KMath

Could be pronounced as key-math. The Kotlin Mathematics library was initially intended as a Kotlin-based analog to Python's NumPy library. Later we found that kotlin is a much more flexible language and allows superior architecture designs. In contrast to numpy and scipy it is modular and has a lightweight core. The numpy-like experience could be achieved with kmath-for-real extension module.

Documentation site

Publications and talks

Goal

Provide a flexible and powerful API to work with mathematics abstractions in Kotlin-multiplatform (JVM, JS, Native and Wasm).
Provide basic multiplatform implementations for those abstractions (without significant performance optimization).
Provide bindings and wrappers with those abstractions for popular optimized platform libraries.

Non-goals

Be like NumPy. It was the idea at the beginning, but we decided that we can do better in API.
Provide the best performance out of the box. We have specialized libraries for that. Need only API wrappers for them.
Cover all cases as immediately and in one bundle. We will modularize everything and add new features gradually.
Provide specialized behavior in the core. API is made generic on purpose, so one needs to specialize for types, like for Float64 in the core. For that we will have specialization modules like kmath-for-real, which will give a better experience for those who want to work with specific types.

Contributing

The project requires a lot of additional work. The most important thing we need is feedback about what features are required the most. Feel free to create feature requests. We are also welcome to code contributions, especially in issues marked with good first issue label.

Project roadmap will be available at GitHub Projects.

Features and stability

KMath is a modular library. Different modules provide different features with different API stability guarantees. All core modules are released with the same version, but with different API change policy. The features are described in module definitions below. The module stability could have the following levels:

PROTOTYPE. On this level there are no compatibility guarantees. All methods and classes form those modules could break any moment. You can still use it, but be sure to fix the specific version.
EXPERIMENTAL. The general API is decided, but some changes could be made. Volatile API is marked with @UnstableKMathAPI or other stability warning annotations.
DEVELOPMENT. API breaking generally follows semantic versioning ideology. There could be changes in minor versions, but not in patch versions. API is protected with binary-compatibility-validator tool.
STABLE. The API stabilized. Breaking changes are allowed only in major releases.

Modules

benchmarks

Maturity: EXPERIMENTAL

kmath-ast

Maturity: EXPERIMENTAL

Features:

expression-language : Expression language and its parser

mst-jvm-codegen : Dynamic MST to JVM bytecode compiler

mst-js-codegen : Dynamic MST to JS compiler

rendering : Extendable MST rendering

kmath-commons

Commons math binding for kmath

Maturity: EXPERIMENTAL

kmath-complex

Complex numbers and quaternions.

Maturity: PROTOTYPE

Features:

complex : Complex numbers operations

quaternion : Quaternions and their composition

kmath-core

Core classes, algebra definitions, basic linear algebra

Maturity: DEVELOPMENT

Features:

algebras : Algebraic structures like rings, spaces and fields.

nd : Many-dimensional structures and operations on them.

linear : Basic linear algebra operations (sums, products, etc.), backed by the Space API.

buffers : One-dimensional structure

expressions : By writing a single mathematical expression once, users will be able to apply different types of

domains : Domains

autodiff : Automatic differentiation

Parallel linear algebra : Parallel implementation for LinearAlgebra

kmath-coroutines

Maturity: EXPERIMENTAL

kmath-dimensions

A proof of concept module for adding type-safe dimensions to structures

Maturity: PROTOTYPE

kmath-ejml

Maturity: PROTOTYPE

Features:

ejml-vector : Point implementations.

ejml-matrix : Matrix implementation.

ejml-linear-space : LinearSpace implementations.

kmath-for-real

Extension module that should be used to achieve numpy-like behavior. All operations are specialized to work with Double numbers without declaring algebraic contexts. One can still use generic algebras though.

Maturity: EXPERIMENTAL

Features:

DoubleVector : Numpy-like operations for Buffers/Points

DoubleMatrix : Numpy-like operations for 2d real structures

grids : Uniform grid generators

kmath-functions

Functions, integration and interpolation

Maturity: EXPERIMENTAL

Features:

piecewise : Piecewise functions.

polynomials : Polynomial functions.

linear interpolation : Linear XY interpolator.

spline interpolation : Cubic spline XY interpolator.

integration : Univariate and multivariate quadratures

kmath-geometry

Maturity: PROTOTYPE

kmath-histograms

Maturity: PROTOTYPE

kmath-jupyter

Maturity: PROTOTYPE

kmath-kotlingrad

Kotlin∇ integration module

Maturity: EXPERIMENTAL

Features:

differentiable-mst-expression : MST based DifferentiableExpression.

scalars-adapters : Conversions between Kotlin∇'s SFun and MST

kmath-memory

An API and basic implementation for arranging objects in a continuous memory block.

Maturity: DEVELOPMENT

kmath-multik

JetBrains Multik connector

Maturity: PROTOTYPE

kmath-ojalgo

Ojalgo bindings for kmath

Maturity: PROTOTYPE

kmath-optimization

Maturity: EXPERIMENTAL

kmath-stat

Maturity: EXPERIMENTAL

kmath-symja

Symja integration module

Maturity: PROTOTYPE

kmath-tensorflow

Google tensorflow connector

Maturity: PROTOTYPE

kmath-tensors

Maturity: PROTOTYPE

Features:

tensor algebra : Basic linear algebra operations on tensors (plus, dot, etc.)

tensor algebra with broadcasting : Basic linear algebra operations implemented with broadcasting.

linear algebra operations : Advanced linear algebra operations like LU decomposition, SVD, etc.

kmath-viktor

Binding for https://github.com/JetBrains-Research/viktor

Maturity: DEPRECATED

test-utils

Maturity: EXPERIMENTAL

Multi-platform support

KMath is developed as a multi-platform library, which means that most of the interfaces are declared in common source sets like common source sets and implemented there wherever it is possible. In some cases, features are delegated to platform-specific implementations even if they could be provided in the common module for performance reasons. Currently, Kotlin/JVM is the primary platform, however, Kotlin/Native, Kotlin/JS and Kotlin/Wasm contributions and feedback are also welcome.

Performance

Performance of mathematical operations is hard to achieve without a lot of effort. KMath focus is to provide a reasonable performance for common cases, out of the box and good interoperability with optimized libraries for edge cases. For example, one could prototype an algorithm using KMath core implementations and then use Multik or Ojalgo for performance-critical parts just by adding a dependency and algebra context switch.

As for core implementations, we expect to focus on creating a convenient universal API first and then work on increasing performance for specific cases. We expect the worst KMath benchmarks will perform better than native Python, but worse than optimized native/SciPy (mostly due to boxing operations on primitive numbers). The best performance of optimized parts could be better than SciPy.

Requirements

KMath currently relies on JDK 21 for compilation and execution of Kotlin-JVM part.

Repositories

Intermediate releases are published to Kotlin.Link repository.

repositories {
    maven("https://repo.kotlin.link")
}

dependencies {
    api("space.kscience:kmath-core:$version")
    // api("space.kscience:kmath-core-jvm:$version") for jvm-specific version
}