GSL 的簡介

The library provides a wide range of mathematical routines such as random number generators, special functions and least-squares fitting. There are over 1000 functions in total with an extensive test suite.

專案位置在http://www.gnu.org/software/gsl/

第一個範例:

#include <stdio.h>
#include <gsl/gsl_sf_bessel.h>

int
main (void)
{
  double x = 5.0;
  double y = gsl_sf_bessel_J0 (x);
  printf ("J0(%g) = %.18e\n", x, y);
  return 0;
}

編譯後執行可得到，

$ ./tutor01
J0(5) = -1.775967713143382920e-01

再試一個例子

#include <stdio.h>
#include <gsl/gsl_blas.h>

int
main (void)
{
  double a[] = { 0.11, 0.12, 0.13,
                 0.21, 0.22, 0.23 };

  double b[] = { 1011, 1012,
                 1021, 1022,
                 1031, 1032 };

  double c[] = { 0.00, 0.00,
                 0.00, 0.00 };

  gsl_matrix_view A = gsl_matrix_view_array(a, 2, 3);
  gsl_matrix_view B = gsl_matrix_view_array(b, 3, 2);
  gsl_matrix_view C = gsl_matrix_view_array(c, 2, 2);

  /* Compute C = A B */

  gsl_blas_dgemm (CblasNoTrans, CblasNoTrans,
                  1.0, &A.matrix, &B.matrix,
                  0.0, &C.matrix);

  printf ("[ %g, %g\n", c[0], c[1]);
  printf ("  %g, %g ]\n", c[2], c[3]);

  return 0;  
}

編譯執行後，

$ ./tutor02
[ 367.76, 368.12
674.06, 674.72 ]

再來一例，求解x^5=1 的根

#include <stdio.h>
#include <gsl/gsl_poly.h>

int
main (void)
{
  int i;
  /* coefficients of P(x) =  -1 + x^5  */
  double a[6] = { -1, 0, 0, 0, 0, 1 };  
  double z[10];

  gsl_poly_complex_workspace * w 
      = gsl_poly_complex_workspace_alloc (6);
  
  gsl_poly_complex_solve (a, 6, w, z);

  gsl_poly_complex_workspace_free (w);

  for (i = 0; i < 5; i++)
    {
      printf ("z%d = %+.18f %+.18f\n", 
              i, z[2*i], z[2*i+1]);
    }

  return 0;
}

編譯執行後可得

$ ./tutor03
z0 = -0.809016994374947229 +0.587785252292473137
z1 = -0.809016994374947229 -0.587785252292473137
z2 = +0.309016994374947562 +0.951056516295153531
z3 = +0.309016994374947562 -0.951056516295153531
z4 = +1.000000000000000222 +0.000000000000000000

完全是用之前提到的makefile 來編譯:

CFLAGS = -g -Wall -std=gnu99 -O3  
#LDLIBS= `pkg-config --libs gsl`
LDLIBS=-lgsl -lgslcblas -lm 
OBJECTS=
CC=gcc

$(P): $(OBJECTS)






#include <stdio.h>
#include <gsl/gsl_multiset.h>

int
main (void)
{
  gsl_multiset * c;
  size_t i;

  printf ("All multisets of {0,1,2,3} by size:\n") ;
  for (i = 0; i <= 4; i++)
    {
      c = gsl_multiset_calloc (4, i);
      do
        {
          printf ("{");
          gsl_multiset_fprintf (stdout, c, " %u");
          printf (" }\n");
        }
      while (gsl_multiset_next (c) == GSL_SUCCESS);
      gsl_multiset_free (c);
    }

  return 0;
}

編譯執行後

$ ./tutor04
All multisets of {0,1,2,3} by size:
{ }
{ 0 }
{ 1 }
{ 2 }
{ 3 }
{ 0 0 }
{ 0 1 }
{ 0 2 }
{ 0 3 }
{ 1 1 }

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本書是作者做科學計算時的一些C語言的實戰心得，

而常用的函式庫就是GSL