Model.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"\\nSo I created 100 random datasets in Data Generator of between 50-100 points and 2-10 dimensional X points\\nand sigma of between 0-1. You can change those values and make new datasets if you want easily in the last box of \\nData Generator.\\n\\nThe second box here is my solve least squares, ridge regression, and ALS code.\\nThe third box loads the datasets (change the 100 to a different value if you change the number of datasets) with the \\nfirst function. It creates many lambda values (right now 100, so we have a 100x100 matrix overall). get_points \\nrandomly chooses approximately #rows*#cols*p + #rows + #cols points as training data and \\n#rows*#cols*q + #rows + #cols points as test data. get_MSE gives the \\nMSE for that dataset and lambda value. generate_data calculates the MSE for all of those and\\nformats it so ALS can run.\\n\\nThings to mess around with: rank, as currently it's using 2. p and q are the approximate percentage of the matrix\\nthat is filled. MSE_iters is how precise the MSE is. ALS_lam is how regularized the ALS is.\\n\""
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "So I created 100 random datasets in Data Generator of between 50-100 points and 2-10 dimensional X points\n",
    "and sigma of between 0-1. You can change those values and make new datasets if you want easily in the last box of \n",
    "Data Generator.\n",
    "\n",
    "The second box here is my solve least squares, ridge regression, and ALS code.\n",
    "The third box loads the datasets (change the 100 to a different value if you change the number of datasets) with the \n",
    "first function. It creates many lambda values (right now 100, so we have a 100x100 matrix overall). get_points \n",
    "randomly chooses approximately #rows*#cols*p + #rows + #cols points as training data and \n",
    "#rows*#cols*q + #rows + #cols points as test data. get_MSE gives the \n",
    "MSE for that dataset and lambda value. generate_data calculates the MSE for all of those and\n",
    "formats it so ALS can run.\n",
    "\n",
    "Things to mess around with: rank, as currently it's using 2. p and q are the approximate percentage of the matrix\n",
    "that is filled. MSE_iters is how precise the MSE is. ALS_lam is how regularized the ALS is.\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.model_selection import train_test_split\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import sparse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def solve_ls(X, y):\n",
    "    inv = np.linalg.inv(np.dot(X.T, X))\n",
    "    a = np.dot(inv, X.T)\n",
    "    return np.dot(a, y)\n",
    "\n",
    "def solve_rr(X, y, lam):\n",
    "    inv = np.linalg.inv(np.dot(X.T, X) + lam * np.identity(np.shape(X)[1]))\n",
    "    a = np.dot(inv, X.T)\n",
    "    return np.dot(a, y)\n",
    "\n",
    "#John's ALS code\n",
    "def ALS(data_train, data_test, k=2, lam=0.02, max_iter=100, verbose = False):\n",
    "    '''\n",
    "    data_train and data_test are lists of tuples (row, column, MSE)\n",
    "    these need to be integers so we need to map each dataset and lambda value to an integer (MSE need not be integer)\n",
    "    \n",
    "    k is rank\n",
    "    lam is the regularizer on the least squares call in each step\n",
    "    \n",
    "    my code also has offsets b_u and b_v\n",
    "    the prediction for entry (a, i) is (b_u[a] + b_v[i] + np.dot(u[a].T, v[i])[0][0])\n",
    "    '''\n",
    "    # size of the problem\n",
    "    n = max(d[0] for d in data_train)+1 # datasets\n",
    "    m = max(d[1] for d in data_train)+1 # lambda values\n",
    "    # which entries are set in each row and column and the MSE\n",
    "    us_from_v = [[] for i in range(m)]  # II (i-index-set)\n",
    "    vs_from_u = [[] for a in range(n)]  # AI (a-index set)\n",
    "    for (a, i, r) in data_train:\n",
    "        us_from_v[i].append((a, r))\n",
    "        vs_from_u[a].append((i, r))\n",
    "    # Initial guesses for u, b_u, v, b_v\n",
    "    # Note that u and v are lists of column vectors (rows of U, V).\n",
    "    u, b_u, v, b_v = ([np.random.normal(1/k, size=(k,1)) for a in range(n)],\n",
    "          np.zeros(n),\n",
    "          [np.random.normal(1/k, size=(k,1)) for i in range(m)],\n",
    "          np.zeros(m))\n",
    "    for itr in range(max_iter):\n",
    "        if itr%5 == 0 and verbose:\n",
    "            print(itr)\n",
    "        for i in range(len(u)): #run ls on u\n",
    "            X_mat = np.array([np.append(np.array([1]), v[a[0]].T[0]) for a in vs_from_u[i]])\n",
    "            y_vec = np.array([[a[1] - b_v[a[0]]] for a in vs_from_u[i]])\n",
    "            if len(X_mat) > 0:\n",
    "                sol = solve_rr(X_mat, y_vec, lam)\n",
    "                b_u[i] = sol[0]\n",
    "                u[i] = sol[1:]\n",
    "        for j in range(len(v)): #run ls on v\n",
    "            X_mat = np.array([np.append(np.array([1]), u[a[0]].T[0]) for a in us_from_v[j]])\n",
    "            y_vec = np.array([[a[1] - b_u[a[0]]] for a in us_from_v[j]])\n",
    "            if len(X_mat) > 0:\n",
    "                sol = solve_rr(X_mat, y_vec, lam)\n",
    "                b_v[j] = sol[0][0]\n",
    "                v[j] = sol[:][1:]\n",
    "            \n",
    "    # TODO: Evaluate using some error metric measured on test set\n",
    "    error = 0\n",
    "    count = 0\n",
    "    for (a, i, r) in data_test:\n",
    "        count += 1\n",
    "        error += (b_u[a] + b_v[i] + np.dot(u[a].T, v[i])[0][0] - r) ** 2\n",
    "    error = error / count\n",
    "    return (u, b_u, v, b_v, error)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def load_datasets():\n",
    "    dataset_dic = {}\n",
    "    for i in range(100):\n",
    "        X_df = pd.read_csv('gendata/example_dataset' + str(i + 1) + '.csv')\n",
    "        dataset_dic[i] = X_df\n",
    "    return dataset_dic\n",
    "\n",
    "lambda_dic = {lamb + 60: 10 ** (-.05 * lamb) for lamb in range(-60, 40)}\n",
    "  \n",
    "def get_points(m, n, p, q):\n",
    "    train_points = set()\n",
    "\n",
    "    for i in range(m):\n",
    "        j = np.random.randint(0, n)\n",
    "        train_points.add((i, j))\n",
    "    for j in range(n):\n",
    "        i = np.random.randint(0, m)\n",
    "        if (i, j) not in train_points:\n",
    "            train_points.add((i, j))\n",
    "    for i in range(m):\n",
    "        for j in range(n):\n",
    "            if np.random.random() < p:\n",
    "                if (i, j) not in train_points:\n",
    "                    train_points.add((i, j))\n",
    "\n",
    "    test_points = set()\n",
    "\n",
    "    for i in range(m):\n",
    "        for j in range(n):\n",
    "            if np.random.random() < q:\n",
    "                if (i, j) not in train_points:\n",
    "                    test_points.add((i, j))\n",
    "                    \n",
    "    return train_points, test_points\n",
    "\n",
    "def get_MSE(X_df, lam, iters = 1, size = 0.5):\n",
    "    MSE = 0\n",
    "    for _ in range(iters):\n",
    "        train, test = train_test_split(X_df, test_size=size)\n",
    "        X_train, Y_train = np.array(train.drop('Y', axis=1)), np.transpose(np.array([train['Y']]))\n",
    "        X_1 = np.hstack((np.ones(shape = (len(X_train), 1)), X_train))\n",
    "        sol = solve_rr(X_1, Y_train, lam)\n",
    "        X_test, Y_test = np.array(test.drop('Y', axis=1)), np.transpose(np.array([test['Y']]))\n",
    "        X_2 = np.hstack((np.ones(shape = (len(X_test), 1)), X_test))\n",
    "        MSE += np.linalg.norm(X_2@sol - Y_test) / len(X_2)\n",
    "    return MSE / iters\n",
    "\n",
    "def generate_data(dataset_dic, lambda_dic, points, iters = 1, size = 0.5):\n",
    "    data = []\n",
    "    for (i, j) in points:\n",
    "        MSE = get_MSE(dataset_dic[i], lambda_dic[j], iters, size)\n",
    "        data.append((i, j, MSE))                    \n",
    "    return data     "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_ALS(p=0.05, q=0.1, MSE_iters=10, rank = 2, ALS_lam = 0.02, ALS_iters = 100, verbose = False):\n",
    "    dataset_dic = load_datasets()\n",
    "    if verbose: print('loaded datasets')\n",
    "    train_pts, test_pts = get_points(len(dataset_dic), len(lambda_dic), p = p, q = q)\n",
    "    if verbose: print('generated points')\n",
    "    data_train = generate_data(dataset_dic, lambda_dic, train_pts, iters = MSE_iters)\n",
    "    if verbose: print('generated train list')\n",
    "    data_test = generate_data(dataset_dic, lambda_dic, test_pts, iters = MSE_iters)\n",
    "    if verbose: print('generated test list')\n",
    "    u, b_u, v, b_v, error = ALS(data_train, data_test, k=rank, lam=ALS_lam, max_iter=ALS_iters)\n",
    "    if verbose: print('finished ALS. Error {}'.format(error))\n",
    "    return error\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "p, q = 0.05, 0.1\n",
    "MSE_iters = 10\n",
    "dataset_dic = load_datasets()\n",
    "train_pts, test_pts = get_points(len(dataset_dic), len(lambda_dic), p = p, q = q)\n",
    "data_train = generate_data(dataset_dic, lambda_dic, train_pts, iters = MSE_iters)\n",
    "data_test = generate_data(dataset_dic, lambda_dic, test_pts, iters = MSE_iters)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "vals = [x[2] for x in data_test]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error with rank 2 and als_lam 0.0 is 19121.143571842666\n",
      "Error with rank 2 and als_lam 0.02 is 0.0005436655236343179\n",
      "Error with rank 2 and als_lam 0.04 is 0.0006301680461849621\n",
      "Error with rank 2 and als_lam 0.06 is 0.0008248270353622123\n",
      "Error with rank 2 and als_lam 0.08 is 0.0007097211324746214\n",
      "Error with rank 2 and als_lam 0.1 is 0.0008363401906133342\n",
      "Error with rank 2 and als_lam 0.12 is 0.0012329358008907338\n",
      "Error with rank 2 and als_lam 0.14 is 0.0013159234879363054\n",
      "Error with rank 2 and als_lam 0.16 is 0.0011029406844145246\n",
      "Error with rank 2 and als_lam 0.18 is 0.0012523162404151293\n",
      "Error with rank 3 and als_lam 0.0 is 7.903798942422541e+41\n",
      "Error with rank 3 and als_lam 0.02 is 0.0005751785397961071\n",
      "Error with rank 3 and als_lam 0.04 is 0.0009052526312427642\n",
      "Error with rank 3 and als_lam 0.06 is 0.0010542072147205436\n",
      "Error with rank 3 and als_lam 0.08 is 0.000853092116854198\n",
      "Error with rank 3 and als_lam 0.1 is 0.0010895942969095145\n",
      "Error with rank 3 and als_lam 0.12 is 0.0012960137084276036\n",
      "Error with rank 3 and als_lam 0.14 is 0.0009757907318988916\n",
      "Error with rank 3 and als_lam 0.16 is 0.0017812071799734124\n",
      "Error with rank 3 and als_lam 0.18 is 0.0013860414048152891\n",
      "Error with rank 4 and als_lam 0.0 is 1.944442862836349e+44\n",
      "Error with rank 4 and als_lam 0.02 is 0.0010572904717582401\n",
      "Error with rank 4 and als_lam 0.04 is 0.000872110065338877\n",
      "Error with rank 4 and als_lam 0.06 is 0.0006910834524617366\n",
      "Error with rank 4 and als_lam 0.08 is 0.0008131471138612852\n",
      "Error with rank 4 and als_lam 0.1 is 0.0008514566580904597\n",
      "Error with rank 4 and als_lam 0.12 is 0.0014564686605022209\n",
      "Error with rank 4 and als_lam 0.14 is 0.0015428473498042474\n",
      "Error with rank 4 and als_lam 0.16 is 0.0014696367593216185\n",
      "Error with rank 4 and als_lam 0.18 is 0.0018644477825984686\n",
      "Error with rank 5 and als_lam 0.0 is 6.413919582389994e+166\n",
      "Error with rank 5 and als_lam 0.02 is 0.000581449569959844\n",
      "Error with rank 5 and als_lam 0.04 is 0.0009901305826286071\n",
      "Error with rank 5 and als_lam 0.06 is 0.0008189093895994635\n",
      "Error with rank 5 and als_lam 0.08 is 0.0010224946118238835\n",
      "Error with rank 5 and als_lam 0.1 is 0.0012941549242245134\n",
      "Error with rank 5 and als_lam 0.12 is 0.001145907877584706\n",
      "Error with rank 5 and als_lam 0.14 is 0.0011703766579975918\n",
      "Error with rank 5 and als_lam 0.16 is 0.0015052682907986256\n",
      "Error with rank 5 and als_lam 0.18 is 0.0014059136145309404\n",
      "Error with rank 6 and als_lam 0.0 is 1.8097068807081622e+305\n",
      "Error with rank 6 and als_lam 0.02 is 0.0010544838470233036\n",
      "Error with rank 6 and als_lam 0.04 is 0.0009778016191030253\n",
      "Error with rank 6 and als_lam 0.06 is 0.0010338928991687154\n",
      "Error with rank 6 and als_lam 0.08 is 0.0008429265268621604\n",
      "Error with rank 6 and als_lam 0.1 is 0.0007978292087940381\n",
      "Error with rank 6 and als_lam 0.12 is 0.0011574013517289892\n",
      "Error with rank 6 and als_lam 0.14 is 0.0011796350324660943\n",
      "Error with rank 6 and als_lam 0.16 is 0.0013121851842472353\n",
      "Error with rank 6 and als_lam 0.18 is 0.0014397449326487577\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:61: RuntimeWarning: overflow encountered in double_scalars\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error with rank 7 and als_lam 0.0 is inf\n",
      "Error with rank 7 and als_lam 0.02 is 0.0005820397768904043\n",
      "Error with rank 7 and als_lam 0.04 is 0.0005441272123401879\n",
      "Error with rank 7 and als_lam 0.06 is 0.0009471543260609829\n",
      "Error with rank 7 and als_lam 0.08 is 0.0008226216433239703\n",
      "Error with rank 7 and als_lam 0.1 is 0.0009406002045681447\n",
      "Error with rank 7 and als_lam 0.12 is 0.0013086029246397789\n",
      "Error with rank 7 and als_lam 0.14 is 0.0014162159392216954\n",
      "Error with rank 7 and als_lam 0.16 is 0.0014104904300491037\n",
      "Error with rank 7 and als_lam 0.18 is 0.001678408979585491\n",
      "Error with rank 8 and als_lam 0.0 is inf\n",
      "Error with rank 8 and als_lam 0.02 is 0.0008370370690508126\n",
      "Error with rank 8 and als_lam 0.04 is 0.0007921634863170435\n",
      "Error with rank 8 and als_lam 0.06 is 0.0007832260962429133\n",
      "Error with rank 8 and als_lam 0.08 is 0.0010646985073703868\n",
      "Error with rank 8 and als_lam 0.1 is 0.0011244350596085163\n",
      "Error with rank 8 and als_lam 0.12 is 0.0010847663697065482\n",
      "Error with rank 8 and als_lam 0.14 is 0.0011712835397840288\n",
      "Error with rank 8 and als_lam 0.16 is 0.0014338863336696647\n",
      "Error with rank 8 and als_lam 0.18 is 0.0013263600307163376\n",
      "Error with rank 9 and als_lam 0.0 is inf\n",
      "Error with rank 9 and als_lam 0.02 is 0.0009490774509773852\n",
      "Error with rank 9 and als_lam 0.04 is 0.0006378471855589639\n",
      "Error with rank 9 and als_lam 0.06 is 0.0008283276456027201\n",
      "Error with rank 9 and als_lam 0.08 is 0.0008881419930789768\n",
      "Error with rank 9 and als_lam 0.1 is 0.0010171746409589138\n",
      "Error with rank 9 and als_lam 0.12 is 0.0010305776017020733\n",
      "Error with rank 9 and als_lam 0.14 is 0.001066910380735872\n",
      "Error with rank 9 and als_lam 0.16 is 0.001304028263507983\n",
      "Error with rank 9 and als_lam 0.18 is 0.001830239453977756\n"
     ]
    }
   ],
   "source": [
    "ranks = [i for i in range(2, 10)]\n",
    "als_lams = [2*i/100. for i in range(0, 10)]\n",
    "errors = []\n",
    "\n",
    "for r in ranks:\n",
    "    temp = []f\n",
    "    for l in als_lams:\n",
    "        err = run_ALS(rank = r, ALS_lam = l)\n",
    "#         print(\"Error with rank {} and als_lam {} is {}\".format(r, l, err))\n",
    "        temp.append(err)\n",
    "    errors.append(temp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0009675726296254285"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2ada0033898>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i,  values in enumerate(errors):\n",
    "    rank = ranks[i]\n",
    "    corr_errs = values[1:]\n",
    "    plt.plot(als_lams[1:], corr_errs, label='Rank {}'.format(rank))\n",
    "\n",
    "plt.legend()\n",
    "plt.xlabel('ALS_Lambda Value')\n",
    "plt.ylabel('MSE')\n",
    "plt.title('MSE of ALS Matrix estimation varying Ranks and ALS_Lambda')\n",
    "plt.savefig('Graphs/MSE_Ranks_ALS.png', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2ada00e90b8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "min_errs = []\n",
    "best_lambda = []\n",
    "for err_vals in errors:\n",
    "    min_errs.append(min(err_vals))\n",
    "    best_lambda.append(als_lams[np.argmin(err_vals)])\n",
    "    \n",
    "plt.plot(ranks, min_errs)\n",
    "plt.xlabel('Rank')\n",
    "plt.ylabel('Minimum ALS error')\n",
    "plt.title('Minimum ALS error by rank')\n",
    "plt.savefig('Graphs/ALS_By_Rank.png', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2ada01c0e80>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(best_lambda)\n",
    "plt.xlabel('Best ALS Lambda')\n",
    "plt.ylabel('Frequency')\n",
    "# plt.ylabel('Best ALS Lambda')\n",
    "plt.title('Histogram of best ALS lambdas for each rank')\n",
    "plt.savefig('Graphs/Lambda_Hist.png', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.2859622568295395"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(min(min_errs)), ranks[np.argmin(min_errs)]\n",
    "np.mean(vals)/np.sqrt(min(min_errs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_matrix(data_train, n, m):\n",
    "    \"\"\"\n",
    "    Helper function to build the needed matrix for SV thresholding\n",
    "    \"\"\"\n",
    "    Y = np.full((n, m), fill_value=np.NaN)\n",
    "    for row, col, value in data_train:\n",
    "        Y[row-1][col-1] = value\n",
    "#         print('replacing')\n",
    "    return Y\n",
    "\n",
    "def standardize(array, min_val, max_val):\n",
    "    \"\"\"\n",
    "    Makes so that all values standardized between -1 and 1.\n",
    "    \"\"\"\n",
    "    return (array - (min_val + max_val)/2)/((max_val - min_val)/2)\n",
    "\n",
    "def unstandardize(array, min_val, max_val):\n",
    "    \"\"\"\n",
    "    Undoes standardization of function above.\n",
    "    \"\"\"\n",
    "    return array * ((max_val - min_val)/2) + (min_val+max_val)/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def SV_thresholding_soft(data_train, data_test, eta=2):\n",
    "    \"\"\"\n",
    "    Similar inputs to John's function above.\n",
    "    Eta: hyperparameter than controls the thresholding of singular values. Higher eta = higher threshold.\n",
    "    Threshold = (2 + eta) * sqrt( max(n, m) * p_hat), where p_hat is percentage of values\n",
    "    filled in.\n",
    "    \"\"\"\n",
    "    n = max(d[0] for d in data_train)+1 # datasets\n",
    "    m = max(d[1] for d in data_train)+1 # lambda values\n",
    "    min_mse = min(d[2] for d in data_train)\n",
    "    max_mse = max(d[2] for d in data_train)\n",
    "\n",
    "    Y_train = build_matrix(data_train, n, m)\n",
    "    Y_train = standardize(Y_train, min_mse, max_mse)\n",
    "    Y_test = build_matrix(data_test, n, m)\n",
    "    \n",
    "    Y_prime = np.nan_to_num(Y_train)\n",
    "    \n",
    "    Y_prime = sparse.csr_matrix(Y_prime)\n",
    "    U, sigma, Vh = SVD(Y_prime)\n",
    "    #Flip ordering to get largest to smallest\n",
    "    sigma = sigma[::-1]\n",
    "    U = U[::-1]\n",
    "    Vh = Vh[::-1]\n",
    "    \n",
    "    \n",
    "    p_hat = len(data_train)/(n * m) #percentage of ratings filled in.\n",
    "    A_hat = 0\n",
    "    threshold = (2+eta)*np.sqrt(max(n, m)*p_hat)\n",
    "        \n",
    "    greater = True\n",
    "    i = 0\n",
    "    while greater and i < min(n, m):\n",
    "        s = sigma[i]\n",
    "        greater = s >= threshold\n",
    "        if isinstance(Y_prime, np.ndarray):\n",
    "            A_hat += max(s- threshold, 0) * np.array([U[i]]).T @ np.array([Vh[i]])\n",
    "        else:\n",
    "            A_hat += max(s - threshold, 0) * U[:, i:i+1] @ Vh[i:i+1, :]\n",
    "        i+= 1\n",
    "\n",
    "    print(\"Used the first {} values when eta = {}\".format(i, eta))\n",
    "    \n",
    "    A_hat /= p_hat    \n",
    "\n",
    "    A_hat[A_hat < -1] = -1\n",
    "    A_hat[A_hat > 1] = 1\n",
    "    \n",
    "    err = 0\n",
    "\n",
    "    new_pred = unstandardize(A_hat, min_val = min_mse, max_val = max_mse)\n",
    "    new_pred = np.around(new_pred)\n",
    "    for row, col, rat in data_test:\n",
    "        err += (A_hat[row-1][col-1] - rat)**2\n",
    "\n",
    "    mean_err = err/len(data_test)\n",
    "    return mean_err\n",
    "\n",
    "def SVD(Y):\n",
    "    \"\"\"\n",
    "    Calculates SVD. Function used dpeneds on datatype (now using sparse matrices)\n",
    "    \"\"\"\n",
    "    if isinstance(Y, np.ndarray):\n",
    "        U, sigma, vH = np.linalg.svd(Y) # TODO: compute SV decomposition of a matrix Y\n",
    "    else:\n",
    "        U, sigma, vH = sparse.linalg.svds(Y, k = min(Y.shape)-1)\n",
    "    return U, sigma, vH"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Used the first 41 values when eta = -1.5\n",
      "MSE of 0.4268300855319633 with eta -1.5\n",
      "Used the first 34 values when eta = -1.4\n",
      "MSE of 0.3675676247948291 with eta -1.4\n",
      "Used the first 27 values when eta = -1.3\n",
      "MSE of 0.2885457356163811 with eta -1.3\n",
      "Used the first 21 values when eta = -1.2\n",
      "MSE of 0.2267642586443635 with eta -1.2\n",
      "Used the first 16 values when eta = -1.1\n",
      "MSE of 0.17448853849998425 with eta -1.1\n",
      "Used the first 10 values when eta = -1.0\n",
      "MSE of 0.13733509878409503 with eta -1.0\n",
      "Used the first 8 values when eta = -0.9\n",
      "MSE of 0.10221641184500599 with eta -0.9\n",
      "Used the first 5 values when eta = -0.8\n",
      "MSE of 0.0749214351746957 with eta -0.8\n",
      "Used the first 3 values when eta = -0.7\n",
      "MSE of 0.05994069937298109 with eta -0.7\n",
      "Used the first 2 values when eta = -0.6\n",
      "MSE of 0.04684746401789605 with eta -0.6\n",
      "Used the first 2 values when eta = -0.5\n",
      "MSE of 0.03663347321084444 with eta -0.5\n",
      "Used the first 2 values when eta = -0.3999999999999999\n",
      "MSE of 0.02948058349359503 with eta -0.3999999999999999\n",
      "Used the first 2 values when eta = -0.30000000000000004\n",
      "MSE of 0.024428734634464617 with eta -0.30000000000000004\n",
      "Used the first 2 values when eta = -0.19999999999999996\n",
      "MSE of 0.02231534582991303 with eta -0.19999999999999996\n",
      "Used the first 1 values when eta = -0.10000000000000009\n",
      "MSE of 0.02224770128182838 with eta -0.10000000000000009\n",
      "Used the first 1 values when eta = 0.0\n",
      "MSE of 0.02224770128182838 with eta 0.0\n",
      "Used the first 1 values when eta = 0.10000000000000009\n",
      "MSE of 0.02224770128182838 with eta 0.10000000000000009\n",
      "Used the first 1 values when eta = 0.19999999999999996\n",
      "MSE of 0.02224770128182838 with eta 0.19999999999999996\n",
      "Used the first 1 values when eta = 0.30000000000000004\n",
      "MSE of 0.02224770128182838 with eta 0.30000000000000004\n",
      "Used the first 1 values when eta = 0.3999999999999999\n",
      "MSE of 0.02224770128182838 with eta 0.3999999999999999\n",
      "Used the first 1 values when eta = 0.5\n",
      "MSE of 0.02224770128182838 with eta 0.5\n"
     ]
    }
   ],
   "source": [
    "ets = [-1.5 + i/10. for i in range(21)]\n",
    "SV_mses = []\n",
    "for eta in ets:\n",
    "    err = SV_thresholding_soft(data_train, data_test, eta = eta)\n",
    "    print('MSE of {} with eta {}'.format(err, eta))\n",
    "    SV_mses.append(err)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x25b9aa8bd68>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ets, SV_mses)\n",
    "plt.xlabel('Eta')\n",
    "plt.ylabel('MSE')\n",
    "plt.title('MSE of Singular Value Thresholding by Eta')\n",
    "plt.savefig('Graphs/SVT_MSE.png', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mH14rqZXrN3HF8xP5cPoiTu7ThpuO7kaNal7P4JzLLmVWpwBcCnQjeO7gOWAlwV1IDqhfM49Hzsjnkv078vyX8zhl6BgWrVwfd1jOOVcqke4+Kiws5QJ1zGxl5kJKL9vOFBK99dVCrvnPJOrWqMaDp/emV9tGcYfknHNA2d599Kyk+pLqEDyv8I2k35dFkJXN4bu05L8X7UmNvBxOfmgML345L+6QnHOuRKJcPuoanhkcA7wFtAVOz2hUFdjOLerz+iV70XeHxvzh5cnc+NoUNm3ZGndYzjkXSZSkkCcpjyApvGZmm6hgzVWUt4a1q/PEWX04b+8deHL0XE57ZCxLVnvPbs657BclKTwEzAHqAJ9IakdQ2ezSqJabw5+P6MpdJ/Vk0rzlHHv/Z8xevLr4FZ1zLkbFJgUzu8fMWpnZ4RbUSn8P7J/50CqHY3ZrxQvn92Pthi0c/8DnjJ+7LO6QnHOuSOk62bkqaZYBS4BRZvZdpgMrSjbffZTO3KVrGPz4lyxYvo67T+7JgO4ti1/JOefKSFncfVQvaahP0APbCEknl0mUVUi7JnV4+cI96bZ9fS4cNoHHRsWWV51zrkjVilpgZr/pKQ1AUmPgfeD5TAVVWTWuU51nz9uDy5//Hze/MZX5P6/j+iO6kJPj/UA757JDlIrmXzGzZQR9NbtSqJmXy/2n9eas/u157LPvuOS5CazftCXusJxzDihFUpB0APBzBmKpMnJzxI1HdeP6I7rw1lc/MuiRsfy8ZmPcYTnnXNGXjyR9xW+fR2gMLADOyGRQVcW5e3egZYNaXPniRI5/8HOeGNyXtk1qxx2Wc64KKzIpAEcmTRuw1MzWZDCeKueIXVvSvH4NzntqHMc98BmPntmHHm0axh2Wc66KKvLykZnNTRq+94SQGX3aN+blC/ekZl4uJw8dwwfTfoo7JOdcFVXiOgWXGTs2q8t/L9qTjs3rct5T4xg2Np5+qJ1zVZsnhSzSvF5Nnh+yB/vt1Jw/vzKFf749na1bvZkp51z5idJ0dh1JOeF4Z0kDwwbyXAbUqVGNoaf35tTd23L/R7O46sWJbNzsraw658pHlDOFT4CakloRdMt5FvBEcStJqinpC0mTwn6Yf/MwnKQakl6QNFPSWEntSxZ+5VQtN4e/H9Od3x+6E69OXMDgx79gzYbNcYflnKsCoiQFmdla4Djg32Z2LNA1wnobgAPMrAfQExggaY+kMucAP5tZR+BO4LbooVdukrh4/47c/rsejP1uGac/OpYV6zbFHZZzrpKLlBQk9QNOA94M56W7lRUACxS0FZ0XDskXyI8GngzHXwIOlORPSyc4vndr7ju1F1/9sIJTho5hqffL4JzLoChJ4QrgOuAVM/taUgdgZJSNS8qVNBFYBLxnZmOTirQC5gGY2WZgBdAkxXaGSBonadzixYuj7LpSGdC9BQ+fkc+sxas5aegYflyxPu6QnHOVVJT+FD42s4HAveH0bDO7LMrGzWyLmfUEWgN9JXVPKpLqrOA3t9uY2VAzyzez/GbNmkXZdaWz307Neersvvy4Yj0nPjSaecvWxh2Sc64SinL3UT9JU4Fp4XQPSfeXZCdmthz4CBiQtGg+0CbcbjWgAeC90BRh9w5NGHbu7qxYt4nfPTiamYu8JzfnXNmKcvnoLuBQYCmAmU0C9iluJUnNJDUMx2sBBwHTk4oNB84Mx08APrSiev1xAPRo05Dnh+zB5q1bOemh0Uxd4D2jOufKTqSH18xsXtKsKG09twRGSpoMfElQp/CGpJslDQzLPAo0kTQTuAq4NmLcVVqXlvV58fx+VK+Ww8lDR/O/773RWudc2YiSFOZJ2hMwSdUlXUN4KSkdM5tsZruZ2a5m1t3Mbg7n/8XMhofj683sd2bW0cz6mtnsbXo1VUiHZnV58fx+NKpTnUGPjGX0rKVxh+ScqwSiJIULgIsJ7hSaT/DMwcWZDMpF06ZxbV48vx/bN6zF4Me/YOQ3i+IOyTlXwUW5+2iJmZ1mZtuZWXMzG2Rm/rM0S2xXvyYvnN+Pjs3rMuSpcYz4amHcITnnKrAodx89Lumx5KE8gnPRFPT9vGvrhlz87AReHj8/7pCccxVUlMtHbxA8yfwmQdtH9QG/FzLLNKiVx9Pn9KXfjk24+j+TeHqMN73tnCu5KM1VvJw4Lek54P2MReRKrXb1ajx6Zh8ueXYCN7w6hbUbNnP+vjvGHZZzrgIpTX8KnYC2ZR2IKxs183J5YFBvjty1JbeOmM6d730bd0jOuQqk2DMFSasImp5Q+PdH4I8Zjsttg7zcHO4+eTdq5uVy9wcz6N2uEft0rprNgzjnSibK3Uf1zKx+wt/OyZeUXPbJzRG3HNOdHZrW4S+vTWH9pijPGzrnqroik4KkXumG8gzSlU7NvFxuGtiNOUvXMvQTfy7QOVe8dJePbk+zzIADyjgWlwH7dG7GEbu05L6RMzmmZyvaNqkdd0jOuSxWZFIws/3LMxCXOTcc2ZWPvlnEjcOn8NjgPng/Rs65okS6+0hSd0knSjqjYMh0YK7stGhQkysP7szIbxbz7tSf4g7HOZfFojzRfCPw73DYH/gnMDDtSi7rnLlne3ZuUY+bhn/N2o2b4w7HOZelopwpnAAcCPxoZmcBPYAaGY3Klbm83Bz+dkx3FqxYz78/nBl3OM65LBUlKawzs63AZkn1Cfpb7pDZsFwm9GnfmBN6t+bhT2Yz46dVcYfjnMtCUZLCuLAHtYeB8cAE4IuMRuUy5rrDdqZOjWrc8NoUvJM751yyKA+vXWRmy83sQeBg4MzwMpKrgJrUrcHvD92JMbOX8drEBXGH45zLMukeXpsq6c+SCltUM7M5Zja5fEJzmXJK37b0aN2AW96cxsr1m+IOxzmXRdKdKZwC1AXelTRW0hWSto+6YUltJI2UNE3S15IuT1FmP0krJE0Mh7+U4jW4EgqawNiFpWs2cMe73mCec+4XRSYFM5tkZteZ2Y7A5UA7YIykDyWdF2Hbm4GrzawLsAdwsaSuKcp9amY9w+Hm0rwIV3K7tG7A6Xu046nRc5jyw4q4w3HOZYlID6+Z2RgzuxI4A2gE3BthnYVmNiEcXwVMI+jn2WWJqw/ZicZ1qnP9q1PYutUrnZ1z0R5e6yPpDklzgZuAoZTwy11Se2A3YGyKxf0kTZI0QlK3ItYfImmcpHGLFy8uya5dGg1q5fGnw7swcd5yXhg3L+5wnHNZIF1F8/9JmgU8ACwA+pvZvmb2gJktiboDSXWBl4ErzGxl0uIJQDsz60HwxPSrqbZhZkPNLN/M8ps1834BytKxu7Wi7w6Nue3t6SxbszHucJxzMUt3prABOCz8Mv6XmZW4N3hJeQQJYZiZ/Td5uZmtNLPV4fhbQJ6kpiXdjys9Keh3YfX6zdw2Ynrc4TjnYpauovkmMyv1rSkKmuJ8FJhmZncUUaZFWA5JfcN4lpZ2n650Om9Xj3P22oEXxs1j/NxlcYfjnItRafpojqo/cDpwQMItp4dLukDSBWGZE4ApkiYB9wAnmz9mG4vLDuxEywY1+fMrU9i8ZWvc4TjnYpK2j+bwV3xrMytxLaSZjSLo1zldmXuJcCeTy7w6Napx41FdueCZCTw1ei5n77VD3CE552KQ9kwh/NWesvLXVT6HdmvBvp2bccd73/LTyvVxh+Oci0GUy0djJPXJeCQudpK4aWA3Nm7Zyi1vTos7HOdcDKIkhf2B0ZJmSZos6StJ3v5RJdW+aR0u2m9HXp+0gM9mRr7z2DlXSURJCocBOwIHAEcBR4Z/XSV1wb470q5JbW54bQrrN22JOxznXDmK0nT2XDObC6wDLGFwlVTNvFxuPro7sxev4XcPjmbesrVxh+ScKydRmrkYKGkG8B3wMTAHGJHhuFzM9u3cjEfOyGfO0jUcde8oPv7WmxdxriqIcvnobwStnH5rZjsQ9Nf8WUajclnhoK7b8fole9Gifk0GP/4F93wwwxvOc66Si5IUNpnZUiBHUo6ZjQR6ZjgulyXaN63DKxf155ierbjjvW8596lxrFjrHfM4V1lFSQrLw0btPgGGSbqboK8EV0XUqp7LHSf24Oaju/HpjMUcde8opi5IbtvQOVcZREkKRxNUMl8JvA3Mwu8+qnIkcUa/9jw/pB8bNm/h2Ps/4+XxJW4j0TmX5aLcfbTGzLaY2WYze9LM7gkvJ7kqqHe7Rrxx6d7s1rYhV/9nEte/+hUbNvttq85VFun6U1glaWWKYZUkv3ZQhTWrV4Nnztmd8/fpwDNjvuekh8awcMW6uMNyzpWBdE1n1zOz+imGemZWvzyDdNmnWm4O1x3ehQdO68WMn1Zx5D2j+NyfgHauwovynELbVEN5BOey32G7tOS1S/aiUZ3qDHp0LA9+PAtv/dy5iitKRfObCcMHwGz84TWXoGPzurx2cX8O26Ul/xgxnQueGc+q9X7bqnMVUZSK5l0Shk5AX2BU5kNzFUmdGtW495TduP6ILrw/bRFH3/sZc5euiTss51wJlbjnNTObAHhT2u43JHHu3h149tzdWbpmI1e/OMmfgHaugolSp3BVwnCNpGeBYhvCkdRG0khJ0yR9LenyFGUk6R5JM8NmuXuV8nW4LLJ7hyb8+YgujJv7My9P8GcZnKtIopwp1EsYahDULRwdYb3NwNVm1oWg7aSLJXVNKnMY0CkchgAPRIzbZbkTerWmd7tG3DpiOsvXbow7HOdcRFHqFG5KGP5uZsPMrNi+Gs1sYXipCTNbBUwDWiUVOxp4ygJjgIaSWpbidbgsk5MjbjmmOyvWbeKf73wTdzjOuYiqFVdA0vAUs1cA44CHoiQISe2B3YCxSYtaAfMSpueH8xYmrT+E4EyCtm39btiKokvL+gzesz2PffYdJ+a3oWebhnGH5JwrRpTLR98Bq4GHw2El8BPQOZxOK2xM72XgCjNLfhJaKVb5Tc2kmQ01s3wzy2/WrFmEkF22uOKgTjSrW4PrX/2KLV7p7FzWi5IUdjOzU83s9XAYBPQ1s4uBtBXDkvIIEsIwM/tviiLzgTYJ062BBRFjdxVAvZp53HBkV6b8sJJhY+fGHY5zrhhRkkKzxCeYw/Gm4WSRNYiSBDwKTDOzO4ooNhw4I7wLaQ9ghZktLKKsq6CO3LUle3Vsyv975xsWr9oQdzjOuTSiJIWrgVHh7aUfAZ8Cv5dUB3gyzXr9gdOBAyRNDIfDJV0g6YKwzFsET0jPJLgUdVFpX4jLXpK4+ehubNi0lVvfmhZ3OM65NIqtaDaztyR1AnYmqAOYnlC5fFea9UaRus4gsYwBF0cP11VUHZrVZcg+Hbh35ExO7NOGPTo0iTsk51wKUZ9o7g10A3YFTpR0RuZCcpXVxft3pHWjWtzw6hQ2bt4adzjOuRSiPNH8NPAvYC+C5i36APkZjstVQrWq53LTwG7MWLSaxz77Lu5wnHMpFHv5iCABdDVvD9mVgQO7bMfBXbfj7vdnMLDH9mzfsFbcITnnEkS5fDQFaJHpQFzVceNRXTGMm1+fGncozrkkUZJCU2CqpHckDS8YMh2Yq7xaN6rNpQd04u2vf2Tk9EVxh+OcSxDl8tFfMx2Eq3rO27sD/50wnxuHf02/HZtQMy837pCcc0RrEO/jVEN5BOcqr+rVcvjb0d35ftlaHvhoVtzhOOdCRSYFSaPCv6skrUwYVklKbsPIuRLbs2NTBvbYngc+nsV3S7yXNueyQZFJwcz2Cv/WM7P6CUM9M6tffiG6yuz6I7pQPTeHG4d/jd/g5lz80p0p1A4btCuY3knSlZKOLZ/QXFXQvH5Nrj6kM598u5gRU36MOxznqrx0dQpvA+0BJHUERgMdgEsk/SPzobmq4vQ92tG1ZX1ufn0qqzdsjjsc56q0dEmhkZnNCMfPBJ4zs0sJutA8IuORuSqjWm4OfzumOz+uXM89H8wofgXnXMakSwqJF3gPAN4DMLONgDdc48pU73aNOLlPGx4d9R3f/Lgq7nCcq7LSJYXJkv4l6UqgI/AugCTvU9FlxB8G7Ey9mtW44dUpXunsXEzSJYXzgCUE9QqHmNnacH5XggbynCtTjetU59oBO/PFnGW8POGHuMNxrkpKd0vqOjP7h5ldbmaTEuZ/bmZPl094rqo5Mb95apL+AAAXD0lEQVQNPds05La3p7PGK52dK3dR+1Nwrlzk5IgbjuzK4lUbeOhjf9LZufLmScFlnd7tGnHkri0Z+ulsFq5YF3c4zlUp6R5eezr8e3lpNizpMUmLJE0pYvl+klYk9N/8l9Lsx1VOfxywM1u3wr/e+TbuUJyrUtKdKfSW1A44W1IjSY0ThwjbfgIYUEyZT82sZzjcHDVoV/m1aVybs/q35+UJ85nyw4q4w3GuykiXFB4keKp5Z2B80jCuuA2b2SfAsjKI0VVRF+3fkcZ1qnPLm1P9FlXnykm6u4/uMbMuwGNm1sHMdkgYOpTR/vtJmiRphKRuRRWSNETSOEnjFi9eXEa7dtmuQa08rjioE2NmL+P9ad4Zj3PlIUp/ChdK6iHpknDYtYz2PQFoZ2Y9gH8Dr6aJYaiZ5ZtZfrNmzcpo964iOKVvWzo0q8Otb01j0xZ/kN65TCs2KUi6DBgGNA+HYZIu3dYdm9lKM1sdjr8F5Elquq3bdZVLXm4OfzqsC7OXrGHYmLlxh+NcpRflltRzgd3N7C9m9hdgD4KnnbeJpBaSFI73DWNZuq3bdZXPgV2as+eOTbj7gxmsWLcp7nCcq9SiJAUBWxKmt4Tz0q8kPUfQ3PZOkuZLOkfSBZIuCIucAEyRNAm4BzjZvDbRpSCJPx/RheXrNnHfyJlxh+NcpVYtQpnHgbGSXgmnjwEeLW4lMzulmOX3AvdG2L9zdNu+Acf3as0Tn81h0O7taNukdtwhOVcpRalovgM4i+D20p+Bs8zsrkwH5lyyaw7Zidwccdvb0+MOxblKK8qZAmY2geBuIedi06JBTYbs04G7P5jB2XOX0btdlGconXMl4W0fuQrl/H070LxeDf72xjR/oM25DPCk4CqU2tWrcc0hOzFx3nJen7ww7nCcq3SiPKdwW5R5zpWX43u3pkvL+tw2YjrrN20pfgXnXGRRzhQOTjHvsLIOxLmocnPE9Ud04Yfl63ji8zlxh+NcpZKu6ewLJX1F8JzB5IThO2By+YXo3G/179iUA3Zuzn0fzmTp6g1xh+NcpZHuTOFZ4ChgePi3YOhtZoPKITbn0vrT4TuzdtMW7np/RtyhOFdppGsldYWZzQkfQpsPbAIMqCupbXkF6FxROjavx6l92/LsF98zc9GquMNxrlKIUtF8CfAT8B7wZji8keG4nIvkioM6UTsvl1vf8gfanCsLUSqarwB2MrNuZrZLOJRV89nObZMmdWtw0f4d+WD6Ij6buSTucJyr8KIkhXmA94fostZZ/dvTqmEtbnlzGlu2+gNtzm2LKElhNvCRpOskXVUwZDow56KqmZfLHw/bmWkLV/LyhPlxh+NchRYlKXxPUJ9QHaiXMDiXNY7atSU92zTkX+98w9qNm+MOx7kKq9gG8czspvIIxLltIYkbjuzC8Q+M5qGPZ3PlwZ3jDsm5CqnYpCBpJMGtqL9iZgdkJCLnSql3u8YcsUtLHvx4Fkfu2pJO2/kJrXMlFaXp7GsSxmsCxwN+fu6y0o0DuzJ69lIuf34ir17cn+rVvM1H50oiSic74xOGz8zsKmD3cojNuRJrXq8mtx2/K1MXruT2976JOxznKpwoD681ThiaSjoUaBFhvcckLZI0pYjlknSPpJlhm0q9ShG/c79xcNftOKVvW4Z+MpvRs5bGHY5zFUqUc+vxwLjw72jgauCcCOs9AQxIs/wwoFM4DAEeiLBN5yK54cgutG9Sh6tfnMiKtZviDse5CiPK5aMdzKxD+LeTmR1iZqMirPcJQb/ORTkaeMoCY4CGklpGD925otWuXo27TurJT6s2cMNrKU9WnXMpRLl8lCfpMkkvhcMlkvLKYN+tCJ6WLjA/nJcqhiGSxkkat3jx4jLYtasKerRpyBUHdmL4pAW8+r8f4g7HuQohyuWjB4DewP3h0JuyudSjFPNStlFgZkPNLN/M8ps1a1YGu3ZVxUX7dyS/XSNueHUK839eG3c4zmW9KEmhj5mdaWYfhsNZQJ8y2Pd8oE3CdGtgQRls17lCuTnizpN6YsBVL0zytpGcK0aUpLBF0o4FE5I6AGXRMe5w4IzwLqQ9gBVm5j2xuzLXpnFtbhrYjS/mLOOhT2bFHY5zWS3Kw2u/B0ZKmk1wyacdcFZxK0l6DtgPaCppPnAjkAdgZg8CbwGHAzOBtVG26VxpHderFR9OX8Qd737L3h2bsUvrBnGH5FxWklnxp9OSagA7ESSF6WYWW6e4+fn5Nm7cuLh27yqw5Ws3MuCuT6ldI5c3L92bWtVz4w7JuXIjabyZ5RdXLsrdR7nAoQS/+g8ELvams11F1LB2dW4/sQezF6/h729NjTsc57JSlDqF14HBQBO86WxXwfXv2JTz9t6BZ8Z8z4fTf4o7HOeyTpQ6hdbe/aarTK45dCc+nbGEP7w0mbev2IemdWvEHZJzWSPKmcIISYdkPBLnykmNarncc8purFy/mT++NJko9WrOVRVRksIY4BVJ6yStlLRK0spMB+ZcJnXerh7XHbYzH0xfxLCx38cdjnNZI0pSuB3oB9Q2s/pmVs/M6mc4Lucy7sx+7dm7U1NueXMqsxavjjsc57JClKQwA5hifo7tKpmcHPGv3/WgVl4uVzw/kY2bt8YdknOxi5IUFgIfSbpO0lUFQ6YDc648bFe/Jrcetytf/bCCuz/4Nu5wnItdlKTwHfABUJ1fbketm8mgnCtPA7q34KT8Ntz/0Sy++C5da+/OVX7F3pJqZjclTkuqCRyVsYici8FfjurKmO+WcuEz4+nSsmpVmbVpXJu/H9OdnJxUDRe7qibKcwoFTzUfApwS/h0F/CeDcTlXrurUqMZ9p/bi1hHTWLepLNp7rBjWbNjMqJlLOGKXluzVqWnc4bgskDYpSNoHOBU4AvgC6A90MDNvmN5VOt1bNWDYuXvEHUa5Wr9pC/1u/YBnxsz1pOCANHUKYcum/wA+A7qa2fHAOk8IzlUeNfNyObFPG96b9hM/rlgfdzguC6SraH6ZoHvMk4CjJNWhiJ7RnHMV12l927HVjOe+8If4XJqkYGaXA+2BO4D9gW+BZpJOlOR3HzlXSbRtUpt9OzfjuS++Z9MWf1ajqkt7S6oFPjSz8wgSxKnAMcCczIfmnCsvp+/RjkWrNvD+VG85tqqL8pwCAGa2ycxeN7NT+XXfys65Cm6/nZrTqmEtnh4zN+5QXMwiJ4VEZrYuSjlJAyR9I2mmpGtTLB8sabGkieFwbmnicc5tm9wccerubfl81lJmLvJ2oKqyUiWFKMJnG+4DDgO6AqdI6pqi6Atm1jMcHslUPM659E7q04a8XDFsrJ8tVGUZSwpAX2Cmmc02s43A88DRGdyfc24bNK1bg8O6t+Sl8fNZu3Fz3OG4mKRNCpJaS7pG0muSvpT0iaT7JR0hqbiE0gqYlzA9P5yX7HhJkyW9JCllXYWkIZLGSRq3ePHiYnbrnCut0/u1Y9X6zbw+aUHcobiYpHt47XHgMWAjcBtBExcXAe8DA4BR4RPPRW4ixbzk5xxeB9qH3X2+DzyZakNmNtTM8s0sv1mzZml26ZzbFvntGrHTdvV4avRc75GuikrXzMXtZjYlxfwpwH8lVQfapll/Pr++S6k18KufH2a2NGHyYYLk45yLiSQG9WvHDa9OYeK85ezWtlHcIblylu7htVQJIXH5RjObmabIl0AnSTuECeRkYHhiAUktEyYHAtOKD9k5l0nH7taKOtVzeWaMP+FcFRXbSqqkr/jtZZ8VwDjglqRf+4XMbLOkS4B3gFzgMTP7WtLNwDgzGw5cJmkgsBlYBgwu9StxzpWJujWqcWyvVrw4bj7XH9GFRnWqxx2SK0cq7rqhpH8CW4Bnw1knh39XAnuZWbn2rZCfn2/jxo0rz106V+VM/3ElA+76lD8f3oXz9ukQdziuDEgab2b5xZWL0p9CfzPrnzD9laTPzKy/pEGlD9E5l612blGfPu0b8czYuZyz1w7eAU8VEuU5hbqSdi+YkNSXX7rj9JuZnaukBu3RjrlL1/LpzCVxh+LKUZQzhXOBx8KWUUVw2eicsCntWzMZnHMuPgO6t6BJneo8M2Yu+3b2W8Griih9NH8J7CKpAUEdxPKExS9mLDLnXKxqVMvlpD5tePDjWfywfB2tGtaKOyRXDoq9fCSpgaQ7gA+A9yXdHiYI51wld+rubTHgee+Ap8qIUqfwGLAKODEcVgKPZzIo51x2aN2oNgfs1JznvpjHxs3eAU9VECUp7GhmN4YN2802s5sAv0fNuSpiUL92LFm9gXe+/jHuUFw5iJIU1knaq2BCUn8gUn8KzrmKb99OzWjTuBbPeAc8VUKUpHABcJ+kOZLmAPcC52c0Kudc1sjJEaft3o6x3y3j259WxR2Oy7Bik4KZTTKzHsCuwK5mthvQKeOROeeyxon5baheLYdhfrZQ6ZWkj+aVZrYynLwzQ/E457JQ4zrVOWKXlrw84QfWbPBnViuz0va85s+8O1fFDNqjHas3bOa1id4BT2VW2qTgvW84V8X0atuQLi3r89ToOd4BTyVW5BPNRTSZDcFZwnYZi8g5l5Ukcfoe7fjTK18x4fuf6d2ucdwhuQxI18zFkeUWhXOuQji65/bc+tY0nhnzvSeFSird5aPvzWxuUQOAJK9bcK4KqVOjGsf1asWbkxeydPWGuMNxGZAuKYyUdKmkX/XDLKm6pAMkPQmcmdnwnHPZZtAe7di4ZSv/GT8/7lBcBqRLCgMIelx7TtICSVMlzQZmAKcAd5rZE+UQo3Mui3Tarh6779CYYWPnsmWrVzhXNkUmBTNbb2b3h72utQMOBHqZWTszO8/MJha3cUkDJH0jaaaka1MsryHphXD5WEntt+G1OOfKyen92jFv2To++XZx3KG4MhbpllQz22RmC5P6UkhLUi5wH3AY0BU4RVLXpGLnAD+bWUeCB+Jui7p951x8DunagqZ1a3h7SJVQlJ7XSqsvMNPMZgNIeh44GpiaUOZo4K/h+EvAvZJkfhO0c1mterUcTunbhntHzuTgOz6OO5wq46Q+bTh378w2Up3JpNAKmJcwPR/YvagyZrZZ0gqgCfCrTmElDQGGALRt2xbnXPzO3LM9P/y8jvWbt8QdSpXRtG6NjO8jk0kh1e2qyWcAUcpgZkOBoQD5+fl+FuFcFmhatwZ3nNQz7jBcGSttMxdRzAfaJEy3BpIbTSksI6ka0ABYlsGYnHPOpZHJpPAl0EnSDpKqAycDw5PKDOeXZx1OAD70+gTnnItPxi4fhXUElwDvALnAY2b2taSbgXFmNhx4FHha0kyCM4STMxWPc8654mWyTgEzewt4K2neXxLG1wO/y2QMzjnnosvk5SPnnHMVjCcF55xzhTwpOOecK+RJwTnnXCFVtDtAJS0GStvgSlOSnpbOEtkaF2RvbB5XyXhcJVMZ42pnZs2KK1ThksK2kDTOzPLjjiNZtsYF2Rubx1UyHlfJVOW4/PKRc865Qp4UnHPOFapqSWFo3AEUIVvjguyNzeMqGY+rZKpsXFWqTsE551x6Ve1MwTnnXBqeFJxzzhWqdElB0u8kfS1pq6Qib92SNEfSV5ImShqXML+xpPckzQj/NiqvuCS1kTRS0rSw7OUJy/4q6Ycw3omSDi+vuMJyAyR9I2mmpGsT5u8gaWx4vF4Im0kvi7iKfR8k7Z9wPCZKWi/pmHDZE5K+S1hWJr3BRP18SNqSsO/hCfPjPF49JY0O3+/Jkk5KWFamx6uoz0vC8hrh658ZHo/2CcuuC+d/I+nQbYmjFHFdJWlqeHw+kNQuYVnK97Sc4hosaXHC/s9NWHZm+L7PkHRm8rolZmaVagC6ADsBHwH5acrNAZqmmP9P4Npw/FrgtvKKC2gJ9ArH6wHfAl3D6b8C18RxvAiaPp8FdACqA5MS4noRODkcfxC4sIziKtH7ADQmaH69djj9BHBCBo5XpLiA1UXMj+14AZ2BTuH49sBCoGFZH690n5eEMhcBD4bjJwMvhONdw/I1gB3C7eSWY1z7J3yGLiyIK917Wk5xDQbuTbFuY2B2+LdRON5oW+KpdGcKZjbNzL7Zhk0cDTwZjj8JHLPtUUWLy8wWmtmEcHwVMI2gH+uMiXi8+gIzzWy2mW0EngeOliTgAOClsFyZHS9K/j6cAIwws7VltP+ilPrzEffxMrNvzWxGOL4AWAQU+4RrKaT8vKSJ9yXgwPD4HA08b2YbzOw7YGa4vXKJy8xGJnyGxhD0GJlpUY5XUQ4F3jOzZWb2M/AeMGBbgql0SaEEDHhX0nhJQxLmb2dmCyH4kgaaxxFceDq9GzA2YfYl4WntY2V1WSuiVsC8hOn54bwmwHIz25w0vyyU9H04GXguad7fw+N1p6Sy6vE8alw1JY2TNKbgkhZZdLwk9SX4VTorYXZZHa+iPi8py4THYwXB8YmybibjSnQOMCJhOtV7Wp5xHR++Py9JKujquMyPV0Y72ckUSe8DLVIs+rOZvRZxM/3NbIGk5sB7kqab2SdZEBeS6gIvA1eY2cpw9gPA3wiS2d+A24GzyykupZhnaeZHki6uqNsIt9MS2IWgl78C1wE/EnzxDQX+CNxcjnG1DT9fHYAPJX0FrExRLq7j9TRwppltDWeX+nil2kWKecmvMyOfqWJE3rakQUA+sG/C7N+8p2Y2K9X6GYjrdeA5M9sg6QKCs6wDIq5bIhUyKZjZQWWwjQXh30WSXiE4hfsE+ElSSzNbGP7zLCrPuCTlESSEYWb234Rt/5RQ5mHgjXKMaz7QJmG6NbCAoGGuhpKqhb/2CuZvc1ySSvI+nAi8YmabEra9MBzdIOlx4JryjCvh8zVb0kcEZ30vE/PxklQfeBO43szGJGy71McrhaI+L6nKzJdUDWhAUCcUZd1MxoWkgwgS7b5mtqFgfhHvaVkkhWLjMrOlCZMPA7clrLtf0rofbUswVfLykaQ6kuoVjAOHAFPCxcOBghr8M4HIv/DLIC4R9Fs9zczuSFrWMmHyWH6Jtzx8CXRScOdMdYJLNcMtqOkaSXA9H8r2eJXkfTiFpEtHBccrPKbHUHbHq9i4JDUquPwiqSnQH5ga9/EK37tXgKfM7D9Jy8ryeKX8vKSJ9wTgw/D4DAdODu9O2gHoBHyxDbGUKC5JuwEPAQPNbFHC/JTvaTnGlfj/P5CgvhGCs+NDwvgaEXyXJZ4xl1xZ1qJnw0DwhTkf2AD8BLwTzt8eeCsc70BQwz8J+JrgMkrB+k2AD4AZ4d/G5RjXXgSnfpOBieFweLjsaeCrcNlwoGV5xRVOH05wN9SspOPVgeCfdibwH6BGGcWV8n0gOKV/JKFce+AHICdp/Q/D4zUFeAaoW15xAXuG+54U/j0nG44XMAjYlPDZmgj0zMTxSvV5IbgcNTAcrxm+/pnh8eiQsO6fw/W+AQ4ri+NTgrjeD/8PCo7P8OLe03KK61aC76pJBD8sdk5Y9+zwOM4EztrWWLyZC+ecc4Wq5OUj55xzqXlScM45V8iTgnPOuUKeFJxzzhXypOCcc66QJwXnSiCppcyJBS1aSrpCUu2443NuW/ktqc6VgKTVZlY3xfw5BK3MLin/qJwrO36m4Nw2knQZwcN+IyWNDOc9EDae9rWkm+KN0Lno/EzBuRKQtIXgidYCt5rZC8lnCpIam9kySbkETxhfZmaTyz9i50qmQjaI51yM1plZlF7JTgybZK9G0HlSV4ImSpzLap4UnCtjYUNu1wB9zOxnSU8QtPXjXNbzOgXnysYqgi5UAeoDa4AVkrYDDostKudKyM8UnCuZWpImJky/bWbXEnRMM0LSQjPbX9L/CFq1nA18FkegzpWGVzQ755wr5JePnHPOFfKk4JxzrpAnBeecc4U8KTjnnCvkScE551whTwrOOecKeVJwzjlX6P8D3A2EXgUHHJUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x25b9aced518>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "svs_used = [41, 34, 27, 21, 16, 10, 8, 5, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1]\n",
    "plt.plot(ets, np.log(svs_used))\n",
    "plt.xlabel('Eta')\n",
    "plt.ylabel('(Log) Amount of Singular Values Used')\n",
    "plt.title('Singular Value Thresholding SV Used by Eta')\n",
    "plt.savefig('Graphs/SVT_Used.png', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((100, 6), (6, 100))"
      ]
     },
     "execution_count": 236,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "U.shape, Vh.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "metadata": {},
   "outputs": [],
   "source": [
    "U_new = U[::-1]\n",
    "Vh_new = Vh[::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True])"
      ]
     },
     "execution_count": 251,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Vh_new[0] == Vh[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}