.dt):round(inpParams.tEnd/tParams.dt))-100,.68*c*ones(size(tSteps(round(inpParams.tStart/tParams.dt):round(inpParams.tEnd/tParams.dt)))),'k');
+            %legend('V1','24c');
+            annotation('textbox', [0.54,0.505,0.1,0.1],'String', 'V1','FontSize',fsizelab,'LineStyle','None');
+            annotation('textbox', [0.55,0.85,0.1,0.1],'String', '24c','FontSize',fsizelab,'LineStyle','None');
+            %h = ylabel('Change in firing rate (Hz)','FontSize', fsize);%set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [-.01, 6.2, -0.9]);%bad
+            set(gca,'FontSize',fsizelab,'box','off');annotation('textbox', [0.13,0.85,0.1,0.1],'String', '250 ms','FontSize',fsizelab,'LineStyle','None');
+            set(gca,'ycolor',get(gcf,'color') ) ;     
+        end
+        %h = ylabel('Change in firing rate (Hz)','FontSize', fsize);%set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [-.01, 6.2, -0.9]);%bad
+         if muval==1
+%             saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 1 muEE weak', 'pdf')
+         else
+%             saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 1 muEE blowup', 'pdf')
+      %       saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 1B', 'pdf')
+
+         end
+     end    
+end
+
+if caseval == 9
+    load propagation.mat
+    hFig2 = figure();
+
+    set(hFig2,'units', 'centimeters', 'Position', [0 0 7.1 1.6],'PaperUnits','centimeters','PaperPosition',[0. .15 7.1 1.6],'PaperSize',[6.6 2.])     
+
+    fsize = 6; fsizelab = 6; 
+    
+    semilogy(1:29,100*ratios0/ratios0(1),'.-','LineWidth',lw,'MarkerSize',fsizelab,'Color',[0.4660, 0.6740, 0.1880]);hold on;
+    semilogy(1:29,100*ratios1/ratios1(1),'.-','LineWidth',lw,'MarkerSize',fsizelab,'Color',[0.4940,0.1840,0.5560]);  
+    set(gca,'Ytick',logspace(-2,2,3),'YTickLabel',['10^{-2}';'10^{0} ';'10^{2} ']);
+    legend({'weak GBA','strong GBA'},'Position',[0.69 0.85 0.1 0.1],'Box','off','FontSize',fsize);  %  'Position',[0.71 0.84 0.1 0.1]     
+    %xlabel('Areas','FontSize',fsize);
+    set(gca,'FontSize',fsizelab);
+    set(gca,'Xtick',1:1:29,'box','off');
+    areapt = ['  V1 ';'  V2 ';'  V4 ';'  DP ';'  MT ';'  8m ';'  5  ';'  8l ';' TEO ';'  2  ';'  F1 ';' STPc';'  7A ';' 46d ';'  10 ';'9/46v';'9/46d';'  F5 ';' TEpd';' PBr ';' 7m  ';' 7B  ';'  F2 ';' STPi';' PROm';' F7  ';' 8B  ';' STPr';' 24c ']; %timept = ['';'0';'';'';'1';'';'';'2'];
+    %set(gca,'XTickLabel',areapt);
+    set(gca,'XTickLabel',[])
+    ax = gca;ax.XTickLabelRotation = 90; 
+    h = ylabel(sprintf('Peak firing rate (Hz)'),'FontSize',fsize);
+    pos = get(h, 'Position');set(h, 'Position', pos + [-.02, .26, -0.9]);%
+     
+    %pos = get(h, 'Position');set(h, 'Position', pos + [-.02, -.06, -0.9]);%
+      
+ %   saveas(hFig2, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 4 propgoodmaxrate', 'pdf');    
+     saveas(hFig2, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 3B', 'pdf');    
+
+end
+
+if caseval == 10
+    load prop10.mat; for10mean = meangamma; for10sig = siggamma; 
+    load prop20.mat; for20mean = meangamma; for20sig = siggamma; 
+    load prop30.mat; for30mean = meangamma; for30sig = siggamma; 
+    load prop40.mat; for40mean = meangamma; for40sig = siggamma; 
+  
+    hFig2 = figure();
+
+    set(hFig2,'units', 'centimeters', 'Position', [0 0 7.1 2.3],'PaperUnits','centimeters','PaperPosition',[0. .01 7.1 2.3],'PaperSize',[6.6 2.3])     
+    
+    fsize = 6; fsizelab = 6; 
+    
+    errorbar(1:29,for10mean,for10sig,'.-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));hold on;
+
+    errorbar(1:29,for40mean,for40sig,'.-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(2,:));
+    xlabel('Areas','FontSize',fsize);
+    set(gca,'FontSize',fsizelab);
+    set(gca,'Xtick',1:1:29,'box','off');%set(gca,'Xtick',0:1:28,'box','off');
+    areapt = ['  V1 ';'  V2 ';'  V4 ';'  DP ';'  MT ';'  8m ';'  5  ';'  8l ';' TEO ';'  2  ';'  F1 ';' STPc';'  7A ';' 46d ';'  10 ';'9/46v';'9/46d';'  F5 ';' TEpd';' PBr ';' 7m  ';' 7B  ';'  F2 ';' STPi';' PROm';' F7  ';' 8B  ';' STPr';' 24c ']; %timept = ['';'0';'';'';'1';'';'';'2'];
+    set(gca,'XTickLabel',areapt);
+    set(gca,'ylim',[.0012 .005],'Ytick',0.001:.002:.005);%,'YTickLabel',['0.001';'0.003';'0.005']);
+    ax = gca;ax.XTickLabelRotation = 90; 
+    h = ylabel(sprintf('Gamma power'),'FontSize',fsize);%set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [-.02, 0., -0.9]);%
+    %saveas(hFig2, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 4 gamma', 'pdf');    
+     saveas(hFig2, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 3C', 'pdf');    
+
+end
+
+if caseval == 11
+    load 'maxpeakbad_control.mat'; load 'maxpeakbad_nofb.mat'; load 'maxpeakbad_arimean.mat'; load 'maxpeakbad_geomean.mat'; load 'maxpeakbad_nohier.mat';
+    load 'maxpeakgood_control.mat'; load 'maxpeakgood_nofb.mat'; load 'maxpeakgood_arimean.mat'; load 'maxpeakgood_geomean.mat';load 'maxpeakgood_nohier.mat';
+    nodelen=1:29;nodelen=nodelen';
+    cy = [237 177 32]/255;
+    hFig = figure();
+    set(hFig,'units', 'centimeters', 'Position', [0 0 7.5 4.5],'PaperUnits','centimeters','PaperPosition',[.05 .05 7.5 4.5],'PaperSize',[8.6 4.4]) ;
+    semilogy(nodelen-1,100*(maxpeakbad_control)/maxpeakbad_control(1,1),'.-','LineWidth',lw,'MarkerSize',fsizelab,'Color','k');hold on;
+    semilogy(nodelen-1,100*(maxpeakbad_nofb)/maxpeakbad_nofb(1,1),'.-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));hold on;
+    semilogy(nodelen-1,100*(maxpeakbad_geomean)/maxpeakbad_geomean(1,1),'.-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(2,:));hold on;
+%     semilogy(nodelen-1,100*(maxpeakbad_arimean)/maxpeakbad_arimean(1,1),'.-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cy);hold on;
+
+    %if caseval==1   
+        hold on; semilogy((6:2:8)-1,100*(maxpeakbad_nofb(6:2:8,1))/maxpeakbad_nofb(1,1),':','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));
+        hold on; semilogy((9:2:11)-1,100*(maxpeakbad_nofb(9:2:11,1))/maxpeakbad_nofb(1,1),':','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));
+        set(gca,'Ytick',logspace(-6,2,3),'YTickLabel',['10^{-6}';'10^{-2}';'10^{2} '],'ylim',[1e-8 1e2]);
+    %else
+    %    set(gca,'Ytick',logspace(-4,2,4),'YTickLabel',['10^{-4}';'10^{-2}';'10^{0} ';'10^{2} ']);
+        %legend({'weak GBA','no fb','geom. mean'},'Position',[0.68 0.35 0.1 0.1],'Box','off','FontSize',fsize);  
+%         legend({'weak GBA','no fb','geom. mean','ari. mean'},'Position',[0.9 0.4 0.1 0.1],'Box','off','FontSize',fsize);  
+
+    %end
+    
+    xlabel('Areas','FontSize',fsize);
+    set(gca,'FontSize',fsizelab);
+    set(gca,'Xtick',0:1:28,'box','off');
+    areapt = ['  V1 ';'  V2 ';'  V4 ';'  DP ';'  MT ';'  8m ';'  5  ';'  8l ';' TEO ';'  2  ';'  F1 ';' STPc';'  7A ';' 46d ';'  10 ';'9/46v';'9/46d';'  F5 ';' TEpd';' PBr ';' 7m  ';' 7B  ';'  F2 ';' STPi';' PROm';' F7  ';' 8B  ';' STPr';' 24c ']; %timept = ['';'0';'';'';'1';'';'';'2'];
+    set(gca,'XTickLabel',areapt);
+    ax = gca;ax.XTickLabelRotation = 90; 
+    h = ylabel('Maximum firing rate (Hz)','FontSize',fsize);%set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [-.02, 0., -0.9]);%
+    %title('Weak case');
+    
+    hFig2 = figure();
+    set(hFig2,'units', 'centimeters', 'Position', [0 0 7.5 4.5],'PaperUnits','centimeters','PaperPosition',[.05 .05 7.5 4.5],'PaperSize',[7. 4.4]) ;
+    semilogy(nodelen-1,100*(maxpeakgood_control)/maxpeakgood_control(1,1),'.-','LineWidth',lw,'MarkerSize',fsizelab,'Color','k');hold on;
+    semilogy(nodelen-1,100*(maxpeakgood_nofb)/maxpeakgood_nofb(1,1),'.-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));hold on;
+    semilogy(nodelen-1,100*(maxpeakgood_geomean)/maxpeakgood_geomean(1,1),'.-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(2,:));hold on;
+%     semilogy(nodelen-1,100*(maxpeakgood_arimean)/maxpeakgood_arimean(1,1),'.-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cy);hold on;
+
+    %if caseval==1   
+        hold on; semilogy((6:2:8)-1,100*(maxpeakgood_nofb(6:2:8,1))/maxpeakgood_nofb(1,1),':','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));
+        hold on; semilogy((9:2:11)-1,100*(maxpeakgood_nofb(9:2:11,1))/maxpeakgood_nofb(1,1),':','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));
+        set(gca,'Ytick',logspace(-6,2,3),'YTickLabel',['10^{-6}';'10^{-2}';'10^{2} '],'ylim',[1e-8 1e2]);
+    %else
+    %    set(gca,'Ytick',logspace(-4,2,4),'YTickLabel',['10^{-4}';'10^{-2}';'10^{0} ';'10^{2} ']);
+        legend({'weak GBA','no fb','geom. mean'},'Position',[0.68 0.35 0.1 0.1],'Box','off','FontSize',fsize); 
+%         legend({'weak GBA','no fb','geom. mean','ari. mean'},'Position',[0.65 0.4 0.1 0.1],'Box','off','FontSize',fsize); 
+
+      %  title('strong GBA case')
+    %end
+    
+    xlabel('Areas','FontSize',fsize);
+    set(gca,'FontSize',fsizelab);
+    set(gca,'Xtick',0:1:28,'box','off');
+    areapt = ['  V1 ';'  V2 ';'  V4 ';'  DP ';'  MT ';'  8m ';'  5  ';'  8l ';' TEO ';'  2  ';'  F1 ';' STPc';'  7A ';' 46d ';'  10 ';'9/46v';'9/46d';'  F5 ';' TEpd';' PBr ';' 7m  ';' 7B  ';'  F2 ';' STPi';' PROm';' F7  ';' 8B  ';' STPr';' 24c ']; %timept = ['';'0';'';'';'1';'';'';'2'];
+    set(gca,'XTickLabel',areapt);
+    ax = gca;ax.XTickLabelRotation = 90; 
+    h = ylabel('Maximum firing rate (Hz)','FontSize',fsize);%set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [-.02, 0., -0.9]);%
+
+%     saveas(hFig,'/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/supp fig bad nofb geo mean'); 
+%     saveas(hFig2,'/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/supp fig good no fb geo mean'); 
+%     
+%     saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/supp fig bad nofb ari geo mean', 'pdf');
+%     saveas(hFig2, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/supp fig good no fb ari geo mean', 'pdf');
+
+    hFig = figure(); %control and no hierarchy. 
+    set(hFig,'units', 'centimeters', 'Position', [0 0 7.5 4.5],'PaperUnits','centimeters','PaperPosition',[.05 .05 7.5 4.5],'PaperSize',[8.6 4.4]) ;
+    semilogy(nodelen-1,100*(maxpeakbad_nohier)/maxpeakbad_nohier(1,1),'.-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));hold on;
+    semilogy(nodelen-1,100*(maxpeakgood_nohier)/maxpeakgood_nohier(1,1),'.-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(2,:));hold on;
+
+    h2a = semilogy(nodelen-1,100*(maxpeakbad_control)/maxpeakbad_control(1,1),'-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));hold on;
+    h2b = semilogy(nodelen-1,100*(maxpeakgood_control)/maxpeakgood_control(1,1),'-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(2,:));hold on;
+    h2a.Color(4)=0.4; h2b.Color(4)=0.4; 
+           
+    set(gca,'Ytick',logspace(-6,2,3),'YTickLabel',['10^{-6}';'10^{-2}';'10^{2} '],'ylim',[1e-6 1e2]);
+    %legend({'control: weak GBA','control: strong GBA,','no hier.: weak GBA','no hier.: strong GBA'},'Position',[0.68 0.35 0.1 0.1],'Box','off','FontSize',fsize);  
+    legend({'weak GBA','strong GBA'},'Position',[0.78 0.85 0.1 0.1],'Box','off','FontSize',fsize);  
+    xlabel('Areas','FontSize',fsize);
+    set(gca,'FontSize',fsizelab);
+    set(gca,'Xtick',0:1:28,'box','off');
+    areapt = ['  V1 ';'  V2 ';'  V4 ';'  DP ';'  MT ';'  8m ';'  5  ';'  8l ';' TEO ';'  2  ';'  F1 ';' STPc';'  7A ';' 46d ';'  10 ';'9/46v';'9/46d';'  F5 ';' TEpd';' PBr ';' 7m  ';' 7B  ';'  F2 ';' STPi';' PROm';' F7  ';' 8B  ';' STPr';' 24c ']; %timept = ['';'0';'';'';'1';'';'';'2'];
+    set(gca,'XTickLabel',areapt);
+    ax = gca;ax.XTickLabelRotation = 90; 
+    h = ylabel('Maximum firing rate (Hz)','FontSize',fsize);%set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [-.02, 0., -0.9]);%
+   %  saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/supp fig control no hier', 'pdf');
+
+
+    hFig = figure(); %control and no feedback. 
+    set(hFig,'units', 'centimeters', 'Position', [0 0 7.5 4.5],'PaperUnits','centimeters','PaperPosition',[.05 .05 7.5 4.5],'PaperSize',[8.6 4.4]) ;
+    h2a = semilogy(nodelen-1,100*(maxpeakbad_control)/maxpeakbad_control(1,1),'-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));hold on;
+    h2b = semilogy(nodelen-1,100*(maxpeakgood_control)/maxpeakgood_control(1,1),'-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(2,:));hold on;
+    h2a.Color(4)=0.4; h2b.Color(4)=0.4; 
+   
+    semilogy(nodelen-1,100*(maxpeakbad_nofb)/maxpeakbad_nofb(1,1),'.-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));hold on;
+        hold on; semilogy((6:2:8)-1,100*(maxpeakbad_nofb(6:2:8,1))/maxpeakbad_nofb(1,1),':','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));
+        hold on; semilogy((9:2:11)-1,100*(maxpeakbad_nofb(9:2:11,1))/maxpeakbad_nofb(1,1),':','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));
+    semilogy(nodelen-1,100*(maxpeakgood_nofb)/maxpeakgood_nofb(1,1),'.-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(2,:));hold on;
+        hold on; semilogy((6:2:8)-1,100*(maxpeakgood_nofb(6:2:8,1))/maxpeakgood_nofb(1,1),':','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(2,:));
+        hold on; semilogy((9:2:11)-1,100*(maxpeakgood_nofb(9:2:11,1))/maxpeakgood_nofb(1,1),':','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(2,:));
+        
+    set(gca,'Ytick',logspace(-6,2,3),'YTickLabel',['10^{-6}';'10^{-2}';'10^{2} '],'ylim',[1e-8 1e2]);
+    %legend({'control: weak GBA','control: strong GBA,','no fb: weak GBA','no fb: strong GBA'},'Position',[0.68 0.35 0.1 0.1],'Box','off','FontSize',fsize);  
+    xlabel('Areas','FontSize',fsize);
+    set(gca,'FontSize',fsizelab);
+    set(gca,'Xtick',0:1:28,'box','off');
+    areapt = ['  V1 ';'  V2 ';'  V4 ';'  DP ';'  MT ';'  8m ';'  5  ';'  8l ';' TEO ';'  2  ';'  F1 ';' STPc';'  7A ';' 46d ';'  10 ';'9/46v';'9/46d';'  F5 ';' TEpd';' PBr ';' 7m  ';' 7B  ';'  F2 ';' STPi';' PROm';' F7  ';' 8B  ';' STPr';' 24c ']; %timept = ['';'0';'';'';'1';'';'';'2'];
+    set(gca,'XTickLabel',areapt);
+    ax = gca;ax.XTickLabelRotation = 90; 
+    h = ylabel('Maximum firing rate (Hz)','FontSize',fsize);%set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [-.02, 0., -0.9]);%
+  %   saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/supp fig control nofb', 'pdf');
+    
+
+    hFig = figure(); %control and geom mean. 
+    set(hFig,'units', 'centimeters', 'Position', [0 0 7.5 4.5],'PaperUnits','centimeters','PaperPosition',[.05 .05 7.5 4.5],'PaperSize',[8.6 4.4]) ;
+    h2a = semilogy(nodelen-1,100*(maxpeakbad_control)/maxpeakbad_control(1,1),'-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));hold on;
+    h2b = semilogy(nodelen-1,100*(maxpeakgood_control)/maxpeakgood_control(1,1),'-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(2,:));hold on;
+    h2a.Color(4)=0.4; h2b.Color(4)=0.4; 
+    
+    semilogy(nodelen-1,100*(maxpeakbad_geomean)/maxpeakbad_geomean(1,1),'.-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));hold on;
+    semilogy(nodelen-1,100*(maxpeakgood_geomean)/maxpeakgood_geomean(1,1),'.-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(2,:));hold on;
+        
+    set(gca,'Ytick',logspace(-6,2,3),'YTickLabel',['10^{-6}';'10^{-2}';'10^{2} '],'ylim',[1e-6 1e2]);
+    %legend({'control: weak GBA','control: strong GBA,','no hier.: weak GBA','no hier.: strong GBA'},'Position',[0.68 0.35 0.1 0.1],'Box','off','FontSize',fsize);  
+    xlabel('Areas','FontSize',fsize);
+    set(gca,'FontSize',fsizelab);
+    set(gca,'Xtick',0:1:28,'box','off');
+    areapt = ['  V1 ';'  V2 ';'  V4 ';'  DP ';'  MT ';'  8m ';'  5  ';'  8l ';' TEO ';'  2  ';'  F1 ';' STPc';'  7A ';' 46d ';'  10 ';'9/46v';'9/46d';'  F5 ';' TEpd';' PBr ';' 7m  ';' 7B  ';'  F2 ';' STPi';' PROm';' F7  ';' 8B  ';' STPr';' 24c ']; %timept = ['';'0';'';'';'1';'';'';'2'];
+    set(gca,'XTickLabel',areapt);
+    ax = gca;ax.XTickLabelRotation = 90; 
+    h = ylabel('Maximum firing rate (Hz)','FontSize',fsize);%set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [-.02, 0., -0.9]);%
+  %   saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/supp fig control geomean', 'pdf');
+
+
+    hFig = figure(); %control and ari. mean. 
+    set(hFig,'units', 'centimeters', 'Position', [0 0 7.5 4.5],'PaperUnits','centimeters','PaperPosition',[.05 .05 7.5 4.5],'PaperSize',[8.6 4.4]) ;
+    h2a = semilogy(nodelen-1,100*(maxpeakbad_control)/maxpeakbad_control(1,1),'-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));hold on;
+    h2b = semilogy(nodelen-1,100*(maxpeakgood_control)/maxpeakgood_control(1,1),'-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(2,:));hold on;
+    h2a.Color(4)=0.4; h2b.Color(4)=0.4; 
+    
+    semilogy(nodelen-1,100*(maxpeakbad_arimean)/maxpeakbad_arimean(1,1),'.-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));hold on;
+    semilogy(nodelen-1,100*(maxpeakgood_arimean)/maxpeakgood_arimean(1,1),'.-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(2,:));hold on;
+        
+    set(gca,'Ytick',logspace(-4,2,3),'YTickLabel',['10^{-4}';'10^{-1}';'10^{2} '],'ylim',[1e-4 1e2]);
+    %legend({'control: weak GBA','control: strong GBA,','no hier.: weak GBA','no hier.: strong GBA'},'Position',[0.68 0.35 0.1 0.1],'Box','off','FontSize',fsize);  
+    xlabel('Areas','FontSize',fsize);
+    set(gca,'FontSize',fsizelab);
+    set(gca,'Xtick',0:1:28,'box','off');
+    areapt = ['  V1 ';'  V2 ';'  V4 ';'  DP ';'  MT ';'  8m ';'  5  ';'  8l ';' TEO ';'  2  ';'  F1 ';' STPc';'  7A ';' 46d ';'  10 ';'9/46v';'9/46d';'  F5 ';' TEpd';' PBr ';' 7m  ';' 7B  ';'  F2 ';' STPi';' PROm';' F7  ';' 8B  ';' STPr';' 24c ']; %timept = ['';'0';'';'';'1';'';'';'2'];
+    set(gca,'XTickLabel',areapt);
+    ax = gca;ax.XTickLabelRotation = 90; 
+    h = ylabel('Maximum firing rate (Hz)','FontSize',fsize);%set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [-.02, 0., -0.9]);%
+ %    saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/supp fig control arimean', 'pdf');
+   
+
+ load maxpeakbad_arimeannohier.mat; load maxpeakgood_arimeannohier.mat; 
+ load maxpeakbad_arimeanlochier.mat; load maxpeakgood_arimeanlochier.mat;
+    
+    hFig = figure(); %control and no hierarchy plus ari mean. 
+    set(hFig,'units', 'centimeters', 'Position', [0 0 7.5 4.5],'PaperUnits','centimeters','PaperPosition',[.05 .05 7.5 4.5],'PaperSize',[8.6 4.4]) ;
+    semilogy(nodelen-1,100*(maxpeakbad_arimeannohier)/maxpeakbad_arimeannohier(1,1),'.-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));hold on;
+    semilogy(nodelen-1,100*(maxpeakgood_arimeannohier)/maxpeakgood_arimeannohier(1,1),'.-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(2,:));hold on;
+    h2a = semilogy(nodelen-1,100*(maxpeakbad_control)/maxpeakbad_control(1,1),'-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));hold on;
+    h2b = semilogy(nodelen-1,100*(maxpeakgood_control)/maxpeakgood_control(1,1),'-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(2,:));hold on;
+    h2a.Color(4)=0.4; h2b.Color(4)=0.4;           
+    set(gca,'Ytick',logspace(-6,2,3),'YTickLabel',['10^{-6}';'10^{-2}';'10^{2} '],'ylim',[1e-6 1e2]);
+    %legend({'weak GBA','strong GBA'},'Position',[0.78 0.85 0.1 0.1],'Box','off','FontSize',fsize);  
+    xlabel('Areas','FontSize',fsize);
+    set(gca,'FontSize',fsizelab);
+    set(gca,'Xtick',0:1:28,'box','off');
+    areapt = ['  V1 ';'  V2 ';'  V4 ';'  DP ';'  MT ';'  8m ';'  5  ';'  8l ';' TEO ';'  2  ';'  F1 ';' STPc';'  7A ';' 46d ';'  10 ';'9/46v';'9/46d';'  F5 ';' TEpd';' PBr ';' 7m  ';' 7B  ';'  F2 ';' STPi';' PROm';' F7  ';' 8B  ';' STPr';' 24c ']; %timept = ['';'0';'';'';'1';'';'';'2'];
+    set(gca,'XTickLabel',areapt);
+    ax = gca;ax.XTickLabelRotation = 90; 
+    h = ylabel('Maximum firing rate (Hz)','FontSize',fsize);%set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [-.02, 0., -0.9]);%
+    %saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/suppfigcontrol_arimean_nohier', 'pdf');
+ 
+    hFig = figure(); %control and no hierarchy plus ari mean. 
+    set(hFig,'units', 'centimeters', 'Position', [0 0 7.5 4.5],'PaperUnits','centimeters','PaperPosition',[.05 .05 7.5 4.5],'PaperSize',[8.6 4.4]) ;
+    semilogy(nodelen-1,100*(maxpeakbad_arimeanlochier)/maxpeakbad_arimeanlochier(1,1),'.-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));hold on;
+    semilogy(nodelen-1,100*(maxpeakgood_arimeanlochier)/maxpeakgood_arimeanlochier(1,1),'.-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(2,:));hold on;
+    h2a = semilogy(nodelen-1,100*(maxpeakbad_control)/maxpeakbad_control(1,1),'-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));hold on;
+    h2b = semilogy(nodelen-1,100*(maxpeakgood_control)/maxpeakgood_control(1,1),'-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(2,:));hold on;
+    h2a.Color(4)=0.4; h2b.Color(4)=0.4;           
+    %set(gca,'Ytick',logspace(-6,2,3),'YTickLabel',['10^{-6}';'10^{-2}';'10^{2} '],'ylim',[1e-6 1e2]);
+    set(gca,'Ytick',logspace(-4,2,3),'YTickLabel',['10^{-4}';'10^{-1}';'10^{2} '],'ylim',[1e-4 1e2]);
+    %legend({'weak GBA','strong GBA'},'Position',[0.78 0.85 0.1 0.1],'Box','off','FontSize',fsize);  
+    xlabel('Areas','FontSize',fsize);
+    set(gca,'FontSize',fsizelab);
+    set(gca,'Xtick',0:1:28,'box','off');
+    areapt = ['  V1 ';'  V2 ';'  V4 ';'  DP ';'  MT ';'  8m ';'  5  ';'  8l ';' TEO ';'  2  ';'  F1 ';' STPc';'  7A ';' 46d ';'  10 ';'9/46v';'9/46d';'  F5 ';' TEpd';' PBr ';' 7m  ';' 7B  ';'  F2 ';' STPi';' PROm';' F7  ';' 8B  ';' STPr';' 24c ']; %timept = ['';'0';'';'';'1';'';'';'2'];
+    set(gca,'XTickLabel',areapt);
+    ax = gca;ax.XTickLabelRotation = 90; 
+    h = ylabel('Maximum firing rate (Hz)','FontSize',fsize);%set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [-.02, 0., -0.9]);%
+    %saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/suppfigcontrol_arimean_loc_hier', 'pdf');
+
+end
+
+
+if caseval == 12
+    
+%     colorb = 'yes';
+%     d=-100;
+%     if colorb == 'yes'
+%        fsizelab = 7; fsize=7;mksize = 3;
+%        hFig = figure();set(hFig,'units', 'centimeters', 'Position', [0 0 4. 2.],'PaperUnits','centimeters','PaperPosition',[.1 .1 4. 2.],'PaperSize',[4.7 2.]) 
+%        surf(peaks);cmap=colormap('hot');h=colorbar;set(h,'Ticks',[],'ycolor',get(gcf,'color'),'box','off'); ylabel(h, 'Activity','FontSize',fsizelab);
+%        %w = h.LineWidth;h.LineWidth = 1.;
+%        saveas(hFig,'/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig colorbar'); 
+%        saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig colorbar', 'pdf');
+% 
+%     end
+    
+    
+    load /Users/maddy/Dropbox/rishicode_maddy070115/caret2/brate;  
+    load /Users/maddy/Dropbox/rishicode_maddy070115/caret2/grate;    
+    load /Users/maddy/Dropbox/rishicode_maddy070115/caret2/bspike;  
+    load /Users/maddy/Dropbox/rishicode_maddy070115/caret2/gspike;
+    
+    load /Users/maddy/Dropbox/rishicode_maddy070115/caret2/badcons_4pt5;
+    load /Users/maddy/Dropbox/rishicode_maddy070115/caret2/goodcons_5pt5;
+    load /Users/maddy/Dropbox/rishicode_maddy070115/caret2/nofbgoodcons_5pt5;
+    load /Users/maddy/Dropbox/rishicode_maddy070115/caret2/cons_5;
+
+    load /Users/maddy/Dropbox/rishicode_maddy070115/caret2/brateS1;  
+    load /Users/maddy/Dropbox/rishicode_maddy070115/caret2/grateS1;    
+
+    nNodes = 29;
+   
+    cmap=colormap('hot');
+    % Take value between 0 and 1 and a matrix. Return the nth row of the matrix, where n/length(mat) is closest to x.
+    f=@(x,mat) mat(round(x*(length(mat)-1))+1,:);
+    %various caret figures. 
+    
+  %   logTau = min(.8,1.8*(1 - brate)); d=1;
+  %   logTau = min(.8,1.8*(1 - grate)); d=2;
+  %   logTau = (1-bspike); d=3;
+  %   logTau = (1-gspike); d=4;
+  %   logTau =  1-  badcons_4pt5;d=5;
+  %   logTau =  1 - goodcons_5pt5;d=6;
+  %   logTau =  1 - nofbgoodcons_5pt5;d=7;
+  %   logTau =  1 - cons_5;d=8;
+  
+  %   logTau = min(.8,1.8*(1 - brateS1)); d=-1;
+  %   logTau = min(.8,1.8*(1 - grateS1)); d=-2;
+     
+    if d==1
+    fid = fopen('/Users/maddy/Dropbox/rishicode_maddy070115/caret2/maddy badrate/Macaque.composite_june2012.areacolor','w');
+    end
+    if d==2
+    fid = fopen('/Users/maddy/Dropbox/rishicode_maddy070115/caret2/maddy goodrate/Macaque.composite_june2012.areacolor','w');
+    end
+    if d==3
+    fid = fopen('/Users/maddy/Dropbox/rishicode_maddy070115/caret2/maddy badspike/Macaque.composite_june2012.areacolor','w');
+    end
+    if d==4
+    fid = fopen('/Users/maddy/Dropbox/rishicode_maddy070115/caret2/maddy goodspike/Macaque.composite_june2012.areacolor','w');
+    end
+    if d==5
+    fid = fopen('/Users/maddy/Dropbox/rishicode_maddy070115/caret2/maddy badcons/Macaque.composite_june2012.areacolor','w');
+    end
+    if d==6
+    fid = fopen('/Users/maddy/Dropbox/rishicode_maddy070115/caret2/maddy goodcons/Macaque.composite_june2012.areacolor','w');
+    end
+    if d==7
+    fid = fopen('/Users/maddy/Dropbox/rishicode_maddy070115/caret2/maddy nofbgoodcons/Macaque.composite_june2012.areacolor','w');
+    end
+    if d==8
+    fid = fopen('/Users/maddy/Dropbox/rishicode_maddy070115/caret2/maddy cons5/Macaque.composite_june2012.areacolor','w');
+    end
+    
+    if d==-1
+    fid = fopen('/Users/maddy/Dropbox/rishicode_maddy070115/caret2/maddy badrateS1/Macaque.composite_june2012.areacolor','w');
+    end
+    if d==-2
+    fid = fopen('/Users/maddy/Dropbox/rishicode_maddy070115/caret2/maddy goodrateS1/Macaque.composite_june2012.areacolor','w');
+    end
+    
+    areaList{16}='9_46v'; areaList{17}='9_46d';
+    os1='   '; os2='      ';
+    fprintf(fid,'%s<Area_Color_File>\n',os1);
+    
+    if d > 4
+    list1rate = 1+[6,9,10,11,15,17,19,22,23,24,25,27,28];
+           for j = 1:length(list1rate) %new. 
+           logTau(list1rate(j)) = 0;
+           end
+    end
+   
+    
+    for i=1:nNodes
+        
+%         if d > 4 %5,6,7 - only look at rate areas that propagate. 
+%           %list1rate = [6,9,10,11,15,17,19,22,23,24,25,27,28];
+%           if logTau(i) < 0 %> 1
+%               logTau(i) = 0; % areas that show weak propagation. 
+%           end
+%         end
+        if d==7
+            if logTau(i) < 0 
+                logTau(i) = 0;
+            end
+        end
+
+        currCol=round(255*f(logTau(i),cmap));
+        fprintf(fid,'%s<Color>\n',os1);
+        fprintf(fid,'%s<name><![CDATA[%s_M132]]></name>\n',os2,areaList{i});
+        fprintf(fid,'%s<red>%d</red>\n',os2,currCol(1));
+        fprintf(fid,'%s<green>%d</green>\n',os2,currCol(2));
+        fprintf(fid,'%s<blue>%d</blue>\n',os2,currCol(3));
+        fprintf(fid,'%s<pointSize>2.0</pointSize>\n',os2);
+        fprintf(fid,'%s<lineSize>1.0</lineSize>\n',os2);
+        fprintf(fid,'%s<symbol><![CDATA[POINT]]></symbol>\n',os2);
+        fprintf(fid,'%s<sumscolorid><![CDATA[]]></sumscolorid>\n',os2);
+        fprintf(fid,'%s</Color>\n',os1);
+    end;
+    fprintf(fid,'%s</Area_Color_File>\n',os1);
+    fclose(fid);
+
+end
+
+if caseval == 13
+    cvosc(1,1:3) = [237/255, 177/255, 32/255]; cvosc(2,1:3) = [217/255 83/255 25/255];%color scheme.
+
+   load oscillations.mat  
+   hFig = figure();
+   set(hFig,'units', 'centimeters', 'Position', [0 0 5 1],'PaperUnits','centimeters','PaperPosition',[.05 .05 5 1],'PaperSize',[5.1 1.1]) ;
+   plot(time, r2,'-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cvosc(1,:));
+   set(gca,'xcolor',get(gcf,'color'),'ycolor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',[],'Xtick',[],'XLim',[2.7 3.6],'YLim',[-1 9]);
+
+   saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 3Aosc1', 'pdf')
+   
+   hFig = figure();
+   set(hFig,'units', 'centimeters', 'Position', [0 0 5 1],'PaperUnits','centimeters','PaperPosition',[.05 .05 5 1],'PaperSize',[5.1 1.1]) ;
+   plot(time, r5,'-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cvosc(2,:));
+   set(gca,'xcolor',get(gcf,'color'),'ycolor',get(gcf,'color'),'FontSize',fsizelab,'box','off','Ytick',[],'Xtick',[],'XLim',[2.7 3.6],'YLim',[-2.5 3]);
+   hold on;plot(time(501:801),-1.5*ones(size(time(501:801))),'k');
+   saveas(hFig, '/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/main fig 3Aosc2', 'pdf')
+    
+end
+
+if caseval == 14
+
+tParams.dt=2e-4; %new
+tParams.nSteps=3e4;
+
+tSteps=(1:tParams.nSteps)*tParams.dt;
+
+%omegaEI = 19.7 ; muEE = 33.7 ; %weak gba
+%omegaEI = 25.2 ; muEE = 51.5;  %strong gba
+
+
+   %contour for  large scale system --- long range muEE and wEI 
+   %paramvar1=31:.1:53; paramvar2=19:.1:26;
+paramvar1=31:5:53; paramvar2=19:5:26;
+ampE1_A = zeros(length(paramvar2),length(paramvar1));
+ampElast_A = zeros(length(paramvar2),length(paramvar1));
+
+
+    for tvar1=1:length(paramvar1)
+     for tvar2=1:length(paramvar2)
+    
+        var1here=paramvar1(tvar1); var2here=paramvar2(tvar2);
+        muEE=var1here; omegaEI=var2here;
+             disp([muEE,omegaEI]);
+
+        localParams.ee=betaE*omegaEE*(1+netwParams.alpha*netwParams.hier);%rsc*2.29119*(1+netwParams.alpha*netwParams.hier);
+        localParams.ie=betaI*omegaIE*(1+netwParams.alpha*netwParams.hier);%rsc*6.09552*(1+netwParams.alpha*netwParams.hier);
+        localParams.ei=-betaE*omegaEI; %-1.29954;
+        localParams.ii=-betaI*omegaII; %-4.40204;        
+        ldParams.ee=betaE*muEE*(1+netwParams.alpha*netwParams.hier);%rsc*2.29119*(1+netwParams.alpha*netwParams.hier);
+        ldParams.ie=betaI*muIE*(1+netwParams.alpha*netwParams.hier);%rsc*6.09552*(1+netwParams.alpha*netwParams.hier);
+        ldConns.ee= bsxfun(@times,flnMat,ldParams.ee);
+        ldConns.ie= bsxfun(@times,flnMat,ldParams.ie);
+
+        nNodes=size(ldConns.ee,1);
+        wEe=diag(-1+localParams.ee)+ldConns.ee;
+        wEi=localParams.ei*eye(nNodes);%these ws would be 29x29 identity matrices. 
+        wIe=diag(localParams.ie)+ldConns.ie;
+        wIi=(-1+localParams.ii)*eye(nNodes);%compare this to eqn 4 - where does -1 come from??
+        %result=[wEe/localParams.tauE wEi/localParams.tauE;wIe/localParams.tauI wIi/localParams.tauI];
+        A = [wEe/localParams.tauE wEi/localParams.tauE;...
+            wIe/localParams.tauI wIi/localParams.tauI];
+
+        currParams.A=A; 
+
+        B=currParams.A;%B=params.A;
+                B(1:nNodes,:)=B(1:nNodes,:)*localParams.tauE;
+                B((nNodes+1):end,:)=B((nNodes+1):end,:)*localParams.tauI;
+                currs=-B*currParams.desiredSs; %currs=-B*params.desiredSs;
+
+        localParams.bgExc=currs(1:nNodes); localParams.bgInh=currs((nNodes+1):end);
+        bgCurr=[localParams.bgExc; localParams.bgInh];%bg = background
+
+        combMat=A;
+        combMat(1:nNodes,:)=combMat(1:nNodes,:)*localParams.tauE;
+        combMat((nNodes+1):end,:)=combMat((nNodes+1):end,:)*localParams.tauI;
+        sstate=-combMat\bgCurr;%which is -bgCurr/combMat %this is steady state. 
+
+        netwParams.initConds.exc=sstate(1:nNodes); netwParams.initConds.inh=sstate((nNodes+1):end);
+
+        inpParams=struct('tStart',2,'tEnd',2.25,'ampl',22.05*1.9);
+        
+        areaInput.inp=zeros(tParams.nSteps,1);
+        areaInput.inp(round(inpParams.tStart/tParams.dt):round(inpParams.tEnd/tParams.dt))=inpParams.ampl;
+
+            popRates = runNetworkAreaInputNEW(tParams,localParams,netwParams,ldConns,areaInput,'threshLinear');
+            %maxpeak=zeros(nNodes,1);
+            %for r=1:nNodes
+            %maxpeak(r,1)=max(popRates.exc(r,(toplotstart:toplotend))-popRates.exc(r,toplotstart));
+            %end
+    
+    %ampratio(tvar2, tvar1) = (maxpeak(nNodes,1)/maxpeak(1,1));
+   maxstate=zeros(nNodes,1); toggle=0; statecheck=[popRates.exc ; popRates.inh];
+ 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%let oscillations be...remove below code for now to
+
+  if((max(statecheck(nNodes,:)) > statecheck(nNodes,tParams.nSteps)) )
+    ampE1_A(tvar2,tvar1) = max(statecheck(1,:)-statecheck(1,1));
+    ampElast_A(tvar2,tvar1) = max(statecheck(nNodes,:)-statecheck(nNodes,1));
+  end
+  
+     if((max(statecheck(nNodes,:)) == statecheck(nNodes,tParams.nSteps)) || (max(statecheck(nNodes,:))>1e8))%firing rate beyond max
+        ampE1_A(tvar2,tvar1) = 1; ampElast_A(tvar2,tvar1) = 1;
+     end
+     
+     end
+    end
+    
+     %save('big_sys_ampE1_A','ampE1_A'); save('big_sys_ampElast_A','ampElast_A');
+     ampratio = (ampElast_A./ampE1_A);
+     %save('big_sys_ampratio','ampratio');
+    load big_sys_ampratio; 
+    
+
+    paramvar1=31:.1:53; paramvar2=19:.1:26;
+    hFig = figure(); fsizelab = 7; fsize=7;mksize = 4;
+    set(hFig,'units', 'centimeters', 'Position', [0 0 7. 4.],'PaperUnits','centimeters','PaperPosition',[.1 .1 7. 4.],'PaperSize',[7 4.3]) 
+    %for i = 1:71; for j = 1:221; if ampratio(i,j) ==1;  ampratio(i,j)=1e-7; end;end;end; %revision added.    
+    ax=gca; pos=get(gca,'pos');
+    [C,h] = contourf(paramvar1,paramvar2,log10(ampratio),20);%,'Position',[pos(1)+pos(3)+.1 pos(2) .1 pos(4)]);    
+    xlabel('Global E to E coupling','FontSize', fsize); ylabel('Local I to E coupling','FontSize', fsize);
+    annotation('textbox', [0.4,0.35,0.1,0.1],'Color','k','String', 'unstable','FontSize',fsizelab,'LineStyle','None');
+    shading flat;set(h,'LineColor','none');h = colorbar;ylabel(h, 'Propagation ratio','FontSize',fsizelab);
+    %set(h,'Ticks',[0,4,8]);%colorbar('Ticks',[0,1,2,3]);  
+    x1=get(gca,'position');x=get(h,'Position');x(3)=0.03;set(h,'Position',x);set(gca,'position',x1);
+    set(gca,'FontSize',fsizelab);
+
+    omegaEIbefore = 19.7 ; muEEbefore = 33.7 ; omegaEIafter = 25.2 ; muEEafter = 51.5;
+
+    hold on; plot(muEEbefore, omegaEIbefore, 'x','LineWidth',.1,'MarkerEdgeColor',cv(1,:),'MarkerFaceColor',cv(1,:),'Markersize',mksize-2);
+    hold on;plot(muEEafter,omegaEIafter,'x','LineWidth',.1,'MarkerEdgeColor',cv(2,:),'MarkerFaceColor',cv(2,:),'Markersize',mksize-2);
+    %caxis([0 9.5]);
+    colormap(hot); %revision added.   
+    %saveas(hFig,'/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/suppcontourbigmat.pdf'); 
+    
+end
+
+
+if caseval == 15
+   mfrange = 0:.05:.2; 
+   %mfrange = 0:.005:.2; 
+   
+   propratbad = zeros(length(mfrange),1);
+   propratgood = zeros(length(mfrange),1);
+   
+   for vary = 1:length(mfrange)
+       mf = mfrange(vary); 
+       
+       for count=1:2
+        if count==1
+            omegaEI = 19.7 ; muEE = 33.7 ; 
+        else
+            omegaEI = 25.2 ; muEE = 51.5;
+        end
+        
+        localParams.ee=betaE*omegaEE*(1+netwParams.alpha*netwParams.hier);
+        localParams.ie=betaI*omegaIE*(1+netwParams.alpha*netwParams.hier);
+        localParams.ei=-betaE*omegaEI;
+        localParams.ii=-betaI*omegaII;         
+             
+        ldParams.ee=betaE*muEE*(1+netwParams.alpha*netwParams.hier);
+        ldParams.ie=betaI*muIE*(1+netwParams.alpha*netwParams.hier);    
+       
+        ldConns.ee= bsxfun(@times,flnMat,ldParams.ee);
+        ldConns.ie= bsxfun(@times,flnMat,ldParams.ie);
+
+        
+            burkmat = zeros(nNodes, nNodes);
+            %mf = .2;  %vary mf. 
+            %burkhalter like scaling of long range E to I. 
+            for r = 1:nNodes 
+                for s = 1:nNodes
+                    burkmat(r,s) = max(0,netwParams.hier(r,1) - netwParams.hier(s,1));
+                    %burkmat(r,s) = netwParams.hier(r,1) - netwParams.hier(s,1);
+                end ;
+            end;
+            burkmat = 1 + mf*burkmat;
+            ldConns.ie = bsxfun(@times,ldConns.ie,burkmat);
+        
+        
+        nNodes=size(ldConns.ee,1);
+        wEe=diag(-1+localParams.ee)+ldConns.ee;
+        wEi=localParams.ei*eye(nNodes);%these ws would be 29x29 identity matrices. 
+        wIe=diag(localParams.ie)+ldConns.ie;
+        wIi=(-1+localParams.ii)*eye(nNodes);
+        A = [wEe/localParams.tauE wEi/localParams.tauE;...
+            wIe/localParams.tauI wIi/localParams.tauI];
+
+        currParams.A=A; 
+
+        B=currParams.A;%B=params.A;
+                B(1:nNodes,:)=B(1:nNodes,:)*localParams.tauE;
+                B((nNodes+1):end,:)=B((nNodes+1):end,:)*localParams.tauI;
+                currs=-B*currParams.desiredSs; 
+
+        localParams.bgExc=currs(1:nNodes); localParams.bgInh=currs((nNodes+1):end);
+        bgCurr=[localParams.bgExc; localParams.bgInh];%bg = background
+
+        combMat=A;
+        combMat(1:nNodes,:)=combMat(1:nNodes,:)*localParams.tauE;
+        combMat((nNodes+1):end,:)=combMat((nNodes+1):end,:)*localParams.tauI;
+        sstate=-combMat\bgCurr;
+
+        netwParams.initConds.exc=sstate(1:nNodes); netwParams.initConds.inh=sstate((nNodes+1):end);
+
+        inpParams=struct('tStart',2,'tEnd',2.25,'ampl',22.05*1.9);
+        
+        areaInput.inp=zeros(tParams.nSteps,1);
+        areaInput.inp(round(inpParams.tStart/tParams.dt):round(inpParams.tEnd/tParams.dt))=inpParams.ampl;
+
+        if (count == 1)
+            popRatesbad=runNetworkAreaInputNEW(tParams,localParams,netwParams,ldConns,areaInput,'threshLinear');
+            maxpeakbad=zeros(nNodes,1);
+            for r=1:nNodes
+            maxpeakbad(r,1)=max(popRatesbad.exc(r,(toplotstart:toplotend))-popRatesbad.exc(r,toplotstart));
+            end
+        else
+            popRatesgood=runNetworkAreaInputNEW(tParams,localParams,netwParams,ldConns,areaInput,'threshLinear');
+            maxpeakgood=zeros(nNodes,1);
+            for r=1:nNodes
+            maxpeakgood(r,1)=max(popRatesgood.exc(r,(toplotstart:toplotend))-popRatesgood.exc(r,toplotstart));
+            end
+        end
+    
+       end
+       
+       propratbad(vary,1) = maxpeakbad(nNodes,1)/maxpeakbad(1,1);
+       propratgood(vary,1) = maxpeakgood(nNodes,1)/maxpeakgood(1,1);
+       
+
+   end
+  
+
+    %mfrange = 0:.005:.2;
+    %load propratgood; load propratbad;
+    hFig = figure();  
+    set(hFig,'units', 'centimeters', 'Position', [0 0 7.5 4.5],'PaperUnits','centimeters','PaperPosition',[.05 .05 7.5 4.5],'PaperSize',[8.6 4.4]) ;
+    semilogy(mfrange,propratbad,'-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(1,:));
+    hold on;semilogy(mfrange,propratgood,'-','LineWidth',lw,'MarkerSize',fsizelab,'Color',cv(2,:));
+    legend({'weak GBA','strong GBA'},'Position',[0.68 0.78 0.1 0.1],'Box','off','FontSize',fsize); 
+    %set(gca,'Ytick',logspace(-7,-1,3),'YTickLabel',['10^{-7}';'10^{-4}';'10^{2} '],'ylim',[1e-4 1e2]);set(gca,'FontSize',fsizelab,'box','off');
+    set(gca,'Ytick',logspace(-7,-1,3),'YTickLabel',['10^{-7}';'10^{-4}';'10^{-1}'],'ylim',[1e-7 1e-1],'box','off');
+    xlabel('Hierarchical inhibitory tuning','FontSize',fsize);
+    set(gca,'FontSize',fsizelab);
+    %set(gca,'Xtick',0:1:28,'box','off');
+    h = ylabel('Propagation ratio','FontSize',fsize);%set(h, 'Units', 'Normalized');pos = get(h, 'Position');set(h, 'Position', pos + [-.02, 0., -0.9]);%
+    %saveas(hFig,'/Users/maddy/Dropbox/rishicode_maddy070115/signal propagation paper/paper figures v2/suppburkhalter.pdf'); 
+ 
+end
\ No newline at end of file
diff --git a/benchmarks/src/model/Matlab/runNetworkAreaInputNEW.m b/benchmarks/src/model/Matlab/runNetworkAreaInputNEW.m
new file mode 100644
index 0000000..afed497
--- /dev/null
+++ b/benchmarks/src/model/Matlab/runNetworkAreaInputNEW.m
@@ -0,0 +1,70 @@
+% Run simulations of the network with input to a particular area and noise
+
+function result=runNetworkAreaInputNEW(tStruct,localParams,netwParams,ldConns,areaInput,fiCurveType)
+
+nNodes=size(ldConns.ee,1);
+
+state.exc=zeros(nNodes,1); state.inh=zeros(size(state.exc));
+
+if(isfield(netwParams,'initConds'))
+    state.exc=netwParams.initConds.exc; state.inh=netwParams.initConds.inh;
+end;
+
+%  recording rates across areas
+popRates.exc=zeros(nNodes,tStruct.nSteps); 
+%29 rows corresponding to 29 nodes..for each row see progress of state over
+%time. corresponding to columns. 
+popRates.inh=zeros(size(popRates.exc));
+popRates.exc(:,1)=state.exc; popRates.inh(:,1)=state.inh;
+%setting initial states. 
+
+% Define f-I curve
+
+switch fiCurveType
+    case 'threshLinear'
+        tmpZeros=zeros(size(state.exc));
+        excFI=@(x) max(x,tmpZeros);
+        inhFI=@(x) max(x,tmpZeros);
+        fprintf('Threshold linear f-I curve');
+        excFInew=@(x) max(x,10*ones(29,1));
+        inhFInew=@(x) max(x,35*ones(29,1));
+        
+end;
+
+% Noise std can vary between areas.
+noiseStd=localParams.noiseStd/sqrt(tStruct.dt);
+
+format long; toy=0;
+
+for i=2:tStruct.nSteps
+
+    if(areaInput.inp(i)==0 && toy==0)
+        state.exc = 10*ones(nNodes,1);state.inh = 35*ones(nNodes,1);
+    else    
+        toy=1;
+
+    state.excI=ldConns.ee*state.exc+localParams.ee.*state.exc+...
+        localParams.ei.*state.inh+localParams.bgExc+noiseStd.*randn(nNodes,1);
+    state.inhI=ldConns.ie*state.exc+localParams.ie.*state.exc+...
+        localParams.ii.*state.inh+localParams.bgInh+noiseStd.*randn(nNodes,1);
+
+    % Add in the area specific input (single area, exc population)
+    state.excI(areaInput.idx)=state.excI(areaInput.idx)+areaInput.inp(i);
+    % Now update the state using these currents
+
+   state.exc = excFInew(state.exc+(tStruct.dt/localParams.tauE).*(-state.exc+excFI(state.excI)));
+   state.inh = inhFInew(state.inh+(tStruct.dt/localParams.tauI)*(-state.inh+inhFI(state.inhI)));
+   
+   if(min(min(state.exc))<10)
+         disp(i)
+   end
+     
+    end
+    % And record
+    popRates.exc(:,i)=state.exc; popRates.inh(:,i)=state.inh;
+    %this gives firing rates filled columnwise (timewise) 
+end;
+
+result=popRates;
+
+
diff --git a/benchmarks/src/model/Matlab/subgraphData.mat b/benchmarks/src/model/Matlab/subgraphData.mat
new file mode 100644
index 0000000..6223e64
Binary files /dev/null and b/benchmarks/src/model/Matlab/subgraphData.mat differ
diff --git a/benchmarks/src/model/Matlab/subgraphWiring29.mat b/benchmarks/src/model/Matlab/subgraphWiring29.mat
new file mode 100644
index 0000000..2788fcc
Binary files /dev/null and b/benchmarks/src/model/Matlab/subgraphWiring29.mat differ
diff --git a/benchmarks/src/model/linear.py b/benchmarks/src/model/linear.py
new file mode 100644
index 0000000..37d7421
--- /dev/null
+++ b/benchmarks/src/model/linear.py
@@ -0,0 +1,1317 @@
+# -*- coding: utf-8 -*-
+
+
+import numbers
+from typing import Dict, Optional, Union, Callable
+
+import jax
+import jax.numpy as jnp
+import numba
+import numpy as np
+
+from brainpy import math as bm
+from brainpy._src import connect, initialize as init
+from brainpy._src.context import share
+from brainpy._src.dnn.base import Layer
+from brainpy._src.mixin import SupportOnline, SupportOffline, SupportSTDP
+from brainpy.check import is_initializer
+from brainpy.connect import csr2csc
+from brainpy.errors import MathError
+from brainpy.initialize import XavierNormal, ZeroInit, Initializer, parameter
+from brainpy.types import ArrayType, Sharding
+
+__all__ = [
+  'Dense', 'Linear',
+  'Identity',
+  'AllToAll',
+  'OneToOne',
+  'MaskedLinear',
+  'CSRLinear', 'EventCSRLinear',
+  'JitFPHomoLinear', 'JitFPUniformLinear', 'JitFPNormalLinear',
+  'EventJitFPHomoLinear', 'EventJitFPNormalLinear', 'EventJitFPUniformLinear',
+]
+
+
+class Dense(Layer, SupportSTDP, SupportOnline, SupportOffline):
+  r"""A linear transformation applied over the last dimension of the input.
+
+  Mathematically, this node can be defined as:
+
+  .. math::
+
+     y = x  \cdot weight + b
+
+  Parameters
+  ----------
+  num_in: int
+    The number of the input feature. A positive integer.
+  num_out: int
+    The number of the output features. A positive integer.
+  W_initializer: optional, Initializer
+    The weight initialization.
+  b_initializer: optional, Initializer
+    The bias initialization.
+  mode: Mode
+    Enable training this node or not. (default True)
+  """
+
+  def __init__(
+      self,
+      num_in: int,
+      num_out: int,
+      W_initializer: Union[Initializer, Callable, ArrayType] = XavierNormal(),
+      b_initializer: Optional[Union[Initializer, Callable, ArrayType]] = ZeroInit(),
+      mode: Optional[bm.Mode] = None,
+      name: Optional[str] = None,
+  ):
+    super(Dense, self).__init__(mode=mode, name=name)
+
+    # shape
+    self.num_in = num_in
+    self.num_out = num_out
+    if num_in < 0:
+      raise ValueError(f'Received an invalid value for `num_out`, expected '
+                       f'a positive integer. Received: num_in={num_in}')
+    if num_out < 0:
+      raise ValueError(f'Received an invalid value for `num_out`, expected '
+                       f'a positive integer. Received: num_out={num_out}')
+
+    # weight initializer
+    self.W_initializer = W_initializer
+    self.bias_initializer = b_initializer
+    is_initializer(W_initializer, 'weight_initializer')
+    is_initializer(b_initializer, 'bias_initializer', allow_none=True)
+
+    # parameter initialization
+    W = parameter(self.W_initializer, (num_in, self.num_out))
+    b = parameter(self.bias_initializer, (self.num_out,))
+    if isinstance(self.mode, bm.TrainingMode):
+      W = bm.TrainVar(W)
+      b = None if (b is None) else bm.TrainVar(b)
+    self.W = W
+    self.b = b
+
+    # fitting parameters
+    self.online_fit_by = None  # support online training
+    self.offline_fit_by = None  # support offline training
+    self.fit_record = dict()
+
+  def __repr__(self):
+    return (f'{self.__class__.__name__}(name={self.name}, '
+            f'num_in={self.num_in}, '
+            f'num_out={self.num_out}, '
+            f'mode={self.mode})')
+
+  def update(self, x):
+    x = bm.as_jax(x)
+    res = x @ self.W
+    if self.b is not None:
+      res += self.b
+
+    # online fitting data
+    if share.load('fit', False) and self.online_fit_by is not None:
+      self.fit_record['input'] = x
+      self.fit_record['output'] = res
+
+    # offline fitting data
+    if share.load('fit', False) and self.offline_fit_by is not None:
+      self.fit_record['input'] = x
+      self.fit_record['output'] = res
+    return res
+
+  def online_init(self):
+    if self.b is None:
+      num_input = self.num_in
+    else:
+      num_input = self.num_in + 1
+    self.online_fit_by.register_target(feature_in=num_input, identifier=self.name)
+
+  def online_fit(self,
+                 target: ArrayType,
+                 fit_record: Dict[str, ArrayType]):
+    if not isinstance(target, (bm.ndarray, jnp.ndarray)):
+      raise MathError(f'"target" must be a tensor, but got {type(target)}')
+    x = fit_record['input']
+    y = fit_record['output']
+    if x.ndim != 2:
+      raise ValueError(f'"ff" must be a 2D tensor with shape of (num_sample, '
+                       f'num_feature), but we got {x.shape}')
+    if target.ndim != 2:
+      raise ValueError(f'"target" must be a 2D tensor with shape of (num_sample, '
+                       f'num_feature), but we got {target.shape}')
+    if x.shape[0] != target.shape[0]:
+      raise ValueError(f'Batch size of the input and target data should be '
+                       f'the same, while we got {x.shape[0]} != {target.shape[0]}.')
+    if target.shape[1] != y.shape[1]:
+      raise MathError(f'The output dimension of output and target data should be '
+                      f'the same, while we got {target.shape[1]} != {y.shape[1]}')
+
+    # data
+    if self.b is not None:
+      x = jnp.concatenate([jnp.ones((x.shape[0], 1)), x], axis=-1)
+
+    # fitting
+    dW = self.online_fit_by.call(target=target, input=x, output=y, identifier=self.name)
+
+    # assign trained weights
+    if self.b is None:
+      self.W += dW
+    else:
+      db, dW = jnp.split(dW, [1])
+      self.b += db[0]
+      self.W += dW
+
+  def offline_fit(self,
+                  target: ArrayType,
+                  fit_record: Dict[str, ArrayType]):
+    """The offline training interface for the Dense node."""
+    # data checking
+    if not isinstance(target, (bm.ndarray, jnp.ndarray)):
+      raise MathError(f'"targets" must be a tensor, but got {type(target)}')
+    xs = fit_record['input']
+    ys = fit_record['output']
+    if xs.ndim != 3:
+      raise ValueError(f'"ffs" must be a 3D tensor with shape of (num_sample, num_time, '
+                       f'num_feature), but we got {xs.shape}')
+    if target.ndim != 3:
+      raise ValueError(f'"targets" must be a 3D tensor with shape of (num_sample, num_time, '
+                       f'num_feature), but we got {target.shape}')
+    if ys.shape != target.shape:
+      raise ValueError(f'The shapes of output and target data should be '
+                       f'the same, while we got {ys.shape} != {target.shape}.')
+    if xs.shape[0] != target.shape[0]:
+      raise ValueError(f'Batch size of the input and target data should be '
+                       f'the same, while we got {xs.shape[0]} != {target.shape[0]}.')
+    if xs.shape[1] != target.shape[1]:
+      raise MathError(f'The time dimension of input and target data should be '
+                      f'the same, while we got {xs.shape[1]} != {target.shape[1]}')
+
+    # get input and target training data
+    if self.b is not None:
+      xs = jnp.concatenate([jnp.ones(xs.shape[:2] + (1,)), xs], axis=-1)  # (..., 1 + num_ff_input)
+
+    # solve weights by offline training methods
+    weights = self.offline_fit_by(target, xs, ys)
+
+    # assign trained weights
+    if self.b is None:
+      self.W.value = weights
+    else:
+      bias, Wff = jnp.split(weights, [1])
+      self.W.value = Wff
+      self.b.value = bias[0]
+
+  def stdp_update(
+      self,
+      on_pre: Dict = None,
+      on_post: Dict = None,
+      w_min: numbers.Number = None,
+      w_max: numbers.Number = None
+  ):
+    if isinstance(self.W, float):
+      raise ValueError(f'Cannot update the weight of a constant node.')
+    if not isinstance(self.W, bm.Variable):
+      self.tracing_variable('W', self.W, self.W.shape)
+    if on_pre is not None:
+      spike = on_pre['spike']
+      trace = on_pre['trace']
+      self.W.value = dense_on_pre(self.W.value, spike, trace, w_min, w_max)
+    if on_post is not None:
+      spike = on_post['spike']
+      trace = on_post['trace']
+      self.W.value = dense_on_post(self.W.value, spike, trace, w_min, w_max)
+
+
+Linear = Dense
+
+
+class Identity(Layer):
+  r"""A placeholder identity operator that is argument-insensitive.
+  """
+
+  def __init__(self, *args, **kwargs) -> None:
+    super(Identity, self).__init__(*args, **kwargs)
+
+  def update(self, x):
+    return x
+
+
+@numba.njit(nogil=True, fastmath=True, parallel=False)
+def _cpu_dense_on_pre(weight, spike, trace, w_min, w_max, out_w):
+  out_w[:] = weight
+  for i in numba.prange(spike.shape[0]):
+    if spike[i]:
+      out_w[i] = np.clip(out_w[i] + trace, w_min, w_max)
+
+
+dense_on_pre_prim = bm.XLACustomOp(_cpu_dense_on_pre)
+
+
+def dense_on_pre(weight, spike, trace, w_min, w_max):
+  if w_min is None:
+    w_min = -np.inf
+  if w_max is None:
+    w_max = np.inf
+  return dense_on_pre_prim(weight, spike, trace, w_min, w_max,
+                           outs=[jax.ShapeDtypeStruct(weight.shape, weight.dtype)])[0]
+
+
+@numba.njit(nogil=True, fastmath=True, parallel=False)
+def _cpu_dense_on_post(weight, spike, trace, w_min, w_max, out_w):
+  out_w[:] = weight
+  for i in numba.prange(spike.shape[0]):
+    if spike[i]:
+      out_w[:, i] = np.clip(out_w[:, i] + trace, w_min, w_max)
+
+
+dense_on_post_prim = bm.XLACustomOp(_cpu_dense_on_post)
+
+
+def dense_on_post(weight, spike, trace, w_min, w_max):
+  if w_min is None:
+    w_min = -np.inf
+  if w_max is None:
+    w_max = np.inf
+  return dense_on_post_prim(weight, spike, trace, w_min, w_max,
+                            outs=[jax.ShapeDtypeStruct(weight.shape, weight.dtype)])[0]
+
+
+class AllToAll(Layer, SupportSTDP):
+  """Synaptic matrix multiplication with All2All connections.
+
+  Args:
+    num_pre: int. The number of neurons in the presynaptic neuron group.
+    num_post: int. The number of neurons in the postsynaptic neuron group.
+    weight: The synaptic weights.
+    sharding: The sharding strategy. 
+    include_self: bool. Whether connect the neuron with at the same position.
+    mode: Mode. The computing mode.
+    name: str. The object name.
+  """
+
+  def __init__(
+      self,
+      num_pre: int,
+      num_post: int,
+      weight: Union[float, ArrayType, Callable],
+      sharding: Optional[Sharding] = None,
+      include_self: bool = True,
+      mode: Optional[bm.Mode] = None,
+      name: Optional[str] = None,
+  ):
+    super().__init__(mode=mode, name=name)
+
+    self.num_pre = num_pre
+    self.num_post = num_post
+    self.include_self = include_self
+    self.sharding = sharding
+
+    weight = init.parameter(weight, (self.num_pre, self.num_post), sharding=sharding)
+    if isinstance(self.mode, bm.TrainingMode):
+      weight = bm.TrainVar(weight)
+    self.weight = weight
+
+  def update(self, pre_val):
+    if bm.ndim(self.weight) == 0:  # weight is a scalar
+      if isinstance(self.mode, bm.BatchingMode):
+        assert pre_val.ndim == 2, 'Under the batching mode, the input should be a 2D array.'
+        post_val = bm.sum(pre_val, keepdims=True, axis=1)
+      else:
+        assert pre_val.ndim == 1, 'Under the NonBatching mode, the input should be a 1D array.'
+        post_val = bm.sum(pre_val)
+      if not self.include_self:
+        if self.num_pre == self.num_post:
+          post_val = post_val - pre_val
+        elif self.num_pre > self.num_post:
+          val = pre_val[:self.num_post]
+          post_val = post_val - val
+        else:
+          val = bm.concatenate([pre_val, bm.zeros(self.num_post - self.num_pre)])
+          post_val = post_val - val
+      post_val = self.weight * post_val
+
+    else:  # weight is a matrix
+      assert self.weight.ndim == 2, '"weight" must be a 2D matrix.'
+      if not self.include_self:
+        post_val = pre_val @ bm.fill_diagonal(self.weight, 0., inplace=False)
+      else:
+        post_val = pre_val @ self.weight
+    return post_val
+
+  def stdp_update(
+      self,
+      on_pre: Dict = None,
+      on_post: Dict = None,
+      w_min: numbers.Number = None,
+      w_max: numbers.Number = None
+  ):
+    if isinstance(self.weight, float):
+      raise ValueError(f'Cannot update the weight of a constant node.')
+    if not isinstance(self.weight, bm.Variable):
+      self.tracing_variable('weight', self.weight, self.weight.shape)
+    if on_pre is not None:
+      spike = on_pre['spike']
+      trace = on_pre['trace']
+      self.weight.value = dense_on_pre(self.weight.value, spike, trace, w_min, w_max)
+    if on_post is not None:
+      spike = on_post['spike']
+      trace = on_post['trace']
+      self.weight.value = dense_on_post(self.weight.value, spike, trace, w_min, w_max)
+
+
+class OneToOne(Layer, SupportSTDP):
+  """Synaptic matrix multiplication with One2One connection.
+
+  Args:
+    num: int. The number of neurons.
+    weight: The synaptic weight.
+    sharding: The sharding strategy. 
+    mode: The computing mode.
+    name: The object name.
+
+  """
+
+  def __init__(
+      self,
+      num: int,
+      weight: Union[float, ArrayType, Callable],
+      sharding: Optional[Sharding] = None,
+      mode: Optional[bm.Mode] = None,
+      name: Optional[str] = None,
+  ):
+    super().__init__(mode=mode, name=name)
+
+    self.num = num
+    self.sharding = sharding
+
+    weight = init.parameter(weight, (self.num,), sharding=sharding)
+    if isinstance(self.mode, bm.TrainingMode):
+      weight = bm.TrainVar(weight)
+    self.weight = weight
+
+  def update(self, pre_val):
+    return pre_val * self.weight
+
+  def stdp_update(
+      self,
+      on_pre: Dict = None,
+      on_post: Dict = None,
+      w_min: numbers.Number = None,
+      w_max: numbers.Number = None
+  ):
+    if isinstance(self.weight, float):
+      raise ValueError(f'Cannot update the weight of a constant node.')
+    if not isinstance(self.weight, bm.Variable):
+      self.tracing_variable('weight', self.weight, self.weight.shape)
+    if on_pre is not None:
+      spike = on_pre['spike']
+      trace = on_pre['trace']
+      self.weight.value += spike * trace
+    if on_post is not None:
+      spike = on_post['spike']
+      trace = on_post['trace']
+      self.weight.value += spike * trace
+
+
+class MaskedLinear(Layer, SupportSTDP):
+  r"""Synaptic matrix multiplication with masked dense computation.
+
+  It performs the computation of:
+
+  .. math::
+
+     y = x @ M
+
+  where :math:`y` is the postsynaptic value, :math:`x` the presynaptic value,
+  :math:`M` the synaptic weight using a dense matrix.
+
+  >>> import brainpy as bp
+  >>> l = bp.dnn.MaskedLinear(bp.conn.FixedProb(0.1, pre=100, post=100),
+  >>>                         weight=0.1)
+
+  Args:
+    conn: TwoEndConnector. The connection.
+    weight: Synaptic weights. Can be a scalar, array, or callable function.
+    mask_fun: Masking function.
+    sharding: The sharding strategy. 
+    mode: The synaptic computing mode.
+    name: The synapse model name.
+  """
+
+  def __init__(
+      self,
+      conn: connect.TwoEndConnector,
+      weight: Union[float, ArrayType, Callable],
+      mask_fun: Callable = Identity(),
+      sharding: Optional[Sharding] = None,
+      mode: Optional[bm.Mode] = None,
+      name: Optional[str] = None,
+  ):
+    super().__init__(name=name, mode=mode)
+
+    assert isinstance(conn, connect.TwoEndConnector)
+    self.conn = conn
+    self.sharding = sharding
+    self.mask_fun = mask_fun
+
+    # weight
+    weight = init.parameter(weight, (conn.pre_num, conn.post_num), sharding=sharding)
+    if isinstance(self.mode, bm.TrainingMode):
+      weight = bm.TrainVar(weight)
+    self.weight = weight
+
+    # connection
+    self.mask = bm.sharding.partition(self.conn.require('conn_mat'), sharding=sharding)
+
+  def update(self, x):
+    return x @ self.mask_fun(self.weight * self.mask)
+
+  def stdp_update(
+      self,
+      on_pre: Dict = None,
+      on_post: Dict = None,
+      w_min: numbers.Number = None,
+      w_max: numbers.Number = None
+  ):
+    if isinstance(self.weight, float):
+      raise ValueError(f'Cannot update the weight of a constant node.')
+    if not isinstance(self.weight, bm.Variable):
+      self.tracing_variable('weight', self.weight, self.weight.shape)
+    if on_pre is not None:
+      spike = on_pre['spike']
+      trace = on_pre['trace']
+      self.weight.value = dense_on_pre(self.weight.value, spike, trace, w_min, w_max)
+    if on_post is not None:
+      spike = on_post['spike']
+      trace = on_post['trace']
+      self.weight.value = dense_on_post(self.weight.value, spike, trace, w_min, w_max)
+
+
+class _CSRLayer(Layer, SupportSTDP):
+  def __init__(
+      self,
+      conn: connect.TwoEndConnector,
+      weight: Union[float, ArrayType, Callable],
+      sharding: Optional[Sharding] = None,
+      mode: Optional[bm.Mode] = None,
+      name: Optional[str] = None,
+      transpose: bool = True,
+  ):
+    super().__init__(name=name, mode=mode)
+
+    assert isinstance(conn, connect.TwoEndConnector)
+    assert sharding is None, 'Currently this model does not support sharding.'
+    self.conn = conn
+    self.sharding = sharding
+    self.transpose = transpose
+
+    # connection
+    self.indices, self.indptr = self.conn.require('csr')
+
+    # weight
+    weight = init.parameter(weight, (self.indices.size,))
+    if isinstance(self.mode, bm.TrainingMode):
+      weight = bm.TrainVar(weight)
+    self.weight = weight
+
+  def stdp_update(
+      self,
+      on_pre: Dict = None,
+      on_post: Dict = None,
+      w_min: numbers.Number = None,
+      w_max: numbers.Number = None
+  ):
+    if bm.isscalar(self.weight):
+      raise ValueError(f'When using STDP to update synaptic weights, the weight cannot be a scalar.')
+    if self.weight.shape != self.indices.shape:
+      raise ValueError(f'The shape of weight should be the same as the shape of sparse weight {self.weight.shape}.')
+    if not isinstance(self.weight, bm.Variable):
+      self.tracing_variable('weight', self.weight, self.weight.shape)
+    if on_pre is not None:   # update on presynaptic spike
+      spike = on_pre['spike']
+      trace = on_pre['trace']
+      self.weight.value = csr_on_pre_update(self.weight.value, self.indices, self.indptr, spike, trace, w_min, w_max)
+    if on_post is not None:  # update on postsynaptic spike
+      if not hasattr(self, '_pre_ids'):
+        with jax.ensure_compile_time_eval():
+          self._pre_ids, self._post_indptr, self.w_indices = csr2csc(
+            [self.indices, self.indptr], self.conn.post_num, data=np.arange(self.weight.size)
+          )
+      spike = on_post['spike']
+      trace = on_post['trace']
+      self.weight.value = csc_on_post_update(self.weight.value, self._pre_ids, self._post_indptr,
+                                             self.w_indices, spike, trace, w_min, w_max)
+
+
+class CSRLinear(_CSRLayer):
+  r"""Synaptic matrix multiplication with CSR sparse computation.
+
+  It performs the computation of:
+
+  .. math::
+
+     y = x @ M
+
+  where :math:`y` is the postsynaptic value, :math:`x` the presynaptic value,
+  :math:`M` the synaptic weight using a CSR sparse matrix.
+
+  Args:
+    conn: TwoEndConnector. The connection.
+    weight: Synaptic weights. Can be a scalar, array, or callable function.
+    sharding: The sharding strategy. 
+    mode: The synaptic computing mode.
+    name: The synapse model name.
+  """
+
+  def __init__(
+      self,
+      conn: connect.TwoEndConnector,
+      weight: Union[float, ArrayType, Callable],
+      sharding: Optional[Sharding] = None,
+      mode: Optional[bm.Mode] = None,
+      name: Optional[str] = None,
+      method: str = None,
+      transpose: bool = True,
+  ):
+    super().__init__(name=name, mode=mode, conn=conn, weight=weight, sharding=sharding, transpose=transpose)
+    self.method = method
+
+  def update(self, x):
+    if x.ndim == 1:
+      return bm.sparse.csrmv(self.weight, self.indices, self.indptr, x,
+                             shape=(self.conn.pre_num, self.conn.post_num),
+                             method=self.method, transpose=self.transpose)
+    elif x.ndim > 1:
+      shapes = x.shape[:-1]
+      x = bm.flatten(x, end_dim=-2)
+      y = jax.vmap(self._batch_csrmv)(x)
+      return bm.reshape(y, shapes + (y.shape[-1],))
+    else:
+      raise ValueError
+
+  def _batch_csrmv(self, x):
+    return bm.sparse.csrmv(self.weight, self.indices, self.indptr, x,
+                           shape=(self.conn.pre_num, self.conn.post_num),
+                           method=self.method, transpose=self.transpose)
+
+class EventCSRLinear(_CSRLayer):
+  r"""Synaptic matrix multiplication with event CSR sparse computation.
+
+  It performs the computation of:
+
+  .. math::
+
+     y = x @ M
+
+  where :math:`y` is the postsynaptic value, :math:`x` the presynaptic spikes,
+  :math:`M` the synaptic weight using a CSR sparse matrix.
+
+  Args:
+    conn: TwoEndConnector. The connection.
+    weight: Synaptic weights. Can be a scalar, array, or callable function.
+    sharding: The sharding strategy.
+    mode: The synaptic computing mode.
+    name: The synapse model name.
+  """
+
+  def __init__(
+      self,
+      conn: connect.TwoEndConnector,
+      weight: Union[float, ArrayType, Callable],
+      sharding: Optional[Sharding] = None,
+      mode: Optional[bm.Mode] = None,
+      name: Optional[str] = None,
+      transpose: bool = True,
+      method: str = None,
+  ):
+    super().__init__(name=name, mode=mode, conn=conn, weight=weight, sharding=sharding, transpose=transpose)
+    self.method = method
+
+  def update(self, x):
+    if x.ndim == 1:
+      if self.method is None:
+        return bm.event.csrmv_taichi(self.weight, self.indices, self.indptr, x,
+                            shape=(self.conn.pre_num, self.conn.post_num),
+                            transpose=self.transpose,)[0]
+      else:
+        return bm.event.csrmv(self.weight, self.indices, self.indptr, x,
+                            shape=(self.conn.pre_num, self.conn.post_num),
+                            transpose=self.transpose,)
+    elif x.ndim > 1:
+      shapes = x.shape[:-1]
+      x = bm.flatten(x, end_dim=-2)
+      y = jax.vmap(self._batch_csrmv)(x)
+      return bm.reshape(y, shapes + (y.shape[-1],))
+    else:
+      raise ValueError
+
+  def _batch_csrmv(self, x):
+    if self.method is None:
+        return bm.event.csrmv_taichi(self.weight, self.indices, self.indptr, x,
+                          shape=(self.conn.pre_num, self.conn.post_num),
+                          transpose=self.transpose,)[0]
+    else:
+        return bm.event.csrmv(self.weight, self.indices, self.indptr, x,
+                          shape=(self.conn.pre_num, self.conn.post_num),
+                          transpose=self.transpose,)
+
+@numba.njit(nogil=True, fastmath=True, parallel=False)
+def _cpu_csr_on_pre_update(w, indices, indptr, spike, trace, w_min, w_max, out_w):
+  out_w[:] = w
+  w_min = w_min[()]
+  w_max = w_max[()]
+  for i in numba.prange(spike.shape[0]):  # pre id
+    if spike[i]:
+      for k in range(indptr[i], indptr[i + 1]):  # synapse id
+        j = indices[k]  # post id
+        # out_w[k] = np.clip(out_w[k] + trace[j], w_min, w_max)
+        out_w[k] = np.minimum(np.maximum(out_w[k] + trace[j], w_min), w_max)
+
+csr_on_pre_update_prim = bm.XLACustomOp(_cpu_csr_on_pre_update)
+
+
+def csr_on_pre_update(w, indices, indptr, spike, trace, w_min=None, w_max=None):
+  if w_min is None:
+    w_min = -np.inf
+  if w_max is None:
+    w_max = np.inf
+  return csr_on_pre_update_prim(w, indices, indptr, spike, trace, w_min, w_max,
+                                outs=[jax.ShapeDtypeStruct(w.shape, w.dtype)])[0]
+
+@numba.njit(nogil=True, fastmath=True, parallel=False)
+def _cpu_csc_on_pre_update(w, post_ids, indptr, w_ids, spike, trace, w_min, w_max, out_w):
+  out_w[:] = w
+  w_min = w_min[()]
+  w_max = w_max[()]
+  for i in numba.prange(spike.shape[0]):  # post id
+    if spike[i]:
+      for k in range(indptr[i], indptr[i + 1]):
+        j = post_ids[k]  # pre id
+        l = w_ids[k]  # syn id
+        out_w[l] = np.minimum(np.maximum(out_w[l] + trace[j], w_min), w_max)
+
+
+csc_on_pre_update_prim = bm.XLACustomOp(_cpu_csc_on_pre_update)
+
+
+def csc_on_post_update(w, post_ids, indptr, w_ids, spike, trace, w_min=None, w_max=None):
+  if w_min is None:
+    w_min = -np.inf
+  if w_max is None:
+    w_max = np.inf
+  return csc_on_pre_update_prim(w, post_ids, indptr, w_ids, spike, trace, w_min, w_max,
+                                outs=[jax.ShapeDtypeStruct(w.shape, w.dtype)])[0]
+
+
+
+class CSCLinear(Layer):
+  r"""Synaptic matrix multiplication with CSC sparse computation.
+
+  It performs the computation of:
+
+  .. math::
+
+     y = x @ M
+
+  where :math:`y` is the postsynaptic value, :math:`x` the presynaptic value,
+  :math:`M` the synaptic weight using a CSC sparse matrix.
+
+  Args:
+    conn: TwoEndConnector. The connection.
+    weight: Synaptic weights. Can be a scalar, array, or callable function.
+    sharding: The sharding strategy.
+    mode: The synaptic computing mode.
+    name: The synapse model name.
+  """
+
+  def __init__(
+      self,
+      conn: connect.TwoEndConnector,
+      weight: Union[float, ArrayType, Callable],
+      sharding: Optional[Sharding] = None,
+      mode: Optional[bm.Mode] = None,
+      name: Optional[str] = None,
+  ):
+    super().__init__(name=name, mode=mode)
+
+    assert isinstance(conn, connect.TwoEndConnector)
+    self.conn = conn
+    self.sharding = sharding
+
+
+class BcsrMM(Layer):
+  r"""Synaptic matrix multiplication with BCSR sparse computation.
+
+  It performs the computation of:
+
+  .. math::
+
+     y = x @ M
+
+  where :math:`y` is the postsynaptic value, :math:`x` the presynaptic value,
+  :math:`M` the synaptic weight using a BCSR sparse matrix.
+
+  Args:
+    conn: TwoEndConnector. The connection.
+    weight: Synaptic weights. Can be a scalar, array, or callable function.
+    sharding: The sharding strategy. 
+    mode: The synaptic computing mode.
+    name: The synapse model name.
+  """
+
+  def __init__(
+      self,
+      conn: connect.TwoEndConnector,
+      weight: Union[float, ArrayType, Callable],
+      sharding: Optional[Sharding] = None,
+      mode: Optional[bm.Mode] = None,
+      name: Optional[str] = None,
+  ):
+    super().__init__(name=name, mode=mode)
+
+    assert isinstance(conn, connect.TwoEndConnector)
+    self.conn = conn
+    self.sharding = sharding
+
+
+class BcscMM(Layer):
+  r"""Synaptic matrix multiplication with BCSC sparse computation.
+
+  It performs the computation of:
+
+  .. math::
+
+     y = x @ M
+
+  where :math:`y` is the postsynaptic value, :math:`x` the presynaptic value,
+  :math:`M` the synaptic weight using a BCSC sparse matrix.
+
+  Args:
+    conn: TwoEndConnector. The connection.
+    weight: Synaptic weights. Can be a scalar, array, or callable function.
+    sharding: The sharding strategy. 
+    mode: The synaptic computing mode.
+    name: The synapse model name.
+  """
+
+  def __init__(
+      self,
+      conn: connect.TwoEndConnector,
+      weight: Union[float, ArrayType, Callable],
+      sharding: Optional[Sharding] = None,
+      mode: Optional[bm.Mode] = None,
+      name: Optional[str] = None,
+  ):
+    super().__init__(name=name, mode=mode)
+
+    assert isinstance(conn, connect.TwoEndConnector)
+    self.conn = conn
+    self.sharding = sharding
+
+
+class JitFPHomoLinear(Layer):
+  r"""Synaptic matrix multiplication with the just-in-time connectivity.
+
+  It performs the computation of:
+
+  .. math::
+
+     y = x @ M
+
+  where :math:`y` is the postsynaptic value, :math:`x` the presynaptic variable,
+  :math:`M` the synaptic weights which has the fixed sparse connectivity and weights.
+  Particularly, the connectivity in :math:`M` is sampled from a fixed probability :math:`prob`,
+  and at each connection, the synaptic value is the same :math:`weight`.
+
+  Args:
+    num_in: int. The number of the input feature. A positive integer.
+    num_out: int. The number of the input feature. A positive integer.
+    prob: float. The connectivity probability.
+    weight: float. The synaptic value at each position.
+    seed: int. The random seed used to keep the reproducibility of the connectivity.
+    transpose: bool. Transpose the JIT matrix or not. Default False.
+    atomic: bool. Compute the post-synaptic value with the atomic summation. Default False.
+       May be changed in the future.
+    sharding: The sharding strategy.
+    mode: The synaptic computing mode.
+    name: The synapse model name.
+  """
+
+  def __init__(
+      self,
+      num_in: int,
+      num_out: int,
+      prob: float,
+      weight: float,
+      seed: Optional[int] = None,
+      sharding: Optional[Sharding] = None,
+      mode: Optional[bm.Mode] = None,
+      name: Optional[str] = None,
+      transpose: bool = False,
+      atomic: bool = False,
+  ):
+    super().__init__(name=name, mode=mode)
+
+    self.prob = prob
+    self.sharding = sharding
+    self.transpose = transpose
+    self.seed = np.random.randint(0, 100000) if seed is None else seed
+    self.atomic = atomic
+    self.num_in = num_in
+    self.num_out = num_out
+
+    # weight
+    if isinstance(self.mode, bm.TrainingMode):
+      weight = bm.TrainVar(weight)
+    self.weight = weight
+
+  def update(self, x):
+    if x.ndim == 1:
+      return bm.jitconn.mv_prob_homo(x, self.weight, self.prob, self.seed,
+                                     shape=(self.num_out, self.num_in),
+                                     transpose=self.transpose,
+                                     outdim_parallel=not self.atomic)
+    elif x.ndim == 2:
+      return jax.vmap(self._batch_mv)(x)
+    elif x.ndim > 2:
+      shapes = x.shape[:-1]
+      x = bm.flatten(x, end_dim=-2)
+      y = jax.vmap(self._batch_mv)(x)
+      return bm.reshape(y, shapes + (y.shape[-1],))
+    else:
+      raise ValueError
+
+  def _batch_mv(self, x):
+    return bm.jitconn.mv_prob_homo(x, self.weight, self.prob, self.seed,
+                                   shape=(self.num_out, self.num_in),
+                                   transpose=self.transpose,
+                                   outdim_parallel=not self.atomic)
+
+
+class JitFPUniformLinear(Layer):
+  r"""Synaptic matrix multiplication with the just-in-time connectivity.
+
+  It performs the computation of:
+
+  .. math::
+
+     y = x @ M
+
+  where :math:`y` is the postsynaptic value, :math:`x` the presynaptic variable,
+  :math:`M` the synaptic weights which has the fixed sparse connectivity and weights.
+  Particularly, the connectivity in :math:`M` is sampled from a fixed probability :math:`prob`,
+  and at each connection, the synaptic value is sample from a uniform distribution :math:`U(w_{low}, w_{high})`.
+
+  Args:
+    num_in: int. The number of the input feature. A positive integer.
+    num_out: int. The number of the input feature. A positive integer.
+    prob: float. The connectivity probability.
+    w_low: float. The lowest value of the uniform distribution.
+    w_high: float. The highest value of the uniform distribution.
+    seed: int. The random seed used to keep the reproducibility of the connectivity.
+    transpose: bool. Transpose the JIT matrix or not. Default False.
+    atomic: bool. Compute the post-synaptic value with the atomic summation. Default False.
+       May be changed in the future.
+    sharding: The sharding strategy.
+    mode: The synaptic computing mode.
+    name: The synapse model name.
+  """
+
+  def __init__(
+      self,
+      num_in: int,
+      num_out: int,
+      prob: float,
+      w_low: float,
+      w_high: float,
+      seed: Optional[int] = None,
+      sharding: Optional[Sharding] = None,
+      mode: Optional[bm.Mode] = None,
+      name: Optional[str] = None,
+      transpose: bool = False,
+      atomic: bool = False,
+  ):
+    super().__init__(name=name, mode=mode)
+
+    self.prob = prob
+    self.sharding = sharding
+    self.transpose = transpose
+    self.seed = np.random.randint(0, 100000) if seed is None else seed
+    self.atomic = atomic
+    self.num_in = num_in
+    self.num_out = num_out
+
+    # weight
+    self.w_low = w_low
+    self.w_high = w_high
+
+  def update(self, x):
+    if x.ndim == 1:
+      return bm.jitconn.mv_prob_uniform(x, self.w_low, self.w_high, self.prob, self.seed,
+                                        shape=(self.num_out, self.num_in),
+                                        transpose=self.transpose,
+                                        outdim_parallel=not self.atomic)
+    elif x.ndim == 2:
+      return jax.vmap(self._batch_mv)(x)
+    elif x.ndim > 2:
+      shapes = x.shape[:-1]
+      x = bm.flatten(x, end_dim=-2)
+      y = jax.vmap(self._batch_mv)(x)
+      return bm.reshape(y, shapes + (y.shape[-1],))
+    else:
+      raise ValueError
+
+  def _batch_mv(self, x):
+    return bm.jitconn.mv_prob_uniform(x, self.w_low, self.w_high, self.prob, self.seed,
+                                      shape=(self.num_out, self.num_in),
+                                      transpose=self.transpose,
+                                      outdim_parallel=not self.atomic)
+
+
+class JitFPNormalLinear(Layer):
+  r"""Synaptic matrix multiplication with the just-in-time connectivity.
+
+  It performs the computation of:
+
+  .. math::
+
+     y = x @ M
+
+  where :math:`y` is the postsynaptic value, :math:`x` the presynaptic variable,
+  :math:`M` the synaptic weights which has the fixed sparse connectivity and weights.
+  Particularly, the connectivity in :math:`M` is sampled from a fixed probability :math:`prob`,
+  and at each connection, the synaptic value is sample from a normal distribution :math:`N(\mu, \sigma)`.
+
+  Args:
+    num_in: int. The number of the input feature. A positive integer.
+    num_out: int. The number of the input feature. A positive integer.
+    prob: float. The connectivity probability.
+    w_mu: float. The center of the normal distribution.
+    w_sigma: float. The standard variance of the normal distribution.
+    seed: int. The random seed used to keep the reproducibility of the connectivity.
+    transpose: bool. Transpose the JIT matrix or not. Default False.
+    atomic: bool. Compute the post-synaptic value with the atomic summation. Default False.
+       May be changed in the future.
+    sharding: The sharding strategy.
+    mode: The synaptic computing mode.
+    name: The synapse model name.
+  """
+
+  def __init__(
+      self,
+      num_in: int,
+      num_out: int,
+      prob: float,
+      w_mu: float,
+      w_sigma: float,
+      seed: Optional[int] = None,
+      sharding: Optional[Sharding] = None,
+      transpose: bool = False,
+      atomic: bool = False,
+      mode: Optional[bm.Mode] = None,
+      name: Optional[str] = None,
+  ):
+    super().__init__(name=name, mode=mode)
+
+    self.prob = prob
+    self.sharding = sharding
+    self.transpose = transpose
+    self.seed = np.random.randint(0, 100000) if seed is None else seed
+    self.atomic = atomic
+    self.num_in = num_in
+    self.num_out = num_out
+
+    # weight
+    self.w_mu = w_mu
+    self.w_sigma = w_sigma
+
+  def update(self, x):
+    if x.ndim == 1:
+      return bm.jitconn.mv_prob_normal(x, self.w_mu, self.w_sigma, self.prob, self.seed,
+                                       shape=(self.num_out, self.num_in),
+                                       transpose=self.transpose,
+                                       outdim_parallel=not self.atomic)
+    elif x.ndim == 2:
+      return jax.vmap(self._batch_mv)(x)
+    elif x.ndim > 2:
+      shapes = x.shape[:-1]
+      x = bm.flatten(x, end_dim=-2)
+      y = jax.vmap(self._batch_mv)(x)
+      return bm.reshape(y, shapes + (y.shape[-1],))
+    else:
+      raise ValueError
+
+  def _batch_mv(self, x):
+    return bm.jitconn.mv_prob_normal(x, self.w_mu, self.w_sigma, self.prob, self.seed,
+                                     shape=(self.num_out, self.num_in),
+                                     transpose=self.transpose,
+                                     outdim_parallel=not self.atomic)
+
+
+class EventJitFPHomoLinear(Layer):
+  r"""Synaptic matrix multiplication with the just-in-time connectivity.
+
+  It performs the computation of:
+
+  .. math::
+
+     y = x @ M
+
+  where :math:`y` is the postsynaptic value, :math:`x` the presynaptic spikes,
+  :math:`M` the synaptic weights which has the fixed sparse connectivity and weights.
+  Particularly, the connectivity in :math:`M` is sampled from a fixed probability :math:`prob`,
+  and at each connection, the synaptic value is the same :math:`weight`.
+
+  Args:
+    num_in: int. The number of the input feature. A positive integer.
+    num_out: int. The number of the input feature. A positive integer.
+    prob: float. The connectivity probability.
+    weight: float. The synaptic value at each position.
+    seed: int. The random seed used to keep the reproducibility of the connectivity.
+    transpose: bool. Transpose the JIT matrix or not. Default False.
+    atomic: bool. Compute the post-synaptic value with the atomic summation. Default False.
+       May be changed in the future.
+    sharding: The sharding strategy.
+    mode: The synaptic computing mode.
+    name: The synapse model name.
+  """
+
+  def __init__(
+      self,
+      num_in: int,
+      num_out: int,
+      prob: float,
+      weight: float,
+      seed: Optional[int] = None,
+      sharding: Optional[Sharding] = None,
+      mode: Optional[bm.Mode] = None,
+      name: Optional[str] = None,
+      transpose: bool = False,
+      atomic: bool = True,
+      method: str = None,
+  ):
+    super().__init__(name=name, mode=mode)
+
+    self.prob = prob
+    self.sharding = sharding
+    self.transpose = transpose
+    self.seed = np.random.randint(0, 1000000) if seed is None else seed
+    self.atomic = atomic
+    self.num_in = num_in
+    self.num_out = num_out
+    self.method = method
+
+    # weight
+    if isinstance(self.mode, bm.TrainingMode):
+      weight = bm.TrainVar(weight)
+    self.weight = weight
+
+  def update(self, x):
+    if x.ndim == 1:
+      if self.method is None:
+        event_jitconn_mv = bm.jitconn.event_mv_prob_homo_taichi
+      else:
+        event_jitconn_mv = bm.jitconn.event_mv_prob_homo
+      return event_jitconn_mv(x, self.weight, self.prob, self.seed,
+                                           shape=(self.num_out, self.num_in),
+                                           transpose=self.transpose,
+                                           outdim_parallel=not self.atomic)
+    elif x.ndim == 2:
+      return jax.vmap(self._batch_mv)(x)
+    elif x.ndim > 2:
+      shapes = x.shape[:-1]
+      x = bm.flatten(x, end_dim=-2)
+      y = jax.vmap(self._batch_mv)(x)
+      return bm.reshape(y, shapes + (y.shape[-1],))
+    else:
+      raise ValueError
+
+  def _batch_mv(self, x):
+    if self.method is None:
+      event_jitconn_mv = bm.jitconn.event_mv_prob_homo_taichi
+    else:
+      event_jitconn_mv = bm.jitconn.event_mv_prob_homo
+      return event_jitconn_mv(x, self.weight, self.prob, self.seed,
+                                        shape=(self.num_out, self.num_in),
+                                        transpose=self.transpose,
+                                        outdim_parallel=not self.atomic)
+
+
+class EventJitFPUniformLinear(Layer):
+  r"""Synaptic matrix multiplication with the just-in-time connectivity.
+
+  It performs the computation of:
+
+  .. math::
+
+     y = x @ M
+
+  where :math:`y` is the postsynaptic value, :math:`x` the presynaptic spikes,
+  :math:`M` the synaptic weights which has the fixed sparse connectivity and weights.
+  Particularly, the connectivity in :math:`M` is sampled from a fixed probability :math:`prob`,
+  and at each connection, the synaptic value is sample from a uniform distribution :math:`U(w_{low}, w_{high})`.
+
+  Args:
+    num_in: int. The number of the input feature. A positive integer.
+    num_out: int. The number of the input feature. A positive integer.
+    prob: float. The connectivity probability.
+    w_low: float. The lowest value of the uniform distribution.
+    w_high: float. The highest value of the uniform distribution.
+    seed: int. The random seed used to keep the reproducibility of the connectivity.
+    transpose: bool. Transpose the JIT matrix or not. Default False.
+    atomic: bool. Compute the post-synaptic value with the atomic summation. Default False.
+       May be changed in the future.
+    sharding: The sharding strategy.
+    mode: The synaptic computing mode.
+    name: The synapse model name.
+  """
+
+  def __init__(
+      self,
+      num_in: int,
+      num_out: int,
+      prob: float,
+      w_low: float,
+      w_high: float,
+      seed: Optional[int] = None,
+      sharding: Optional[Sharding] = None,
+      mode: Optional[bm.Mode] = None,
+      name: Optional[str] = None,
+      transpose: bool = False,
+      atomic: bool = True,
+      method: str = None,
+  ):
+    super().__init__(name=name, mode=mode)
+
+    self.prob = prob
+    self.sharding = sharding
+    self.transpose = transpose
+    self.seed = np.random.randint(0, 100000) if seed is None else seed
+    self.atomic = atomic
+    self.num_in = num_in
+    self.num_out = num_out
+    self.method = method
+
+    # weight
+    self.w_low = w_low
+    self.w_high = w_high
+
+  def update(self, x):
+    if x.ndim == 1:
+      if self.method is None:
+        event_jitconn_mv = bm.jitconn.event_mv_prob_uniform_taichi
+      else:
+        event_jitconn_mv = bm.jitconn.event_mv_prob_uniform
+      return event_jitconn_mv(x, self.w_low, self.w_high, self.prob, self.seed,
+                                              shape=(self.num_out, self.num_in),
+                                              transpose=self.transpose,
+                                              outdim_parallel=not self.atomic)
+    elif x.ndim == 2:
+      return jax.vmap(self._batch_mv)(x)
+    elif x.ndim > 2:
+      shapes = x.shape[:-1]
+      x = bm.flatten(x, end_dim=-2)
+      y = jax.vmap(self._batch_mv)(x)
+      return bm.reshape(y, shapes + (y.shape[-1],))
+    else:
+      raise ValueError
+
+  def _batch_mv(self, x):
+    if self.method is None:
+      event_jitconn_mv = bm.jitconn.event_mv_prob_uniform_taichi
+    else:
+      event_jitconn_mv = bm.jitconn.event_mv_prob_uniform
+    return event_jitconn_mv(x, self.w_low, self.w_high, self.prob, self.seed,
+                                              shape=(self.num_out, self.num_in),
+                                              transpose=self.transpose,
+                                              outdim_parallel=not self.atomic)
+
+
+class EventJitFPNormalLinear(Layer):
+  r"""Synaptic matrix multiplication with the just-in-time connectivity.
+
+  It performs the computation of:
+
+  .. math::
+
+     y = x @ M
+
+  where :math:`y` is the postsynaptic value, :math:`x` the presynaptic spikes,
+  :math:`M` the synaptic weights which has the fixed sparse connectivity and weights.
+  Particularly, the connectivity in :math:`M` is sampled from a fixed probability :math:`prob`,
+  and at each connection, the synaptic value is sample from a normal distribution :math:`N(\mu, \sigma)`.
+
+  Args:
+    num_in: int. The number of the input feature. A positive integer.
+    num_out: int. The number of the input feature. A positive integer.
+    prob: float. The connectivity probability.
+    w_mu: float. The center of the normal distribution.
+    w_sigma: float. The standard variance of the normal distribution.
+    seed: int. The random seed used to keep the reproducibility of the connectivity.
+    transpose: bool. Transpose the JIT matrix or not. Default False.
+    atomic: bool. Compute the post-synaptic value with the atomic summation. Default False.
+       May be changed in the future.
+    sharding: The sharding strategy.
+    mode: The synaptic computing mode.
+    name: The synapse model name.
+  """
+
+  def __init__(
+      self,
+      num_in: int,
+      num_out: int,
+      prob: float,
+      w_mu: float,
+      w_sigma: float,
+      seed: Optional[int] = None,
+      sharding: Optional[Sharding] = None,
+      transpose: bool = False,
+      atomic: bool = True,
+      mode: Optional[bm.Mode] = None,
+      name: Optional[str] = None,
+      method: str = None,
+  ):
+    super().__init__(name=name, mode=mode)
+
+    self.prob = prob
+    self.sharding = sharding
+    self.transpose = transpose
+    self.seed = np.random.randint(0, 100000) if seed is None else seed
+    self.atomic = atomic
+    self.num_in = num_in
+    self.num_out = num_out
+    self.method = method
+
+    # weight
+    self.w_mu = w_mu
+    self.w_sigma = w_sigma
+
+  def update(self, x):
+    if x.ndim == 1:
+      if self.method is None:
+        event_jitconn_mv = bm.jitconn.event_mv_prob_normal_taichi
+      else:
+        event_jitconn_mv = bm.jitconn.event_mv_prob_normal
+      return event_jitconn_mv(x, self.w_mu, self.w_sigma, self.prob, self.seed,
+                                             shape=(self.num_out, self.num_in),
+                                             transpose=self.transpose,
+                                             outdim_parallel=not self.atomic)
+    elif x.ndim == 2:
+      return jax.vmap(self._batch_mv)(x)
+    elif x.ndim > 2:
+      shapes = x.shape[:-1]
+      x = bm.flatten(x, end_dim=-2)
+      y = jax.vmap(self._batch_mv)(x)
+      return bm.reshape(y, shapes + (y.shape[-1],))
+    else:
+      raise ValueError
+
+  def _batch_mv(self, x):
+    if self.method is None:
+      event_jitconn_mv = bm.jitconn.event_mv_prob_normal_taichi
+    else:
+      event_jitconn_mv = bm.jitconn.event_mv_prob_normal
+    return event_jitconn_mv(x, self.w_mu, self.w_sigma, self.prob, self.seed,
+                                             shape=(self.num_out, self.num_in),
+                                             transpose=self.transpose,
+                                             outdim_parallel=not self.atomic)
diff --git a/benchmarks/src/model/multiarea.py b/benchmarks/src/model/multiarea.py
new file mode 100644
index 0000000..35adf34
--- /dev/null
+++ b/benchmarks/src/model/multiarea.py
@@ -0,0 +1,175 @@
+import time
+import functools
+
+import brainpy as bp
+import brainpy.math as bm
+from brainpy import neurons
+
+import matplotlib.pyplot as plt
+import numpy as np
+from jax import vmap
+from scipy.io import loadmat
+
+
+def syn_fun(pre_spike, weight, seed, prob, shape):
+  return bm.jitconn.event_mv_prob_homo(pre_spike, weight, prob, seed, shape=shape, transpose=True)
+
+
+class MultiAreaNet(bp.Network):
+  def __init__(
+      self, hier, conn, delay_mat, muIE=0.0475, muEE=.0375, wII=.075,
+      wEE=.01, wIE=.075, wEI=.0375, extE=15.4, extI=14.0, alpha=4.,
+  ):
+    super(MultiAreaNet, self).__init__()
+
+    # data
+    self.hier = hier
+    self.conn = conn
+    self.delay_mat = delay_mat
+
+    # parameters
+    self.muIE = muIE
+    self.muEE = muEE
+    self.wII = wII
+    self.wEE = wEE
+    self.wIE = wIE
+    self.wEI = wEI
+    self.extE = extE
+    self.extI = extI
+    self.alpha = alpha
+    num_area = hier.size
+    self.num_area = num_area
+    self.num_E = 1600
+    self.num_I = 400
+
+    # neuron models
+    self.E = neurons.LIF((num_area, 1600),
+                         V_th=-50., V_reset=-60.,
+                         V_rest=-70., tau=20., tau_ref=2.,
+                         noise=3. / bm.sqrt(20.),
+                         V_initializer=bp.init.Uniform(-70., -50.),
+                         method='exp_auto',
+                         keep_size=True,
+                         ref_var=True)
+    self.I = neurons.LIF((num_area, 400), V_th=-50., V_reset=-60.,
+                         V_rest=-70., tau=10., tau_ref=2., noise=3. / bm.sqrt(10.),
+                         V_initializer=bp.init.Uniform(-70., -50.),
+                         method='exp_auto',
+                         keep_size=True,
+                         ref_var=True)
+
+    # delays
+    self.intra_delay_step = int(2. / bm.get_dt())
+    self.E_delay_steps = bm.asarray(delay_mat.T / bm.get_dt(), dtype=int)
+    bm.fill_diagonal(self.E_delay_steps, self.intra_delay_step)
+    self.Edelay = bm.LengthDelay(self.E.spike, delay_len=int(self.E_delay_steps.max()))
+    self.Idelay = bm.LengthDelay(self.I.spike, delay_len=self.intra_delay_step)
+
+    # synapse model
+    self.f_EE_current = vmap(functools.partial(syn_fun, prob=0.1, shape=(self.num_E, self.num_E)))
+    self.f_EI_current = vmap(functools.partial(syn_fun, prob=0.1, shape=(self.num_E, self.num_I)))
+    self.f_IE_current = vmap(functools.partial(syn_fun, prob=0.1, shape=(self.num_I, self.num_E)),
+                             in_axes=(0, None, 0))
+    self.f_II_current = vmap(functools.partial(syn_fun, prob=0.1, shape=(self.num_I, self.num_I)),
+                             in_axes=(0, None, 0))
+
+    # synapses from I
+    self.intra_I2E_conn = bm.random.random((num_area, 400, 1600)) < 0.1
+    self.intra_I2I_conn = bm.random.random((num_area, 400, 400)) < 0.1
+    self.intra_I2E_weight = -wEI
+    self.intra_I2I_weight = -wII
+
+    # synapses from E
+    # self.E2E_conns = [bm.random.random((num_area, 1600, 1600)) < 0.1 for _ in range(num_area)]
+    self.E2I_conns = [bm.random.random((num_area, 1600, 400)) < 0.1 for _ in range(num_area)]
+    self.E2E_weights = (1 + alpha * hier) * muEE * conn.T  # inter-area connections
+    bm.fill_diagonal(self.E2E_weights, (1 + alpha * hier) * wEE)  # intra-area connections
+    self.E2I_weights = (1 + alpha * hier) * muIE * conn.T  # inter-area connections
+    bm.fill_diagonal(self.E2I_weights, (1 + alpha * hier) * wIE)  # intra-area connections
+    self.E_seeds = bm.random.randint(0, 100000, (num_area, num_area * 2))
+    self.I_seeds = bm.random.randint(0, 100000, (num_area * 2))
+
+  def update(self, v1_input):
+    self.E.input[0] += v1_input
+    self.E.input += self.extE
+    self.I.input += self.extI
+    E_not_ref = bm.logical_not(self.E.refractory)
+    I_not_ref = bm.logical_not(self.I.refractory)
+
+    # synapses from E
+    for i in range(self.num_area):
+      delayed_E_spikes = self.Edelay(self.E_delay_steps[i], i).astype(float)
+      current = self.f_EE_current(delayed_E_spikes, self.E2E_weights[i], self.E_seeds[i, :self.num_area])
+      self.E.V += current * E_not_ref  # E2E
+      current = self.f_EI_current(delayed_E_spikes, self.E2I_weights[i], self.E_seeds[i, self.num_area:])
+      self.I.V += current * I_not_ref  # E2I
+
+    # synapses from I
+    delayed_I_spikes = self.Idelay(self.intra_delay_step).astype(float)
+    current = self.f_IE_current(delayed_I_spikes, self.intra_I2E_weight, self.I_seeds[:self.num_area])
+    self.E.V += current * E_not_ref  # I2E
+    current = self.f_II_current(delayed_I_spikes, self.intra_I2I_weight, self.I_seeds[self.num_area:])
+    self.I.V += current * I_not_ref  # I2I
+
+    # updates
+    self.Edelay.update(self.E.spike)
+    self.Idelay.update(self.I.spike)
+    self.E.update()
+    self.I.update()
+
+
+def raster_plot(xValues, yValues, duration):
+  ticks = np.round(np.arange(0, 29) + 0.5, 2)
+  areas = ['V1', 'V2', 'V4', 'DP', 'MT', '8m', '5', '8l', 'TEO', '2', 'F1',
+           'STPc', '7A', '46d', '10', '9/46v', '9/46d', 'F5', 'TEpd', 'PBr',
+           '7m', '7B', 'F2', 'STPi', 'PROm', 'F7', '8B', 'STPr', '24c']
+  N = len(ticks)
+  plt.figure(figsize=(8, 6))
+  plt.plot(xValues, yValues / (4 * 400), '.', markersize=1)
+  plt.plot([0, duration], np.arange(N + 1).repeat(2).reshape(-1, 2).T, 'k-')
+  plt.ylabel('Area')
+  plt.yticks(np.arange(N))
+  plt.xlabel('Time [ms]')
+  plt.ylim(0, N)
+  plt.yticks(ticks, areas)
+  plt.xlim(0, duration)
+  plt.tight_layout()
+  plt.show()
+
+
+# hierarchy values
+hierVals = loadmat('Matlab/hierValspython.mat')
+hierValsnew = hierVals['hierVals'].flatten()
+hier = bm.asarray(hierValsnew / max(hierValsnew))  # hierarchy normalized.
+
+# fraction of labeled neurons
+flnMatp = loadmat('Matlab/efelenMatpython.mat')
+conn = bm.asarray(flnMatp['flnMatpython'].squeeze())  # fln values..Cij is strength from j to i
+
+# Distance
+speed = 3.5  # axonal conduction velocity
+distMatp = loadmat('Matlab/subgraphWiring29.mat')
+distMat = distMatp['wiring'].squeeze()  # distances between areas values..
+delayMat = bm.asarray(distMat / speed)
+
+pars = dict(extE=14.2, extI=14.7, wII=.075, wEE=.01, wIE=.075, wEI=.0375, muEE=.0375, muIE=0.0475)
+inps = dict(value=15, duration=150)
+
+inputs, length = bp.inputs.section_input(values=[0, inps['value'], 0.],
+                                         durations=[300., inps['duration'], 500],
+                                         return_length=True)
+
+# bm.set_platform('cpu')
+
+net = MultiAreaNet(hier, conn, delayMat, **pars)
+step_run = bm.jit(net.step_run)
+
+t0 = time.time()
+step_run(0, 0.)
+t1 = time.time()
+
+t2 = time.time()
+step_run(1, 0.)
+t3 = time.time()
+
+print(f'Compilation time {(t1 - t0) - (t3 - t2)} s')
diff --git a/benchmarks/src/model/multiple_area_customized_op.py b/benchmarks/src/model/multiple_area_customized_op.py
new file mode 100644
index 0000000..b7d88d6
--- /dev/null
+++ b/benchmarks/src/model/multiple_area_customized_op.py
@@ -0,0 +1,461 @@
+
+import jax
+import jax.numpy as jnp
+import numpy as np
+
+from brainpy._src.dependency_check import import_taichi
+from brainpy._src.math.interoperability import as_jax
+from brainpy._src.math.ndarray import _get_dtype
+from brainpy._src.math.op_register import XLACustomOp
+from brainpy._src.math.tifunc import (lfsr88_key, lfsr88_uniform, lfsr88_normal, lfsr88_random_integers)
+from typing import Tuple, Optional
+
+ti = import_taichi()
+
+def multiple_area_customized_op_E(
+        events: jax.Array,
+        weight: float,
+        conn_prob: float,
+        seed: Optional[int] = None,
+        *,
+        shape: Tuple[int, int],
+        area_num: int,
+        transpose: bool = False,
+        outdim_parallel: bool = False,
+):
+    events = as_jax(events)
+    if isinstance(weight, float): weight = as_jax(weight)
+    weight = jnp.atleast_1d(as_jax(weight))
+    conn_len = jnp.ceil(1 / conn_prob) * 2 - 1
+    conn_len = jnp.asarray(jnp.atleast_1d(conn_len), dtype=jnp.int32)
+    if seed is None:
+        with jax.ensure_compile_time_eval():
+            seed = np.random.randint(0, int(1e8), 1)
+    seed = jnp.atleast_1d(jnp.asarray(seed, dtype=jnp.uint32))
+    return raw_multiple_area_customized_op_E(events, weight, conn_len, seed, shape=shape, area_num=area_num,
+                                            transpose=transpose, outdim_parallel=outdim_parallel)[0]
+    
+
+def multiple_area_customized_op_I(
+        events: jax.Array,
+        weight: float,
+        conn_prob: float,
+        seed: Optional[int] = None,
+        *,
+        shape: Tuple[int, int],
+        area_num: int,
+        transpose: bool = False,
+        outdim_parallel: bool = False,
+):
+    events = as_jax(events)
+    if isinstance(weight, float): weight = as_jax(weight)
+    weight = jnp.atleast_1d(as_jax(weight))
+    conn_len = jnp.ceil(1 / conn_prob) * 2 - 1
+    conn_len = jnp.asarray(jnp.atleast_1d(conn_len), dtype=jnp.int32)
+    if seed is None:
+        with jax.ensure_compile_time_eval():
+            seed = np.random.randint(0, int(1e8), 1)
+    seed = jnp.atleast_1d(jnp.asarray(seed, dtype=jnp.uint32))
+    return raw_multiple_area_customized_op_I(events, weight, conn_len, seed, shape=shape, area_num=area_num,
+                                            transpose=transpose, outdim_parallel=outdim_parallel)[0]
+
+@ti.kernel
+def _multiple_area_event_mv_prob_homo_bool_irregular_cpu_E(
+        events: ti.types.ndarray(ndim=1),
+        weight: ti.types.ndarray(ndim=1),
+        clen: ti.types.ndarray(ndim=1),
+        seed: ti.types.ndarray(ndim=1),
+        out: ti.types.ndarray(ndim=2)
+):
+    num_row = out.shape[1]
+    num_col = events.shape[0]
+    clen0 = clen[0]
+
+    for i_col in range(num_col):
+        if events[i_col]:
+            for i_area in range(out.shape[0]):
+                key = lfsr88_key(seed[i_area] + i_col)
+                key, i_row = lfsr88_random_integers(key, 0, clen0 - 1)
+                while i_row < num_row:
+                    out[i_area, i_row] += weight[i_area]
+                    key, inc = lfsr88_random_integers(key, 1, clen0)
+                    i_row += inc
+
+
+@ti.kernel
+def _multiple_area_event_mv_prob_homo_bool_irregular_gpu_E(
+        events: ti.types.ndarray(ndim=1),
+        weight: ti.types.ndarray(ndim=1),
+        clen: ti.types.ndarray(ndim=1),
+        seed: ti.types.ndarray(ndim=1),
+        out: ti.types.ndarray(ndim=2)
+):
+    num_row = out.shape[1]
+    num_col = events.shape[0]
+    clen0 = clen[0]
+    step = ti.uint32(ti.max((num_row + 1) >> 5, 1))
+
+    for i in range(num_col * 32):
+        i_col = i >> 5
+        if events[i_col]:
+            for i_area in range(out.shape[0]):
+                index = i & 31
+                i_row = step * index + 1
+                end = ti.min(i_row + step, num_row)
+
+                key = lfsr88_key(seed[i_area] + i)
+                key, inc = lfsr88_random_integers(key, 0, clen0 - 1)
+                i_row += inc
+                while i_row < end:
+                    out[i_area, i_row] += weight[i_area]
+                    key, inc = lfsr88_random_integers(key, 1, clen0)
+                    i_row += inc
+
+
+@ti.kernel
+def _multiple_area_event_mv_prob_homo_irregular_cpu_E(
+        events: ti.types.ndarray(ndim=1),
+        weight: ti.types.ndarray(ndim=1),
+        clen: ti.types.ndarray(ndim=1),
+        seed: ti.types.ndarray(ndim=1),
+        out: ti.types.ndarray(ndim=2)
+):
+    num_row = out.shape[1]
+    num_col = events.shape[0]
+    clen0 = clen[0]
+
+    for i_col in range(num_col):
+        if events[i_col] != 0.:
+            for i_area in range(out.shape[0]):
+                key = lfsr88_key(seed[i_area] + i_col)
+                key, i_row = lfsr88_random_integers(key, 0, clen0 - 1)
+                while i_row < num_row:
+                    out[i_area, i_row] += weight[i_area]
+                    key, inc = lfsr88_random_integers(key, 1, clen0)
+                    i_row += inc
+
+
+@ti.kernel
+def _multiple_area_event_mv_prob_homo_irregular_gpu_E(
+        events: ti.types.ndarray(ndim=1),
+        weight: ti.types.ndarray(ndim=1),
+        clen: ti.types.ndarray(ndim=1),
+        seed: ti.types.ndarray(ndim=1),
+        out: ti.types.ndarray(ndim=2)
+):
+    num_row = out.shape[1]
+    num_col = events.shape[0]
+    clen0 = clen[0]
+    step = ti.uint32(ti.max((num_row + 1) >> 5, 1))
+
+    for i in range(num_col * 32):
+        i_col = i >> 5
+        if events[i_col] != 0.:
+            for i_area in range(out.shape[0]):
+                index = i & 31
+                i_row = step * index + 1
+                end = ti.min(i_row + step, num_row)
+
+                key = lfsr88_key(seed[i_area] + i)
+                key, inc = lfsr88_random_integers(key, 0, clen0 - 1)
+                i_row += inc
+                while i_row < end:
+                    out[i_area, i_row] += weight[i_area]
+                    key, inc = lfsr88_random_integers(key, 1, clen0)
+                    i_row += inc
+
+
+def _reverse(shape):
+    return shape[::-1]
+
+
+def _general_checking_E(vector, clen, seed, shape, area_num, transpose, outdim_parallel, *weights):
+    if vector.ndim != 1:
+        raise ValueError('vector should be a 1D vector.')
+    if len(shape) != 2:
+        raise ValueError('shape should be a length-2 tuple.')
+    if seed.ndim != 1:
+        raise ValueError('seed must be a 1D scalar.')
+    if clen.ndim != 1:
+        raise ValueError('conn_prob must be a 1D scalar.')
+    if type(area_num) != int:
+        raise ValueError('area_num must be an integer.')
+
+    assert _get_dtype(clen) in [jnp.int16, jnp.int32, jnp.int64, jnp.uint16, jnp.uint32, jnp.uint64]
+    assert _get_dtype(seed) in [jnp.int16, jnp.int32, jnp.int64, jnp.uint16, jnp.uint32, jnp.uint64]
+
+    for weight in weights:
+        if weight.ndim != 1:
+            raise ValueError('weight must be a 1D scalar.')
+        assert _get_dtype(weight) in [jnp.float16, jnp.float32, jnp.float64], '"weight" must be float valued.'
+
+    if not isinstance(outdim_parallel, bool):
+        raise ValueError('outdim_parallel must be boolean value.')
+    if not isinstance(transpose, bool):
+        raise ValueError('transpose must be boolean value.')
+
+    if transpose:
+        out_shape = (area_num, shape[1])
+        if vector.shape[0] != shape[0]:
+            raise ValueError(f'Shape mismatch, vec {vector.shape} @ mat {shape}.')
+        shape = _reverse(shape)
+    else:
+        if vector.shape[0] != shape[1]:
+            raise ValueError(f'Shape mismatch, mat {shape} @ vec ({vector.shape[0]},).')
+        out_shape = (area_num, shape[0])
+
+    return shape, out_shape
+
+
+def _event_checking_E(vector, clen, seed, shape, area_num, transpose, outdim_parallel, *weights):
+    assert _get_dtype(vector) in [jnp.bool_, jnp.float16, jnp.float32, jnp.float64]
+    return _general_checking_E(vector, clen, seed, shape, area_num, transpose, outdim_parallel, *weights)
+
+
+def _define_multiple_area_event_mv_prob_homo_irregular_prim_E(cpu_kernel, gpu_kernel):
+    prim = XLACustomOp(cpu_kernel=cpu_kernel, gpu_kernel=gpu_kernel)
+    return prim
+
+
+_multiple_area_event_mv_prob_homo_bool_irregular_p_E = _define_multiple_area_event_mv_prob_homo_irregular_prim_E(
+    cpu_kernel=_multiple_area_event_mv_prob_homo_bool_irregular_cpu_E,
+    gpu_kernel=_multiple_area_event_mv_prob_homo_bool_irregular_gpu_E
+)
+
+_multiple_area_event_mv_prob_homo_irregular_p_E = _define_multiple_area_event_mv_prob_homo_irregular_prim_E(
+    cpu_kernel=_multiple_area_event_mv_prob_homo_irregular_cpu_E,
+    gpu_kernel=_multiple_area_event_mv_prob_homo_irregular_gpu_E
+)
+
+
+def raw_multiple_area_customized_op_E(
+        events: jax.Array,
+        weight: jax.Array,  # vector with size 1
+        conn_len: jax.Array,  # vector with size 1
+        seed: jax.Array,  # vector with size 1
+        *,
+        shape: Tuple[int, int],
+        area_num: int,
+        transpose: bool = False,
+        outdim_parallel: bool = False,
+) -> jax.Array:
+    mat_shape, out_shape = _event_checking_E(events, conn_len, seed, shape, area_num, transpose, outdim_parallel, weight)
+
+    if outdim_parallel:
+        raise NotImplementedError('Not implement outdim_parallel=True')
+    else:
+        if events.dtype == jnp.bool_:
+            prim = _multiple_area_event_mv_prob_homo_bool_irregular_p_E
+        else:
+            prim = _multiple_area_event_mv_prob_homo_irregular_p_E
+    
+    return prim(events,
+                weight,
+                conn_len,
+                seed,
+                outs=[jax.ShapeDtypeStruct(shape=out_shape, dtype=weight.dtype)],
+                shape=mat_shape,
+                area_num=area_num,
+                transpose=transpose,
+                outdim_parallel=outdim_parallel)
+
+    
+@ti.kernel
+def _multiple_area_event_mv_prob_homo_bool_irregular_cpu_I(
+        events: ti.types.ndarray(ndim=2),
+        weight: ti.types.ndarray(ndim=1),
+        clen: ti.types.ndarray(ndim=1),
+        seed: ti.types.ndarray(ndim=1),
+        out: ti.types.ndarray(ndim=2)
+):
+    num_row = out.shape[1]
+    num_col = events.shape[1]
+    weight0 = weight[0]
+    clen0 = clen[0]
+
+    for i_col in range(num_col):
+        for i_area in range(out.shape[0]):
+            if events[i_area, i_col]:
+                key = lfsr88_key(seed[i_area] + i_col)
+                key, i_row = lfsr88_random_integers(key, 0, clen0 - 1)
+                while i_row < num_row:
+                    out[i_area, i_row] += weight0
+                    key, inc = lfsr88_random_integers(key, 1, clen0)
+                    i_row += inc
+
+
+@ti.kernel
+def _multiple_area_event_mv_prob_homo_bool_irregular_gpu_I(
+        events: ti.types.ndarray(ndim=1),
+        weight: ti.types.ndarray(ndim=1),
+        clen: ti.types.ndarray(ndim=1),
+        seed: ti.types.ndarray(ndim=1),
+        out: ti.types.ndarray(ndim=2)
+):
+    num_row = out.shape[1]
+    num_col = events.shape[0]
+    weight0 = weight[0]
+    clen0 = clen[0]
+    step = ti.uint32(ti.max((num_row + 1) >> 5, 1))
+
+    for i in range(num_col * 32):
+        i_col = i >> 5
+        for i_area in range(out.shape[0]):
+            if events[i_area, i_col]:
+                index = i & 31
+                i_row = step * index + 1
+                end = ti.min(i_row + step, num_row)
+
+                key = lfsr88_key(seed[i_area] + i)
+                key, inc = lfsr88_random_integers(key, 0, clen0 - 1)
+                i_row += inc
+                while i_row < end:
+                    out[i_area, i_row] += weight0
+                    key, inc = lfsr88_random_integers(key, 1, clen0)
+                    i_row += inc
+
+
+@ti.kernel
+def _multiple_area_event_mv_prob_homo_irregular_cpu_I(
+        events: ti.types.ndarray(ndim=1),
+        weight: ti.types.ndarray(ndim=1),
+        clen: ti.types.ndarray(ndim=1),
+        seed: ti.types.ndarray(ndim=1),
+        out: ti.types.ndarray(ndim=2)
+):
+    num_row = out.shape[1]
+    num_col = events.shape[1]
+    weight0 = weight[0]
+    clen0 = clen[0]
+
+    for i_col in range(num_col):
+        for i_area in range(out.shape[0]):
+            if events[i_area, i_col] != 0.:
+                key = lfsr88_key(seed[i_area] + i_col)
+                key, i_row = lfsr88_random_integers(key, 0, clen0 - 1)
+                while i_row < num_row:
+                    out[i_area, i_row] += weight0
+                    key, inc = lfsr88_random_integers(key, 1, clen0)
+                    i_row += inc
+
+
+@ti.kernel
+def _multiple_area_event_mv_prob_homo_irregular_gpu_I(
+        events: ti.types.ndarray(ndim=1),
+        weight: ti.types.ndarray(ndim=1),
+        clen: ti.types.ndarray(ndim=1),
+        seed: ti.types.ndarray(ndim=1),
+        out: ti.types.ndarray(ndim=2)
+):
+    num_row = out.shape[1]
+    num_col = events.shape[0]
+    weight0 = weight[0]
+    clen0 = clen[0]
+    step = ti.uint32(ti.max((num_row + 1) >> 5, 1))
+
+    for i in range(num_col * 32):
+        i_col = i >> 5
+        for i_area in range(out.shape[0]):
+            if events[i_area, i_col] != 0.:
+                index = i & 31
+                i_row = step * index + 1
+                end = ti.min(i_row + step, num_row)
+
+                key = lfsr88_key(seed[i_area] + i)
+                key, inc = lfsr88_random_integers(key, 0, clen0 - 1)
+                i_row += inc
+                while i_row < end:
+                    out[i_area, i_row] += weight0
+                    key, inc = lfsr88_random_integers(key, 1, clen0)
+                    i_row += inc
+
+def _general_checking_I(vector, clen, seed, shape, area_num, transpose, outdim_parallel, *weights):
+    if vector.ndim != 2:
+        raise ValueError('vector should be a 2D vector.')
+    if len(shape) != 2:
+        raise ValueError('shape should be a length-2 tuple.')
+    if seed.ndim != 1:
+        raise ValueError('seed must be a 1D scalar.')
+    if clen.ndim != 1:
+        raise ValueError('conn_prob must be a 1D scalar.')
+    if type(area_num) != int:
+        raise ValueError('area_num must be an integer.')
+
+    assert _get_dtype(clen) in [jnp.int16, jnp.int32, jnp.int64, jnp.uint16, jnp.uint32, jnp.uint64]
+    assert _get_dtype(seed) in [jnp.int16, jnp.int32, jnp.int64, jnp.uint16, jnp.uint32, jnp.uint64]
+
+    for weight in weights:
+        if weight.ndim != 1:
+            raise ValueError('weight must be a 1D scalar.')
+        assert _get_dtype(weight) in [jnp.float16, jnp.float32, jnp.float64], '"weight" must be float valued.'
+
+    if not isinstance(outdim_parallel, bool):
+        raise ValueError('outdim_parallel must be boolean value.')
+    if not isinstance(transpose, bool):
+        raise ValueError('transpose must be boolean value.')
+
+    if transpose:
+        out_shape = (area_num, shape[1])
+        if vector.shape[1] != shape[0]:
+            raise ValueError(f'Shape mismatch, vec {vector.shape} @ mat {shape}.')
+        shape = _reverse(shape)
+    else:
+        if vector.shape[1] != shape[1]:
+            raise ValueError(f'Shape mismatch, mat {shape} @ vec ({vector.shape[0]},).')
+        out_shape = (area_num, shape[0])
+
+    return shape, out_shape
+
+
+def _event_checking_I(vector, clen, seed, shape, area_num, transpose, outdim_parallel, *weights):
+    assert _get_dtype(vector) in [jnp.bool_, jnp.float16, jnp.float32, jnp.float64]
+    return _general_checking_I(vector, clen, seed, shape, area_num, transpose, outdim_parallel, *weights)
+
+
+def _define_multiple_area_event_mv_prob_homo_irregular_prim_I(cpu_kernel, gpu_kernel):
+    prim = XLACustomOp(cpu_kernel=cpu_kernel, gpu_kernel=gpu_kernel)
+    return prim
+
+
+_multiple_area_event_mv_prob_homo_bool_irregular_p_I = _define_multiple_area_event_mv_prob_homo_irregular_prim_I(
+    cpu_kernel=_multiple_area_event_mv_prob_homo_bool_irregular_cpu_I,
+    gpu_kernel=_multiple_area_event_mv_prob_homo_bool_irregular_gpu_I
+)
+
+_multiple_area_event_mv_prob_homo_irregular_p_I = _define_multiple_area_event_mv_prob_homo_irregular_prim_I(
+    cpu_kernel=_multiple_area_event_mv_prob_homo_irregular_cpu_I,
+    gpu_kernel=_multiple_area_event_mv_prob_homo_irregular_gpu_I
+)
+
+
+def raw_multiple_area_customized_op_I(
+        events: jax.Array,
+        weight: jax.Array,  # vector with size 1
+        conn_len: jax.Array,  # vector with size 1
+        seed: jax.Array,  # vector with size 1
+        *,
+        shape: Tuple[int, int],
+        area_num: int,
+        transpose: bool = False,
+        outdim_parallel: bool = False,
+) -> jax.Array:
+    mat_shape, out_shape = _event_checking_I(events, conn_len, seed, shape, area_num, transpose, outdim_parallel, weight)
+
+    if outdim_parallel:
+        raise NotImplementedError('Not implement outdim_parallel=True')
+    else:
+        if events.dtype == jnp.bool_:
+            prim = _multiple_area_event_mv_prob_homo_bool_irregular_p_I
+        else:
+            prim = _multiple_area_event_mv_prob_homo_irregular_p_I
+    
+    return prim(events,
+                weight,
+                conn_len,
+                seed,
+                outs=[jax.ShapeDtypeStruct(shape=out_shape, dtype=weight.dtype)],
+                shape=mat_shape,
+                area_num=area_num,
+                transpose=transpose,
+                outdim_parallel=outdim_parallel)
+
diff --git a/benchmarks/src/model/test_COBA.py b/benchmarks/src/model/test_COBA.py
new file mode 100644
index 0000000..1a313a0
--- /dev/null
+++ b/benchmarks/src/model/test_COBA.py
@@ -0,0 +1,214 @@
+import brainpy as bp
+import brainpy.math as bm
+import pandas as pd
+import os
+from time import time
+from functools import partial
+
+from linear import EventCSRLinear, EventJitFPHomoLinear, EventJitFPUniformLinear, EventJitFPNormalLinear
+
+EventCSRLinear_brainpylib = partial(EventCSRLinear, method='brainpylib')
+EventCSRLinear_taichi = partial(EventCSRLinear, method=None)
+EventJitFPHomoLinear_brainpylib = partial(EventJitFPHomoLinear, method='brainpylib')
+EventJitFPHomoLinear_taichi = partial(EventJitFPHomoLinear, method=None)
+EventJitFPUniformLinear_brainpylib = partial(EventJitFPUniformLinear, method='brainpylib')
+EventJitFPUniformLinear_taichi = partial(EventJitFPUniformLinear, method=None)
+EventJitFPNormalLinear_brainpylib = partial(EventJitFPNormalLinear, method='brainpylib')
+EventJitFPNormalLinear_taichi = partial(EventJitFPNormalLinear, method=None)
+
+
+bm.set_platform('gpu')
+bm.disable_gpu_memory_preallocation()
+
+post_nums = [400, 4000, 40000, 400000, 4000000]
+conn_nums = [20, 40, 80, 100]
+# conn_nums = [80]
+comm_types = {
+    # 'CSRLinear': (bp.dnn.CSRLinear, bp.dnn.CSRLinear_taichi),
+    'EventCSRLinear': (EventCSRLinear_brainpylib, EventCSRLinear_taichi),
+    # 'JitFPHomoLinear': (bp.dnn.JitFPHomoLinear, bp.dnn.JitFPHomoLinear_taichi),
+    # 'JitFPUniformLinear': (bp.dnn.JitFPUniformLinear, bp.dnn.JitFPUniformLinear_taichi),
+    # 'JitFPNormalLinear': (bp.dnn.JitFPNormalLinear, bp.dnn.JitFPNormalLinear_taichi),
+    'EventJitFPHomoLinear': (EventJitFPHomoLinear_brainpylib, EventJitFPHomoLinear_taichi),
+    'EventJitFPUniformLinear': (EventJitFPUniformLinear_brainpylib, EventJitFPUniformLinear_taichi),
+    'EventJitFPNormalLinear': (EventJitFPNormalLinear_brainpylib, EventJitFPNormalLinear_taichi)
+    }
+E_PROB = 0.75
+I_PROB = 0.25
+SEED = 1234
+E_WEIGHT = 0.6
+E_W_LOW = 0.3
+E_W_HIGH = 0.9
+E_W_MU = 0.6
+E_W_SIGMA = 0.01
+I_WEIGHT = 6.7
+I_W_LOW = 6.4
+I_W_HIGH = 7.0
+I_W_MU = 6.7
+I_W_SIGMA = 0.01
+
+RUNNING_TIME = 100
+if bm.get_platform() == 'cpu':
+    RUNNING_TIME = 10
+
+
+class EINet(bp.DynSysGroup):
+    def __init__(self, post_num, conn_num, comm_type, comm_class):
+        super().__init__()
+        self.exc_num = int(post_num * E_PROB)
+        self.inh_num = int(post_num * I_PROB)
+        self.N = bp.dyn.LifRef(post_num, V_rest=-60., V_th=-50., V_reset=-60., tau=20., tau_ref=5.,
+                           V_initializer=bp.init.Normal(-55., 2.))
+        self.delay = bp.VarDelay(self.N.spike, entries={'I': None})
+        if comm_type == 'CSRLinear' or comm_type == 'EventCSRLinear':
+            self.E = bp.dyn.HalfProjAlignPostMg(comm=comm_class(bp.conn.FixedProb(conn_num/post_num, pre = self.exc_num, post = post_num, seed=SEED, allow_multi_conn=True), weight=E_WEIGHT),
+                                        syn=bp.dyn.Expon.desc(size=post_num, tau=5.),
+                                        out=bp.dyn.COBA.desc(E=0.),
+                                        post=self.N)
+            self.I = bp.dyn.HalfProjAlignPostMg(comm=comm_class(bp.conn.FixedProb(conn_num/post_num, pre = self.inh_num, post = post_num, seed=SEED, allow_multi_conn=True), weight=I_WEIGHT),
+                                        syn=bp.dyn.Expon.desc(size=post_num, tau=5.),
+                                        out=bp.dyn.COBA.desc(E=-80.),
+                                        post=self.N)
+        elif comm_type == 'JitFPHomoLinear' or comm_type == 'EventJitFPHomoLinear':
+            self.E = bp.dyn.HalfProjAlignPostMg(comm=comm_class(self.exc_num, post_num, prob=conn_num/post_num, weight=E_WEIGHT, seed=SEED),
+                                        syn=bp.dyn.Expon.desc(size=post_num, tau=5.),
+                                        out=bp.dyn.COBA.desc(E=0.),
+                                        post=self.N)
+            self.I = bp.dyn.HalfProjAlignPostMg(comm=comm_class(self.inh_num, post_num, prob=conn_num/post_num, weight=I_WEIGHT, seed=SEED),
+                                        syn=bp.dyn.Expon.desc(size=post_num, tau=5.),
+                                        out=bp.dyn.COBA.desc(E=-80.),
+                                        post=self.N)
+        elif comm_type == 'JitFPUniformLinear' or comm_type == 'EventJitFPUniformLinear':
+            self.E = bp.dyn.HalfProjAlignPostMg(comm=comm_class(self.exc_num, post_num, prob=conn_num/post_num, w_low=E_W_LOW, w_high=E_W_HIGH, seed=SEED),
+                                        syn=bp.dyn.Expon.desc(size=post_num, tau=5.),
+                                        out=bp.dyn.COBA.desc(E=0.),
+                                        post=self.N)
+            self.I = bp.dyn.HalfProjAlignPostMg(comm=comm_class(self.inh_num, post_num, prob=conn_num/post_num, w_low=I_W_LOW, w_high=I_W_HIGH, seed=SEED),
+                                        syn=bp.dyn.Expon.desc(size=post_num, tau=5.),
+                                        out=bp.dyn.COBA.desc(E=-80.),
+                                        post=self.N)
+        elif comm_type == 'JitFPNormalLinear' or comm_type == 'EventJitFPNormalLinear':
+            self.E = bp.dyn.HalfProjAlignPostMg(comm=comm_class(self.exc_num, post_num, prob=conn_num/post_num, w_mu=E_W_MU, w_sigma=E_W_SIGMA, seed=SEED),
+                                        syn=bp.dyn.Expon.desc(size=post_num, tau=5.),
+                                        out=bp.dyn.COBA.desc(E=0.),
+                                        post=self.N)
+            self.I = bp.dyn.HalfProjAlignPostMg(comm=comm_class(self.inh_num, post_num, prob=conn_num/post_num, w_mu=I_W_MU, w_sigma=I_W_SIGMA, seed=SEED),
+                                        syn=bp.dyn.Expon.desc(size=post_num, tau=5.),
+                                        out=bp.dyn.COBA.desc(E=-80.),
+                                        post=self.N)
+        else:
+            raise NotImplementedError
+        
+    def update(self, input):
+        spk = self.delay.at('I')
+        self.E(spk[:self.exc_num])
+        self.I(spk[self.exc_num:])
+        self.delay(self.N(input))
+        return self.N.spike.value
+    
+def test(post_num, conn_num, comm_type):
+    print(f'Post num: {post_num}, conn num: {conn_num}, comm type: {comm_type}')
+    comm_brainpylib = comm_types[comm_type][0]
+    comm_taichi = comm_types[comm_type][1]
+    net_brainpylib = EINet(post_num, conn_num, comm_type, comm_brainpylib)
+    net_taichi = EINet(post_num, conn_num, comm_type, comm_taichi)
+
+    indices = bm.arange(RUNNING_TIME)
+
+    bm.for_loop(lambda i: net_brainpylib.step_run(i, 20.), indices)
+    time0 = time()
+    bm.for_loop(lambda i: net_brainpylib.step_run(i, 20.), indices)
+    time1 = time()
+    time2 = time()
+    bm.for_loop(lambda i: net_brainpylib.step_run(i, 20.), indices)
+    time3 = time()
+    time4 = time()
+    bm.for_loop(lambda i: net_brainpylib.step_run(i, 20.), indices)
+    time5 = time()
+    time6 = time()
+    bm.for_loop(lambda i: net_brainpylib.step_run(i, 20.), indices)
+    time7 = time()
+    time8 = time()
+    bm.for_loop(lambda i: net_brainpylib.step_run(i, 20.), indices)
+    time9 = time()
+    time10 = time()
+    bm.for_loop(lambda i: net_brainpylib.step_run(i, 20.), indices)
+    time11 = time()
+    time12 = time()
+    bm.for_loop(lambda i: net_brainpylib.step_run(i, 20.), indices)
+    time13 = time()
+    time14 = time()
+    bm.for_loop(lambda i: net_brainpylib.step_run(i, 20.), indices)
+    time15 = time()
+    time16 = time()
+    bm.for_loop(lambda i: net_brainpylib.step_run(i, 20.), indices)
+    time17 = time()
+    time18 = time()
+    bm.for_loop(lambda i: net_brainpylib.step_run(i, 20.), indices)
+    time19 = time()
+
+    bm.for_loop(lambda i: net_taichi.step_run(i, 20.), indices)
+    time20 = time()
+    bm.for_loop(lambda i: net_taichi.step_run(i, 20.), indices)
+    time21 = time()
+    time22 = time()
+    bm.for_loop(lambda i: net_taichi.step_run(i, 20.), indices)
+    time23 = time()
+    time24 = time()
+    bm.for_loop(lambda i: net_taichi.step_run(i, 20.), indices)
+    time25 = time()
+    time26 = time()
+    bm.for_loop(lambda i: net_taichi.step_run(i, 20.), indices)
+    time27 = time()
+    time28 = time()
+    bm.for_loop(lambda i: net_taichi.step_run(i, 20.), indices)
+    time29 = time()
+    time30 = time()
+    bm.for_loop(lambda i: net_taichi.step_run(i, 20.), indices)
+    time31 = time()
+    time32 = time()
+    bm.for_loop(lambda i: net_taichi.step_run(i, 20.), indices)
+    time33 = time()
+    time34 = time()
+    bm.for_loop(lambda i: net_taichi.step_run(i, 20.), indices)
+    time35 = time()
+    time36 = time()
+    bm.for_loop(lambda i: net_taichi.step_run(i, 20.), indices)
+    time37 = time()
+    time38 = time()
+    bm.for_loop(lambda i: net_taichi.step_run(i, 20.), indices)
+    time39 = time()
+    
+    bm.clear_buffer_memory()
+
+    print(f'BrainPylib: {(time1 - time0)*1000}, {(time3 - time2)*1000}, {(time5 - time4)*1000}, {(time7 - time6)*1000}, {(time9 - time8)*1000}, {(time11 - time10)*1000}, {(time13 - time12)*1000}, {(time15 - time14)*1000}, {(time17 - time16)*1000}, {(time19 - time18)*1000}')
+    print(f'Taichi: {(time21 - time20)*1000}, {(time23 - time22)*1000}, {(time25 - time24)*1000}, {(time27 - time26)*1000}, {(time29 - time28)*1000}, {(time31 - time30)*1000}, {(time33 - time32)*1000}, {(time35 - time34)*1000}, {(time37 - time36)*1000}, {(time39 - time38)*1000}')
+
+    return (time1 - time0)*1000, (time3 - time2)*1000, (time5 - time4)*1000, (time7 - time6)*1000, (time9 - time8)*1000, (time11 - time10)*1000, (time13 - time12)*1000, (time15 - time14)*1000, (time17 - time16)*1000, (time19 - time18)*1000, \
+        (time21 - time20)*1000, (time23 - time22)*1000, (time25 - time24)*1000, (time27 - time26)*1000, (time29 - time28)*1000, (time31 - time30)*1000, (time33 - time32)*1000, (time35 - time34)*1000, (time37 - time36)*1000, (time39 - time38)*1000
+
+df = pd.DataFrame(columns=['post_num', 'conn_num', 'comm_type', 'device',
+                           'brainpylib_time1', 'brainpylib_time2', 'brainpylib_time3', 'brainpylib_time4', 'brainpylib_time5', 'brainpylib_time6', 'brainpylib_time7', 'brainpylib_time8', 'brainpylib_time9', 'brainpylib_time10',
+                           'taichi_time1', 'taichi_time2', 'taichi_time3', 'taichi_time4', 'taichi_time5', 'taichi_time6', 'taichi_time7', 'taichi_time8', 'taichi_time9', 'taichi_time10'])
+PATH = os.path.dirname(os.path.abspath(__file__))
+if bm.get_platform() == 'cpu':
+    for post_num in post_nums:
+        for conn_num in conn_nums:
+            for comm_type in comm_types:
+                brainpylib_time1, brainpylib_time2, brainpylib_time3, brainpylib_time4, brainpylib_time5, brainpylib_time6, brainpylib_time7, brainpylib_time8, brainpylib_time9, brainpylib_time10, \
+                    taichi_time1, taichi_time2, taichi_time3, taichi_time4, taichi_time5, taichi_time6, taichi_time7, taichi_time8, taichi_time9, taichi_time10 = test(post_num, conn_num, comm_type)
+                df.loc[df.shape[0]] = [post_num, conn_num, comm_type, 'cpu',
+                                   brainpylib_time1, brainpylib_time2, brainpylib_time3, brainpylib_time4, brainpylib_time5, brainpylib_time6, brainpylib_time7, brainpylib_time8, brainpylib_time9, brainpylib_time10,
+                                   taichi_time1, taichi_time2, taichi_time3, taichi_time4, taichi_time5, taichi_time6, taichi_time7, taichi_time8, taichi_time9, taichi_time10]
+                df.to_csv(f'{PATH}/benchmark_cpu.csv', index=False)
+
+if bm.get_platform() == 'gpu':
+    for post_num in post_nums:
+        for conn_num in conn_nums:
+            for comm_type in comm_types:
+                brainpylib_time1, brainpylib_time2, brainpylib_time3, brainpylib_time4, brainpylib_time5, brainpylib_time6, brainpylib_time7, brainpylib_time8, brainpylib_time9, brainpylib_time10, \
+                    taichi_time1, taichi_time2, taichi_time3, taichi_time4, taichi_time5, taichi_time6, taichi_time7, taichi_time8, taichi_time9, taichi_time10 = test(post_num, conn_num, comm_type)
+                df.loc[df.shape[0]] = [post_num, conn_num, comm_type, 'gpu',
+                                   brainpylib_time1, brainpylib_time2, brainpylib_time3, brainpylib_time4, brainpylib_time5, brainpylib_time6, brainpylib_time7, brainpylib_time8, brainpylib_time9, brainpylib_time10,
+                                   taichi_time1, taichi_time2, taichi_time3, taichi_time4, taichi_time5, taichi_time6, taichi_time7, taichi_time8, taichi_time9, taichi_time10]
+                df.to_csv(f'{PATH}/benchmark_gpu.csv', index=False)
\ No newline at end of file
diff --git a/benchmarks/src/model/test_COBA_spks.py b/benchmarks/src/model/test_COBA_spks.py
new file mode 100644
index 0000000..3aa599c
--- /dev/null
+++ b/benchmarks/src/model/test_COBA_spks.py
@@ -0,0 +1,152 @@
+import brainpy as bp
+import brainpy.math as bm
+import pandas as pd
+import os
+from time import time
+from functools import partial
+from linear import EventCSRLinear, EventJitFPHomoLinear, EventJitFPUniformLinear, EventJitFPNormalLinear
+
+bm.set_platform('gpu')
+bm.disable_gpu_memory_preallocation()
+
+
+EventCSRLinear_brainpylib = partial(EventCSRLinear, method='brainpylib')
+EventCSRLinear_taichi = partial(EventCSRLinear, method=None)
+EventJitFPHomoLinear_brainpylib = partial(EventJitFPHomoLinear, method='brainpylib')
+EventJitFPHomoLinear_taichi = partial(EventJitFPHomoLinear, method=None)
+EventJitFPUniformLinear_brainpylib = partial(EventJitFPUniformLinear, method='brainpylib')
+EventJitFPUniformLinear_taichi = partial(EventJitFPUniformLinear, method=None)
+EventJitFPNormalLinear_brainpylib = partial(EventJitFPNormalLinear, method='brainpylib')
+EventJitFPNormalLinear_taichi = partial(EventJitFPNormalLinear, method=None)
+
+
+post_nums = [400, 4000, 40000, 400000, 4000000]
+conn_nums = [20, 40, 80, 100]
+# conn_nums = [80]
+comm_types = {
+    # 'CSRLinear': (bp.dnn.CSRLinear, bp.dnn.CSRLinear_taichi),
+    # 'EventCSRLinear': (EventCSRLinear_brainpylib, EventCSRLinear_taichi),
+    # 'JitFPHomoLinear': (bp.dnn.JitFPHomoLinear, bp.dnn.JitFPHomoLinear_taichi),
+    # 'JitFPUniformLinear': (bp.dnn.JitFPUniformLinear, bp.dnn.JitFPUniformLinear_taichi),
+    # 'JitFPNormalLinear': (bp.dnn.JitFPNormalLinear, bp.dnn.JitFPNormalLinear_taichi),
+    'EventJitFPHomoLinear': (EventJitFPHomoLinear_brainpylib, EventJitFPHomoLinear_taichi),
+    'EventJitFPUniformLinear': (EventJitFPUniformLinear_brainpylib, EventJitFPUniformLinear_taichi),
+    'EventJitFPNormalLinear': (EventJitFPNormalLinear_brainpylib, EventJitFPNormalLinear_taichi)
+    }
+E_PROB = 0.75
+I_PROB = 0.25
+SEED = 1234
+E_WEIGHT = 0.6
+E_W_LOW = 0.3
+E_W_HIGH = 0.9
+E_W_MU = 0.6
+E_W_SIGMA = 0.01
+I_WEIGHT = 6.7
+I_W_LOW = 6.4
+I_W_HIGH = 7.0
+I_W_MU = 6.7
+I_W_SIGMA = 0.01
+
+RUNNING_TIME = 1000
+# if bm.get_platform() == 'cpu':
+#     RUNNING_TIME = 10
+
+
+class EINet(bp.DynSysGroup):
+    def __init__(self, post_num, conn_num, comm_type, comm_class):
+        super().__init__()
+        self.exc_num = int(post_num * E_PROB)
+        self.inh_num = int(post_num * I_PROB)
+        self.N = bp.dyn.LifRef(post_num, V_rest=-60., V_th=-50., V_reset=-60., tau=20., tau_ref=5.,
+                           V_initializer=bp.init.Normal(-55., 2.))
+        self.delay = bp.VarDelay(self.N.spike, entries={'I': None})
+        if comm_type == 'CSRLinear' or comm_type == 'EventCSRLinear':
+            self.E = bp.dyn.HalfProjAlignPostMg(comm=comm_class(bp.conn.FixedProb(conn_num/post_num, pre = self.exc_num, post = post_num, seed=SEED, allow_multi_conn=True), weight=E_WEIGHT),
+                                        syn=bp.dyn.Expon.desc(size=post_num, tau=5.),
+                                        out=bp.dyn.COBA.desc(E=0.),
+                                        post=self.N)
+            self.I = bp.dyn.HalfProjAlignPostMg(comm=comm_class(bp.conn.FixedProb(conn_num/post_num, pre = self.inh_num, post = post_num, seed=SEED, allow_multi_conn=True), weight=I_WEIGHT),
+                                        syn=bp.dyn.Expon.desc(size=post_num, tau=5.),
+                                        out=bp.dyn.COBA.desc(E=-80.),
+                                        post=self.N)
+        elif comm_type == 'JitFPHomoLinear' or comm_type == 'EventJitFPHomoLinear':
+            self.E = bp.dyn.HalfProjAlignPostMg(comm=comm_class(self.exc_num, post_num, prob=conn_num/post_num, weight=E_WEIGHT, seed=SEED, atomic=True),
+                                        syn=bp.dyn.Expon.desc(size=post_num, tau=5.),
+                                        out=bp.dyn.COBA.desc(E=0.),
+                                        post=self.N)
+            self.I = bp.dyn.HalfProjAlignPostMg(comm=comm_class(self.inh_num, post_num, prob=conn_num/post_num, weight=I_WEIGHT, seed=SEED, atomic=True),
+                                        syn=bp.dyn.Expon.desc(size=post_num, tau=5.),
+                                        out=bp.dyn.COBA.desc(E=-80.),
+                                        post=self.N)
+        elif comm_type == 'JitFPUniformLinear' or comm_type == 'EventJitFPUniformLinear':
+            self.E = bp.dyn.HalfProjAlignPostMg(comm=comm_class(self.exc_num, post_num, prob=conn_num/post_num, w_low=E_W_LOW, w_high=E_W_HIGH, seed=SEED, atomic=True),
+                                        syn=bp.dyn.Expon.desc(size=post_num, tau=5.),
+                                        out=bp.dyn.COBA.desc(E=0.),
+                                        post=self.N)
+            self.I = bp.dyn.HalfProjAlignPostMg(comm=comm_class(self.inh_num, post_num, prob=conn_num/post_num, w_low=I_W_LOW, w_high=I_W_HIGH, seed=SEED, atomic=True),
+                                        syn=bp.dyn.Expon.desc(size=post_num, tau=5.),
+                                        out=bp.dyn.COBA.desc(E=-80.),
+                                        post=self.N)
+        elif comm_type == 'JitFPNormalLinear' or comm_type == 'EventJitFPNormalLinear':
+            self.E = bp.dyn.HalfProjAlignPostMg(comm=comm_class(self.exc_num, post_num, prob=conn_num/post_num, w_mu=E_W_MU, w_sigma=E_W_SIGMA, seed=SEED, atomic=True),
+                                        syn=bp.dyn.Expon.desc(size=post_num, tau=5.),
+                                        out=bp.dyn.COBA.desc(E=0.),
+                                        post=self.N)
+            self.I = bp.dyn.HalfProjAlignPostMg(comm=comm_class(self.inh_num, post_num, prob=conn_num/post_num, w_mu=I_W_MU, w_sigma=I_W_SIGMA, seed=SEED, atomic=True),
+                                        syn=bp.dyn.Expon.desc(size=post_num, tau=5.),
+                                        out=bp.dyn.COBA.desc(E=-80.),
+                                        post=self.N)
+        else:
+            raise NotImplementedError
+        
+    def update(self, input):
+        spk = self.delay.at('I')
+        self.E(spk[:self.exc_num])
+        self.I(spk[self.exc_num:])
+        self.delay(self.N(input))
+        return self.N.spike.value
+    
+def test_spks(post_num, conn_num, comm_type):
+    print(f'Post num: {post_num}, conn num: {conn_num}, comm type: {comm_type}')
+    comm_brainpylib = comm_types[comm_type][0]
+    comm_taichi = comm_types[comm_type][1]
+    net_brainpylib = EINet(post_num, conn_num, comm_type, comm_brainpylib)
+    net_taichi = EINet(post_num, conn_num, comm_type, comm_taichi)
+
+    indices = bm.arange(RUNNING_TIME)
+
+    brainpylib_spks = bm.for_loop(lambda i: net_brainpylib.step_run(i, 20.), indices)
+    taichi_spks = bm.for_loop(lambda i: net_taichi.step_run(i, 20.), indices)
+    
+    brainpylib_spk = brainpylib_spks.sum() / (RUNNING_TIME/1000) / post_num
+    taichi_spk = taichi_spks.sum() / (RUNNING_TIME/1000) / post_num
+    
+
+    print(f'BrainPyLib spks: {brainpylib_spk}')
+    print(f'Taichi spks: {taichi_spk}')
+    
+    return brainpylib_spk, taichi_spk
+
+df = pd.DataFrame(columns=['post_num', 'conn_num', 'comm_type', 'device',
+                           'brainpylib_spk',
+                           'taichi_spk',])
+PATH = os.path.dirname(os.path.abspath(__file__))
+if bm.get_platform() == 'cpu':
+    for post_num in post_nums:
+        for conn_num in conn_nums:
+            for comm_type in comm_types:
+                brainpylib_spks, taichi_spks = test_spks(post_num, conn_num, comm_type)
+                df.loc[df.shape[0]] = [post_num, conn_num, comm_type, 'cpu',
+                                       brainpylib_spks,
+                                       taichi_spks]
+                df.to_csv(f'{PATH}/benchmark_spks_cpu.csv', index=False)
+
+if bm.get_platform() == 'gpu':
+    for post_num in post_nums:
+        for conn_num in conn_nums:
+            for comm_type in comm_types:
+               brainpylib_spks, taichi_spks = test_spks(post_num, conn_num, comm_type)
+               df.loc[df.shape[0]] = [post_num, conn_num, comm_type, 'gpu',
+                                      brainpylib_spks,
+                                      taichi_spks]
+               df.to_csv(f'{PATH}/benchmark_spks_gpu.csv', index=False)
\ No newline at end of file
diff --git a/benchmarks/src/model/test_MultipleArea.py b/benchmarks/src/model/test_MultipleArea.py
new file mode 100644
index 0000000..51afd1f
--- /dev/null
+++ b/benchmarks/src/model/test_MultipleArea.py
@@ -0,0 +1,510 @@
+from time import time
+import functools
+
+import brainpy as bp
+import brainpy.math as bm
+from brainpy import neurons
+
+import matplotlib.pyplot as plt
+import numpy as np
+import pandas as pd
+from jax import vmap
+import os
+from scipy.io import loadmat
+
+from multiple_area_customized_op import (multiple_area_customized_op_E as syn_fun_E,
+                                          multiple_area_customized_op_I as syn_fun_I)
+
+bm.set_platform('gpu')
+bm.disable_gpu_memory_preallocation()
+
+PATH = os.path.dirname(os.path.abspath(__file__))
+
+neuron_nums = [
+    200, 
+    2000, 
+    20000, 
+    200000, 
+    # 2000000
+]
+conn_nums = [
+    20, 
+    40, 
+    80,
+    100 
+]
+
+E_PROB = 0.8
+I_PROB = 0.2
+muIE = 0.0475
+muEE = 0.0375
+wII = 0.075
+wEE = 0.01
+wIE = 0.075
+wEI = 0.0375
+extE = 14.2
+extI = 14.7
+alpha = 4.
+
+RUNNING_TIME = 10
+if bm.get_platform() == 'cpu':
+    RUNNING_TIME = 3
+
+syn_func_types = [
+    'event_mv_prob_homo',
+    # 'event_mv_prob_uniform',
+    # 'event_mv_prob_normal',
+]
+
+# hierarchy values
+hierVals = loadmat(f'{PATH}/Matlab/hierValspython.mat')
+hierValsnew = hierVals['hierVals'].flatten()
+hier = bm.asarray(hierValsnew / max(hierValsnew))  # hierarchy normalized.
+
+# fraction of labeled neurons
+flnMatp = loadmat(f'{PATH}/Matlab/efelenMatpython.mat')
+conn = bm.asarray(flnMatp['flnMatpython'].squeeze())  # fln values..Cij is strength from j to i
+
+# Distance
+speed = 3.5  # axonal conduction velocity
+distMatp = loadmat(f'{PATH}/Matlab/subgraphWiring29.mat')
+distMat = distMatp['wiring'].squeeze()  # distances between areas values..
+delayMat = bm.asarray(distMat / speed)
+
+
+class MultiAreaNet_brainpylib(bp.Network):
+    def __init__(
+            self, hier, conn, delay_mat, neuron_num, conn_prob, syn_fun_type, syn_fun
+    ):
+        super(MultiAreaNet_brainpylib, self).__init__()
+
+        # data
+        self.hier = hier
+        self.conn = conn
+        self.delay_mat = delay_mat
+
+        # parameters
+        self.exc_num = int(neuron_num * E_PROB)
+        self.inh_num = int(neuron_num * I_PROB)
+        self.conn_prob = conn_prob
+        self.syn_fun_type = syn_fun_type
+
+        self.muIE = muIE
+        self.muEE = muEE
+        self.wII = wII
+        self.wEE = wEE
+        self.wIE = wIE
+        self.wEI = wEI
+        self.extE = extE
+        self.extI = extI
+        self.alpha = alpha
+        num_area = hier.size
+        self.num_area = num_area
+        self.num_E = self.exc_num
+        self.num_I = self.inh_num
+
+        # neuron models
+        self.E = neurons.LIF((num_area, self.exc_num),
+                             V_th=-50., V_reset=-60.,
+                             V_rest=-70., tau=20., tau_ref=2.,
+                             noise=3. / bm.sqrt(20.),
+                             V_initializer=bp.init.Uniform(-70., -50.),
+                             method='exp_auto',
+                             keep_size=True,
+                             ref_var=True)
+        self.I = neurons.LIF((num_area, self.inh_num), V_th=-50., V_reset=-60.,
+                             V_rest=-70., tau=10., tau_ref=2., noise=3. / bm.sqrt(10.),
+                             V_initializer=bp.init.Uniform(-70., -50.),
+                             method='exp_auto',
+                             keep_size=True,
+                             ref_var=True)
+
+        # delays
+        self.intra_delay_step = int(2. / bm.get_dt())
+        self.E_delay_steps = bm.asarray(delay_mat.T / bm.get_dt(), dtype=int)
+        bm.fill_diagonal(self.E_delay_steps, self.intra_delay_step)
+        self.Edelay = bm.LengthDelay(self.E.spike, delay_len=int(self.E_delay_steps.max()))
+        self.Idelay = bm.LengthDelay(self.I.spike, delay_len=self.intra_delay_step)
+
+        # synapse model
+        self.f_EE_current = vmap(functools.partial(syn_fun, prob=conn_prob, shape=(self.num_E, self.num_E)))
+        self.f_EI_current = vmap(functools.partial(syn_fun, prob=conn_prob, shape=(self.num_E, self.num_I)))
+        self.f_IE_current = vmap(functools.partial(syn_fun, prob=conn_prob, shape=(self.num_I, self.num_E)),
+                                in_axes=(0, None, 0))
+        self.f_II_current = vmap(functools.partial(syn_fun, prob=conn_prob, shape=(self.num_I, self.num_I)),
+                                in_axes=(0, None, 0))
+
+
+        # synapses from I
+        # self.intra_I2E_conn = bm.random.random((num_area, self.inh_num, self.exc_num)) < conn_prob
+        # self.intra_I2I_conn = bm.random.random((num_area, self.inh_num, self.inh_num)) < conn_prob
+        self.intra_I2E_weight = -wEI
+        self.intra_I2I_weight = -wII
+
+        # synapses from E
+        # self.E2E_conns = [bm.random.random((num_area, 1600, 1600)) < 0.1 for _ in range(num_area)]
+        # self.E2I_conns = [bm.random.random((num_area, self.exc_num, self.inh_num)) < conn_prob for _ in range(num_area)]
+        self.E2E_weights = (1 + alpha * hier) * muEE * conn.T  # inter-area connections
+        bm.fill_diagonal(self.E2E_weights, (1 + alpha * hier) * wEE)  # intra-area connections
+        self.E2I_weights = (1 + alpha * hier) * muIE * conn.T  # inter-area connections
+        bm.fill_diagonal(self.E2I_weights, (1 + alpha * hier) * wIE)  # intra-area connections
+        self.E_seeds = bm.random.randint(0, 100000, (num_area, num_area * 2))
+        self.I_seeds = bm.random.randint(0, 100000, (num_area * 2))
+
+    def update(self, v1_input):
+        self.E.input[0] += v1_input
+        self.E.input += self.extE
+        self.I.input += self.extI
+        E_not_ref = bm.logical_not(self.E.refractory)
+        I_not_ref = bm.logical_not(self.I.refractory)
+
+        if self.syn_fun_type == 'event_mv_prob_homo':
+            # synapses from E
+            for i in range(self.num_area):
+                delayed_E_spikes = self.Edelay(self.E_delay_steps[i], i).astype(float)
+                current = self.f_EE_current(delayed_E_spikes, self.E2E_weights[i], self.E_seeds[i, :self.num_area])
+                self.E.V += current * E_not_ref  # E2E
+                current = self.f_EI_current(delayed_E_spikes, self.E2I_weights[i], self.E_seeds[i, self.num_area:])
+                self.I.V += current * I_not_ref  # E2I
+
+            # synapses from I
+            delayed_I_spikes = self.Idelay(self.intra_delay_step).astype(float)
+            current = self.f_IE_current(delayed_I_spikes, self.intra_I2E_weight, self.I_seeds[:self.num_area])
+            self.E.V += current * E_not_ref  # I2E
+            current = self.f_II_current(delayed_I_spikes, self.intra_I2I_weight, self.I_seeds[self.num_area:])
+            self.I.V += current * I_not_ref  # I2I
+        elif self.syn_fun_type == 'event_mv_prob_uniform':
+            # synapses from E
+            for i in range(self.num_area):
+                delayed_E_spikes = self.Edelay(self.E_delay_steps[i], i).astype(float)
+                current = self.f_EE_current(delayed_E_spikes, self.E2E_weights[i] - 0.03, self.E2E_weights[i] + 0.03, self.E_seeds[i, :self.num_area])
+                self.E.V += current * E_not_ref  # E2E
+                current = self.f_EI_current(delayed_E_spikes, self.E2E_weights[i] - 0.03, self.E2E_weights[i] + 0.03, self.E_seeds[i, self.num_area:])
+                self.I.V += current * I_not_ref  # E2I
+
+            # synapses from I
+            delayed_I_spikes = self.Idelay(self.intra_delay_step).astype(float)
+            current = self.f_IE_current(delayed_I_spikes, self.intra_I2E_weight - 0.03, self.intra_I2E_weight + 0.03, self.I_seeds[:self.num_area])
+            self.E.V += current * E_not_ref  # I2E
+            current = self.f_II_current(delayed_I_spikes, self.intra_I2E_weight - 0.03, self.intra_I2E_weight + 0.03, self.I_seeds[self.num_area:])
+            self.I.V += current * I_not_ref  # I2I
+        elif self.syn_fun_type == 'event_mv_prob_normal':
+            # synapses from E
+            for i in range(self.num_area):
+                delayed_E_spikes = self.Edelay(self.E_delay_steps[i], i).astype(float)
+                current = self.f_EE_current(delayed_E_spikes, self.E2E_weights[i], 0.01, self.E_seeds[i, :self.num_area])
+                self.E.V += current * E_not_ref  # E2E
+                current = self.f_EI_current(delayed_E_spikes, self.E2I_weights[i], 0.01, self.E_seeds[i, self.num_area:])
+                self.I.V += current * I_not_ref  # E2I
+
+            # synapses from I
+            delayed_I_spikes = self.Idelay(self.intra_delay_step).astype(float)
+            current = self.f_IE_current(delayed_I_spikes, self.intra_I2E_weight, 0.01, self.I_seeds[:self.num_area])
+            self.E.V += current * E_not_ref  # I2E
+            current = self.f_II_current(delayed_I_spikes, self.intra_I2I_weight, 0.01, self.I_seeds[self.num_area:])
+            self.I.V += current * I_not_ref  # I2I
+
+        # updates
+        self.Edelay.update(self.E.spike)
+        self.Idelay.update(self.I.spike)
+        self.E.update()
+        self.I.update()
+
+
+class MultiAreaNet_taichi(bp.Network):
+    def __init__(
+            self, hier, conn, delay_mat, neuron_num, conn_prob, syn_fun_type, syn_fun_E, syn_fun_I
+    ):
+        super(MultiAreaNet_taichi, self).__init__()
+
+        # data
+        self.hier = hier
+        self.conn = conn
+        self.delay_mat = delay_mat
+
+        # parameters
+        self.exc_num = int(neuron_num * E_PROB)
+        self.inh_num = int(neuron_num * I_PROB)
+        self.conn_prob = conn_prob
+        self.syn_fun_type = syn_fun_type
+
+        self.muIE = muIE
+        self.muEE = muEE
+        self.wII = wII
+        self.wEE = wEE
+        self.wIE = wIE
+        self.wEI = wEI
+        self.extE = extE
+        self.extI = extI
+        self.alpha = alpha
+        num_area = hier.size
+        self.num_area = num_area
+        self.num_E = self.exc_num
+        self.num_I = self.inh_num
+
+        # neuron models
+        self.E = neurons.LIF((num_area, self.exc_num),
+                             V_th=-50., V_reset=-60.,
+                             V_rest=-70., tau=20., tau_ref=2.,
+                             noise=3. / bm.sqrt(20.),
+                             V_initializer=bp.init.Uniform(-70., -50.),
+                             method='exp_auto',
+                             keep_size=True,
+                             ref_var=True)
+        self.I = neurons.LIF((num_area, self.inh_num), V_th=-50., V_reset=-60.,
+                             V_rest=-70., tau=10., tau_ref=2., noise=3. / bm.sqrt(10.),
+                             V_initializer=bp.init.Uniform(-70., -50.),
+                             method='exp_auto',
+                             keep_size=True,
+                             ref_var=True)
+
+        # delays
+        self.intra_delay_step = int(2. / bm.get_dt())
+        self.E_delay_steps = bm.asarray(delay_mat.T / bm.get_dt(), dtype=int)
+        bm.fill_diagonal(self.E_delay_steps, self.intra_delay_step)
+        self.Edelay = bm.LengthDelay(self.E.spike, delay_len=int(self.E_delay_steps.max()))
+        self.Idelay = bm.LengthDelay(self.I.spike, delay_len=self.intra_delay_step)
+
+        # synapse model
+        self.f_EE_current = functools.partial(syn_fun_E, prob=conn_prob, shape=(self.num_E, self.num_E), area_num=num_area)
+        self.f_EI_current = functools.partial(syn_fun_E, prob=conn_prob, shape=(self.num_E, self.num_I), area_num=num_area)
+        self.f_IE_current = functools.partial(syn_fun_I, prob=conn_prob, shape=(self.num_I, self.num_E), area_num=num_area)
+        self.f_II_current = functools.partial(syn_fun_I, prob=conn_prob, shape=(self.num_I, self.num_I), area_num=num_area)
+
+
+        # synapses from I
+        # self.intra_I2E_conn = bm.random.random((num_area, self.inh_num, self.exc_num)) < conn_prob
+        # self.intra_I2I_conn = bm.random.random((num_area, self.inh_num, self.inh_num)) < conn_prob
+        self.intra_I2E_weight = -wEI
+        self.intra_I2I_weight = -wII
+
+        # synapses from E
+        # self.E2E_conns = [bm.random.random((num_area, 1600, 1600)) < 0.1 for _ in range(num_area)]
+        # self.E2I_conns = [bm.random.random((num_area, self.exc_num, self.inh_num)) < conn_prob for _ in range(num_area)]
+        self.E2E_weights = (1 + alpha * hier) * muEE * conn.T  # inter-area connections
+        bm.fill_diagonal(self.E2E_weights, (1 + alpha * hier) * wEE)  # intra-area connections
+        self.E2I_weights = (1 + alpha * hier) * muIE * conn.T  # inter-area connections
+        bm.fill_diagonal(self.E2I_weights, (1 + alpha * hier) * wIE)  # intra-area connections
+        self.E_seeds = bm.random.randint(0, 100000, (num_area, num_area * 2))
+        self.I_seeds = bm.random.randint(0, 100000, (num_area * 2))
+
+    def update(self, v1_input):
+        self.E.input[0] += v1_input
+        self.E.input += self.extE
+        self.I.input += self.extI
+        E_not_ref = bm.logical_not(self.E.refractory)
+        I_not_ref = bm.logical_not(self.I.refractory)
+
+        if self.syn_fun_type == 'event_mv_prob_homo':
+            # synapses from E
+            for i in range(self.num_area):
+                delayed_E_spikes = self.Edelay(self.E_delay_steps[i], i).astype(float)
+                delayed_E_spikes = delayed_E_spikes[i]
+                current = self.f_EE_current(delayed_E_spikes, self.E2E_weights[i], self.E_seeds[i, :self.num_area])
+                self.E.V += current * E_not_ref  # E2E
+                current = self.f_EI_current(delayed_E_spikes, self.E2I_weights[i], self.E_seeds[i, self.num_area:])
+                self.I.V += current * I_not_ref  # E2I
+
+            # synapses from I
+            delayed_I_spikes = self.Idelay(self.intra_delay_step).astype(float)
+            current = self.f_IE_current(delayed_I_spikes, self.intra_I2E_weight, self.I_seeds[:self.num_area])
+            self.E.V += current * E_not_ref  # I2E
+            current = self.f_II_current(delayed_I_spikes, self.intra_I2I_weight, self.I_seeds[self.num_area:])
+            self.I.V += current * I_not_ref  # I2I
+        elif self.syn_fun_type == 'event_mv_prob_uniform':
+            # synapses from E
+            for i in range(self.num_area):
+                delayed_E_spikes = self.Edelay(self.E_delay_steps[i], i).astype(float)
+                current = self.f_EE_current(delayed_E_spikes, self.E2E_weights[i] - 0.03, self.E2E_weights[i] + 0.03, self.E_seeds[i, :self.num_area])
+                self.E.V += current * E_not_ref  # E2E
+                current = self.f_EI_current(delayed_E_spikes, self.E2E_weights[i] - 0.03, self.E2E_weights[i] + 0.03, self.E_seeds[i, self.num_area:])
+                self.I.V += current * I_not_ref  # E2I
+
+            # synapses from I
+            delayed_I_spikes = self.Idelay(self.intra_delay_step).astype(float)
+            current = self.f_IE_current(delayed_I_spikes, self.intra_I2E_weight - 0.03, self.intra_I2E_weight + 0.03, self.I_seeds[:self.num_area])
+            self.E.V += current * E_not_ref  # I2E
+            current = self.f_II_current(delayed_I_spikes, self.intra_I2E_weight - 0.03, self.intra_I2E_weight + 0.03, self.I_seeds[self.num_area:])
+            self.I.V += current * I_not_ref  # I2I
+        elif self.syn_fun_type == 'event_mv_prob_normal':
+            # synapses from E
+            for i in range(self.num_area):
+                delayed_E_spikes = self.Edelay(self.E_delay_steps[i], i).astype(float)
+                current = self.f_EE_current(delayed_E_spikes, self.E2E_weights[i], 0.01, self.E_seeds[i, :self.num_area])
+                self.E.V += current * E_not_ref  # E2E
+                current = self.f_EI_current(delayed_E_spikes, self.E2I_weights[i], 0.01, self.E_seeds[i, self.num_area:])
+                self.I.V += current * I_not_ref  # E2I
+
+            # synapses from I
+            delayed_I_spikes = self.Idelay(self.intra_delay_step).astype(float)
+            current = self.f_IE_current(delayed_I_spikes, self.intra_I2E_weight, 0.01, self.I_seeds[:self.num_area])
+            self.E.V += current * E_not_ref  # I2E
+            current = self.f_II_current(delayed_I_spikes, self.intra_I2I_weight, 0.01, self.I_seeds[self.num_area:])
+            self.I.V += current * I_not_ref  # I2I
+
+        # updates
+        self.Edelay.update(self.E.spike)
+        self.Idelay.update(self.I.spike)
+        self.E.update()
+        self.I.update()
+
+def raster_plot(xValues, yValues, duration):
+    ticks = np.round(np.arange(0, 29) + 0.5, 2)
+    areas = ['V1', 'V2', 'V4', 'DP', 'MT', '8m', '5', '8l', 'TEO', '2', 'F1',
+             'STPc', '7A', '46d', '10', '9/46v', '9/46d', 'F5', 'TEpd', 'PBr',
+             '7m', '7B', 'F2', 'STPi', 'PROm', 'F7', '8B', 'STPr', '24c']
+    N = len(ticks)
+    plt.figure(figsize=(8, 6))
+    plt.plot(xValues, yValues / (4 * 400), '.', markersize=1)
+    plt.plot([0, duration], np.arange(N + 1).repeat(2).reshape(-1, 2).T, 'k-')
+    plt.ylabel('Area')
+    plt.yticks(np.arange(N))
+    plt.xlabel('Time [ms]')
+    plt.ylim(0, N)
+    plt.yticks(ticks, areas)
+    plt.xlim(0, duration)
+    plt.tight_layout()
+    plt.show()
+
+
+def syn_fun_homo_brainpylib(pre_spike, weight, seed, prob, shape):
+    return bm.jitconn.event_mv_prob_homo(pre_spike, weight, prob, seed, shape=shape, transpose=True)
+
+def syn_fun_homo_taichi_E(pre_spike, weight, seed, prob, shape, area_num):
+    return syn_fun_E(pre_spike, weight, prob, seed, shape=shape, area_num=area_num, transpose=True)
+
+def syn_fun_homo_taichi_I(pre_spike, weight, seed, prob, shape, area_num):
+    return syn_fun_I(pre_spike, weight, prob, seed, shape=shape, area_num=area_num, transpose=True)
+
+
+def syn_fun_uniform_brainpylib(pre_spike, w_low, w_high, seed, prob, shape):
+    return bm.jitconn.event_mv_prob_uniform(pre_spike, w_low, w_high, prob, seed, shape=shape, transpose=True)
+
+
+def syn_fun_uniform_taichi(pre_spike, w_low, w_high, seed, prob, shape):
+    return bm.jitconn.event_mv_prob_uniform_taichi(pre_spike, w_low, w_high, prob, seed, shape=shape, transpose=True)
+
+
+def syn_fun_normal_brainpylib(pre_spike, w_mu, w_sigma, prob, seed, shape):
+    return bm.jitconn.event_mv_prob_normal(pre_spike, w_mu, w_sigma, prob, seed, shape=shape, transpose=True)
+
+
+def syn_fun_normal_taichi(pre_spike, w_mu, w_sigma, prob, seed, shape):
+    return bm.jitconn.event_mv_prob_normal_taichi(pre_spike, w_mu, w_sigma, prob, seed, shape=shape, transpose=True)
+
+
+def test(neuron_num, conn_num, syn_func_type):
+    print(f'neuron nums: {neuron_num}, conn num: {conn_num} syn func type: {syn_func_type}')
+    conn_prob = conn_num / neuron_num
+    if syn_func_type == 'event_mv_prob_homo':
+        net_brainpylib = MultiAreaNet_brainpylib(hier, conn, delayMat, neuron_num, conn_prob, syn_func_type, syn_fun_homo_brainpylib)
+        net_taichi = MultiAreaNet_taichi(hier, conn, delayMat, neuron_num, conn_prob, syn_func_type, syn_fun_homo_taichi_E, syn_fun_homo_taichi_I)
+    elif syn_func_type == 'event_mv_prob_uniform':
+        net_brainpylib = MultiAreaNet_brainpylib(hier, conn, delayMat, neuron_num, conn_prob, syn_func_type, syn_fun_uniform_brainpylib)
+        net_taichi = MultiAreaNet_taichi(hier, conn, delayMat, neuron_num, conn_prob, syn_func_type, syn_fun_uniform_taichi)
+    elif syn_func_type == 'event_mv_prob_normal':
+        net_brainpylib = MultiAreaNet_brainpylib(hier, conn, delayMat, neuron_num, conn_prob, syn_func_type, syn_fun_normal_brainpylib)
+        net_taichi = MultiAreaNet_taichi(hier, conn, delayMat, neuron_num, conn_prob, syn_func_type, syn_fun_normal_taichi)
+    else:
+        raise NotImplementedError
+    
+    indices = bm.arange(RUNNING_TIME)
+    
+    bm.for_loop(lambda i: net_brainpylib.step_run(i, 20.), indices)
+    time0 = time()
+    bm.for_loop(lambda i: net_brainpylib.step_run(i, 20.), indices)
+    time1 = time()
+    time2 = time()
+    bm.for_loop(lambda i: net_brainpylib.step_run(i, 20.), indices)
+    time3 = time()
+    time4 = time()
+    bm.for_loop(lambda i: net_brainpylib.step_run(i, 20.), indices)
+    time5 = time()
+    time6 = time()
+    bm.for_loop(lambda i: net_brainpylib.step_run(i, 20.), indices)
+    time7 = time()
+    time8 = time()
+    bm.for_loop(lambda i: net_brainpylib.step_run(i, 20.), indices)
+    time9 = time()
+    time10 = time()
+    bm.for_loop(lambda i: net_brainpylib.step_run(i, 20.), indices)
+    time11 = time()
+    time12 = time()
+    bm.for_loop(lambda i: net_brainpylib.step_run(i, 20.), indices)
+    time13 = time()
+    time14 = time()
+    bm.for_loop(lambda i: net_brainpylib.step_run(i, 20.), indices)
+    time15 = time()
+    time16 = time()
+    bm.for_loop(lambda i: net_brainpylib.step_run(i, 20.), indices)
+    time17 = time()
+    time18 = time()
+    bm.for_loop(lambda i: net_brainpylib.step_run(i, 20.), indices)
+    time19 = time()
+
+    bm.for_loop(lambda i: net_taichi.step_run(i, 20.), indices)
+    time20 = time()
+    bm.for_loop(lambda i: net_taichi.step_run(i, 20.), indices)
+    time21 = time()
+    time22 = time()
+    bm.for_loop(lambda i: net_taichi.step_run(i, 20.), indices)
+    time23 = time()
+    time24 = time()
+    bm.for_loop(lambda i: net_taichi.step_run(i, 20.), indices)
+    time25 = time()
+    time26 = time()
+    bm.for_loop(lambda i: net_taichi.step_run(i, 20.), indices)
+    time27 = time()
+    time28 = time()
+    bm.for_loop(lambda i: net_taichi.step_run(i, 20.), indices)
+    time29 = time()
+    time30 = time()
+    bm.for_loop(lambda i: net_taichi.step_run(i, 20.), indices)
+    time31 = time()
+    time32 = time()
+    bm.for_loop(lambda i: net_taichi.step_run(i, 20.), indices)
+    time33 = time()
+    time34 = time()
+    bm.for_loop(lambda i: net_taichi.step_run(i, 20.), indices)
+    time35 = time()
+    time36 = time()
+    bm.for_loop(lambda i: net_taichi.step_run(i, 20.), indices)
+    time37 = time()
+    time38 = time()
+    bm.for_loop(lambda i: net_taichi.step_run(i, 20.), indices)
+    time39 = time()
+
+    print(f'BrainPylib: {(time1 - time0)*1000}, {(time3 - time2)*1000}, {(time5 - time4)*1000}, {(time7 - time6)*1000}, {(time9 - time8)*1000}, {(time11 - time10)*1000}, {(time13 - time12)*1000}, {(time15 - time14)*1000}, {(time17 - time16)*1000}, {(time19 - time18)*1000}')
+    print(f'Taichi: {(time21 - time20)*1000}, {(time23 - time22)*1000}, {(time25 - time24)*1000}, {(time27 - time26)*1000}, {(time29 - time28)*1000}, {(time31 - time30)*1000}, {(time33 - time32)*1000}, {(time35 - time34)*1000}, {(time37 - time36)*1000}, {(time39 - time38)*1000}')
+
+    return (time1 - time0)*1000, (time3 - time2)*1000, (time5 - time4)*1000, (time7 - time6)*1000, (time9 - time8)*1000, (time11 - time10)*1000, (time13 - time12)*1000, (time15 - time14)*1000, (time17 - time16)*1000, (time19 - time18)*1000, \
+        (time21 - time20)*1000, (time23 - time22)*1000, (time25 - time24)*1000, (time27 - time26)*1000, (time29 - time28)*1000, (time31 - time30)*1000, (time33 - time32)*1000, (time35 - time34)*1000, (time37 - time36)*1000, (time39 - time38)*1000
+
+df = pd.DataFrame(columns=['neuron_num', 'conn_num', 'syn_func_type', 'device',
+                           'brainpylib_time1', 'brainpylib_time2', 'brainpylib_time3', 'brainpylib_time4', 'brainpylib_time5', 'brainpylib_time6', 'brainpylib_time7', 'brainpylib_time8', 'brainpylib_time9', 'brainpylib_time10',
+                           'taichi_time1', 'taichi_time2', 'taichi_time3', 'taichi_time4', 'taichi_time5', 'taichi_time6', 'taichi_time7', 'taichi_time8', 'taichi_time9', 'taichi_time10'])
+
+
+if bm.get_platform() == 'cpu':
+    for neuron_num in neuron_nums:
+        for conn_num in conn_nums:
+            for syn_func_type in syn_func_types:
+                brainpylib_time1, brainpylib_time2, brainpylib_time3, brainpylib_time4, brainpylib_time5, brainpylib_time6, brainpylib_time7, brainpylib_time8, brainpylib_time9, brainpylib_time10, \
+                    taichi_time1, taichi_time2, taichi_time3, taichi_time4, taichi_time5, taichi_time6, taichi_time7, taichi_time8, taichi_time9, taichi_time10 = test(neuron_num, conn_num, syn_func_type)
+                df.loc[df.shape[0]] = [neuron_num, conn_num, syn_func_type, 'cpu',
+                                    brainpylib_time1, brainpylib_time2, brainpylib_time3, brainpylib_time4, brainpylib_time5, brainpylib_time6, brainpylib_time7, brainpylib_time8, brainpylib_time9, brainpylib_time10,
+                                    taichi_time1, taichi_time2, taichi_time3, taichi_time4, taichi_time5, taichi_time6, taichi_time7, taichi_time8, taichi_time9, taichi_time10]
+                df.to_csv(f'{PATH}/benchmark_MultipleArea_cpu.csv', index=False)
+
+if bm.get_platform() == 'gpu':
+    for neuron_num in neuron_nums:
+        for conn_num in conn_nums:
+            for syn_func_type in syn_func_types:
+                brainpylib_time1, brainpylib_time2, brainpylib_time3, brainpylib_time4, brainpylib_time5, brainpylib_time6, brainpylib_time7, brainpylib_time8, brainpylib_time9, brainpylib_time10, \
+                    taichi_time1, taichi_time2, taichi_time3, taichi_time4, taichi_time5, taichi_time6, taichi_time7, taichi_time8, taichi_time9, taichi_time10 = test(neuron_num, conn_num, syn_func_type)
+                df.loc[df.shape[0]] = [neuron_num, conn_num, syn_func_type, 'gpu',
+                                    brainpylib_time1, brainpylib_time2, brainpylib_time3, brainpylib_time4, brainpylib_time5, brainpylib_time6, brainpylib_time7, brainpylib_time8, brainpylib_time9, brainpylib_time10,
+                                    taichi_time1, taichi_time2, taichi_time3, taichi_time4, taichi_time5, taichi_time6, taichi_time7, taichi_time8, taichi_time9, taichi_time10]
+                df.to_csv(f'{PATH}/benchmark_MultipleArea_gpu.csv', index=False)
+                
+
diff --git a/benchmarks/src/model/test_MultipleArea_spks.py b/benchmarks/src/model/test_MultipleArea_spks.py
new file mode 100644
index 0000000..ed20741
--- /dev/null
+++ b/benchmarks/src/model/test_MultipleArea_spks.py
@@ -0,0 +1,449 @@
+from time import time
+import functools
+
+import brainpy as bp
+import brainpy.math as bm
+from brainpy import neurons
+
+import matplotlib.pyplot as plt
+import numpy as np
+import pandas as pd
+from jax import vmap
+import os
+from scipy.io import loadmat
+
+from multiple_area_customized_op import (multiple_area_customized_op_E as syn_fun_E,
+                                          multiple_area_customized_op_I as syn_fun_I)
+
+bm.set_platform('gpu')
+bm.disable_gpu_memory_preallocation()
+
+PATH = os.path.dirname(os.path.abspath(__file__))
+
+neuron_nums = [
+    200, 
+    2000, 
+    20000, 
+    200000, 
+    # 2000000
+]
+conn_nums = [
+    20, 
+    40, 
+    80,
+    100 
+]
+
+E_PROB = 0.75
+I_PROB = 0.25
+muIE = 0.0475
+muEE = 0.0375
+wII = 0.075
+wEE = 0.01
+wIE = 0.075
+wEI = 0.0375
+extE = 14.2
+extI = 14.7
+alpha = 4.
+
+RUNNING_TIME = 10
+if bm.get_platform() == 'cpu':
+    RUNNING_TIME = 10
+
+syn_func_types = [
+    'event_mv_prob_homo',
+    # 'event_mv_prob_uniform',
+    # 'event_mv_prob_normal',
+]
+
+# hierarchy values
+hierVals = loadmat(f'{PATH}/Matlab/hierValspython.mat')
+hierValsnew = hierVals['hierVals'].flatten()
+hier = bm.asarray(hierValsnew / max(hierValsnew))  # hierarchy normalized.
+
+# fraction of labeled neurons
+flnMatp = loadmat(f'{PATH}/Matlab/efelenMatpython.mat')
+conn = bm.asarray(flnMatp['flnMatpython'].squeeze())  # fln values..Cij is strength from j to i
+
+# Distance
+speed = 3.5  # axonal conduction velocity
+distMatp = loadmat(f'{PATH}/Matlab/subgraphWiring29.mat')
+distMat = distMatp['wiring'].squeeze()  # distances between areas values..
+delayMat = bm.asarray(distMat / speed)
+
+
+class MultiAreaNet_brainpylib(bp.Network):
+    def __init__(
+            self, hier, conn, delay_mat, neuron_num, conn_prob, syn_fun_type, syn_fun
+    ):
+        super(MultiAreaNet_brainpylib, self).__init__()
+
+        # data
+        self.hier = hier
+        self.conn = conn
+        self.delay_mat = delay_mat
+
+        # parameters
+        self.exc_num = int(neuron_num * E_PROB)
+        self.inh_num = int(neuron_num * I_PROB)
+        self.conn_prob = conn_prob
+        self.syn_fun_type = syn_fun_type
+
+        self.muIE = muIE
+        self.muEE = muEE
+        self.wII = wII
+        self.wEE = wEE
+        self.wIE = wIE
+        self.wEI = wEI
+        self.extE = extE
+        self.extI = extI
+        self.alpha = alpha
+        num_area = hier.size
+        self.num_area = num_area
+        self.num_E = self.exc_num
+        self.num_I = self.inh_num
+
+        # neuron models
+        self.E = neurons.LIF((num_area, self.exc_num),
+                             V_th=-50., V_reset=-60.,
+                             V_rest=-70., tau=20., tau_ref=2.,
+                             noise=3. / bm.sqrt(20.),
+                             V_initializer=bp.init.Uniform(-70., -50.),
+                             method='exp_auto',
+                             keep_size=True,
+                             ref_var=True)
+        self.I = neurons.LIF((num_area, self.inh_num), V_th=-50., V_reset=-60.,
+                             V_rest=-70., tau=10., tau_ref=2., noise=3. / bm.sqrt(10.),
+                             V_initializer=bp.init.Uniform(-70., -50.),
+                             method='exp_auto',
+                             keep_size=True,
+                             ref_var=True)
+
+        # delays
+        self.intra_delay_step = int(2. / bm.get_dt())
+        self.E_delay_steps = bm.asarray(delay_mat.T / bm.get_dt(), dtype=int)
+        bm.fill_diagonal(self.E_delay_steps, self.intra_delay_step)
+        self.Edelay = bm.LengthDelay(self.E.spike, delay_len=int(self.E_delay_steps.max()))
+        self.Idelay = bm.LengthDelay(self.I.spike, delay_len=self.intra_delay_step)
+
+        # synapse model
+        self.f_EE_current = vmap(functools.partial(syn_fun, prob=conn_prob, shape=(self.num_E, self.num_E)))
+        self.f_EI_current = vmap(functools.partial(syn_fun, prob=conn_prob, shape=(self.num_E, self.num_I)))
+        self.f_IE_current = vmap(functools.partial(syn_fun, prob=conn_prob, shape=(self.num_I, self.num_E)),
+                                in_axes=(0, None, 0))
+        self.f_II_current = vmap(functools.partial(syn_fun, prob=conn_prob, shape=(self.num_I, self.num_I)),
+                                in_axes=(0, None, 0))
+
+
+        # synapses from I
+        # self.intra_I2E_conn = bm.random.random((num_area, self.inh_num, self.exc_num)) < conn_prob
+        # self.intra_I2I_conn = bm.random.random((num_area, self.inh_num, self.inh_num)) < conn_prob
+        self.intra_I2E_weight = -wEI
+        self.intra_I2I_weight = -wII
+
+        # synapses from E
+        # self.E2E_conns = [bm.random.random((num_area, 1600, 1600)) < 0.1 for _ in range(num_area)]
+        # self.E2I_conns = [bm.random.random((num_area, self.exc_num, self.inh_num)) < conn_prob for _ in range(num_area)]
+        self.E2E_weights = (1 + alpha * hier) * muEE * conn.T  # inter-area connections
+        bm.fill_diagonal(self.E2E_weights, (1 + alpha * hier) * wEE)  # intra-area connections
+        self.E2I_weights = (1 + alpha * hier) * muIE * conn.T  # inter-area connections
+        bm.fill_diagonal(self.E2I_weights, (1 + alpha * hier) * wIE)  # intra-area connections
+        self.E_seeds = bm.random.randint(0, 100000, (num_area, num_area * 2))
+        self.I_seeds = bm.random.randint(0, 100000, (num_area * 2))
+
+    def update(self, v1_input):
+        self.E.input[0] += v1_input
+        self.E.input += self.extE
+        self.I.input += self.extI
+        E_not_ref = bm.logical_not(self.E.refractory)
+        I_not_ref = bm.logical_not(self.I.refractory)
+
+        if self.syn_fun_type == 'event_mv_prob_homo':
+            # synapses from E
+            for i in range(self.num_area):
+                delayed_E_spikes = self.Edelay(self.E_delay_steps[i], i).astype(float)
+                current = self.f_EE_current(delayed_E_spikes, self.E2E_weights[i], self.E_seeds[i, :self.num_area])
+                self.E.V += current * E_not_ref  # E2E
+                current = self.f_EI_current(delayed_E_spikes, self.E2I_weights[i], self.E_seeds[i, self.num_area:])
+                self.I.V += current * I_not_ref  # E2I
+
+            # synapses from I
+            delayed_I_spikes = self.Idelay(self.intra_delay_step).astype(float)
+            current = self.f_IE_current(delayed_I_spikes, self.intra_I2E_weight, self.I_seeds[:self.num_area])
+            self.E.V += current * E_not_ref  # I2E
+            current = self.f_II_current(delayed_I_spikes, self.intra_I2I_weight, self.I_seeds[self.num_area:])
+            self.I.V += current * I_not_ref  # I2I
+        elif self.syn_fun_type == 'event_mv_prob_uniform':
+            # synapses from E
+            for i in range(self.num_area):
+                delayed_E_spikes = self.Edelay(self.E_delay_steps[i], i).astype(float)
+                current = self.f_EE_current(delayed_E_spikes, self.E2E_weights[i] - 0.03, self.E2E_weights[i] + 0.03, self.E_seeds[i, :self.num_area])
+                self.E.V += current * E_not_ref  # E2E
+                current = self.f_EI_current(delayed_E_spikes, self.E2E_weights[i] - 0.03, self.E2E_weights[i] + 0.03, self.E_seeds[i, self.num_area:])
+                self.I.V += current * I_not_ref  # E2I
+
+            # synapses from I
+            delayed_I_spikes = self.Idelay(self.intra_delay_step).astype(float)
+            current = self.f_IE_current(delayed_I_spikes, self.intra_I2E_weight - 0.03, self.intra_I2E_weight + 0.03, self.I_seeds[:self.num_area])
+            self.E.V += current * E_not_ref  # I2E
+            current = self.f_II_current(delayed_I_spikes, self.intra_I2E_weight - 0.03, self.intra_I2E_weight + 0.03, self.I_seeds[self.num_area:])
+            self.I.V += current * I_not_ref  # I2I
+        elif self.syn_fun_type == 'event_mv_prob_normal':
+            # synapses from E
+            for i in range(self.num_area):
+                delayed_E_spikes = self.Edelay(self.E_delay_steps[i], i).astype(float)
+                current = self.f_EE_current(delayed_E_spikes, self.E2E_weights[i], 0.01, self.E_seeds[i, :self.num_area])
+                self.E.V += current * E_not_ref  # E2E
+                current = self.f_EI_current(delayed_E_spikes, self.E2I_weights[i], 0.01, self.E_seeds[i, self.num_area:])
+                self.I.V += current * I_not_ref  # E2I
+
+            # synapses from I
+            delayed_I_spikes = self.Idelay(self.intra_delay_step).astype(float)
+            current = self.f_IE_current(delayed_I_spikes, self.intra_I2E_weight, 0.01, self.I_seeds[:self.num_area])
+            self.E.V += current * E_not_ref  # I2E
+            current = self.f_II_current(delayed_I_spikes, self.intra_I2I_weight, 0.01, self.I_seeds[self.num_area:])
+            self.I.V += current * I_not_ref  # I2I
+
+        # updates
+        self.Edelay.update(self.E.spike)
+        self.Idelay.update(self.I.spike)
+        self.E.update()
+        self.I.update()
+        return self.E.spike.value, self.I.spike.value
+
+
+class MultiAreaNet_taichi(bp.Network):
+    def __init__(
+            self, hier, conn, delay_mat, neuron_num, conn_prob, syn_fun_type, syn_fun_E, syn_fun_I
+    ):
+        super(MultiAreaNet_taichi, self).__init__()
+
+        # data
+        self.hier = hier
+        self.conn = conn
+        self.delay_mat = delay_mat
+
+        # parameters
+        self.exc_num = int(neuron_num * E_PROB)
+        self.inh_num = int(neuron_num * I_PROB)
+        self.conn_prob = conn_prob
+        self.syn_fun_type = syn_fun_type
+
+        self.muIE = muIE
+        self.muEE = muEE
+        self.wII = wII
+        self.wEE = wEE
+        self.wIE = wIE
+        self.wEI = wEI
+        self.extE = extE
+        self.extI = extI
+        self.alpha = alpha
+        num_area = hier.size
+        self.num_area = num_area
+        self.num_E = self.exc_num
+        self.num_I = self.inh_num
+
+        # neuron models
+        self.E = neurons.LIF((num_area, self.exc_num),
+                             V_th=-50., V_reset=-60.,
+                             V_rest=-70., tau=20., tau_ref=2.,
+                             noise=3. / bm.sqrt(20.),
+                             V_initializer=bp.init.Uniform(-70., -50.),
+                             method='exp_auto',
+                             keep_size=True,
+                             ref_var=True)
+        self.I = neurons.LIF((num_area, self.inh_num), V_th=-50., V_reset=-60.,
+                             V_rest=-70., tau=10., tau_ref=2., noise=3. / bm.sqrt(10.),
+                             V_initializer=bp.init.Uniform(-70., -50.),
+                             method='exp_auto',
+                             keep_size=True,
+                             ref_var=True)
+
+        # delays
+        self.intra_delay_step = int(2. / bm.get_dt())
+        self.E_delay_steps = bm.asarray(delay_mat.T / bm.get_dt(), dtype=int)
+        bm.fill_diagonal(self.E_delay_steps, self.intra_delay_step)
+        self.Edelay = bm.LengthDelay(self.E.spike, delay_len=int(self.E_delay_steps.max()))
+        self.Idelay = bm.LengthDelay(self.I.spike, delay_len=self.intra_delay_step)
+
+        # synapse model
+        self.f_EE_current = functools.partial(syn_fun_E, prob=conn_prob, shape=(self.num_E, self.num_E), area_num=num_area)
+        self.f_EI_current = functools.partial(syn_fun_E, prob=conn_prob, shape=(self.num_E, self.num_I), area_num=num_area)
+        self.f_IE_current = functools.partial(syn_fun_I, prob=conn_prob, shape=(self.num_I, self.num_E), area_num=num_area)
+        self.f_II_current = functools.partial(syn_fun_I, prob=conn_prob, shape=(self.num_I, self.num_I), area_num=num_area)
+
+
+        # synapses from I
+        # self.intra_I2E_conn = bm.random.random((num_area, self.inh_num, self.exc_num)) < conn_prob
+        # self.intra_I2I_conn = bm.random.random((num_area, self.inh_num, self.inh_num)) < conn_prob
+        self.intra_I2E_weight = -wEI
+        self.intra_I2I_weight = -wII
+
+        # synapses from E
+        # self.E2E_conns = [bm.random.random((num_area, 1600, 1600)) < 0.1 for _ in range(num_area)]
+        # self.E2I_conns = [bm.random.random((num_area, self.exc_num, self.inh_num)) < conn_prob for _ in range(num_area)]
+        self.E2E_weights = (1 + alpha * hier) * muEE * conn.T  # inter-area connections
+        bm.fill_diagonal(self.E2E_weights, (1 + alpha * hier) * wEE)  # intra-area connections
+        self.E2I_weights = (1 + alpha * hier) * muIE * conn.T  # inter-area connections
+        bm.fill_diagonal(self.E2I_weights, (1 + alpha * hier) * wIE)  # intra-area connections
+        self.E_seeds = bm.random.randint(0, 100000, (num_area, num_area * 2))
+        self.I_seeds = bm.random.randint(0, 100000, (num_area * 2))
+
+    def update(self, v1_input):
+        self.E.input[0] += v1_input
+        self.E.input += self.extE
+        self.I.input += self.extI
+        E_not_ref = bm.logical_not(self.E.refractory)
+        I_not_ref = bm.logical_not(self.I.refractory)
+
+        if self.syn_fun_type == 'event_mv_prob_homo':
+            # synapses from E
+            for i in range(self.num_area):
+                delayed_E_spikes = self.Edelay(self.E_delay_steps[i], i).astype(float)
+                delayed_E_spikes = delayed_E_spikes[i]
+                current = self.f_EE_current(delayed_E_spikes, self.E2E_weights[i], self.E_seeds[i, :self.num_area])
+                self.E.V += current * E_not_ref  # E2E
+                current = self.f_EI_current(delayed_E_spikes, self.E2I_weights[i], self.E_seeds[i, self.num_area:])
+                self.I.V += current * I_not_ref  # E2I
+
+            # synapses from I
+            delayed_I_spikes = self.Idelay(self.intra_delay_step).astype(float)
+            current = self.f_IE_current(delayed_I_spikes, self.intra_I2E_weight, self.I_seeds[:self.num_area])
+            self.E.V += current * E_not_ref  # I2E
+            current = self.f_II_current(delayed_I_spikes, self.intra_I2I_weight, self.I_seeds[self.num_area:])
+            self.I.V += current * I_not_ref  # I2I
+        elif self.syn_fun_type == 'event_mv_prob_uniform':
+            # synapses from E
+            for i in range(self.num_area):
+                delayed_E_spikes = self.Edelay(self.E_delay_steps[i], i).astype(float)
+                current = self.f_EE_current(delayed_E_spikes, self.E2E_weights[i] - 0.03, self.E2E_weights[i] + 0.03, self.E_seeds[i, :self.num_area])
+                self.E.V += current * E_not_ref  # E2E
+                current = self.f_EI_current(delayed_E_spikes, self.E2E_weights[i] - 0.03, self.E2E_weights[i] + 0.03, self.E_seeds[i, self.num_area:])
+                self.I.V += current * I_not_ref  # E2I
+
+            # synapses from I
+            delayed_I_spikes = self.Idelay(self.intra_delay_step).astype(float)
+            current = self.f_IE_current(delayed_I_spikes, self.intra_I2E_weight - 0.03, self.intra_I2E_weight + 0.03, self.I_seeds[:self.num_area])
+            self.E.V += current * E_not_ref  # I2E
+            current = self.f_II_current(delayed_I_spikes, self.intra_I2E_weight - 0.03, self.intra_I2E_weight + 0.03, self.I_seeds[self.num_area:])
+            self.I.V += current * I_not_ref  # I2I
+        elif self.syn_fun_type == 'event_mv_prob_normal':
+            # synapses from E
+            for i in range(self.num_area):
+                delayed_E_spikes = self.Edelay(self.E_delay_steps[i], i).astype(float)
+                current = self.f_EE_current(delayed_E_spikes, self.E2E_weights[i], 0.01, self.E_seeds[i, :self.num_area])
+                self.E.V += current * E_not_ref  # E2E
+                current = self.f_EI_current(delayed_E_spikes, self.E2I_weights[i], 0.01, self.E_seeds[i, self.num_area:])
+                self.I.V += current * I_not_ref  # E2I
+
+            # synapses from I
+            delayed_I_spikes = self.Idelay(self.intra_delay_step).astype(float)
+            current = self.f_IE_current(delayed_I_spikes, self.intra_I2E_weight, 0.01, self.I_seeds[:self.num_area])
+            self.E.V += current * E_not_ref  # I2E
+            current = self.f_II_current(delayed_I_spikes, self.intra_I2I_weight, 0.01, self.I_seeds[self.num_area:])
+            self.I.V += current * I_not_ref  # I2I
+
+        # updates
+        self.Edelay.update(self.E.spike)
+        self.Idelay.update(self.I.spike)
+        self.E.update()
+        self.I.update()
+
+        return self.E.spike.value, self.I.spike.value
+
+def raster_plot(xValues, yValues, duration):
+    ticks = np.round(np.arange(0, 29) + 0.5, 2)
+    areas = ['V1', 'V2', 'V4', 'DP', 'MT', '8m', '5', '8l', 'TEO', '2', 'F1',
+             'STPc', '7A', '46d', '10', '9/46v', '9/46d', 'F5', 'TEpd', 'PBr',
+             '7m', '7B', 'F2', 'STPi', 'PROm', 'F7', '8B', 'STPr', '24c']
+    N = len(ticks)
+    plt.figure(figsize=(8, 6))
+    plt.plot(xValues, yValues / (4 * 400), '.', markersize=1)
+    plt.plot([0, duration], np.arange(N + 1).repeat(2).reshape(-1, 2).T, 'k-')
+    plt.ylabel('Area')
+    plt.yticks(np.arange(N))
+    plt.xlabel('Time [ms]')
+    plt.ylim(0, N)
+    plt.yticks(ticks, areas)
+    plt.xlim(0, duration)
+    plt.tight_layout()
+    plt.show()
+
+
+def syn_fun_homo_brainpylib(pre_spike, weight, seed, prob, shape):
+    return bm.jitconn.event_mv_prob_homo(pre_spike, weight, prob, seed, shape=shape, transpose=True)
+
+def syn_fun_homo_taichi_E(pre_spike, weight, seed, prob, shape, area_num):
+    return syn_fun_E(pre_spike, weight, prob, seed, shape=shape, area_num=area_num, transpose=True)
+
+def syn_fun_homo_taichi_I(pre_spike, weight, seed, prob, shape, area_num):
+    return syn_fun_I(pre_spike, weight, prob, seed, shape=shape, area_num=area_num, transpose=True)
+
+
+def syn_fun_uniform_brainpylib(pre_spike, w_low, w_high, seed, prob, shape):
+    return bm.jitconn.event_mv_prob_uniform(pre_spike, w_low, w_high, prob, seed, shape=shape, transpose=True)
+
+
+def syn_fun_uniform_taichi(pre_spike, w_low, w_high, seed, prob, shape):
+    return bm.jitconn.event_mv_prob_uniform_taichi(pre_spike, w_low, w_high, prob, seed, shape=shape, transpose=True)
+
+
+def syn_fun_normal_brainpylib(pre_spike, w_mu, w_sigma, prob, seed, shape):
+    return bm.jitconn.event_mv_prob_normal(pre_spike, w_mu, w_sigma, prob, seed, shape=shape, transpose=True)
+
+
+def syn_fun_normal_taichi(pre_spike, w_mu, w_sigma, prob, seed, shape):
+    return bm.jitconn.event_mv_prob_normal_taichi(pre_spike, w_mu, w_sigma, prob, seed, shape=shape, transpose=True)
+
+
+def test(neuron_num, conn_num, syn_func_type):
+    print(f'neuron nums: {neuron_num}, conn num: {conn_num} sys func type: {syn_func_type}')
+    conn_prob = conn_num / neuron_num
+    if syn_func_type == 'event_mv_prob_homo':
+        net_brainpylib = MultiAreaNet_brainpylib(hier, conn, delayMat, neuron_num, conn_prob, syn_func_type, syn_fun_homo_brainpylib)
+        net_taichi = MultiAreaNet_taichi(hier, conn, delayMat, neuron_num, conn_prob, syn_func_type, syn_fun_homo_taichi_E, syn_fun_homo_taichi_I)
+    elif syn_func_type == 'event_mv_prob_uniform':
+        net_brainpylib = MultiAreaNet_brainpylib(hier, conn, delayMat, neuron_num, conn_prob, syn_func_type, syn_fun_uniform_brainpylib)
+        net_taichi = MultiAreaNet_taichi(hier, conn, delayMat, neuron_num, conn_prob, syn_func_type, syn_fun_uniform_taichi)
+    elif syn_func_type == 'event_mv_prob_normal':
+        net_brainpylib = MultiAreaNet_brainpylib(hier, conn, delayMat, neuron_num, conn_prob, syn_func_type, syn_fun_normal_brainpylib)
+        net_taichi = MultiAreaNet_taichi(hier, conn, delayMat, neuron_num, conn_prob, syn_func_type, syn_fun_normal_taichi)
+    else:
+        raise NotImplementedError
+    
+    indices = bm.arange(RUNNING_TIME)
+
+    brainpylib_e_spks, brainpylib_i_spks = bm.for_loop(lambda i: net_brainpylib.step_run(i, 20.), indices)
+
+    taichi_e_spks, taichi_i_spks = bm.for_loop(lambda i: net_taichi.step_run(i, 20.), indices)
+
+    brainpylib_e_spks = brainpylib_e_spks.sum() / (RUNNING_TIME/1000) / net_brainpylib.num_E
+    brainpylib_i_spks = brainpylib_i_spks.sum() / (RUNNING_TIME/1000) / net_brainpylib.num_I
+    taichi_e_spks = taichi_e_spks.sum() / (RUNNING_TIME/1000) / net_taichi.num_E
+    taichi_i_spks = taichi_i_spks.sum() / (RUNNING_TIME/1000) / net_taichi.num_I
+
+    return brainpylib_e_spks, brainpylib_i_spks, taichi_e_spks, taichi_i_spks
+
+
+df = pd.DataFrame(columns=['neuron_num', 'conn_num', 'syn_func_type', 'device',
+                           'brainpylib_e_spk', 'brainpylib_i_spk',
+                           'taichi_e_spk', 'taichi_i_spk'])
+
+
+if bm.get_platform() == 'cpu':
+    for neuron_num in neuron_nums:
+        for conn_num in conn_nums:
+            for syn_func_type in syn_func_types:
+                brainpylib_e_spks, brainpylib_i_spks, taichi_e_spks, taichi_i_spks = test(neuron_num, conn_num, syn_func_type)
+                df.loc[df.shape[0]] = [neuron_num, conn_num, syn_func_type, 'cpu',
+                                    brainpylib_e_spks, brainpylib_i_spks, taichi_e_spks, taichi_i_spks]
+                df.to_csv(f'{PATH}/benchmark_MultipleArea_spks_cpu.csv', index=False)
+
+if bm.get_platform() == 'gpu':
+    for neuron_num in neuron_nums:
+        for conn_num in conn_nums:
+            for syn_func_type in syn_func_types:
+                brainpylib_e_spks, brainpylib_i_spks, taichi_e_spks, taichi_i_spks = test(neuron_num, conn_num, syn_func_type)
+                df.loc[df.shape[0]] = [neuron_num, conn_num, syn_func_type, 'gpu',
+                                    brainpylib_e_spks, brainpylib_i_spks, taichi_e_spks, taichi_i_spks]
+                df.to_csv(f'{PATH}/benchmark_MultipleArea_spks_gpu.csv', index=False)
\ No newline at end of file