22. PCA Feature Selection.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# df = pd.read_csv(r'/home/uia72388/Share_A/New Data/MYDATA.csv', index_col=0)\n",
    "# df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "39"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vneed=[]\n",
    "for i in df.columns:\n",
    "    if (df[i].isnull().sum()==0):\n",
    "        vneed.append(i)\n",
    "    else:\n",
    "        continue\n",
    "len(vneed)        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# df1= df.loc[:, vneed]\n",
    "# for i, x in enumerate(df1.columns):\n",
    "#     print(i, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# df1['box0.classval'].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# df1['box0.sign_class.'].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    102728\n",
       "6     36114\n",
       "2     16281\n",
       "5     15314\n",
       "4     12932\n",
       "1      5228\n",
       "3      4376\n",
       "Name: box0.classval, dtype: int64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1['box0.classval'].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "df1['box0.classvalnew'] = df1['box0.classval'].copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/uia72388/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:2: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  \n",
      "/home/uia72388/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:3: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n",
      "/home/uia72388/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:4: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  after removing the cwd from sys.path.\n",
      "/home/uia72388/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:5: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  \"\"\"\n",
      "/home/uia72388/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:6: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  \n",
      "/home/uia72388/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:7: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  import sys\n",
      "/home/uia72388/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:8: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  \n"
     ]
    }
   ],
   "source": [
    "# do this by making dict mapping or df[df['box0.classval']==0] or df1['box0.classvalnew'].loc[df1['box0.classval'] ==0] = 1\n",
    "df1['box0.classvalnew'][np.where(df1['box0.classval']==0)[0]] =1\n",
    "df1['box0.classvalnew'][np.where(df1['box0.classval']==1)[0]] =2\n",
    "df1['box0.classvalnew'][np.where(df1['box0.classval']==2)[0]] =3\n",
    "df1['box0.classvalnew'][np.where(df1['box0.classval']==3)[0]] =4\n",
    "df1['box0.classvalnew'][np.where(df1['box0.classval']==4)[0]] =5\n",
    "df1['box0.classvalnew'][np.where(df1['box0.classval']==5)[0]] =6\n",
    "df1['box0.classvalnew'][np.where(df1['box0.classval']==6)[0]] =7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1    102728\n",
       "7     36114\n",
       "3     16281\n",
       "6     15314\n",
       "5     12932\n",
       "2      5228\n",
       "4      4376\n",
       "Name: box0.classvalnew, dtype: int64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1['box0.classvalnew'].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 0    102728\n",
    "# 6     36114\n",
    "# 2     16281\n",
    "# 5     15314\n",
    "# 4     12932\n",
    "# 1      5228\n",
    "# 3      4376"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1\n",
       "1    1\n",
       "2    1\n",
       "3    1\n",
       "4    1\n",
       "Name: box0.classvalnew, dtype: int64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1['box0.classvalnew'].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# for i, x in enumerate(df1.columns):\n",
    "#     print(i, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # df.columns[[1,2,5]]\n",
    "# # cols=[1,2,4,5]\n",
    "# data= df1.drop(df1.columns[[0,3,6,12,13,14,31,39]], axis=1)\n",
    "# data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "X= data.values\n",
    "y = df1['box0.classvalnew'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((192973, 32), (192973,))"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape, y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1, 2, 3, 4, 5, 6, 7]), 7)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.unique(y) , len(np.unique(y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA as sklearnPCA\n",
    "\n",
    "sklearn_pca = sklearnPCA(n_components=2)\n",
    "X_pca = sklearn_pca.fit_transform(X)\n",
    "\n",
    "def plot_pca():\n",
    "\n",
    "    ax = plt.subplot(111)\n",
    "\n",
    "    for label in range(1, 8):\n",
    "        plt.scatter(x=X_pca[:,0][y == label],\n",
    "                y=X_pca[:,1][y == label],\n",
    "                alpha=0.5,\n",
    "                #label=newdict[label]\n",
    "                )\n",
    "\n",
    "    plt.xlabel('PC1')\n",
    "    plt.ylabel('PC2')\n",
    "\n",
    "    #leg = plt.legend(loc='upper right', fancybox=True)\n",
    "    #leg.get_frame().set_alpha(0.5)\n",
    "    #plt.title('PCA: Iris projection onto the first 2 principal components')\n",
    "\n",
    "    # hide axis ticks\n",
    "    plt.tick_params(axis=\"both\", which=\"both\", bottom=\"off\", top=\"off\",  \n",
    "            labelbottom=\"on\", left=\"off\", right=\"off\", labelleft=\"on\")\n",
    "\n",
    "    # remove axis spines\n",
    "    ax.spines[\"top\"].set_visible(False)  \n",
    "    ax.spines[\"right\"].set_visible(False)\n",
    "    ax.spines[\"bottom\"].set_visible(False)\n",
    "    ax.spines[\"left\"].set_visible(False)    \n",
    "\n",
    "    plt.tight_layout\n",
    "    plt.grid()\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/uia72388/anaconda3/lib/python3.6/site-packages/sklearn/discriminant_analysis.py:388: UserWarning: Variables are collinear.\n",
      "  warnings.warn(\"Variables are collinear.\")\n"
     ]
    }
   ],
   "source": [
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA\n",
    "\n",
    "# LDA\n",
    "sklearn_lda = LDA(n_components=2)\n",
    "X_lda_sklearn = sklearn_lda.fit_transform(X, y)\n",
    "\n",
    "def plot_scikit_lda(X, title):\n",
    "\n",
    "    ax = plt.subplot(111)\n",
    "    for label in range(1,8):\n",
    "        plt.scatter(x=X[:,0][y == label],\n",
    "                    y=X[:,1][y == label] * -1, # flip the figure\n",
    "                    alpha=0.5)\n",
    "                    #label=newdict[label])\n",
    "\n",
    "    plt.xlabel('LD1')\n",
    "    plt.ylabel('LD2')\n",
    "\n",
    "    #leg = plt.legend(loc='upper right', fancybox=True)\n",
    "    #leg.get_frame().set_alpha(0.5)\n",
    "    plt.title(title)\n",
    "\n",
    "    # hide axis ticks\n",
    "    plt.tick_params(axis=\"both\", which=\"both\", bottom=\"off\", top=\"off\",  \n",
    "            labelbottom=\"on\", left=\"off\", right=\"off\", labelleft=\"on\")\n",
    "\n",
    "    # remove axis spines\n",
    "    ax.spines[\"top\"].set_visible(False)  \n",
    "    ax.spines[\"right\"].set_visible(False)\n",
    "    ax.spines[\"bottom\"].set_visible(False)\n",
    "    ax.spines[\"left\"].set_visible(False)    \n",
    "\n",
    "    plt.grid()\n",
    "    plt.tight_layout\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/uia72388/anaconda3/lib/python3.6/site-packages/matplotlib/cbook/deprecation.py:107: MatplotlibDeprecationWarning: Passing one of 'on', 'true', 'off', 'false' as a boolean is deprecated; use an actual boolean (True/False) instead.\n",
      "  warnings.warn(message, mplDeprecation, stacklevel=1)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_pca()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/uia72388/anaconda3/lib/python3.6/site-packages/matplotlib/cbook/deprecation.py:107: MatplotlibDeprecationWarning: Passing one of 'on', 'true', 'off', 'false' as a boolean is deprecated; use an actual boolean (True/False) instead.\n",
      "  warnings.warn(message, mplDeprecation, stacklevel=1)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_scikit_lda(X_lda_sklearn, title= 'lda')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import pylab as pl\n",
    "from sklearn import datasets\n",
    "from sklearn.decomposition import PCA\n",
    "\n",
    "# load dataset\n",
    "# iris = datasets.load_iris()\n",
    "# df = pd.DataFrame(iris.data, columns=iris.feature_names)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# normalize data\n",
    "from sklearn import preprocessing\n",
    "data_scaled = pd.DataFrame(preprocessing.scale(data),columns = data.columns) \n",
    "\n",
    "# PCA\n",
    "pca = PCA(n_components=2)\n",
    "pca.fit_transform(data_scaled)\n",
    "\n",
    "# Dump components relations with features:\n",
    "dfnew  =pd.DataFrame(pca.components_,columns=data.columns,index = ['PC-1','PC-2'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# dfnew"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "#np.where(df1['box0.area']==0.031181)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.03118095,  0.01612597,  0.00730797,  0.02285152,  0.0393811 ,\n",
       "        -0.02314098, -0.02018007, -0.25572681, -0.2682648 ,  0.00187989,\n",
       "        -0.39811075,  0.39551466,  0.39811075, -0.12480279,  0.39811075,\n",
       "         0.00637763, -0.03671128,  0.01430933,  0.16770914,  0.01789011,\n",
       "        -0.09910585, -0.07526144, -0.08069502,  0.00567427, -0.05611526,\n",
       "         0.32901857,  0.06319582,  0.06789109, -0.05442566,  0.10988263,\n",
       "         0.01157501,  0.15363461],\n",
       "       [ 0.51310824,  0.02532298, -0.04114552,  0.51204961,  0.52317003,\n",
       "         0.08911908,  0.12425091, -0.27703253, -0.12068004, -0.01245408,\n",
       "         0.08777963, -0.08870674, -0.08777963, -0.09286278, -0.08777963,\n",
       "         0.00156227,  0.02210422, -0.00220645, -0.00937552,  0.00994181,\n",
       "        -0.10432559, -0.09090872, -0.02805832,  0.02639117, -0.0631695 ,\n",
       "        -0.06836259,  0.03207588,  0.03215042,  0.02424857, -0.06800964,\n",
       "        -0.01835102, -0.08024046]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.components_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 32)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.components_.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# dfnew.abs().sum(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "#pcs means eigenvectors. find greatest eigen values. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "#fit_transform n=2\n",
    "#pca.transform(X)[:, :ncomp] , pca.transform(X)[:, :ncomp].shape\n",
    "# ncomp = 2\n",
    "# Xhat = np.dot(pca.transform(X)[:, :ncomp], pca.components_[:ncomp, :])\n",
    "# Xhat += mu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'trans' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-35-3c21d1cbfef4>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mtrans\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcomps\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'trans' is not defined"
     ]
    }
   ],
   "source": [
    "#trans.shape, comps.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[-1.17313670e-09,  1.19986147e-08, -1.15722008e-09, ...,\n",
       "         -8.13183202e-10, -7.86898603e-10, -8.13046328e-10],\n",
       "        [ 1.05291668e-08,  3.56523365e-08,  1.06095655e-08, ...,\n",
       "          2.82946325e-09,  2.80371267e-09,  2.76834885e-09]]), (2, 192973))"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# inv = np.linalg.pinv(trans)\n",
    "# inv , inv.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Xhat = np.dot(inv, comps)\n",
    "# Xhat += mu\n",
    "# Xhat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Xhat = np.dot(pca.transform(X)[:, :ncomp], pca.components_[:ncomp, :])\n",
    "# Xhat += mu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "sc = StandardScaler()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[-0.4795529 , -0.06175153, -0.17944134, ..., -0.48573786,\n",
       "         -0.07213757, -0.38968905],\n",
       "        [ 4.94981319, -0.08782903, -0.17944134, ..., -0.48573786,\n",
       "         -0.07213757, -0.38968905],\n",
       "        [-0.47298663,  0.14128049, -0.17944134, ..., -0.48573786,\n",
       "         -0.07213757, -0.38968905],\n",
       "        ...,\n",
       "        [-0.33415695,  0.06745067, -0.17944134, ..., -0.48573786,\n",
       "         -0.07213757, -0.38968905],\n",
       "        [-0.32336951, -0.06175153, -0.17944134, ..., -0.48573786,\n",
       "         -0.07213757, -0.38968905],\n",
       "        [-0.33415695, -0.18533624, -0.17944134, ..., -0.48573786,\n",
       "         -0.07213757, -0.38968905]]), (192973, 32))"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xstd = sc.fit_transform(X)\n",
    "Xstd, Xstd.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[ 1.00000518, -0.00413405, -0.03833391, ..., -0.02582052,\n",
       "         -0.00789836, -0.03466189],\n",
       "        [-0.00413405,  1.00000518,  0.31806623, ...,  0.04546347,\n",
       "          0.00229746,  0.03493667],\n",
       "        [-0.03833391,  0.31806623,  1.00000518, ...,  0.03425834,\n",
       "         -0.01092788,  0.04681411],\n",
       "        ...,\n",
       "        [-0.02582052,  0.04546347,  0.03425834, ...,  1.00000518,\n",
       "          0.13493505,  0.81541342],\n",
       "        [-0.00789836,  0.00229746, -0.01092788, ...,  0.13493505,\n",
       "          1.00000518, -0.02811137],\n",
       "        [-0.03466189,  0.03493667,  0.04681411, ...,  0.81541342,\n",
       "         -0.02811137,  1.00000518]]), (32, 32))"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cov_mat = np.cov(Xstd.T)\n",
    "cov_mat , cov_mat.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.530571498929031 : [-3.11809488e-02 -5.13108252e-01  6.29161297e-02  5.49287725e-02\n",
      "  1.64658974e-01 -1.00452378e-01  7.93656284e-01 -1.25339184e-01\n",
      "  4.59767355e-03  9.68025501e-06 -8.65245203e-02 -2.55403823e-02\n",
      "  9.46388168e-03 -1.29007460e-01 -8.58166076e-02 -6.80881788e-03\n",
      "  1.46590234e-02 -5.47994116e-04  5.81552508e-02 -1.03140907e-02\n",
      " -8.22702367e-02  3.51116777e-03 -2.88370722e-02  3.11576963e-02\n",
      "  2.98315657e-02  7.32311702e-03 -2.08191671e-02  1.27443065e-03\n",
      " -1.75322192e-16  3.44111084e-16  2.83679216e-16 -1.87432227e-17] \n",
      "\n",
      "3.156978680542683 : [-1.61258886e-02 -2.53180021e-02  1.04382508e-01 -1.51097118e-01\n",
      " -4.59396405e-01 -3.51188598e-01 -3.66423877e-02 -2.74261177e-01\n",
      " -2.78356307e-02  7.73438298e-04 -8.77370558e-02  1.05450575e-02\n",
      " -8.73260149e-02  1.42427244e-01 -4.35365149e-01  4.58150940e-01\n",
      " -1.62044435e-01 -1.33248386e-01  1.74799043e-01  3.58690898e-02\n",
      "  6.97717174e-02 -1.16710726e-01 -5.58377245e-02 -4.27166344e-02\n",
      "  4.66140054e-02 -7.50731032e-02  6.13449849e-02 -8.73657891e-02\n",
      " -1.33962922e-16  5.44830318e-16 -4.18146258e-16 -2.33125755e-16] \n",
      "\n",
      "2.6487752326120773 : [-7.30785252e-03  4.11506205e-02  1.05411231e-01 -6.22962783e-02\n",
      " -2.45267008e-01 -3.52399821e-01 -9.79117787e-03  2.60757771e-02\n",
      "  1.04661185e-02 -2.37062834e-03  1.65568252e-02  4.15531619e-02\n",
      " -2.37158675e-03 -2.45006877e-01  3.50848196e-01 -3.56389685e-01\n",
      "  1.04457998e-01 -1.51169320e-01  4.53827989e-01 -1.45770567e-03\n",
      " -2.15642800e-01 -1.35064095e-01  2.72050631e-01 -1.43493912e-01\n",
      "  5.33471719e-02  4.78302344e-02  1.12139251e-01 -2.62878030e-01\n",
      "  2.68359646e-17 -1.52862948e-16 -2.36604625e-16  2.08045008e-16] \n",
      "\n",
      "1.990053620465841 : [-2.28515279e-02 -5.12050305e-01  3.34399795e-02  9.21083254e-02\n",
      "  2.28884198e-01 -1.11211647e-02 -5.10573337e-01 -5.73020154e-01\n",
      " -3.81871115e-02 -3.30674952e-04 -5.91094296e-02  2.52420817e-03\n",
      " -6.87815482e-04 -7.85288368e-02  2.99653911e-02 -9.70824362e-02\n",
      "  3.86398594e-02  2.91671429e-02  3.55686463e-02 -2.11092288e-02\n",
      " -7.70869333e-02  1.41643522e-02 -5.33815194e-03  2.23354596e-02\n",
      "  1.12524461e-02  1.64301128e-02 -1.64228223e-02  1.21733612e-02\n",
      " -4.11571449e-02  2.25681900e-01 -1.56684931e-02 -1.64955926e-02] \n",
      "\n",
      "1.6507360754406248 : [-3.93810858e-02 -5.23168552e-01  7.98881958e-02  1.60291699e-02\n",
      "  3.47802397e-02 -1.44782436e-01 -2.94380257e-01  7.44633347e-01\n",
      "  4.35687522e-02 -1.50001401e-03 -8.62146540e-02 -1.50480560e-02\n",
      " -1.26548497e-02 -3.13232843e-02 -1.35934031e-01  1.07947064e-01\n",
      " -3.67282829e-02 -2.64157710e-02  6.96323516e-02  4.51077049e-03\n",
      " -2.78384871e-02 -1.79364336e-02 -4.46859302e-02  1.47591762e-02\n",
      "  2.61996620e-02 -2.02745091e-02 -7.42874322e-03 -1.36310257e-02\n",
      "  6.83724074e-04  6.94298504e-03  4.62330538e-02  3.07197485e-02] \n",
      "\n",
      "1.4905966617948176 : [ 0.02314096 -0.08911541  0.47397724 -0.13814314 -0.12206316  0.26995459\n",
      "  0.01982425 -0.03552555  0.00227584 -0.00387716  0.34947225  0.01830112\n",
      " -0.03137552 -0.02238486 -0.01747451 -0.01721987  0.00218067 -0.02429911\n",
      " -0.06068438  0.03013967  0.06417146  0.0916554   0.06917794 -0.02884715\n",
      " -0.06854798  0.02938609  0.00519994 -0.10669285  0.00981006  0.09961782\n",
      "  0.66335099  0.44076637] \n",
      "\n",
      "0.07889679414499165 : [ 2.01800570e-02 -1.24247183e-01  4.74462089e-01 -1.35573524e-01\n",
      " -1.18370967e-01  2.57109312e-01 -6.85591733e-04  1.61990342e-02\n",
      "  5.25610304e-03 -3.93949882e-03  3.39822793e-01  1.70694618e-02\n",
      " -3.19155936e-02 -2.43075590e-02 -2.66629528e-02 -9.59358471e-03\n",
      " -3.75133930e-04 -2.58631063e-02 -5.52394731e-02  3.01312461e-02\n",
      "  6.15715839e-02  8.94470306e-02  6.53632454e-02 -2.75236191e-02\n",
      " -6.60147296e-02  2.76765303e-02  4.63255624e-03 -1.06501891e-01\n",
      " -9.91515827e-03 -1.00685054e-01 -6.70457664e-01 -4.45488436e-01] \n",
      "\n",
      "0.052184952108852115 : [ 0.25572676  0.27702989  0.20411396 -0.02226875  0.16984908 -0.24739572\n",
      "  0.05281824  0.11132867  0.01713094 -0.00460752  0.01548421 -0.02274437\n",
      " -0.06692565 -0.14603947 -0.2877367  -0.03937369  0.11671783  0.04181902\n",
      " -0.10492138 -0.08191903 -0.16736385  0.02596306  0.01527874  0.10525341\n",
      " -0.00332952  0.10595689 -0.06687385  0.02384176 -0.12748354  0.69904577\n",
      " -0.04853289 -0.05109481] \n",
      "\n",
      "0.12557638658151504 : [ 2.68264747e-01  1.20676947e-01  2.32143700e-01  8.06660866e-03\n",
      "  2.63288722e-01 -2.71112994e-01 -1.20999447e-01 -7.95741983e-02\n",
      "  5.18762076e-03 -5.09231482e-03 -3.88744070e-03 -2.36879931e-02\n",
      " -7.25323678e-02 -1.85136068e-01 -3.00360766e-01 -7.63868649e-02\n",
      "  1.39552527e-01  5.53440491e-02 -1.00931225e-01 -9.58496798e-02\n",
      " -2.07667640e-01  3.29846300e-02  1.46423765e-02  1.21482902e-01\n",
      "  3.27574106e-04  1.20183407e-01 -7.79637106e-02  2.99988957e-02\n",
      "  1.18019421e-01 -6.47150021e-01  4.49299019e-02  4.73016360e-02] \n",
      "\n",
      "0.001764286801423789 : [-1.87972946e-03  1.24830778e-02  3.04462393e-02  1.07321604e-02\n",
      "  4.45482473e-02 -4.65714470e-02  4.96877768e-03 -5.96635865e-04\n",
      " -5.75986599e-03  7.83337480e-04  1.41312007e-01 -5.90793694e-03\n",
      "  1.75200591e-02  2.66547410e-02  3.44292872e-02  1.71366532e-03\n",
      " -7.65199348e-02  7.74875070e-02  1.39911314e-01 -5.65091036e-01\n",
      "  1.00945296e-01 -1.54824837e-01 -8.72846346e-03 -2.51023755e-01\n",
      " -3.10349849e-02 -3.46705826e-01 -6.34846146e-01  1.28952242e-02\n",
      "  8.04880681e-17 -1.07396768e-16  6.01951437e-17 -4.47343967e-17] \n",
      "\n",
      "1.3653233961959306 : [ 0.39811075 -0.08777958 -0.10130456  0.04359839 -0.14838321  0.07540931\n",
      "  0.00723006 -0.0011858   0.03448684  0.28800569  0.01907992 -0.12775162\n",
      " -0.09558876  0.00562638  0.04816379 -0.02927632 -0.08913429  0.02806106\n",
      "  0.02136405 -0.00339191 -0.02749499  0.00184104 -0.01718793 -0.03021673\n",
      " -0.01905371  0.01509087  0.00561158  0.04751224  0.51760716 -0.11915699\n",
      " -0.25385706 -0.52226664] \n",
      "\n",
      "0.34416260423011075 : [-3.95514673e-01  8.87068190e-02  1.18679025e-01 -3.61152274e-02\n",
      "  1.48091274e-01 -7.86032945e-02 -7.44286662e-03  2.49004527e-03\n",
      " -3.29177329e-02  8.66142283e-01 -2.20813771e-02  1.18771446e-01\n",
      "  8.53205920e-02  8.20241707e-03 -3.91318577e-02  3.26067106e-02\n",
      "  9.89097138e-02 -3.07537777e-02 -2.43470531e-02  5.80230254e-03\n",
      "  1.29642110e-02 -6.94875468e-04  1.77521311e-02  3.64506154e-02\n",
      "  1.61409050e-02 -1.96803553e-02 -9.56490665e-03 -4.90960486e-02\n",
      " -1.01704701e-14  8.07420581e-15 -4.97921494e-14 -1.50963560e-13] \n",
      "\n",
      "0.3882225506470535 : [-0.39811075  0.08777958  0.10130456 -0.04359839  0.14838321 -0.07540931\n",
      " -0.00723006  0.0011858  -0.03448684 -0.28800569 -0.01907992  0.12775162\n",
      "  0.09558876 -0.00562638 -0.04816379  0.02927632  0.08913429 -0.02806106\n",
      " -0.02136405  0.00339191  0.02749499 -0.00184104  0.01718793  0.03021673\n",
      "  0.01905371 -0.01509087 -0.00561158 -0.04751224  0.79080672 -0.04976625\n",
      " -0.06764219  0.04875171] \n",
      "\n",
      "0.5540530837572024 : [ 1.24802812e-01  9.28652825e-02  2.68160183e-01 -2.75515795e-01\n",
      "  7.45370360e-02  1.06777418e-01 -2.39507443e-02 -1.15526460e-02\n",
      " -2.88631648e-03  3.81166452e-03 -3.26681727e-01 -2.70750597e-01\n",
      "  6.48823496e-01 -7.67420164e-02  1.46984926e-02 -8.07436488e-02\n",
      " -2.28495425e-01  6.94364329e-02  2.16674733e-01  7.56425441e-02\n",
      "  1.59087461e-03  1.64525899e-02 -2.40076719e-01  2.31207376e-02\n",
      "  3.55072735e-02 -1.44260335e-01  3.73067925e-02  7.11413352e-02\n",
      " -4.87503618e-17  9.24194613e-17 -5.04596920e-16 -1.07011196e-15] \n",
      "\n",
      "0.5980119486712989 : [-0.39811075  0.08777958  0.10130456 -0.04359839  0.14838321 -0.07540931\n",
      " -0.00723006  0.0011858  -0.03448684 -0.28800569 -0.01907992  0.12775162\n",
      "  0.09558876 -0.00562638 -0.04816379  0.02927632  0.08913429 -0.02806106\n",
      " -0.02136405  0.00339191  0.02749499 -0.00184104  0.01718793  0.03021673\n",
      "  0.01905371 -0.01509087 -0.00561158 -0.04751224 -0.27319956 -0.06939075\n",
      " -0.18621487 -0.57101835] \n",
      "\n",
      "0.647767841699927 : [-6.37752715e-03 -1.52567106e-03 -5.35888419e-02 -1.32352005e-03\n",
      "  2.41550995e-02 -7.07871399e-02  5.66583598e-03  9.51886867e-04\n",
      " -1.52600988e-02 -3.26961911e-04 -9.77178503e-02 -1.31026143e-02\n",
      " -1.69448217e-02 -2.23526037e-02  1.46791245e-02  1.09315909e-02\n",
      " -1.51688821e-02 -1.98773060e-02  1.09673900e-01 -2.65021249e-01\n",
      "  1.18008655e-01  1.97962176e-01 -5.51621327e-02  1.79384604e-01\n",
      " -8.57055217e-01 -3.33754980e-02  1.98416717e-01 -1.84736726e-01\n",
      " -1.61764274e-17 -8.69163703e-17  6.36549646e-17  9.13753158e-17] \n",
      "\n",
      "0.684361037553882 : [ 3.67113389e-02 -2.21219256e-02  1.37383954e-02  8.56173595e-02\n",
      " -3.44587336e-02 -1.23505752e-01  6.37619442e-03 -1.69839846e-03\n",
      "  3.38761152e-03 -9.32524829e-04  2.09085214e-01  4.19437689e-02\n",
      "  4.24403303e-02 -7.09172486e-04  1.11892174e-01 -4.50520431e-02\n",
      " -1.44518818e-02  3.26156126e-01 -2.62075646e-01 -1.94231584e-01\n",
      " -4.31575073e-02 -3.43083663e-01 -4.02659473e-01  1.67827496e-01\n",
      "  1.59522044e-01 -2.72858087e-01  3.67360136e-01 -3.93193997e-01\n",
      " -1.82935417e-17 -2.32279353e-17  1.04392141e-16  2.36498260e-16] \n",
      "\n",
      "1.1465985728914754 : [-1.43094390e-02  2.22406143e-03  1.51769972e-02  1.85704487e-02\n",
      " -2.89944712e-02  7.95760906e-03  2.50645424e-03 -7.70434539e-04\n",
      "  6.79176164e-03 -9.85096715e-04 -1.23314863e-01 -8.21947437e-03\n",
      "  9.27012659e-03  3.62543917e-02  1.70736043e-02  7.62266092e-02\n",
      "  1.49024091e-01  4.32974403e-01  1.09165709e-02  3.50749491e-01\n",
      " -1.40170293e-02 -1.99319444e-01 -2.21544857e-01 -3.36311080e-01\n",
      " -2.35310550e-01  4.07230961e-01 -3.36029971e-01 -3.26228528e-01\n",
      " -1.83311413e-16  7.53351349e-17  1.12571535e-16  2.04457225e-16] \n",
      "\n",
      "1.1023087290824423 : [-1.67709108e-01  9.37191493e-03 -2.19493107e-01 -2.50964784e-01\n",
      " -6.72517357e-02  2.03073566e-01 -1.53174743e-02  1.48012443e-02\n",
      " -6.57146938e-02  1.96289686e-02 -4.13432355e-02  2.56962745e-01\n",
      " -1.73605748e-01 -3.39813066e-01 -3.76366388e-01 -3.62755774e-01\n",
      " -4.88655606e-01  1.81964498e-01  2.03106905e-02 -1.06356353e-01\n",
      " -6.22027410e-02  3.43377668e-02 -4.33590440e-02 -1.07989665e-01\n",
      "  3.76727531e-02  1.18985783e-01  5.21665119e-02 -5.10291284e-02\n",
      "  7.38281611e-17  1.27093459e-16 -1.23684613e-15 -3.42554319e-15] \n",
      "\n",
      "1.074801608439306 : [-1.78902971e-02 -9.93089173e-03 -3.67907384e-02 -9.24685752e-02\n",
      " -8.32163270e-02  1.37798829e-01 -1.83046323e-03 -4.67447651e-03\n",
      "  2.00205079e-02 -3.39905271e-03 -1.44273842e-01 -7.70841782e-02\n",
      " -3.86445944e-02  4.57315637e-02  1.09519161e-01  9.49380830e-02\n",
      " -1.09524997e-01  8.63232057e-02  9.41046782e-02 -1.21216347e-01\n",
      "  3.97248290e-02 -1.24263780e-02  2.00836035e-01  7.17140316e-01\n",
      "  1.87858072e-01  2.45634101e-01 -3.18794589e-01 -3.39655407e-01\n",
      " -2.27621989e-17  3.91274679e-18  8.20840385e-17  5.44155898e-16] \n",
      "\n",
      "0.8086437393849413 : [ 9.91058113e-02  1.04345040e-01 -1.12870562e-01  1.42572393e-01\n",
      "  1.78223662e-01  9.38727239e-02 -2.40121756e-02 -4.18809792e-03\n",
      "  5.47888899e-03  1.31052301e-03  1.20066041e-01  1.38298263e-01\n",
      " -7.19747852e-02 -4.45664504e-01  4.88937302e-02  2.75359179e-01\n",
      " -1.17612243e-01 -2.68568426e-01  1.14151993e-01  3.87313593e-01\n",
      " -9.73974478e-02  1.58084406e-01 -1.86604397e-01  5.90333318e-02\n",
      " -1.33753910e-02 -3.66951022e-01 -2.05796948e-01 -3.00828138e-01\n",
      "  9.44638369e-17 -3.57588059e-17 -1.46479151e-16 -6.53768573e-17] \n",
      "\n",
      "0.8568560098451542 : [ 7.52615761e-02  9.08957571e-02  1.37852432e-01  3.02653382e-02\n",
      "  2.52178114e-01  2.76590848e-01  2.91273450e-05  1.20213787e-02\n",
      "  4.37430382e-02  2.17578324e-03 -1.25187958e-01  1.83305892e-01\n",
      " -1.31077722e-01 -2.05560818e-01  1.60958620e-01  5.17075963e-01\n",
      " -3.76729630e-02  1.48261166e-01  2.92080239e-01 -2.68083691e-01\n",
      " -5.21847992e-02 -2.55333802e-01  1.14978062e-01 -1.27571618e-01\n",
      "  5.56724622e-02  1.83433008e-01  3.02131319e-01  1.26438093e-01\n",
      "  4.38429889e-16 -4.71317062e-18  2.67588153e-16  4.51135822e-16] \n",
      "\n",
      "0.872713992935171 : [ 8.06950401e-02  2.80549389e-02  1.56662487e-01  1.05202859e-01\n",
      "  3.15860119e-01 -3.19563480e-01  1.92980562e-02 -3.78179469e-03\n",
      " -2.99787817e-02 -1.72426850e-04  8.00941419e-02  7.44504259e-02\n",
      "  1.95881492e-04  2.27437584e-01  2.31747600e-01 -4.76666852e-03\n",
      " -6.83029736e-01 -1.49295280e-01 -1.80677653e-01  1.15079198e-01\n",
      "  1.46373814e-01 -1.02811815e-01  1.31061133e-01 -8.25367092e-02\n",
      " -5.35222434e-02  1.94118980e-01 -8.94222499e-03 -7.19933754e-02\n",
      " -7.62180079e-17  9.89186619e-17 -9.13970317e-17 -1.25289219e-17] \n",
      "\n",
      "1.0015564201052503 : [-5.67418584e-03 -2.64007508e-02  4.13033151e-02 -2.73512544e-02\n",
      " -7.08845894e-02  2.28996720e-01 -5.21035136e-03  8.11616680e-04\n",
      " -2.61848678e-02 -3.49944197e-03 -2.65953191e-01 -7.17057028e-02\n",
      "  1.22226551e-02 -1.23450132e-01 -9.09511977e-02 -6.76792341e-02\n",
      "  2.45393002e-02 -3.28035955e-01 -3.68443711e-01  7.25370487e-02\n",
      " -1.47236554e-01 -6.47336961e-01  2.45401109e-01  2.64295955e-02\n",
      " -2.39845385e-01 -1.47160625e-01 -6.53738864e-02 -1.37934611e-02\n",
      "  1.41455955e-16 -1.68920110e-16  2.43029902e-16  8.74352008e-16] \n",
      "\n",
      "0.993378362071276 : [ 5.61153311e-02  6.31753218e-02 -6.69065836e-02  2.34671377e-01\n",
      "  3.01564922e-01  2.46331528e-01  1.42378061e-02  2.73017431e-02\n",
      " -4.33689909e-02 -2.44596009e-03  9.11603081e-02 -1.42143293e-01\n",
      "  9.61629599e-03  4.41769376e-01 -4.10024181e-01 -1.68348331e-01\n",
      "  2.09501555e-02 -5.41613397e-02  3.89937163e-01  5.44233809e-02\n",
      " -6.96503637e-02 -1.00570259e-01  1.75276159e-01 -7.41267671e-02\n",
      "  4.76767756e-02 -1.07786287e-01  1.41489530e-01 -3.39339216e-01\n",
      " -3.66226260e-16 -2.47764808e-17  1.35896930e-16  1.17581895e-16] \n",
      "\n",
      "0.9234379187748217 : [-3.29018569e-01  6.83605341e-02 -3.60323620e-02 -2.79690901e-02\n",
      "  8.74716919e-02 -6.22453788e-02 -2.52078103e-02 -2.80824403e-02\n",
      "  3.17928789e-01 -2.63550336e-03  2.06421380e-01 -7.50988563e-01\n",
      " -2.56498464e-01 -2.09593979e-01 -1.23071232e-03  5.24671660e-02\n",
      " -1.35917839e-01  9.43122255e-02  4.74797937e-02  6.00034296e-02\n",
      "  1.39995221e-03 -8.37000003e-02  7.47935033e-03 -5.57783462e-03\n",
      " -3.39605548e-02  4.19502318e-03  5.37113090e-02  8.66877715e-02\n",
      "  2.62671911e-17 -1.78854581e-17  1.40621919e-16  7.99826614e-16] \n",
      "\n",
      "0.9479072191519026 : [-6.31958327e-02 -3.20767719e-02 -7.11693788e-02 -4.01296046e-01\n",
      "  6.33500501e-02  1.78824862e-02  1.22599139e-02  2.38821347e-03\n",
      " -2.33512677e-02 -1.19713825e-02  7.84012205e-02  1.60572248e-02\n",
      " -8.17092310e-02  3.38421167e-01  1.59546569e-01  1.51525139e-01\n",
      " -9.51244918e-02  5.64094776e-02 -4.95313186e-02  5.42564265e-03\n",
      " -7.70604698e-01  1.10575079e-01 -1.54618348e-02 -1.13076045e-02\n",
      " -1.07037755e-01 -1.10778425e-01 -4.48036203e-02  2.82158804e-02\n",
      " -1.37011716e-16 -2.13849887e-17  7.61531579e-16  2.17738397e-15] \n",
      "\n",
      "0.9639266023076579 : [-6.78910844e-02 -3.21537752e-02 -2.07325474e-01  3.44110518e-01\n",
      " -1.86658976e-01  1.06556303e-03 -1.83063145e-02 -4.32891729e-03\n",
      " -7.64002563e-03  7.75277159e-03  3.40317392e-01 -5.07759170e-02\n",
      "  5.89507290e-01 -1.78719279e-01 -1.37402451e-01  2.02654058e-01\n",
      " -9.81343056e-02 -1.06530726e-02 -1.12846052e-01 -1.55749963e-01\n",
      " -2.75306115e-01  4.95488818e-02  1.99534680e-01 -4.63056985e-02\n",
      " -5.24508380e-02  2.62514588e-01  2.77925574e-03 -3.50521256e-02\n",
      "  2.58579930e-17  9.99401194e-17 -6.47441612e-16 -1.58913406e-15] \n",
      "\n",
      "6.892336321762433e-16 : [ 5.44255943e-02 -2.42408873e-02  1.28091604e-02 -2.69184416e-03\n",
      " -1.74945864e-02 -9.83470444e-02  2.66835267e-03 -3.20759753e-03\n",
      "  1.98893157e-02  4.84762278e-04 -1.36662331e-01  2.51544902e-02\n",
      "  4.50230782e-02 -6.89175278e-02 -1.71234852e-02  9.13908180e-02\n",
      " -3.76112675e-02  5.43166502e-01 -1.48211139e-01  1.86206107e-01\n",
      "  8.34525516e-02  1.67334671e-01  6.16526248e-01 -5.93695464e-02\n",
      " -2.42364198e-02 -4.14239490e-01  5.88080694e-02 -6.19475994e-02\n",
      "  3.11914176e-17  6.98509283e-17 -9.23732283e-17 -1.16860908e-16] \n",
      "\n",
      "9.518249770634096e-17 : [-1.09882642e-01  6.80124256e-02  2.65517200e-01  4.44358583e-01\n",
      " -2.00087578e-01  8.56777948e-02 -1.80438164e-04 -3.40144427e-02\n",
      "  6.50537418e-01 -1.00237095e-02 -2.55538109e-01  1.99986855e-01\n",
      " -5.89179244e-02  1.14619272e-01 -1.34736036e-02 -1.22465025e-01\n",
      " -1.41691156e-01  3.64502566e-02  7.59037745e-03 -2.12153851e-02\n",
      " -2.20513959e-01  1.08356190e-01 -1.01664486e-01  3.81415554e-02\n",
      " -2.25027497e-02 -7.32658019e-02 -5.16384454e-02  6.18064790e-02\n",
      "  6.78652423e-16  3.49819014e-17  8.84585457e-16  2.43655751e-15] \n",
      "\n",
      "-4.526369302967906e-16 : [-1.15749022e-02  1.83455652e-02  4.38733907e-02  8.55608024e-03\n",
      "  2.02085102e-04  7.98874253e-02 -4.99657862e-03 -2.14778662e-04\n",
      " -5.96577909e-02 -3.63701285e-03 -3.70662296e-01 -2.55748151e-01\n",
      " -8.25895856e-02 -3.35786762e-02  5.75671769e-02  8.81598564e-02\n",
      "  2.91189071e-02 -2.17855131e-01 -3.22468574e-01 -3.01500953e-01\n",
      " -2.82286267e-02  3.65656373e-01  1.41828087e-02 -3.65316334e-01\n",
      "  2.13347885e-01  6.93456882e-02  7.72935770e-02 -4.45042757e-01\n",
      " -9.10286344e-17 -1.19310238e-16  8.76662896e-17  5.09881816e-16] \n",
      "\n",
      "-5.424509365833757e-16 : [-1.53634647e-01  8.02420615e-02  2.57442776e-01  4.42003848e-01\n",
      " -1.82992689e-01  4.59238246e-02  6.54194796e-03  4.49121352e-02\n",
      " -6.71890871e-01 -1.03186269e-02 -1.22474281e-01 -1.69475257e-01\n",
      " -1.88914874e-01 -2.54095593e-02  5.92461093e-02 -3.77713234e-02\n",
      " -1.38728859e-01  1.41018738e-01  7.23581317e-02  3.24577039e-02\n",
      " -1.89364134e-01  4.66782431e-02 -9.05902190e-02  8.91630747e-02\n",
      " -2.55027598e-02 -6.18629598e-02 -3.31489376e-02  1.70087030e-01\n",
      " -4.04411056e-16 -2.07121868e-16  2.54015141e-16  1.11061942e-15] \n",
      "\n"
     ]
    }
   ],
   "source": [
    "evals, evecs = np.linalg.eig(cov_mat)\n",
    "for x,y in zip(evals,evecs):\n",
    "    print(x, ':', y, '\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(32, 32, (32, 32))"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(evals) , len(evecs), evecs.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tot: 32.000165827166654\n",
      "var_exp: [0.17282946372214836, 0.09865507252661031, 0.08277379707711983, 0.06218885337076528, 0.051585235037726794, 0.04658090429423245, 0.002465512040503613, 0.0016307713025833608, 0.003924241744863288, 5.5133676836324125e-05, 0.04266613503098895, 0.010755025648583754, 0.012131891839056365, 0.017314069144192906, 0.018687776554070685, 0.02024264015375827, 0.021386171598301258, 0.035831019722968635, 0.03444696927622273, 0.03358737621062105, 0.025269985904211794, 0.026776611548610264, 0.027272170952135424, 0.03129847593648954, 0.03104291294728054, 0.02885728542040447, 0.029621947094635784, 0.030122550224078184, 2.153843939118328e-17, 2.974437639492963e-18, -1.4144830771861905e-17, -1.695150392385967e-17]\n",
      "cumsum_varexp: [0.17282946 0.27148454 0.35425833 0.41644719 0.46803242 0.51461333\n",
      " 0.51707884 0.51870961 0.52263385 0.52268898 0.56535512 0.57611015\n",
      " 0.58824204 0.60555611 0.62424388 0.64448652 0.66587269 0.70170371\n",
      " 0.73615068 0.76973806 0.79500805 0.82178466 0.84905683 0.8803553\n",
      " 0.91139822 0.9402555  0.96987745 1.         1.         1.\n",
      " 1.         1.        ]\n"
     ]
    }
   ],
   "source": [
    "tot = sum(evals)\n",
    "var_exp = [(i/tot) for i in evals]\n",
    "cumvar_exp = np.cumsum(var_exp)\n",
    "print('tot:', tot)\n",
    "print('var_exp:', var_exp)\n",
    "print('cumsum_varexp:', cumvar_exp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "sns.set_style('whitegrid')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,10))\n",
    "plt.bar(range(1,33), var_exp, alpha=0.5, align='center', label= 'individual explained variance')\n",
    "plt.step(range(1,33), cumvar_exp, where='mid', label='cumm. explained variance')\n",
    "plt.xlabel('Principal Components', fontsize=15)\n",
    "plt.ylabel('Explained variance ratio', fontsize=15)\n",
    "plt.legend(loc='best', frameon=True,prop={'size':15})\n",
    "plt.title('EVR vs PCs', fontsize=20)\n",
    "#plt.xticks(range(1,33))\n",
    "plt.show()\n",
    "plt.savefig('EVR.jpg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# for i, x, y in zip(range(1,33), data.columns, var_exp):\n",
    "#     print(i, ':', x, ':', y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# for i, x in zip(range(1,33), data.columns):\n",
    "#     print(i, ':', x)"
   ]
  },
  {
   "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}