gosl

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README

Gosl – Go scientific library

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Gosl is a Go library to develop Artificial Intelligence and High-Performance Scientific Computations.

NOTICE 2020-02-14 Thank you, Contributors!!! 😃

The library tries to be as general and as easy as possible. Gosl considers the use of both Go concurrency routines and parallel computing using the message passing interface (MPI). Gosl has several modules (sub-packages) for a variety of tasks in scientific computing, image analysis, and data post-processing.

Gosl includes high-performant linear algebra functions (wrapping MKL, OpenBLAS, LAPACK, SuiteSparse, UMFPACK...), fast Fourier transform algorithms (wrapping FFTW), numerical integration (wrapping QUADPACK), functions and structures for geometry calculations (e.g. 3D transfinite interpolation, grid search, octree...), random numbers generation (SFMT and DSFMT) and probability distributions, optimisation and graph algorithms, plotting and visualisation using the VTK, and much more.

Gosl has also solvers to (stiff or not) ordinary differential equations and several tools for 2D/3D mesh generation to assist on the development of solvers for partial differential equations.

We now give focus to Machine Learning (see ml package) and Big Data (see h5 package). We are also planning wrappers to powerful tools such as CNTK, TensorFlow, and Hadoop. We have a wrapper to OpenCV in the works as well.

Resources

  1. Examples and benchmarks
  2. White papers
  3. Documentation
  4. Contributing and TODO

Installation

Gosl works on Windows, macOS, and Linux (Debian, Ubuntu).

For installation instructions, click on: Installation on Windows Installation on macOS Installation on Linux/Debian/Ubuntu

Alternatively, to use Docker, click on: Docker image

The Docker image contains Ubuntu and all the dependencies, including MPI and VTK.

docker pull gosl/gosl

Usage

Type:

cd /tmp && mkdir -p try-gosl && cd try-gosl
go mod init try-gosl

Create the file try-gosl/main.go:

package main

import (
	"github.com/cpmech/gosl/fun"
	"github.com/cpmech/gosl/io"
)

func main() {
	i0 := fun.ModBesselI0(-10)
	io.Pf("Modified Bessel I0(-10) = %g\n", i0)
}

Run:

go run main.go

Output:

Modified Bessel I0(-10) = 2815.716628466253

Sub-packages

Gosl includes the following sub-packages:

  1. chk – Check code and unit test tools
  2. io – Input/output, read/write files, and print commands
  3. io/h5 – Read/write HDF5 (Big Data) files
  4. utl – Utilities. Lists. Dictionaries. Simple Numerics
  5. utl/al – Utilities. (Naive) Implementation of Classic algorithms and structures (e.g. Linked Lists)
  6. plt – Plotting and drawing (png and eps)
  7. mpi – Message Passing Interface for parallel computing
  8. la – Linear Algebra: vector, matrix, efficient sparse solvers, eigenvalues, decompositions, etc.
  9. la/mkl – Lower level linear algebra using Intel MKL
  10. la/oblas – Lower level linear algebra using OpenBLAS
  11. num/qpck – Go wrapper to QUADPACK for numerical integration
  12. num – Fundamental numerical methods such as root solvers, non-linear solvers, numerical derivatives and quadrature
  13. fun – Special functions, DFT, FFT, Bessel, elliptical integrals, orthogonal polynomials, interpolators
  14. fun/dbf – Database of functions of a scalar and a vector like f(t,{x}) (e.g. time-space)
  15. fun/fftw – Go wrapper to FFTW for fast Fourier Transforms
  16. gm – Geometry algorithms and structures
  17. gm/msh – Mesh structures and interpolation functions for FEA, including quadrature over polyhedra
  18. gm/tri – Mesh generation: triangles and Delaunay triangulation (wrapping Triangle)
  19. gm/rw – Mesh generation: read/write routines
  20. graph – Graph theory structures and algorithms
  21. opt – Numerical optimization: Interior Point, Conjugate Gradients, Powell, Grad Descent, more
  22. rnd – Random numbers and probability distributions
  23. rnd/dsfmt – Go wrapper to dSIMD-oriented Fast Mersenne Twister
  24. rnd/sfmt – Go wrapper to SIMD-oriented Fast Mersenne Twister
  25. vtk – 3D Visualisation with the VTK tool kit
  26. ode – Solvers for ordinary differential equations
  27. ml – Machine learning algorithms
  28. ml/imgd – Machine learning. Auxiliary functions for handling images
  29. pde – Solvers for partial differential equations (FDM, Spectral, FEM)
  30. tsr – Tensors, continuum mechanics, and tensor algebra (e.g. eigendyads)

We are currently working on the following additional packages:

  1. img - Image and machine learning algorithms for images
  2. img/ocv - Wrapper to OpenCV

About the filenames

  1. t_something_test.go is a unit test. We have several of them! Some usage information can be learned from these files.
  2. t_something_main.go is a test with a main function to be run with go run ... or mpirun -np ? go run ... (replace ? with the number of cpus).
  3. t_b_something_test.go is a benchmark test. Run benchmarks with go test -run=XXX -bench=.

Design strategies

Here, we call structure any user-defined type. These are simply Go types defined as struct. One may think of these structures as classes. Gosl has several global functions as well and tries to avoid complicated constructions.

An allocated structure (instance) is called an object and functions attached to this object are called methods. In Gosl, the variable holding the pointer to an object is always named o (lower case "o"). This variable is similar to the self or this keywords in other languages (Python, C++, respectively).

Functions that allocate a pointer to a structure are prefixed with New; for instance: NewIsoSurf. Some structures require an explicit call to another function to release allocated memory. Be aware of this requirement! In this case, the function is named Free and appears in a few sub-packages that use CGO. Also, some objects may need to be initialized before use. In this case, functions named Init have to be called.

The directories corresponding to each package have a README.md file that should help with understanding the library. Also, there are links to pkg.go.dev where all functions, structures, and variables are well explained.

Test coverage

We aim for a 100% test coverage! Despite trying our best to accomplish this goal, full coverage is difficult, in particular with (sub)packages that involve Panic or figure generation. Nonetheless, critical algorithms are completely tested.

We use the following bash macro frequently to check our test coverage:

gocov() {
    go test -coverprofile=/tmp/cv.out
    go tool cover -html=/tmp/cv.out
}
Some results from cover.run

Bibliography

The following works take advantage of Gosl:

  1. Pedroso DM, Bonyadi MR, Gallagher M (2017) Parallel evolutionary algorithm for single and multi-objective optimisation: differential evolution and constraints handling, Applied Soft Computing http://dx.doi.org/10.1016/j.asoc.2017.09.006 paper available here
  2. Pedroso DM (2017) FORM reliability analysis using a parallel evolutionary algorithm, Structural Safety 65:84-99 http://dx.doi.org/10.1016/j.strusafe.2017.01.001
  3. Pedroso DM, Zhang YP, Ehlers W (2017) Solution of liquid-gas-solid coupled equations for porous media considering dynamics and hysteretic retention behaviour, Journal of Engineering Mechanics 04017021 http://dx.doi.org/10.1061/(ASCE)EM.1943-7889.0001208
  4. Pedroso DM (2015) A solution to transient seepage in unsaturated porous media. Computer Methods in Applied Mechanics and Engineering, 285:791-816 http://dx.doi.org/10.1016/j.cma.2014.12.009
  5. Pedroso DM (2015) A consistent u-p formulation for porous media with hysteresis. Int. Journal for Numerical Methods in Engineering, 101(8):606-634 http://dx.doi.org/10.1002/nme.4808

Authors and license

See the AUTHORS file.

Unless otherwise noted, the Gosl source files are distributed under the BSD-style license found in the LICENSE file.

Directories

Path Synopsis
Package chk contains functions for checking and testing computations
 Package chk contains functions for checking and testing computations
Package examples contains several examples using Gosl.
 Package examples contains several examples using Gosl.
benchmark
Package benchmark contains some benchmark tests using Gosl.
 Package benchmark contains some benchmark tests using Gosl.
pde
Package ex contains some examples using Gosl/pde.
 Package ex contains some examples using Gosl/pde.
fun
Package fun (functions) implements special functions such as elliptical, orthogonal polynomials, Bessel, discrete Fourier transform, polynomial interpolators, and more.
 Package fun (functions) implements special functions such as elliptical, orthogonal polynomials, Bessel, discrete Fourier transform, polynomial interpolators, and more.
dbf
Package dbf implements a database of f(t,{x}) functions (e.g.
 Package dbf implements a database of f(t,{x}) functions (e.g.
fftw
Package fftw wraps the FFTW library to perform Fourier Transforms using the "fast" method by Cooley and Tukey
 Package fftw wraps the FFTW library to perform Fourier Transforms using the "fast" method by Cooley and Tukey
gm
Package gm (geometry and meshes) implements auxiliary functions for handling geometry and mesh structures
 Package gm (geometry and meshes) implements auxiliary functions for handling geometry and mesh structures
msh
Package msh defines mesh data structures and implements interpolation functions for finite element analyses (FEA)
 Package msh defines mesh data structures and implements interpolation functions for finite element analyses (FEA)
rw
Package rw implements reader and writers for geometry files such as the STEP file format
 Package rw implements reader and writers for geometry files such as the STEP file format
tri
Package tri wraps Triangle to perform mesh generation a Delaunay triangulation
 Package tri wraps Triangle to perform mesh generation a Delaunay triangulation
Package graph implements solvers based on Graph theory
 Package graph implements solvers based on Graph theory
io
Package io (input/output) implements auxiliary functions for printing, parsing, handling files, directories, etc.
 Package io (input/output) implements auxiliary functions for printing, parsing, handling files, directories, etc.
h5
Package h5 wraps the HDF5 library.
 Package h5 wraps the HDF5 library.
la
Package la implements functions and structure for Linear Algebra computations.
 Package la implements functions and structure for Linear Algebra computations.
data
Package data wraps test_mat from https://people.sc.fsu.edu/~jburkardt/f_src/test_mat/test_mat.html This package should be used in tests only
 Package data wraps test_mat from https://people.sc.fsu.edu/~jburkardt/f_src/test_mat/test_mat.html This package should be used in tests only
mkl
Package mkl implements lower-level linear algebra routines using MKL for maximum efficiency.
 Package mkl implements lower-level linear algebra routines using MKL for maximum efficiency.
oblas
Package oblas implements lower-level linear algebra routines using OpenBLAS for maximum efficiency.
 Package oblas implements lower-level linear algebra routines using OpenBLAS for maximum efficiency.
ml
Package ml implements Machine Learning algorithms
 Package ml implements Machine Learning algorithms
imgd
Package imgd (image-data) adds functionality to process image-data, e.g.
 Package imgd (image-data) adds functionality to process image-data, e.g.
Package mpi wraps the Message Passing Interface for parallel computations
 Package mpi wraps the Message Passing Interface for parallel computations
num
Package num implements fundamental numerical methods such as numerical derivative and quadrature, root finding solvers (Brent's and Newton's methods), among others.
 Package num implements fundamental numerical methods such as numerical derivative and quadrature, root finding solvers (Brent's and Newton's methods), among others.
qpck
Package qpck wraps the QUADPACK library for numerical integration
 Package qpck wraps the QUADPACK library for numerical integration
Package ode implements solvers for ordinary differential equations, including explicit and implicit Runge-Kutta methods; e.g.
 Package ode implements solvers for ordinary differential equations, including explicit and implicit Runge-Kutta methods; e.g.
Package opt implements routines for solving optimisation problems
 Package opt implements routines for solving optimisation problems
Package pde implements numerical methods for the solution of Partial Differential Equations.
 Package pde implements numerical methods for the solution of Partial Differential Equations.
Package plt contains functions for plotting, drawing in 2D or 3D, and generationg PNG and EPS files
 Package plt contains functions for plotting, drawing in 2D or 3D, and generationg PNG and EPS files
Package rnd implements random numbers generators (wrapping the standard functions or the Mersenne Twister library).
 Package rnd implements random numbers generators (wrapping the standard functions or the Mersenne Twister library).
Package tools holds a number of tools.
 Package tools holds a number of tools.
Package tsr implements Tensors using the smart approach by considering the Mandel's basis
 Package tsr implements Tensors using the smart approach by considering the Mandel's basis
utl
Package utl implements functions for simplifying calculations and allocation of structures such as slices and slices of slices.
 Package utl implements functions for simplifying calculations and allocation of structures such as slices and slices of slices.
al
Package al implements classical algorithms such as Queue, Stack and others Package al implements classical algorithms such as Queue, Stack and others Package al implements classical algorithms such as Queue, Stack and others
 Package al implements classical algorithms such as Queue, Stack and others Package al implements classical algorithms such as Queue, Stack and others Package al implements classical algorithms such as Queue, Stack and others
Package vtk wraps the visualisation tool kit (VTK) for drawing 3D surfaces (scalar fields, vector fields, etc.)
 Package vtk wraps the visualisation tool kit (VTK) for drawing 3D surfaces (scalar fields, vector fields, etc.)

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