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Added Lab1 report #12

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Added Lab1 report
VIGGEEN Jan 19, 2020
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374 changes: 374 additions & 0 deletions Lab-1/viktorme-report.ipynb
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "lab1_matrixalgorithms.ipynb",
"provenance": [],
"collapsed_sections": []
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "6RgtXlfYO_i7",
"colab_type": "text"
},
"source": [
"# **Lab 1: Matrix algorithms**\n",
"**Viktor Meyer - DD2363 Methods in Scientific Computing**"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "9x_J5FVuPzbm",
"colab_type": "text"
},
"source": [
"# **Abstract**"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "6UFTSzW7P8kL",
"colab_type": "text"
},
"source": [
"This lab is an exercise in matrix operations. The mandatory part includes scalar product, matrix-vector product and matrix-matrix product. There is also an extra assignment euclidean norm or euclidian distance."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "28xLGz8JX3Hh",
"colab_type": "text"
},
"source": [
"# **Environment**"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "D2PYNusD08Wa",
"colab_type": "text"
},
"source": [
"To have access to the neccessary modules you have to run this cell."
]
},
{
"cell_type": "code",
"metadata": {
"id": "Xw7VlErAX7NS",
"colab_type": "code",
"colab": {}
},
"source": [
"# Load neccessary modules.\n",
"from google.colab import files\n",
"\n",
"import time\n",
"import numpy as np\n",
"\n",
"from matplotlib import pyplot as plt\n",
"from matplotlib import tri\n",
"from matplotlib import axes\n",
"from mpl_toolkits.mplot3d import Axes3D"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "gnO3lhAigLev",
"colab_type": "text"
},
"source": [
"# **Introduction**"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "l5zMzgPlRAF6",
"colab_type": "text"
},
"source": [
"The methods to be implemented were covered in the first lectures and definitions are available in the lecture notes: LN-DD2363-part1.pdf\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "WeFO9QMeUOAu",
"colab_type": "text"
},
"source": [
"# **Methods**"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "I5Kf3qRyY5J5",
"colab_type": "text"
},
"source": [
"### Scalar Product ###"
]
},
{
"cell_type": "code",
"metadata": {
"colab_type": "code",
"outputId": "5463ca4e-73b9-40c0-bd06-958e76b35400",
"id": "PbnT724f5mfQ",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 68
}
},
"source": [
"# LN-DD2363-part1.pdf, pp. 7\n",
"x = np.array([0, 3, -7])\n",
"y = np.array([2, 3, 1])\n",
"\n",
"def scalar(x, y):\n",
" result = 0\n",
" assert(x.size == y.size)\n",
" for i in range(x.size):\n",
" result += x[i]*y[i]\n",
" \n",
" return result\n",
"\n",
"print(\"x = \", x)\n",
"print(\"y = \", y)\n",
"print('scalar(x, y) =',scalar(x, y))"
],
"execution_count": 65,
"outputs": [
{
"output_type": "stream",
"text": [
"x = [ 0 3 -7]\n",
"y = [2 3 1]\n",
"scalar(x, y) = 2\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "k9b0yn9qF_Jq"
},
"source": [
"### Matrix-Vector product ###"
]
},
{
"cell_type": "code",
"metadata": {
"colab_type": "code",
"outputId": "2ad783ee-22d5-46bb-a184-44e6036d1ee1",
"id": "401b1-yLGFaH",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 85
}
},
"source": [
"# LN-DD2363-part1.pdf, pp. 22\n",
"x = np.array([2, 1, 0])\n",
"A = np.matrix(\"1 -1 2; 0 -3 1\")\n",
"\n",
"def matrixvectorproduct(x, A):\n",
" b = np.zeros(A.shape[0])\n",
" assert(A.shape[1] == x.size)\n",
" for colIndex in range(A.shape[0]):\n",
" for rowIndex in range(A.shape[1]):\n",
" b[colIndex] += x[rowIndex]*A[colIndex, rowIndex]\n",
" return b\n",
"\n",
"print(\"x = \", x)\n",
"print(\"A = \", A)\n",
"print('matrixvectorproduct(x, A) =', matrixvectorproduct(x, A))"
],
"execution_count": 66,
"outputs": [
{
"output_type": "stream",
"text": [
"x = [2 1 0]\n",
"A = [[ 1 -1 2]\n",
" [ 0 -3 1]]\n",
"matrixvectorproduct(x, A) = [ 1. -3.]\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "lVE-mL2SDDZu"
},
"source": [
"### Matrix-Matrix product ###"
]
},
{
"cell_type": "code",
"metadata": {
"colab_type": "code",
"outputId": "8e285832-68da-43ad-bde6-4f37d93b265a",
"id": "BBZekOW0DGxN",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 136
}
},
"source": [
"# LN-DD2363-part1.pdf, pp. 24\n",
"A = np.matrix(\"0 4 -2; -4 -3 0\")\n",
"B = np.matrix(\"0 1; 1 -1; 2 3\")\n",
"\n",
"def matrixmatrixproduct(A, B):\n",
" C = np.matrix(np.zeros((A.shape[0], B.shape[1])))\n",
" assert(A.shape[1] == B.shape[0])\n",
" for rowIndex in range(A.shape[0]):\n",
" for colIndex in range(B.shape[1]):\n",
" for offset in range(A.shape[1]):\n",
" C[rowIndex, colIndex] += A[rowIndex, offset]*B[offset, colIndex]\n",
" return C\n",
"\n",
"print(\"A = \", A)\n",
"print(\"B = \", B)\n",
"print('matrixmatrixproduct(A, B) =', matrixmatrixproduct(A, B))"
],
"execution_count": 67,
"outputs": [
{
"output_type": "stream",
"text": [
"A = [[ 0 4 -2]\n",
" [-4 -3 0]]\n",
"B = [[ 0 1]\n",
" [ 1 -1]\n",
" [ 2 3]]\n",
"matrixmatrixproduct(A, B) = [[ 0. -10.]\n",
" [ -3. -1.]]\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "l9zEl6bG6lg3"
},
"source": [
"### Euclidian distance ###"
]
},
{
"cell_type": "code",
"metadata": {
"colab_type": "code",
"outputId": "e8351a3e-d446-481d-9bd4-5ef5eb35bff9",
"id": "b52PSKkj6nbm",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 68
}
},
"source": [
"# LN-DD2363-part1.pdf, pp. 24\n",
"x = np.array([-1, 2, 3])\n",
"y = np.array([4, 0, -3])\n",
"\n",
"def euclideandistance(x, y):\n",
" result = 0\n",
" assert(x.size == y.size)\n",
" for i in range(x.size):\n",
" result += (x[i]-y[i])*(x[i]-y[i])\n",
" result = np.sqrt(result)\n",
" return result\n",
"\n",
"print(\"x = \", x)\n",
"print(\"y = \", y)\n",
"print('euclideandistance(x, y) =', euclideandistance(x, y))"
],
"execution_count": 68,
"outputs": [
{
"output_type": "stream",
"text": [
"x = [-1 2 3]\n",
"y = [ 4 0 -3]\n",
"euclideandistance(x, y) = 8.06225774829855\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "SsQLT38gVbn_",
"colab_type": "text"
},
"source": [
"# **Results**"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "RLwlnOzuV-Cd",
"colab_type": "text"
},
"source": [
"The results appear to be correctly implemented and match what is found in e.g the examples at: \n",
"* http://tutorial.math.lamar.edu/Classes/CalcII/DotProduct.aspx\n",
"* https://mathinsight.org/matrix_vector_multiplication\n",
"* http://rosalind.info/glossary/euclidean-distance/"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "_4GLBv0zWr7m",
"colab_type": "text"
},
"source": [
"# **Discussion**"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "6bcsDSoRXHZe",
"colab_type": "text"
},
"source": [
"The results were as expected since the operations were rather simple and basic in terms of linear algebra."
]
}
]
}
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