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eigen/unsupported/test/bessel_functions.cpp

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Add Bessel functions to SpecialFunctions. - Split SpecialFunctions files in to a separate BesselFunctions file. In particular add: - Modified bessel functions of the second kind k0, k1, k0e, k1e - Bessel functions of the first kind j0, j1 - Bessel functions of the second kind y0, y1
2019-09-15 00:16:47 +08:00
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#include "main.h"
#include "../Eigen/SpecialFunctions"
template<typename X, typename Y>
void verify_component_wise(const X& x, const Y& y)
{
for(Index i=0; i<x.size(); ++i)
{
if((numext::isfinite)(y(i))) {
VERIFY_IS_APPROX( x(i), y(i) );
}
else if((numext::isnan)(y(i)))
VERIFY((numext::isnan)(x(i)));
else
VERIFY_IS_EQUAL( x(i), y(i) );
}
}
template<typename ArrayType> void array_bessel_functions()
{
// Test Bessel function i0. Reference results obtained with SciPy.
{
ArrayType x(21);
ArrayType expected(21);
ArrayType res(21);
x << -20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0, -2.0, 0.0,
2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0;
expected << 4.35582826e+07, 6.21841242e+06, 8.93446228e+05, 1.29418563e+05,
1.89489253e+04, 2.81571663e+03, 4.27564116e+02, 6.72344070e+01,
1.13019220e+01, 2.27958530e+00, 1.00000000e+00, 2.27958530e+00,
1.13019220e+01, 6.72344070e+01, 4.27564116e+02, 2.81571663e+03,
1.89489253e+04, 1.29418563e+05, 8.93446228e+05, 6.21841242e+06,
4.35582826e+07;
CALL_SUBTEST(res = i0(x);
verify_component_wise(res, expected););
}
// Test Bessel function i0e. Reference results obtained with SciPy.
{
ArrayType x(21);
ArrayType expected(21);
ArrayType res(21);
x << -20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0, -2.0, 0.0,
2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0;
expected << 0.0897803118848, 0.0947062952128, 0.100544127361,
0.107615251671, 0.116426221213, 0.127833337163, 0.143431781857,
0.16665743264, 0.207001921224, 0.308508322554, 1.0, 0.308508322554,
0.207001921224, 0.16665743264, 0.143431781857, 0.127833337163,
0.116426221213, 0.107615251671, 0.100544127361, 0.0947062952128,
0.0897803118848;
CALL_SUBTEST(res = i0e(x);
verify_component_wise(res, expected););
}
// Test Bessel function i1. Reference results obtained with SciPy.
{
ArrayType x(21);
ArrayType expected(21);
ArrayType res(21);
x << -20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0, -2.0, 0.0,
2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0;
expected << -4.24549734e+07, -6.04313324e+06, -8.65059436e+05, -1.24707259e+05,
-1.81413488e+04, -2.67098830e+03, -3.99873137e+02, -6.13419368e+01,
-9.75946515e+00, -1.59063685e+00, 0.00000000e+00, 1.59063685e+00,
9.75946515e+00, 6.13419368e+01, 3.99873137e+02, 2.67098830e+03,
1.81413488e+04, 1.24707259e+05, 8.65059436e+05, 6.04313324e+06,
4.24549734e+07;
CALL_SUBTEST(res = i1(x);
verify_component_wise(res, expected););
}
// Test Bessel function i1e. Reference results obtained with SciPy.
{
ArrayType x(21);
ArrayType expected(21);
ArrayType res(21);
x << -20.0, -18.0, -16.0, -14.0, -12.0, -10.0, -8.0, -6.0, -4.0, -2.0, 0.0,
2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0, 20.0;
expected << -0.0875062221833, -0.092036796872, -0.0973496147565,
-0.103697667463, -0.11146429929, -0.121262681384, -0.134142493293,
-0.152051459309, -0.178750839502, -0.215269289249, 0.0, 0.215269289249,
0.178750839502, 0.152051459309, 0.134142493293, 0.121262681384,
0.11146429929, 0.103697667463, 0.0973496147565, 0.092036796872,
0.0875062221833;
CALL_SUBTEST(res = i1e(x);
verify_component_wise(res, expected););
}
// Test Bessel function j0. Reference results obtained with SciPy.
{
ArrayType x(77);
ArrayType expected(77);
ArrayType res(77);
x << -38., -37., -36., -35., -34., -33., -32., -31., -30.,
-29., -28., -27., -26., -25., -24., -23., -22., -21., -20., -19.,
-18., -17., -16., -15., -14., -13., -12., -11., -10., -9., -8.,
-7., -6., -5., -4., -3., -2., -1., 0., 1., 2., 3.,
4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14.,
15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36.,
37., 38.;
expected << 0.11433274, 0.01086237, -0.10556738,
-0.12684568, -0.03042119, 0.09727067, 0.13807901, 0.05120815,
-0.08636798, -0.14784876, -0.07315701, 0.07274192, 0.15599932,
0.09626678, -0.05623027, -0.16241278, -0.12065148, 0.03657907,
0.16702466, 0.14662944, -0.01335581, -0.16985425, -0.17489907,
-0.01422447, 0.17107348, 0.2069261 , 0.04768931, -0.1711903 ,
-0.24593576, -0.09033361, 0.17165081, 0.30007927, 0.15064526,
-0.17759677, -0.39714981, -0.26005195, 0.22389078, 0.76519769,
1. , 0.76519769, 0.22389078, -0.26005195, -0.39714981,
-0.17759677, 0.15064526, 0.30007927, 0.17165081, -0.09033361,
-0.24593576, -0.1711903 , 0.04768931, 0.2069261 , 0.17107348,
-0.01422447, -0.17489907, -0.16985425, -0.01335581, 0.14662944,
0.16702466, 0.03657907, -0.12065148, -0.16241278, -0.05623027,
0.09626678, 0.15599932, 0.07274192, -0.07315701, -0.14784876,
-0.08636798, 0.05120815, 0.13807901, 0.09727067, -0.03042119,
-0.12684568, -0.10556738, 0.01086237, 0.11433274;
CALL_SUBTEST(res = j0(x);
verify_component_wise(res, expected););
}
// Test Bessel function j1. Reference results obtained with SciPy.
{
ArrayType x(81);
ArrayType expected(81);
ArrayType res(81);
x << -40., -39., -38., -37., -36., -35., -34., -33., -32., -31., -30.,
-29., -28., -27., -26., -25., -24., -23., -22., -21., -20., -19.,
-18., -17., -16., -15., -14., -13., -12., -11., -10., -9., -8.,
-7., -6., -5., -4., -3., -2., -1., 0., 1., 2., 3.,
4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14.,
15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36.,
37., 38., 39., 40.;
expected << -0.12603832, -0.0640561 , 0.05916189, 0.13058004, 0.08232981,
-0.04399094, -0.13297118, -0.10061965, 0.02658903, 0.13302432,
0.11875106, -0.0069342 , -0.13055149, -0.13658472, -0.01504573,
0.12535025, 0.15403807, 0.03951932, -0.11717779, -0.17112027,
-0.06683312, 0.10570143, 0.18799489, 0.09766849, -0.09039718,
-0.20510404, -0.13337515, 0.07031805, 0.2234471 , 0.1767853 ,
-0.04347275, -0.24531179, -0.23463635, 0.00468282, 0.27668386,
0.32757914, 0.06604333, -0.33905896, -0.57672481, -0.44005059,
0. , 0.44005059, 0.57672481, 0.33905896, -0.06604333,
-0.32757914, -0.27668386, -0.00468282, 0.23463635, 0.24531179,
0.04347275, -0.1767853 , -0.2234471 , -0.07031805, 0.13337515,
0.20510404, 0.09039718, -0.09766849, -0.18799489, -0.10570143,
0.06683312, 0.17112027, 0.11717779, -0.03951932, -0.15403807,
-0.12535025, 0.01504573, 0.13658472, 0.13055149, 0.0069342 ,
-0.11875106, -0.13302432, -0.02658903, 0.10061965, 0.13297118,
0.04399094, -0.08232981, -0.13058004, -0.05916189, 0.0640561 ,
0.12603832;
CALL_SUBTEST(res = j1(x);
verify_component_wise(res, expected););
}
// Test Bessel function k0e. Reference results obtained with SciPy.
{
ArrayType x(42);
ArrayType expected(42);
ArrayType res(42);
x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.,
13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.,
39., 40.;
expected << 1.97933385, 1.52410939, 1.14446308, 0.84156822,
0.6977616 , 0.60929767, 0.54780756, 0.50186313, 0.4658451 ,
0.43662302, 0.41229555, 0.39163193, 0.3737955 , 0.35819488,
0.34439865, 0.33208364, 0.32100235, 0.31096159, 0.30180802,
0.29341821, 0.28569149, 0.27854488, 0.2719092 , 0.26572635,
0.25994703, 0.25452917, 0.2494366 , 0.24463801, 0.24010616,
0.23581722, 0.23175022, 0.22788667, 0.22421014, 0.22070602,
0.21736123, 0.21416406, 0.21110397, 0.20817141, 0.20535778,
0.20265524, 0.20005668, 0.19755558;
CALL_SUBTEST(res = k0e(x);
verify_component_wise(res, expected););
}
// Test Bessel function k0. Reference results obtained with SciPy.
{
ArrayType x(42);
ArrayType expected(42);
ArrayType res(42);
x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.,
13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.,
39., 40.;
expected << 1.54150675, 0.92441907, 4.21024438e-01, 1.13893873e-01,
3.47395044e-02, 1.11596761e-02, 3.69109833e-03, 1.24399433e-03,
4.24795742e-04, 1.46470705e-04, 5.08813130e-05, 1.77800623e-05,
6.24302055e-06, 2.20082540e-06, 7.78454386e-07, 2.76137082e-07,
9.81953648e-08, 3.49941166e-08, 1.24946640e-08, 4.46875334e-09,
1.60067129e-09, 5.74123782e-10, 2.06176797e-10, 7.41235161e-11,
2.66754511e-11, 9.60881878e-12, 3.46416156e-12, 1.24987740e-12,
4.51286453e-13, 1.63053459e-13, 5.89495073e-14, 2.13247750e-14,
7.71838266e-15, 2.79505752e-15, 1.01266123e-15, 3.67057597e-16,
1.33103515e-16, 4.82858338e-17, 1.75232770e-17, 6.36161716e-18,
2.31029936e-18, 8.39286110e-19;
CALL_SUBTEST(res = k0(x);
verify_component_wise(res, expected););
}
// Test Bessel function k0e. Reference results obtained with SciPy.
{
ArrayType x(42);
ArrayType expected(42);
ArrayType res(42);
x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.,
13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.,
39., 40.;
expected << 1.97933385, 1.52410939, 1.14446308, 0.84156822,
0.6977616 , 0.60929767, 0.54780756, 0.50186313,
0.4658451 , 0.43662302, 0.41229555, 0.39163193,
0.3737955 , 0.35819488, 0.34439865, 0.33208364,
0.32100235, 0.31096159, 0.30180802, 0.29341821,
0.28569149, 0.27854488, 0.2719092 , 0.26572635,
0.25994703, 0.25452917, 0.2494366 , 0.24463801,
0.24010616, 0.23581722, 0.23175022, 0.22788667,
0.22421014, 0.22070602, 0.21736123, 0.21416406,
0.21110397, 0.20817141, 0.20535778, 0.20265524,
0.20005668, 0.19755558;
CALL_SUBTEST(res = k0e(x);
verify_component_wise(res, expected););
}
// Test Bessel function k1. Reference results obtained with SciPy.
{
ArrayType x(42);
ArrayType expected(42);
ArrayType res(42);
x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.,
13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.,
39., 40.;
expected << 3.74702597, 1.65644112, 6.01907230e-01, 1.39865882e-01,
4.01564311e-02, 1.24834989e-02, 4.04461345e-03, 1.34391972e-03,
4.54182487e-04, 1.55369212e-04, 5.36370164e-05, 1.86487735e-05,
6.52086067e-06, 2.29075746e-06, 8.07858841e-07, 2.85834365e-07,
1.01417294e-07, 3.60715712e-08, 1.28570417e-08, 4.59124963e-09,
1.64226697e-09, 5.88305797e-10, 2.11029922e-10, 7.57898116e-11,
2.72493059e-11, 9.80699893e-12, 3.53277807e-12, 1.27369078e-12,
4.59568940e-13, 1.65940011e-13, 5.99574032e-14, 2.16773200e-14,
7.84189960e-15, 2.83839927e-15, 1.02789171e-15, 3.72416929e-16,
1.34991783e-16, 4.89519373e-17, 1.77585196e-17, 6.44478588e-18,
2.33973340e-18, 8.49713195e-19;
CALL_SUBTEST(res = k1(x);
verify_component_wise(res, expected););
}
// Test Bessel function k1e. Reference results obtained with SciPy.
{
ArrayType x(42);
ArrayType expected(42);
ArrayType res(42);
x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.,
13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.,
39., 40.;
expected << 4.81127659, 2.73100971, 1.63615349, 1.03347685,
0.80656348, 0.68157595, 0.60027386, 0.54217591,
0.49807158, 0.46314909, 0.43462525, 0.41076657,
0.39043094, 0.37283175, 0.35740757, 0.34374563,
0.33153489, 0.32053597, 0.31056123, 0.30146131,
0.29311559, 0.2854255 , 0.27830958, 0.27169987,
0.26553913, 0.25977879, 0.25437733, 0.249299 ,
0.24451285, 0.23999191, 0.2357126 , 0.23165413,
0.22779816, 0.22412841, 0.22063036, 0.21729103,
0.21409878, 0.21104314, 0.20811462, 0.20530466,
0.20260547, 0.20000997;
CALL_SUBTEST(res = k1e(x);
verify_component_wise(res, expected););
}
// Test Bessel function y0. Reference results obtained with SciPy.
{
ArrayType x(42);
ArrayType expected(42);
ArrayType res(42);
x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.,
13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.,
39., 40.;
expected << -0.93157302, -0.44451873, 0.08825696, 0.51037567, 0.37685001,
-0.01694074, -0.30851763, -0.28819468, -0.02594974, 0.22352149,
0.2499367 , 0.05567117, -0.16884732, -0.22523731, -0.07820786,
0.12719257, 0.2054643 , 0.095811 , -0.0926372 , -0.18755216,
-0.10951969, 0.0626406 , 0.17020176, 0.1198876 , -0.03598179,
-0.15283403, -0.12724943, 0.01204463, 0.13521498, 0.13183647,
0.00948116, -0.11729573, -0.13383266, -0.02874248, 0.09913483,
0.13340405, 0.04579799, -0.08085609, -0.13071488, -0.06066076,
0.06262353, 0.12593642;
CALL_SUBTEST(res = y0(x);
verify_component_wise(res, expected););
}
// Test Bessel function y1. Reference results obtained with SciPy.
{
ArrayType x(42);
ArrayType expected(42);
ArrayType res(42);
x << 0.25, 0.5, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.,
13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,
26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.,
39., 40.;
expected << -2.70410523, -1.47147239, -0.78121282, -0.10703243,
0.32467442, 0.39792571, 0.14786314, -0.17501034, -0.30266724,
-0.15806046, 0.10431458, 0.24901542, 0.16370554, -0.05709922,
-0.21008141, -0.16664484, 0.02107363, 0.17797517, 0.16720504,
0.00815513, -0.14956011, -0.16551161, -0.03253926, 0.12340586,
0.1616692 , 0.05305978, -0.09882996, -0.15579655, -0.07025124,
0.07552213, 0.14803412, 0.08442557, -0.05337283, -0.13854483,
-0.09578012, 0.03238588, 0.12751273, 0.10445477, -0.01262946,
-0.11514066, -0.11056411, -0.00579351;
CALL_SUBTEST(res = y1(x);
verify_component_wise(res, expected););
}
}
EIGEN_DECLARE_TEST(bessel_functions)
{
CALL_SUBTEST_1(array_bessel_functions<ArrayXf>());
CALL_SUBTEST_2(array_bessel_functions<ArrayXd>());
}
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