| // 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 = bessel_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 = bessel_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 = bessel_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 = bessel_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 = bessel_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 = bessel_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 = bessel_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 = bessel_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 = bessel_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 = bessel_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 = bessel_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 = bessel_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 = bessel_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>()); |
| } |
