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mpHarm88mpHarm88
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add linalg solution
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‎day_04/03_linalg.ipynb

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{
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"nbformat": 4,
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"nbformat_minor": 0,
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.7.4"
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},
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"colab": {
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"name": "03_linalg.ipynb",
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"provenance": []
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}
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},
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "zz2gPozLCcpL"
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},
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"source": [
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"### Solve using Numpy\n",
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"\n",
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"3x + 5y = 6\n",
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"\n",
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"7x - 5y = 9\n",
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"\n",
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"---\n",
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"\n",
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"x + y + z = 6\n",
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"\n",
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"y + z = -4\n",
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" \n",
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"2x + 5y - z = 27\n",
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"\n",
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"---\n",
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"\n",
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"x + y = 4\n",
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"\n",
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"2x + 2y = 8"
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "QyJ3X01uCcpM"
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},
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"source": [
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"import numpy as np"
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],
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "wKhsBrp-CcpM"
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},
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"source": [
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"### Question 1\n",
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"\n",
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"3x + 5y = 6\n",
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"\n",
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"7x - 5y = 9"
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/"
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},
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"id": "7Oq8hIBPCcpM",
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"outputId": "07c80148-14b4-48c8-b3d6-7f7304b25683"
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},
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"source": [
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"# Create a coefficients matrix\n",
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"coeff_matrix = np.array(\n",
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" [[3, 5],\n",
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" [7, -5]]\n",
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")\n",
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"\n",
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"# Results Matrix\n",
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"result_matrix = np.array(\n",
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" [[6],\n",
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" [9]]\n",
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")\n",
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"\n",
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"# Calculate the results\n",
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"results = np.linalg.inv(coeff_matrix).dot(result_matrix)\n",
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"\n",
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"# Check Answer\n",
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"x = results[0]\n",
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"y = results[1]\n",
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"\n",
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"check_answer = (3*x) + (5*y)\n",
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"print(f\"Answer to 3x+5y = 6 where x={x[0]} and y={y[0]}: {check_answer[0]}\\n\")\n",
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"\n",
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"check_answer2 = (7*x)-(5*y)\n",
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"print(f\"Answer to 7x-5y = 9 where x={x[0]} and y={y[0]}: {check_answer2[0]}\")"
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],
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"execution_count": null,
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"outputs": [
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{
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"output_type": "stream",
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"text": [
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"Answer to 3x+5y = 6 where x=1.5 and y=0.30000000000000004: 6.0\n",
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"\n",
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"Answer to 7x-5y = 9 where x=1.5 and y=0.30000000000000004: 9.0\n"
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],
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"name": "stdout"
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}
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "5TCyikB9CcpN"
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},
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"source": [
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"### Question 2\n",
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"\n",
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"x + y + z = 6\n",
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"\n",
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" y + z = -4\n",
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" \n",
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"2x + 5y - z = 27"
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/"
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},
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"id": "cPpkBVtyCcpN",
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"outputId": "41526cf5-dc53-4b26-93fc-a81d7b1d974b"
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},
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"source": [
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"# Create a coefficients matrix\n",
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"coeff_matrix = np.array(\n",
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" [[1, 1, 1],\n",
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" [0, 1, 1],\n",
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" [2, 5, -1]]\n",
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")\n",
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"\n",
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"# Results Matrix\n",
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"result_matrix = np.array(\n",
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" [[6],\n",
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" [-4],\n",
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" [27]]\n",
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")\n",
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"\n",
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"# Calculate the results\n",
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"results = np.linalg.inv(coeff_matrix).dot(result_matrix)\n",
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"\n",
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"# Check Answer\n",
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"x = results[0]\n",
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"y = results[1]\n",
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"z = results[2]\n",
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"\n",
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"check_answer3 = x+y+z\n",
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"print(f\"Answer to x+y+z = 6 where x={x[0]}, y={y[0]}, z={z[0]}: {check_answer3[0]}\\n\")\n",
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"check_answer4 = y+z\n",
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"print(f\"Answer to y+z = -4 where y={y[0]} and z={z[0]}: {check_answer4[0]}\\n\")\n",
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"check_answer5 = (2*x) + (5*y) - z\n",
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"print(f\"Answer to 2x+5y-z = 27 where x={x[0]}, y={y[0]}, z={z[0]}: {check_answer5[0]}\\n\")"
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],
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"execution_count": null,
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"outputs": [
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{
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"output_type": "stream",
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"text": [
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"Answer to x+y+z = 6 where x=10.000000000000002, y=0.5, z=-4.5: 6.000000000000002\n",
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"\n",
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"Answer to y+z = -4 where y=0.5 and z=-4.5: -4.0\n",
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"\n",
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"Answer to 2x+5y-z = 27 where x=10.000000000000002, y=0.5, z=-4.5: 27.000000000000004\n",
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"\n"
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],
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"name": "stdout"
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}
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "kDn2tHPsCcpO"
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},
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"source": [
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"### Question 3\n",
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"\n",
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"x + y = 4\n",
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"\n",
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"2x + 2y = 8"
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/"
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},
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"id": "9Ge8JwKMCcpO",
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"outputId": "a83f2ff7-65f7-449a-88a5-27ab1c92bccc"
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},
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"source": [
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"# Create a coefficients matrix\n",
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"# We add a small value to the diagonal values so we dont end up with a determinant of 0\n",
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"coeff_matrix = np.array(\n",
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" [[1, 1.00001],\n",
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" [2.00001, 2]\n",
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" ]\n",
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")\n",
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"\n",
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"# Results Matrix\n",
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"result_matrix = np.array(\n",
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" [[4],\n",
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" [8]]\n",
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")\n",
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"\n",
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"# Calculate the results\n",
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"results = np.linalg.inv(coeff_matrix).dot(result_matrix)\n",
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"\n",
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"# Check Answer\n",
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"x = results[0]\n",
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"y = results[1]\n",
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"\n",
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"check_answer6 = x+y\n",
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"print(f\"Answer to x+y = 4 where x={x[0]} and y={y[0]}: {check_answer6[0]}\\n\")\n",
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"check_answer7 = (2*x) + (2*y)\n",
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"print(f\"Answer to 2x+2y = 4 where x={x[0]} and y={y[0]}: {check_answer7[0]}\\n\")"
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],
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"execution_count": null,
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"outputs": [
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{
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"output_type": "stream",
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"text": [
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"Answer to x+y = 4 where x=2.666657777794171 and y=1.3333288889261894: 3.9999866667203605\n",
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"\n",
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"Answer to 2x+2y = 4 where x=2.666657777794171 and y=1.3333288889261894: 7.999973333440721\n",
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"\n"
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],
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"name": "stdout"
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}
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]
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}
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]
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}

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