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aleaDataSignal
Commit 6b974123 authored by vincentvigon's avatar vincentvigon
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3 premier chap de 'alea'

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    .gitignore
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    **/__pycache__
    **/.ipynb_checkpoints/
    **/.DS_Store
    **/build
    \ No newline at end of file
    .idea/inspectionProfiles/Project_Default.xml
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    <inspection_tool class="PyCompatibilityInspection" enabled="true" level="WARNING" enabled_by_default="true">
    <option name="ourVersions">
    <value>
    <list size="1">
    <list size="3">
    <item index="0" class="java.lang.String" itemvalue="3.5" />
    <item index="1" class="java.lang.String" itemvalue="3.6" />
    <item index="2" class="java.lang.String" itemvalue="3.7" />
    </list>
    </value>
    </option>
    ......
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    <option name="languageLevel" value="ES6" />
    </component>
    <component name="ProjectRootManager" version="2" project-jdk-name="Python 3.6" project-jdk-type="Python SDK" />
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    </project>
    \ No newline at end of file
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    alea/00-python_de_base.ipynb
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    alea/08-Chaine_de_Markov.ipynb
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    ......@@ -19,302 +19,6 @@
    "np.set_printoptions(precision=3,suppress=True)"
    ]
    },
    {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
    "## Préliminaires d'algèbre linéaire\n",
    "\n",
    "Attention, en numpy les vecteurs, les matrices lignes et les matrices colonnes sont des objets différents:\n",
    "\n",
    "* vecteur.shape = (?)\n",
    "* matrice_ligne.shape = (1,?)\n",
    "* matrice_colonne.shape = (?,1)\n",
    "* matrice_quelconque.shape = (?,?)\n",
    "\n",
    "Observez bien les sorties consoles: les vecteurs s'écrivent avec 1 crochet, les matrices avec 2 crochets.\n",
    "\n"
    ]
    },
    {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
    "### Multiplication matricielle\n",
    "\n",
    "`np.matmul()` s'applique uniquement entre matrices."
    ]
    },
    {
    "cell_type": "code",
    "execution_count": 16,
    "metadata": {},
    "outputs": [
    {
    "name": "stdout",
    "output_type": "stream",
    "text": [
    "\n",
    "mat_col\n",
    " [[1.]\n",
    " [1.]\n",
    " [1.]]\n",
    "\n",
    "mat_lin\n",
    " [[1. 1. 1.]]\n",
    "\n",
    "mat_square\n",
    " [[1. 1. 1.]\n",
    " [1. 1. 1.]\n",
    " [1. 1. 1.]]\n",
    "\n",
    "mat_square × mat_col\n",
    " [[3.]\n",
    " [3.]\n",
    " [3.]]\n",
    "\n",
    "mat_lin × mat_square\n",
    " [[3. 3. 3.]]\n",
    "\n",
    "mat_lin × mat_square × mat_col\n",
    " [[9.]]\n"
    ]
    }
    ],
    "source": [
    "size=3\n",
    "mat_col=np.ones(shape=[size,1])\n",
    "mat_lin=np.ones(shape=[1,size])\n",
    "mat_square=np.ones(shape=[size,size])\n",
    "\n",
    "print(\"\\nmat_col\\n\",mat_col)\n",
    "print(\"\\nmat_lin\\n\",mat_lin)\n",
    "print(\"\\nmat_square\\n\",mat_square)\n",
    "\n",
    "print(\"\\nmat_square × mat_col\\n\",np.matmul(mat_square,mat_col) )\n",
    "print(\"\\nmat_lin × mat_square\\n\",np.matmul(mat_lin,mat_square))\n",
    "print(\"\\nmat_lin × mat_square × mat_col\\n\", np.matmul(np.matmul(mat_lin,mat_square),mat_col))\n"
    ]
    },
    {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
    "sinon on peut utiliser `np.dot()` qui permet les multiplications matrice × vecteur, matrice × matrice, vecteur × vecteur (=produit scalaire)"
    ]
    },
    {
    "cell_type": "code",
    "execution_count": 17,
    "metadata": {},
    "outputs": [
    {
    "name": "stdout",
    "output_type": "stream",
    "text": [
    "\n",
    "vec0 × vec1\n",
    " 6.0\n",
    "\n",
    "vec0 × mat_square\n",
    " [3. 3. 3.]\n",
    "\n",
    "mat_square × vec0\n",
    " [3. 3. 3.]\n",
    "\n",
    "mat_square × mat_square\n",
    " [[3. 3. 3.]\n",
    " [3. 3. 3.]\n",
    " [3. 3. 3.]]\n"
    ]
    }
    ],
    "source": [
    "size=3\n",
    "vec0=np.ones(shape=[size])\n",
    "vec1=2*np.ones(shape=[size])\n",
    "mat_square=np.ones(shape=[size,size])\n",
    "\n",
    "print(\"\\nvec0 × vec1\\n\",np.dot(vec0,vec1))\n",
    "print(\"\\nvec0 × mat_square\\n\",np.dot(vec0,mat_square))\n",
    "print(\"\\nmat_square × vec0\\n\",np.dot(mat_square,vec0))\n",
    "print(\"\\nmat_square × mat_square\\n\",np.dot(mat_square,mat_square))"
    ]
    },
    {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
    "et si vous avez python 3.5+, vous pouver utilisez l'opérateur @ qui rend les codes plus lisibles"
    ]
    },
    {
    "cell_type": "code",
    "execution_count": 18,
    "metadata": {},
    "outputs": [
    {
    "name": "stdout",
    "output_type": "stream",
    "text": [
    "\n",
    "vec0 × vec1\n",
    " 6.0\n",
    "\n",
    "vec0 × mat_square\n",
    " [3. 3. 3.]\n",
    "\n",
    "mat_square × vec0\n",
    " [3. 3. 3.]\n",
    "\n",
    "mat_square × mat_square\n",
    " [[3. 3. 3.]\n",
    " [3. 3. 3.]\n",
    " [3. 3. 3.]]\n"
    ]
    }
    ],
    "source": [
    "print(\"\\nvec0 × vec1\\n\",vec0 @ vec1)\n",
    "print(\"\\nvec0 × mat_square\\n\",vec0 @ mat_square)\n",
    "print(\"\\nmat_square × vec0\\n\",mat_square @ vec0)\n",
    "print(\"\\nmat_square × mat_square\\n\",mat_square @ mat_square)"
    ]
    },
    {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
    "***Exo:*** Multipliez matriciellement des matrices de taille non-compatible.\n",
    "Extrayez la partie intéressante du message d'erreur."
    ]
    },
    {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
    "### inverse et transposée \n",
    "\n",
    "Notez que le pseudo-inverse permet d'inverser les matrices non-inversibles (testez). "
    ]
    },
    {
    "cell_type": "code",
    "execution_count": 19,
    "metadata": {},
    "outputs": [
    {
    "name": "stdout",
    "output_type": "stream",
    "text": [
    "\n",
    "mat\n",
    " [[1. 0. 2.]\n",
    " [0. 1. 0.]\n",
    " [0. 0. 1.]]\n",
    "\n",
    "mat^T\n",
    " [[1. 0. 0.]\n",
    " [0. 1. 0.]\n",
    " [2. 0. 1.]]\n",
    "\n",
    "mat^(-1)\n",
    " [[ 1. 0. -2.]\n",
    " [ 0. 1. 0.]\n",
    " [ 0. 0. 1.]]\n",
    "\n",
    "mat^(-1)-pseudo-inverse\n",
    " [[ 1. 0. -2.]\n",
    " [ 0. 1. 0.]\n",
    " [ 0. 0. 1.]]\n"
    ]
    }
    ],
    "source": [
    "size=3\n",
    "mat=np.zeros(shape=[size,size])\n",
    "for i in range(size):\n",
    " mat[i,i]=1\n",
    "mat[0,size-1]=2\n",
    "\n",
    "\n",
    "print(\"\\nmat\\n\",mat )\n",
    "print(\"\\nmat^T\\n\",mat.T)\n",
    "print(\"\\nmat^(-1)\\n\",np.linalg.inv(mat))\n",
    "print(\"\\nmat^(-1)-pseudo-inverse\\n\",np.linalg.pinv(mat))"
    ]
    },
    {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
    "### vecteur propre et valeur propre\n",
    "\n",
    "Souvenez-vous qu'en anglais valeur/vecteur 'propre' c'est 'eigen' value/vector"
    ]
    },
    {
    "cell_type": "code",
    "execution_count": 20,
    "metadata": {},
    "outputs": [
    {
    "name": "stdout",
    "output_type": "stream",
    "text": [
    "\n",
    "mat\n",
    " [[0.085 0.287 0.206 0.422]\n",
    " [0.191 0.262 0.253 0.295]\n",
    " [0.244 0.07 0.06 0.626]\n",
    " [0.383 0.001 0.161 0.454]]\n",
    "\n",
    "eigVal\n",
    " [ 1. 0.122 -0.195 -0.066]\n",
    "\n",
    "eigVec\n",
    " [[-0.5 -0.416 -0.418 0.39 ]\n",
    " [-0.5 -0.763 0.307 0.432]\n",
    " [-0.5 0.402 -0.739 -0.813]\n",
    " [-0.5 0.287 0.43 -0.036]]\n"
    ]
    }
    ],
    "source": [
    "size=4\n",
    "\"\"\"une matrice aléatoire auquel on fait subir une opération de normalisation (laquelle?)\"\"\"\n",
    "mat=np.random.uniform(low=0,high=10,size=[size,size])\n",
    "rowSum=np.sum(mat,axis=1)\n",
    "\"\"\" mat[i,j]=mat[i,j]/rowSum(i) \"\"\"\n",
    "for i in range(size): mat[i,:]/=rowSum[i]\n",
    "\n",
    "eigVal,eigVec=np.linalg.eig(mat)\n",
    "print(\"\\nmat\\n\", mat )\n",
    "print(\"\\neigVal\\n\",np.real(eigVal))\n",
    "print(\"\\neigVec\\n\", np.real(eigVec))"
    ]
    },
    {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
    "***A vous:*** \n",
    "\n",
    "* Pourquoi 1 est-il valeur propre ? Quel est le vecteur propre associé? `np.linalg.eig` donne-t-il les vecteurs propres à droite ou à gauche? Sont-ils disposés en ligne ou bien en colonne?\n",
    "\n",
    "* Toutes les matrices sont-elles diagonalisables? A quoi servent les np.real()? \n",
    "\n",
    "* laquelle de ces deux formules est la bonne ?\n",
    "\n",
    " Diag = P^-1 @ mat @ P \n",
    "\n",
    "ou\n",
    "\n",
    " Diag = P @ mat @ P^-1\n",
    " \n",
    "Vérifiez avec python. Aide: Pour transformez un vecteur en matrice diagonale, utilisez `np.diag(vecteur)`"
    ]
    },
    {
    "cell_type": "markdown",
    "metadata": {},
    ......
    alea/10-RadomVec_GaussianVec.ipynb
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    ......@@ -273,7 +273,7 @@
    "\n",
    "Réponse: on peut faire des stats maintenant! \n",
    "* estimer la variance du bruit\n",
    "* estimre la variances des estimateurs $\\hat w_i$\n",
    "* estimer la variances des estimateurs $\\hat w_i$\n",
    "* faire un test pour savoir si l'un des $w_i$ est nul. Ce qui revient à dire que le i-ième input n'a aucune influence sur l'output. Ce genre de considération est importante, car on cherche à expliquer l'output de la manière la plus simple possible. \n",
    "\n",
    "Au travail:"
    ......@@ -460,9 +460,9 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
    "version": "3.5.0"
    "version": "3.6.5"
    }
    },
    "nbformat": 4,
    "nbformat_minor": 1
    "nbformat_minor": 2
    }
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    {
    "cells": [
    {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
    "# Permutation aléatoire"
    ]
    },
    {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": []
    },
    {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": []
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    {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": []
    },
    {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": []
    },
    {
    "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": "3.6.5"
    }
    },
    "nbformat": 4,
    "nbformat_minor": 2
    }
    alea/boook.tplx 0 → 100644
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    % Default to the notebook output style
    ((* if not cell_style is defined *))
    ((* set cell_style = 'style_ipython.tplx' *))
    ((* endif *))
    % Inherit from the specified cell style.
    ((* extends cell_style *))
    %===============================================================================
    % Latex Book
    %===============================================================================
    ((* block predoc *))
    ((( super() )))
    ((* block tableofcontents *))\tableofcontents((* endblock tableofcontents *))
    ((* endblock predoc *))
    ((* block docclass *))
    \documentclass[9pt, twocolumn, landscape,A4,reprint, floatfix, groupaddress, prb]{book}
    \usepackage{placeins}
    \AtBeginDocument{
    \heavyrulewidth=.08em
    \lightrulewidth=.05em
    \cmidrulewidth=.03em
    \belowrulesep=.65ex
    \belowbottomsep=0pt
    \aboverulesep=.4ex
    \abovetopsep=0pt
    \cmidrulesep=\doublerulesep
    \cmidrulekern=.5em
    \defaultaddspace=.5em
    \addtolength{\voffset}{-0.5in}
    \addtolength{\hoffset}{-0.5in}
    \addtolength{\textheight}{1in}
    \addtolength{\textwidth}{1in}
    }
    %\addtolength{\voffset}{-0.5in}
    %\addtolength{\hoffset}{-0.5in}
    \usepackage[francais]{babel} % Pour la langue française
    \setlength{\itemsep}{0pt}
    \setlength{\columnsep}{0.5in}
    % Force floating figures to be [H]
    \usepackage{float}
    \floatplacement{figure}{H}
    \usepackage{amsmath}
    \usepackage{amssymb}
    \usepackage{mathrsfs}
    \usepackage{makeidx}
    \usepackage{listings}
    \usepackage[svgnames]{xcolor} % Required for colour specification
    \definecolor{dkgreen}{rgb}{0,0.6,0}
    \definecolor{gray}{rgb}{0.5,0.5,0.5}
    \definecolor{mauve}{rgb}{0.58,0,0.82}
    \definecolor{verylightgray}{rgb}{0.9,0.9,0.9}
    \lstset{frame=tb,
    language=Python,
    aboveskip=3mm,
    belowskip=3mm,
    showstringspaces=false,
    columns=flexible,
    basicstyle={\small\ttfamily},
    numbers=none,
    numberstyle=\tiny\color{gray},
    keywordstyle=\color{blue},
    commentstyle=\color{dkgreen},
    stringstyle=\color{mauve},
    breaklines=true,
    breakatwhitespace=false,
    tabsize=3,
    otherkeywords={self},
    backgroundcolor=\color{verylightgray},
    }
    %\usepackage{showframe}
    \definecolor{pythonblue}{rgb}{0.21,0.45,0.65}
    \definecolor{pythonyellow}{rgb}{1.,0.77,0.18}
    \parindent=0pt
    \setlength{\parskip}{1.5ex plus 1.0ex minus 0.5ex}
    %\renewcommand{\labelitemi}{$\bullet$}
    ((* endblock docclass *))
    ((* block markdowncell scoped *))
    ((( cell.source | citation2latex | strip_files_prefix | convert_pandoc('markdown', 'json',extra_args=[]) | resolve_references | convert_pandoc('json','latex', extra_args=["--top-level-division=chapter"]) )))
    ((* endblock markdowncell *))
    ((* block maketitle *))
    \begin{titlepage}
    %\vspace*{\baselineskip}
    \centering
    {\Large Vincent Vigon}
    %\vspace*{0.167\textheight}
    \raggedleft
    \textbf{\fontsize{30}{36}\selectfont Python}\\[\baselineskip]
    % \textbf{\textcolor{pythonblue}{\fontsize{50}{60}\selectfont Python}}\\[\baselineskip]
    \textcolor{pythonyellow}{\fontsize{30}{36}\selectfont \textit{pour les proba-stats}}
    %\vspace*{0.1\textheight}
    \centering
    \includegraphics{img/champi.jpg}
    \vfill
    {\large Université de Strasbourg}
    \end{titlepage}
    ((* endblock maketitle *))
    ((*- block any_cell -*))
    ((*- if not 'hide' in cell['metadata'].get('tags', {}) -*))
    ((( super() )))
    ((*- endif -*))
    ((*- endblock any_cell -*))
    ((* block input scoped *))
    \begin{lstlisting}[breaklines]
    (((cell.source)))
    \end{lstlisting}
    ((* endblock input *))
    alea/build/index.html
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    ......@@ -11779,11 +11779,11 @@ div#notebook {
    <h3 id="Master-2-DUAS-Unistra,--2017-2018">Master 2 DUAS Unistra, 2017-2018<a class="anchor-link" href="#Master-2-DUAS-Unistra,--2017-2018">&#182;</a></h3><hr>
    <h1 id="Programmer-en-Python">Programmer en Python<a class="anchor-link" href="#Programmer-en-Python">&#182;</a></h1><hr>
    <h2 id="Contenu">Contenu<a class="anchor-link" href="#Contenu">&#182;</a></h2><ul>
    <li><strong>Le langage (1)</strong> - <a href="02-histogramme_densite.html">html</a> - <a href="02-histogramme_densite.slides.html">diaporama</a></li>
    <li><strong>Les généralités</strong> - <a href="04-plusDeLois.html">html</a> - <a href="04-plusDeLois.slides.html">diaporama</a></li>
    <li><strong>histogramme</strong> - <a href="02-histogramme_densite.html">html</a> - <a href="02-histogramme_densite.slides.html">diaporama</a></li>
    <li><strong>plus de loi</strong> - <a href="04-plusDeLois.html">html</a> - <a href="04-plusDeLois.slides.html">diaporama</a></li>
    </ul>
    <p><strong>Exécuter en ligne</strong>
    <a href="https://mybinder.org/v2/gh/boileaum/cours-python/master"><img style="display: inline" src="https://mybinder.org/badge.svg"></a></p>
    <p><strong>Exécuter en ligne</strong></p>
    <p><a href="https://mybinder.org/v2/gh/vincentvigon/aleaDataSignal.git/master"><img style="display: inline" src="https://mybinder.org/badge.svg"></a></p>
    <p><strong>Télécharger le</strong> <a href="cours-python.pdf"><strong>pdf</strong></a></p>
    <p><strong>Sources sur </strong><a href="https://gitlab.math.unistra.fr/mm2act/cours-python"><strong>GitLab</strong></a></p>
    <hr>
    ......
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    alea/make_pdf.py 0 → 100644
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    """
    Convert notebooks listed in `chapters` into latex and then a PDF.
    Note:
    - The notebooks are first copied into the build_pdf directory (with a chapter
    number prepended).
    """
    import re
    import subprocess
    import os
    chapters = ['02-histogramme_densite',
    '04-plusDeLois']
    # To test a subset, adjust the list of chapters and
    # remove the build_pdf directory before running this script.
    build_dir = 'build_pdf/'
    if not os.path.exists(build_dir):
    os.makedirs(build_dir)
    # os.system('cp -r exact_solvers '+build_dir)
    # os.system('cp -r utils '+build_dir)
    # os.system('cp *.html '+build_dir)
    # os.system('cp -r figures '+build_dir)
    # os.system('cp riemann.tplx '+build_dir)
    # os.system('cp *.cls '+build_dir)
    # os.system('cp *.css '+build_dir)
    # os.system('cp riemann.bib '+build_dir)