eigen/unsupported/test/bessel_functions.cpp

// 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>());
}