Simple HMWS v Potency.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     Assay  Sample1  Sample2  Sample3  Sample4  Sample5\n",
      "0    HMWS%     1.36     0.96     0.76     1.06     0.86\n",
      "1  Potency    94.20    98.20   105.20   102.20   100.20\n",
      "   Sample1  Sample2  Sample3  Sample4  Sample5\n",
      "0     1.36     0.96     0.76     1.06     0.86\n",
      "1    94.20    98.20   105.20   102.20   100.20\n",
      "         %HMWS  Potency\n",
      "Sample1   1.36     94.2\n",
      "Sample2   0.96     98.2\n",
      "Sample3   0.76    105.2\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1df48595a58>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1df48580320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt \n",
    "%matplotlib inline\n",
    "\n",
    "df = pd.read_csv(\"ExampleData1.csv\")\n",
    "\n",
    "print(df.head(8))\n",
    "\n",
    "df.drop(\"Assay\", axis=1, inplace=True)\n",
    "\n",
    "print(df.head(3))\n",
    "\n",
    "fig = plt.figure()\n",
    "fig.subplots_adjust(top=0.8)\n",
    "ax1 = fig.add_subplot(211)\n",
    "ax1.set_ylabel('Potency')\n",
    "ax1.set_xlabel('%HMWS')\n",
    "ax1.set_title('Potency vs. HMWS')\n",
    "\n",
    "dfPlot = df.T\n",
    "dfPlot.columns = ['%HMWS', 'Potency'] \n",
    "print(dfPlot.head(3))\n",
    "\n",
    "dfPlot.plot(kind = 'scatter', x=0, y=1, ax=ax1)\n",
    "\n",
    "# df.T.plot(kind='scatter', x=0, y=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1df46e20400>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1df46e4c160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Subtract the row mean value from each value in each row\n",
    "df2 = df.sub(df.mean(axis=1), axis=0)\n",
    "\n",
    "df2.head(3)\n",
    "\n",
    "df2.T.plot(kind='scatter', x=0, y=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.36, -0.04, -0.24,  0.06, -0.14],\n",
       "       [-5.8 , -1.8 ,  5.2 ,  2.2 ,  0.2 ]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = df2.values\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A * Atranspose gives the Covariance Matrix\n",
      "[[ 0.053 -0.79 ]\n",
      " [-0.79  17.2  ]] \n",
      "\n",
      "eigenvalue 1:  0.016679894446109955\n",
      "eigenvalue 2:  17.23632010555389 \n",
      "\n",
      "eigenvalues\n",
      "[1.66798944e-02 1.72363201e+01] \n",
      "\n",
      "eigenvectors\n",
      "[[-0.99894483  0.04592631]\n",
      " [-0.04592631 -0.99894483]] \n",
      "\n",
      "SVD\n",
      "Matrix U\n",
      "[[-0.04592631  0.99894483]\n",
      " [ 0.99894483  0.04592631]] \n",
      "\n",
      "Sigma\n",
      "[1.72363201e+01 1.66798944e-02] \n",
      "\n",
      "Matrix V transpose\n",
      "[[-0.04592631  0.99894483]\n",
      " [ 0.99894483  0.04592631]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from math import sqrt\n",
    "from scipy.linalg import svd\n",
    "\n",
    "\n",
    "# A = np.matrix([[0.36, -0.04, -0.24, 0.06, -0.14],\n",
    "#                [5.8, 1.8, -5.2, -2.2, -0.2]])\n",
    "\n",
    "# A_length = int(A.shape[1])\n",
    "\n",
    "# AAT = np.dot(A,A.T)/(A_length-1)\n",
    "\n",
    "A_Length = int(df2.shape[1])\n",
    "AAT = np.dot(df2, df2.T)/(A_Length-1)\n",
    "\n",
    "print('A * Atranspose gives the Covariance Matrix')\n",
    "print(AAT, '\\n')\n",
    "\n",
    "eigenvalues, eigenvectors = np.linalg.eig(AAT)\n",
    "\n",
    "e1, e2 = eigenvalues\n",
    "print('eigenvalue 1: ', e1)\n",
    "print('eigenvalue 2: ', e2, '\\n')\n",
    "\n",
    "print('eigenvalues')\n",
    "print (eigenvalues, '\\n')\n",
    "print('eigenvectors')\n",
    "print (eigenvectors, '\\n')\n",
    "\n",
    "print('SVD')\n",
    "\n",
    "# SVD\n",
    "U, s, VT = svd(AAT)\n",
    "print('Matrix U')\n",
    "print(U, '\\n')\n",
    "print('Sigma')\n",
    "print(s, '\\n')\n",
    "print('Matrix V transpose')\n",
    "print(VT)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.79\n",
      "0.053\n",
      "17.200000000000003\n"
     ]
    }
   ],
   "source": [
    "#Manual calculation of Variances and Covariances\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from math import sqrt\n",
    "\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn import preprocessing\n",
    "import matplotlib.pyplot as plt \n",
    "%matplotlib inline\n",
    "\n",
    "m = np.array([0.36, -0.04, -0.24, 0.06, -0.14])\n",
    "\n",
    "#m_mag = sqrt(0.36**2 + 0.04**2 + 0.24**2 + 0.06**2 + 0.14**2)\n",
    "#mN = m/m_mag\n",
    "\n",
    "n = np.array([5.8, 1.8, -5.2, -2.2, -0.2])\n",
    "\n",
    "#n_mag = sqrt(5.8**2 + 1.8**2 + 5.2**2 + 2.2**2 + 0.2*2)\n",
    "#nN = n/n_mag\n",
    "\n",
    "\n",
    "v = np.dot(m,n.T)\n",
    "\n",
    "var_m = np.dot(m,m.T)/(len(n)-1)\n",
    "\n",
    "var_n = np.dot(n,n.T)/(len(n)-1)\n",
    "\n",
    "covar = v/(len(n)-1)\n",
    "\n",
    "print (covar)\n",
    "print(var_m)\n",
    "print(var_n)\n",
    "\n",
    "# need to normalize to length 1\n",
    "\n",
    "\n",
    "#eigenvalues, eigenvectors = np.linalg.eig(m)\n",
    "#print (eigenvalues)\n",
    "#print (eigenvectors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "df.sub(df.mean(axis=1), axis=0)"
   ]
  }
 ],
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