test.c

This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY without ev

/* interpolation/test.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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
 */


/* Author:  G. Jungman
 */
#include <config.h>
#include <stddef.h>
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <gsl/gsl_test.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_interp.h>
#include <gsl/gsl_ieee_utils.h>

int
test_bsearch(void)
{
  double x_array[5] = { 0.0, 1.0, 2.0, 3.0, 4.0 };
  size_t index_result;
  int status = 0;
  int s;

  /* check an interior point */
  index_result = gsl_interp_bsearch(x_array, 1.5, 0, 4);
  s = (index_result != 1);
  status += s;
  gsl_test (s, "simple bsearch");

  /* check that we get the last interval if x == last value */
  index_result = gsl_interp_bsearch(x_array, 4.0, 0, 4);
  s = (index_result != 3);
  status += s;
  gsl_test (s, "upper endpoint bsearch");

  /* check that we get the first interval if x == first value */
  index_result = gsl_interp_bsearch(x_array, 0.0, 0, 4);
  s = (index_result != 0);
  status += s;
  gsl_test (s, "lower endpoint bsearch");

  /* check that we get correct interior boundary behaviour */
  index_result = gsl_interp_bsearch(x_array, 2.0, 0, 4);
  s = (index_result != 2);
  status += s;
  gsl_test (s, "degenerate bsearch");

  /* check out of bounds above */
  index_result = gsl_interp_bsearch(x_array, 10.0, 0, 4);
  s = (index_result != 3);
  status += s;
  gsl_test (s, "out of bounds bsearch +");

  /* check out of bounds below */
  index_result = gsl_interp_bsearch(x_array, -10.0, 0, 4);
  s = (index_result != 0);
  status += s;
  gsl_test (s, "out of bounds bsearch -");

  return status;
}



typedef double TEST_FUNC (double);
typedef struct _xy_table xy_table;

struct _xy_table
  {
    double * x;
    double * y;
    size_t n;
  };

xy_table make_xy_table (double x[], double y[], size_t n);

xy_table
make_xy_table (double x[], double y[], size_t n)
{
  xy_table t;
  t.x = x;
  t.y = y;
  t.n = n;
  return t;
}

static int
test_interp (
  const xy_table * data_table,
  const gsl_interp_type * T,
  xy_table * test_table,
  xy_table * test_d_table,
  xy_table * test_i_table
  )
{
  int status = 0, s1, s2, s3;
  size_t i;

  gsl_interp_accel *a = gsl_interp_accel_alloc ();
  gsl_interp *interp = gsl_interp_alloc (T, data_table->n);

  gsl_interp_init (interp, data_table->x, data_table->y, data_table->n);

  for (i = 0; i < test_table->n; i++)
    {
      double x = test_table->x[i];
      double y;
      double deriv;
      double integ;
      double diff_y, diff_deriv, diff_integ;
      s1 = gsl_interp_eval_e (interp, data_table->x, data_table->y, x, a, &y);
      s2 = gsl_interp_eval_deriv_e (interp, data_table->x, data_table->y, x, a, &deriv);
      s3 = gsl_interp_eval_integ_e (interp, data_table->x, data_table->y, test_table->x[0], x, a, &integ);

      gsl_test (s1, "gsl_interp_eval_e %s", gsl_interp_name(interp));
      gsl_test (s2, "gsl_interp_eval_deriv_e %s", gsl_interp_name(interp));
      gsl_test (s3, "gsl_interp_eval_integ_e %s", gsl_interp_name(interp));

      gsl_test_abs (y, test_table->y[i], 1e-10, "%s %d", gsl_interp_name(interp), i);
      gsl_test_abs (deriv, test_d_table->y[i], 1e-10, "%s deriv %d", gsl_interp_name(interp), i);
      gsl_test_abs (integ, test_i_table->y[i], 1e-10, "%s integ %d", gsl_interp_name(interp), i);

      diff_y = y - test_table->y[i];
      diff_deriv = deriv - test_d_table->y[i];
      diff_integ = integ - test_i_table->y[i];
      if (fabs (diff_y) > 1.e-10 || fabs(diff_deriv) > 1.0e-10 || fabs(diff_integ) > 1.0e-10) {
        status++;
      }
    }

  gsl_interp_accel_free (a);
  gsl_interp_free (interp);

  return status;
}

static int
test_linear (void)
{
  int s;

  double data_x[4] = { 0.0, 1.0, 2.0, 3.0 };
  double data_y[4] = { 0.0, 1.0, 2.0, 3.0 };
  double test_x[6] = { 0.0, 0.5, 1.0, 1.5, 2.5, 3.0 };
  double test_y[6] = { 0.0, 0.5, 1.0, 1.5, 2.5, 3.0 };
  double test_dy[6] = { 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 };
  double test_iy[6] = { 0.0, 0.125, 0.5, 9.0/8.0, 25.0/8.0, 9.0/2.0 };

  xy_table data_table = make_xy_table(data_x, data_y, 4);
  xy_table test_table = make_xy_table(test_x, test_y, 6);
  xy_table test_d_table = make_xy_table(test_x, test_dy, 6);
  xy_table test_i_table = make_xy_table(test_x, test_iy, 6);

  s = test_interp (&data_table, gsl_interp_linear, &test_table, &test_d_table, &test_i_table);
  gsl_test (s, "linear interpolation");
  return s;
}

static int
test_polynomial (void)
{
  int s;

  double data_x[4] = { 0.0, 1.0, 2.0, 3.0 };
  double data_y[4] = { 0.0, 1.0, 2.0, 3.0 };
  double test_x[6] = { 0.0, 0.5, 1.0, 1.5, 2.5, 3.0 };
  double test_y[6] = { 0.0, 0.5, 1.0, 1.5, 2.5, 3.0 };
  double test_dy[6] = { 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 };
  double test_iy[6] = { 0.0, 0.125, 0.5, 9.0/8.0, 25.0/8.0, 9.0/2.0 };

  xy_table data_table = make_xy_table(data_x, data_y, 4);
  xy_table test_table = make_xy_table(test_x, test_y, 6);
  xy_table test_d_table = make_xy_table(test_x, test_dy, 6);
  xy_table test_i_table = make_xy_table(test_x, test_iy, 6);

  s = test_interp (&data_table, gsl_interp_polynomial, &test_table, &test_d_table, &test_i_table);
  gsl_test (s, "polynomial interpolation");
  return s;
}


static int
test_cspline (void)
{
  int s;

  double data_x[3] = { 0.0, 1.0, 2.0 };
  double data_y[3] = { 0.0, 1.0, 2.0 };
  double test_x[4] = { 0.0, 0.5, 1.0, 2.0 };
  double test_y[4] = { 0.0, 0.5, 1.0, 2.0 };
  double test_dy[4] = { 1.0, 1.0, 1.0, 1.0 };
  double test_iy[4] = { 0.0, 0.125, 0.5, 2.0 };

  xy_table data_table = make_xy_table(data_x, data_y, 3);
  xy_table test_table = make_xy_table(test_x, test_y, 4);
  xy_table test_d_table = make_xy_table(test_x, test_dy, 4);
  xy_table test_i_table = make_xy_table(test_x, test_iy, 4);

  s = test_interp (&data_table, gsl_interp_cspline, &test_table, &test_d_table, &test_i_table);
  gsl_test (s, "cspline interpolation");
  return s;
}

static int
test_cspline2 (void)
{
  /* Test taken from Young & Gregory, A Survey of Numerical
     Mathematics, Vol 1 Chapter 6.8 */
  
  int s;

  double data_x[6] = { 0.0, 0.2, 0.4, 0.6, 0.8, 1.0 };

  double data_y[6] = { 1.0, 
                       0.961538461538461, 0.862068965517241, 
                       0.735294117647059, 0.609756097560976, 
                       0.500000000000000 } ;

  double test_x[50] = {  
    0.00, 0.02, 0.04, 0.06, 0.08, 0.10, 0.12, 0.14, 0.16, 0.18, 
    0.20, 0.22, 0.24, 0.26, 0.28, 0.30, 0.32, 0.34, 0.36, 0.38, 
    0.40, 0.42, 0.44, 0.46, 0.48, 0.50, 0.52, 0.54, 0.56, 0.58, 
    0.60, 0.62, 0.64, 0.66, 0.68, 0.70, 0.72, 0.74, 0.76, 0.78,
    0.80, 0.82, 0.84, 0.86, 0.88, 0.90, 0.92, 0.94, 0.96, 0.98 };

  double test_y[50] = { 
    1.000000000000000, 0.997583282975581, 0.995079933416512, 
    0.992403318788142, 0.989466806555819, 0.986183764184894, 
    0.982467559140716, 0.978231558888635, 0.973389130893999, 
    0.967853642622158, 0.961538461538461, 0.954382579685350, 
    0.946427487413627, 0.937740299651188, 0.928388131325928, 
    0.918438097365742, 0.907957312698524, 0.897012892252170, 
    0.885671950954575, 0.874001603733634, 0.862068965517241, 
    0.849933363488199, 0.837622973848936, 0.825158185056786, 
    0.812559385569085, 0.799846963843167, 0.787041308336369, 
    0.774162807506023, 0.761231849809467, 0.748268823704033, 
    0.735294117647059, 0.722328486073082, 0.709394147325463, 
    0.696513685724764, 0.683709685591549, 0.671004731246381, 
    0.658421407009825, 0.645982297202442, 0.633709986144797, 
    0.621627058157454, 0.609756097560976, 0.598112015427308, 
    0.586679029833925, 0.575433685609685, 0.564352527583445, 
    0.553412100584061, 0.542588949440392, 0.531859618981294, 
    0.521200654035625, 0.510588599432241};

  double test_dy[50] = { 
    -0.120113913432180, -0.122279726798445, -0.128777166897241,
    -0.139606233728568, -0.154766927292426, -0.174259247588814,
    -0.198083194617734, -0.226238768379184, -0.258725968873165,
    -0.295544796099676, -0.336695250058719, -0.378333644186652,
    -0.416616291919835, -0.451543193258270, -0.483114348201955,
    -0.511329756750890, -0.536189418905076, -0.557693334664512,
    -0.575841504029200, -0.590633926999137, -0.602070603574326,
    -0.611319695518765, -0.619549364596455, -0.626759610807396,
    -0.632950434151589, -0.638121834629033, -0.642273812239728,
    -0.645406366983674, -0.647519498860871, -0.648613207871319,
    -0.648687494015019, -0.647687460711257, -0.645558211379322,
    -0.642299746019212, -0.637912064630930, -0.632395167214473,
    -0.625749053769843, -0.617973724297039, -0.609069178796061,
    -0.599035417266910, -0.587872439709585, -0.576731233416743,
    -0.566762785681043, -0.557967096502484, -0.550344165881066,
    -0.543893993816790, -0.538616580309654, -0.534511925359660,
    -0.531580028966807, -0.529820891131095};

  double test_iy[50] = {
    0.000000000000000, 0.019975905023535, 0.039902753768792, 
    0.059777947259733, 0.079597153869625, 0.099354309321042, 
    0.119041616685866, 0.138649546385285, 0.158166836189794, 
    0.177580491219196, 0.196875783942601, 0.216036382301310,
    0.235045759060558, 0.253888601161251, 0.272550937842853,
    0.291020140643388, 0.309284923399436, 0.327335342246135,
    0.345162795617181, 0.362760024244829, 0.380121111159890,
    0.397241442753010, 0.414117280448683, 0.430745332379281,
    0.447122714446318, 0.463246950320456, 0.479115971441505,
    0.494728117018421, 0.510082134029305, 0.525177177221407,
    0.540012809111123, 0.554589001813881, 0.568906157172889,
    0.582965126887879, 0.596767214344995, 0.610314174616794,
    0.623608214462242, 0.636651992326715, 0.649448618342004,
    0.662001654326309, 0.674315113784241, 0.686393423540581,
    0.698241001711602, 0.709861835676399, 0.721259443710643,
    0.732436874986582, 0.743396709573044, 0.754141058435429,
    0.764671563435718, 0.774989397332469 };

  xy_table data_table = make_xy_table(data_x, data_y, 6);
  xy_table test_table = make_xy_table(test_x, test_y, 50);
  xy_table test_d_table = make_xy_table(test_x, test_dy, 50);
  xy_table test_i_table = make_xy_table(test_x, test_iy, 50);

  s = test_interp (&data_table, gsl_interp_cspline, &test_table, &test_d_table, &test_i_table);
  gsl_test (s, "cspline 1/(1+x^2) interpolation");
  return s;
}

static int
test_cspline3 (void)
{
  /* This data has been chosen to be random (uneven spacing in x and y)
     and the exact cubic spine solution computed using Octave */
  
  int s;
  
  double data_x[7] = {   
    -1.2139767065644265,
    -0.792590494453907,
    -0.250954683125019,
    0.665867809951305,
    0.735655088722706,
    0.827622053027153,
    1.426592227816582  
  };

  double data_y[7] = {   
    -0.00453877449035645,
    0.49763182550668716,
    0.17805472016334534,
    0.40514493733644485,
    -0.21595209836959839,
    0.47405586764216423,
    0.46561462432146072
  } ;

  double test_x[19] = {
    -1.2139767065644265,
    -1.0735146358609200,
    -0.9330525651574135,
    -0.7925904944539071,
    -0.6120452240109444,
    -0.4314999535679818,
    -0.2509546831250191,
    0.0546528145670890,
    0.3602603122591972,
    0.6658678099513053,
    0.6891302362084388,
    0.7123926624655723,
    0.7356550887227058,
    0.7663107434908548,
    0.7969663982590039,
    0.8276220530271530,
    1.0272787779569625,
    1.2269355028867721,
    1.4265922278165817,
  };

  double test_y[19] = { 
    -0.00453877449035645,
    0.25816917628390590,
    0.44938881397673230,
    0.49763182550668716,
    0.31389980410075147,
    0.09948951681196887,
    0.17805472016334534,
    1.27633142487980233,
    2.04936553432792001,
    0.40514493733644485,
    0.13322324792901385,
    -0.09656315924697809,
    -0.21595209836959839,
    -0.13551147728045118,
    0.13466779030061801,
    0.47405586764216423,
    1.68064089899304370,
    1.43594739539458649,
    0.46561462432146072
  };

  double test_dy[19] = { 
    1.955137555965937,
    1.700662049790549,
    0.937235531264386,
    -0.335141999612553,
    -1.401385073563169,
    -0.674982149482761,
    1.844066772628670,
    4.202528085784793,
    -0.284432022227558,
    -11.616813551408383,
    -11.272731243226174,
    -7.994209291156876,
    -1.781247695200491,
    6.373970868827501,
    10.597456848997197,
    10.889210245308570,
    1.803124267866902,
    -3.648527318598099,
    -5.465744514086432,
  };

  double test_iy[19] = {
    0.000000000000000,
    0.018231117234914,
    0.069178822023139,
    0.137781019634897,
    0.213936442847744,
    0.249280997744777,
    0.267492946016120,
    0.471372708120518,
    1.014473660088477,
    1.477731933018837,
    1.483978291717981,
    1.484256847945450,
    1.480341742628893,
    1.474315901028282,
    1.473972210647307,
    1.483279773396950,
    1.728562698140330,
    2.057796448999396,
    2.253662886537457,
  };

  xy_table data_table = make_xy_table(data_x, data_y, 7);
  xy_table test_table = make_xy_table(test_x, test_y, 19);
  xy_table test_d_table = make_xy_table(test_x, test_dy, 19);
  xy_table test_i_table = make_xy_table(test_x, test_iy, 19);

  s = test_interp (&data_table, gsl_interp_cspline, &test_table, &test_d_table, &test_i_table);
  gsl_test (s, "cspline arbitrary data interpolation");
  return s;
}

static int
test_csplinep (void)
{
  /* This data has been chosen to be random (uneven spacing in x and y)
     and the exact cubic spine solution computed using Octave */
  
  int s;
  
  double data_x[11] = {   
    0.000000000000000,
    0.130153674349869,
    0.164545962312740,
    0.227375461261537,
    0.256465324353657,
    0.372545206874658,
    0.520820016781720,
    0.647654717733075,
    0.753429306654340,
    0.900873984827658,
    1.000000000000000,
  };

  double data_y[11] = {   
    0.000000000000000,
    0.729629261832041,
    0.859286331568207,
    0.989913099419008,
    0.999175006262120,
    0.717928599519215,
    -0.130443237213363,
    -0.800267961158980,
    -0.999767873040527,
    -0.583333769240853,
    -0.000000000000000,
  } ;

  double test_x[31] = {
    0.000000000000000,
    0.043384558116623,
    0.086769116233246,