matmul_via_inner_and_outer_product.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from numpy.random import randn\n",
    "np.random.seed(123)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = randn(4, 4)\n",
    "y = randn(4, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.80325051,  0.23031978, -1.38165191,  4.56466603],\n",
       "       [ 3.04420914,  3.11381025, -4.21803106,  6.38565951],\n",
       "       [ 3.01796772,  1.9908307 ,  1.49058155,  0.70471186],\n",
       "       [ 3.43633441,  2.96637292,  1.80363195,  1.67459407]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res0 = x.dot(y)\n",
    "res0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.80325051,  0.23031978, -1.38165191,  4.56466603],\n",
       "       [ 3.04420914,  3.11381025, -4.21803106,  6.38565951],\n",
       "       [ 3.01796772,  1.9908307 ,  1.49058155,  0.70471186],\n",
       "       [ 3.43633441,  2.96637292,  1.80363195,  1.67459407]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res1 = np.outer(x[:, 0], y[0, :])\n",
    "res1 += np.outer(x[:, 1], y[1, :])\n",
    "res1 += np.outer(x[:, 2], y[2, :])\n",
    "res1 += np.outer(x[:, 3], y[3, :])\n",
    "res1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.80325051,  0.23031978, -1.38165191,  4.56466603],\n",
       "       [ 3.04420914,  3.11381025, -4.21803106,  6.38565951],\n",
       "       [ 3.01796772,  1.9908307 ,  1.49058155,  0.70471186],\n",
       "       [ 3.43633441,  2.96637292,  1.80363195,  1.67459407]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res2 = np.zeros((4, 4))\n",
    "for i in range(4):\n",
    "    res2 += np.expand_dims(x[:, i], 1).dot(np.expand_dims(y[i, :], 0))\n",
    "res2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(res0, res1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(res0, res2)"
   ]
  }
 ],
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