/* 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,
0.058431714902395,
0.066042568341453,
0.074023729976459,
0.082381540184189,
0.091120527805195,
0.100243410143811,
0.109751092968147,
0.119642670510092,
0.129915425465314,
0.140564828993259,
0.151584540717153,
0.162966408723997,
0.174700469564574,
0.186774948253444,
0.199176258268946,
0.211889001553197,
0.224895968512091,
0.238178138015305,
0.251714677396289,
0.265482942452275,
0.279458477444273,
0.312726362409309,
0.346648754292945,
0.380914974633193,
0.415237358187469,
0.449351252932597,
0.483015020064806,
0.516010033999735,
0.548140682372425,
0.579234366037328,
0.609141499068300,
0.637735508758604,
0.664912835620912,
0.690592933387298,
0.714718269009247,
0.737254322657649,
0.758189587722801,
0.777535570814405,
0.795326791761572,
0.811620783612819,
0.826498092636068,
0.840062278318649,
0.852439913367300,
0.863780583708163,
0.874256888486789,
0.884064440068133,
0.893421864036559,
0.902570799195836,
0.911775897569142,
0.921324824399059,
0.931528258147577
};
xy_table data_table = make_xy_table(data_x, data_y, 3);
xy_table test_table = make_xy_table(test_x, test_y, 61);
xy_table test_d_table = make_xy_table(test_x, test_dy, 61);
xy_table test_i_table = make_xy_table(test_x, test_iy, 61);
s = test_interp (&data_table, gsl_interp_cspline_periodic, &test_table, &test_d_table, &test_i_table);
gsl_test (s, "cspline periodic 3pt interpolation");
return s;
}
static int
test_akima (void)
{
int s;
double data_x[5] = { 0.0, 1.0, 2.0, 3.0, 4.0 };
double data_y[5] = { 0.0, 1.0, 2.0, 3.0, 4.0 };
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, 5);
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_akima, &test_table, &test_d_table, &test_i_table);
gsl_test (s, "akima interpolation");
return s;
}
static int
test_steffen1 (void)
{
int s;
double data_x[5] = { 0.0, 1.0, 2.0, 3.0, 4.0 };
double data_y[5] = { 0.0, 1.0, 2.0, 3.0, 4.0 };
double test_x[6] = { 0.0, 0.5, 1.0, 2.0, 2.5, 3.95 };
double test_y[6] = { 0.0, 0.5, 1.0, 2.0, 2.5, 3.95 };
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, 2.0, 3.125, 7.80125 };
xy_table data_table = make_xy_table(data_x, data_y, 5);
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_steffen, &test_table, &test_d_table, &test_i_table);
gsl_test (s, "steffen interpolation test 1");
return s;
}
static int
test_steffen2 (void)
{
int s;
double data_x[30] = {
4.673405471947611, 4.851675778029557, 6.185473620119991,
7.066003430727031, 7.236222118389267, 7.82067161881444,
8.054504031621493, 8.615033792800752, 9.16666529764867,
9.442092828126395, 10.719577968900381, 11.741967577609238,
12.564881194673035, 12.938424721515084, 12.985892202096888,
13.995771653255744, 14.459157783380315, 15.834857667614848,
15.887779086499942, 18.64645279534696, 19.256361741244287,
19.85100457105047, 19.943627313550987, 20.5033910115468,
20.895380493234843, 21.759942483053962, 21.948984866760803,
22.2504057728461, 22.741860290952104, 23.088720630939164 };
double data_y[30] = {
-6.131584089652438, 4.997132870704837, 9.50359639889188,
-3.788474042493764, 1.98825324341826, -6.553460294945401,
8.44565760012345, -3.643687601520438, -4.720262269613782,
-5.31956608504474, 4.7484698519996655, 1.8191111043001218,
2.7234424260251124, -7.282776099988966, -6.966038807035955,
2.6047260012112545, -3.6363485275348033, -4.124714595822157,
-4.820986899771757, -2.8550035950284602, 6.017204757558943,
6.7275899382734075, -9.423359755713639, -0.3645325139870703,
6.925739188986089, -0.07843256857855074, 1.6744315603866244,
-8.332083151442944, 6.059246349756446, -7.360159198725659 };
double test_x[129] = {
4.6734054719476106,4.8516757780295574,4.8575586235375265,
5.0417117751274407,5.2258649267173567,5.4100180783072727,
5.5941712298971886,5.7783243814871028,5.9624775330770188,
6.1466306846669347,6.1854736201199909,6.3307838362568507,
6.5149369878467667,6.6990901394366809,6.8832432910265968,
7.0660034307270312,7.0673964426165128,7.236222118389267,
7.2515495942064288,7.4357027457963438,7.6198558973862589,
7.8040090489761749,7.8206716188144396,7.9881622005660908,
8.0545040316214926,8.172315352156005,8.356468503745921,
8.5406216553358369,8.6150337928007517,8.7247748069257529,
8.9089279585156689,9.0930811101055831,9.1666652976486702,
9.277234261695499,9.4420928281263947,9.461387413285415,
9.645540564875331,9.8296937164652469,10.013846868055161,
10.198000019645077,10.382153171234993,10.566306322824907,
10.719577968900381,10.750459474414823,10.934612626004739,
11.118765777594655,11.302918929184571,11.487072080774485,
11.671225232364399,11.741967577609238,11.855378383954315,
12.039531535544231,12.223684687134147,12.407837838724063,
12.564881194673035,12.591990990313979,12.776144141903895,
12.938424721515084,12.960297293493811,12.985892202096888,
13.144450445083727,13.328603596673641,13.512756748263556,
13.696909899853472,13.881063051443387,13.995771653255744,
14.065216203033303,14.249369354623219,14.433522506213134,
14.459157783380315,14.617675657803051,14.801828809392966,
14.985981960982881,15.170135112572796,15.354288264162712,
15.538441415752628,15.722594567342544,15.834857667614848,
15.90674771893246,15.887779086499942,16.090900870522375,
16.27505402211229,16.459207173702204,16.643360325292122,
16.827513476882036,17.01166662847195,17.195819780061868,
17.379972931651782,17.5641260832417,17.748279234831614,
17.932432386421532,18.116585538011446,18.300738689601364,
18.484891841191278,18.64645279534696,18.669044992781188,
18.853198144371106,19.03735129596102,19.221504447550938,
19.256361741244287,19.405657599140852,19.58981075073077,
19.773963902320684,19.851004571050471,19.958117053910598,
19.943627313550987,20.142270205500516,20.32642335709043,
20.5033910115468,20.510576508680348,20.694729660270262,
20.87888281186018,20.895380493234843,21.063035963450094,
21.247189115040012,21.431342266629926,21.61549541821984,
21.759942483053962,21.799648569809754,21.948984866760803,
21.983801721399669,22.167954872989586,22.250405772846101,
22.352108024579501,22.536261176169418,22.720414327759332,
22.741860290952104,22.90456747934925,23.088720630939164 };
double test_y[129] = {
-6.1315840896524376, 4.9971328707048368, 5.0367975988827167,
6.1897906340782765, 7.170975366812117, 7.9803517970842286,
8.6179199248946077, 9.083679750243256, 9.3776312731301772,
9.4997744935553676, 9.5035963988918795, 8.5371013292095554,
5.3135045284256019, 1.2120062346303317, -2.3083133782071208,
-3.788474042493764, -3.7873197326712797, 1.98825324341826,
1.9709370138809248, -0.31768851396215103, -4.2211558425051745,
-6.5330277558649303, -6.5534602949454008, 5.5087083141507147,
8.4456576001234502, 7.1443430435268214, 1.9932653799771245,
-2.8426372908118083, -3.6436876015204378, -3.9926784426485034,
-4.3315242293057175, -4.5849882013553547, -4.7202622696137819,
-5.0157009305506106, -5.3195660850447402, -5.3127453670702938,
-4.6348437675141847, -3.1014810884327102, -1.0745634258401102,
1.0840031242494419, 3.0123124658217071, 4.3484585028624627,
4.7484698519996655, 4.740613456600772, 4.4142234654988952,
3.7574719541934956, 2.9757785771330334, 2.274562988765974,
1.8592448435407634, 1.8191111043001218, 1.8659054809992697,
2.0883298868527498, 2.3859686670095699, 2.6372078307738107,
2.7234424260251124, 2.5729816013335247, -3.258105131647655,
-7.2827760999889657, -7.179945071809863, -6.9660388070359547,
-5.5662805880783406, -3.3905902235190721, -1.0497645733987406,
1.0095869363327665, 2.3408548797255095, 2.6047260012112545,
2.2325150500282476, -0.91241316251151927, -3.5649171021138555,
-3.6363485275348033, -3.7309363021244821, -3.8038342533632736,
-3.8503835649797429, -3.8846412514674595, -3.920664327319995,
-3.9725098070309213, -4.0542347050938083, -4.1247145958221569,
-4.8208939493861829, -4.8209868997717571, -4.8103284962540727,
-4.7822416973267625, -4.7366335526042516, -4.6735040620865389,
-4.5928532257736272, -4.4946810436655156, -4.3789875157622005,
-4.2457726420636881, -4.0950364225699714, -3.9267788572810582,
-3.7409999461969403, -3.537699689317626, -3.3168780866431069,
-3.0785351381733914, -2.8550035950284602, -2.7914506045621672,
-0.46968123806956008, 3.263658433044764, 5.8622198554846658,
6.0172047575589431, 6.3291356295622618, 6.5905310151592165,
6.7156659481449141, 6.7275899382734075, -9.4118959280855066,
-9.4233597557136388, -7.6111870705157543, -3.9651685725226056,
-0.36453251398707032, -0.23537781181431175, 4.0332797539781309,
6.899794364641159, 6.9257391889860891, 6.2377210430025594,
4.3902665602806792, 2.1878722453596344, 0.44278317319805183,
-0.078432568578550743, 0.12107113682074738, 1.6744315603866244,
1.3047436323966959, -6.4955024539509765, -8.3320831514429443,
-6.7382472104931805, 0.61052993339902706, 5.9794239504090552,
6.0592463497564459, 1.5387265272596853, -7.3601591987256612 };
double test_dy[129] = {
62.426083204466224, 6.757341159173202, 6.727537246743899,
5.7945730211610407, 4.8616087955781726, 3.9286445699953054,
2.9956803444124378, 2.0627161188295791, 1.1297518932467119,
0.1967876676638447, 0, -12.480296842307126,
-21.209126982426163, -22.014768399615317, -14.897221093874615,
0, 1.65274069980919, 0,
-2.2393981239975669, -19.714311699236049, -19.77742868994725,
-2.4287490961310456, 0, 78.213312807624717,
0, -20.358420305108574, -31.350476855816961,
-16.93545425712459, -3.9032385156832157, -2.5401833171916435,
-1.3740294011308083, -1.6128919418291603, -2.1012124848241789,
-2.8800570317456784, 0, 0.70341285683675259,
6.3314138906742139, 9.9941697310971538, 11.69168037810557,
11.42394583169949, 9.1909660918788916, 4.992741158643824,
0, -0.50358091648162351, -2.8552721239834269,
-4.0914806331173992, -4.2122064438835425, -3.2174495562818706,
-1.1072099703123885, 0, 0.78347408424733667,
1.5221058615312819, 1.6003417148468082, 1.018181644193916,
0, -10.817925943273289, -39.490030870551372,
0, 8.0126635338650072, 6.7986203849007927,
10.557804177353285, 12.667135433334296, 12.351260158262027,
9.6101783521364421, 4.44389001495753, 0,
-10.1306309231183, -19.882866043398995, -4.7826445467139278,
-0.70998925548225966, -0.49283947499262398, -0.31159279753453034,
-0.20667940230488324, -0.17809928930368468, -0.22585245853093405,
-0.3499389099866323, -0.55035864367077902, -0.70998925548225966,
0.0098004308855327432, 0, 0.10494594234665755,
0.20009145380778143, 0.2952369652689053, 0.39038247673003107,
0.48552798819115495, 0.58067349965227877, 0.67581901111340459,
0.77096452257452841, 0.86611003403565412, 0.96125554549677805,
1.0564010569579039, 1.1515465684190276, 1.2466920798801533,
1.3418375913412772, 1.4253105022449177, 4.1661049863071913,
18.74497348837053, 19.496500284294363, 6.4206853740787171,
2.3892836005304425, 1.7894106566060179, 1.0494805960296585,
0.30955053545331346, 0, 1.5724451183167569,
0, 16.386389851530527, 21.613477536080744,
17.603560096681914, 18.338573561497682, 23.697110333020628,
3.1105642331329868, 0, -7.5982202651552164,
-11.73098890423519, -11.453053366134201, -6.7644136508523696,
0, 9.2309078320594402, 0,
-20.350273706124355, -39.581660196515507, 0,
28.835095151183879, 42.753317235684989, 7.3325239511975031,
0, -47.053315974301256, -38.688209637869583 };
double test_iy[129] = {
0, 0.046311303303274043, 0.07582542065258166,
1.1121678097008914, 2.345017979757877, 3.7427368904558875,
5.2736855014272832, 6.9062247723044061, 8.6087156627196464,
10.349519132305348, 10.718617229125304, 12.051326255780914,
13.351310568583624, 13.954434023333466, 13.833375399536308,
13.23478503216295, 13.229508179502936, 13.081569421202504,
13.111955459764134, 13.313565584429645, 12.895822708651364,
11.856586384851303, 11.747502930901248, 11.477166081331394,
11.968731461589641, 12.910617813249443, 13.783041410703255,
13.664096839344904, 13.416752727534579, 12.996373500853053,
12.226613834386363, 11.406286934906419, 11.064147626707395,
10.526693424249395, 9.6682418398824055, 9.5656469982362644,
8.633802142647145, 7.911116775692733, 7.5218036771498298,
7.5234294786346014, 7.9069146636026106, 8.5965335673487839,
9.3034583640488648, 9.4500169740341917, 10.299608964240058,
11.055524261651918, 11.675840089542856, 12.156462347951148,
12.53112561368027, 12.660771626086403, 12.868892222896084,
13.230897278463143, 13.642654271367054, 14.106816365848598,
14.529836204259333, 14.602291235557717, 14.620235691106975,
13.678281413948246, 13.51979351456291, 13.338827208895861,
12.337400222501822, 11.506721190837634, 11.098761199438101,
11.102808164918775, 11.425905470576772, 11.714428553431798,
11.886459852625201, 12.035570442032403, 11.580639494361572,
11.488113239473538, 10.903735363611753, 10.209447282562856,
9.5043766268555689, 8.7920812597559994, 8.0735304010092825,
7.347104626839644, 6.6085958699503662, 6.1496664193039994,
5.821344166329677, 5.9127911070795323, 4.9342652985615576,
4.050745397809842, 3.1740110751228041, 2.3072889415487108,
1.4538056081358768, 0.61678768593257072, -0.20053821401294236,
-0.99494548065234767, -1.7632075029373926, -2.5020976698197641,
-3.2083893702512087, -3.8788559931834152, -4.5102709275681283,
-5.0994075623570394, -5.5789032190742072, -5.6428026999265457,
-5.9842769011998804, -5.729140886963938, -4.8519085924998322,
-4.6444581063590329, -3.7217151397093993, -2.5300254086689806,
-1.3027452894525609, -0.78475347239267057, -1.0460847630211827,
-0.90959826921338605, -2.6553766359304607, -3.7360597404585745,
-4.1087031972797643, -4.1108616867222691, -3.776307276733156,
-2.7114490122334045, -2.5973338374383879, -1.4760729895576692,
-0.48580494729501034, 0.11910209432525942, 0.34807359178739627,
0.36262668088219696, 0.3622604193055981, 0.51348240778475363,
0.56740090208414018, 0.14380211642697149, -0.48989527970345625,
-1.2810928311228711, -1.8846453955503084, -1.1777647142370817,
-1.0483932372566702, -0.32646483194908105, -0.88612247621927298 };
xy_table data_table = make_xy_table(data_x, data_y, 30);
xy_table test_table = make_xy_table(test_x, test_y, 129);
xy_table test_d_table = make_xy_table(test_x, test_dy, 129);
xy_table test_i_table = make_xy_table(test_x, test_iy, 129);
s = test_interp (&data_table, gsl_interp_steffen, &test_table, &test_d_table, &test_i_table);
gsl_test (s, "steffen interpolation test 2");
return s;
}
int
main (int argc, char **argv)
{
int status = 0;
gsl_ieee_env_setup ();
argc = 0; /* prevent warnings about unused parameters */
argv = 0;
status += test_bsearch();
status += test_linear();
status += test_polynomial();
status += test_cspline();
status += test_cspline2();
status += test_cspline3();
status += test_csplinep();
status += test_csplinep2();
status += test_akima();
status += test_steffen1();
status += test_steffen2();
status += test_interp2d_main();
exit (gsl_test_summary());
}