README
¶
Gosl – Go scientific library
Gosl is a Go library to develop Artificial Intelligence and High-Performance Scientific Computations.
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
Installation
Gosl works on Windows, macOS, and Linux (Debian, Ubuntu).
For installation instructions, click on:
Alternatively, to use Docker, click on:
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:
- chk – Check code and unit test tools
- io – Input/output, read/write files, and print commands
- io/h5 – Read/write HDF5 (Big Data) files
- utl – Utilities. Lists. Dictionaries. Simple Numerics
- utl/al – Utilities. (Naive) Implementation of Classic algorithms and structures (e.g. Linked Lists)
- plt – Plotting and drawing (png and eps)
- mpi – Message Passing Interface for parallel computing
- la – Linear Algebra: vector, matrix, efficient sparse solvers, eigenvalues, decompositions, etc.
- la/mkl – Lower level linear algebra using Intel MKL
- la/oblas – Lower level linear algebra using OpenBLAS
- num/qpck – Go wrapper to QUADPACK for numerical integration
- num – Fundamental numerical methods such as root solvers, non-linear solvers, numerical derivatives and quadrature
- fun – Special functions, DFT, FFT, Bessel, elliptical integrals, orthogonal polynomials, interpolators
- fun/dbf – Database of functions of a scalar and a vector like f(t,{x}) (e.g. time-space)
- fun/fftw – Go wrapper to FFTW for fast Fourier Transforms
- gm – Geometry algorithms and structures
- gm/msh – Mesh structures and interpolation functions for FEA, including quadrature over polyhedra
- gm/tri – Mesh generation: triangles and Delaunay triangulation (wrapping Triangle)
- gm/rw – Mesh generation: read/write routines
- graph – Graph theory structures and algorithms
- opt – Numerical optimization: Interior Point, Conjugate Gradients, Powell, Grad Descent, more
- rnd – Random numbers and probability distributions
- rnd/dsfmt – Go wrapper to dSIMD-oriented Fast Mersenne Twister
- rnd/sfmt – Go wrapper to SIMD-oriented Fast Mersenne Twister
- vtk – 3D Visualisation with the VTK tool kit
- ode – Solvers for ordinary differential equations
- ml – Machine learning algorithms
- ml/imgd – Machine learning. Auxiliary functions for handling images
- pde – Solvers for partial differential equations (FDM, Spectral, FEM)
- tsr – Tensors, continuum mechanics, and tensor algebra (e.g. eigendyads)
We are currently working on the following additional packages:
- img - Image and machine learning algorithms for images
- img/ocv - Wrapper to OpenCV
About the filenames
t_something_test.gois a unit test. We have several of them! Some usage information can be learned from these files.t_something_main.gois a test with a main function to be run withgo run ...ormpirun -np ? go run ...(replace ? with the number of cpus).t_b_something_test.gois a benchmark test. Run benchmarks withgo 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 godoc.org 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
- chk test coverage
- io test coverage
- utl test coverage
- utl/al test coverage
- fun/dbf test coverage
- gm/tri test coverage
- gm/rw test coverage
- rnd test coverage
- rnd/dsfmt test coverage
- rnd/sfmt test coverage
Bibliography
The following works take advantage of Gosl:
- 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
- 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
- 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
- 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
- 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. |
|
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 |
|
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 |
|
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. |
|
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. |
|
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 |
|
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). |
|
dsfmt
Package dsfmt wraps the dSFMT Double precision SIMD-oriented Fast Mersenne Twister
|
Package dsfmt wraps the dSFMT Double precision SIMD-oriented Fast Mersenne Twister |
|
sfmt
Package sfmt wraps the SFMT SIMD-oriented Fast Mersenne Twister
|
Package sfmt wraps the SFMT SIMD-oriented Fast Mersenne Twister |
|
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 |
|
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.) |