mathtoolbox

Mathematical tools (interpolation, dimensionality reduction, optimization, etc.) written in C++11 and Eigen.

Algorithms

Scattered Data Interpolation and Function Approximation

• rbf-interpolation: Radial basis function (RBF) interpolation
• gaussian-process-regression: Gaussian process regression (GPR)

Dimensionality Reduction and Low-Dimensional Embedding

• classical-mds: Classical multi-dimensional scaling (MDS)
• som: Self-organizing map (SOM)

Numerical Optimization

• backtracking-line-search: Backtracking line search
• bayesian-optimization: Bayesian optimization
• bfgs: BFGS method
• gradient-descent: Gradient descent method
• l-bfgs: Limited-memory BFGS method
• strong-wolfe-conditions-line-search: Strong Wolfe conditions line search

Linear Algebra

• log-determinant: Log-determinant
• matrix-inversion: Matrix inversion techniques

Utilities

• acquisition-functions: Acquisition functions
• constants: Constants
• data-normalization: Data normalization
• kernel-functions: Kernel functions
• probability-distributions: Probability distributions

Dependencies

Main Library

• Eigen http://eigen.tuxfamily.org/ (brew install eigen / sudo apt install libeigen3-dev)

Python Bindings

• pybind11 https://github.com/pybind/pybind11 (included as gitsubmodule)

Examples

• optimization-test-function https://github.com/yuki-koyama/optimization-test-functions (included as gitsubmodule)
• timer https://github.com/yuki-koyama/timer (included as gitsubmodule)

Use as a C++ Library

mathtoolbox uses CMake https://cmake.org/ for building source codes. This library can be built, for example, by

git clone https://github.com/yuki-koyama/mathtoolbox.git --recursive
cd mathtoolbox
mkdir build
cd build
cmake ../
make

and optionally it can be installed to the system by

make install

When the CMake parameter MATHTOOLBOX_BUILD_EXAMPLES is set ON, the example applications are also built. (The default setting is OFF.) This is done by

cmake ../ -DMATHTOOLBOX_BUILD_EXAMPLES=ON
make

When the CMake parameter MATHTOOLBOX_PYTHON_BINDINGS is set ON, the example applications are also built. (The default setting is OFF.) This is done by

cmake ../ -DMATHTOOLBOX_PYTHON_BINDINGS=ON
make

Prerequisites

macOS:

brew install eigen

Ubuntu:

sudo apt install libeigen3-dev

Use as a Python Library

pymathtoolbox is a (sub)set of Python bindings of mathtoolbox. Tested on Python 3.8, 3.9.

It can be installed via PyPI:

pip install git+https://github.com/yuki-koyama/mathtoolbox

Prerequisites

macOS

brew install cmake eigen

Ubuntu 22.04

sudo apt install cmake libeigen3-dev

Examples

See python-examples.

Gallery

Bayesian optimization (bayesian-optimization) solves a one-dimensional optimization problem using only a small number of function-evaluation queries.

Classical multi-dimensional scaling (classical-mds) is applied to pixel RGB values of a target image to embed them into a two-dimensional space.

Self-organizing map (som) is also applicable to pixel RGB values of a target image to learn a two-dimensional color manifold.

Projects Using mathtoolbox

• SelPh [CHI 2016] https://github.com/yuki-koyama/selph
  • classical-mds
• Sequential Line Search [SIGGRAPH 2017] https://github.com/yuki-koyama/sequential-line-search
  • acquisition-functions, data-normalization, kernel-functions, log-determinant, and probability-distributions
• Sequential Gallery [SIGGRAPH 2020] https://github.com/yuki-koyama/sequential-gallery
  • acquisition-functions and probability-distributions
• elasty https://github.com/yuki-koyama/elasty
  • l-bfgs

Contributing

Bug reports, suggestions, feature requests, and PRs are highly welcomed.

Licensing

The MIT License.