Untitled.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from PIL import Image\n",
    "import glob\n",
    "import math\n",
    "import scipy.spatial.distance as dista\n",
    "\n",
    "mu_vec = np.array([0,0])\n",
    "cov_mat = np.array([[1,0.8],[0.8,1]])\n",
    "amostra = np.random.multivariate_normal(mu_vec, cov_mat, 5).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.31289219, -0.79760781,  0.1912598 ,  0.34213575,  0.73757266],\n",
       "       [ 2.06162072, -1.51279125, -0.09993132,  0.66550034,  0.05302814]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "amostra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "x=amostra[:,0]\n",
    "y=amostra[:,1]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mahalanobis(x, y, eigenvalues, k):\n",
    "    distance=[]\n",
    "    for i in range(2):\n",
    "        distance.append(np.sum(np.divide((np.subtract(x[i],y)**2)[:2],eigenvalues[:2])))\n",
    "    return distance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.487722794441794"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cov_mat\n",
    "distance = dista.mahalanobis(x, y, np.linalg.inv(cov_mat))\n",
    "distance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 2)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigenvalues, _ = np.linalg.eig(cov_mat)\n",
    "_.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.368604390147599"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist = np.sum(np.divide((x-y)**2, eigenvalues))\n",
    "dist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.56"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigenvalues=[150,2]\n",
    "x=[[1,2],[5,6]]\n",
    "y=[4,5]\n",
    "\n",
    "(((1-4)**2)/150) + (((2-5)**2)/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5066666666666667"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(((5-4)**2)/150)+(((6-5)**2)/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([9, 9], dtype=int32)"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.subtract(x[0],y)**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.1"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(np.divide((np.subtract(x[0],y)**2)[:2],eigenvalues[:2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5.1, 0.5666666666666667]"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist = mahalanobis(x, y, eigenvalues, 2)\n",
    "dist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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