Numerical Linear Algebra project.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Intel(R) Data Analytics Acceleration Library (Intel(R) DAAL) solvers for sklearn enabled: https://intelpython.github.io/daal4py/sklearn.html\n"
     ]
    }
   ],
   "source": [
    "import pickle\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn.metrics import r2_score\n",
    "from scipy.stats.stats import pearsonr\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.metrics import mean_absolute_error\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.linear_model import Lasso\n",
    "from scipy.linalg import lstsq\n",
    "import timeit\n",
    "from scipy import linalg\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy\n",
    "from sklearn.decomposition import TruncatedSVD\n",
    "from sklearn.decomposition import NMF\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#to Run this you need to download the follwing files and locate them in the code dirctory:\n",
    "#https://drive.google.com/file/d/1ubvNbmcf9I6rUfksey4oJAZ66Jd-rcM2/view?usp=sharing\n",
    "#https://drive.google.com/file/d/1FMI6bnzDydZ1pfMmBYg10fJQ2ffryZgD/view?usp=sharing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#evalute the model fucntion- MSE\n",
    "def compute_mean_and_std_test (y_predicted, y_observed):\n",
    "    MSE = mean_squared_error(y_predicted, y_observed)\n",
    "    #pearson = pearsonr(np.array(y_predicted).reshape((-1,)), np.array(y_observed).reshape((-1,)))\n",
    "    #r2 = r2_score(y_predicted, y_observed)\n",
    "    #MAE = mean_absolute_error(y_predicted, y_observed)\n",
    "#     print(\"pearson:\",pearson)\n",
    "#     print(\"R2:\",r2)\n",
    "    print(\"MSE:\",MSE)\n",
    "#     print(\"MAE:\",MAE)   \n",
    "\n",
    "    return MSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#compute the matrix rank and the its condition number\n",
    "def matrix_rank_and_condition_number (M, tol=None, hermitian=False):\n",
    "    M = np.asarray(M)\n",
    "    if M.ndim < 2:\n",
    "        return int(not np.all(M==0))\n",
    "    S = np.linalg.svd(M, compute_uv=False, hermitian=hermitian)\n",
    "    if tol is None:\n",
    "        tol = S.max(axis=-1, keepdims=True) * np.max(M.shape[-2:]) * np.finfo(S.dtype).eps\n",
    "    else:\n",
    "        tol = np.asarray(tol)[..., newaxis]\n",
    "    return np.count_nonzero(S > tol, axis=-1), S[0]/S[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define randomized SVD function\n",
    "def rSVD(X,r,q,p):\n",
    "    # Step 1: Sample column space of X with P matrix\n",
    "    ny = X.shape[1]\n",
    "    P = np.random.randn(ny,r+p)\n",
    "    Z = X @ P\n",
    "    for k in range(q):\n",
    "        Z = X @ (X.T @ Z)\n",
    "\n",
    "    Q, R = np.linalg.qr(Z,mode='reduced')\n",
    "\n",
    "    # Step 2: Compute SVD on projected Y = Q.T @ X\n",
    "    Y = Q.T @ X\n",
    "    UY, S, VT = np.linalg.svd(Y,full_matrices=0)\n",
    "    U = Q @ UY\n",
    "\n",
    "    return U, S, VT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#diffrent types of LS solvers \n",
    "def ls_qr(A, b):\n",
    "    #     q, r = linalg.qr(A, mode='economic')\n",
    "    #     _, n = r.shape\n",
    "    #     X = np.linalg.solve(r, q.T @ b)\n",
    "    _, X, _ = linalg.lapack.dgels(A, b)\n",
    "    return X\n",
    "\n",
    "def ls_cholesky(A, b):\n",
    "    XT_X = A.T @ A\n",
    "    XT_b = A.T @ b\n",
    "    c, low = linalg.cho_factor(XT_X)\n",
    "    X = linalg.cho_solve((c, low), XT_b)\n",
    "    return X\n",
    "\n",
    "def ls_given_reduced_Truncated_SVD (u, s, b):\n",
    "    u_T = u.T\n",
    "    s_inv = 1/s\n",
    "    X = np.diag(s_inv) @ (u_T @ b)\n",
    "    return X\n",
    "\n",
    "def ls_given_SVD (u, s, v_T, b):\n",
    "    u_T = u.T\n",
    "    v = v_T.T\n",
    "    s_inv = 1/s\n",
    "    X = v @ ( np.diag(s_inv) @ (u_T @ b))\n",
    "    return X\n",
    "def ls_using_pesudo_inverse  (A, b):\n",
    "    A_T_A_inv = linalg.inv (A.T @ A)\n",
    "    X = A_T_A_inv @ (A.T @ b)\n",
    "    return X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#apply the certain model type \n",
    "def train_and_test_model (X_train, X_test, y_train, y_test, model_type, u=None, s=None ,vh=None):\n",
    "    mdl, predicted_y_train, predicted_y_test = None, None, None\n",
    "    start, stop = None, None\n",
    "    if (model_type == \"linear_regression\"):\n",
    "        start = timeit.default_timer()\n",
    "        mdl = LinearRegression().fit(X_train, y_train)\n",
    "        stop = timeit.default_timer()\n",
    "        print(model_type+' Time: ', stop - start) \n",
    "        predicted_y_test = mdl.predict(X_test)\n",
    "        predicted_y_train = mdl.predict(X_train)\n",
    "    elif (model_type == 'lasso_regression'):\n",
    "        start = timeit.default_timer()\n",
    "        mdl = Lasso(alpha=0.0001, max_iter=1000)\n",
    "        mdl.fit(X_train, y_train)\n",
    "        stop = timeit.default_timer()\n",
    "        print(model_type+' Time: ', stop - start) \n",
    "        predicted_y_test = mdl.predict(X_test)\n",
    "        predicted_y_train = mdl.predict(X_train)\n",
    "    elif (model_type == 'LS_regression'):\n",
    "        X_train_new = np.concatenate((X_train, np.full((X_train.shape[0], 1), 1)), axis=1)\n",
    "        start = timeit.default_timer()\n",
    "        p, res, rnk, s = lstsq(X_train_new, y_train)\n",
    "        stop = timeit.default_timer()\n",
    "        print(model_type+' Time: ', stop - start)\n",
    "        X_test_new = np.concatenate((X_test, np.full((X_test.shape[0], 1), 1)), axis=1)\n",
    "        predicted_y_test = np.matmul(X_test_new, p)\n",
    "        predicted_y_train = np.matmul(X_train_new, p)\n",
    "    elif (model_type == 'LS'):\n",
    "        start = timeit.default_timer()\n",
    "        p, res, rnk, s = lstsq(X_train, y_train, lapack_driver='gelss')\n",
    "        stop = timeit.default_timer()\n",
    "        print(model_type+' Time: ', stop - start)\n",
    "        predicted_y_test = np.matmul(X_test, p)\n",
    "        predicted_y_train = np.matmul(X_train, p)\n",
    "    elif(model_type == 'LS_QR'):\n",
    "        start = timeit.default_timer()\n",
    "        p = ls_qr(X_train, y_train)\n",
    "        stop = timeit.default_timer()\n",
    "        print(model_type+' Time: ', stop - start)                \n",
    "        predicted_y_test = np.matmul(X_test, p)\n",
    "        predicted_y_train = np.matmul(X_train, p)\n",
    "    elif(model_type == 'LS_cholesky'):\n",
    "        start = timeit.default_timer()\n",
    "        p = ls_cholesky(X_train, y_train)\n",
    "        stop = timeit.default_timer()\n",
    "        print(model_type+' Time: ', stop - start)\n",
    "        predicted_y_test = np.matmul(X_test, p)\n",
    "        predicted_y_train = np.matmul(X_train, p)\n",
    "    elif(model_type == \"LS_given_reduced_Truncated_SVD\"):\n",
    "        start = timeit.default_timer()\n",
    "        p = ls_given_reduced_Truncated_SVD (u, s, y_train)\n",
    "        stop = timeit.default_timer()\n",
    "        print(model_type+' Time: ', stop - start)\n",
    "        predicted_y_test = X_test @ p\n",
    "        predicted_y_train = X_train @ p\n",
    "    elif (model_type == \"LS_given_SVD\"):\n",
    "        start = timeit.default_timer()\n",
    "        p = ls_given_SVD (u, s, vh, y_train)\n",
    "        stop = timeit.default_timer()\n",
    "        print(model_type+' Time: ', stop - start)\n",
    "        predicted_y_test = X_test @ p\n",
    "        predicted_y_train = X_train @ p\n",
    "    elif (model_type == \"LS_using_pesudo_inverse\"):\n",
    "        start = timeit.default_timer()\n",
    "        p = ls_using_pesudo_inverse (X_train, y_train)\n",
    "        stop = timeit.default_timer()\n",
    "        print(model_type+' Time: ', stop - start)\n",
    "        predicted_y_test = X_test @ p\n",
    "        predicted_y_train = X_train @ p\n",
    "    elif (model_type == \"LS_RRQR\"):\n",
    "        start = timeit.default_timer()\n",
    "        p, res, rnk, s = lstsq(X_train, y_train, lapack_driver='gelsy')\n",
    "        stop = timeit.default_timer()\n",
    "        print(model_type+' Time: ', stop - start)\n",
    "        predicted_y_test = np.matmul(X_test, p)\n",
    "        predicted_y_train = np.matmul(X_train, p)\n",
    "\n",
    "        \n",
    "    print(\"test\")\n",
    "    test_reaults = compute_mean_and_std_test (predicted_y_test, y_test)\n",
    "    print(\"train\")\n",
    "    train_reaults = compute_mean_and_std_test (predicted_y_train, y_train)\n",
    "    return test_reaults, train_reaults, stop - start"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "seq_PATH = \"1-s2.0-S1097276517308730-mmc2.xlsx\"\n",
    "normalized_levels_PATH = \"1-s2.0-S1097276517308730-mmc3.xlsx\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "filename = 'features_1-7kmers.sav'\n",
    "Fetures = pickle.load(open(filename, 'rb'))\n",
    "features = Fetures.toarray()\n",
    "del Fetures\n",
    "y = np.matrix(pd.read_excel (A_minus_normalized_levels_PATH)) [1:,1:].astype('float32')\n",
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(features, y, test_size=0.22, random_state=31)\n",
    "y_train_without_y0 = y_train[:,1:]\n",
    "y_test_without_y0 = y_test[:,1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def svd_iterations (X_train, X_test, y_train, y_test, ranks, X_with_y0_OR_without):\n",
    "    y_train_without_y0 = y_train[:,1:]\n",
    "    y_test_without_y0 = y_test[:,1:]\n",
    "    if(X_with_y0_OR_without == \"X_with_y0\"):\n",
    "        X_train = np.concatenate((X_train, y_train[:,0]), axis=1)\n",
    "        X_test = np.concatenate((X_test, y_test[:,0]), axis=1)\n",
    "\n",
    "    \n",
    "    u, s, vh = np.linalg.svd(X_train, full_matrices=False)\n",
    "    v = vh.T\n",
    "    \n",
    "    \n",
    "    solutions_types = [\"LS_cholesky\", \"LS_QR\", \"LS_RRQR\", \"LS\", \"LS_using_pesudo_inverse\"]\n",
    "    results_dict ={\"LS_cholesky\": {\"test_reaults\": [], \"train_reaults\": [], \"time\": []},\n",
    "                   \"LS_QR\" : {\"test_reaults\": [], \"train_reaults\": [], \"time\": []},\n",
    "                   \"LS_RRQR\": {\"test_reaults\": [], \"train_reaults\": [], \"time\": []},\n",
    "                   \"LS\" : {\"test_reaults\": [], \"train_reaults\": [], \"time\": []},\n",
    "                   \"LS_using_pesudo_inverse\" : {\"test_reaults\": [], \"train_reaults\": [], \"time\": []},\n",
    "                   \"condition_number\" : []\n",
    "                   }\n",
    "    if(X_with_y0_OR_without == \"X_with_y0\"):\n",
    "        solutions_types = solutions_types+[\"LS_given_reduced_Truncated_SVD\", \"LS_given_SVD\"]\n",
    "        results_dict.update( {\"LS_given_reduced_Truncated_SVD\" : {\"test_reaults\": [], \"train_reaults\": [], \"time\": []},\n",
    "                          \"LS_given_SVD\" : {\"test_reaults\": [], \"train_reaults\": [], \"time\": []}}\n",
    "                       )\n",
    "    \n",
    "    for r in ranks:\n",
    "        print(\"rank: \",r)\n",
    "        #compute the reduced matrix\n",
    "        u_r = u[:,:r]\n",
    "        s_r = s[:r]\n",
    "        v_r = v[:,:r]\n",
    "        results_dict [\"condition_number\"].append(s_r[0]/s_r[r-1])\n",
    "        X_train_svd_r = u_r @ np.diag(s_r)\n",
    "        X_test_svd_r = X_test @ v_r\n",
    "        \n",
    "        if (X_with_y0_OR_without == \"X_without_y0\"):\n",
    "            X_train_svd_r = np.concatenate((X_train_svd_r, y_train[:,0]), axis=1)\n",
    "            X_test_svd_r = np.concatenate((X_test_svd_r, y_test[:,0]), axis=1)\n",
    "         #solve for the different types of solvers  \n",
    "        for solutions_type in solutions_types:\n",
    "            if(solutions_type != \"LS_given_SVD\"):\n",
    "                test_reaults, train_reaults, time = train_and_test_model (X_train_svd_r, X_test_svd_r, y_train_without_y0, y_test_without_y0, solutions_type, u_r, s_r, v_r.T)\n",
    "            else:\n",
    "                test_reaults, train_reaults, time = train_and_test_model (X_train, X_test, y_train_without_y0, y_test_without_y0, solutions_type, u_r, s_r, v_r.T)   \n",
    "            results_dict[solutions_type][\"test_reaults\"].append(test_reaults)\n",
    "            results_dict[solutions_type][\"train_reaults\"].append(train_reaults)\n",
    "            results_dict[solutions_type][\"time\"].append(time)\n",
    "            \n",
    "    return results_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def randomized_svd_iterations (X_train, X_test, y_train, y_test, ranks, X_with_y0_OR_without):\n",
    "    y_train_without_y0 = y_train[:,1:]\n",
    "    y_test_without_y0 = y_test[:,1:]\n",
    "    \n",
    "    if(X_with_y0_OR_without == \"X_with_y0\"):\n",
    "        X_train = np.concatenate((X_train, y_train[:,0]), axis=1)\n",
    "        X_test = np.concatenate((X_test, y_test[:,0]), axis=1)\n",
    "    \n",
    "    solutions_types = [\"LS_cholesky\", \"LS_QR\", \"LS_RRQR\", \"LS\", \"LS_using_pesudo_inverse\"]\n",
    "    results_dict ={\"LS_cholesky\": {\"test_reaults\": [], \"train_reaults\": [], \"time\": []},\n",
    "                   \"LS_QR\" : {\"test_reaults\": [], \"train_reaults\": [], \"time\": []},\n",
    "                   \"LS_RRQR\": {\"test_reaults\": [], \"train_reaults\": [], \"time\": []},\n",
    "                   \"LS\" : {\"test_reaults\": [], \"train_reaults\": [], \"time\": []},\n",
    "                   \"LS_using_pesudo_inverse\" : {\"test_reaults\": [], \"train_reaults\": [], \"time\": []},\n",
    "                   \"condition_number\" : [],\n",
    "                   \"Ramdomized_SVD_time\" : []\n",
    "                   }\n",
    "    if(X_with_y0_OR_without == \"X_with_y0\"):\n",
    "        solutions_types = solutions_types+[\"LS_given_reduced_Truncated_SVD\", \"LS_given_SVD\"]\n",
    "        results_dict.update( {\"LS_given_reduced_Truncated_SVD\" : {\"test_reaults\": [], \"train_reaults\": [], \"time\": []},\n",
    "                          \"LS_given_SVD\" : {\"test_reaults\": [], \"train_reaults\": [], \"time\": []}}\n",
    "                       )\n",
    "    \n",
    "    for r in ranks:\n",
    "        print(\"rank: \",r)\n",
    "        #compute the reduced matrix\n",
    "        start = timeit.default_timer()\n",
    "        p, q = 10, 1\n",
    "        u, s, vh = rSVD(X_train, r, q, p)\n",
    "        u_r = u[:,:-p]\n",
    "        s_r = s[:-p]\n",
    "        v_r = vh.T[:,:-p]\n",
    "        stop = timeit.default_timer()\n",
    "        print(u_r.shape)\n",
    "        print('randomized Time: ', stop - start)\n",
    "        results_dict[\"Ramdomized_SVD_time\"].append(stop - start)\n",
    "        results_dict [\"condition_number\"].append(s_r[0]/s_r[r-1])\n",
    "        X_train_svd_r = u_r @ np.diag(s_r)\n",
    "        X_test_svd_r = X_test @ v_r\n",
    "        \n",
    "        if (X_with_y0_OR_without == \"X_without_y0\"):\n",
    "            X_train_svd_r = np.concatenate((X_train_svd_r, y_train[:,0]), axis=1)\n",
    "            X_test_svd_r = np.concatenate((X_test_svd_r, y_test[:,0]), axis=1)\n",
    "         #solve for the different types of solvers  \n",
    "        for solutions_type in solutions_types:\n",
    "            if(solutions_type != \"LS_given_SVD\"):\n",
    "                test_reaults, train_reaults, time = train_and_test_model (X_train_svd_r, X_test_svd_r, y_train_without_y0, y_test_without_y0, solutions_type, u_r, s_r, v_r.T)\n",
    "            else:\n",
    "                test_reaults, train_reaults, time = train_and_test_model (X_train, X_test, y_train_without_y0, y_test_without_y0, solutions_type, u_r, s_r, v_r.T)   \n",
    "            results_dict[solutions_type][\"test_reaults\"].append(test_reaults)\n",
    "            results_dict[solutions_type][\"train_reaults\"].append(train_reaults)\n",
    "            results_dict[solutions_type][\"time\"].append(time)\n",
    "            \n",
    "    return results_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def NMF_iterations (X_train, X_test, y_train, y_test, ranks):\n",
    "    y_train_without_y0 = y_train[:,1:]\n",
    "    y_test_without_y0 = y_test[:,1:]\n",
    "    \n",
    "    solutions_types = [\"LS_RRQR\", \"LS\"] #can't solve with cholesky because it's not positive definie, and can't solve using QR and pesudo inverse as the matrix is singular \n",
    "    results_dict ={\"LS_RRQR\": {\"test_reaults\": [], \"train_reaults\": [], \"time\": []},\n",
    "                   \"LS\" : {\"test_reaults\": [], \"train_reaults\": [], \"time\": []},\n",
    "                   \"condition_number\" : [],\n",
    "                   \"computed_rank\" : [],\n",
    "                   \"NMF_time\" : []\n",
    "                   }\n",
    "    \n",
    "    for r in ranks:\n",
    "        print(\"rank: \",r)\n",
    "        #compute the reduced matrix\n",
    "        start = timeit.default_timer()\n",
    "        model = NMF(n_components=r, init='random', random_state=0)\n",
    "        X_train_NMF = model.fit_transform(X_train)\n",
    "        stop = timeit.default_timer()\n",
    "        print('NMF Time: ', stop - start)\n",
    "        results_dict[\"NMF_time\"].append(stop - start)\n",
    "        start = timeit.default_timer()\n",
    "        computed_rank, condition_number = matrix_rank_and_condition_number (X_train_NMF, tol=None, hermitian=False)\n",
    "        stop = timeit.default_timer()\n",
    "        print('condition_number and rank compute Time: ', stop - start)\n",
    "        #condition_number = np.linalg.cond(X_train_NMF) \n",
    "        results_dict [\"condition_number\"].append(condition_number)\n",
    "        results_dict [\"computed_rank\"].append(computed_rank)\n",
    "        print(\"condition_number: \", condition_number)\n",
    "        print(\"computed_rank:\", computed_rank)\n",
    "        X_test_NMF = model.transform(X_test)\n",
    "        \n",
    "        X_train_NMF_with_y0 = np.concatenate((X_train_NMF, y_train[:,0]), axis=1)\n",
    "        X_test_NMFa_with_y0 = np.concatenate((X_test_NMF, y_test[:,0]), axis=1)\n",
    "        \n",
    "         #solve for the different types of solvers  \n",
    "        for solutions_type in solutions_types:\n",
    "            test_reaults, train_reaults, time = train_and_test_model (X_train_NMF_with_y0, X_test_NMFa_with_y0, y_train_without_y0, y_test_without_y0, solutions_type)\n",
    "            results_dict[solutions_type][\"test_reaults\"].append(test_reaults)\n",
    "            results_dict[solutions_type][\"train_reaults\"].append(train_reaults)\n",
    "            results_dict[solutions_type][\"time\"].append(time)\n",
    "            \n",
    "    return results_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ranks_SVD = []\n",
    "for i in range(1,10):\n",
    "    ranks_SVD.append(i*10)\n",
    "for i in range(1,31):\n",
    "    ranks_SVD.append(i*100)\n",
    "for i in range (1,11):\n",
    "    ranks_SVD.append(3000+i*300)\n",
    "for i in range(1,8):\n",
    "    ranks_SVD.append(6000+i*500)\n",
    "for i in range(1,12):\n",
    "    ranks_SVD.append(9500+i*1000)\n",
    "ranks_SVD.append(21845)\n",
    "results_dict_truncate_full_SVD_X_with_y0 = svd_iterations(X_train, X_test, y_train, y_test, ranks_SVD, X_with_y0_OR_without=\"X_with_y0\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ranks_randomized = []\n",
    "for i in range(1,10):\n",
    "    ranks_randomized.append(i*10)\n",
    "for i in range(1,31):\n",
    "    ranks_randomized.append(i*100)\n",
    "\n",
    "ranks_randomized = ranks_randomized + [5100, 7000, 11500, 16500, 19500, 20500]\n",
    "ranks_randomized = ranks_randomized + [21845]\n",
    "results_dict_randomized = randomized_svd_iterations(X_train, X_test, y_train, y_test, ranks_randomized, X_with_y0_OR_without=\"X_with_y0\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ranks_NMF = [10,100, 200, 400, 600, 800, 1000, 1200, 1400]\n",
    "results_dict_NMF = NMF_iterations(X_train, X_test, y_train, y_test, ranks_NMF)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train_with_y0 = np.concatenate((X_train, y_train[:,0]), axis=1)\n",
    "X_test_with_y0 = np.concatenate((X_test, y_test[:,0]), axis=1)\n",
    "\n",
    "     \n",
    "u, s, vh = np.linalg.svd(X_train_with_y0, full_matrices=False)\n",
    "\n",
    "solutions_types = [\"LS_QR\", \"LS_RRQR\", \"LS\", \"LS_given_SVD\", \"LS_using_pesudo_inverse\"]\n",
    "results_dict_full_sized_problem = {\"LS_QR\" : {\"test_reaults\": [], \"train_reaults\": [], \"time\": []},\n",
    "                                   \"LS_RRQR\": {\"test_reaults\": [], \"train_reaults\": [], \"time\": []},\n",
    "                                   \"LS\" : {\"test_reaults\": [], \"train_reaults\": [], \"time\": []},\n",
    "                                   \"LS_given_SVD\" : {\"test_reaults\": [], \"train_reaults\": [], \"time\": []},\n",
    "                                   \"LS_using_pesudo_inverse\" : {\"test_reaults\": [], \"train_reaults\": [], \"time\": []}\n",
    "                                   }\n",
    "for solutions_type in solutions_types:\n",
    "    test_reaults, train_reaults, time = train_and_test_model (X_train_with_y0, X_test_with_y0, y_train_without_y0, y_test_without_y0, solutions_type, u, s, vh)   \n",
    "    results_dict_full_sized_problem[solutions_type][\"test_reaults\"].append(test_reaults)\n",
    "    results_dict_full_sized_problem[solutions_type][\"train_reaults\"].append(train_reaults)\n",
    "    results_dict_full_sized_problem[solutions_type][\"time\"].append(time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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h4GvFZRJXQkRERGLhyJeEDup6AAJQWNYBY6UuhoiIiETRaka+Xn/9dchkMuOVhq3BdM0/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\nqYjJFxEREZGKmHwRERERqeh/OoV8wR6gfaoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 650x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig=plt.figure(figsize=(3.25, 1.5), dpi= 200, facecolor='w', edgecolor='k')\n",
    "plt.plot(ranks_SVD[:-2],\n",
    "         results_dict_truncate_full_SVD_X_with_y0[\"LS_cholesky\"][\"test_reaults\"][:-2],\n",
    "           ':X', markersize=2, linewidth=1, label='All solvers - MSE test')\n",
    "\n",
    "\n",
    "plt.plot(ranks_SVD[:-2],\n",
    "         results_dict_truncate_full_SVD_X_with_y0[\"LS_cholesky\"][\"train_reaults\"][:-2],\n",
    "           ':X', markersize=2, linewidth=1, label='All solvers - MSE train')\n",
    "\n",
    "\n",
    "plt.tick_params(axis='both', which='major', labelsize=5)\n",
    "plt.tick_params(axis='both', which='minor', labelsize=5)\n",
    "plt.legend( fontsize=5)\n",
    "plt.xlabel(\"p - The reduced dimension\", fontsize=5)\n",
    "plt.ylabel(\"MSE\", fontsize=5)\n",
    "plt.savefig(\"SVD_MSE_with_y0_plot.png\", dpi=200, bbox_inches = \"tight\")\n",
    "plt.show()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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oAAC8fv0af/31FyZNmlSnerp06YLXr18jN1f0GkCPHj2Cra0tzMzMoK+vj6FD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a9Dewct9M7quBVl1TDV1t/fxeCqU91Tr6a6Tnm+6Jzs4fDr87C5PgF0yCNwGpHrbvVMZmJiYhAV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\nm6mPsQKJIgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 650x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"LS_cholesky\", \"LS_QR\", \"LS_RRQR\", \"LS\", \"LS_using_pesudo_inverse\"\n",
    "\"LS_given_reduced_Truncated_SVD\", \"LS_given_SVD\"\n",
    "fig=plt.figure(figsize=(3.25, 1.75), dpi= 200, facecolor='w', edgecolor='k')\n",
    "plt.plot(ranks_SVD,\n",
    "         results_dict_truncate_full_SVD_X_with_y0[\"LS_cholesky\"][\"time\"],\n",
    "           ':X',  markersize=2, linewidth=1, label='Cholesky solver')\n",
    "plt.plot(ranks_SVD,\n",
    "         results_dict_truncate_full_SVD_X_with_y0[\"LS_QR\"][\"time\"],\n",
    "           ':X',  markersize=2, linewidth=1, label='QR solver')\n",
    "plt.plot(ranks_SVD,\n",
    "         results_dict_truncate_full_SVD_X_with_y0[\"LS\"][\"time\"],\n",
    "           ':X',  markersize=2, linewidth=1, label='SVD solver')\n",
    "plt.plot(ranks_SVD,\n",
    "         results_dict_truncate_full_SVD_X_with_y0[\"LS_using_pesudo_inverse\"][\"time\"],\n",
    "           ':X',  markersize=2, linewidth=1, label='Pesudo inverse solver')\n",
    "plt.plot(ranks_SVD,\n",
    "         results_dict_truncate_full_SVD_X_with_y0[\"LS_given_reduced_Truncated_SVD\"][\"time\"],\n",
    "           ':X',  markersize=2, linewidth=1, label='Straightforward solution for the PCA variant')\n",
    "\n",
    "plt.tick_params(axis='both', which='major', labelsize=5)\n",
    "plt.tick_params(axis='both', which='minor', labelsize=5)\n",
    "plt.legend( fontsize=5)\n",
    "plt.xlabel(\"p - The reduced dimension\", fontsize=5)\n",
    "plt.ylabel(\"Execution time [sec]\", fontsize=5)\n",
    "plt.savefig(\"SVD_TIME_with_y0_plot.png\", dpi= 200, bbox_inches = \"tight\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YMWFY6hReB6MRAAAA0K9GDqmPj11wbOoMXifX0wAAAIB+s2Hnvmjv7E6dwRtgNAIAAAD6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\nQ+zc15E6hTJhNAI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OV+Xp8kryHS3/vcfXafn27gJo+/5G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\nRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1440x1280 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig=plt.figure(figsize=(18, 16), dpi= 80, facecolor='w', edgecolor='k')\n",
    "plt.plot(ranks_SVD,\n",
    "         results_dict_truncate_full_SVD_X_with_y0[\"condition_number\"],\n",
    "           ':X', markersize=3, label='condition_number')\n",
    "\n",
    "plt.yscale(\"log\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "results_tests = results_dict_NMF[\"LS\"][\"test_reaults\"]\n",
    "results_train = results_dict_NMF[\"LS\"][\"train_reaults\"]\n",
    "NMF_time = results_dict_NMF[\"NMF_time\"]\n",
    "NMF_time_in_houres = [x/3600 for x in NMF_time]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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cvYWl5beAVcX48ePxzz//4NixY3B0dER0dDR69uwp0Zl/0qRJEAqF+PnnnwEABw8ehIKC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\nAAAJfAMR7Ta8h1JnhAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 650x300 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(3.25, 1.5), dpi= 200, facecolor='w', edgecolor='k')\n",
    "ax = fig.add_subplot(111)\n",
    "ax2 = ax.twinx()\n",
    "\n",
    "\n",
    "l1,  = ax.plot(ranks_NMF,\n",
    "         results_tests,\n",
    "           ':X', markersize=2, linewidth=1, label='SVD solver- MSE for test')\n",
    "l2, = ax.plot(ranks_NMF,\n",
    "         results_train,\n",
    "           ':X', markersize=2, linewidth=1, label='SVD solver- MSE for train')\n",
    "l3, = ax2.plot(ranks_NMF,\n",
    "         NMF_time_in_houres, \n",
    "           '-X', color='black', markersize=2, linewidth=1, label='NMF time cmputation')\n",
    "\n",
    "ax2.legend(handles=[l1, l2, l3], fontsize=5)\n",
    "\n",
    "ax.set_xlabel(\"p - The reduced dimension\", fontsize=5)\n",
    "ax.set_ylabel(\"MSE\", fontsize=5)\n",
    "ax2.set_ylabel(\"Execution time [houres]\", fontsize=5)\n",
    "ax.tick_params(axis='both', which='major', labelsize=5)\n",
    "ax.tick_params(axis='both', which='minor', labelsize=5)\n",
    "ax2.tick_params(axis='both', which='major', labelsize=5)\n",
    "ax2.tick_params(axis='both', which='minor', labelsize=5)\n",
    "plt.tight_layout()\n",
    "plt.savefig(\"NMF_plot.png\", dpi= 200)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Lfm5WvHw0oW7NouCNEEIIITyMMfxy7j56LT+B6GtpXLqfqyVipvtg7Qh3bkWE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\nTkSuQmCC\n",
      "text/plain": [
       "<Figure size 650x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig=plt.figure(figsize=(3.25, 1.5), dpi= 200, facecolor='w', edgecolor='k')\n",
    "plt.tight_layout()\n",
    "plt.plot(ranks_randomized,\n",
    "         results_dict_randomized[\"Ramdomized_SVD_time\"]+[3200],\n",
    "           '--X',  markersize=3, linewidth=1, label=' rank-$p$ Randomized SVD execution time')\n",
    "\n",
    "plt.plot(21845, 1140, ':X',  markersize=3, color=\"red\", label='Redcuced SVD execution time')\n",
    "plt.axhline(y=1140,xmax=0.95, color='black', linestyle=\"--\", linewidth=1)\n",
    "\n",
    "plt.tick_params(axis='both', which='major', labelsize=5)\n",
    "plt.tick_params(axis='both', which='minor', labelsize=5)\n",
    "plt.xlabel(\"p - The reduced dimension\", fontsize=5)\n",
    "plt.ylabel(\"Execution time [sec]\", fontsize=5)\n",
    "\n",
    "plt.legend( fontsize=6)\n",
    "plt.savefig(\"Randomized_SVD_time.png\", dpi= 200, bbox_inches = \"tight\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(r\"Xtain_with_y0_SVD_full.sav\", \"rb\") as input_file:\n",
    "    [u, s, vh] = pickle.load(input_file)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EmfrGYNc0YcbiY4M5FJon1JhQqzeYJ840n0jTYLx0vNkEHJ3ecSbOmHdh0eBohabVaxRy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\nRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 650x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig=plt.figure(figsize=(3.25, 1.5), dpi= 200, facecolor='w', edgecolor='k')\n",
    "plt.tight_layout()\n",
    "plt.semilogy(s)\n",
    "plt.axvline(x=20481, color='black', linestyle=\"--\", linewidth=1, label='Line at n=20481')\n",
    "plt.xlabel(\"n - The singular value number\", fontsize=5)\n",
    "plt.ylabel(\"The singular value\", fontsize=5)\n",
    "plt.tick_params(axis='both', which='major', labelsize=5)\n",
    "plt.tick_params(axis='both', which='minor', labelsize=5)\n",
    "plt.legend()\n",
    "plt.savefig(\"singular_values_with_y0.png\",  dpi= 200, bbox_inches = \"tight\")\n",
    "plt.show()"
   ]
  }
 ],
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