Numerical Methods with Python, Numpy and Matplotlib

Overview

Numerical Bric-a-Brac

Collections of numerical techniques with Python and standard computational packages (Numpy, SciPy, Numba, Matplotlib ...).

Differential Equations

Differential Equations describe many physical systems

Notebooks
implicit_solver
GitHub
Implementation of Baraff's "Large steps in cloth simulation."
spring_integrator
Analytic solution to damped spring
poisson_solver
Diffusion problem
laplace_inpainting
Laplace inpainting to restore an image

Optimizations

Those notebooks are the core algorithms for supervised and unsupervised learning in Machine learning.

Machine Learning Notebooks
Supervised Learning
linear_regression
Linear regression from scratch
polynomial_regression
Polynomial regression from scratch
logistic_regression
Logistic regression from scratch
multiclass_classifiation
Multiclass Classification with Scikit-learn
support_vector_machine
Support Vector Machine (SVM) with Scikit-learn
Unsupervised Learning
k_means
K-means clustering from scratch
Other Notebooks
multivariable_optimizations
Multivariable Optimizations (Gradient Descent and Newton's methods)

Linear Algebra

Standard linear algebra algorithms

Notebooks
inverse_kinematic
Inverse kinematics using least square methods to solve the ill-posed problem
radial_basis_kernels
Interpolation with Radial Basis Functions (RBFs)

Graph Theory

Part of discrete mathematics, graph theory is the study of graphs, a structures used to model pairwise relations between objects. Graph theory includes problems such as the travelling salesman problem and the spectral analysis of graph.

Notebooks
graph_matrix
List matrices describing a finite graph.
graph_coloring
Greedy algorithm for graph coloring.
dijkstra
Find the shortest paths between nodes in a graph.
spectral_graph_theory
Spectral Graph Thoery - PLACEHOLDER (WIP).

Neural Network

Artificial neural networks are composed of artificial neurons organized into layers. Neural networks are employed for regression analysis (function approximation) and classification problems.

Notebooks
ConvNets
face_keypoints
Facial keypoints detection
conv_net
Image classification on CIFAR-10 using CNN
res_net
Image classification on CIFAR-10 using ResNet
Generative Models
ae_fashion_mnist
Autoencoder on Fashion MNIST
variational_autoencoder
Variational autoencoder on MNIST

Stencil Codes

Stencil codes are at the heart of many numerical solvers and physical simulation codes. They are of particular interest in scientific computing research for solving partial differential equations, image processing, cellular automata, etc. The Finite Difference Method (FDM) is closely related to stencil codes.

Notebooks
poisson_solver
Diffusion problem
laplace_inpainting
Laplace inpainting to restore an image
convolution
Image processing with convolution kernels
conway
Cellular automata with Conway's game of life rules

Dimensionality Reduction

Dimensionality reduction is the process of converting data from a high-dimensional space to a low-dimensional space (subspace). A lower dimension representation aids in comprehending meaningful properties (such as latent variables), compressing the data, and removing noise from the original data.

Notebooks
pca_transform
Optimal transformation of a point cloud with PCA
svd_compression
Image compression with Singular Value Decomposition
autoencoder
Autoencoder on Fashion MNIST
eigenfaces
Eigenfaces for face recognition on Olivetti faces dataset

Miscellaneous

Random notebooks about dynamic programming and monte carlo methods

Notebooks
markov_chain
Example of ML pipeline with Snakemake
dynamic_programming
Dynamic programming Examples
monte_carlo_integration
Examples of Monte Carlo integrations
subspace_deformation
Skeletal Subspace Deformation
path_tracing
GitHub
Monte Carlo Path Tracing
markov_chain
Generate authors names from the Collection of Poems from Poetry Foundation
Owner
Vincent Bonnet
Vincent Bonnet
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