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diff --git "a/Chapitre 1 - Systemes equations lineaires/1.1. Introduction et d\303\251finition.ipynb" "b/Chapitre 1 - Systemes equations lineaires/1.1. Introduction et d\303\251finition.ipynb"
index 9b6e716..e87b7a8 100644
--- "a/Chapitre 1 - Systemes equations lineaires/1.1. Introduction et d\303\251finition.ipynb"
+++ "b/Chapitre 1 - Systemes equations lineaires/1.1. Introduction et d\303\251finition.ipynb"
@@ -1,292 +1,292 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Concept(s)-clé(s) et théorie\n",
"\n",
"### DÉFINITION 1 :\n",
"\n",
"Une **équation linéaire** aux inconnues $x_1,\\ldots,x_n$ à coefficients réels est une équation de la forme\n",
"\n",
"$$a_1x_1+a_2x_2+\\cdots+a_nx_n=b,$$ \n",
"où $a_1,a_2,\\ldots,a_n,b\\in \\mathbb{R}.$\n",
" \n",
"---\n",
"### DÉFINITION 2 :\n",
"\n",
"On appelle **système d'équations linéaires** (ou simplement système linéaire) une famille d'équations linéaires aux inconnues $x_1,\\ldots,x_n$ à coefficients réels de la forme \n",
"\n",
"$$S=\\left\\{\\begin{array}{ccccccc}\n",
"a_{11}x_1 &+a_{12}x_2 & + &\\cdots &+a_{1n}x_n &= &b_1 \\\\\n",
"a_{21}x_1 &+a_{22}x_2 & + &\\cdots &+a_{2n}x_n &= &b_2 \\\\\n",
"\\vdots & & & &\\vdots & \\vdots &\\vdots \\\\\n",
"a_{m1}x_1 &+a_{m2}x_2 & + &\\cdots &+a_{mn}x_n &= &b_m\n",
"\\end{array},\\right. $$\n",
"\n",
"où $a_{ij},b_i\\in \\mathbb{R}$ pour tout $1\\leq i\\leq m$ et tout $1\\leq j\\leq n.$ \n",
"\n",
"Aussi, on dit qu'une suite ordonnée de $n$ nombres réels $\\alpha=(\\alpha_1,\\ldots,\\alpha_n)$ est une *solution du système linéaire* $S$ si toutes les égalités du système sont vérifiées lorsque l'on remplace $x_j$ par $\\alpha_j,$ ceci pout tout $1\\leq j\\leq n.$"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import Librairie.AL_Fct as al"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### EXEMPLE 1\n",
"\n",
"Dans ce premier exemple nous nous familiarisons avec les équations et les ensembles de solutions. Soit \n",
"$$ \n",
"a_{1}x_{1} + a_{2}x_{2} + \\ldots a_{n}x_{n}=b_1.\n",
"$$ \n",
"On utilise *la syntaxe suivante pour définir les coefficients* de l'équation \n",
"\n",
"$$\n",
"\\begin{align*}\n",
"A&=[a_1, a_2, \\ldots, a_n]\\\\\n",
"b&=[b_1].\n",
"\\end{align*}\n",
"$$\n",
"\n",
"---\n",
"Dans la case ci-dessous, entrer les coefficients de l'équation \n",
"$$3x_1 + 2x_2=7$$\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"al.bgc('seashell')\n",
"#Toutes les valeurs sont initialisées à 1\n",
"\n",
"A = [1,1] \n",
"b = [1]\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"al.printEq(A,b)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On utilise *la syntaxe suivante pour entrer une solution* d'une équation\n",
"$$\\rm{alpha}=[\\alpha_1, \\alpha_2, \\ldots, \\alpha_n]$$"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"al.bgc('seashell')\n",
"#Toutes les valeurs sont initialisées à 1\n",
"\n",
"alpha = [1, 1] #solution"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"isSol = [al.SolOfEq(alpha, A+b, 1)]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### **EXERCICE 1**\n",
"\n",
"Enter l'équation $$ \\frac{2}{5}x_1 -4x_2 + x_3 = 8$$ et donner une solution $$\\alpha=(\\alpha_1, \\alpha_2, \\alpha_3).$$\n",
"\n",
"Vous pouvez aussi adapter le code à l'équation de votre choix."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"al.bgc('seashell')\n",
"\n",
"#Par défaut, les valeurs sont fixées à 1\n",
"\n",
"A = [1, 1, 1] \n",
"b =[1]\n",
"alpha = [1, 1, 1] #solution "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"al.printEq(A,b)\n",
"isSol=[al.SolOfEq(alpha, A+b,1)]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### EXEMPLE 2\n",
"\n",
"Dans cet exercice nous nous familiarisonns avec les systèmes d'équations. La partie ci-dessous vous demande de rentrer un système d'équation. \n",
"\n",
"Soit\n",
"$$S=\\left\\{\\begin{array}{ccccccc}\n",
"a_{11}x_1 &+a_{12}x_2 & + &\\cdots &+a_{1n}x_n &= &b_1 \\\\\n",
"a_{21}x_1 &+a_{22}x_2 & + &\\cdots &+a_{2n}x_n &= &b_2 \\\\\n",
"\\vdots & & & &\\vdots & \\vdots &\\vdots \\\\\n",
"a_{m1}x_1 &+a_{m2}x_2 & + &\\cdots &+a_{mn}x_n &= &b_m\n",
"\\end{array},\\right. $$\n",
"\n",
"On utilise *la syntaxe suivante pour entrer les coefficients du système*\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"A&=\\quad [\\quad [ a_{11} , a_{12}, \\ldots, a_{1n} ], \\quad [ a_{21}, a_{22}, \\ldots, a_{2n}]\\quad, \\ldots , \\quad[a_{m1}, a_{m2}, \\ldots, a_{mn}]\\quad]\\\\\n",
"b&=\\quad [\\quad b_1, b_2, \\ldots, b_m \\quad]\n",
"\\end{align*}$$\n",
"\n",
"---\n",
"Essayer d'entrer le système d'équations ci-dessous\n",
"\n",
"$$\\begin{cases}\n",
"x_1 &- & 3 x_2 && = 4\\\\\n",
"-x_1 & + & 4 x_2 && = 5\n",
"\\end{cases}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"al.bgc('seashell')\n",
"\n",
"#Par défaut, les valeurs sont fixées à 1\n",
"\n",
"A = [ [1, 1], [1, 1]] \n",
"b=[1, 1] \n",
"alpha = [1, 1] #solution"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"al.printSyst(A,b)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"al.SolOfSyst(alpha, A,b)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### **EXERCICE 2**\n",
" \n",
"Entrer le système suivant et donner une solution du système.\n",
"\n",
"$$\\begin{cases}\n",
"&2x_1 -3 x_2 + x_3&&=-5\\\\\n",
"&-\\dfrac{1}{3}x_1 + x_3&&= 2\\\\\n",
"&x_1 + 4x_2 -x_3 &&=0\n",
"\\end{cases}\n",
"$$\n",
"\n",
"Vous pouvez aussi adapter le code à l'équation de votre choix."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"al.bgc('seashell')\n",
"#Par défaut, les valeurs sont fixées à 1\n",
"\n",
"A = [[1,1,1], [1,1,1], [1,1,1]]\n",
"b =[1,1,1]\n",
"alpha =[1,1,1] #solution\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"al.printSyst(A,b)\n",
"al.SolOfSyst(alpha, A,b)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[Passez au notebook du chapitre 1.2: Nombre de solutions d'un système](./1.2.%20Nombre%20de%20solution%20d'un%20système.ipynb)"
]
}
],
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"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
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+ "version": "3.7.2"
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diff --git "a/Chapitre 1 - Systemes equations lineaires/1.2. Nombre de solution d'un syst\303\250me.ipynb" "b/Chapitre 1 - Systemes equations lineaires/1.2. Nombre de solution d'un syst\303\250me.ipynb"
index 8e6471c..889365d 100644
--- "a/Chapitre 1 - Systemes equations lineaires/1.2. Nombre de solution d'un syst\303\250me.ipynb"
+++ "b/Chapitre 1 - Systemes equations lineaires/1.2. Nombre de solution d'un syst\303\250me.ipynb"
@@ -1,95614 +1,593 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Concept(s)-clé(s) et théorie\n",
"\n",
"On considère un système d'équations linéaires aux inconnues $x_1,\\ldots,x_n$\n",
"\n",
"$$S=\\left\\{\\begin{array}{ccccccc}\n",
"a_{11}x_1 &+a_{12}x_2 & + &\\cdots &+a_{1n}x_n &= &b_1 \\\\\n",
"a_{21}x_1 &+a_{22}x_2 & + &\\cdots &+a_{2n}x_n &= &b_2 \\\\\n",
"\\vdots & & & &\\vdots & \\vdots &\\vdots \\\\\n",
"a_{m1}x_1 &+a_{m2}x_2 & + &\\cdots &+a_{mn}x_n &= &b_m\n",
"\\end{array},\\right. $$\n",
"\n",
"où $a_{ij},b_i\\in \\mathbb{R}$ pour tout $1\\leq i\\leq m$ et tout $1\\leq j\\leq n.$ \n",
"\n",
"---\n",
- "Un système d'équations linéaires à coefficients réels satisfait à précisément une des conditions suivantes.\n",
+ "Un système d'équations linéaires à coefficients réels satisfait précisément une des conditions suivantes.\n",
"\n",
"1.Le système ne possède aucune solution.\n",
"\n",
"2.Le système possède une solution unique.\n",
"\n",
"3.Le système possède une infinité de solutions.\n"
]
},
{
"cell_type": "code",
- "execution_count": 1,
+ "execution_count": null,
"metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- " <script type=\"text/javascript\">\n",
- " window.PlotlyConfig = {MathJaxConfig: 'local'};\n",
- " if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}\n",
- " if (typeof require !== 'undefined') {\n",
- " require.undef(\"plotly\");\n",
- " requirejs.config({\n",
- " paths: {\n",
- " 'plotly': ['https://cdn.plot.ly/plotly-latest.min']\n",
- " }\n",
- " });\n",
- " require(['plotly'], function(Plotly) {\n",
- " window._Plotly = Plotly;\n",
- " });\n",
- " }\n",
- " </script>\n",
- " "
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
+ "outputs": [],
"source": [
"import Librairie.AL_Fct as al\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import plotly\n",
"import plotly.graph_objs as go\n",
"import pandas as pd\n",
"import random\n",
"from IPython.core.magic import register_cell_magic\n",
"from IPython.display import HTML, display"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### EXEMPLE 1\n",
"\n",
"Nous allons travailler avec un système de $2$ inconnues, $2$ équations:\n",
"\n",
"$$\n",
"\\begin{cases}\n",
"a_{11}x_1 + a_{12}x_2=b_1\\\\\n",
"a_{21}x_1 + a_{22}x_2=b_2.\n",
"\\end{cases}\n",
"$$\n",
"\n",
"On utilise *la syntaxe suivante pour entrer les coefficients du système*\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"A&=\\quad [\\quad [ a_{11} , a_{12}, \\ldots, a_{1n} ], \\quad [ a_{21}, a_{22}, \\ldots, a_{2n}]\\quad, \\ldots , \\quad[a_{m1}, a_{m2}, \\ldots, a_{mn}]\\quad]\\\\\n",
"b&=\\quad [\\quad b_1, b_2, \\ldots, b_m \\quad]\n",
"\\end{align*}$$\n",
"\n",
"---\n",
"Entrer le système ci-dessous - ou n'importe quel système de votre choix. Après avoir étudié les deux droites, entrer une solution du système\n",
"\n",
"$$\n",
"\\begin{cases}\n",
"-2x_1 + x_2=2\\\\\n",
"2x_1 -2x_2=1.\n",
"\\end{cases}\n",
"$$\n"
]
},
{
"cell_type": "code",
- "execution_count": 2,
+ "execution_count": null,
"metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- "<img src onerror=\"var cell = this.closest('.jp-CodeCell');var editor = cell.querySelector('.jp-Editor');editor.style.background='seashell';this.parentNode.removeChild(this)\">"
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- "text/plain": [
- "<IPython.core.display.HTML object>"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
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+ "outputs": [],
"source": [
"al.bgc('seashell')\n",
"#Par défaut, les coefficients sont fixés à 1 et n=2, m=2\n",
"\n",
"A = [ [-2,1] , [2,-2]]\n",
"b = [2,1]"
]
},
{
"cell_type": "code",
- "execution_count": 3,
+ "execution_count": null,
"metadata": {},
- "outputs": [
- {
- "data": {
- "text/latex": [
- "$\\begin{cases}-2x_1+x_2=2\\\\2x_1-2x_2=1\\\\\\end{cases}$"
- ],
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"source": [
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- "La suite entrée est une solution de l'équation 1\n",
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"### **EXERCICE 1**\n",
"\n",
"Pour chacun des cas ci-dessous, déterminer la/les solution(s) des systèmes. \n",
"\n",
" $$ \n",
"a)\\quad \\begin{cases}\n",
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"\\end{cases} \\hspace{1cm} b) \\quad \\begin{cases}\n",
"x_1 - x_2&=\\phantom{-}2\\\\\n",
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"$$\n"
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"source": [
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"al.SolOfSyst(alpha, A,b)\n",
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"### **EXERCICE 2**\n",
"\n",
"Pour chacun des cas ci-dessous, déterminer la/les solution(s) des systèmes. \n",
"\n",
"$$ \n",
"a)\\quad \\begin{cases}\n",
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"\\end{cases} \\hspace{1cm}\n",
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\"#ab63fa\", \"#FFA15A\", \"#19d3f3\", \"#FF6692\", \"#B6E880\", \"#FF97FF\", \"#FECB52\"], \"font\": {\"color\": \"#2a3f5f\"}, \"geo\": {\"bgcolor\": \"white\", \"lakecolor\": \"white\", \"landcolor\": \"#E5ECF6\", \"showlakes\": true, \"showland\": true, \"subunitcolor\": \"white\"}, \"hoverlabel\": {\"align\": \"left\"}, \"hovermode\": \"closest\", \"mapbox\": {\"style\": \"light\"}, \"paper_bgcolor\": \"white\", \"plot_bgcolor\": \"#E5ECF6\", \"polar\": {\"angularaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"radialaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"scene\": {\"xaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"yaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"zaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}}, \"shapedefaults\": {\"line\": {\"color\": \"#2a3f5f\"}}, \"ternary\": {\"aaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"baxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"caxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"title\": {\"x\": 0.05}, \"xaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}, \"yaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}}}, \"width\": 800},\n",
- " {\"responsive\": true}\n",
- " ).then(function(){\n",
- " \n",
- "var gd = document.getElementById('b9d4cff4-98b4-4571-bfbc-451f00641992');\n",
- "var x = new MutationObserver(function (mutations, observer) {{\n",
- " var display = window.getComputedStyle(gd).display;\n",
- " if (!display || display === 'none') {{\n",
- " console.log([gd, 'removed!']);\n",
- " Plotly.purge(gd);\n",
- " observer.disconnect();\n",
- " }}\n",
- "}});\n",
- "\n",
- "// Listen for the removal of the full notebook cells\n",
- "var notebookContainer = gd.closest('#notebook-container');\n",
- "if (notebookContainer) {{\n",
- " x.observe(notebookContainer, {childList: true});\n",
- "}}\n",
- "\n",
- "// Listen for the clearing of the current output cell\n",
- "var outputEl = gd.closest('.output');\n",
- "if (outputEl) {{\n",
- " x.observe(outputEl, {childList: true});\n",
- "}}\n",
- "\n",
- " })\n",
- " };\n",
- " });\n",
- " </script>\n",
- " </div>"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
+ "outputs": [],
"source": [
"al.printSyst(A,b)\n",
"al.Plot3DSys(-10,10,100,A,b)"
]
},
{
"cell_type": "code",
- "execution_count": 10,
+ "execution_count": null,
"metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "La suite entrée n'est pas une solution de l'équation 1\n",
- "La suite entrée n'est pas une solution de l'équation 2\n",
- "La suite entrée n'est pas une solution de l'équation 3\n",
- "Ce n'est pas une solution du système\n"
- ]
- },
- {
- "data": {
- "text/plain": [
- "False"
- ]
- },
- "execution_count": 10,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
+ "outputs": [],
"source": [
- "alpha = [1,1,1]\n",
+ "alpha = [1, 1, 1]\n",
"al.SolOfSyst(alpha, A,b)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### **EXERCICE 3**\n",
"#code 1.2.Ex3\n",
"\n",
- "À l'aide des graphes interactifs ci-dessous, trouver les valeurs des paramètres $h$ et $k$ pour que les systèmes a), b), c) e d) admettent, si possible,\n",
+ "À l'aide des graphes interactifs ci-dessous, trouver les valeurs des paramètres $h$ et $k$ pour que les systèmes a), b), c) et d) admettent, si possible,\n",
"1. aucune solution\n",
"2. une unique solution\n",
"3. une infinité de solution \n",
"\n",
"\n",
"$$ \n",
"a)\\begin{cases}\n",
"x_1 +5 x_2&=h\\\\\n",
"-2x_1 -10 x_2&=18\n",
"\\end{cases} \\hspace{1cm} b) \\begin{cases}\n",
"hx_1 + x_2&=3\\\\\n",
"-2x_1 - x_2&=-1\n",
"\\end{cases}\\hspace{1cm} c) \\begin{cases}\n",
"3x_1 + hx_2&=1\\\\\n",
"x_1 + 3x_2&=h\n",
"\\end{cases}\\hspace{1cm} d) \\begin{cases}\n",
"kx_1 + x_2&=h\\\\\n",
"3x_1 -5x_2&=2\n",
"\\end{cases}\n",
"$$"
]
},
{
"cell_type": "code",
- "execution_count": 11,
+ "execution_count": null,
"metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- " <script type=\"text/javascript\">\n",
- " window.PlotlyConfig = {MathJaxConfig: 'local'};\n",
- " if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}\n",
- " if (typeof require !== 'undefined') {\n",
- " require.undef(\"plotly\");\n",
- " requirejs.config({\n",
- " paths: {\n",
- " 'plotly': ['https://cdn.plot.ly/plotly-latest.min']\n",
- " }\n",
- " });\n",
- " require(['plotly'], function(Plotly) {\n",
- " window._Plotly = Plotly;\n",
- " });\n",
- " }\n",
- " </script>\n",
- " "
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
+ "outputs": [],
"source": [
"import plotly as py\n",
"import numpy as np\n",
"plotly.offline.init_notebook_mode(connected=True)\n",
"import plotly.graph_objs as go\n",
"from ipywidgets import interactive, HBox, VBox, widgets, interact, FloatSlider"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## CASE a)"
]
},
{
"cell_type": "code",
- "execution_count": 12,
+ "execution_count": null,
"metadata": {},
- "outputs": [
- {
- "data": {
- "text/latex": [
- "$\\begin{cases}x_1+5x_2=0\\\\-2x_1-10x_2=18\\\\\\end{cases}$"
- ],
- "text/plain": [
- "<IPython.core.display.Latex object>"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- },
- {
- "data": {
- "application/vnd.jupyter.widget-view+json": {
- "model_id": "f1d0199fde4e4ed5bf2774cdb514e043",
- "version_major": 2,
- "version_minor": 0
- },
- "text/plain": [
- "VBox(children=(FigureWidget({\n",
- " 'data': [{'name': 'a) Droite 1',\n",
- " 'type': 'scatter',\n",
- " …"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
+ "outputs": [],
"source": [
"A=[[1, 5], [-2, -10]] # we initialize the problem. The values of h and k must be fixed to one specific value here\n",
"b=[0, 18]\n",
"al.printSyst(A, b) # the system printed below shows the values of h and k inserted here!!\n",
"\n",
"data=[]\n",
"x=np.linspace(-5,5,11)\n",
"m=len(A)\n",
"MatCoeff = [A[i]+[b[i]]for i in range(m)] #becomes augmented matrix\n",
"MatCoeff=np.array(MatCoeff)\n",
"\n",
"for i in range(len(MatCoeff)):\n",
" trace=go.Scatter(x=x, y=(MatCoeff[i,2]-MatCoeff[i,0]*x)/MatCoeff[i,1], name='a) Droite %d'%(i+1))\n",
" data.append(trace)\n",
"\n",
"f=go.FigureWidget(data=data,\n",
" layout=go.Layout(xaxis=dict(\n",
" range=[-5, 5]\n",
" ),\n",
" yaxis=dict(\n",
" range=[-10, 10]\n",
" ) )\n",
"\n",
")\n",
"#def update_y(coeff, cof):\n",
" # MatCoeff= [[coeff, 1, cof]]\n",
" # MatCoeff=np.array(MatCoeff)\n",
" # f.data[0].y=(MatCoeff[0,2]-MatCoeff[0,0]*x)/MatCoeff[0,1]\n",
"def update_y(h):\n",
" MatCoeff = [[1, 5, h]]\n",
" MatCoeff=np.array(MatCoeff)\n",
" f.data[0].y=(MatCoeff[0,2]-MatCoeff[0,0]*x)/MatCoeff[0,1]\n",
" \n",
"freq_slider = interactive(update_y, h=(-15, 15, 1/2)) \n",
"vb = VBox((f, freq_slider))\n",
"vb.layout.align_items = 'center'\n",
"vb"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## CASE b)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
- "A=[[1, 1], [-2,-2]] # we initialize the problem. The value of h is fixed\n",
+ "A=[[1, 1], [-2,-1]] # we initialize the problem. The value of h is fixed\n",
"b=[3, -1]\n",
"al.printSyst(A, b) # the system printed below shows the value of h inserted here\n",
"\n",
"m=len(A)\n",
"MatCoeff = [A[i]+[b[i]]for i in range(m)] #becomes augmented matrix\n",
"MatCoeff=np.array(MatCoeff)\n",
"data=[]\n",
"x=np.linspace(-5,5,11)\n",
"MatCoeff=np.array(MatCoeff)\n",
"for i in range(len(MatCoeff)):\n",
" trace=go.Scatter(x=x, y= (MatCoeff[i,2]-MatCoeff[i,0]*x)/MatCoeff[i,1], name='b) Droite %d'%(i+1))\n",
" data.append(trace)\n",
" \n",
"f=go.FigureWidget(data=data,\n",
" layout=go.Layout(xaxis=dict(\n",
" range=[-5, 5]\n",
" ),\n",
" yaxis=dict(\n",
" range=[-10, 10]\n",
" ) )\n",
" \n",
")\n",
"#def update_y(coeff, cof):\n",
" # MatCoeff= [[coeff, 1, cof]]\n",
" # MatCoeff=np.array(MatCoeff)\n",
" # f.data[0].y=(MatCoeff[0,2]-MatCoeff[0,0]*x)/MatCoeff[0,1]\n",
"#coefficients=[[h,1,3]]\n",
"def mat(k):\n",
" h=k\n",
" MatCoeff=[[h,1,3]]\n",
" return MatCoeff\n",
"def update_y(h):\n",
" MatCoeff= mat(h)\n",
" MatCoeff=np.array(MatCoeff)\n",
" f.data[0].y=(MatCoeff[0,2]-MatCoeff[0,0]*x)/MatCoeff[0,1]\n",
" \n",
"freq_slider = interactive(update_y, h=(-10, 10, 1/2)) \n",
"\n",
"vb = VBox((f, freq_slider))\n",
"vb.layout.align_items = 'center'\n",
"vb"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## CASE c)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"A=[[3, 1], [1, 3]] # we initialize the problem. The values of h and k are fixed\n",
"b=[1, 1]\n",
"al.printSyst(A, b) # the system printed below shows the values of h and k inserted here\n",
"\n",
"m=len(A)\n",
"MatCoeff = [A[i]+[b[i]]for i in range(m)] #becomes augmented matrix\n",
"MatCoeff=np.array(MatCoeff)\n",
"data=[]\n",
"x=np.linspace(-25,25,101)\n",
"MatCoeff=np.array(MatCoeff)\n",
"for i in range(len(MatCoeff)):\n",
" trace=go.Scatter(x=x, y= (MatCoeff[i,2]-MatCoeff[i,0]*x)/MatCoeff[i,1], name='c) Droite %d'%(i+1))\n",
" data.append(trace)\n",
" \n",
"f=go.FigureWidget(data=data,\n",
" layout=go.Layout(xaxis=dict(\n",
" range=[-25, 25]\n",
" ),\n",
" yaxis=dict(\n",
" range=[-50, 50]\n",
" ) )\n",
" \n",
")\n",
"#def update_y(coeff, cof):\n",
" # MatCoeff= [[coeff, 1, cof]]\n",
" # MatCoeff=np.array(MatCoeff)\n",
" # f.data[0].y=(MatCoeff[0,2]-MatCoeff[0,0]*x)/MatCoeff[0,1]\n",
"def mat(h):\n",
" MatCoeff= [[h, 3, 1],[3, 1, h] ]\n",
" return MatCoeff\n",
"\n",
"def update_y(h):\n",
" MatCoeff= mat(h)\n",
" MatCoeff=np.array(MatCoeff)\n",
" f.data[0].y=(MatCoeff[0,2]-MatCoeff[0,0]*x)/MatCoeff[0,1]\n",
" f.data[1].y=(MatCoeff[1,2]-MatCoeff[1,0]*x)/MatCoeff[1,1]\n",
"\n",
"freq_slider = interactive(update_y, h=(-20, 20, 1)) \n",
"\n",
"vb = VBox((f, freq_slider))\n",
"vb.layout.align_items = 'center'\n",
"vb"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## CASE d)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"A=[[1, 1], [3, -5]] # we initialize the problem. The values of h and k are fixed\n",
"b=[1, 2]\n",
"al.printSyst(A, b) # the system printed below shows the values of h and k inserted here\n",
"\n",
"m=len(A)\n",
"MatCoeff = [A[i]+[b[i]]for i in range(m)] #becomes augmented matrix\n",
"MatCoeff=np.array(MatCoeff)\n",
"data=[]\n",
"x=np.linspace(-15,15,101)\n",
"MatCoeff=np.array(MatCoeff)\n",
"for i in range(len(MatCoeff)):\n",
" trace=go.Scatter(x=x, y= (MatCoeff[i,2]-MatCoeff[i,0]*x)/MatCoeff[i,1], name='d) Droite %d'%(i+1))\n",
" data.append(trace)\n",
" \n",
"f=go.FigureWidget(data=data,\n",
" layout=go.Layout(xaxis=dict(\n",
" range=[-15, 15]\n",
" ),\n",
" yaxis=dict(\n",
" range=[-10, 10]\n",
" ) )\n",
" \n",
")\n",
"#def update_y(coeff, cof):\n",
" # MatCoeff= [[coeff, 1, cof]]\n",
" # MatCoeff=np.array(MatCoeff)\n",
" # f.data[0].y=(MatCoeff[0,2]-MatCoeff[0,0]*x)/MatCoeff[0,1]\n",
"def update_y(h, k):\n",
- " MatCoeff= [[h, 1, k],[2, -5, 5] ]\n",
+ " MatCoeff= [[k, 1, h],[2, -5, 5] ]\n",
" MatCoeff=np.array(MatCoeff)\n",
" f.data[0].y=(MatCoeff[0,2]-MatCoeff[0,0]*x)/MatCoeff[0,1]\n",
"\n",
" \n",
" f.data[1].y=(MatCoeff[1,2]-MatCoeff[1,0]*x)/MatCoeff[1,1]\n",
"\n",
"freq_slider = interactive(update_y, h=(-10, 10, 1/10),k=(-10, 10, 1))\n",
"\n",
"vb = VBox((f, freq_slider))\n",
"vb.layout.align_items = 'center'\n",
"vb"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercice 4\n",
"\n",
- "À l'aide des graphes interactifs ci-dessous, trouver les valeurs des paramètre $h$ pour que le système admet, si possible,\n",
+ "À l'aide des graphes interactifs ci-dessous, trouver les valeurs des paramètre $h$ pour que le système admette, si possible,\n",
"1. aucune solution\n",
"2. une unique solution\n",
"3. une infinité de solution \n",
"\n",
"$$ \n",
"\\begin{cases}\n",
"hx_1 -2 x_2 &=4\\\\\n",
"-2x_1 +h x_2&=-4\\\\\n",
"x_1 - x_2 &=h\n",
"\\end{cases} \\hspace{1cm}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"A=[[1, -2], [-2, 1], [1, -1]] # we initialize the problem. The values of h and k are fixed\n",
"b=[4, -4, 2]\n",
"al.printSyst(A, b) # the system printed below shows the values of h and k inserted here\n",
"\n",
"m=len(A)\n",
"MatCoeff = [A[i]+[b[i]]for i in range(m)] #becomes augmented matrix\n",
"MatCoeff=np.array(MatCoeff)\n",
"data=[]\n",
"x=np.linspace(-25,25,101)\n",
"MatCoeff=np.array(MatCoeff)\n",
"for i in range(len(MatCoeff)):\n",
" trace=go.Scatter(x=x, y=(MatCoeff[i,2]-MatCoeff[i,0]*x)/MatCoeff[i,1], name='c) Droite %d'%(i+1))\n",
" data.append(trace)\n",
" \n",
"f=go.FigureWidget(data=data,\n",
" layout=go.Layout(xaxis=dict(\n",
" range=[-25, 25]\n",
" ),\n",
" yaxis=dict(\n",
" range=[-50, 50]\n",
" ) )\n",
" \n",
")\n",
"#def update_y(coeff, cof):\n",
" # MatCoeff= [[coeff, 1, cof]]\n",
" # MatCoeff=np.array(MatCoeff)\n",
" # f.data[0].y=(MatCoeff[0,2]-MatCoeff[0,0]*x)/MatCoeff[0,1]\n",
"def mat(h):\n",
" MatCoeff= [[h, -2, 4], [-2, h, -4], [1, -1, h]]\n",
" return MatCoeff\n",
"\n",
+ "# Do something to avoid dividing by 0 (even if the graph still working, error is printed)\n",
"def update_y(h):\n",
" MatCoeff= mat(h)\n",
" MatCoeff=np.array(MatCoeff)\n",
" f.data[0].y=(MatCoeff[0,2]-MatCoeff[0,0]*x)/MatCoeff[0,1]\n",
" f.data[1].y=(MatCoeff[1,2]-MatCoeff[1,0]*x)/MatCoeff[1,1]\n",
" f.data[2].y=(MatCoeff[2,2]-MatCoeff[2,0]*x)/MatCoeff[2,1]\n",
"\n",
"freq_slider = interactive(update_y, h=(-20, 20, 1)) \n",
"\n",
"vb = VBox((f, freq_slider))\n",
"vb.layout.align_items = 'center'\n",
"vb"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[Passez au notebook du chapitre 1.3-4: Notation Matricielle](./1.3-4.%20Notation%20Matricielle.ipynb)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.6.9"
+ "version": "3.7.2"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
diff --git "a/Chapitre 2 - Algebre matricielle/2.4 Syst\303\250mes d'\303\251quations et matrices.ipynb" "b/Chapitre 2 - Algebre matricielle/2.4 Syst\303\250mes d'\303\251quations et matrices.ipynb"
index e10945b..c5bfadd 100644
--- "a/Chapitre 2 - Algebre matricielle/2.4 Syst\303\250mes d'\303\251quations et matrices.ipynb"
+++ "b/Chapitre 2 - Algebre matricielle/2.4 Syst\303\250mes d'\303\251quations et matrices.ipynb"
@@ -1,353 +1,414 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# **Concept(s)-clé(s) et théorie**\n",
"\n",
+ "## Théorème\n",
"Soit $A$ une matrice $n\\times n $ inversible. Alors pour tout vecteur $\\overrightarrow{b}\\in \\mathbb{R}^n$, l'équation $A\\overrightarrow{x}=\\overrightarrow{b}$ admet pour unique solution le vecteur $$\n",
- "\\overrightarrow{\\tilde{x}}=A^{-1}\\overrightarrow{b}$$\n",
- "De plus, si le système $A\\overrightarrow{x} = \\overrightarrow{b}$ admet une solution unique $\\overrightarrow{\\tilde{x}}$, alors $A$ est inversible et son inverse est tel que $\\overrightarrow{\\tilde{x}} = A^{-1}\\overrightarrow{b}$ pour chaque $\\overrightarrow{b} \\in \\mathbb{R}^n$."
+ "\\overrightarrow{\\tilde{x}}=A^{-1}\\overrightarrow{b}$$"
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 2,
"metadata": {
"scrolled": true
},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ " <script type=\"text/javascript\">\n",
+ " window.PlotlyConfig = {MathJaxConfig: 'local'};\n",
+ " if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}\n",
+ " if (typeof require !== 'undefined') {\n",
+ " require.undef(\"plotly\");\n",
+ " requirejs.config({\n",
+ " paths: {\n",
+ " 'plotly': ['https://cdn.plot.ly/plotly-latest.min']\n",
+ " }\n",
+ " });\n",
+ " require(['plotly'], function(Plotly) {\n",
+ " window._Plotly = Plotly;\n",
+ " });\n",
+ " }\n",
+ " </script>\n",
+ " "
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/html": [
+ " <script type=\"text/javascript\">\n",
+ " window.PlotlyConfig = {MathJaxConfig: 'local'};\n",
+ " if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}\n",
+ " if (typeof require !== 'undefined') {\n",
+ " require.undef(\"plotly\");\n",
+ " requirejs.config({\n",
+ " paths: {\n",
+ " 'plotly': ['https://cdn.plot.ly/plotly-latest.min']\n",
+ " }\n",
+ " });\n",
+ " require(['plotly'], function(Plotly) {\n",
+ " window._Plotly = Plotly;\n",
+ " });\n",
+ " }\n",
+ " </script>\n",
+ " "
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
"source": [
"import Librairie.AL_Fct as al\n",
"import Corrections.corrections as corrections\n",
"import numpy as np"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "### EXAMPLE 1\n",
- "Consider the linear system $Ax=b$, with:\n",
+ "### EXEMPLE 1\n",
+ "Considérez le système linéaire $ Ax = b $, avec:\n",
"\\begin{equation}\n",
"A = \n",
"\\begin{bmatrix}\n",
"2 & 0 & 1\\\\\n",
"0 & 3 & 4 \\\\\n",
"2 & 2 & 1\n",
"\\end{bmatrix}; \\qquad b = \n",
"\\begin{bmatrix}\n",
"2\\\\\n",
"4\\\\\n",
"3\\\\\n",
"\\end{bmatrix};\n",
"\\end{equation}\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"A = [[2, 0, 1], [0, 3, 4], [2, 2, 1]]\n",
"b = [[2], [4], [3]]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "#### TASK 1: solve the linear system taking advantage of the Gauss elimination method"
+ "#### ÉTAPE 1: résoudre le système linéaire en utilisant la méthode d'élimination de Gauss"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"print('Vous allez échelonner la matrice augmenteé')\n",
"al.printAAug(A,b)\n",
"[i,j,r,alpha]= al.manualEch(A)\n",
"MatriceList=[np.array(A)]\n",
"RHSList = [np.array(b)]\n",
"m=np.concatenate((A,b), axis=1)\n",
"print('\\033[1mExecutez la ligne suivante pour effectuer l\\'opération choisie \\033[0m')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"m=al.echelonnage(i, j, r, alpha, A, m, MatriceList, RHSList)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
- "print('Insert here the value of the computed solution')\n",
- "x1 = [[11/16], [1/2], [5/8]]\n",
+ "print('Insérez ici la valeur de la solution calculée')\n",
+ "x1 = [[1], [1], [1]]\n",
"res1 = al.SolOfSyst(x1, A, b)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "#### TASK 2: compute the inverse of matrix A ([see the Notebook 2.3](./2.3%20Matrices%20carrées%2C%20inversibles.ipynb)) and derive the solution to the linear system according to the obtained result"
+ "#### TASK 2: calculer l'inverse de la matrice A ([voir le Notebook 2.3](./2.3%20Matrices%20carrées%2C%20inversibles.ipynb)) et dériver la solution du système linéaire en fonction du résultat obtenu"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"I=[[1,0,0],[0,1,0],[0,0,1]]\n",
"print('Vous allez échelonner la matrice augmenteé avec la matrice identité')\n",
"al.printA(A,I)\n",
"[i,j,r,alpha]= al.manualEch(A,I)\n",
"m=np.concatenate((A,I), axis=1)\n",
"MatriceList=[A]\n",
"RhSList=[I]\n",
"print('\\033[1mExecutez la ligne suivante pour effectuer l\\'opération choisie \\033[0m')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"m=al.echelonnage(i,j,r,alpha,A,m,MatriceList,RhSList)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
- "print('Insert here the value of the computed solution')\n",
- "A_inv = [[0.3125,-0.125,0.1875], [-0.5,0,0.5], [0.375,0.25,-0.375]]\n",
+ "print('Insérez ici la valeur de la solution calculée')\n",
+ "A_inv = [[1,0,0], [0,1,0], [0,0,1]]\n",
"x2 = np.dot(np.array(A_inv), np.array(b))\n",
"res2 = al.SolOfSyst(x2, A, b)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"if res1 and res2:\n",
- " print(f'You are right! And additionally x1={x1} is the only solution to the linear system!')"
+ " print(f'Tu as raison! Et en plus, x1 = {x1} est la seule solution au système linéaire')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "### EXERCISE 1\n",
- "Consider the generic linear system $Ax=b$ with $A \\in \\mathbb{R}^{n \\times n}$ and $b \\in \\mathbb{R}^n$; mark those of the following statements which could be true for some values of $A$ and $b$:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {
- "scrolled": true
- },
- "outputs": [],
- "source": [
- "corrections.Ex1Chapitre2_4()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### EXERCISE 2\n",
- "Consider the following system of equations:\n",
+ "### EXERCICE 1\n",
+ "Considérez le système d'équations suivant:\n",
"\\begin{equation}\n",
"\\begin{cases}\n",
"x_1 + 2x_2 - x_3 &=0\\\\\n",
"2x_1 - x_2 - x_3 &=1\\\\\n",
"x_1 - 2x_2 + x_3 &=2\n",
"\\end{cases}\n",
"\\end{equation}\n",
- "Which of the following statements is true?"
+ "Laquelle des affirmations suivantes est correcte?"
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 4,
"metadata": {
"scrolled": true
},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "application/vnd.jupyter.widget-view+json": {
+ "model_id": "582406aa85cb40d9a7dbbbbb19a61cc6",
+ "version_major": 2,
+ "version_minor": 0
+ },
+ "text/plain": [
+ "interactive(children=(Checkbox(value=False, description='Le système admet une solution unique et elle est:$$\\\\…"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
"source": [
- "corrections.Ex2Chapitre2_4()"
+ "corrections.Ex1Chapitre2_4()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "#### You can run the following cells to help yourself in computing the solution of the linear system and the inverse of matrix $A$"
+ "#### Vous pouvez exécuter les cellules suivantes pour vous aider à calculer (éventuellement) la solution du système linéaire et l'inverse de la matrice $A$, si elle existe"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"A = [[1,2,-1],[2,-1,-1],[1,-2,1]]\n",
"b = [[1], [-2], [1]]"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"print('Vous allez échelonner la matrice augmenteé')\n",
"al.printAAug(A,b)\n",
"[i,j,r,alpha]= al.manualEch(A)\n",
"MatriceList=[np.array(A)]\n",
"RHSList = [np.array(b)]\n",
"m=np.concatenate((A,b), axis=1)\n",
"print('\\033[1mExecutez la ligne suivante pour effectuer l\\'opération choisie \\033[0m')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"m=al.echelonnage(i, j, r, alpha, A, m, MatriceList, RHSList)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"I=[[1,0,0],[0,1,0],[0,0,1]]\n",
"print('Vous allez échelonner la matrice augmenteé avec la matrice identité')\n",
"al.printA(A,I)\n",
"[i,j,r,alpha]= al.manualEch(A,I)\n",
"m=np.concatenate((A,I), axis=1)\n",
"MatriceList=[A]\n",
"RhSList=[I]\n",
"print('\\033[1mExecutez la ligne suivante pour effectuer l\\'opération choisie \\033[0m')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"m=al.echelonnage(i,j,r,alpha,A,m,MatriceList,RhSList)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "### EXERCISE 3\n",
- "Consider the linear system $Ax=b$ with:\n",
+ "### EXERCICE 2\n",
+ "\n",
+ "Considérez le système linéaire $Ax = b$ avec:\n",
"\\begin{equation}\n",
"A = \n",
"\\begin{bmatrix}\n",
"1 & 3 & 2\\\\\n",
"0 & 4 & 1\\\\\n",
"1 & -5 & 0\n",
"\\end{bmatrix}\n",
"\\qquad b=\n",
"\\begin{bmatrix}\n",
"3\\\\\n",
"5\\\\\n",
"\\alpha\n",
"\\end{bmatrix}\n",
"\\end{equation}\n",
- "Which of the following statements is true?"
+ "Laquelle des affirmations suivantes est correcte?"
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 5,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "application/vnd.jupyter.widget-view+json": {
+ "model_id": "308254240ce34aef8905bac8d621bbf5",
+ "version_major": 2,
+ "version_minor": 0
+ },
+ "text/plain": [
+ "interactive(children=(Checkbox(value=False, description=\"Le système n'admet une solution unique que si $\\\\alph…"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
"source": [
- "corrections.Ex3Chapitre2_4()"
+ "corrections.Ex2Chapitre2_4()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[Passez au notebook 2.5: Matrices élémentaires](2.5%20Matrices%20élémentaires.ipynb)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
diff --git "a/Chapitre 2 - Algebre matricielle/2.5 Matrices \303\251l\303\251mentaires.ipynb" "b/Chapitre 2 - Algebre matricielle/2.5 Matrices \303\251l\303\251mentaires.ipynb"
index 6b7feb0..887c5d0 100644
--- "a/Chapitre 2 - Algebre matricielle/2.5 Matrices \303\251l\303\251mentaires.ipynb"
+++ "b/Chapitre 2 - Algebre matricielle/2.5 Matrices \303\251l\303\251mentaires.ipynb"
@@ -1,266 +1,211 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# **Concept(s)-clé(s) et théorie**\n",
"\n",
- "Une matrice élémentaire (de taille $n \\times n$) est une matrice obtenue en effectuant une (et une seule) opération élémentaire, de type (I), (II) ou (III), sur les lignes de la matrice $I_n.$ Concrétement, on adoptera les notations suivantes.\n",
+ "## Rappel\n",
"\n",
- "1. La matrice $T_{ij}$ est la matrice obtenue en échangeant les lignes $i$ et $j$ de $I_n.$\n",
- "2. La matrice $D_r(\\lambda)$ est la matrice obtenue en multipliant la $r$-ème ligne de $I_n$ par $\\lambda \\in \\mathbb{R}.$\n",
- "3. La matrice $L_{rs}(\\lambda)$ est la matrice obtenue en ajoutant $\\lambda$ fois la ligne $s$ à la ligne $r$ de $I_n.$"
+ "Etant donné une matrice générique $A \\in M_{m \\times n}(\\mathbb{R})$, nous définissons les opérations élémentaires de type:\n",
+ "* (I): échanger deux lignes de matrice A\n",
+ "* (II): multiplier une ligne de matrice A par un scalaire\n",
+ "* (III): ajouter à une ligne de matrice A le multiple d'une autre ligne de la même matrice\n",
+ "\n",
+ "## Définition\n",
+ "Une matrice élémentaire (de taille $n \\times n$) est une matrice obtenue en effectuant une (et une seule) opération élémentaire, de type (I), (II) ou (III), sur les lignes de la matrice $I_n$ (i.e. la matrice d'identité de taille $n \\times n$). Concrétement, on adoptera les notations suivantes:\n",
+ "\n",
+ "* (I) La matrice $T_{ij}$ est la matrice obtenue en échangeant les lignes $i$ et $j$ de $I_n$.\n",
+ "* (II) La matrice $D_r(\\lambda)$ est la matrice obtenue en multipliant la $r$-ème ligne de $I_n$ par $\\lambda \\in \\mathbb{R}$.\n",
+ "* (III) La matrice $L_{rs}(\\lambda)$ est la matrice obtenue en ajoutant $\\lambda$ fois la ligne $s$ à la ligne $r$ de $I_n$.\n",
+ "\n",
+ "## Théorème\n",
+ "Soient $A \\in M_{m \\times n}(\\mathbb{R})$ une matrice arbitraire et $E \\in M_{m \\times m}(\\mathbb{R})$ une matrice élémentaire de type (I), (II) ou (III). Alors $EA$ est la matrice obtenue en effectuant sur les lignes de $A$ l'opération de type (I), (II) ou (III), qui définit la matrice $E$.\n",
+ "\n",
+ "## Corollaire\n",
+ "Les matrices élémentaires sont inversibles. On a en effet:\n",
+ "* (I): $T_{ij}^{-1} = T_{ji} = T_{ij}$\n",
+ "* (II): $D_r(\\lambda)^{-1} = D_r(\\lambda^{-1})$\n",
+ "* (III): $L_{rs}(\\lambda)^{-1} = L_{rs}(-\\lambda)$"
]
},
{
"cell_type": "code",
- "execution_count": 2,
+ "execution_count": null,
"metadata": {},
- "outputs": [
- {
- "data": {
- "text/html": [
- " <script type=\"text/javascript\">\n",
- " window.PlotlyConfig = {MathJaxConfig: 'local'};\n",
- " if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}\n",
- " if (typeof require !== 'undefined') {\n",
- " require.undef(\"plotly\");\n",
- " requirejs.config({\n",
- " paths: {\n",
- " 'plotly': ['https://cdn.plot.ly/plotly-latest.min']\n",
- " }\n",
- " });\n",
- " require(['plotly'], function(Plotly) {\n",
- " window._Plotly = Plotly;\n",
- " });\n",
- " }\n",
- " </script>\n",
- " "
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
+ "outputs": [],
"source": [
"import Librairie.AL_Fct as al\n",
+ "import Corrections.corrections as corrections\n",
"import numpy as np\n",
"from numpy.linalg import *\n",
- "from numpy.linalg import multi_dot\n",
"from ipywidgets import interact_manual"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
+ "## Exercice 1\n",
"Soient les deux matrices élémentaires ci-dessous.\n",
"$$\n",
- "E_1=\\begin{pmatrix}\n",
+ "E_1=\\begin{bmatrix}\n",
"1 & 0 & 0 & 0\\\\\n",
"0 & 1 & 0 & -6 \\\\\n",
"0 & 0 & 1 &0 \\\\\n",
"0 & 0 & 0 & 1\n",
- "\\end{pmatrix}\\hspace{3cm}\n",
- "E_2=\\begin{pmatrix}\n",
+ "\\end{bmatrix}\\hspace{3cm}\n",
+ "E_2=\\begin{bmatrix}\n",
"0 & 0 & 1 & 0\\\\\n",
"0 & 1 & 0 & 0 \\\\\n",
"1 & 0 & 0 &0 \\\\\n",
"0 & 0 & 0& 1\n",
- "\\end{pmatrix}\n",
+ "\\end{bmatrix}\n",
"$$\n",
- "Laquelle des affirmations ci-dessous est correcte?\n"
+ "**ÉTAPE 1**: Laquelle des affirmations ci-dessous est correcte?\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
- "from IPython.display import display, Latex\n",
- "from ipywidgets import Button, HBox, VBox,Layout\n",
- "import ipywidgets as widgets\n",
- " # OK PUT in AL_FCT\n",
- "\n",
- "a=widgets.Checkbox(\n",
- " value=False,\n",
- " description=r'\\(E_1E_2\\) multiplie la ligne 4 par -6 et échange les lignes 2 et 3',\n",
- " disabled=False,\n",
- " layout=Layout(width='80%', height='40px')\n",
- ")\n",
- "b=widgets.Checkbox(\n",
- " value=False,\n",
- " description=r'\\(E_1E_2\\) ajoute 6 fois la ligne 4 à la ligne 2 et échange les lignes 1 et 3',\n",
- " disabled=False,\n",
- " layout=Layout(width='80%', height='40px')\n",
- "\n",
- ")\n",
- "c=widgets.Checkbox(\n",
- " value=False,\n",
- " description=r'\\(E_1E_2\\) échange les lignes 1 et 3 et ajoute -6 fois la ligne 4 à la ligne 2',\n",
- " disabled=False,\n",
- " layout=Layout(width='80%', height='40px')\n",
- ")\n",
- "d=widgets.Checkbox(\n",
- " value=False,\n",
- " description=r\"\\(E_1E_2\\) ajoute -6 fois la ligne 4 à la ligne 2 et échange les lignes 1 et 2\",\n",
- " disabled=False,\n",
- " layout=Layout(width='80%', height='40px')\n",
- ")\n",
- "def correction(a,b,c,d): \n",
- " if c and not(a) and not(d) and not(b):\n",
- " print(\"C'est correct! Par exemple, si on applique le produit à la matrice ci-dessous\")\n",
- " A=np.asmatrix([[1, -1,0,0], [0, 0 ,0,1], [1,2,1,2],[1,0,0,1]])\n",
- " B=np.asmatrix([[1,0,0,0],[0,1,0,-6],[0,0,1,0],[0,0,0,1]])\n",
- " C=np.asmatrix([[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]])\n",
- " al.printA(A)\n",
- " print(\"on obtient\")\n",
- " al.printA(np.linalg.multi_dot([B,C,A]))\n",
- " else:\n",
- " print(\"C'est faux.\")\n",
- "\n",
- "out=interact_manual(correction,a=a,b=b,c=c,d=d)\n",
- " "
+ "corrections.Ex1aChapitre2_5()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "Donner l'inverse de $E_1E_2$"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "inverse=[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]"
+ "**ÉTAPE 2**: Donner l'inverse de $E_1E_2$\n",
+ "\n",
+ "**Aide** \n",
+ "Considérez deux matrices inversibles $A, B \\in M_{n \\times n}(\\mathbb{R})$; alors $$(AB)^{- 1}=B^{- 1}A^{- 1}$$\n",
+ "\n",
+ "*Observation*: Inverser l'effet de $n$ opérations élémentaires consécutives consiste à appliquer l'inverse de chaque opération, de la dernière à la première."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
- "if inverse==[[0,0,1,0],[0,1,0,6],[1,0,0,0],[0,0,0,1]]:\n",
- " print(\"C'est correct!\")"
+ "print('Insérez ici la valeur de la matrice inverse')\n",
+ "inverse= [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]\n",
+ "corrections.Ex1bChapitre2_5(inverse)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
+ "## Exercice 2\n",
"Soient $A$ et $B$ les deux matrices ci-dessous. \n",
"\n",
"$$\n",
- "A=\\begin{pmatrix}\n",
+ "A=\\begin{bmatrix}\n",
"-2 &1& 4\\\\\n",
"1 & 0 & 2\\\\\n",
"-1 & -\\dfrac{1}{2} & 3\n",
- "\\end{pmatrix}, \\hspace{2em}\n",
- "B=\\begin{pmatrix}\n",
+ "\\end{bmatrix}, \\hspace{2em}\n",
+ "B=\\begin{bmatrix}\n",
"-1 & -\\dfrac{1}{2} & 3 \\\\\n",
- "5 & -2 & -6\\\\\n",
+ "5 & 2 & -10\\\\\n",
"-10 & 5 & 20\n",
- "\\end{pmatrix}\n",
+ "\\end{bmatrix}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"A=[[-2,1,4],[1,0,2],[-1, -1/2 , 3]]\n",
- "B=[[-1, -1/2, 3],[5, -2, -6],[-10,5,20]]"
+ "B=[[-1, -1/2, 3],[5, 2, -10],[-10,5,20]]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On passe de la matrice $A$ à la matrice $B$ à l'aide de trois matrices élémentaires $T_{ij}$, $D_{r}(\\lambda)$ et $L_{rs}(\\lambda)$\n",
"$$\n",
"L_{rs}(\\lambda) \\cdot D_{r}(\\lambda)\\cdot T_{ij}\\cdot A =B\n",
"$$\n",
"\n",
- "Trouver les trois matrices."
+ "**ÉTAPE 1**: Trouvez les 3 matrices et insérez-les ci-dessous."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"T=[[1,0,0],[0,1,0],[0,0,1]]\n",
- "D=[[5,0,0],[0,1,0],[0,0,1]]\n",
+ "D=[[1,0,0],[0,1,0],[0,0,1]]\n",
"L=[[1,0,0],[0,1,0],[0,0,1]]"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
- "#OK put in the al_FCt file\n",
- "if ~(B-np.linalg.multi_dot([L,D,T,A])).any():\n",
- " print(\"C'est correct!\")\n",
- "else :\n",
- " str='Il faut entrer la/les matrice(s) '\n",
- " if (np.asmatrix(T)-np.asmatrix([[0,0,1],[0,1,0],[1,0,0]])).any():\n",
- " str=str+ ' T '\n",
- " if (np.asmatrix(D)-np.asmatrix([[5,0,0],[0,1,0],[0,0,1]])).any():\n",
- " str=str+ ' D '\n",
- " if L!=[[1,0,0],[-2,1,0],[0,0,1]]:\n",
- " str=str+ ' L '\n",
- " str=str + 'à nouveau. Le produit des matrices entrées vaut'\n",
- " print(str)\n",
- " al.printA(np.linalg.multi_dot([L,D,T,A]))\n",
- " \n"
+ "corrections.Ex2aChapitre2_5(A, B, T, D, L)"
]
},
{
- "cell_type": "code",
- "execution_count": null,
+ "cell_type": "markdown",
"metadata": {},
- "outputs": [],
- "source": []
+ "source": [
+ "**ÉTAPE 2**: Donner l'inverse de $L_{rs}(\\lambda) \\cdot D_{r}(\\lambda)\\cdot T_{ij}$"
+ ]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
- "source": []
+ "source": [
+ "print('Insérez ici la valeur de la matrice inverse')\n",
+ "inverse= [[1,0,0],[0,1,0],[0,0,1]]\n",
+ "corrections.Ex2bChapitre2_5(inverse)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "[Passez au notebook 2.6-7: Critéres d'inversibilité](2.6-2.7%20Critères%20d'inversibilité.ipynb)"
+ ]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
diff --git "a/Chapitre 2 - Algebre matricielle/2.6-2.7 Crit\303\250res d'inversibilit\303\251.ipynb" "b/Chapitre 2 - Algebre matricielle/2.6-2.7 Crit\303\250res d'inversibilit\303\251.ipynb"
index 3898d99..3db2739 100644
--- "a/Chapitre 2 - Algebre matricielle/2.6-2.7 Crit\303\250res d'inversibilit\303\251.ipynb"
+++ "b/Chapitre 2 - Algebre matricielle/2.6-2.7 Crit\303\250res d'inversibilit\303\251.ipynb"
@@ -1,52 +1,161 @@
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "# **Concept(s)-clé(s) et théorie**\n"
+ "# **Concept(s)-clé(s) et théorie**\n",
+ "\n",
+ "## PREMIER CRITÈRE D'INVERSIBILITÉ \n",
+ "Une matrice $A \\in M_{n \\times n}(\\mathbb{R})$ est inversible si et seulement si le système homogène $Ax=0$ possède une solution unique, à savoir, la solution triviale.\n",
+ "\n",
+ "## COROLLAIRE DU PREMIER CRITÈRE D'INVERSIBILITÉ \n",
+ "Soit $A \\in M_{n \\times n}(\\mathbb{R})$ alors les deux affirmations suivantes sont vérifiées.\n",
+ "\n",
+ "1. La matrice $A$ est inversible si et seulement s'il existe $B \\in M_{n \\times n}(\\mathbb{R})$ telle que $BA = I_n$.\n",
+ "2. La matrice $A$ est inversible si et seulement s'il existe $C \\in M_{n \\times n}(\\mathbb{R})$ telle que $AC = I_n$.\n",
+ "\n",
+ "## RAPPEL: ALGORITHME POUR TROUVER L'INVERSE D'UNE MATRICE DONNÉE\n",
+ "Soit $A \\in M_{n \\times n}(\\mathbb{R})$ une matrice carrée. Afin de déterminer si $A$ est inversible et de calculer son inverse (lorsque c'est possible), on procède comme suit :\n",
+ "\n",
+ "1. Ecrire les matrices $A$ et $I_n$ l'une à côté de l'autre, formant ainsi une nouvelle matrice de taille $n \\times 2n$\n",
+ "2. Opérer sur les lignes de cette matrice ainsi obtenue, afin de réduire le côté gauche à $I_n$\n",
+ "3. Si l'on y arrive, alors $A$ est inversible et son inverse $A^{-1}$ est donnée par la matrice à droite."
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 1,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ " <script type=\"text/javascript\">\n",
+ " window.PlotlyConfig = {MathJaxConfig: 'local'};\n",
+ " if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}\n",
+ " if (typeof require !== 'undefined') {\n",
+ " require.undef(\"plotly\");\n",
+ " requirejs.config({\n",
+ " paths: {\n",
+ " 'plotly': ['https://cdn.plot.ly/plotly-latest.min']\n",
+ " }\n",
+ " });\n",
+ " require(['plotly'], function(Plotly) {\n",
+ " window._Plotly = Plotly;\n",
+ " });\n",
+ " }\n",
+ " </script>\n",
+ " "
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "text/html": [
+ " <script type=\"text/javascript\">\n",
+ " window.PlotlyConfig = {MathJaxConfig: 'local'};\n",
+ " if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}\n",
+ " if (typeof require !== 'undefined') {\n",
+ " require.undef(\"plotly\");\n",
+ " requirejs.config({\n",
+ " paths: {\n",
+ " 'plotly': ['https://cdn.plot.ly/plotly-latest.min']\n",
+ " }\n",
+ " });\n",
+ " require(['plotly'], function(Plotly) {\n",
+ " window._Plotly = Plotly;\n",
+ " });\n",
+ " }\n",
+ " </script>\n",
+ " "
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
"source": [
- "import AL_Fct as al\n",
+ "import Librairie.AL_Fct as al\n",
+ "import Corrections.corrections as corrections\n",
"import numpy as np\n",
"from numpy.linalg import *\n",
"from numpy.linalg import multi_dot\n",
"from ipywidgets import interact_manual"
]
},
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### EXERCICE 1\n",
+ "Considérez le système linéaire générique $Ax=b$ avec $A \\in \\mathbb{R}^{n \\times n}$ et $b \\in \\mathbb{R}^n$; marquez celles des déclarations suivantes qui pourraient être vraies pour certaines valeurs de $A$ et $b$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "application/vnd.jupyter.widget-view+json": {
+ "model_id": "b450561f0bd64af6a9dee858cf2bd58b",
+ "version_major": 2,
+ "version_minor": 0
+ },
+ "text/plain": [
+ "interactive(children=(Checkbox(value=False, description='$A^{-1}$ existe et le système admet plusieurs solutio…"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "corrections.Ex1Chapitre2_6_7()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# IDEA\n",
+ "\n",
+ "1. Remainder exercise to compute the inverse of a square matrix\n",
+ "2. Give 3 matrices and tell which of those is invertible and which is not\n",
+ "3. Give two matrices (one with parameter); identify the value of the parameter (or the values) that makes the matrices one the inverse of the other"
+ ]
+ },
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.6.8"
+ "version": "3.7.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
diff --git a/Chapitre 2 - Algebre matricielle/Corrections/corrections.py b/Chapitre 2 - Algebre matricielle/Corrections/corrections.py
index edaf3fc..6538b80 100644
--- a/Chapitre 2 - Algebre matricielle/Corrections/corrections.py
+++ b/Chapitre 2 - Algebre matricielle/Corrections/corrections.py
@@ -1,495 +1,612 @@
import sys
sys.path.insert(0, './../')
import numpy as np
import plotly
plotly.offline.init_notebook_mode(connected=True)
import ipywidgets as widgets
from IPython.display import display, Latex
from ipywidgets import interact_manual, Layout
from Librairie.AL_Fct import printA, texMatrix, isDiag, isSym
def Ex2Chapitre2_1():
"""Provides the correction of exercise 2 of notebook 2_1
"""
a = widgets.Checkbox(
value=False,
description=r'Il existe \(\lambda\in \mathbb{R}\) tel que \((A-\lambda B)^T\) soit échelonnée réduite',
disabled=False,
layout=Layout(width='80%', height='30px')
)
b = widgets.Checkbox(
value=False,
description=r'Il existe \(\lambda\in \mathbb{R}\) tel que \((A-\lambda B)^T\) soit échelonnée (mais pas réduite)',
disabled=False,
layout=Layout(width='80%', height='30px')
)
c = widgets.Checkbox(
value=False,
description=r"Il n'existe pas de \(\lambda\in \mathbb{R}\) tel que \((A-\lambda B)^T\) soit échelonnée",
disabled=False,
layout=Layout(width='80%', height='30px')
)
def correction(a, b, c):
if a and not c and not b:
display(Latex("C'est correct! Pour $\lambda=-3$ La matrice échelonnée réduite est:"))
A = [[1, 0, -2, 3], [0, 1, -1, 7]]
printA(A)
else:
print("C'est faux.")
interact_manual(correction, a=a, b=b, c=c)
return
def Ex3Chapitre2_1():
"""Provides the correction of exercise 3 of notebook 2_1
"""
a = widgets.Checkbox(
value=False,
description=r'\(C_{32}\) vaut -14',
disabled=False,
layout=Layout(width='80%', height='30px')
)
b = widgets.Checkbox(
value=False,
description=r'\(C_{32}\) vaut 14',
disabled=False,
layout=Layout(width='80%', height='30px')
)
c = widgets.Checkbox(
value=False,
description=r'\(C_{32}\) vaut -10',
disabled=False,
layout=Layout(width='80%', height='30px')
)
d = widgets.Checkbox(
value=False,
description=r"\(C_{32}\) n'existe pas",
disabled=False,
layout=Layout(width='80%', height='30px')
)
def correction(a, b, c, d):
if c and not a and not b and not d:
display(Latex("C'est correct! La matrice C vaut:"))
A = [[-6, 64], [-32, -22], [28, -10], [-2, 6]]
printA(A)
else:
print("C'est faux.")
interact_manual(correction, a=a, b=b, c=c, d=d)
return
def Ex1Chapitre2_2():
"""Provides the correction of exercise 1 of notebook 2_2
"""
a = widgets.Checkbox(
value=False,
description=r'Le produit $A \cdot B$ vaut: <br>'
r'\begin{equation*} \qquad A \cdot B = \begin{bmatrix}-1 & 4\\-3& -3\\2 & 0\end{bmatrix}\end{equation*}',
disabled=False,
layout=Layout(width='100%', height='110px')
)
b = widgets.Checkbox(
value=False,
description=r'Le produit $A \cdot B$ vaut: <br>'
r'\begin{equation*} \qquad A \cdot B =\begin{bmatrix}-1 & 8\\-3& 3\\-2 & 4\end{bmatrix}\end{equation*}',
disabled=False,
layout=Layout(width='100%', height='110px')
)
c = widgets.Checkbox(
value=False,
description=r'Le produit $A \cdot B$ vaut: <br>'
r'\begin{equation*} \qquad A \cdot B =\begin{bmatrix}5 & -4\\1 & 0\end{bmatrix}\end{equation*}',
disabled=False,
layout=Layout(width='100%', height='90px')
)
d = widgets.Checkbox(
value=False,
description=r"Le produit $A \cdot B$ n'est pas définie",
disabled=False,
layout=Layout(width='100%', height='60px')
)
def correction(a, b, c, d):
if b and not a and not c and not d:
print("C'est correct!")
else:
print("C'est faux.")
interact_manual(correction, a=a, b=b, c=c, d=d)
return
def Ex2Chapitre2_2():
"""Provides the correction of exercise 2 of notebook 2_2
"""
a = widgets.Checkbox(
value=False,
description=r'Le produit $A \cdot B$ appartient à $M_{3 \times 3}(\mathbb{R})$',
disabled=False,
layout=Layout(width='80%', height='50px')
)
b = widgets.Checkbox(
value=False,
description=r'Le produit $A \cdot B$ appartient à $M_{3 \times 2}(\mathbb{R})$',
disabled=False,
layout=Layout(width='80%', height='50px')
)
c = widgets.Checkbox(
value=False,
description=r'Le produit $A \cdot B$ appartient à $M_{2 \times 1}(\mathbb{R})$',
disabled=False,
layout=Layout(width='80%', height='50px')
)
d = widgets.Checkbox(
value=False,
description=r"$A \cdot B$ n'est pas définie",
disabled=False,
layout=Layout(width='80%', height='50px')
)
def correction(a, b, c, d):
if c and not a and not b and not d:
A = [[14], [6]]
texA = '$' + texMatrix(A) + '$'
display(Latex(r"C'est correct! Le produit $ A \cdot B$ vaut: $A \cdot B$ = " + texA))
else:
print("C'est faux.")
interact_manual(correction, a=a, b=b, c=c, d=d)
return
def Ex3Chapitre2_2():
"""Provides the correction of exercise 3 of notebook 2_2
"""
display(Latex("Insert the values of a and b as floating point numbers"))
a = widgets.FloatText(
value=0.0,
step=0.1,
description='a:',
disabled=False
)
b = widgets.FloatText(
value=0.0,
step=0.1,
description='b:',
disabled=False
)
display(a)
display(b)
def f():
A = np.array([[-1, 2], [5, -2]])
B = np.array([[-1, 1], [a.value, b.value]])
AB = np.dot(A,B)
texAB = '$' + texMatrix(AB) + '$'
BA = np.dot(B,A)
texBA = '$' + texMatrix(BA) + '$'
if a.value == 5/2 and b.value == -3/2:
display(Latex(r"Correcte! Le produits $A \cdot B$ et $B \cdot A$ valent chacun: " + texAB))
else:
display(Latex(r"Incorrecte! Le produit $A \cdot B$ vaut " + texAB + r"et par contre le produit "
r"$B \cdot A$ vaut " + texBA + r" Entrez de nouvelles valeurs!"))
interact_manual(f)
return
def Ex1Chapitre2_3(A, B, C):
"""Provides the correction to exercise 1 of notebook 2_3
:param A: original matrix
:type A: list[list] or numpy.ndarray
:param B: matrix such that A+B should be diagonal
:type B: list[list] or numpy.ndarray
:param C: matrix such that A+C should be symmetric and not diagonal
:type C: list[list] or numpy.ndarray
:return:
:rtype:
"""
if not type(A) is np.ndarray:
A = np.array(A)
if not type(B) is np.ndarray:
B = np.array(B)
if not type(C) is np.ndarray:
C = np.array(C)
ans1 = isDiag(A+B)
ans2 = isSym(A+C) and not isDiag(A+C)
if ans1 and ans2:
print('Correcte!')
else:
print('Incorrecte! Entrez des nouvelles valeurs pur le matrices B et C!\n')
if ans1:
print("A+B est bien diagonale!")
else:
print("A+B est n'est pas diagonale!")
texAB = '$' + texMatrix(A+B) + '$'
display(Latex(r"A+B=" + texAB))
if ans2:
print("A+C est bien symétrique et non diagonale!")
elif isSym(A + C) and isDiag(A + C):
print("A+C est bien symétrique mais elle est aussi diagonale!")
else:
print("A + C n'est pas symétrique")
texAC = '$' + texMatrix(A + C) + '$'
display(Latex(r"A+C=" + texAC))
return
def Ex2Chapitre2_3():
"""Provides the correction to exercise 2 of notebook 2_3
"""
a = widgets.Checkbox(
value=False,
description=r'$(A^{-1})^T$ et $(A^T)^{-1}$ sont triangulaires supérieures mais différentes',
disabled=False,
layout=Layout(width='80%', height='40px')
)
b = widgets.Checkbox(
value=False,
description=r'$(A^{-1})^T$ et $(A^T)^{-1}$ sont triangulaires inférieures mais différentes',
disabled=False,
layout=Layout(width='80%', height='40px')
)
c = widgets.Checkbox(
value=False,
description=r'$(A^{-1})^T$ et $(A^T)^{-1}$ sont triangulaires inférieures et identiques',
disabled=False,
layout=Layout(width='80%', height='40px')
)
d = widgets.Checkbox(
value=False,
description=r'$(A^{-1})^T$ et $(A^T)^{-1}$ sont triangulaires supérieures et identiques',
disabled=False,
layout=Layout(width='80%', height='40px')
)
def correction(a, b, c, d):
if d and not a and not c and not b:
A = np.array(([-1, 0, 0], [3, 1/2, 0], [1, 2, 1]))
res = np.transpose(np.linalg.inv(A))
texAres = '$' + texMatrix(res) + '$'
display(Latex("C'est correct! $(A^T)^{-1}$ est donnée par: $\quad$" + texAres))
else:
display(Latex("C'est faux."))
interact_manual(correction, a=a, b=b, c=c, d=d)
return
-
def Ex1Chapitre2_4():
- """Provides the correction to exercise 1 of notebook 2_4
+ """Provides the correction to exercise 2 of notebook 2_4
"""
a = widgets.Checkbox(
value=False,
- description=r'$A^{-1}$ exists and the system admits multiple solutions, whichever $b$',
+ description=r'Le système admet une solution unique et elle est:'
+ r'$$\qquad \qquad x = \begin{bmatrix} 1&4/3&4/3\end{bmatrix}^T$$',
disabled=False,
- layout=Layout(width='80%', height='40px')
+ layout=Layout(width='80%', height='70px')
)
b = widgets.Checkbox(
value=False,
- description=r'$A^{-1}$ exists and the system admits either a unique solution or multiple solutions '
- r'depending on the value of $b$',
+ description=r"Le système n'admet aucune solution",
disabled=False,
layout=Layout(width='80%', height='40px')
-
)
c = widgets.Checkbox(
value=False,
- description=r'$A$ is invertible and the system admits a unique solution, whichever $b$',
+ description=r'Le système admet une solution unique et elle est:'
+ r'$$\qquad \qquad x = \begin{bmatrix} 1&4/3&8/3\end{bmatrix}^T$$',
disabled=False,
- layout=Layout(width='80%', height='40px')
+ layout=Layout(width='80%', height='70px')
+
)
d = widgets.Checkbox(
value=False,
- description=r'$A^{-1}$ exists and the system admits at least one solution, whichever $b$',
+ description=r'Le système admet plusieurs solutions',
disabled=False,
layout=Layout(width='80%', height='40px')
)
e = widgets.Checkbox(
value=False,
- description=r'$A$ is not invertible and the system admits either a unique or multiple solutions, depending on '
- r'the value of $b$',
+ description=r'$A$ est inversible et son inverse est: <br>'
+ r'$$\qquad \qquad A^{-1} = \begin{bmatrix} 1/2&0&1/2\\1/2&-1/3&5/3\\1/2&-2/3&5/6\end{bmatrix}$$',
disabled=False,
- layout=Layout(width='80%', height='40px')
+ layout=Layout(width='80%', height='100px')
)
f = widgets.Checkbox(
value=False,
- description=r'$A$ is not invertible and the system admits a unique solution, whichever $b$',
+ description=r"$A$ n'est pas inversible",
disabled=False,
layout=Layout(width='80%', height='40px')
)
g = widgets.Checkbox(
value=False,
- description=r'The system admits a unique solution and $A$ is not invertible',
- disabled=False,
- layout=Layout(width='80%', height='40px')
- )
- h = widgets.Checkbox(
- value=False,
- description=r'The system admits a unique solution and $A$ is invertible',
+ description=r'$A$ est inversible et son inverse est:'
+ r'$$\qquad \qquad A^{-1} = \begin{bmatrix} 1/2&0&1/2\\1/2&-1/3&5/3\\1/2&-2/3&-1/2\end{bmatrix}$$',
disabled=False,
- layout=Layout(width='80%', height='40px')
+ layout=Layout(width='80%', height='100x')
)
- def correction(a, b, c, d, e, f, g, h):
- if c and d and h and not a and not b and not e and not f and not g:
+ def correction(a, b, c, d, e, f, g):
+ if c and e and not a and not b and not d and not f and not g:
display(Latex("C'est correct!"))
else:
display(Latex("C'est faux."))
- interact_manual(correction, a=a, b=b, c=c, d=d, e=e, f=f, g=g, h=h)
+ interact_manual(correction, a=a, b=b, c=c, d=d, e=e, f=f, g=g)
return
def Ex2Chapitre2_4():
- """Provides the correction to exercise 2 of notebook 2_4
+ """Provides the correction to exercise 3 of notebook 2_4
"""
a = widgets.Checkbox(
value=False,
- description=r'The system admits a unique solution and it is:'
- r'$$\qquad x = \begin{bmatrix} 1&4/3&4/3\end{bmatrix}^T$$',
+ description=r"Le système n'admet une solution unique que si $\alpha < 2$",
disabled=False,
- layout=Layout(width='80%', height='70px')
+ layout=Layout(width='80%', height='40px')
)
b = widgets.Checkbox(
value=False,
- description=r'The system does not admit any solution',
+ description=r"Le système n'admet une solution unique que si $\alpha \geq 2$",
disabled=False,
layout=Layout(width='80%', height='40px')
)
c = widgets.Checkbox(
value=False,
- description=r'The system admits a unique solution and it is:'
- r'$$\qquad x = \begin{bmatrix} 1&4/3&8/3\end{bmatrix}^T$$',
+ description=r'Le système admet une solution unique $\forall \alpha \in \mathbb{R}$',
disabled=False,
- layout=Layout(width='80%', height='70px')
+ layout=Layout(width='80%', height='40px')
)
d = widgets.Checkbox(
value=False,
- description=r'The system admits multiple solutions',
+ description=r"Le système n'admet aucune solution si $\alpha < 2$, alors qu'il admet une solution unique si "
+ r"$\alpha \geq 2$",
disabled=False,
layout=Layout(width='80%', height='40px')
)
e = widgets.Checkbox(
value=False,
- description=r'$A$ is invertible and its inverse is: <br>'
- r'$$\qquad A^{-1} = \begin{bmatrix} 1/2&0&1/2\\1/2&-1/3&5/3\\1/2&-2/3&5/6\end{bmatrix}$$',
+ description=r"Le système admet plusieurs solutions si $\alpha \neq 2$, alors qu'il admet une solution unique si"
+ r" $\alpha = 2$",
disabled=False,
- layout=Layout(width='80%', height='100px')
+ layout=Layout(width='80%', height='40px')
)
f = widgets.Checkbox(
value=False,
- description=r'$A$ is not invertible',
+ description=r"Le système n'admet jamais une solution unique, quelle que soit $\alpha \in \mathbb{R}$",
disabled=False,
layout=Layout(width='80%', height='40px')
)
- g = widgets.Checkbox(
- value=False,
- description=r'$A$ is invertible and its inverse is: <br>'
- r'$$\qquad A^{-1} = \begin{bmatrix} 1/2&0&1/2\\1/2&-1/3&5/3\\1/2&-2/3&-1/2\end{bmatrix}$$',
- disabled=False,
- layout=Layout(width='80%', height='100x')
- )
- def correction(a, b, c, d, e, f, g):
- if c and e and not a and not b and not d and not f and not g:
+ def correction(a, b, c, d, e, f):
+ if f and not a and not b and not c and not d and not e:
display(Latex("C'est correct!"))
else:
display(Latex("C'est faux."))
- interact_manual(correction, a=a, b=b, c=c, d=d, e=e, f=f, g=g)
+ interact_manual(correction, a=a, b=b, c=c, d=d, e=e, f=f)
return
-def Ex3Chapitre2_4():
- """Provides the correction to exercise 3 of notebook 2_4
+def Ex1aChapitre2_5():
+ """Provides the correction to exercise 1a of notebook 2_5
"""
a = widgets.Checkbox(
value=False,
- description=r'The system admits unique solution only if $\alpha < 2$',
+ description=r'\(E_1E_2\) multiplie la ligne 4 par -6 et échange les lignes 2 et 3',
disabled=False,
layout=Layout(width='80%', height='40px')
)
b = widgets.Checkbox(
value=False,
- description=r'The system admits unique solution only if $\alpha \geq 2$',
+ description=r'\(E_1E_2\) ajoute 6 fois la ligne 4 à la ligne 2 et échange les lignes 1 et 3',
disabled=False,
layout=Layout(width='80%', height='40px')
+
)
c = widgets.Checkbox(
value=False,
- description=r'The system admits unique solution $\forall \alpha \in \mathbb{R}$',
+ description=r'\(E_1E_2\) échange les lignes 1 et 3 et ajoute -6 fois la ligne 4 à la ligne 2',
+ disabled=False,
+ layout=Layout(width='80%', height='40px')
+ )
+ d = widgets.Checkbox(
+ value=False,
+ description=r"\(E_1E_2\) ajoute -6 fois la ligne 4 à la ligne 2 et échange les lignes 1 et 2",
disabled=False,
layout=Layout(width='80%', height='40px')
+ )
+
+ def correction(a, b, c, d):
+ if c and not(a) and not(d) and not(b):
+ print("C'est correct! Par exemple, si on applique le produit à la matrice ci-dessous")
+ A=[[1,-1,0,0], [0,0,0,1], [1,2,1,2], [1,0,0,1]]
+ B=[[1,0,0,0], [0,1,0,-6], [0,0,1,0], [0,0,0,1]]
+ C=[[0,0,1,0], [0,1,0,0], [1,0,0,0], [0,0,0,1]]
+ BCA = np.linalg.multi_dot([B,C,A])
+ texA = '$' + texMatrix(A) + '$'
+ texBCA = '$' + texMatrix(BCA) + '$'
+ display(Latex('$\qquad A = $' + texA))
+ print("on obtient")
+ display((Latex('$\qquad \hat{A} = $' + texBCA)))
+ else:
+ print("C'est faux.")
+
+ interact_manual(correction,a=a,b=b,c=c,d=d)
+
+ return
+
+
+def Ex1bChapitre2_5(inv):
+ """Provides the correction to exercise 1b of notebook 2_5
+ :param inv: inverse of the matrix to be calculated
+ :type inv: list[list]
+ """
+
+ if inv == [[0, 0, 1, 0], [0, 1, 0, 6], [1, 0, 0, 0], [0, 0, 0, 1]]:
+ print("C'est correct!")
+ else:
+ print("C'est faux.")
+
+ return
+
+
+def Ex2aChapitre2_5(A, B, T, D, L):
+ """Provides the correction to exercise 2a of notebook 2_5
+
+ :param A: starting matrix
+ :type A: list[list]
+ :param B: target matrix
+ :type B: list[list]
+ :param T: permutation (type I) matrix
+ :type T: list[list]
+ :param D: scalar multiplication (type II) matrix
+ :type D: list[list]
+ :param L: linear combination (type III) matrix
+ :type L: list[list]
+ """
+
+ if ~(B - np.linalg.multi_dot([L, D, T, A])).any():
+ print("C'est correct!")
+ else:
+ print("C'est faux.")
+ str = 'Il faut entrer la/les matrice(s) {'
+ if (np.asmatrix(T) - np.asmatrix([[0, 0, 1], [0, 1, 0], [1, 0, 0]])).any():
+ str = str + ' T, '
+ if (np.asmatrix(D) - np.asmatrix([[1, 0, 0], [0, 1, 0], [0, 0, 5]])).any():
+ str = str + ' D, '
+ if (np.asmatrix(L) - np.asmatrix([[1, 0, 0], [-4, 1, 0], [0, 0, 1]])).any():
+ str = str + ' L, '
+ str = str + '}. Le produit des matrices entrées vaut:'
+ print(str)
+ tmp = np.linalg.multi_dot([L, D, T, A])
+ texM = '$' + texMatrix(tmp) + '$'
+ display(Latex('$\qquad \hat{B} = $' + texM))
+
+ return
+
+
+def Ex2bChapitre2_5(inv):
+ """Provides the correction to exercise 2b of notebook 2_5
+
+ :param inv: inverse of the matrix to be calculated
+ :type inv: list[list]
+ """
+
+ if inv == [[0,0,1/5], [4,1,0], [1,0,0]]:
+ print("C'est correct!")
+ else:
+ print("C'est faux.")
+
+ return
+
+
+def Ex1Chapitre2_6_7():
+ """Provides the correction to exercise 1 of notebook 2_4
+ """
+
+ a = widgets.Checkbox(
+ value=False,
+ description=r'$A^{-1}$ existe et le système admet plusieurs solutions, quelle que soit la valeur de $b$',
+ disabled=False,
+ layout=Layout(width='80%', height='40px')
+ )
+ b = widgets.Checkbox(
+ value=False,
+ description=r'$A^{-1}$ existe et le système admet une solution unique ou plusieurs solutions en fonction '
+ r'de la valeur de $b$',
+ disabled=False,
+ layout=Layout(width='80%', height='40px')
+
+ )
+ c = widgets.Checkbox(
+ value=False,
+ description=r'$A$ est inversible et le système admet une solution unique, quelle que soit la valeur de $b$',
+ disabled=False,
+ layout=Layout(width='80%', height='40px')
)
d = widgets.Checkbox(
value=False,
- description=r'The system does not admit any solution if $\alpha < 2$, while it admits unique solution'
- r' if $\alpha \geq 2$',
+ description=r'$A^{-1}$ existe et le système admet au moins une solution, quelle que soit la valeur de $b$',
disabled=False,
layout=Layout(width='80%', height='40px')
)
e = widgets.Checkbox(
value=False,
- description=r'The system admits multiple solutions if $\alpha \neq 2$, while it admits unique solution '
- r'for $\alpha == 2$',
+ description=r"$A$ n'est pas inversible et le système admet une unique solution ou plusieurs solutions, "
+ r"selon la valeur de $b$ ",
disabled=False,
layout=Layout(width='80%', height='40px')
)
f = widgets.Checkbox(
value=False,
- description=r'The system never admits a unique solution, whichever $\alpha \in \mathbb{R}$',
+ description=r"$A$ n'est pas inversible et le système admet une solution unique, "
+ r"quelle que soit la valeur de $b$",
+ disabled=False,
+ layout=Layout(width='80%', height='40px')
+ )
+ g = widgets.Checkbox(
+ value=False,
+ description=r"Le système admet une solution unique et $A$ n'est pas inversible",
+ disabled=False,
+ layout=Layout(width='80%', height='40px')
+ )
+ h = widgets.Checkbox(
+ value=False,
+ description=r'Le système admet une solution unique et $A$ est inversible',
disabled=False,
layout=Layout(width='80%', height='40px')
)
- def correction(a, b, c, d, e, f):
- if f and not a and not b and not c and not d and not e:
+ def correction(a, b, c, d, e, f, g, h):
+ if c and d and h and not a and not b and not e and not f and not g:
display(Latex("C'est correct!"))
else:
display(Latex("C'est faux."))
- interact_manual(correction, a=a, b=b, c=c, d=d, e=e, f=f)
+ interact_manual(correction, a=a, b=b, c=c, d=d, e=e, f=f, g=g, h=h)
return
+
+
diff --git "a/Chapitre 4 - Bases et dimension/4.1-4.2. D\303\251pendance et ind\303\251pendance lin\303\251aire.ipynb" "b/Chapitre 4 - Bases et dimension/4.1-4.2. D\303\251pendance et ind\303\251pendance lin\303\251aire.ipynb"
new file mode 100644
index 0000000..2075e75
--- /dev/null
+++ "b/Chapitre 4 - Bases et dimension/4.1-4.2. D\303\251pendance et ind\303\251pendance lin\303\251aire.ipynb"
@@ -0,0 +1,316 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Concept(s)-clé(s) et théorie\n",
+ "\n",
+ "### DÉFINITION 1\n",
+ "\n",
+ "Soient $V$ un $\\mathbb{R}$-espace vectoriel et $S\\subset V$ une collection de vecteurs dans $V.$ On dit que $S$ est linéairement dépendante (ou liée) s'il existe des vecteurs distincts $v_1,\\ldots,v_r\\in S$ et des scalaires $\\lambda_1,\\ldots,\\lambda_r\\in \\mathbb{R}$ non tous nuls tels que $\\lambda_1v_1+\\cdots+\\lambda_rv_r=0.$ (Autrement dit, s'il existe une combinaison linéaire (non triviale) de vecteurs de $S$ qui se réduit au vecteur nul.) S'il n'existe pas de tels vecteurs dans $S,$ alors on dit que $S$ est linéairement indépendante (ou libre).\n",
+ "\n",
+ "### PROPOSITION 1\n",
+ "\n",
+ "Soient $V$ un $\\mathbb{R}$-espace vectoriel et $v_1,\\ldots,v_r\\in V$ des vecteurs de $V.$ Alors ces derniers sont linéairement dépendants si et seulement s'il existe $1\\leq i\\leq r$ tels que $v_i\\in \\mbox{Vect}(\\{v_1,\\ldots,v_{i-1},v_{i+1},\\ldots,v_r\\}),$ c'est-à-dire si et seulement si l'on peut exprimer un des vecteurs de la liste comme une combinaison linéaire des autres.\n",
+ "\n",
+ "### PROPOSITION 2\n",
+ "\n",
+ "Soient $V$ un $\\mathbb{R}$-espace vectoriel et $S\\subset V$ une famille libre de vecteurs dans $V.$ Alors tout sous-ensemble $T\\subset S$ est aussi libre.\n",
+ "\n",
+ "### PROPOSITION 3\n",
+ "\n",
+ "Soient $V$ un $\\mathbb{R}$-espace vectoriel et $S\\subset V$ une famille liée de vecteurs dans $V.$ Alors toute collection de vecteurs $T$ contenant $S$ est également liée."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%cd ..\n",
+ "import Librairie.AL_Fct as al\n",
+ "import numpy as np\n",
+ "from IPython.display import display, Markdown, Latex\n",
+ "import plotly.graph_objs as go\n",
+ "import plotly\n",
+ "import ipywidgets as widgets\n",
+ "from ipywidgets import interact, interactive, fixed, interact_manual, Layout"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### EXERCICE 1\n",
+ "\n",
+ "Soient:\n",
+ "\n",
+ "$$v_1 = \\begin{pmatrix} 1 \\\\ 0 \\\\ 2 \\end{pmatrix} \\ \\ v_2 = \\begin{pmatrix} 0 \\\\ 1 \\\\ 0 \\end{pmatrix} \\ \\ v_3 = \\begin{pmatrix} 1 \\\\ 1 \\\\ 1 \\end{pmatrix}$$\n",
+ "\n",
+ "Trouver une combinaison linéaire telle que:\n",
+ "\n",
+ "$$\\lambda_1 v_1 + \\lambda_2 v_2 + \\lambda_3 v_3 = \\begin{pmatrix} 3 \\\\ 5 \\\\ 4 \\end{pmatrix}$$\n",
+ "\n",
+ "Entrez les coefficients $\\lambda_i$ dans le vecteur ci-dessous puis exécutez les deux cellules pour vérifier votre réponse."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "source_hidden": true
+ }
+ },
+ "outputs": [],
+ "source": [
+ "def verification_1():\n",
+ " v = np.array([[1, 0, 2], [0, 1, 0], [1, 1, 1]]).transpose()\n",
+ " e = np.array([3, 5, 4])\n",
+ " s = np.array(solution)\n",
+ " r = v @ s\n",
+ " if np.allclose(e, r):\n",
+ " display(Markdown(\"**Correction:** C'est correct!\"))\n",
+ " else:\n",
+ " display(Markdown(\"**Correction:** C'est incorrect car: $\\lambda_1 v_1 + \\lambda_2 v_2 + \\lambda_3 v_3 = \\\\begin{pmatrix} %s \\\\\\\\ %s \\\\\\\\ %s \\end{pmatrix} \\\\neq \\\\begin{pmatrix} %s \\\\\\\\ %s \\\\\\\\ %s \\end{pmatrix}$\" % (r[0], r[1], r[2], e[0], e[1], e[2])))\n",
+ " \n",
+ " #plotly.offline.init_notebook_mode(connected=True)\n",
+ " \n",
+ " w = s * v\n",
+ " \n",
+ " x = np.cumsum(np.insert(w[0], 0, 0))\n",
+ " y = np.cumsum(np.insert(w[1], 0, 0))\n",
+ " z = np.cumsum(np.insert(w[2], 0, 0))\n",
+ "\n",
+ " pairs = [(0,1), (1,2), (2, 3)]\n",
+ "\n",
+ " x_lines = list()\n",
+ " y_lines = list()\n",
+ " z_lines = list()\n",
+ "\n",
+ " for p in pairs:\n",
+ " for i in range(2):\n",
+ " x_lines.append(x[p[i]])\n",
+ " y_lines.append(y[p[i]])\n",
+ " z_lines.append(z[p[i]])\n",
+ " x_lines.append(None)\n",
+ " y_lines.append(None)\n",
+ " z_lines.append(None)\n",
+ "\n",
+ " trace1 = go.Scatter3d(\n",
+ " x=x_lines,\n",
+ " y=y_lines,\n",
+ " z=z_lines,\n",
+ " mode='lines+markers',\n",
+ " name='Combinaison linéaire entrée',\n",
+ " marker_symbol='cross'\n",
+ " )\n",
+ "\n",
+ " trace2 = go.Scatter3d(\n",
+ " x=[0, e[0]],\n",
+ " y=[0, e[1]],\n",
+ " z=[0, e[2]],\n",
+ " mode='lines+markers',\n",
+ " name='Résultat attendu',\n",
+ " )\n",
+ "\n",
+ " fig = go.Figure(data=[trace1, trace2])\n",
+ "\n",
+ " fig.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "solution = [1, 0, 2] # Réponse à compléter\n",
+ "\n",
+ "verification_1()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### EXERCICE 2\n",
+ "\n",
+ "D'après les mêmes données que l'exercice 1, la collection des vecteurs $v_1$, $v_2$, $v_3$ et $\\begin{pmatrix} 3 \\\\ 0 \\\\ 4 \\end{pmatrix}$ est-elle liée ?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "source_hidden": true
+ }
+ },
+ "outputs": [],
+ "source": [
+ "radio = widgets.RadioButtons(\n",
+ " options=['Oui, les vecteurs sont dépendants', 'Non, les vecteurs sont indépendants'],\n",
+ " layout={'width': 'max-content'},\n",
+ " value=None,\n",
+ " description='Réponse:',\n",
+ ")\n",
+ "\n",
+ "button = widgets.Button(description='Vérifier')\n",
+ "\n",
+ "out = widgets.Output()\n",
+ "\n",
+ "display(radio)\n",
+ "display(button)\n",
+ "display(out)\n",
+ "\n",
+ "def verification_2(e):\n",
+ " if radio.value is not None:\n",
+ " out.clear_output()\n",
+ " with out:\n",
+ " if radio.value.startswith('Oui'):\n",
+ " display(Markdown(\"C'est incorrect, il existe $\\lambda_1$, $\\lambda_2$ et $\\lambda_3$ tels que $\\lambda_1 v_1 + \\lambda_2 v_2 + \\lambda_3 v_3 - \\\\begin{pmatrix} 3 \\\\\\\\ 0 \\\\\\\\ 4 \\end{pmatrix} = 0$.\"))\n",
+ " else:\n",
+ " display(Markdown(\"C'est correct!\"))\n",
+ "\n",
+ "button.on_click(verification_2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### EXERCICE 3\n",
+ "\n",
+ "Les collections de vecteurs suivantes sont-elles liées ?"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "source_hidden": true
+ }
+ },
+ "outputs": [],
+ "source": [
+ "def exercice_3(answer):\n",
+ " radio = widgets.RadioButtons(\n",
+ " options=['Oui, les vecteurs sont dépendants', 'Non, les vecteurs sont indépendants'],\n",
+ " layout={'width': 'max-content'},\n",
+ " value=None,\n",
+ " description='Réponse:',\n",
+ " )\n",
+ "\n",
+ " button = widgets.Button(description='Vérifier')\n",
+ "\n",
+ " out = widgets.Output()\n",
+ "\n",
+ " display(radio)\n",
+ " display(button)\n",
+ " display(out)\n",
+ "\n",
+ " def verification_3(e):\n",
+ " if radio.value is not None:\n",
+ " out.clear_output()\n",
+ " with out:\n",
+ " if radio.value.startswith('Oui') == answer:\n",
+ " display(Markdown(\"C'est correct!\"))\n",
+ " else:\n",
+ " display(Markdown(\"C'est incorrect!\"))\n",
+ "\n",
+ " button.on_click(verification_3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### (a)\n",
+ "\n",
+ "$$v_1 = \\begin{pmatrix} 1 \\\\ 1 \\\\ 1 \\end{pmatrix} \\ \\ v_2 = \\begin{pmatrix} 1 \\\\ 2 \\\\ 1 \\end{pmatrix} \\ \\ v_3 = \\begin{pmatrix} 0 \\\\ 1 \\\\ 0 \\end{pmatrix}$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "source_hidden": true
+ }
+ },
+ "outputs": [],
+ "source": [
+ "exercice_3(True)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### (b)\n",
+ "\n",
+ "$$v_1 = \\begin{pmatrix} 1 \\\\ 0 \\\\ 4 \\end{pmatrix} \\ \\ v_2 = \\begin{pmatrix} 6 \\\\ 12 \\\\ 7 \\end{pmatrix} \\ \\ v_3 = \\begin{pmatrix} 0 \\\\ 9 \\\\ 7 \\end{pmatrix} \\ \\ v_4 = \\begin{pmatrix} 1 \\\\ 1 \\\\ 1 \\end{pmatrix}$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "source_hidden": true
+ }
+ },
+ "outputs": [],
+ "source": [
+ "exercice_3(True)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### (c)\n",
+ "\n",
+ "$$v_1 = \\begin{pmatrix} 1 \\\\ 0 \\\\ -1 \\end{pmatrix} \\ \\ v_2 = \\begin{pmatrix} 1 \\\\ 1 \\\\ 0 \\end{pmatrix} \\ \\ v_3 = \\begin{pmatrix} 0 \\\\ 1 \\\\ -1 \\end{pmatrix}$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "jupyter": {
+ "source_hidden": true
+ }
+ },
+ "outputs": [],
+ "source": [
+ "exercice_3(True)"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.6.8"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/Chapitre 4 - Bases et dimension/Prototypes.txt b/Chapitre 4 - Bases et dimension/Prototypes.txt
new file mode 100644
index 0000000..d0b27a0
--- /dev/null
+++ b/Chapitre 4 - Bases et dimension/Prototypes.txt
@@ -0,0 +1,3 @@
+Ressources complémentaires (hébergées sur le drive pour ne pas surcharger le dépôt) :
+
+https://drive.google.com/drive/folders/1tvgU6sx5Blwx-KriIPu7vP4iYlyLIAn9?usp=sharing
\ No newline at end of file
diff --git a/Chapitre 4 - Bases et dimension/courseware_script.ipynb b/Chapitre 4 - Bases et dimension/courseware_script.ipynb
new file mode 100644
index 0000000..72196c7
--- /dev/null
+++ b/Chapitre 4 - Bases et dimension/courseware_script.ipynb
@@ -0,0 +1,88 @@
+{
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import html\n",
+ "import re"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# A small script to efficiently extract the courseware latex macros\n",
+ "def decode(s):\n",
+ " d = html.unescape(s)\n",
+ " def remove_html(html):\n",
+ " if not html: return html\n",
+ " innerText = re.compile('<!--[\\s\\S]*?-->').sub('', html)\n",
+ " while innerText.find('>') >= 0:\n",
+ " text = re.compile('<[^<>]+?>').sub('', innerText)\n",
+ " if text == innerText:\n",
+ " break\n",
+ " innerText = text\n",
+ "\n",
+ " return innerText.strip()\n",
+ " d = remove_html(d)\n",
+ " d = d.replace(\"\\\\(\", \"$\").replace(\"\\\\)\", \"$\")\n",
+ " d = d.replace(\"\\n\", \"\\n\\n\")\n",
+ " return d"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "s = \"\"\"\n",
+ "&lt;p&gt;Soient \\(V\\) un \\(\\mathbb{R}\\)-espace vectoriel et \\(S\\subset V\\) une collection de vecteurs dans \\(V.\\) On dit que \\(S\\) est &lt;em&gt;lin&amp;eacute;airement d&amp;eacute;pendante&lt;/em&gt; (ou &lt;em&gt;li&amp;eacute;e&lt;/em&gt;) s&#39;il existe des vecteurs distincts \\(v_1,\\ldots,v_r\\in S\\) et des scalaires \\(\\lambda_1,\\ldots,\\lambda_r\\in \\mathbb{R}\\) non tous nuls tels que \\(\\lambda_1v_1+\\cdots+\\lambda_rv_r=0.\\) (Autrement dit, s&#39;il existe une combinaison lin&amp;eacute;aire (non triviale) de vecteurs de \\(S\\) qui se r&amp;eacute;duit au vecteur nul.) S&#39;il n&#39;existe pas de tels vecteurs dans \\(S,\\) alors on dit que \\(S\\) est &lt;em&gt;lin&amp;eacute;airement ind&amp;eacute;pendante&lt;/em&gt; (ou &lt;em&gt;libre&lt;/em&gt;).&lt;/p&gt;\n",
+ "&lt;h3&gt;&lt;span style=&#34;text-decoration: underline; color: #ff6600;&#34;&gt;REMARQUE 2 :&lt;/span&gt;&lt;/h3&gt;\n",
+ "&lt;p&gt;Si \\(0\\in S,\\) alors \\(S\\) est li&amp;eacute;e car \\(\\lambda\\cdot 0=0\\) pour tout \\(\\lambda\\in \\mathbb{R}.\\)&lt;/p&gt;\n",
+ "&lt;p&gt;&amp;nbsp;&lt;/p&gt;\n",
+ "&lt;/div&gt;\n",
+ "\"\"\"\n",
+ "\n",
+ "print(decode(s))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from IPython.display import display, Markdown, Latex\n",
+ "\n",
+ "display(Markdown(decode(s)))"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.6.8"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/Librairie/AL_Fct.py b/Librairie/AL_Fct.py
index 831d3d5..567fd6c 100644
--- a/Librairie/AL_Fct.py
+++ b/Librairie/AL_Fct.py
@@ -1,1268 +1,1370 @@
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Wed Mar 13 16:42:29 2019
@author: jecker
"""
from __future__ import division
import numpy as np
from IPython.display import display, Latex
import plotly
import plotly.graph_objs as go
plotly.offline.init_notebook_mode(connected=True)
from IPython.core.magic import register_cell_magic
from IPython.display import HTML
import ipywidgets as widgets
import random
from ipywidgets import interact_manual
@register_cell_magic
def bgc(color):
script = (
"var cell = this.closest('.jp-CodeCell');"
"var editor = cell.querySelector('.jp-Editor');"
"editor.style.background='{}';"
"this.parentNode.removeChild(this)"
).format(color)
display(HTML('<img src onerror="{}">'.format(script)))
###############################################################################
## PRINTS Equations, systems, matrix
def printMonomial(coeff, index=None, include_zeros=False):
"""Prints the monomial coeff*x_{index} in optimal way
:param coeff: value of the coefficient
:type coeff: float
:param index: index of the monomial. If None, only the numerical value of the coefficient is displayed
:type index: int or NoneType
:param include_zeros: if True, monomials of type 0x_n are printed. Defaults to False
:type include_zeros: bool
:return: string representative of the monomial
:rtype: str
"""
if index is not None:
coeff = abs(coeff)
if coeff % 1:
return str(round(coeff, 3)) + ('x_' + str(index) if index is not None else "")
elif not coeff:
if index is None:
return str(0)
else:
return str(0) + 'x_' + str(index) if include_zeros else ""
elif coeff == 1:
return 'x_' + str(index) if index is not None else str(int(coeff))
elif coeff == -1:
return 'x_' + str(index) if index is not None else str(int(coeff))
else:
return str(int(coeff)) + ('x_' + str(index) if index is not None else "")
def printPlusMinus(coeff, include_zeros=False):
"""Prints a plus or minus sign, depending on the sign of the coefficient
:param coeff: value of the coefficient
:type coeff: float
:param include_zeros: if True, 0-coefficients are assigned a "+" sign
:type include_zeros: bool
:return: "+" if the coefficient is positive, "-" if it is negative, "" if it is 0
:rtype: str
"""
if coeff > 0:
return "+"
elif coeff < 0:
return "-"
else:
return "+" if include_zeros else ""
def strEq(n, coeff):
"""Method that provides the Latex string of a linear equation, given the number of unknowns and the values
of the coefficients. If no coefficient value is provided, then a symbolic equation with `n` unknowns is plotted.
In particular:
* **SYMBOLIC EQUATION**: if the number of unknowns is either 1 or 2, then all the equation is
displayed while, if the number of unknowns is higher than 2, only the first and last term of the equation
are displayed
* **NUMERICAL EQUATION**: whichever the number of unknowns, the whole equation is plotted. Numerical values
of the coefficients are rounded to the third digit
:param n: number of unknowns of the equation
:type n: int
:param coeff: coefficients of the linear equation. It must be [] if a symbolic equation is desired
:type: list[float]
:return: Latex string representing the equation
:rtype: str
"""
Eq = ''
if not len(coeff):
if n is 1:
Eq = Eq + 'a_1x_1 = b'
elif n is 2:
Eq = Eq + 'a_1x_1 + a_2x_2 = b'
else:
Eq = Eq + 'a_1x_1 + \ldots + ' + 'a_' + str(n) + 'x_' + str(n) + '= b'
else:
all_zeros = len(set(coeff[:-1])) == 1 and not coeff[0] # check if all lhs coefficients are 0
start_put_sign = all_zeros
if n is 1:
Eq += "-" if coeff[0] < 0 else ""
Eq += printMonomial(coeff[0], index=1, include_zeros=all_zeros) + "=" + printMonomial(coeff[-1])
else:
Eq += "-" if coeff[0] < 0 else ""
Eq += printMonomial(coeff[0], index=1, include_zeros=all_zeros)
start_put_sign = start_put_sign or coeff[0] is not 0
for i in range(1, n):
Eq += printPlusMinus(coeff[i], include_zeros=all_zeros) if start_put_sign \
else "-" if coeff[i] < 0 else ""
Eq += printMonomial(coeff[i], index=i+1, include_zeros=all_zeros)
start_put_sign = start_put_sign or coeff[i] is not 0
Eq += "=" + printMonomial(coeff[-1])
return Eq
def printEq(coeff, b, *args):
"""Method that prints the Latex string of a linear equation, given the values of the coefficients. If no coefficient
value is provided, then a symbolic equation with `n` unknowns is plotted. In particular:
* **SYMBOLIC EQUATION**: if the number of unknowns is either 1 or 2, then all the equation is
displayed while, if the number of unknowns is higher than 2, only the first and last term of the equation
are displayed
* **NUMERICAL EQUATION**: whichever the number of unknowns, the whole equation is plotted. Numerical values
of the coefficients are rounded to the third digit
:param coeff: coefficients of the left-hand side of the linear equation
:type: list[float]
:param b: right-hand side coefficient of the linear equation
:type b: float
:param *args: optional; if passed, it contains the number of unknowns to be considered. If not passed, all the
unknowns are considered, i.e. n equals the length of the coefficients list
:type: *args: list
"""
if len(args) == 1:
n = args[0]
else:
n = len(coeff)
coeff = coeff + b
texEq = '$'
texEq = texEq + strEq(n, coeff)
texEq = texEq + '$'
display(Latex(texEq))
return
def printSyst(A, b, *args):
"""Method that prints a linear system of `n` unknowns and `m` equations. If `A` and `b` are empty, then a symbolic
system is printed; otherwise a system containing the values of the coefficients stored in `A` and `b`, approximated
up to their third digit is printed.
:param A: left-hand side matrix. It must be [] if a symbolic system is desired
:type: list[list[float]]
:param b: right-hand side vector. It must be [] if a symbolic system is desired
:type b: list[float]
:param args: optional; if not empty, it is a list of two integers representing the number of equations of the
linear system (i.e. `m`) and the number of unknowns of the system (i.e. `n`)
:type: list
"""
if (len(args) == 2) or (len(A) == len(b)): # ensures that MatCoeff has proper dimensions
if len(args) == 2:
m = args[0]
n = args[1]
else:
m = len(A)
n = len(A[0])
texSyst = '$\\begin{cases}'
Eq_list = []
if len(A) and len(b):
if type(b[0]) is list:
b = np.array(b).astype(float)
A = np.concatenate((A, b), axis=1)
else:
A = [A[i] + [b[i]] for i in range(0, m)] # becomes augmented matrix
A = np.array(A) # just in case it's not
for i in range(m):
if not len(A) or not len(b):
Eq_i = ''
if n is 1:
Eq_i = Eq_i + 'a_{' + str(i + 1) + '1}' + 'x_1 = b_' + str(i + 1)
elif n is 2:
Eq_i = Eq_i + 'a_{' + str(i + 1) + '1}' + 'x_1 + ' + 'a_{' + str(i + 1) + '2}' + 'x_2 = b_' + str(
i + 1)
else:
Eq_i = Eq_i + 'a_{' + str(i + 1) + '1}' + 'x_1 + \ldots +' + 'a_{' + str(i + 1) + str(
n) + '}' + 'x_' + str(n) + '= b_' + str(i + 1)
else:
Eq_i = strEq(n, A[i, :]) # attention A is (A|b)
Eq_list.append(Eq_i)
texSyst = texSyst + Eq_list[i] + '\\\\'
texSyst = texSyst + '\\end{cases}$'
display(Latex(texSyst))
else:
print("La matrice des coefficients n'a pas les bonnes dimensions")
return
def texMatrix(*args):
"""Method which produces the Latex string corresponding to the input matrix.
.. note:: if two inputs are passed, they represent A and b respectively; as a result the augmented matrix A|B is
plotted. Otherwise, if the input is unique, just the matrix A is plotted
:param args: input arguments; they could be either a matrix and a vector or a single matrix
:type args: list[list] or list[numpy.ndarray]
:return: Latex string representing the input matrix or the input matrix augmented by the input vector
:rtype: str
"""
if len(args) == 2: # matrice augmentée
if not type(args[0]) is np.ndarray:
A = np.array(args[0]).astype(float)
else:
A = args[0].astype(float)
m = A.shape[1]
if not type(args[1]) is np.array:
b = np.array(args[1]).astype(float)
else:
b = args[1].astype(float)
A = np.concatenate((A, b), axis=1)
texApre = '\\left[\\begin{array}{'
texA = ''
for i in np.asarray(A):
texALigne = ''
texALigne = texALigne + str(round(i[0], 4) if i[0] % 1 else int(i[0]))
if texA == '':
texApre = texApre + 'c'
for j in i[1:m]:
if texA == '':
texApre = texApre + 'c'
texALigne = texALigne + ' & ' + str(round(j, 4) if j % 1 else int(j))
if texA == '':
texApre = texApre + '| c'
for j in i[m:]:
if texA == '':
texApre = texApre + 'c'
texALigne = texALigne + ' & ' + str(round(j, 4) if j % 1 else int(j))
texALigne = texALigne + ' \\\\'
texA = texA + texALigne
texA = texApre + '} ' + texA[:-2] + ' \\end{array}\\right]'
elif len(args) == 1: # matrice des coefficients
if not type(args[0]) is np.ndarray:
A = np.array(args[0]).astype(float)
else:
A = args[0].astype(float)
texApre = '\\left[\\begin{array}{'
texA = ''
for i in np.asarray(A):
texALigne = ''
texALigne = texALigne + str(round(i[0], 4) if i[0] % 1 else int(i[0]))
if texA == '':
texApre = texApre + 'c'
for j in i[1:]:
if texA == '':
texApre = texApre + 'c'
texALigne = texALigne + ' & ' + str(round(j, 4) if j % 1 else int(j))
texALigne = texALigne + ' \\\\'
texA = texA + texALigne
texA = texApre + '} ' + texA[:-2] + ' \\end{array}\\right]'
else:
print("Ce n'est pas une matrice des coefficients ni une matrice augmentée")
texA = ''
return texA
def printA(*args):
"""Method which prints the input matrix.
.. note:: if two inputs are passed, they represent A and b respectively; as a result the augmented matrix A|B is
plotted. Otherwise, if the input is unique, just the matrix A is plotted
:param args: input arguments; they could be either a matrix and a vector or a single matrix
:type args: list
"""
texA = '$' + texMatrix(*args) + '$'
display(Latex(texA))
return
def printEquMatrices(*args):
"""Method which prints the list of input matrices.
.. note:: if two inputs are passed, they represent the list of coefficient matrices A and the list of rhs b
respectively; as a result the augmented matrices A|B are plotted. Otherwise, if the input is unique, just the
matrices A are plotted
:param args: input arguments; they could be either a list of matrices and a list of vectors or
a single list of matrices
:type args: list
"""
# list of matrices is M=[M1, M2, ..., Mn] where Mi=(Mi|b)
if len(args) == 2:
listOfMatrices = args[0]
listOfRhS = args[1]
texEqu = '$' + texMatrix(listOfMatrices[0], listOfRhS[0])
for i in range(1, len(listOfMatrices)):
texEqu = texEqu + '\\quad \\sim \\quad' + texMatrix(listOfMatrices[i], listOfRhS[i])
texEqu = texEqu + '$'
display(Latex(texEqu))
else:
listOfMatrices = args[0]
texEqu = '$' + texMatrix(listOfMatrices[0])
for i in range(1, len(listOfMatrices)):
texEqu = texEqu + '\\quad \\sim \\quad' + texMatrix(listOfMatrices[i])
texEqu = texEqu + '$'
display(Latex(texEqu))
return
# %% Functions to enter something
def EnterInt(n=None):
"""Function to allow the user to enter a non-negative integer
:param n: first integer, passed to the function. If null or negative or None, an integer is requested to the user.
Defaults to None
:type n: int or NoneType
:return: positive integer
:rtype: int
"""
while type(n) is not int or (type(n) is int and n <= 0):
try:
n = int(n)
if n <= 0:
print("Le nombre ne peut pas être négatif o zero!")
print("Entrez à nouveau: ")
n = input()
except:
if n is not None:
print("Ce n'est pas un entier!")
print("Entrez à nouveau:")
n = input()
else:
print("Entrez un entier positif")
n = input()
return n
def EnterListReal(n):
"""Function which allows the user to enter a list of `n` real numbers
:param n: number of real numbers in the desired list
:type n: int
:return: list of `n` real numbers
:rtype: list[float]
"""
if n < 0:
print(f"Impossible de générer une liste de {n} nombres réels")
elif n == 0:
return []
else:
print(f"Entrez une liste de {n} nombres réels")
coeff = None
while type(coeff) is not list:
try:
coeff = input()
coeff = [float(eval(x)) for x in coeff.split(',')]
if len(coeff) != n:
print("Vous n'avez pas entré le bon nombre de réels!")
print("Entrez à nouveau : ")
coeff = input()
except:
print("Ce n'est pas le bon format!")
print("Entrez à nouveau")
coeff = input()
return coeff
def SolOfEq(sol, coeff, i):
"""Method that verifies if `sol` is a solution to the linear equation `i`with coefficients `coeff`
:param sol: candidate solution vector
:type sol: list
:param coeff: coefficients of the linear equation
:type coeff: list
:param i: index of the equation
:type i: int
:return: True if `sol` is a solution, False otherwise
:rtype: bool
"""
try:
assert len(sol) == len(coeff)-1
except AssertionError:
print(f"La suite entrée n'est pas une solution de l'équation {i}; Les dimensions ne correspondent pas")
return False
A = np.array(coeff[:-1])
isSol = abs(np.dot(A, sol) - coeff[-1]) < 1e-8
if isSol:
print(f"La suite entrée est une solution de l'équation {i}")
else:
print(f"La suite entrée n'est pas une solution de l'équation {i}")
return isSol
def SolOfSyst(solution, A, b):
"""Method that verifies if `solution` is a solution to the linear system with left-hand side matrix `A` and
right-hand side vector `b`
:param solution: candidate solution vector
:type solution: list
:param A: left-hand side matrix of the linear system
:type A: list[list[float]] or numpy.ndarray
:param b: right-hand side vector of the linear system
:type b: list[float] or numpy.ndarray
:return: True if `sol` is a solution, False otherwise
:rtype: bool
"""
try:
assert len(solution) == (len(A[0]) if type(A) is list else A.shape[1])
except AssertionError:
print(f"La suite entrée n'est pas une solution du système; Les dimensions ne correspondent pas")
return False
A = [A[i] + [b[i]] for i in range(0, len(A))]
A = np.array(A)
isSol = [SolOfEq(solution, A[i, :], i+1) for i in range(len(A))]
if all(isSol):
print("C'est une solution du système")
return True
else:
print("Ce n'est pas une solution du système")
return False
# PLOTS WITH PLOTLY #
def drawLine(p, d):
"""Method which allows to plot lines, points and arrows in the 2D-place or 3D-space, using plotly library
:param p: point
:type p: list[list[float]]
:param d: direction vector. If made of all zeros, just the reference point is plotted; if different from 0 a line
passing through `p` and with direction `d` is plotted
:type d: list[list[float]]
:return: generated plot
"""
blue = 'rgb(51, 214, 255)'
colors = [blue]
colorscale = [[0.0, colors[0]],
[0.1, colors[0]],
[0.2, colors[0]],
[0.3, colors[0]],
[0.4, colors[0]],
[0.5, colors[0]],
[0.6, colors[0]],
[0.7, colors[0]],
[0.8, colors[0]],
[0.9, colors[0]],
[1.0, colors[0]]]
vec = 0.9 * np.array(d)
if len(p) == 2:
data = []
t = np.linspace(-5, 5, 51)
s = np.linspace(0, 1, 10)
if all(dd == [0] for dd in d):
vector = go.Scatter(x=p[0] + s*0, y=p[1] + s*0, marker=dict(symbol=6, size=12, color=colors[0]),
name ='Point')
else:
trace = go.Scatter(x=p[0] + t * d[0], y=p[1] + t * d[1], name='Droite')
peak = go.Scatter(x=d[0], y=d[1], marker=dict(symbol=6, size=12, color=colors[0]), showlegend=False)
vector = go.Scatter(x=p[0] + s * d[0], y=p[1] + s * d[1], mode='lines',
line=dict(width=5, color=colors[0]), name='Vecteur directeur')
zero = go.Scatter(x=t*0, y=t*0, name='Origine', marker=dict(symbol=6, size=12, color=colors[0]),
showlegend=False)
data.append(vector)
data.append(zero)
if not all(dd == [0] for dd in d):
data.append(trace)
data.append(peak)
fig = go.FigureWidget(data=data)
plotly.offline.iplot(fig)
elif len(p) == 3:
data = [
{
'type': 'cone',
'x': [1], 'y': vec[1], 'z': vec[2],
'u': d[0], 'v': d[1], 'w': d[2],
"sizemode": "absolute",
'colorscale': colorscale,
'sizeref': 1,
"showscale": False,
'hoverinfo': 'none'
}
]
t = np.linspace(-5, 5, 51)
s = np.linspace(0, 1, 10)
zero = go.Scatter3d(x=t*0, y=t*0, z=t*0, name='Origine', marker=dict(size=3), showlegend=False)
if all(dd == [0] for dd in d):
vector = go.Scatter3d(x=p[0] + s*0, y=p[1] + s*0, z=p[2] + s*0, marker=dict(size=5),
name='Point')
else:
trace = go.Scatter3d(x=p[0] + t * d[0], y=p[1] + t * d[1], z=p[2] + t * d[2], mode='lines', name='Droite')
vector = go.Scatter3d(x=p[0] + s * d[0], y=p[1] + s * d[1], z=p[2] + s * d[2], mode='lines',
line=dict(width=5,color=colors[0], dash='solid'), name='Vecteur directeur',
hoverinfo='none')
data.append(zero)
data.append(vector)
if not all(dd == [0] for dd in d):
data.append(trace)
layout = {
'scene': {
'camera': {
'eye': {'x': -0.76, 'y': 1.8, 'z': 0.92}
}
}
}
fig = go.FigureWidget(data=data, layout=layout)
plotly.offline.iplot(fig)
return fig
def Plot2DSys(xL, xR, p, A, b):
"""Function for the graphical visualization of a 2D system of equations, plotting the straight lines characterizing
the different equations appearing in the system
:param xL: left limit of the plot in both coordinates
:type xL: int or float
:param xR: right limit of the plot in both coordinates
:type xR: int or float
:param p: number of points used to draw the straight lines
:type p: int
:param A: matrix of the linear system
:type A: list[list[float]] or numpy.ndarray
:param b: right-hand side vector of the linear system
:type b: list[float] or numpy.ndarray
"""
A = [A[i] + [b[i]] for i in range(0, len(A))]
A = np.array(A)
t = np.linspace(xL, xR, p)
data = []
for i in range(1, len(A) + 1):
if (abs(A[i - 1, 1])) > abs(A[i - 1, 0]):
# p0=[0,A[i-1,2]/A[i-1,1]]
# p1=[1,(A[i-1,2]-A[i-1,0])/A[i-1,1]]
trace = go.Scatter(x=t, y=(A[i-1, 2] - A[i-1, 0] * t) / A[i-1, 1], name='Droite %d' % i)
else:
trace = go.Scatter(x=(A[i-1, 2] - A[i-1, 1] * t) / A[i-1, 0], y=t, name='Droite %d' % i)
data.append(trace)
fig = go.Figure(data=data)
plotly.offline.iplot(fig)
return
def Plot3DSys(xL, xR, p, A, b):
"""Function for the graphical visualization of a 3D system of equations, plotting the straight lines characterizing
the different equations appearing in the system
:param xL: left limit of the plot in all coordinates
:type xL: int or float
:param xR: right limit of the plot in all coordinates
:type xR: int or float
:param p: number of points used to draw the straight lines
:type p: int
:param A: matrix of the linear system
:type A: list[list[float]] or numpy.ndarray
:param b: right-hand side vector of the linear system
:type b: list[float] or numpy.ndarray
"""
- A = [A[i] + [b[i]] for i in range(0, len(A))]
A = np.array(A)
+ b = np.array(b)
gr = 'rgb(102,255,102)'
org = 'rgb(255,117,26)'
# red = 'rgb(255,0,0)'
blue = 'rgb(51, 214, 255)'
colors = [blue, gr, org]
s = np.linspace(xL, xR, p)
t = np.linspace(xL, xR, p)
tGrid, sGrid = np.meshgrid(s, t)
data = []
for i in range(len(A)):
colorscale = [[0.0, colors[i]],
[0.1, colors[i]],
[0.2, colors[i]],
[0.3, colors[i]],
[0.4, colors[i]],
[0.5, colors[i]],
[0.6, colors[i]],
[0.7, colors[i]],
[0.8, colors[i]],
[0.9, colors[i]],
[1.0, colors[i]]]
j = i + 1
if (abs(A[i, 2])) > abs(A[i, 1]): # z en fonction de x,y
x = sGrid
y = tGrid
- surface = go.Surface(x=x, y=y, z=(A[i, 3] - A[i, 0] * x - A[i, 1] * y) / A[i, 2],
+ surface = go.Surface(x=x, y=y, z=(b[i] - A[i, 0] * x - A[i, 1] * y) / A[i, 2],
showscale=False, showlegend=True, colorscale=colorscale, opacity=1, name='Plan %d' % j)
- elif A[i, 2] == 0 and A[i, 1] == 0: # x =b
+
+ elif A[i, 2] == 0 and A[i, 1] == 0:
y = sGrid
z = tGrid
- surface = go.Surface(x=A[i, 3] - A[i, 1] * y, y=y, z=z,
+ surface = go.Surface(x=(b[i] - A[i, 1] * y)/A[i, 0], y=y, z=z,
showscale=False, showlegend=True, colorscale=colorscale, opacity=1, name='Plan %d' % j)
+
else: # y en fonction de x,z
x = sGrid
z = tGrid
- surface = go.Surface(x=x, y=(A[i, 3] - A[i, 0] * x - A[i, 2] * z) / A[i, 1], z=z,
+ surface = go.Surface(x=x, y=(b[i] - A[i, 0] * x - A[i, 2] * z) / A[i, 1], z=z,
showscale=False, showlegend=True, colorscale=colorscale, opacity=1, name='Plan %d' % j)
+
+ data.append(surface)
+ layout = go.Layout(
+ showlegend=True, # not there WHY???? --> LEGEND NOT YET IMPLEMENTED FOR SURFACE OBJECTS!!
+ legend=dict(orientation="h"),
+ autosize=True,
+ width=800,
+ height=800,
+ scene=go.layout.Scene(
+ xaxis=dict(
+ gridcolor='rgb(255, 255, 255)',
+ zerolinecolor='rgb(255, 255, 255)',
+ showbackground=True,
+ backgroundcolor='rgb(230, 230,230)'
+ ),
+ yaxis=dict(
+ gridcolor='rgb(255, 255, 255)',
+ zerolinecolor='rgb(255, 255, 255)',
+ showbackground=True,
+ backgroundcolor='rgb(230, 230,230)'
+ ),
+ zaxis=dict(
+ gridcolor='rgb(255, 255, 255)',
+ zerolinecolor='rgb(255, 255, 255)',
+ showbackground=True,
+ backgroundcolor='rgb(230, 230,230)'
+ )
+ )
+ )
+ fig = go.Figure(data=data, layout=layout)
+ plotly.offline.iplot(fig)
+ return
+
+
+def Plot3DSys_2(xL, xR, p, A, b):
+ """Function for the graphical visualization of a 3D system of equations, plotting the straight lines characterizing
+ the different equations appearing in the system
+
+ :param xL: left limit of the plot in all coordinates
+ :type xL: int or float
+ :param xR: right limit of the plot in all coordinates
+ :type xR: int or float
+ :param p: number of points used to draw the straight lines
+ :type p: int
+ :param A: matrix of the linear system
+ :type A: list[list[float]] or numpy.ndarray
+ :param b: right-hand side vector of the linear system
+ :type b: list[float] or numpy.ndarray
+ """
+ A = np.array(A)
+ b = np.array(b)
+
+ gr = 'rgb(102,255,102)'
+ org = 'rgb(255,117,26)'
+ # red = 'rgb(255,0,0)'
+ blue = 'rgb(51, 214, 255)'
+ colors = [blue, gr, org]
+ s = np.linspace(xL, xR, p)
+ t = np.linspace(xL, xR, p)
+ tGrid, sGrid = np.meshgrid(s, t)
+ data = []
+ for i in range(len(A)):
+ colorscale = [[0.0, colors[i]],
+ [0.1, colors[i]],
+ [0.2, colors[i]],
+ [0.3, colors[i]],
+ [0.4, colors[i]],
+ [0.5, colors[i]],
+ [0.6, colors[i]],
+ [0.7, colors[i]],
+ [0.8, colors[i]],
+ [0.9, colors[i]],
+ [1.0, colors[i]]]
+ j = i + 1
+ if A[i, 2]!= 0.0: # z en fonction de x,y
+ x = sGrid
+ y = tGrid
+ surface = go.Surface(x=x, y=y, z=(b[i] - A[i, 0] * x - A[i, 1] * y) / A[i, 2],
+ showscale=False, showlegend=True, colorscale=colorscale, opacity=1, name='Plan %d' % j)
+
+ elif A[i, 1]!=0: # y en fonction de x,z
+ x = sGrid
+ z = tGrid
+ surface = go.Surface(x=x, y=(b[i]-A[i, 0]*x - A[i, 2]*z)/A[i, 1], z=z,
+ showscale=False, showlegend=True, colorscale=colorscale, opacity=1, name='Plan %d' % j)
+
+ elif A[i, 0]!=0: # x en fonction de y,z
+ y = sGrid
+ z = tGrid
+ surface = go.Surface(x=(b[i] - A[i, 1] * y - A[i,2] * z)/A[i, 0], y=y, z=z,
+ showscale=False, showlegend=True, colorscale=colorscale, opacity=1, name='Plan %d' % j)
+
+ else: # All the coefficient of equation are 0: b==0 -> every combinations are solution, b!=0 -> No solution
+ if b[i] == 0:
+ print("Non constraints on equation", j, "of the system.")
+ else:
+ print("No solution for equation", j, "of the system.")
+
+
+
data.append(surface)
layout = go.Layout(
showlegend=True, # not there WHY???? --> LEGEND NOT YET IMPLEMENTED FOR SURFACE OBJECTS!!
legend=dict(orientation="h"),
autosize=True,
width=800,
height=800,
scene=go.layout.Scene(
xaxis=dict(
gridcolor='rgb(255, 255, 255)',
zerolinecolor='rgb(255, 255, 255)',
showbackground=True,
backgroundcolor='rgb(230, 230,230)'
),
yaxis=dict(
gridcolor='rgb(255, 255, 255)',
zerolinecolor='rgb(255, 255, 255)',
showbackground=True,
backgroundcolor='rgb(230, 230,230)'
),
zaxis=dict(
gridcolor='rgb(255, 255, 255)',
zerolinecolor='rgb(255, 255, 255)',
showbackground=True,
backgroundcolor='rgb(230, 230,230)'
)
)
)
fig = go.Figure(data=data, layout=layout)
plotly.offline.iplot(fig)
return
def isDiag(M):
"""Method which checks if a matrix is diagonal
:param M: input matrix
:type M: list[list[float]] or numpy.ndarray
:return: True if M is diagonal else False
:rtype: bool
"""
if not type(M) is np.ndarray:
M = np.array(M)
i, j = M.shape
try:
assert i == j
except AssertionError:
print("A non-squared matrix cannot be diagonal!")
return False
test = M.reshape(-1)[:-1].reshape(i - 1, j + 1)
return ~np.any(test[:, 1:])
def isSym(M):
"""Method which checks if a matrix is symmetric
:param M: input matrix
:type M: list[list[float]] or numpy.ndarray
:return: True if M is symmetric else False
:rtype: bool
"""
if not type(M) is np.ndarray:
M = np.array(M)
i, j = M.shape
try:
assert i == j
except AssertionError:
print("A non-squared matrix cannot be symmetric!")
return False
return ~np.any(M - np.transpose(M))
# ECHELONNAGE #
def echZero(indice, M):
"""Method which sets to zero the entries of matrix M that correspond to a True value in the boolean vector indice
:param indice: vector of booleans; if an element is True, it means that the element with the corresponding index in
matrix M must be set to 0
:type indice: list[bool]
:param M: matrix to be processed
:type: numpy.ndarray
:return: processed matrix M, where the given entries have been properly set to 0
:rtype: numpy.ndarray
"""
Mat = M[not indice, :].ravel()
Mat = np.concatenate([Mat, M[indice, :].ravel()])
Mat = Mat.reshape(len(M), len(M[0, :]))
return Mat
def Eij(M, i, j):
"""Method to swap line `i` and line `j` of matrix `M`
:param M: matrix to be processed
:type M: numpy.ndarray
:param i: first line index
:type i: int
:param j: second line index
:type j: int
:return: processed matrix, with line `i` and `j` having been swapped
:rtype: numpy.ndarray
"""
M = np.array(M)
M[[i, j], :] = M[[j, i], :]
return M
def Ealpha(M, i, alpha):
"""Method to multiply line `i` of matrix `M` by the scalar coefficient `alpha`
:param M: matrix to be processed
:type M: numpy.ndarray
:param i: reference line index
:type i: int
:param alpha: scalar coefficient
:type alpha: float
:return: processed matrix, with line `i` multiplied by the scalar `alpha`
:rtype: numpy.ndarray
"""
M = np.array(M)
M[i, :] = alpha * M[i, :]
return M
def Eijalpha(M, i, j, alpha):
"""Method to add to line `i` of matrix `M` line `j` of the same matrix, multiplied by the scalar coefficient `alpha`
:param M: matrix to be processed
:type M: numpy.ndarray
:param i: line to be modified
:type i: int
:param j: line whose multiple has tobe added to line `i`
:type j: int
:param alpha: scalar coefficient
:type alpha: float
:return: processed matrix, with line `i` being summed up with line `j` multiplied by `alpha`
:rtype: numpy.ndarray
"""
M = np.array(M)
M[i, :] = M[i, :] + alpha * M[j, :]
return M
def echelonMat(ech, *args):
"""Method to perform Gauss elimination on either the matrix of the coefficients (if `len(args)==1`) or on the
augmented matrix (if `len(args)==2`); the elimination can be either in standard form (if `ech=='E` or in reduced
form (if `ech=='ER'`).
:param ech:
:type ech:
:param args:
:type args:
:return:
:rtype:
"""
if len(args) == 2: # matrice augmentée
A = np.array(args[0]).astype(float)
m = A.shape[0]
n = A.shape[1]
b = args[1]
if type(b[0]) == list:
b = np.array(b).astype(float)
A = np.concatenate((A, b), axis=1)
else:
b = [b[i] for i in range(m)]
A = [A[i] + [b[i]] for i in range(0, m)]
else: # matrice coeff
A = np.array(args[0]).astype(float)
m = A.shape[0]
n = A.shape[1]
if ech == 'E': # Echelonnée
Mat = np.array(A)
Mat = Mat.astype(float) # in case the array in int instead of float.
numPivot = 0
for i in range(len(Mat)):
j = i
while all(abs(Mat[j:, i]) < 1e-15) and j != len(Mat[0, :]) - 1: # if column (or rest of) is 0, take next
j += 1
if j == len(Mat[0, :]) - 1:
if len(Mat[0, :]) > j:
Mat[i + 1:len(Mat), :] = 0
break
if abs(Mat[i, j]) < 1e-15:
Mat[i, j] = 0
zero = abs(Mat[i:, j]) < 1e-15
M = echZero(zero, Mat[i:, :])
Mat[i:, :] = M
Mat = Ealpha(Mat, i, 1 / Mat[i, j]) # usually Mat[i,j]!=0
for k in range(i + 1, len(A)):
Mat = Eijalpha(Mat, k, i, -Mat[k, j])
# Mat[k,:]=[0 if abs(Mat[k,l])<1e-15 else Mat[k,l] for l in range(len(MatCoeff[0,:]))]
numPivot += 1
Mat[abs(Mat) < 1e-15] = 0
print("La matrice est sous la forme échelonnée")
if len(args) == 2:
printEquMatrices([A[:, :n], Mat[:, :n]], [A[:, n:], Mat[:, n:]])
else:
printEquMatrices([A, Mat])
elif ech == 'ER': # Echelonnée réduite
Mat = np.array(A)
Mat = Mat.astype(float) # in case the array in int instead of float.
numPivot = 0
for i in range(len(Mat)):
j = i
while all(abs(Mat[j:, i]) < 1e-15) and j != len(
Mat[0, :]) - 1: # if column (or rest of) is zero, take next column
j += 1
if j == len(Mat[0, :]) - 1:
# ADD ZERO LINES BELOW!!!!!!
if len(Mat[0, :]) > j:
Mat[i + 1:len(Mat), :] = 0
break
if abs(Mat[i, j]) < 1e-15:
Mat[i, j] = 0
zero = abs(Mat[i:, j]) < 1e-15
M = echZero(zero, Mat[i:, :])
Mat[i:, :] = M
Mat = Ealpha(Mat, i, 1 / Mat[i, j]) # normalement Mat[i,j]!=0
for k in range(i + 1, len(A)):
Mat = Eijalpha(Mat, k, i, -Mat[k, j])
# Mat[k,:]=[0 if abs(Mat[k,l])<1e-15 else Mat[k,l] for l in range(len(MatCoeff[0,:]))]
numPivot += 1
Mat[abs(Mat) < 1e-15] = 0
print("La matrice est sous la forme échelonnée")
if len(args) == 2:
printEquMatrices([A[:, :n], Mat[:, :n]], [A[:, n:], Mat[:, n:]])
else:
printEquMatrices([np.asmatrix(A), np.asmatrix(Mat)])
Mat = np.array(Mat)
i = (len(Mat) - 1)
while i >= 1:
while all(
abs(Mat[i, :len(Mat[0]) - 1]) < 1e-15) and i != 0: # if ligne (or rest of) is zero, take next ligne
i -= 1
# we have a lign with one non-nul element
j = i # we can start at pos ij at least the pivot is there
if abs(Mat[i, j]) < 1e-15: # if element Aij=0 take next one --> find pivot
j += 1
# Aij!=0 and Aij==1 if echelonMat worked
for k in range(i): # put zeros above pivot (which is 1 now)
Mat = Eijalpha(Mat, k, i, -Mat[k, j])
i -= 1
print("La matrice est sous la forme échelonnée réduite")
if len(args) == 2:
printEquMatrices([A[:, :n], Mat[:, :n]], [A[:, n:], Mat[:, n:]])
else:
printEquMatrices([A, Mat])
else:
print(f"Méthode d'échelonnage non reconnue {ech}. Méthodes disponibles: 'E' (pour la forme échelonnée standard)"
f", 'ER' (pour la forme échelonnée réduite))")
return np.asmatrix(Mat)
def randomA():
"""Method which generates a random matrix with rows and columns within 1 and 10 and integer entries between -100
and 100
:return: generated random matrix
:rtype: numpy.ndarray
"""
n = random.randint(1, 10)
m = random.randint(1, 10)
A = [[random.randint(-100, 100) for i in range(n)] for j in range(m)]
printA(A)
return np.array(A)
def dimensionA(A):
"""Method which allows the user to enter the matrix dimensions and verifies whether they are correct or not
:param A: reference matrix
:type A: numpy.ndarray
"""
m = widgets.IntText(
value=1,
step=1,
description='m:',
disabled=False
)
n = widgets.IntText(
value=1,
step=1,
description='n:',
disabled=False
)
display(m)
display(n)
def f():
if m.value == A.shape[0] and n.value == A.shape[1]:
print('Correcte!')
else:
print('Incorrecte, entrez de nouvelles valeurs')
interact_manual(f)
return
def manualEch(*args):
"""Method which allows the user to perform the Gauss elimination method on the given input matrix, eventually
extended by the right-hand side vector.
:param args:
:type args:
:return:
:rtype:
"""
if len(args) == 2: # matrice augmentée
A = np.array(args[0]).astype(float)
m = A.shape[0]
b = args[1]
if type(b[0]) is list:
b = np.array(b).astype(float)
A = np.concatenate((A, b), axis=1)
else:
b = [b[i] for i in range(m)]
A = [A[i] + [b[i]] for i in range(m)]
else:
A = np.array(args[0]).astype(float)
m = A.shape[0]
j = widgets.BoundedIntText(
value=1,
min=1,
max=m,
step=1,
description='Ligne j:',
disabled=False
)
i = widgets.BoundedIntText(
value=1,
min=1,
max=m,
step=1,
description='Ligne i:',
disabled=False
)
r = widgets.RadioButtons(
options=['Eij', 'Ei(alpha)', 'Eij(alpha)', 'Revert'],
description='Opération:',
disabled=False
)
alpha = widgets.Text(
value='1',
description='Coeff. alpha:',
disabled=False
)
print("Régler les paramètres et évaluer la cellule suivante")
print("Répéter cela jusqu'à obtenir une forme échelonnée réduite")
display(r)
display(i)
display(j)
display(alpha)
return i, j, r, alpha
def echelonnage(i, j, r, alpha, A, m, *args):
"""Method which performs the Gauss elimination method step described by `r.value` with parameters `ì`, `j` and
`alpha` on matrix `A`
:param i: first reference line
:type i: ipywidgets.Text
:param j: second reference line
:type j: ipywidgets.Text
:param r: RadioButton describing the elementary matricial operation to be performed
:type r: ipywidgets.radioButton
:param alpha: scalar coefficient
:type alpha: ipywidgets.Text
:param A: starting matrix
:type A: numpy.ndarray
:param m: starting augmented matrix
:type m: numpy.ndarray
:param args: either the list of matrices or both the list of matrices and rhs having bee built during the
application of the methos
:type args: list[numpy.ndarray] or tuple(list[numpy.ndarray], list[numpy.ndarray])
:return: processed matrix
:rtype: numpy.ndarray
"""
m = np.array(m).astype(float)
if alpha.value == 0 and r.value in {'Ei(alpha)', 'Eij(alpha)'}:
print('Le coefficient alpha doit être non-nul!')
if r.value == 'Eij':
m = Eij(m, i.value-1, j.value-1)
if r.value == 'Ei(alpha)':
m = Ealpha(m, i.value-1, eval(alpha.value))
if r.value == 'Eij(alpha)':
m = Eijalpha(m, i.value-1, j.value-1, eval(alpha.value))
if len(args) == 2:
A = np.asmatrix(A)
MatriceList = args[0]
RhSList = args[1]
if r.value != 'Revert':
MatriceList.append(m[:, :A.shape[1]])
RhSList.append(m[:, A.shape[1]:])
else:
if len(MatriceList) > 1 and len(RhSList) > 1:
MatriceList.pop()
RhSList.pop()
mat = MatriceList[-1]
rhs = RhSList[-1]
m = np.concatenate((mat,rhs), axis=1)
else:
print("Impossible de revenir sur l'opération!")
printEquMatrices(MatriceList, RhSList)
elif len(args) == 1:
MatriceList = args[0]
if r.value != 'Revert':
MatriceList.append(m)
else:
if len(MatriceList) > 1:
MatriceList.pop()
m = MatriceList[-1]
else:
print("Impossible de revenir sur l'opération!")
printEquMatrices(MatriceList)
else:
print("La liste des matrices ou des matrices et des vecteurs connus doit être donnée en entrée de la fonction!")
raise ValueError
return m
def manualOp(*args):
"""Method which allows the user to perform elementary operations on the given input matrix, eventually extended by
the right-hand side vector.
:param args:
:type args:
:return:
:rtype:
"""
if len(args) == 2: # matrice augmentée
A = np.array(args[0]).astype(float)
M = A.shape[0]
b = args[1]
if type(b[0]) is list:
b = np.array(b).astype(float)
A = np.concatenate((A, b), axis=1)
else:
b = [b[i] for i in range(M)]
A = [A[i] + [b[i]] for i in range(M)]
else:
A = np.array(args[0]).astype(float)
M = A.shape[0]
A = np.array(A) # just in case it's not
i = widgets.BoundedIntText(
value=1,
min=1,
max=M,
step=1,
description='Ligne i:',
disabled=False
)
j = widgets.BoundedIntText(
value=1,
min=1,
max=M,
step=1,
description='Ligne j:',
disabled=False
)
r = widgets.RadioButtons(
options=['Eij', 'Ei(alpha)', 'Eij(alpha)'],
description='Opération:',
disabled=False
)
alpha = widgets.Text(
value='1',
description='Coeff. alpha:',
disabled=False
)
print("Régler les paramètres et cliquer sur RUN INTERACT pour effectuer votre opération")
def f(r, i, j, alpha):
m = A
MatriceList = [A[:, :len(A[0])-1]]
RhSList = [A[:, len(A[0])-1:]]
if alpha == 0 and r != 'Eij':
print('Le coefficient alpha doit être non-nul!')
if r == 'Eij':
m = Eij(m, i-1, j-1)
if r == 'Ei(alpha)':
m = Ealpha(m, i-1, eval(alpha))
if r == 'Eij(alpha)':
m = Eijalpha(m, i-1, j-1, eval(alpha))
MatriceList.append(m[:, :len(A[0])-1])
RhSList.append(m[:, len(A[0])-1:])
printEquMatricesAug(MatriceList, RhSList)
return
interact_manual(f, r=r, i=i, j=j, alpha=alpha)
return
######################################## OBSOLETE ####################################################################
def printEquMatricesAug(listOfMatrices, listOfRhS): # list of matrices is M=[M1, M2, ..., Mn] where Mi=(Mi|b)
texEqu = '$' + texMatrix(listOfMatrices[0], listOfRhS[0])
for i in range(1, len(listOfMatrices)):
texEqu = texEqu + '\\quad \\sim \\quad' + texMatrix(listOfMatrices[i], listOfRhS[i])
texEqu = texEqu + '$'
display(Latex(texEqu))
def echelonMatCoeff(A): # take echelonMAt but without b.
b = [0 for _ in range(len(A))]
Mat = [A[i] + [b[i]] for i in range(len(A))]
Mat = np.array(Mat)
Mat = Mat.astype(float) # in case the array in int instead of float.
numPivot = 0
for i in range(len(Mat)):
j = i
while all(abs(Mat[j:, i]) < 1e-15) and j != len(
Mat[0, :]) - 1: # if column (or rest of) is zero, take next column
j += 1
if j == len(Mat[0, :]) - 1:
# ADD ZERO LINES BELOW!!!!!!
if len(Mat[0, :]) > j:
Mat[i + 1:len(Mat), :] = 0
print("La matrice est sous la forme échelonnée")
printEquMatrices(np.asmatrix(A), np.asmatrix(Mat[:, :len(A[0])]))
break
if abs(Mat[i, j]) < 1e-15:
Mat[i, j] = 0
zero = abs(Mat[i:, j]) < 1e-15
M = echZero(zero, Mat[i:, :])
Mat[i:, :] = M
Mat = Ealpha(Mat, i, 1 / Mat[i, j]) # normalement Mat[i,j]!=0
for k in range(i + 1, len(A)):
Mat = Eijalpha(Mat, k, i, -Mat[k, j])
# Mat[k,:]=[0 if abs(Mat[k,l])<1e-15 else Mat[k,l] for l in range(len(MatCoeff[0,:]))]
numPivot += 1
Mat[abs(Mat) < 1e-15] = 0
# printA(np.asmatrix(Mat[:, :len(A[0])]))
return np.asmatrix(Mat)
def echelonRedMat(A, b):
Mat = echelonMat('ER', A, b)
Mat = np.array(Mat)
MatAugm = np.concatenate((A, b), axis=1)
# MatAugm = [A[i]+[b[i]] for i in range(0,len(A))]
i = (len(Mat) - 1)
while i >= 1:
while all(abs(Mat[i, :len(Mat[0]) - 1]) < 1e-15) and i != 0: # if ligne (or rest of) is zero, take next ligne
i -= 1
# we have a lign with one non-nul element
j = i # we can start at pos ij at least the pivot is there
if abs(Mat[i, j]) < 1e-15: # if element Aij=0 take next one --> find pivot
j += 1
# Aij!=0 and Aij==1 if echelonMat worked
for k in range(i): # put zeros above pivot (which is 1 now)
Mat = Eijalpha(Mat, k, i, -Mat[k, j])
i -= 1
printA(Mat)
print("La matrice est sous la forme échelonnée réduite")
printEquMatrices(MatAugm, Mat)
return np.asmatrix(Mat)
def printEquMatricesOLD(listOfMatrices): # list of matrices is M=[M1, M2, ..., Mn]
texEqu = '$' + texMatrix(listOfMatrices[0])
for i in range(1, len(listOfMatrices)):
texEqu = texEqu + '\\quad \\sim \\quad' + texMatrix(listOfMatrices[i])
texEqu = texEqu + '$'
display(Latex(texEqu))
return
def texMatrixAug(A, b): # return tex expression of one matrix (A|b) where b can also be a matrix
m = len(A[0])
A = np.concatenate((A, b), axis=1)
texApre = '\\left(\\begin{array}{'
texA = ''
for i in np.asarray(A):
texALigne = ''
texALigne = texALigne + str(round(i[0], 3) if i[0] % 1 else int(i[0]))
if texA == '':
texApre = texApre + 'c'
for j in i[1:m]:
if texA == '':
texApre = texApre + 'c'
texALigne = texALigne + ' & ' + str(round(j, 3) if j % 1 else int(j))
if texA == '':
texApre = texApre + '| c'
for j in i[m:]:
if texA == '':
texApre = texApre + 'c'
texALigne = texALigne + ' & ' + str(round(j, 3) if j % 1 else int(j))
texALigne = texALigne + ' \\\\'
texA = texA + texALigne
texA = texApre + '} ' + texA[:-2] + ' \\end{array}\\right)'
return texA
def printAAug(A, b): # Print matrix (A|b)
texA = '$' + texMatrixAug(A, b) + '$'
display(Latex(texA))
return
def printEquMatricesOLD(*args): # M=[M1, M2, ..., Mn] n>1 VERIFIED OK
texEqu = '$' + texMatrix(args[0])
for i in range(1, len(args)):
texEqu = texEqu + '\\quad \\sim \\quad' + texMatrix(args[i])
texEqu = texEqu + '$'
display(Latex(texEqu))
return

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