test_legendre.c

开放gsl矩阵运算

/* specfunc/test_legendre.c
 * 
 * Copyright (C) 1996, 1997, 1998, 1999, 2000 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];
  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);
  sa += ( test_sf_frac_diff(L[0],    1.0 ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(L[10],  -0.18822860717773437500 ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(L[100], -0.06051802596186118687 ) > TEST_TOL0 );
  gsl_test(sa, "  gsl_sf_legendre_Pl_array(100)");
  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_array(100, 5, 0.5, L);
  sa += ( test_sf_frac_diff(L[0],  -460.3466286991656682 ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(L[10],  38852.51334152290535 ) > TEST_TOL0 );
  sa += ( test_sf_frac_diff(L[95],  6.617107444248382171e+08 ) > TEST_TOL0 );
  gsl_test(sa, "  gsl_sf_legendre_Plm_array(100, 5, 0.5)");
  s += sa;

  TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 0, -0.5, &r), -0.24332702369300133776, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 0, 0.5, &r), -0.24332702369300133776, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 0, 0.999, &r), 1.2225754122797385990, TEST_TOL1, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 5, -0.5, &r),    -0.3725739049803293972,     TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 5, 1.0e-08, &r), -3.1377233589376792243e-08, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 5, 0.5, &r),      0.3725739049803293972,     TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 5, 0.999, &r),   -6.236870674727370094e-06,  TEST_TOL2, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 10, -0.5, &r), 0.12876871185785724117, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 10, 0.5, &r), 0.12876871185785724117,  TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_sphPlm_e, (10, 10, 0.999, &r), 1.7320802307583118647e-14, TEST_TOL2, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_legendre_sphPlm_e, (200, 1, -0.5, &r),   0.3302975570099492931, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_sphPlm_e, (200, 1, 0.5, &r),   -0.3302975570099492931, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_legendre_sphPlm_e, (200, 1, 0.999, &r), -1.4069792055546256912, TEST_TOL2, GSL_SUCCESS);

  sa = 0;
  gsl_sf_legendre_sphPlm_array(100, 5, 0.5, L);
  sa += ( test_sf_frac_diff(L[0],   -0.22609703187800460722 ) > TEST_TOL2 );
  sa += ( test_sf_frac_diff(L[10],   0.07452710323813558940 ) > TEST_TOL2 );
  sa += ( test_sf_frac_diff(L[95],   0.25865355990880161717 ) > TEST_TOL2 );
  gsl_test(s, "  gsl_sf_legendre_sphPlm_array(100, 5, 0.5)");
  s += sa;

  TEST_SF(s, gsl_sf_conicalP_half_e, (0.0, -0.5, &r),   0.8573827581049917129, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_half_e, (0.0,  0.5, &r),   0.8573827581049917129, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_half_e, (0.0,  2.0, &r),   0.6062611623284649811, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_half_e, (0.0,  100.0, &r), 0.07979045091636735635, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_conicalP_half_e, (10.0, -0.5, &r),    5.345484922591867188e+08, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_half_e, (10.0,  0.5, &r),    15137.910380385258370, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_half_e, (10.0,  2.0, &r),    0.4992680691891618544, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_half_e, (10.0,  100.0, &r), -0.07272008163718195685, TEST_TOL2, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_conicalP_half_e, (200.0, -1.0e-3, &r),  1.3347639529084185010e+136, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_half_e, (200.0,  1.0e-8, &r),  1.0928098010940058507e+136, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_half_e, (200.0,  0.5, &r),     3.895546021611205442e+90,   TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_half_e, (200.0,  10.0, &r),   -0.04308567180833581268,     TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_half_e, (200.0,  100.0, &r),  -0.04694669186576399194,     TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_half_e, (200.0,  1000.0, &r),  0.023698140704121273277,    TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_half_e, (200.0,  1.0e+8, &r), -0.00006790983312124277891,  TEST_TOL3, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_conicalP_half_e, (1.0e+8,  1.1, &r),   1.1599311133054742944,  TEST_SQRT_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_half_e, (1.0e+8,  100.0, &r), 0.07971967557381557875, TEST_SQRT_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (0.0, -0.5, &r),  1.7956982494514644808, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (0.0,  0.5, &r),  0.8978491247257322404, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (0.0,  2.0, &r),  0.7984204253272901551, TEST_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (0.0,  100.0, &r),  0.4227531369388072584, TEST_TOL0, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (10.0, -0.5, &r),  5.345484922591867181e+07, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (10.0,  0.5, &r),  1513.7910356104985334, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (10.0,  2.0, &r),  0.03439243987215615642, TEST_TOL1, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (10.0,  100.0, &r),  0.003283756665952609624, TEST_TOL2, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (200.0, -0.5, &r),  1.7699538115312304280e+179, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (200.0,  1.0e-8, &r),  5.464049005470029253e+133, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (200.0,  0.5, &r),  1.9477730108056027211e+88, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (200.0,  10.0, &r),  0.0012462575917716355362, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (200.0,  100.0, &r),  -0.0003225881344802625149, TEST_TOL2, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (200.0,  1000.0, &r), -0.00004330652890886567623, TEST_TOL3, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (200.0,  1.0e+8, &r),  2.0943091278037078483e-07, TEST_TOL3, GSL_SUCCESS);

  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (1.0e+8,  1.1, &r), 2.092320445620989618e-09, 16.0*TEST_SQRT_TOL0, GSL_SUCCESS);
  TEST_SF(s, gsl_sf_conicalP_mhalf_e, (1.0e+8,  100.0, &r),  -3.359967833599016923e-11, 256.0*TEST_SQRT_TOL0, GSL_SUCCESS);