Matrix Computations algorithms, chapter one added.

Chapter One.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Matrix Multiplication"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import numpy as np"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Variables for tests"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Constants for tests"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "c_x = np.random.randn(1, 1)\n",
+    "c_y = np.random.randn(1, 1)\n",
+    "c_z = np.random.randn(1, 1)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Vectors for test"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "v_x = np.random.randn(1000, 1)\n",
+    "v_y = np.random.randn(1000, 1)\n",
+    "v_z = np.random.randn(1000, 1)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Matrices for test"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "m_x = np.random.randn(1000, 1000)\n",
+    "m_y = np.random.randn(1000, 1000)\n",
+    "m_z = np.random.randn(1000, 1000)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Algorithm Implementation"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Algorithm 1.1.1: Dot Product"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 51,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def dot_product(x, y):\n",
+    "    c = 0\n",
+    "    \n",
+    "    for i in np.arange(x.size):\n",
+    "        c = c + x[i]*y[i]\n",
+    "        \n",
+    "    return c"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Algorithm 1.1.2: Saxpy"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 52,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def saxpy(a, x, y):\n",
+    "    for i in np.arange(x.size):\n",
+    "        y[i] = y[i] + a*x[i]\n",
+    "    \n",
+    "    return y"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Testing algorithms 1.1.1 and 1.1.2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 60,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n",
+      "Wall time: 1.49 ms\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Test Algorithm 1.1.1 (Dot Product)\n",
+    "%time temp = dot_product(v_x, v_y)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 61,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "CPU times: user 4 ms, sys: 0 ns, total: 4 ms\n",
+      "Wall time: 3.92 ms\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Test Algorithm 1.1.2 (Saxpy)\n",
+    "%time temp = saxpy(c_x, v_x, v_y)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Matrix-Vector Multiplication and the Gaxpy"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Algorithm 1.1.3: Row-Oriented Gaxpy"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 55,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def row_gaxpy(A, x, y):\n",
+    "    for i in np.arange(y.size):\n",
+    "        for j in np.arange(x.size):\n",
+    "            y[i] = y[i] + A[i, j]*x[j]\n",
+    "            \n",
+    "    return y"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Algorithm 1.1.4: Column-Oriented Gaxpy"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 56,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def column_gaxpy(A, x, y):\n",
+    "    for j in np.arange(x.size):\n",
+    "        for i in np.arange(y.size):\n",
+    "            y[i] = y[i] + A[i, j]*x[j]\n",
+    "            \n",
+    "    return y"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "collapsed": true
+   },
+   "source": [
+    "#### Testing algorithms 1.1.3 and 1.1.4"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 57,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "CPU times: user 1.89 s, sys: 0 ns, total: 1.89 s\n",
+      "Wall time: 1.89 s\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Test Row-Oriented Gaxpy\n",
+    "%time temp = row_gaxpy(m_x, v_x, v_y)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 59,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "CPU times: user 1.96 s, sys: 24 ms, total: 1.98 s\n",
+      "Wall time: 1.95 s\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Test Column-Oriented Gaxpy\n",
+    "%time temp = column_gaxpy(m_x, v_x, v_y)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
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