test_legendre.c

该文件为c++的数学函数库!是一个非常有用的编程工具.它含有各种数学函数,为科学计算、工程应用等程序编写提供方便！

/* specfunc/test_legendre.c
 * 
 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002 Gerard Jungman
 * 
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or (at
 * your option) any later version.
 * 
 * This program is distributed in the hope that it will be useful, but
 * WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * General Public License for more details.
 * 
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
 */

/* Author:  G. Jungman */

#include <config.h>
#include <gsl/gsl_test.h>
#include <gsl/gsl_sf.h>
#include "test_sf.h"


int test_legendre(void)
{
  gsl_sf_result r;
  double L[256], DL[256];
  int s = 0;
  int sa;

  TEST_SF(s,  gsl_sf_legendre_P1_e, (-0.5, &r), -0.5, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_legendre_P1_e, ( 0.5, &r), 0.5, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_legendre_P2_e, (0.0, &r), -0.5  , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_legendre_P2_e, (0.5, &r), -0.125, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_legendre_P2_e, (1.0, &r), 1.0  , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_legendre_P2_e, (100.0, &r), 14999.5  , TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s,  gsl_sf_legendre_P3_e, ( -0.5, &r), 0.4375, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_legendre_P3_e, (  0.5, &r), -0.4375, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_legendre_P3_e, (  1.0, &r), 1.0        , TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s,  gsl_sf_legendre_P3_e, (100.0, &r), 2.49985e+06, TEST_TOL0, GSL_SUCCESS);


  TEST_SF(s, gsl_sf_legendre_Pl_e, (1, -0.5, &r), -0.5, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_Pl_e, (1,  1.0e-8, &r), 1.0e-08, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_Pl_e, (1,  0.5, &r), 0.5, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_Pl_e, (1,  1.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS);
 
  TEST_SF(s, gsl_sf_legendre_Pl_e, (10, -0.5, &r), -0.1882286071777345, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_Pl_e, (10,  1.0e-8, &r), -0.24609374999999864648, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_Pl_e, (10,  0.5, &r), -0.18822860717773437500, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_Pl_e, (10,  1.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_legendre_Pl_e, (99, -0.5, &r), 0.08300778172138770477, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_Pl_e, (99,  1.0e-8, &r), -7.958923738716563193e-08, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_Pl_e, (99,  0.5, &r), -0.08300778172138770477, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_Pl_e, (99,  0.999, &r), -0.3317727359254778874, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_Pl_e, (99,  1.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_legendre_Pl_e, (1000, -0.5, &r),   -0.019168251091650277878, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_Pl_e, (1000,  1.0e-8, &r), 0.02522501817709828,     TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_Pl_e, (1000,  0.5, &r),   -0.019168251091650277878, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_Pl_e, (1000,  1.0, &r),    1.0,                     TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_legendre_Pl_e, (4000, -0.5, &r), -0.009585404456573080972, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_Pl_e, (4000,  0.5, &r), -0.009585404456573080972, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_Pl_e, (4000,  1.0, &r), 1.0, TEST_TOL0, GSL_SUCCESS);

  sa = 0;
  gsl_sf_legendre_Pl_array(100, 0.5, L);
  TEST_SF_VAL(sa, L[0],   +0.0,   1.0, TEST_TOL1);
  TEST_SF_VAL(sa, L[10],  +0.0,  -0.18822860717773437500, TEST_TOL1);
  TEST_SF_VAL(sa, L[100], +0.0,  -0.06051802596186118687, TEST_TOL1);
  gsl_test(sa, "gsl_sf_legendre_Pl_array(100, 0.5)");
  s += sa;

  sa = 0;
  gsl_sf_legendre_Pl_deriv_array(100, 0.5, L, DL);
  TEST_SF_VAL(sa, DL[0],   +0.0,   0.0, TEST_TOL1);
  TEST_SF_VAL(sa, DL[1],   +0.0,   1.0, TEST_TOL1);
  TEST_SF_VAL(sa, DL[10],  +0.0,  -2.3171234130859375000, TEST_TOL1);
  TEST_SF_VAL(sa, DL[100], +0.0,  -7.0331691653942815112, TEST_TOL1);
  gsl_test(sa, "gsl_sf_legendre_Pl_deriv_array(100, 0.5)");
  s += sa;
  sa = 0;

  gsl_sf_legendre_Pl_deriv_array(10, 1.0, L, DL);
  TEST_SF_VAL(sa, DL[0],   +0.0,   0.0, TEST_TOL1);
  TEST_SF_VAL(sa, DL[1],   +0.0,   1.0, TEST_TOL1);
  TEST_SF_VAL(sa, DL[10],  +0.0,  55.0, TEST_TOL1);
  gsl_test(sa, "gsl_sf_legendre_Pl_deriv_array(10, 1.0)");
  s += sa;

  gsl_sf_legendre_Pl_deriv_array(10, 1.0 - 1.0e-11, L, DL);
  TEST_SF_VAL(sa, DL[0],   +0.0,   0.0, TEST_TOL1);
  TEST_SF_VAL(sa, DL[1],   +0.0,   1.0, TEST_TOL1);
  TEST_SF_VAL(sa, DL[10],  +0.0,  54.999999985150000001, TEST_TOL1);
  gsl_test(sa, "gsl_sf_legendre_Pl_deriv_array(10, 1.0 - 1.0e-11)");
  s += sa;

  gsl_sf_legendre_Pl_deriv_array(10, -1.0, L, DL);
  TEST_SF_VAL(sa, DL[0],   +0.0,   0.0, TEST_TOL1);
  TEST_SF_VAL(sa, DL[1],   +0.0,   1.0, TEST_TOL1);
  TEST_SF_VAL(sa, DL[10],  +0.0, -55.0, TEST_TOL1);
  gsl_test(sa, "gsl_sf_legendre_Pl_deriv_array(10, -1.0)");
  s += sa;

  gsl_sf_legendre_Pl_deriv_array(10, -1.0 + 1.0e-11, L, DL);
  TEST_SF_VAL(sa, DL[0],   +0.0,   0.0, TEST_TOL1);
  TEST_SF_VAL(sa, DL[1],   +0.0,   1.0, TEST_TOL1);
  TEST_SF_VAL(sa, DL[10],  +0.0, -54.999999985150000001, TEST_TOL1);
  gsl_test(sa, "gsl_sf_legendre_Pl_deriv_array(10, -1.0 + 1.0e-11)");
  s += sa;


  TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 0, -0.5, &r), -0.18822860717773437500, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 0, 1.0e-08, &r), -0.24609374999999864648, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 0, 0.5, &r), -0.18822860717773437500, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 1, -0.5, &r), -2.0066877394361256516, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 1, 1.0e-08, &r), -2.7070312499999951725e-07, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 1, 0.5, &r), 2.0066877394361256516, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 5, -0.5, &r),    -30086.169706116174977,    TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 5, 1.0e-08, &r), -0.0025337812499999964949, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 5, 0.5, &r),      30086.169706116174977,    TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_Plm_e, (10, 5, 0.999, &r),   -0.5036411489013270406,    TEST_TOL1, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_legendre_Plm_e, (100, 5, -0.5, &r), -6.617107444248382171e+08, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_Plm_e, (100, 5, 1.0e-08, &r), 817.8987598063712851, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_Plm_e, (100, 5, 0.5, &r), 6.617107444248382171e+08, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_Plm_e, (100, 5, 0.999, &r), -1.9831610803806212189e+09, TEST_TOL2, GSL_SUCCESS);


  sa = 0;
  gsl_sf_legendre_Plm_deriv_array(100, 2, -1.0 + 1.0/1125899906842624.0, L, DL);
  TEST_SF_VAL(sa, L[0],   +0.0,  5.3290705182007490275e-15, TEST_TOL1);
  TEST_SF_VAL(sa, L[1],   +0.0, -2.6645352591003721471e-14, TEST_TOL1);
  TEST_SF_VAL(sa, L[98],  +0.0,  2.2646284847349109694e-08, TEST_TOL2);
  gsl_test(sa, "gsl_sf_legendre_Plm_deriv_array(100, 2, -1.0 + 2^(-50)");
  s += sa;

  sa = 0;
  gsl_sf_legendre_Plm_deriv_array(100, 2, 1.0 - 1.0/1125899906842624.0, L, DL);
  TEST_SF_VAL(sa, L[0],   +0.0,  5.3290705182007490275e-15, TEST_TOL1);
  TEST_SF_VAL(sa, L[1],   +0.0,  2.6645352591003721471e-14, TEST_TOL1);
  TEST_SF_VAL(sa, L[10],  +0.0,  5.3343995887188313290e-12, TEST_TOL1);
  TEST_SF_VAL(sa, L[98],  +0.0,  2.2646284847349109694e-08, TEST_TOL2);
  gsl_test(sa, "gsl_sf_legendre_Plm_deriv_array(100, 2, 1.0 - 2^(-50)");
  s += sa;

  sa = 0;
  gsl_sf_legendre_Plm_array(100, 5, 0.5, L);
  TEST_SF_VAL(sa, L[0],  +0.0, -460.3466286991656682, TEST_TOL1);
  TEST_SF_VAL(sa, L[10], +0.0,  38852.51334152290535, TEST_TOL1 );
  TEST_SF_VAL(sa, L[95], +0.0,  6.617107444248382171e+08, TEST_TOL1);
  gsl_test(sa, "gsl_sf_legendre_Plm_array(100, 5, 0.5)");
  s += sa;

  sa = 0;
  gsl_sf_legendre_Plm_array(100, 5, 0.999, L);
  TEST_SF_VAL(sa, L[0],  +0.0,  -0.00016883550990916552255, TEST_TOL2);
  TEST_SF_VAL(sa, L[10], +0.0,  -30.651334850159821525, TEST_TOL2 );
  TEST_SF_VAL(sa, L[95], +0.0,  -1.9831610803806212189e+09, TEST_TOL2);
  gsl_test(sa, "gsl_sf_legendre_Plm_array(100, 5, 0.999)");
  s += sa;

  sa = 0;
  gsl_sf_legendre_Plm_array(100, 5, -0.999, L);
  TEST_SF_VAL(sa, L[0],  +0.0,  -0.00016883550990916552255, TEST_TOL2);
  TEST_SF_VAL(sa, L[10], +0.0,  -30.651334850159821525, TEST_TOL2 );
  TEST_SF_VAL(sa, L[95], +0.0,   1.9831610803806212189e+09, TEST_TOL2);
  gsl_test(sa, "gsl_sf_legendre_Plm_array(100, 5, -0.999)");
  s += sa;