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https://github.com/generateme/fastmath

Fast primitive based math library
https://github.com/generateme/fastmath

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Fast primitive based math library

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# fastmath



Math library.



## Documentation



[Codox documentation](https://generateme.github.io/fastmath/index.html)



### Clerk notebooks - WIP



[Index](https://generateme.github.io/fastmath/notebooks/)



* [fastmath.core](https://generateme.github.io/fastmath/notebooks/notebooks/core/)

* [fastmath.random](https://generateme.github.io/fastmath/notebooks/notebooks/random/)

* [fastmath.stats](https://generateme.github.io/fastmath/notebooks/notebooks/stats/)

    * [fastmath.stats.bootstrap](https://generateme.github.io/fastmath/notebooks/notebooks/bootstrap/)

* [fastmath.calculus](https://generateme.github.io/fastmath/notebooks/notebooks/calculus/)

* [fastmath.complex](https://generateme.github.io/fastmath/notebooks/notebooks/complex_quaternion/index.html#complex-numbers)

* [fastmath.quaternion](https://generateme.github.io/fastmath/notebooks/notebooks/complex_quaternion/index.html#quaternions)



## Installation



```clojure

[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.



### MKL



**Important Note**



Fastmath relies on [SMILE](https://haifengl.github.io/) 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](https://github.com/generateme/fastmath/issues/15#issuecomment-1090323385)) but 99% should. If you need `fastmath` to be lighter, please exclude MKL from your path.



#### lein / project.clj



```clojure

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

```



#### deps.edn



```clojure

{: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):



```clojure

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

```



#### MKL Exception



When MKL is not available `fastmath` (SMILE actually, [here](https://github.com/haifengl/smile/blob/master/base/src/main/java/smile/math/blas/BLAS.java#L58) and [here](https://github.com/haifengl/smile/blob/master/base/src/main/java/smile/math/blas/LAPACK.java#L60)) 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](https://github.com/ztellman/primitive-math)



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](https://github.com/jeffhain/jafama) or [Apache Commons Math 3.6.1](http://commons.apache.org/proper/commons-math/index.html)



### 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



* [Apache Commons Math 3.6.1](http://commons.apache.org/proper/commons-math/index.html) - Apache 2.0 Licence

* [SMILE 2.5.0](http://haifengl.github.io/smile/) - Apache 2.0 Licence

* [Jafama FastMath 2.3.1](https://github.com/jeffhain/jafama) - Apache 2.0 Licence

* [PrimitiveMath](https://github.com/ztellman/primitive-math) - MIT Licence

* [JWave](https://github.com/cscheiblich/JWave/) - MIT Licence

* [SSJ](https://github.com/umontreal-simul/ssj) - Apache 2.0 Licence



## Alternatives



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



* [PrimitiveMath](https://github.com/ztellman/primitive-math) - for primitive operators

* [Kixi stats](https://github.com/MastodonC/kixi.stats) - for pure clj(s) statistics/distributions (tends to be 2-10x slower)

* [thi.ng](http://thi.ng/) - for vectors, general math, noise, complex numbers, transforms (fourier)

* [vectorz-clj](https://github.com/mikera/vectorz-clj) - fast vector operations

* [Incanter](https://github.com/incanter/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