/* interpolation/test.c

 * 

 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2014 Gerard Jungman

 * Copyright (C) 2014 Jean-François Caron

 * 

 * 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 3 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>

#include "test2d.c"

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 -");

  /* Test the accelerator */

  {

    size_t i, j, k1 = 0, k2 = 0;

    int t = 0;

    double x = 0;

    double r[16] = { -0.2, 0.0, 0.1, 0.7, 

                     1.0, 1.3, 1.9, 

                     2.0, 2.2, 2.7,

                     3.0, 3.1, 3.6,

                     4.0, 4.1, 4.9 };

    gsl_interp_accel *a = gsl_interp_accel_alloc ();

    /* Run through all the pairs of points */

    while (k1 < 16 && k2 < 16) {

      x = r[t ? k1 : k2];

      t = !t;

      if (t == 0) { 

        k1 = (k1 + 1) % 16; 

        if (k1 == 0) k2++;

      };

      i = gsl_interp_accel_find(a, x_array, 5, x);

      j = gsl_interp_bsearch(x_array, x, 0, 4);

      gsl_test(i != j, "(%u,%u) accelerated lookup vs bsearch (x = %g)", i, j, x);

    }

    gsl_interp_accel_free(a);

  }

  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);

  unsigned int min_size = gsl_interp_type_min_size(T);

  gsl_test_int (min_size, T->min_size, "gsl_interp_type_min_size on %s", gsl_interp_name(interp));

  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,

    0.130153674349869,

    0.141617770337492,

    0.153081866325116,

    0.164545962312740,

    0.185489128629005,

    0.206432294945271,

    0.227375461261537,

    0.237072082292243,

    0.246768703322951,

    0.256465324353657,

    0.295158618527324,

    0.333851912700991,

    0.372545206874658,

    0.421970143510346,

    0.471395080146033,

    0.520820016781720,

    0.563098250432172,

    0.605376484082623,

    0.647654717733075,

    0.682912914040164,

    0.718171110347252,

    0.753429306654340,

    0.802577532712113,

    0.851725758769885,

    0.900873984827658,

    0.933915989885105,

    0.966957994942553,

    1.000000000000000

  };

  double test_y[31] = { 

    0.000000000000000,

    0.268657574670719,

    0.517940878523929,

    0.729629261832041,

    0.777012551497867,

    0.820298314554859,

    0.859286331568207,

    0.918833991960315,

    0.962624749226346,

    0.989913099419008,

    0.996756196601349,

    0.999858105635752,

    0.999175006262120,

    0.959248551766306,

    0.863713527741856,

    0.717928599519215,

    0.470065187871106,

    0.177694938589523,

    -0.130443237213363,

    -0.385093922365765,

    -0.613840011545983,

    -0.800267961158980,

    -0.912498361131651,

    -0.980219217412290,

    -0.999767873040528,

    -0.943635958253643,

    -0.800314354800596,

    -0.583333769240853,

    -0.403689914131666,

    -0.206151346799382,

    -0.000000000000000

  };

  double test_dy[31] = { 

    6.275761975917336,

    6.039181349093287,

    5.382620652895025,

    4.306079887322550,

    3.957389777282752,

    3.591234754612763,

    3.207614819312586,

    2.473048186927024,

    1.702885029353488,

    0.897125346591982,

    0.513561009477969,

    0.125477545550710,

    -0.267125045189792,

    -1.773533414873785,

    -3.141450982859891,

    -4.370877749148106,

    -5.562104227060234,

    -6.171864888961167,

    -6.200159734850907,

    -5.781556055213110,

    -4.974725570010514,

    -3.779668279243120,

    -2.569220222282655,

    -1.254891157670244,

    0.163318914594122,

    2.074985916277011,

    3.711348850147548,

    5.072407716205733,

    5.754438923510391,

    6.155557010080926,

    6.275761975917336

  };

  double test_iy[31] = {

    0.000000000000000,

    0.005864903144198,

    0.023030998930796,

    0.050262495763030,

    0.058902457844100,

    0.068062330564832,

    0.077693991819461,

    0.096340576055474,

    0.116070578226521,

    0.136546192283223,

    0.146181187290769,

    0.155864434185569,

    0.165559443629720,

    0.203636318965633,

    0.239075190181586,

    0.269828050745236,

    0.299428805999600,

    0.315560685785616,

    0.316734151903742,

    0.305773798930857,

    0.284537037103156,

    0.254466034797342,

    0.224146112780097,

    0.190643050847000,

    0.155590744566140,

    0.107448508851745,

    0.064263083957312,

    0.029987183298960,

    0.013618510529526,

    0.003506827320794,

    0.000090064010007,

  };

  xy_table data_table = make_xy_table(data_x, data_y, 11);

  xy_table test_table = make_xy_table(test_x, test_y, 31);

  xy_table test_d_table = make_xy_table(test_x, test_dy, 31);

  xy_table test_i_table = make_xy_table(test_x, test_iy, 31);

  s = test_interp (&data_table, gsl_interp_cspline_periodic, &test_table, &test_d_table, &test_i_table);

  gsl_test (s, "cspline periodic sine interpolation");

  return s;

}

static int

test_csplinep2 (void)

{

  /* This data tests the periodic case n=3 */

  int s;

  double data_x[3] = {   

    0.123,

    0.423,

    1.123

  };

  double data_y[3] = {   

    0.456000000000000,

    1.407056516295154,

    0.456000000000000

  } ;

  double test_x[61] = {

    0.123000000000000,

    0.133000000000000,

    0.143000000000000,

    0.153000000000000,

    0.163000000000000,

    0.173000000000000,

    0.183000000000000,

    0.193000000000000,

    0.203000000000000,

    0.213000000000000,

    0.223000000000000,

    0.233000000000000,

    0.243000000000000,

    0.253000000000000,

    0.263000000000000,

    0.273000000000000,

    0.283000000000000,

    0.293000000000000,

    0.303000000000000,

    0.313000000000000,

    0.323000000000000,

    0.333000000000000,

    0.343000000000000,

    0.353000000000000,

    0.363000000000000,

    0.373000000000000,

    0.383000000000000,

    0.393000000000000,

    0.403000000000000,

    0.413000000000000,

    0.423000000000000,

    0.446333333333333,

    0.469666666666667,

    0.493000000000000,

    0.516333333333333,

    0.539666666666667,

    0.563000000000000,

    0.586333333333333,

    0.609666666666667,

    0.633000000000000,

    0.656333333333333,

    0.679666666666667,

    0.703000000000000,

    0.726333333333333,

    0.749666666666667,

    0.773000000000000,

    0.796333333333333,

    0.819666666666667,

    0.843000000000000,

    0.866333333333333,

    0.889666666666667,

    0.913000000000000,

    0.936333333333333,

    0.959666666666667,

    0.983000000000000,

    1.006333333333333,

    1.029666666666667,

    1.053000000000000,

    1.076333333333333,

    1.099666666666667,

    1.123000000000000

  };

  double test_y[61] = { 

    0.456000000000000,

    0.475443822110923,

    0.497423794931967,

    0.521758764840979,

    0.548267578215809,

    0.576769081434305,

    0.607082120874316,

    0.639025542913690,

    0.672418193930275,

    0.707078920301921,

    0.742826568406475,

    0.779479984621787,

    0.816858015325704,

    0.854779506896076,

    0.893063305710751,

    0.931528258147577,

    0.969993210584403,

    1.008277009399078,

    1.046198500969450,

    1.083576531673367,

    1.120229947888679,

    1.155977595993233,

    1.190638322364879,

    1.224030973381464,

    1.255974395420838,

    1.286287434860848,

    1.314788938079344,

    1.341297751454174,

    1.365632721363187,

    1.387612694184230,

    1.407056516295154,

    1.442092968697928,

    1.463321489456714,

    1.471728359403224,

    1.468299859369172,

    1.454022270186272,

    1.429881872686237,

    1.396864947700781,

    1.355957776061616,

    1.308146638600458,

    1.254417816149018,

    1.195757589539010,

    1.133152239602149,

    1.067588047170148,

    1.000051293074719,

    0.931528258147577,

    0.863005223220435,

    0.795468469125006,

    0.729904276693004,

    0.667298926756143,

    0.608638700146136,

    0.554909877694696,

    0.507098740233537,

    0.466191568594372,

    0.433174643608916,

    0.409034246108881,

    0.394756656925981,

    0.391328156891929,

    0.399735026838439,

    0.420963547597225,

    0.456000000000000

  };

  double test_dy[61] = { 

    1.8115362215145774,

    2.0742089736341924,

    2.3187663635386602,

    2.5452083912279826,

    2.7535350567021584,

    2.9437463599611897,

    3.1158423010050744,

    3.2698228798338147,

    3.4056880964474079,

    3.5234379508458549,

    3.6230724430291570,

    3.7045915729973125,

    3.7679953407503231,

    3.8132837462881874,

    3.8404567896109061,

    3.8495144707184790,

    3.8404567896109061,

    3.8132837462881874,

    3.7679953407503231,

    3.7045915729973125,

    3.6230724430291565,

    3.5234379508458549,

    3.4056880964474074,

    3.2698228798338147,

    3.1158423010050749,

    2.9437463599611897,

    2.7535350567021584,

    2.5452083912279830,

    2.3187663635386597,

    2.0742089736341924,

    1.8115362215145772,

    1.1986331332354823,

    0.6279992234583869,

    0.0996344921833026,

    -0.3864610605897765,

    -0.8302874348608467,

    -1.2318446306299125,

    -1.5911326478969707,

    -1.9081514866620208,

    -2.1829011469250670,

    -2.4153816286861041,

    -2.6055929319451341,

    -2.7535350567021584,

    -2.8592080029571765,

    -2.9226117707101862,

    -2.9437463599611893,

    -2.9226117707101862,

    -2.8592080029571760,

    -2.7535350567021593,

    -2.6055929319451354,

    -2.4153816286861045,

    -2.1829011469250656,

    -1.9081514866620242,

    -1.5911326478969716,

    -1.2318446306299160,

    -0.8302874348608498,

    -0.3864610605897769,

    0.0996344921832995,

    0.6279992234583824,

    1.1986331332354769,

    1.8115362215145772

  };

  double test_iy[61] = {

    0.000000000000000,

    0.004655030170954,

    0.009517330277919,

    0.014611356059886,

    0.019959751719625,

    0.025583349923681,

    0.031501171802382,

    0.037730426949832,

    0.044286513423914,

    0.051183017746288,