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fastmath

A Clojure math library.

Documentation

3.0.0-alpha1 (WIP)

Fastmath book

2.4.0

Codox documentation

Clerk notebooks

Index

Installation

[generateme/fastmath "2.4.0"]

Alpha

[generateme/fastmath "3.0.0-alpha1"]

Source code in the 3.x branch.

2.3.0 GPL warning

Important Note

Fastmath 2.3.0 depends on SMILE 3.0.x which is GPL. That means that Fastmath 2.3.0 also should be treated as GPL. Version 2.4.x fixes it and brings back SMILE LGPL 2.x dependency.

MKL

Important Note

Fastmath relies on SMILE 2.6.0 which relies on BLAS/LAPACK via MKL and/or OpenBlas. MKL (preferred) and OpenBlas are included as dependencies in fastmath. This leads to addional 1GB of jar files. I can't assure that all functionalities will work on OpenBlas (see: #15) but 99% should. If you need fastmath to be lighter, please exclude MKL from your path.

lein / project.clj

[generateme/fastmath "2.4.0" :exclusions [com.github.haifengl/smile-mkl]]

deps.edn

{:deps {generateme/fastmath {:mvn/version "2.4.0"
                             :exclusions [com.github.haifengl/smile-mkl]}}}

If you don't need certain interpolation or clustering methods you can exclude OpenBlas as well (be warned that other things can break):

:exclusions [com.github.haifengl/smile-mkl org.bytedeco/openblas]

MKL Exception

When MKL is not available fastmath (SMILE actually, here and here) will throw two exceptions with full stack traces about lack of MKL. You can safely ignore them.

[main] DEBUG smile.math.blas.LAPACK - Failed to create MKL instance:
java.lang.ClassNotFoundException: smile.math.blas.mkl.MKL
[...]

[main] DEBUG smile.math.blas.BLAS - Failed to create MKL instance:
java.lang.ClassNotFoundException: smile.math.blas.mkl.MKL
[...]

Contribution

NOTE Currently we work on the 3.x branch only. PRs to master branch will not be accepted.

We accept PRs!

  • when fixing a bug/typo/docstring - just push a PR
  • if you want to add a new function or have an idea - please consult it before starting a work
  • if you want to enhance a documentation - please read this wiki page

Content

Code adopted from Zach Tellmans' library.

[* + - / > < >= <= == rem quot mod bit-or bit-and bit-xor bit-not bit-shift-left bit-shift-right unsigned-bit-shift-right inc dec zero? neg? pos? min max even? odd? bool-and bool-or bool-xor bool-not << >> >>> not==]

Math functions

  • Trigonometric functions
  • Power: log, ln, logb, exp, pow, sqrt
  • Rounding functions: round, floor, ceil, trunc, frac, approx + other
  • Normalizations: norm wrap, constrain
  • Interpolations: lerp, cos-interpolation, smooth-interpolation, quad-interpolation, smoothstep
  • Special functions: erf, beta, gamma + other
  • Distance: dist, hypot
  • Sign: sgn, signum, abs
  • Other: gcd, lcm

Most of them backed by Jafama FastMath 2.3.1 or Apache Commons Math 3.6.1

Vector operations protocol and implementations

  • 2d (Vec2), 3d (Vec3) and 4d (Vec4) vector types.
  • ArrayVector for fixed length long vectors (fixed sized double-array)
  • Clojure vector, double array, Number (as 1d vector)

Matrix operations protocol and implementations

  • 2d (Mat2x2), 3d (Mat3x3) and 4d (Mat4x4) matrix types.

With typical basic matrix operations

Complex and Quaternion number functions

  • primitive operations: mult, div, add, sub
  • abs, arg, conjugate, reciprocal, neg
  • atan, asin, acos, csc, sec, tanh, tan, sinh, sin, cosh, cos
  • log, exp, pow
  • sqrt, sq, sqrt1z

Integration, differentiations and solvers

  • Integration: VEGAS/VEGAS+ Monte Carlo, h-adaptive Cubature, h-adaptive Gauss-Kronrod (QuadGK), Simpson, Romberg, Trapezoid, Gauss-Legendre, Midpoint
  • Derivatives - any degree and order of accuracy
  • Gradient and Hessian for multivariate functions
  • Solvers (root finding): brent, bisection, illinois, muller, muller2, pegasus, regula-falsi, ridders, secant

Random numbers

  • Collection of random number generators
  • Random generator functions for each primitive type (drand - double, lrand - long, frand - float, irand - int)
  • Additional RNG functions: brand - true/false, grand - gaussian distributed double
  • Random sequences: from distribution, halton, sobol, R2, sphere, uniform

Distributions

  • Collection of distributions (60+)

Noise

  • 4 noise types: value, gradient, simplex, discrete
  • 3 noise blends: fbm, ridgedmulti, billow
  • Ready to use fbm functions: noise (perlin), vnoise (value noise), simplex
  • Warp noise

Statistics

  • Descriptive statistics: size, min, max, mode, mean, median, percentiles, kurtosis, skewness, IQR, LAV, UAV and other
  • Correlations
  • t-test
  • ACF/PACF
  • histogram
  • Bootstrap
  • Confidence intervals

Bootstrap

Bootstrap functions and confidence intervals

Interpolations

1d, 2d interpolations

Easings

Several easing functions (in, out, in-out)

Transforms

  • Wavelets: 1d, 2d (haar, biorthogonal, symlet, coiflet, daubechies, legendre)
  • 1d Fast Sine, Cosine and Hadamard

Vector fields

Great collection (100+) of R^2->R^2 functions.

Gaussian Processes

Gaussian Processes

Clustering

Various clustering algorithms including K-Means++, DBSCAN, CLARANS, DENCLUE, MEC, Spectral, Deterministic Annealing

Optimization

L-BFGS-B, Gradient, Nelder-Mead, Simplex, Powell, BOBYQA, CMAES, BayesianOptimizer, Linear optimizer

Grids

Hexagonal, squared, triangular, rhomboidal grid functions

Kernels

Collection of various kernels (density, RBF, correlation)

Signal

  • Signal (audio) processing filters and oscillators
  • Smoothing filters: Savitzky-Golay, moving average, kernel smoothing

EFloat

Floating point operations with error bounds

Other

Plenty of constant values

Almost all functions optimized to work with double and long primitives

Supporting libraries

Alternatives

Since this library is only JVM version, you can check following Clojure/ClojureScript libraries as replacement

  • PrimitiveMath - for primitive operators
  • Kixi stats - for pure clj(s) statistics/distributions (tends to be 2-10x slower)
  • thi.ng - for vectors, general math, noise, complex numbers, transforms (fourier)
  • vectorz-clj - fast vector operations
  • Incanter - statistics/distributions/probability

Java

Java classes are compiled for java 1.8

How To Help

If you see place of improvement, I'm accepting PRs.

Licence

  • The Unlicence - up to 1.5.2
  • MIT License - from 1.5.3 (with te exception of 2.3.0 which should be treated as GPL)

Copyright (c) 2024 generateme