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"## Table of contents.ipynb\n",
"* [ma1 Jupyter](ma1%20Jupyter.ipynb)\n",
" - Using Jupyter\n",
" - Cell manipulation\n",
" - Configuration\n",
" - IPython\n",
" - Completion and help\n",
" - Shell under IPython\n",
" - Magic commands\n",
"* [ma1 np01 Numpy Introduction](ma1%20np01%20Numpy%20Introduction.ipynb)\n",
" - NumPy - N-dimensional Array manipulations library\n",
" - Creating an array\n",
" - By redefining its shape\n",
" - Mixing values\n",
" - Basic Operations\n",
" - Browse an array\n",
" - Think vector\n",
"* [ma1 np02 Filtres](ma1%20np02%20Filtres.ipynb)\n",
" - Filter by indices\n",
" - Logical filters\n",
" - A filter = a logical condition\n",
" - `where` to handle non-filter values\n",
" - Update a table with a filter\n",
"* [ma1 np03 Manipulations](ma1%20np03%20Manipulations.ipynb)\n",
" - The axes\n",
" - Arranging a table\n",
" - Reorder axes\n",
" - Changing the order of array elements\n",
" - Aggregation\n",
" - Concatenation\n",
" - Stacking\n",
" - Splitting\n",
" - From Python to Numpy\n",
" - Pandas too\n",
"* [ma1 np05 Notation Einstein](ma1%20np05%20Notation%20Einstein.ipynb)\n",
" - Introduction to Einstein Notation\n",
" - Practical Application\n",
"* [ma1 np06 Linalg pour le calcul matriciel](ma1%20np06%20Linalg%20pour%20le%20calcul%20matriciel.ipynb)\n",
" - Linalg (linear algebra)\n",
" - Basic operations\n",
" - Extraction\n",
" - Matrix operations\n",
"* [ma1 np90 petits exercices](ma1%20np90%20petits%20exercices.ipynb)\n",
" - Numpy - Exercises\n",
" - Square Matrix\n",
" - Vector Norm\n",
" - Sub-Matrix\n",
" - Random Vector\n",
" - Trace\n",
" - Matrix of Multiples of 3\n",
" - Count of 9s\n",
" - Column with the Smallest Average\n",
" - ChessSum\n",
" - 2 Minimums\n",
" - Rows in Order\n",
" - Unique Values\n",
" - Magic Tensor\n",
" - Tensor Slices\n",
"* [ma20 Rappels sur les matrices](ma20%20Rappels%20sur%20les%20matrices.ipynb)\n",
" - Vector\n",
" - Matrices and linear maps\n",
" - Determinant of a matrix\n",
" - Standards\n",
" - Norm of a vector\n",
" - Norm of a matrix\n",
" - Properties\n",
"* [ma21 Transformations isometriques](ma21%20Transformations%20isometriques.ipynb)\n",
" - Isometric transformations\n",
" - Rotation matrix centered at (0,0)\n",
" - Properties\n",
" - Axial Symmetry\n",
" - Translation\n",
" - Exercise 1.1\n",
"* [ma22 Changement de repere](ma22%20Changement%20de%20repere.ipynb)\n",
" - Matrice de passage\n",
" - Vecteurs dans le nouveau repère\n",
" - Matrice de passage vue comme une transformation\n",
" - Points dans le nouveau repère\n",
" - Notre souris dans le nouveau repère\n",
" - Exercice -- Et l'inverse ?\n",
" - Une application linéaire transposée dans le nouveau repère\n",
"* [ma24 Vectors propres](ma24%20Vectors%20propres.ipynb)\n",
" - $A^n \\textbf{x}$\n",
" - Vecteurs propres et valeurs propres\n",
" - Le cas des matrices de rotation\n",
" - Symétrie axiale horizontale\n",
" - Diagonalisation d'une matrice\n",
"* [ma25 Drones -- Exercice](ma25%20Drones%20--%20Exercice.ipynb)\n",
" - Drone show\n",
" - Figure 1\n",
" - Figure 2\n",
" - Figure 3\n",
"* [ma26 Vecteurs propres -- Exercices](ma26%20Vecteurs%20propres%20--%20Exercices.ipynb)\n",
" - Cas d'utilisation des valeurs et vecteurs propres\n",
" - Fibonnacci\n",
" - Google page rank\n",
" - Approche itérative\n",
" - Un autre approche\n",
"* [ma30 ACP](ma30%20ACP.ipynb)\n",
" - Principal component analysis (PCA)\n",
" - A cloud of dots\n",
" - Covariance matrix\n",
"* [ma31 Système d'équations](ma31%20Système%20d'équations.ipynb)\n",
" - Systèmes matriciels\n",
" - Résolution d'un système matriciel\n",
" - Méthode du pivot de Gauss\n",
" - Complexité du pivot de Gauss\n",
" - Décomposition LU (Lower, Upper)\n",
" - Gauss Jordan\n",
" - Comparaison de la vitesse de méthodes\n",
" - Erreurs d'arrondi\n",
" - Solution au problème d'arrondi dans le cas du pivot de Gauss\n",
"* [ma32 Conditionnement d'une matrice](ma32%20Conditionnement%20d'une%20matrice.ipynb)\n",
" - Conditionnement d'une matrice\n",
" - Pourquoi ?\n",
" - Perturbons la matrice\n",
" - Propriétés\n",
" - Préconditionnement\n",
"* [ma34 ACP -- Exercice](ma34%20ACP%20--%20Exercice.ipynb)\n",
" - Exercise: 3D point cloud\n",
" - Experience Data\n",
" - Calculations to find the characteristics of our cloud\n",
"* [ma35 Système matriciel -- Exercices](ma35%20Système%20matriciel%20--%20Exercices.ipynb)\n",
" - Vector Programming\n",
" - Partial Gaussian pivot method\n",
" - Choleski factorization\n",
" - Improve Jacobi\n",
"* [ma40 Méthodes itératives](ma40%20Méthodes%20itératives.ipynb)\n",
" - Numerical simulation\n",
" - Iterative Methods\n",
" - Jacobi method\n",
" - Why does the 2nd case work?\n",
" - Calculation time\n",
"* [ma41 Convergence de Jacobi avec inertie](ma41%20Convergence%20de%20Jacobi%20avec%20inertie.ipynb)\n",
" - Add inertia to Jacobi\n",
" - Let's program inertia for Jacobi\n",
" - Let's study convergence\n",
" - Let's test other matrices with this algorithm\n",
" - Exercise 20.1\n",
" - Normalize\n",
"* [ma42 Surrelaxation pour Gauss-Seidel -- Exercice](ma42%20Surrelaxation%20pour%20Gauss-Seidel%20--%20Exercice.ipynb)\n",
" - Exercise ma21\n",
" - Gauss-Seidel\n",
" - Gauss-Seidel overrelaxation\n",
" - Let's program overrelaxed Gauss-Seidel\n",
" - The good case\n",
" - Study by $w$\n",
"* [ma50 Optimisation - Méthode du gradient](ma50%20Optimisation%20-%20Méthode%20du%20gradient.ipynb)\n",
" - Optimization problem\n",
" - Optimization problem with constraint\n",
" - The gradient method\n",
" - Study of the convergence of the gradient\n",
"* [ma51 x.T A x sur un maillage en Numpy ](ma51%20x.T%20A%20x%20sur%20un%20maillage%20en%20Numpy%20.ipynb)\n",
" - Let's calculate ${\\bf x}^T \\, A \\, {\\bf x} $ with Numpy\n",
" - Test case with A = 2 Id\n",
" - A real case\n",
" - Let's optimize\n",
" - Using a J function and a loop\n",
" - Using `np.tensordot`\n",
" - Conclusion\n",
"* [ma52 Méthode du gradiant pour système matriciel](ma52%20Méthode%20du%20gradiant%20pour%20système%20matriciel.ipynb)\n",
" - Gradient et dérivée\n",
"- A x = b seen as an optimization problem\n",
" - Calculation of derivative\n",
" - Definition\n",
" - Calculate the derivative of J along a direction\n",
" - A symmetrical\n",
" - Gradient and derivative\n",
"* [ma53 Notations du produit scalaire](ma53%20Notations%20du%20produit%20scalaire.ipynb)\n",
" - Writings of the scalar product\n",
" - ${\\bf v} \\,.\\, {\\bf w}$\n",
" - ${\\bf v}^T \\, {\\bf w}$\n",
" - $<{\\bf v}, {\\bf w}>$\n",
"* [ma54 Gradient pour résoudre Ax = b -- Exercice](ma54%20Gradient%20pour%20résoudre%20Ax%20=%20b%20--%20Exercice.ipynb)\n",
" - The gradient method to solve A x = b\n",
" - Introduce inertia\n",
" - Optimal value of µ\n",
"* [ma60 Méthode du gradient conjugué](ma60%20Méthode%20du%20gradient%20conjugué.ipynb)\n",
" - Conjugate gradient method\n",
" - Generate a base of $ℝ^n$\n",
" - The $A {\\bf x} = {\\bf b}$ case\n",
" - Calculation of $μ^k$\n",
" - Property\n",
" - 2nd attempt\n",
" - Let's work in the base of $\\nabla J({\\bf x}^i)$\n",
" - New calculation of μ\n",
"* [ma61 Système matriciel non linéaire](ma61%20Système%20matriciel%20non%20linéaire.ipynb)\n",
" - Système matriciel non linéaire\n",
" - La méthode du point fixe\n",
" - La méthode du point fixe pour résoudre $A({\\bf x}) \\, {\\bf x} = {\\bf b}$\n",
" - Test\n",
" - Appliquons l'inertie\n",
" - La méthode de Newton-Raphson\n",
"* [ma62 Gradient conjugué -- Exercice](ma62%20Gradient%20conjugué%20--%20Exercice.ipynb)\n",
" - Programmer le gradient conjugué\n",
" - Comparons avec le gradient simple\n",
" - Perfs\n",
" - Nombre d'iteration dans les 2 cas\n",
" - Un cas réel\n",
" - Comparaison gradient simple et conjugué\n",
" - Comparaison avec `lin.solve` de Scipy\n",
" - Le gradient conjugué de Scipy (avec Lapack)\n",
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