PY0101EN-5-1-Numpy1D.ipynb

{
  "metadata": {
    "kernelspec": {
      "name": "python",
      "display_name": "Pyolite",
      "language": "python"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "python",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.8"
    }
  },
  "nbformat_minor": 4,
  "nbformat": 4,
  "cells": [
    {
      "cell_type": "markdown",
      "source": "<center>\n    <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-PY0101EN-SkillsNetwork/IDSNlogo.png\" width=\"300\" alt=\"cognitiveclass.ai logo\"  />\n</center>\n\n# 1D Numpy in Python\n\nEstimated time needed: **30** minutes\n\n## Objectives\n\nAfter completing this lab you will be able to:\n\n*   Import and use the `numpy` library\n*   Perform operations with `numpy`\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h2>Table of Contents</h2>\n<div class=\"alert alert-block alert-info\" style=\"margin-thttps://https://https://op/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2022-01-01/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01: 20px\">\n    <ul>\n        <li><a href=\"https://pre/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">List in Python</a></li>\n        <li>\n            <a href=\"https://numpy/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">What is Numpy?</a>\n            <ul>\n                <li><a href=\"https://type/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Type</a></li>\n                <li><a href=\"https://val/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Assign Value</a></li>\n                <li><a href=\"https://slice/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Slicing</a></li>\n                <li><a href=\"https://list/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Assign Value with List</a></li>\n                <li><a href=\"https://other/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Other Attributes</a></li>\n            </ul>\n        </li>\n        <li>\n            <a href=\"op\">Numpy Array Operations</a>\n            <ul>\n                <li><a href=\"https://add/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Array Addition</a></li>\n                <li><a href=\"https://multi/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Array Multiplication</a></li>\n                <li><a href=\"https://prod/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Product of Two Numpy Arrays</a></li>\n                <li><a href=\"https://dot/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Dot Product</a></li>\n                <li><a href=\"https://cons/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Adding Constant to a Numpy Array</a></li>\n            </ul>\n        </li>\n        <li><a href=\"https://math/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Mathematical Functions</a></li>\n        <li><a href=\"https://lin/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Linspace</a></li>\n    </ul>\n\n</div>\n\n<hr>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "### Create a Python List as follows:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Create a python list\n\na = [\"0\", 1, \"two\", \"3\", 4]",
      "metadata": {
        "trusted": true
      },
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "We can access the data via an index:\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-PY0101EN-SkillsNetwork/labs/Module%205/images/NumOneList.png\" width=\"660\" />\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "We can access each element using a square bracket as follows:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Print each element\n\nprint(\"a[0]:\", a[0])\nprint(\"a[1]:\", a[1])\nprint(\"a[2]:\", a[2])\nprint(\"a[3]:\", a[3])\nprint(\"a[4]:\", a[4])",
      "metadata": {
        "trusted": true
      },
      "execution_count": 2,
      "outputs": [
        {
          "name": "stdout",
          "text": "a[0]: 0\na[1]: 1\na[2]: two\na[3]: 3\na[4]: 4\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<hr>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h2 id=\"numpy\">What is Numpy?</h2>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "NumPy is a Python library used for working with arrays, linear algebra, fourier transform, and matrices.A numpy array is similar to a list. NumPy stands for Numerical Python and it is an open source project.The array object in NumPy is called **ndarray**, it provides a lot of supporting functions that make working with ndarray very easy.\n\nArrays are very frequently used in data science, where speed and resources are very important.\n\nNumPy is usually imported under the np alias.\n\nIt's usually fixed in size and each element is of the same type. We can cast a list to a numpy array by first importing `numpy`:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# import numpy library\n\nimport numpy as np ",
      "metadata": {
        "trusted": true
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "We then cast the list as follows:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Create a numpy array\n\na = np.array([0, 1, 2, 3, 4])\na",
      "metadata": {
        "trusted": true
      },
      "execution_count": 4,
      "outputs": [
        {
          "execution_count": 4,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([0, 1, 2, 3, 4])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "Each element is of the same type, in this case integers:\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-PY0101EN-SkillsNetwork/labs/Module%205/images/NumOneNp.png\" width=\"500\" />\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "As with lists, we can access each element via a square bracket:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Print each element\n\nprint(\"a[0]:\", a[0])\nprint(\"a[1]:\", a[1])\nprint(\"a[2]:\", a[2])\nprint(\"a[3]:\", a[3])\nprint(\"a[4]:\", a[4])",
      "metadata": {
        "trusted": true
      },
      "execution_count": 5,
      "outputs": [
        {
          "name": "stdout",
          "text": "a[0]: 0\na[1]: 1\na[2]: 2\na[3]: 3\na[4]: 4\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "### Checking NumPy Version\n\nThe version string is stored under **version** attribute.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "print(np.__version__)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 6,
      "outputs": [
        {
          "name": "stdout",
          "text": "1.22.3\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<h3 id=\"type\">Type</h3>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "If we check the type of the array we get <b>numpy.ndarray</b>:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Check the type of the array\n\ntype(a)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 7,
      "outputs": [
        {
          "execution_count": 7,
          "output_type": "execute_result",
          "data": {
            "text/plain": "numpy.ndarray"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "As numpy arrays contain data of the same type, we can use the attribute \"dtype\" to obtain the data type of the array’s elements. In this case, it's a 64-bit integer:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Check the type of the values stored in numpy array\n\na.dtype",
      "metadata": {
        "trusted": true
      },
      "execution_count": 8,
      "outputs": [
        {
          "execution_count": 8,
          "output_type": "execute_result",
          "data": {
            "text/plain": "dtype('int32')"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "### Try it yourself\n\nCheck the type of the array and Value type for the given array **c**\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "b = np.array([3.1, 11.02, 6.2, 213.2, 5.2])\n\ntype(b)\n\nb.dtype",
      "metadata": {
        "trusted": true
      },
      "execution_count": 12,
      "outputs": [
        {
          "execution_count": 12,
          "output_type": "execute_result",
          "data": {
            "text/plain": "dtype('float64')"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\ntype(b)\n    \nb.dtype \n    \nIf we examine the attribute dtype we see float 64, as the elements are not integers:\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h3 id=\"val\">Assign value</h3>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "We can change the value of the array. Consider the array <code>c</code>:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Create numpy array\n\nc = np.array([20, 1, 2, 3, 4])\nc",
      "metadata": {
        "trusted": true
      },
      "execution_count": 13,
      "outputs": [
        {
          "execution_count": 13,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([20,  1,  2,  3,  4])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "We can change the first element of the array to 100 as follows:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Assign the first element to 100\n\nc[0] = 100\nc",
      "metadata": {
        "trusted": true
      },
      "execution_count": 14,
      "outputs": [
        {
          "execution_count": 14,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([100,   1,   2,   3,   4])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "We can change the 5th element of the array to 0 as follows:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Assign the 5th element to 0\n\nc[4] = 0\nc",
      "metadata": {
        "trusted": true
      },
      "execution_count": 15,
      "outputs": [
        {
          "execution_count": 15,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([100,   1,   2,   3,   0])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "### Try it yourself\n\nAssign the value 20 for the second element in the given array.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "a = np.array([10, 2, 30, 40,50])\n\na[1] = 20\na",
      "metadata": {
        "trusted": true
      },
      "execution_count": 17,
      "outputs": [
        {
          "execution_count": 17,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([10, 20, 30, 40, 50])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\na[1]=20\na\n   \n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h3 id=\"slice\">Slicing</h3>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Like lists, we can slice the numpy array. Slicing in python means taking the elements from the given index to another given index.\n\nWe pass slice like this: \\[start:end].\n\nWe can select the elements from 1 to 3 and assign it to a new numpy array <code>d</code> as follows:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Slicing the numpy array\n\nd = c[1:4]\nd",
      "metadata": {
        "trusted": true
      },
      "execution_count": 18,
      "outputs": [
        {
          "execution_count": 18,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([1, 2, 3])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "We can assign the corresponding indexes to new values as follows:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Set the fourth element and fifth element to 300 and 400\n\nc[3:5] = 300, 400\nc",
      "metadata": {
        "trusted": true
      },
      "execution_count": 19,
      "outputs": [
        {
          "execution_count": 19,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([100,   1,   2, 300, 400])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "We can also define the steps in slicing, like this: \\[start\\:end:step].\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "arr = np.array([1, 2, 3, 4, 5, 6, 7])\n\nprint(arr[1:5:2])",
      "metadata": {
        "trusted": true
      },
      "execution_count": 20,
      "outputs": [
        {
          "name": "stdout",
          "text": "[2 4]\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "If we don't pass start its considered 0\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "print(arr[:4])",
      "metadata": {
        "trusted": true
      },
      "execution_count": 21,
      "outputs": [
        {
          "name": "stdout",
          "text": "[1 2 3 4]\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "If we don't pass end it considers till the length of array.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "print(arr[4:])",
      "metadata": {
        "trusted": true
      },
      "execution_count": 22,
      "outputs": [
        {
          "name": "stdout",
          "text": "[5 6 7]\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "If we don't pass step its considered 1\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "print(arr[1:5:])",
      "metadata": {
        "trusted": true
      },
      "execution_count": 23,
      "outputs": [
        {
          "name": "stdout",
          "text": "[2 3 4 5]\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "### Try it yourself\n\nPrint the even elements in the given array.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "arr = np.array([1, 2, 3, 4, 5, 6, 7, 8])\n\n# both return the same results\nprint(arr[1::2])\nprint(arr[1:8:2])",
      "metadata": {
        "trusted": true
      },
      "execution_count": 28,
      "outputs": [
        {
          "name": "stdout",
          "text": "[2 4 6 8]\n[2 4 6 8]\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\nprint(arr[1:8:2])\n\n    \n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h3 id=\"list\">Assign Value with List</h3>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Similarly, we can use a list to select more than one specific index.\nThe list `select` contains several values:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Create the index list\n\nselect = [0, 2, 3, 4]\nselect",
      "metadata": {
        "trusted": true
      },
      "execution_count": 29,
      "outputs": [
        {
          "execution_count": 29,
          "output_type": "execute_result",
          "data": {
            "text/plain": "[0, 2, 3, 4]"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "We can use the list as an argument in the brackets. The output is the elements corresponding to the particular indexes:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Use List to select elements\n\nd = c[select]\nd",
      "metadata": {
        "trusted": true
      },
      "execution_count": 30,
      "outputs": [
        {
          "execution_count": 30,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([100,   2, 300, 400])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "We can assign the specified elements to a new value. For example, we can assign the values to 100 000 as follows:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Assign the specified elements to new value\n\nc[select] = 100000\nc",
      "metadata": {
        "trusted": true
      },
      "execution_count": 31,
      "outputs": [
        {
          "execution_count": 31,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([100000,      1, 100000, 100000, 100000])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<h3 id=\"other\">Other Attributes</h3>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Let's review some basic array attributes using the array <code>a</code>:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Create a numpy array\n\na = np.array([0, 1, 2, 3, 4])\na",
      "metadata": {
        "trusted": true
      },
      "execution_count": 32,
      "outputs": [
        {
          "execution_count": 32,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([0, 1, 2, 3, 4])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "The attribute <code>size</code> is the number of elements in the array:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Get the size of numpy array\n\na.size",
      "metadata": {
        "trusted": true
      },
      "execution_count": 33,
      "outputs": [
        {
          "execution_count": 33,
          "output_type": "execute_result",
          "data": {
            "text/plain": "5"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "The next two attributes will make more sense when we get to higher dimensions but let's review them. The attribute <code>ndim</code> represents the number of array dimensions, or the rank of the array. In this case, one:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Get the number of dimensions of numpy array\n\na.ndim",
      "metadata": {
        "trusted": true
      },
      "execution_count": 34,
      "outputs": [
        {
          "execution_count": 34,
          "output_type": "execute_result",
          "data": {
            "text/plain": "1"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "The attribute <code>shape</code> is a tuple of integers indicating the size of the array in each dimension:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Get the shape/size of numpy array\n\na.shape",
      "metadata": {
        "trusted": true
      },
      "execution_count": 35,
      "outputs": [
        {
          "execution_count": 35,
          "output_type": "execute_result",
          "data": {
            "text/plain": "(5,)"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "### Try it yourself\n\nFind the size ,dimension and shape for the given array **b**\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "b = np.array([10, 20, 30, 40, 50, 60, 70])\n\nprint('Size: ', b.size, \n      '\\nDimensions: ', b.ndim,\n      '\\nShape: ', b.shape)\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 43,
      "outputs": [
        {
          "name": "stdout",
          "text": "Size:  7 \nDimensions:  1 \nShape:  (7,)\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\nb.size\n\nb.ndim\n\nb.shape\n\n    \n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "### Numpy Statistical Functions\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Create a numpy array\n\na = np.array([1, -1, 1, -1])",
      "metadata": {
        "trusted": true
      },
      "execution_count": 44,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": "# Get the mean of numpy array\n\nmean = a.mean()\nmean",
      "metadata": {
        "trusted": true
      },
      "execution_count": 45,
      "outputs": [
        {
          "execution_count": 45,
          "output_type": "execute_result",
          "data": {
            "text/plain": "0.0"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": "# Get the standard deviation of numpy array\n\nstandard_deviation=a.std()\nstandard_deviation",
      "metadata": {
        "trusted": true
      },
      "execution_count": 46,
      "outputs": [
        {
          "execution_count": 46,
          "output_type": "execute_result",
          "data": {
            "text/plain": "1.0"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": "# Create a numpy array\n\nb = np.array([-1, 2, 3, 4, 5])\nb",
      "metadata": {
        "trusted": true
      },
      "execution_count": 47,
      "outputs": [
        {
          "execution_count": 47,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([-1,  2,  3,  4,  5])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": "# Get the biggest value in the numpy array\n\nmax_b = b.max()\nmax_b",
      "metadata": {
        "trusted": true
      },
      "execution_count": 48,
      "outputs": [
        {
          "execution_count": 48,
          "output_type": "execute_result",
          "data": {
            "text/plain": "5"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": "# Get the smallest value in the numpy array\n\nmin_b = b.min()\nmin_b",
      "metadata": {
        "trusted": true
      },
      "execution_count": 49,
      "outputs": [
        {
          "execution_count": 49,
          "output_type": "execute_result",
          "data": {
            "text/plain": "-1"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "### Try it yourself\n\nFind the sum of maximum and minimum value in the given numpy array\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<hr>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "c = np.array([-10, 201, 43, 94, 502])\n\nprint(\"Max: \", c.max(),\n      \"\\nMin: \", c.min(),\n      \"\\nMin + Max: \", c.max()+c.min())\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 52,
      "outputs": [
        {
          "name": "stdout",
          "text": "Max:  502 \nMin:  -10 \nMin + Max:  492\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\nmax_c = c.max()\nmax_c\n    \nmin_c = c.min()\nmin_c\n    \n    \nSum = (max_c +min_c)\nSum\n\n    \n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h2 id=\"op\">Numpy Array Operations</h2>\n\nYou could use arithmetic operators directly between NumPy arrays\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h3 id=\"add\">Array Addition</h3>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Consider the numpy array <code>u</code>:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "u = np.array([1, 0])\nu",
      "metadata": {
        "trusted": true
      },
      "execution_count": 53,
      "outputs": [
        {
          "execution_count": 53,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([1, 0])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "Consider the numpy array <code>v</code>:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "v = np.array([0, 1])\nv",
      "metadata": {
        "trusted": true
      },
      "execution_count": 54,
      "outputs": [
        {
          "execution_count": 54,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([0, 1])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "We can add the two arrays and assign it to z:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Numpy Array Addition\n\nz = np.add(u, v)\nz",
      "metadata": {
        "trusted": true
      },
      "execution_count": 55,
      "outputs": [
        {
          "execution_count": 55,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([1, 1])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "The operation is equivalent to vector addition:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Plotting functions\n\n\nimport time \nimport sys\nimport numpy as np \n\nimport matplotlib.pyplot as plt\n%matplotlib inline  \n\ndef Plotvec1(u, z, v):\n    \n    ax = plt.axes() # to generate the full window axes\n    ax.arrow(0, 0, *u, head_width=0.05, color='r', head_length=0.1)# Add an arrow to the  U Axes with arrow head width 0.05, color red and arrow head length 0.1\n    plt.text(*(u + 0.1), 'u')#Adds the text u to the Axes \n    \n    ax.arrow(0, 0, *v, head_width=0.05, color='b', head_length=0.1)# Add an arrow to the  v Axes with arrow head width 0.05, color red and arrow head length 0.1\n    plt.text(*(v + 0.1), 'v')#Adds the text v to the Axes \n    \n    ax.arrow(0, 0, *z, head_width=0.05, head_length=0.1)\n    plt.text(*(z + 0.1), 'z')#Adds the text z to the Axes \n    plt.ylim(-2, 2)#set the ylim to bottom(-2), top(2)\n    plt.xlim(-2, 2)#set the xlim to left(-2), right(2)\n\n  \n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 56,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": "# Plot numpy arrays\n\nPlotvec1(u, z, v)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 432x288 with 1 Axes>",
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "### Try it yourself\n\nPerform addition operation on the given numpy array arr1 and arr2:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "arr1 = np.array([10, 11, 12, 13, 14, 15])\narr2 = np.array([20, 21, 22, 23, 24, 25])\n\n# Option 1\narr3 = arr1 + arr2\narr3\n\n# Option 2\narr3 = np.add(arr1, arr2)\narr3",
      "metadata": {
        "trusted": true
      },
      "execution_count": 59,
      "outputs": [
        {
          "execution_count": 59,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([30, 32, 34, 36, 38, 40])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\narr3 = np.add(arr1, arr2)\narr3\n\n    \n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "### Array Subtraction\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Consider the numpy array a:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "a = np.array([10, 20, 30])\na",
      "metadata": {
        "trusted": true
      },
      "execution_count": 60,
      "outputs": [
        {
          "execution_count": 60,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([10, 20, 30])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "Consider the numpy array b:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "b = np.array([5, 10, 15])\nb",
      "metadata": {
        "trusted": true
      },
      "execution_count": 61,
      "outputs": [
        {
          "execution_count": 61,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([ 5, 10, 15])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "We can subtract the two arrays and assign it to c:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "c = np.subtract(a, b)\n\nprint(c)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 62,
      "outputs": [
        {
          "name": "stdout",
          "text": "[ 5 10 15]\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "### Try it yourself\n\nPerform subtraction operation on the given numpy array arr1 and arr2:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "arr1 = np.array([10, 20, 30, 40, 50, 60])\narr2 = np.array([20, 21, 22, 23, 24, 25])\n\narr3 = np.subtract(arr1, arr2)\narr3\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 63,
      "outputs": [
        {
          "execution_count": 63,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([-10,  -1,   8,  17,  26,  35])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\narr3 = np.subtract(arr1, arr2)\narr3\n\n    \n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h3 id=\"multi\">Array Multiplication</h3>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Consider the vector numpy array <code>y</code>:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Create a numpy array\n\nx = np.array([1, 2])\nx",
      "metadata": {
        "trusted": true
      },
      "execution_count": 64,
      "outputs": [
        {
          "execution_count": 64,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([1, 2])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": "# Create a numpy array\n\ny = np.array([2, 1])\ny",
      "metadata": {
        "trusted": true
      },
      "execution_count": 65,
      "outputs": [
        {
          "execution_count": 65,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([2, 1])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "We can multiply every element in the array by 2:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Numpy Array Multiplication\n\nz = np.multiply(x, y)\nz",
      "metadata": {
        "trusted": true
      },
      "execution_count": 66,
      "outputs": [
        {
          "execution_count": 66,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([2, 2])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "This is equivalent to multiplying a vector by a scaler:\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "### Try it yourself\n\nPerform multiply operation on the given numpy array arr1 and arr2:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "arr1 = np.array([10, 20, 30, 40, 50, 60])\narr2 = np.array([2, 1, 2, 3, 4, 5])\n\narr3 = np.multiply(arr1, arr2)\narr3\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 67,
      "outputs": [
        {
          "execution_count": 67,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([ 20,  20,  60, 120, 200, 300])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\narr3 = np.multiply(arr1, arr2)\narr3\n\n    \n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "### Array Division\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Consider the vector numpy array a:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "a = np.array([10, 20, 30])\na",
      "metadata": {
        "trusted": true
      },
      "execution_count": 68,
      "outputs": [
        {
          "execution_count": 68,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([10, 20, 30])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "Consider the vector numpy array b:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "b = np.array([2, 10, 5])\nb",
      "metadata": {
        "trusted": true
      },
      "execution_count": 69,
      "outputs": [
        {
          "execution_count": 69,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([ 2, 10,  5])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "We can divide the two arrays and assign it to c:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "c = np.divide(a, b)\nc",
      "metadata": {
        "trusted": true
      },
      "execution_count": 70,
      "outputs": [
        {
          "execution_count": 70,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([5., 2., 6.])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "### Try it yourself\n\nPerform division operation on the given numpy array arr1 and arr2:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "arr1 = np.array([10, 20, 30, 40, 50, 60])\narr2 = np.array([3, 5, 10, 8, 2, 33])\n\narr3 = np.divide(arr1, arr2)\narr3",
      "metadata": {
        "trusted": true
      },
      "execution_count": 71,
      "outputs": [
        {
          "execution_count": 71,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([ 3.33333333,  4.        ,  3.        ,  5.        , 25.        ,\n        1.81818182])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\narr3 = np.divide(arr1, arr2)\narr3\n\n    \n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h3 id=\"dot\">Dot Product</h3>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "The dot product of the two numpy arrays <code>u</code> and <code>v</code> is given by:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "X = np.array([1, 2])\nY = np.array([3, 2])",
      "metadata": {
        "trusted": true
      },
      "execution_count": 72,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": "# Calculate the dot product\n\nnp.dot(X, Y)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 73,
      "outputs": [
        {
          "execution_count": 73,
          "output_type": "execute_result",
          "data": {
            "text/plain": "7"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": "#Elements of X\nprint(X[0])\nprint(X[1])",
      "metadata": {
        "trusted": true
      },
      "execution_count": 74,
      "outputs": [
        {
          "name": "stdout",
          "text": "1\n2\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "code",
      "source": "#Elements of Y\nprint(Y[0])\nprint(Y[1])",
      "metadata": {
        "trusted": true
      },
      "execution_count": 75,
      "outputs": [
        {
          "name": "stdout",
          "text": "3\n2\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "We are performing the dot product which is shown as below\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<img src =\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-PY0101EN-SkillsNetwork/labs/Module%205/images/dot1.png\"/>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "### Try it yourself\n\nPerform dot operation on the given numpy array ar1 and ar2:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "arr1 = np.array([3, 5])\narr2 = np.array([2, 4])\n\narr3 = np.dot(arr1, arr2)\narr3\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 79,
      "outputs": [
        {
          "execution_count": 79,
          "output_type": "execute_result",
          "data": {
            "text/plain": "26"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\narr3 = np.dot(arr1, arr2)\narr3\n\n    \n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h3 id=\"cons\">Adding Constant to a Numpy Array</h3>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Consider the following array:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Create a constant to numpy array\n\nu = np.array([1, 2, 3, -1]) \nu",
      "metadata": {
        "trusted": true
      },
      "execution_count": 80,
      "outputs": [
        {
          "execution_count": 80,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([ 1,  2,  3, -1])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "Adding the constant 1 to each element in the array:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Add the constant to array\n\nu + 1",
      "metadata": {
        "trusted": true
      },
      "execution_count": 81,
      "outputs": [
        {
          "execution_count": 81,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([2, 3, 4, 0])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "The process is summarised in the following animation:\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-PY0101EN-SkillsNetwork/labs/Module%205/images/NumOneAdd.gif\" width=\"500\" />\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "### Try it yourself\n\nAdd Constant 5 to the given numpy array ar:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "arr = np.array([1, 2, 3, -1]) \n\narr + 5\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 82,
      "outputs": [
        {
          "execution_count": 82,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([6, 7, 8, 4])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\narr + 5\n\n    \n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<hr>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h2 id=\"math\">Mathematical Functions</h2>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "We can access the value of <code>pi</code> in numpy as follows :\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# The value of pi\n\nnp.pi",
      "metadata": {
        "trusted": true
      },
      "execution_count": 83,
      "outputs": [
        {
          "execution_count": 83,
          "output_type": "execute_result",
          "data": {
            "text/plain": "3.141592653589793"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "We can create the following numpy array in Radians:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Create the numpy array in radians\n\nx = np.array([0, np.pi/2 , np.pi])",
      "metadata": {
        "trusted": true
      },
      "execution_count": 84,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "We can apply the function <code>sin</code> to the array <code>x</code> and assign the values to the array <code>y</code>; this applies the sine function to each element in the array:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Calculate the sin of each elements\n\ny = np.sin(x)\ny",
      "metadata": {
        "trusted": true
      },
      "execution_count": 85,
      "outputs": [
        {
          "execution_count": 85,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([0.0000000e+00, 1.0000000e+00, 1.2246468e-16])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<hr>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<h2 id=\"lin\">Linspace</h2>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "A useful function for plotting mathematical functions is <code>linspace</code>.   Linspace returns evenly spaced numbers over a specified interval.\n\n**numpy.linspace(start, stop, num = int value)**\n\nstart  :  start of interval range\n\nstop   :  end of interval range\n\nnum    :  Number of samples to generate.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Makeup a numpy array within [-2, 2] and 5 elements\n\nnp.linspace(-2, 2, num=5)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 86,
      "outputs": [
        {
          "execution_count": 86,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([-2., -1.,  0.,  1.,  2.])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "If we change the parameter <code>num</code> to 9, we get 9 evenly spaced numbers over the interval from -2 to 2:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Make a numpy array within [-2, 2] and 9 elements\n\nnp.linspace(-2, 2, num=9)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 87,
      "outputs": [
        {
          "execution_count": 87,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([-2. , -1.5, -1. , -0.5,  0. ,  0.5,  1. ,  1.5,  2. ])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "We can use the function <code>linspace</code> to generate 100 evenly spaced samples from the interval 0 to 2π:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Make a numpy array within [0, 2π] and 100 elements \n\nx = np.linspace(0, 2*np.pi, num=100)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 88,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "We can apply the sine function to each element in the array <code>x</code> and assign it to the array <code>y</code>:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Calculate the sine of x list\n\ny = np.sin(x)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 89,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": "# Plot the result\n\nplt.plot(x, y)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 90,
      "outputs": [
        {
          "execution_count": 90,
          "output_type": "execute_result",
          "data": {
            "text/plain": "[<matplotlib.lines.Line2D at 0x388f3f8>]"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 432x288 with 1 Axes>",
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "### Try it yourself\n\nMake a numpy array within \\[5, 4] and 6 elements\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "arr = np.linspace(5, 4, 6)\narr\n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 95,
      "outputs": [
        {
          "execution_count": 95,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([5. , 4.8, 4.6, 4.4, 4.2, 4. ])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\nnp.linspace(5, 4, num=6)\n\n    \n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<hr>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "### Iterating 1-D Arrays\n\nIterating means going through elements one by one.\n\nIf we iterate on a 1-D array it will go through each element one by one.\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "If we execute the numpy array, we get in the array format\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "arr1 = np.array([1, 2, 3])\nprint(arr1)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 96,
      "outputs": [
        {
          "name": "stdout",
          "text": "[1 2 3]\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "But if you want to result in the form of the list, then you can use for loop:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "for x in arr1:\n  print(x)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 97,
      "outputs": [
        {
          "name": "stdout",
          "text": "1\n2\n3\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<h2 id=\"quiz\">Quiz on 1D Numpy Array</h2>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Implement the following vector subtraction in numpy: u-v\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute\n\nu = np.array([1, 0])\nv = np.array([0, 1])\nz = u-v\nz",
      "metadata": {
        "trusted": true
      },
      "execution_count": 98,
      "outputs": [
        {
          "execution_count": 98,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([ 1, -1])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\nu - v\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<hr>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Multiply the numpy array z with -2:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute\n\nz = np.array([2, 4])\nz * -2",
      "metadata": {
        "trusted": true
      },
      "execution_count": 100,
      "outputs": [
        {
          "execution_count": 100,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([-4, -8])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\n-2 * z\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<hr>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Consider the list <code>\\[1, 2, 3, 4, 5]</code> and <code>\\[1, 0, 1, 0, 1]</code>. Cast both lists to a numpy array then multiply them together:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute\narr1 = np.array([1, 2, 3, 4, 5])\narr2 = np.array([1, 0, 1, 0, 1])\n\narr1 * arr2",
      "metadata": {
        "trusted": true
      },
      "execution_count": 101,
      "outputs": [
        {
          "execution_count": 101,
          "output_type": "execute_result",
          "data": {
            "text/plain": "array([1, 0, 3, 0, 5])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\na = np.array([1, 2, 3, 4, 5])\nb = np.array([1, 0, 1, 0, 1])\na * b\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<hr>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Import the libraries\n\nimport time \nimport sys\nimport numpy as np \n\nimport matplotlib.pyplot as plt\n%matplotlib inline  \n\ndef Plotvec2(a,b):\n    ax = plt.axes()# to generate the full window axes\n    ax.arrow(0, 0, *a, head_width=0.05, color ='r', head_length=0.1)#Add an arrow to the  a Axes with arrow head width 0.05, color red and arrow head length 0.1\n    plt.text(*(a + 0.1), 'a')\n    ax.arrow(0, 0, *b, head_width=0.05, color ='b', head_length=0.1)#Add an arrow to the  b Axes with arrow head width 0.05, color blue and arrow head length 0.1\n    plt.text(*(b + 0.1), 'b')\n    plt.ylim(-2, 2)#set the ylim to bottom(-2), top(2)\n    plt.xlim(-2, 2)#set the xlim to left(-2), right(2)\n    \n    \n",
      "metadata": {
        "trusted": true
      },
      "execution_count": 102,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "Convert the list <code>\\[-1, 1]</code> and <code>\\[1, 1]</code> to numpy arrays <code>a</code> and <code>b</code>. Then, plot the arrays as vectors using the fuction <code>Plotvec2</code> and find their dot product:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute\na = np.array([-1, 1])\nb = np.array([1, 1])\n\nPlotvec2(a, b)\nprint(\"The dot product is: \", np.dot(a, b))",
      "metadata": {
        "trusted": true
      },
      "execution_count": 104,
      "outputs": [
        {
          "name": "stdout",
          "text": "The dot product is:  0\n",
          "output_type": "stream"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 432x288 with 1 Axes>",
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\n\n\na = np.array([-1, 1])\nb = np.array([1, 1])\nPlotvec2(a, b)\nprint(\"The dot product is\", np.dot(a,b))\n\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<hr>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Convert the list <code>\\[1, 0]</code> and <code>\\[0, 1]</code> to numpy arrays <code>a</code> and <code>b</code>. Then, plot the arrays as vectors using the function <code>Plotvec2</code> and find their dot product:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute\n\na = np.array([1, 0])\nb = np.array([0, 1])\nPlotvec2(a, b)\nprint(\"The dot product is: \", np.dot(a, b))",
      "metadata": {
        "trusted": true
      },
      "execution_count": 105,
      "outputs": [
        {
          "name": "stdout",
          "text": "The dot product is:  0\n",
          "output_type": "stream"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 432x288 with 1 Axes>",
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\na = np.array([1, 0])\nb = np.array([0, 1])\nPlotvec2(a, b)\nprint(\"The dot product is\", np.dot(a, b))\n\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<hr>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Convert the list <code>\\[1, 1]</code> and <code>\\[0, 1]</code> to numpy arrays <code>a</code> and <code>b</code>. Then plot the arrays as vectors using the fuction <code>Plotvec2</code> and find their dot product:\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute\na = np.array([1, 1])\nb = np.array([0, 1])\nPlotvec2(a, b)\nprint(\"The dot product is: \", np.dot(a, b))",
      "metadata": {
        "trusted": true
      },
      "execution_count": 106,
      "outputs": [
        {
          "name": "stdout",
          "text": "The dot product is:  1\n",
          "output_type": "stream"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 432x288 with 1 Axes>",
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\na = np.array([1, 1])\nb = np.array([0, 1])\nPlotvec2(a, b)\nprint(\"The dot product is\", np.dot(a, b))\n\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<hr>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Why are the results of the dot product for <code>\\[-1, 1]</code> and <code>\\[1, 1]</code> and the dot product for <code>\\[1, 0]</code> and <code>\\[0, 1]</code> zero, but not zero for the dot product for <code>\\[1, 1]</code> and <code>\\[0, 1]</code>? <p><i>Hint: Study the corresponding figures, pay attention to the direction the arrows are pointing to.</i></p>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute\nThe dot product is zero because the vectors are perpendicular for questions 4 & t. ",
      "metadata": {},
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\nThe vectors used for question 4 and 5 are perpendicular. As a result, the dot product is zero. \n\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Convert the list <code>\\[1, 2, 3]</code> and <code>\\[8, 9, 10]</code> to numpy arrays <code>arr1</code> and <code>arr2</code>. Then perform <code>Addition</code> , <code>Subtraction</code> , <code>Multiplication</code> , <code>Division</code> and <code>Dot Operation</code> on the <code>arr1</code> and <code>arr2</code>.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute\narr1 = ([1, 2, 3])\narr2 = ([8, 9, 10])\n\narr3 = np.add(arr1, arr2)\nprint(arr3)\n\narr4 = np.subtract(arr1, arr2)\nprint(arr4)\n\narr5 = np.multiply(arr1, arr2)\nprint(arr5)\n\narr6 = np.divide(arr1, arr2)\nprint(arr6)\n\narr7 = np.dot(arr1, arr2)\nprint(arr7)",
      "metadata": {
        "trusted": true
      },
      "execution_count": 110,
      "outputs": [
        {
          "name": "stdout",
          "text": "[ 9 11 13]\n[-7 -7 -7]\n[ 8 18 30]\n[0.125      0.22222222 0.3       ]\n56\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\narr1 = np.array([1, 2, 3])\narr2 = np.array([8, 9, 10])\n\narr3 = np.add(arr1, arr2)\narr3\n\narr4 = np.subtract(arr1, arr2)\narr4\n\narr5 = np.multiply(arr1, arr2)\narr5\n\n\narr6 = np.divide(arr1, arr2)\narr6\n\narr7 = np.dot(arr1, arr2)\narr7\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "Convert the list <code>\\[1, 2, 3, 4, 5]</code> and <code>\\[6, 7, 8, 9, 10]</code> to numpy arrays <code>arr1</code> and <code>arr2</code>. Then find the even and odd numbers from <code>arr1</code> and <code>arr2</code>.\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "# Write your code below and press Shift+Enter to execute\narr1 = np.array([1, 2, 3, 4, 5])\narr2 = np.array([6, 7, 8, 9, 10])\n\narrOdd = arr1[::2]\nprint(arrOdd)\n\narrEven = arr2[::2]\nprint(arrEven)\n\n# solution offered only finds odd numbers from arr1 and even numbers from arr2\n# need to explore append, insert, etc. or some other solution to combine the arrays",
      "metadata": {
        "trusted": true
      },
      "execution_count": 117,
      "outputs": [
        {
          "name": "stdout",
          "text": "[1 3 5]\n[ 6  8 10]\n",
          "output_type": "stream"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": "<details><summary>Click here for the solution</summary>\n\n```python\narr1 = np.array([1, 2, 3, 4, 5])\narr2 = np.array([6, 7, 8, 9, 10])\n\nx = arr1[1:8:2]\nx\n   \ny = arr2[0:8:2]\ny   \n\n```\n\n</details>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "<hr>\n<h2>The last exercise!</h2>\n<p>Congratulations, you have completed your first lesson and hands-on lab in Python. \n<hr>\n",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "## Author\n\n<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\" target=\"_blank\">Joseph Santarcangelo</a>\n\n## Other contributors\n\n<a href=\"https://www.linkedin.com/in/jiahui-mavis-zhou-a4537814a?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkPY0101ENSkillsNetwork19487395-2021-01-01\">Mavis Zhou</a>\n\n## Change Log\n\n| Date (YYYY-MM-DD) | Version | Changed By | Change Description                  |\n| ----------------- | ------- | ---------- | ----------------------------------- |\n| 2022-03-08        | 2.2     | Niveditha  | Modified and added practice problem |\n| 2022-01-10        | 2.1     | Malika     | Removed the readme for GitShare     |\n| 2020-08-26        | 2.0     | Lavanya    | Moved lab to course repo in GitLab  |\n|                   |         |            |                                     |\n|                   |         |            |                                     |\n\n<hr/>\n\n## <h3 align=\"center\"> © IBM Corporation 2020. All rights reserved. <h3/>\n",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "",
      "metadata": {},
      "execution_count": null,
      "outputs": []
    }
  ]
}