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diff --git a/PVCM/cama/en/_Table of contents.ipynb b/PVCM/cama/en/_Table of contents.ipynb new file mode 100644 index 0000000..e8f2e13 --- /dev/null +++ b/PVCM/cama/en/_Table of contents.ipynb @@ -0,0 +1,236 @@ + +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + +"## 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", + + "" + ]}], + "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": "3.6.7" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} + |