| Les deux révisions précédentes Révision précédente Prochaine révision | Révision précédente |
| teaching:methcalchim:start [2020/06/02 03:08] – [Classical numerical methods] villersd | teaching:methcalchim:start [2023/04/12 10:08] (Version actuelle) – [Classical numerical methods] villersd |
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| * Diagonalisation and triangularisation | * Diagonalisation and triangularisation |
| * LU decomposition : factorization in triangular matrices | * LU decomposition : factorization in triangular matrices |
| * [[numerical_integration|Numerical intégration]] (integrals) | |
| * Simpson method and gaussian quadratures | |
| * [[root-finding_algorithm|Root findings : equations f(x) = 0]] | * [[root-finding_algorithm|Root findings : equations f(x) = 0]] |
| * Polynomial equations | * Polynomial equations |
| * Secant method, Regula falsi | * Secant method, Regula falsi |
| * Newton-Raphson method | * Newton-Raphson method |
| | * [[numerical_integration|Numerical intégration]] (integrals) |
| | * Simpson method and gaussian quadratures |
| | |
| | <note tip> |
| | Learning outcomes : |
| | * Systems of linear equations |
| | * failing of the theoretical way to solve a linear system using determinant and cofactors (np complexity) |
| | * triangularisation and diagonalisation principles : algorithm and complexity |
| | * "divide by zero" errors and pivot solutions |
| | * extension towards the matrix inversion |
| | * lower-upper LU decomposition and complexity (N³ for the decomposition step and N² for substitution step). How to solve systems with varying independant vectors |
| | * special matrix require special algorithms : tridiagonal matrix algorithm (Thomas algorithm) |
| | * Root findings |
| | * Bisection method (dichotomy) : simple and robust algorithm, invariant loop, slow convergence |
| | * iterative transformation x = f(x), convergence and divergence situations |
| | * secant and regula falsi methods, Convergence Criterion of the Fixed Point Method |
| | * Newton-Raphson method (use of derivatives), quadratic convergence, failure, tolerance and stop condition |
| | * Van Wijngaardeb-Dekker-Brent method ("black box" in numerical packages) |
| | * Roots of polynomials and Bairstow's method |
| | * Numerical intégration |
| | * Equally Spaced methods (trapezoidal, Simpson), accuracy, error dependance,... |
| | * Gaussian Quadratures and orthogonal polynomials (special integrals, scale transformations, error estimates,...) |
| | </note> |
| |
| ==== Classical numerical methods ==== | ==== Classical numerical methods ==== |
| + discussion of some approximations like [[wp>Bhaskara_I's_sine_approximation_formula|Bhaskara I's sine approximation formula]] | + discussion of some approximations like [[wp>Bhaskara_I's_sine_approximation_formula|Bhaskara I's sine approximation formula]] |
| * [[https://twitter.com/fermatslibrary/status/1267450081151782913]] | * [[https://twitter.com/fermatslibrary/status/1267450081151782913]] |
| | * [[https://medium.com/@mathcube7/chebyshev-interpolation-with-python-2f2e89bb7c30|Chebyshev Interpolation With Python]] Mathcube, Medium, 03/02/2023 |
| |
| === Molecules modelisation and visualization === | === Molecules modelisation and visualization === |
| * Agent base modelling and complex systems | * Agent base modelling and complex systems |
| * cellular automaton | * cellular automaton |
| * Simpy,... | * Simpy, active matter simulations... |
| * Digital image processing, image recognition | * Digital image processing, image recognition |
| * particle tracking,... | * particle tracking,... |
| | * Voronoi diagrams, Delaunay triangulation,... ([[https://towardsdatascience.com/the-fascinating-world-of-voronoi-diagrams-da8fc700fa1b|ref1]]) |
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| ===== References ===== | ===== References ===== |
| | * Gradient descent optimization |
| | * [[https://machinelearningmastery.com/gradient-descent-optimization-from-scratch/|How to Implement Gradient Descent Optimization from Scratch]] By Jason Brownlee on April 16, 2021 |
| | * [[https://towardsdatascience.com/implementing-gradient-descent-in-python-from-scratch-760a8556c31f|Implementing Gradient Descent in Python from Scratch]] Vatsal Sheth, Medium, 18/02/2022 |
| * Bioinformatics | * Bioinformatics |
| * [[http://biopython.org/|Biopython]] | * [[http://biopython.org/|Biopython]] |
| * K-Means | * K-Means |
| * [[http://benalexkeen.com/k-means-clustering-in-python/|K-means Clustering in Python]] | * [[http://benalexkeen.com/k-means-clustering-in-python/|K-means Clustering in Python]] |
| | * [[https://medium.com/thrive-in-ai/k-means-clustering-in-python-9f00b3d7abc3|K Means Clustering in Python]] Rohit Raj, Medium, 02/03/2022 |
| | * [[https://medium.com/thrive-in-ai/classification-algorithms-in-python-5f58a7a27b88|Classification Algorithms in Python]] Rohit Raj, Medium, 15/03/2022 |
| * Applications (suggestions, examples,...) | * Applications (suggestions, examples,...) |
| * [[https://scicomp.stackexchange.com/questions/28195/2d-ising-model-in-python|2D Ising Model in Python]] | * [[https://scicomp.stackexchange.com/questions/28195/2d-ising-model-in-python|2D Ising Model in Python]] |
| * chemistry | * chemistry |
| * misc docs : | * misc docs : |
| * [[https://pdfs.semanticscholar.org/3161/89e419212794e74bf83442f65de96b5320ba.pdf|Extraction of chemical | * [[https://pdfs.semanticscholar.org/3161/89e419212794e74bf83442f65de96b5320ba.pdf|Extraction of chemical structures and reactions from the literature]] |
| structures and reactions from the literature]] | * [[https://medium.com/nerd-for-tech/animating-schrodinger-wave-function-%CF%88-of-a-particle-using-python-with-full-code-5ad9e4852906|Animating Schrodinger Wave Function(ψ) of a Particle Using Python (with full code) - Solving Particle in a Box Using Crank-Nicolson Method]], Kowshik chilamkurthy, Medium, 02/03/2021 |
| | * Blog articles |
| | * [[https://py.plainenglish.io/linear-regression-in-plain-python-3b20bb56b31d|Simple Linear Regression Explained With Python - Explained in details which are easy to understand]] Arjan de Haan, Medium, Jan 23 (+ [[https://github.com/Vepnar/Script-Collection/blob/master/linear-regression/Linear%20regression.ipynb|jupyter notebook]]) |
| | * simpy : [[https://towardsdatascience.com/simulate-real-life-events-in-python-using-simpy-e6d9152a102f|Simulate Real-life Events in Python Using SimPy]] by Khuyen Tran, May, 2021, Medium, Towards Data Science |
| | * Active matter simulations ([[https://arxiv.org/pdf/cond-mat/0611743.pdf|Vicsek]], 1995) : |
| | * [[https://medium.com/swlh/create-your-own-active-matter-simulation-with-python-76fce4a53b6f|Create Your Own Active Matter Simulation (With Python)]] Philip Mocz, The Startup, Medium 2021 + [[https://github.com/pmocz/activematter-python]] |
| | * Fourier transforms : [[https://towardsdatascience.com/fourier-transforms-an-intuitive-visualisation-ba186c7380ee|Fourier Transforms: An Intuitive Visualisation - An intuitive visualization of discrete Fourier transforms applied to simple time-series data]] Diego Unzueta, Towards Data Science, Medium, 17/09/2021 |
| | * Monte-Carlo simulations : [[Monte Carlo Simulation — a practical guide - A versatile method for parameters estimation. Exemplary implementation in Python programming language]] Robert Kwiatkowski, Medium, 31/01/2022 |
| | * régression logistique : [[https://mlu-explain.github.io/logistic-regression/]] |
| | * [[https://towardsdatascience.com/cubic-splines-the-ultimate-regression-model-bd51a9cf396d|Cubic Splines: The Ultimate Regression Model - Why cubic splines are the best regression model out there]] Brendan Artley, Medium, 27/07/2022 |
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| * [[https://medium.freecodecamp.org/an-overview-of-the-gradient-descent-algorithm-8645c9e4de1e|An overview of the Gradient Descent algorithm]] | * [[https://medium.freecodecamp.org/an-overview-of-the-gradient-descent-algorithm-8645c9e4de1e|An overview of the Gradient Descent algorithm]] |
| * [[https://towardsdatascience.com/building-a-logistic-regression-in-python-step-by-step-becd4d56c9c8|Building A Logistic Regression in Python, Step by Step]] | * [[https://towardsdatascience.com/building-a-logistic-regression-in-python-step-by-step-becd4d56c9c8|Building A Logistic Regression in Python, Step by Step]] |
| | * [[https://medium.com/swlh/building-linear-regression-in-python-75a429b0d3ba|Building Linear Regression in Python]] |
| | * [[https://towardsdatascience.com/17-types-of-similarity-and-dissimilarity-measures-used-in-data-science-3eb914d2681|17 types of similarity and dissimilarity measures used in data science]] : explains various methods for computing distances and showing their instances in our daily lives. Additionally, it will introduce you to the pydist2 package. Mahmoud Harmouch, Medium, 14/03/2021 |
| | * [[http://jakevdp.github.io/|Pythonic Perambulations]] de Jake VanderPlas |
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