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GSL

Table of Contents

• Installation
  • OSX
  • Ubuntu
  • ARCUS-B
• Compilation
  • OSX
  • Ubuntu
  • ARCUS-B
• Usage
  • import
  • functions
    • construct matrices and vectors
    • multiply matrices and vectors
    • solve linear equations
    • numerical errors

The GNU Scientific library (GSL) is a powerful C/C++ numerical library.

Installation

This guide assumes you already have a working C/C++ compiler - check by entering gcc --version in Terminal. OSX's default Clang compiler is fine, otherwise this page describes how to install gcc 4.9.

OSX

Apparently GSL can be installed through Homebrew via

brew install gsl

though installing it manually is just as simple, which we now describe.

• Download gsl-latest.tar.gz from the GSL ftp site and unzip it anywhere (e.g. /Downloads)
• Open the unzipped gsl folder in Terminal (e.g. cd ~/Downloads/gsl-2.4
• Run sudo ./configure && make && make install

If the above gives a "permission denied" error, instead try

sudo make clean
sudo chown -R $USER .
./configure && make
make install

You'll now be able to include GSL into your code from anywhere.

Ubuntu

sudo apt-get install libgsl-dev

You'll now be able to include GSL into your code from anywhere.

ARCUS-B

Oh wait, explore the use of...

module load gsl/1.15
module load gsl/1.16
module load gsl/2.1

In the ARCUS terminal, download GSL anywhere

wget "ftp://ftp.gnu.org/gnu/gsl/gsl-latest.tar.gz"

and unzip it

tar -xf gsl-latest.tar.gz

then open the new folder e.g.

cd gsl-2.4

To install without admin permissions, we'll keep the GSL files in a folder called gsl .

Note some newer versions off gcc (e.g. 8) seem incompatible. Use an older version (e.g. gcc/5.3.0) and first call

module load binutils libtool

Replace YOURUSERNAME below with your ARCUS-B username (e.g. abcd1234) and run

export gsdir=/data/oums-quantopo/YOURUSERNAME/gsl

mkdir $gsdir

./configure --prefix=$gsdir && make && make install

We'll need to remember this location when compiling

Compilation

OSX

Compiling GSL with our code is easy; we simply add library flags -lm -lgsl -lgslcblas to our calls to gcc.

For example, we'd adapt the QuEST makefile to include

#
# --- libraries
#
LIBS = -lm -lgsl -lgslcblas

Ubuntu

Exactly as above for OSX.

ARCUS-B

Before compiling on ARCUS-B, we must extend LD_LIBRARY to include our gsl folder (replace YOURUSERNAME below)

export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/data/oums-quantopo/YOURUSERNAME/gsl/lib

This need only be done once each time we SSH into ARCUS.

Our compilation must additionally include the -lm -lgsl -lgslcblas libraries and flags -I/data/oums-quantopo/YOURUSERNAME/gsl/include and -L/data/oums-quantopo/YOURUSERNAME/gsl/lib.

For example, we'd modify the QuEST makefile to include

#
# --- libraries
#
LIBS = -lm -lgsl -lgslcblas

and just after that, insert

#
# --- GSL link
#
GSL_INCLUDE = -I/data/oums-quantopo/YOURUSERNAME/gsl/include
GSL_LINK = -L/data/oums-quantopo/YOURUSERNAME/gsl/lib

and modify the rules list

#
# --- rules
#
%.o: %.c
	$(CC) $(CFLAGS) $(CFLAGS_OMP) $(GSL_INCLUDE) -c $<

%.o: $(QUEST_DIR)/%.c
	$(CC) $(CFLAGS) $(CFLAGS_OMP) $(GSL_INCLUDE) -c $<

and finally the build commands

#
# --- build
#
default:	$(EXE)

$(EXE):		$(OBJ)
		$(CC) $(CFLAGS) $(CFLAGS_OMP) $(GSL_INCLUDE) -o $(EXE) $(OBJ) $(LIBS) $(GSL_LINK)

See a complete example of my QuEST & gsl makefile here.

Usage

import

The many different GSL functions are available in different source files.

For example, to use the matrix, linear equation solver, and matrix multiplication functionalities, respectively include

#include <gsl/gsl_matrix.h>
#include <gsl/gsl_linalg.h>
#include <gsl/gsl_blas.h>

View available functions and their necessary header files can be found here.

functions

Sometimes GSL is so powerful, it's confusing to figure out how to do some simple things. So here are some examples

construct matrices and vectors

Matrices are dynamic objects, indexed from 0, which must be allocated before, and freed after, their use.

#include <gsl/gsl_matrix.h>

gsl_matrix* myMatr = gsl_matrix_alloc(10,20);

// matrix of 8s
for (int i=0; i < 10; i++)
    for (int j=0; j < 20; j++)
        gsl_matrix_set(myMatr, i, j, 8);

int elem = gsl_matrix_get(myMatr, 3, 4);

gsl_matrix_free(myMatr);

For a vector, replace matrix above with vector.

multiply matrices and vectors

GSL's matrix operations come under 'Basic Linear Algebra Subprograms' (BLAS), listed here

#include <gsl/gsl_blas.h>

To multiply matrices matrA and matrB and store the result in matrC (all of which must be previously allocated by gsl_matrix_alloc), call:

gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, matrA, matrB, 0.0, matrC); 

In the name gsl_blas_dgemm, the d refers to double-precision matrices, and the final m refers to matrix. The other arguments are explained here.

To multiply a matrix matrA and a vector vecB and store the result in vecC (previously allocated by gsl_matrix_alloc and gsl_vector_alloc), call:

gsl_blas_dgemv(CblasNoTrans, 1.0, matrA, vecB, 0.0, vecC);

solve linear equations

Linear algebra operations are provided by

#include <gsl/gsl_linalg.h>

Here's how to solve A x = b (or matrA vecX = vecB) for x by LU decomposition, which involves creating an intermediate permutation structure

gsl_permutation* perm = gsl_permutation_alloc(vecB->size);

int swaps;
gsl_linalg_LU_decomp(matrA, perm, &swaps);
gsl_linalg_LU_solve(matrA, perm, vecB, vecX);

gsl_permutation_free(perm);

numerical errors

By default, a numerical error (e.g. attempting to invert a non-invertible matrix) will cause an error message and execution to stop. To instead detect and handle numerical errors, include

#include <gsl/gsl_errno.h>

and call

gsl_set_error_handler_off();

before calling any numerical functions. Then functions (e.g. gsl_linalg_LU_solve) will return an integer 0 for success, otherwise an errorcode of those listed here (e.g. GSL_ERANGE, GSL_EIVANL).