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fastmath

Math library.

Installation

[generateme/fastmath "2.4.0"]

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.

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
[...]

Content

PrimitiveMath

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

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

Apache Commons Math 3.6.1 - Apache 2.0 Licence
SMILE 2.5.0 - Apache 2.0 Licence
Jafama FastMath 2.3.1 - Apache 2.0 Licence
PrimitiveMath - MIT Licence
JWave - MIT Licence
SSJ - Apache 2.0 Licence

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

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)

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