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jeremybenn |
// 2007-02-04 Edward Smith-Rowland <3dw4rd@verizon.net>
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//
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// Copyright (C) 2007, 2009 Free Software Foundation, Inc.
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//
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// This file is part of the GNU ISO C++ Library. This library is free
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// software; you can redistribute it and/or modify it under the
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// terms of the GNU General Public License as published by the
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// Free Software Foundation; either version 3, or (at your option)
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// any later version.
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//
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// This library is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU General Public License along
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// with this library; see the file COPYING3. If not see
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// <http://www.gnu.org/licenses/>.
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// sph_legendre
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// Compare against values generated by the GNU Scientific Library.
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// The GSL can be found on the web: http://www.gnu.org/software/gsl/
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#include <tr1/cmath>
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#if defined(__TEST_DEBUG)
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#include <iostream>
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#define VERIFY(A) \
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if (!(A)) \
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{ \
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std::cout << "line " << __LINE__ \
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<< " max_abs_frac = " << max_abs_frac \
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<< std::endl; \
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}
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#else
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#include <testsuite_hooks.h>
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#endif
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#include "../testcase.h"
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// Test data for l=0, m=0.
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testcase_sph_legendre<double> data001[] = {
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{ 0.28209479177387814, 0, 0,
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0.0000000000000000 },
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{ 0.28209479177387814, 0, 0,
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0.15707963267948966 },
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{ 0.28209479177387814, 0, 0,
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0.31415926535897931 },
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{ 0.28209479177387814, 0, 0,
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0.47123889803846897 },
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{ 0.28209479177387814, 0, 0,
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0.62831853071795862 },
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{ 0.28209479177387814, 0, 0,
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0.78539816339744828 },
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{ 0.28209479177387814, 0, 0,
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0.94247779607693793 },
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{ 0.28209479177387814, 0, 0,
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1.0995574287564276 },
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{ 0.28209479177387814, 0, 0,
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1.2566370614359172 },
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{ 0.28209479177387814, 0, 0,
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1.4137166941154069 },
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{ 0.28209479177387814, 0, 0,
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1.5707963267948966 },
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{ 0.28209479177387814, 0, 0,
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1.7278759594743860 },
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{ 0.28209479177387814, 0, 0,
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1.8849555921538759 },
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{ 0.28209479177387814, 0, 0,
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2.0420352248333655 },
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{ 0.28209479177387814, 0, 0,
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2.1991148575128552 },
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{ 0.28209479177387814, 0, 0,
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2.3561944901923448 },
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{ 0.28209479177387814, 0, 0,
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2.5132741228718345 },
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{ 0.28209479177387814, 0, 0,
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2.6703537555513241 },
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{ 0.28209479177387814, 0, 0,
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2.8274333882308138 },
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{ 0.28209479177387814, 0, 0,
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2.9845130209103035 },
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{ 0.28209479177387814, 0, 0,
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3.1415926535897931 },
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};
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// Test function for l=0, m=0.
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template <typename Tp>
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void test001()
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{
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const Tp eps = std::numeric_limits<Tp>::epsilon();
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Tp max_abs_diff = -Tp(1);
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Tp max_abs_frac = -Tp(1);
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unsigned int num_datum = sizeof(data001)
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/ sizeof(testcase_sph_legendre<double>);
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for (unsigned int i = 0; i < num_datum; ++i)
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{
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const Tp f = std::tr1::sph_legendre(Tp(data001[i].l), Tp(data001[i].m),
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Tp(data001[i].theta));
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const Tp f0 = data001[i].f0;
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const Tp diff = f - f0;
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if (std::abs(diff) > max_abs_diff)
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max_abs_diff = std::abs(diff);
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if (std::abs(f0) > Tp(10) * eps
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&& std::abs(f) > Tp(10) * eps)
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{
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const Tp frac = diff / f0;
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if (std::abs(frac) > max_abs_frac)
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max_abs_frac = std::abs(frac);
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}
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}
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VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
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}
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// Test data for l=1, m=0.
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testcase_sph_legendre<double> data002[] = {
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{ 0.48860251190291992, 1, 0,
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0.0000000000000000 },
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{ 0.48258700419201100, 1, 0,
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0.15707963267948966 },
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{ 0.46468860282345231, 1, 0,
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0.31415926535897931 },
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{ 0.43534802584032634, 1, 0,
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0.47123889803846897 },
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{ 0.39528773562374975, 1, 0,
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0.62831853071795862 },
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{ 0.34549414947133544, 1, 0,
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0.78539816339744828 },
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{ 0.28719335072959390, 1, 0,
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0.94247779607693793 },
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{ 0.22182089855280451, 1, 0,
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1.0995574287564276 },
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{ 0.15098647967228984, 1, 0,
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1.2566370614359172 },
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{ 0.076434272566846345, 1, 0,
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1.4137166941154069 },
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{ 2.9918275112863369e-17, 1, 0,
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1.5707963267948966 },
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{ -0.076434272566846179, 1, 0,
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1.7278759594743860 },
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{ -0.15098647967228976, 1, 0,
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1.8849555921538759 },
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{ -0.22182089855280446, 1, 0,
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2.0420352248333655 },
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{ -0.28719335072959390, 1, 0,
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2.1991148575128552 },
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{ -0.34549414947133544, 1, 0,
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2.3561944901923448 },
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{ -0.39528773562374969, 1, 0,
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2.5132741228718345 },
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{ -0.43534802584032628, 1, 0,
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2.6703537555513241 },
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{ -0.46468860282345231, 1, 0,
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2.8274333882308138 },
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{ -0.48258700419201095, 1, 0,
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2.9845130209103035 },
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{ -0.48860251190291992, 1, 0,
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3.1415926535897931 },
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};
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// Test function for l=1, m=0.
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template <typename Tp>
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void test002()
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{
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const Tp eps = std::numeric_limits<Tp>::epsilon();
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Tp max_abs_diff = -Tp(1);
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Tp max_abs_frac = -Tp(1);
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unsigned int num_datum = sizeof(data002)
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/ sizeof(testcase_sph_legendre<double>);
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for (unsigned int i = 0; i < num_datum; ++i)
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{
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const Tp f = std::tr1::sph_legendre(Tp(data002[i].l), Tp(data002[i].m),
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Tp(data002[i].theta));
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const Tp f0 = data002[i].f0;
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const Tp diff = f - f0;
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if (std::abs(diff) > max_abs_diff)
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max_abs_diff = std::abs(diff);
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if (std::abs(f0) > Tp(10) * eps
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&& std::abs(f) > Tp(10) * eps)
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{
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const Tp frac = diff / f0;
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if (std::abs(frac) > max_abs_frac)
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max_abs_frac = std::abs(frac);
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}
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}
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VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
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}
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// Test data for l=1, m=1.
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testcase_sph_legendre<double> data003[] = {
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{ 0.0000000000000000, 1, 1,
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0.0000000000000000 },
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{ -0.054047192447077917, 1, 1,
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0.15707963267948966 },
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{ -0.10676356364376104, 1, 1,
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0.31415926535897931 },
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{ -0.15685106157558129, 1, 1,
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0.47123889803846897 },
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{ -0.20307636581258243, 1, 1,
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0.62831853071795862 },
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{ -0.24430125595146013, 1, 1,
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0.78539816339744828 },
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{ -0.27951063837942880, 1, 1,
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0.94247779607693793 },
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{ -0.30783754124787122, 1, 1,
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1.0995574287564276 },
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{ -0.32858446219656551, 1, 1,
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1.2566370614359172 },
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{ -0.34124054317667202, 1, 1,
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1.4137166941154069 },
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{ -0.34549414947133567, 1, 1,
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1.5707963267948966 },
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{ -0.34124054317667202, 1, 1,
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1.7278759594743860 },
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{ -0.32858446219656556, 1, 1,
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1.8849555921538759 },
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{ -0.30783754124787127, 1, 1,
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2.0420352248333655 },
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{ -0.27951063837942880, 1, 1,
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2.1991148575128552 },
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{ -0.24430125595146013, 1, 1,
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2.3561944901923448 },
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{ -0.20307636581258248, 1, 1,
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2.5132741228718345 },
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{ -0.15685106157558140, 1, 1,
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2.6703537555513241 },
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{ -0.10676356364376104, 1, 1,
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2.8274333882308138 },
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{ -0.054047192447078167, 1, 1,
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| 231 |
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2.9845130209103035 },
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| 232 |
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{ 0.0000000000000000, 1, 1,
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3.1415926535897931 },
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};
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// Test function for l=1, m=1.
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template <typename Tp>
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void test003()
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{
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const Tp eps = std::numeric_limits<Tp>::epsilon();
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Tp max_abs_diff = -Tp(1);
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Tp max_abs_frac = -Tp(1);
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unsigned int num_datum = sizeof(data003)
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/ sizeof(testcase_sph_legendre<double>);
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for (unsigned int i = 0; i < num_datum; ++i)
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{
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| 247 |
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const Tp f = std::tr1::sph_legendre(Tp(data003[i].l), Tp(data003[i].m),
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| 248 |
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Tp(data003[i].theta));
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const Tp f0 = data003[i].f0;
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| 250 |
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const Tp diff = f - f0;
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| 251 |
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if (std::abs(diff) > max_abs_diff)
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| 252 |
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max_abs_diff = std::abs(diff);
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if (std::abs(f0) > Tp(10) * eps
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| 254 |
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&& std::abs(f) > Tp(10) * eps)
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| 255 |
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{
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| 256 |
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const Tp frac = diff / f0;
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| 257 |
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if (std::abs(frac) > max_abs_frac)
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| 258 |
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max_abs_frac = std::abs(frac);
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| 259 |
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}
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| 260 |
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}
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| 261 |
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VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
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| 262 |
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}
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| 263 |
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| 264 |
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// Test data for l=2, m=0.
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| 265 |
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testcase_sph_legendre<double> data004[] = {
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| 266 |
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{ 0.63078313050504009, 2, 0,
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| 267 |
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0.0000000000000000 },
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| 268 |
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{ 0.60762858760316607, 2, 0,
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| 269 |
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0.15707963267948966 },
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| 270 |
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{ 0.54043148688396569, 2, 0,
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| 271 |
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0.31415926535897931 },
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| 272 |
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{ 0.43576954875556589, 2, 0,
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| 273 |
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0.47123889803846897 },
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| 274 |
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{ 0.30388781294457579, 2, 0,
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| 275 |
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0.62831853071795862 },
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| 276 |
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{ 0.15769578262625994, 2, 0,
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| 277 |
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0.78539816339744828 },
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| 278 |
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{ 0.011503752307944235, 2, 0,
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| 279 |
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0.94247779607693793 },
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| 280 |
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{ -0.12037798350304565, 2, 0,
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| 281 |
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1.0995574287564276 },
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| 282 |
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{ -0.22503992163144573, 2, 0,
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| 283 |
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1.2566370614359172 },
|
| 284 |
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{ -0.29223702235064597, 2, 0,
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| 285 |
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1.4137166941154069 },
|
| 286 |
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{ -0.31539156525252005, 2, 0,
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| 287 |
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1.5707963267948966 },
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| 288 |
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{ -0.29223702235064608, 2, 0,
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| 289 |
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1.7278759594743860 },
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| 290 |
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{ -0.22503992163144584, 2, 0,
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| 291 |
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1.8849555921538759 },
|
| 292 |
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{ -0.12037798350304577, 2, 0,
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| 293 |
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2.0420352248333655 },
|
| 294 |
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{ 0.011503752307944235, 2, 0,
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| 295 |
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2.1991148575128552 },
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| 296 |
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{ 0.15769578262625994, 2, 0,
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| 297 |
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2.3561944901923448 },
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| 298 |
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{ 0.30388781294457567, 2, 0,
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| 299 |
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2.5132741228718345 },
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| 300 |
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{ 0.43576954875556562, 2, 0,
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| 301 |
|
|
2.6703537555513241 },
|
| 302 |
|
|
{ 0.54043148688396569, 2, 0,
|
| 303 |
|
|
2.8274333882308138 },
|
| 304 |
|
|
{ 0.60762858760316585, 2, 0,
|
| 305 |
|
|
2.9845130209103035 },
|
| 306 |
|
|
{ 0.63078313050504009, 2, 0,
|
| 307 |
|
|
3.1415926535897931 },
|
| 308 |
|
|
};
|
| 309 |
|
|
|
| 310 |
|
|
// Test function for l=2, m=0.
|
| 311 |
|
|
template <typename Tp>
|
| 312 |
|
|
void test004()
|
| 313 |
|
|
{
|
| 314 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 315 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 316 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 317 |
|
|
unsigned int num_datum = sizeof(data004)
|
| 318 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 319 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 320 |
|
|
{
|
| 321 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data004[i].l), Tp(data004[i].m),
|
| 322 |
|
|
Tp(data004[i].theta));
|
| 323 |
|
|
const Tp f0 = data004[i].f0;
|
| 324 |
|
|
const Tp diff = f - f0;
|
| 325 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 326 |
|
|
max_abs_diff = std::abs(diff);
|
| 327 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 328 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 329 |
|
|
{
|
| 330 |
|
|
const Tp frac = diff / f0;
|
| 331 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 332 |
|
|
max_abs_frac = std::abs(frac);
|
| 333 |
|
|
}
|
| 334 |
|
|
}
|
| 335 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 336 |
|
|
}
|
| 337 |
|
|
|
| 338 |
|
|
// Test data for l=2, m=1.
|
| 339 |
|
|
testcase_sph_legendre<double> data005[] = {
|
| 340 |
|
|
{ 0.0000000000000000, 2, 1,
|
| 341 |
|
|
0.0000000000000000 },
|
| 342 |
|
|
{ -0.11936529291378727, 2, 1,
|
| 343 |
|
|
0.15707963267948966 },
|
| 344 |
|
|
{ -0.22704627929027449, 2, 1,
|
| 345 |
|
|
0.31415926535897931 },
|
| 346 |
|
|
{ -0.31250239392538215, 2, 1,
|
| 347 |
|
|
0.47123889803846897 },
|
| 348 |
|
|
{ -0.36736859691086526, 2, 1,
|
| 349 |
|
|
0.62831853071795862 },
|
| 350 |
|
|
{ -0.38627420202318979, 2, 1,
|
| 351 |
|
|
0.78539816339744828 },
|
| 352 |
|
|
{ -0.36736859691086526, 2, 1,
|
| 353 |
|
|
0.94247779607693793 },
|
| 354 |
|
|
{ -0.31250239392538226, 2, 1,
|
| 355 |
|
|
1.0995574287564276 },
|
| 356 |
|
|
{ -0.22704627929027435, 2, 1,
|
| 357 |
|
|
1.2566370614359172 },
|
| 358 |
|
|
{ -0.11936529291378740, 2, 1,
|
| 359 |
|
|
1.4137166941154069 },
|
| 360 |
|
|
{ -4.7304946510089748e-17, 2, 1,
|
| 361 |
|
|
1.5707963267948966 },
|
| 362 |
|
|
{ 0.11936529291378714, 2, 1,
|
| 363 |
|
|
1.7278759594743860 },
|
| 364 |
|
|
{ 0.22704627929027429, 2, 1,
|
| 365 |
|
|
1.8849555921538759 },
|
| 366 |
|
|
{ 0.31250239392538226, 2, 1,
|
| 367 |
|
|
2.0420352248333655 },
|
| 368 |
|
|
{ 0.36736859691086526, 2, 1,
|
| 369 |
|
|
2.1991148575128552 },
|
| 370 |
|
|
{ 0.38627420202318979, 2, 1,
|
| 371 |
|
|
2.3561944901923448 },
|
| 372 |
|
|
{ 0.36736859691086526, 2, 1,
|
| 373 |
|
|
2.5132741228718345 },
|
| 374 |
|
|
{ 0.31250239392538232, 2, 1,
|
| 375 |
|
|
2.6703537555513241 },
|
| 376 |
|
|
{ 0.22704627929027449, 2, 1,
|
| 377 |
|
|
2.8274333882308138 },
|
| 378 |
|
|
{ 0.11936529291378781, 2, 1,
|
| 379 |
|
|
2.9845130209103035 },
|
| 380 |
|
|
{ 0.0000000000000000, 2, 1,
|
| 381 |
|
|
3.1415926535897931 },
|
| 382 |
|
|
};
|
| 383 |
|
|
|
| 384 |
|
|
// Test function for l=2, m=1.
|
| 385 |
|
|
template <typename Tp>
|
| 386 |
|
|
void test005()
|
| 387 |
|
|
{
|
| 388 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 389 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 390 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 391 |
|
|
unsigned int num_datum = sizeof(data005)
|
| 392 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 393 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 394 |
|
|
{
|
| 395 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data005[i].l), Tp(data005[i].m),
|
| 396 |
|
|
Tp(data005[i].theta));
|
| 397 |
|
|
const Tp f0 = data005[i].f0;
|
| 398 |
|
|
const Tp diff = f - f0;
|
| 399 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 400 |
|
|
max_abs_diff = std::abs(diff);
|
| 401 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 402 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 403 |
|
|
{
|
| 404 |
|
|
const Tp frac = diff / f0;
|
| 405 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 406 |
|
|
max_abs_frac = std::abs(frac);
|
| 407 |
|
|
}
|
| 408 |
|
|
}
|
| 409 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 410 |
|
|
}
|
| 411 |
|
|
|
| 412 |
|
|
// Test data for l=2, m=2.
|
| 413 |
|
|
testcase_sph_legendre<double> data006[] = {
|
| 414 |
|
|
{ 0.0000000000000000, 2, 2,
|
| 415 |
|
|
0.0000000000000000 },
|
| 416 |
|
|
{ 0.0094528025561622549, 2, 2,
|
| 417 |
|
|
0.15707963267948966 },
|
| 418 |
|
|
{ 0.036885904048903795, 2, 2,
|
| 419 |
|
|
0.31415926535897931 },
|
| 420 |
|
|
{ 0.079613961366457681, 2, 2,
|
| 421 |
|
|
0.47123889803846897 },
|
| 422 |
|
|
{ 0.13345445455470123, 2, 2,
|
| 423 |
|
|
0.62831853071795862 },
|
| 424 |
|
|
{ 0.19313710101159492, 2, 2,
|
| 425 |
|
|
0.78539816339744828 },
|
| 426 |
|
|
{ 0.25281974746848851, 2, 2,
|
| 427 |
|
|
0.94247779607693793 },
|
| 428 |
|
|
{ 0.30666024065673203, 2, 2,
|
| 429 |
|
|
1.0995574287564276 },
|
| 430 |
|
|
{ 0.34938829797428600, 2, 2,
|
| 431 |
|
|
1.2566370614359172 },
|
| 432 |
|
|
{ 0.37682139946702747, 2, 2,
|
| 433 |
|
|
1.4137166941154069 },
|
| 434 |
|
|
{ 0.38627420202318979, 2, 2,
|
| 435 |
|
|
1.5707963267948966 },
|
| 436 |
|
|
{ 0.37682139946702753, 2, 2,
|
| 437 |
|
|
1.7278759594743860 },
|
| 438 |
|
|
{ 0.34938829797428606, 2, 2,
|
| 439 |
|
|
1.8849555921538759 },
|
| 440 |
|
|
{ 0.30666024065673209, 2, 2,
|
| 441 |
|
|
2.0420352248333655 },
|
| 442 |
|
|
{ 0.25281974746848851, 2, 2,
|
| 443 |
|
|
2.1991148575128552 },
|
| 444 |
|
|
{ 0.19313710101159492, 2, 2,
|
| 445 |
|
|
2.3561944901923448 },
|
| 446 |
|
|
{ 0.13345445455470126, 2, 2,
|
| 447 |
|
|
2.5132741228718345 },
|
| 448 |
|
|
{ 0.079613961366457764, 2, 2,
|
| 449 |
|
|
2.6703537555513241 },
|
| 450 |
|
|
{ 0.036885904048903795, 2, 2,
|
| 451 |
|
|
2.8274333882308138 },
|
| 452 |
|
|
{ 0.0094528025561623433, 2, 2,
|
| 453 |
|
|
2.9845130209103035 },
|
| 454 |
|
|
{ 0.0000000000000000, 2, 2,
|
| 455 |
|
|
3.1415926535897931 },
|
| 456 |
|
|
};
|
| 457 |
|
|
|
| 458 |
|
|
// Test function for l=2, m=2.
|
| 459 |
|
|
template <typename Tp>
|
| 460 |
|
|
void test006()
|
| 461 |
|
|
{
|
| 462 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 463 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 464 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 465 |
|
|
unsigned int num_datum = sizeof(data006)
|
| 466 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 467 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 468 |
|
|
{
|
| 469 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data006[i].l), Tp(data006[i].m),
|
| 470 |
|
|
Tp(data006[i].theta));
|
| 471 |
|
|
const Tp f0 = data006[i].f0;
|
| 472 |
|
|
const Tp diff = f - f0;
|
| 473 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 474 |
|
|
max_abs_diff = std::abs(diff);
|
| 475 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 476 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 477 |
|
|
{
|
| 478 |
|
|
const Tp frac = diff / f0;
|
| 479 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 480 |
|
|
max_abs_frac = std::abs(frac);
|
| 481 |
|
|
}
|
| 482 |
|
|
}
|
| 483 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 484 |
|
|
}
|
| 485 |
|
|
|
| 486 |
|
|
// Test data for l=5, m=0.
|
| 487 |
|
|
testcase_sph_legendre<double> data007[] = {
|
| 488 |
|
|
{ 0.93560257962738880, 5, 0,
|
| 489 |
|
|
0.0000000000000000 },
|
| 490 |
|
|
{ 0.77014422942080019, 5, 0,
|
| 491 |
|
|
0.15707963267948966 },
|
| 492 |
|
|
{ 0.35892185032365215, 5, 0,
|
| 493 |
|
|
0.31415926535897931 },
|
| 494 |
|
|
{ -0.090214932090594183, 5, 0,
|
| 495 |
|
|
0.47123889803846897 },
|
| 496 |
|
|
{ -0.36214460396518888, 5, 0,
|
| 497 |
|
|
0.62831853071795862 },
|
| 498 |
|
|
{ -0.35145955579226890, 5, 0,
|
| 499 |
|
|
0.78539816339744828 },
|
| 500 |
|
|
{ -0.11441703594725168, 5, 0,
|
| 501 |
|
|
0.94247779607693793 },
|
| 502 |
|
|
{ 0.17248966720808098, 5, 0,
|
| 503 |
|
|
1.0995574287564276 },
|
| 504 |
|
|
{ 0.32128384287200523, 5, 0,
|
| 505 |
|
|
1.2566370614359172 },
|
| 506 |
|
|
{ 0.24377632246714948, 5, 0,
|
| 507 |
|
|
1.4137166941154069 },
|
| 508 |
|
|
{ 1.0741712853887702e-16, 5, 0,
|
| 509 |
|
|
1.5707963267948966 },
|
| 510 |
|
|
{ -0.24377632246714906, 5, 0,
|
| 511 |
|
|
1.7278759594743860 },
|
| 512 |
|
|
{ -0.32128384287200534, 5, 0,
|
| 513 |
|
|
1.8849555921538759 },
|
| 514 |
|
|
{ -0.17248966720808118, 5, 0,
|
| 515 |
|
|
2.0420352248333655 },
|
| 516 |
|
|
{ 0.11441703594725168, 5, 0,
|
| 517 |
|
|
2.1991148575128552 },
|
| 518 |
|
|
{ 0.35145955579226890, 5, 0,
|
| 519 |
|
|
2.3561944901923448 },
|
| 520 |
|
|
{ 0.36214460396518910, 5, 0,
|
| 521 |
|
|
2.5132741228718345 },
|
| 522 |
|
|
{ 0.090214932090594724, 5, 0,
|
| 523 |
|
|
2.6703537555513241 },
|
| 524 |
|
|
{ -0.35892185032365215, 5, 0,
|
| 525 |
|
|
2.8274333882308138 },
|
| 526 |
|
|
{ -0.77014422942079797, 5, 0,
|
| 527 |
|
|
2.9845130209103035 },
|
| 528 |
|
|
{ -0.93560257962738880, 5, 0,
|
| 529 |
|
|
3.1415926535897931 },
|
| 530 |
|
|
};
|
| 531 |
|
|
|
| 532 |
|
|
// Test function for l=5, m=0.
|
| 533 |
|
|
template <typename Tp>
|
| 534 |
|
|
void test007()
|
| 535 |
|
|
{
|
| 536 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 537 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 538 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 539 |
|
|
unsigned int num_datum = sizeof(data007)
|
| 540 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 541 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 542 |
|
|
{
|
| 543 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data007[i].l), Tp(data007[i].m),
|
| 544 |
|
|
Tp(data007[i].theta));
|
| 545 |
|
|
const Tp f0 = data007[i].f0;
|
| 546 |
|
|
const Tp diff = f - f0;
|
| 547 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 548 |
|
|
max_abs_diff = std::abs(diff);
|
| 549 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 550 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 551 |
|
|
{
|
| 552 |
|
|
const Tp frac = diff / f0;
|
| 553 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 554 |
|
|
max_abs_frac = std::abs(frac);
|
| 555 |
|
|
}
|
| 556 |
|
|
}
|
| 557 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 558 |
|
|
}
|
| 559 |
|
|
|
| 560 |
|
|
// Test data for l=5, m=1.
|
| 561 |
|
|
testcase_sph_legendre<double> data008[] = {
|
| 562 |
|
|
{ 0.0000000000000000, 5, 1,
|
| 563 |
|
|
0.0000000000000000 },
|
| 564 |
|
|
{ -0.36712373713318258, 5, 1,
|
| 565 |
|
|
0.15707963267948966 },
|
| 566 |
|
|
{ -0.54610329010534753, 5, 1,
|
| 567 |
|
|
0.31415926535897931 },
|
| 568 |
|
|
{ -0.45381991493631785, 5, 1,
|
| 569 |
|
|
0.47123889803846897 },
|
| 570 |
|
|
{ -0.15679720635769953, 5, 1,
|
| 571 |
|
|
0.62831853071795862 },
|
| 572 |
|
|
{ 0.16985499419838637, 5, 1,
|
| 573 |
|
|
0.78539816339744828 },
|
| 574 |
|
|
{ 0.34468004499725180, 5, 1,
|
| 575 |
|
|
0.94247779607693793 },
|
| 576 |
|
|
{ 0.28349471119605985, 5, 1,
|
| 577 |
|
|
1.0995574287564276 },
|
| 578 |
|
|
{ 0.044286619339675856, 5, 1,
|
| 579 |
|
|
1.2566370614359172 },
|
| 580 |
|
|
{ -0.21193784177193470, 5, 1,
|
| 581 |
|
|
1.4137166941154069 },
|
| 582 |
|
|
{ -0.32028164857621527, 5, 1,
|
| 583 |
|
|
1.5707963267948966 },
|
| 584 |
|
|
{ -0.21193784177193514, 5, 1,
|
| 585 |
|
|
1.7278759594743860 },
|
| 586 |
|
|
{ 0.044286619339675606, 5, 1,
|
| 587 |
|
|
1.8849555921538759 },
|
| 588 |
|
|
{ 0.28349471119605979, 5, 1,
|
| 589 |
|
|
2.0420352248333655 },
|
| 590 |
|
|
{ 0.34468004499725180, 5, 1,
|
| 591 |
|
|
2.1991148575128552 },
|
| 592 |
|
|
{ 0.16985499419838637, 5, 1,
|
| 593 |
|
|
2.3561944901923448 },
|
| 594 |
|
|
{ -0.15679720635769920, 5, 1,
|
| 595 |
|
|
2.5132741228718345 },
|
| 596 |
|
|
{ -0.45381991493631757, 5, 1,
|
| 597 |
|
|
2.6703537555513241 },
|
| 598 |
|
|
{ -0.54610329010534753, 5, 1,
|
| 599 |
|
|
2.8274333882308138 },
|
| 600 |
|
|
{ -0.36712373713318397, 5, 1,
|
| 601 |
|
|
2.9845130209103035 },
|
| 602 |
|
|
{ 0.0000000000000000, 5, 1,
|
| 603 |
|
|
3.1415926535897931 },
|
| 604 |
|
|
};
|
| 605 |
|
|
|
| 606 |
|
|
// Test function for l=5, m=1.
|
| 607 |
|
|
template <typename Tp>
|
| 608 |
|
|
void test008()
|
| 609 |
|
|
{
|
| 610 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 611 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 612 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 613 |
|
|
unsigned int num_datum = sizeof(data008)
|
| 614 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 615 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 616 |
|
|
{
|
| 617 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data008[i].l), Tp(data008[i].m),
|
| 618 |
|
|
Tp(data008[i].theta));
|
| 619 |
|
|
const Tp f0 = data008[i].f0;
|
| 620 |
|
|
const Tp diff = f - f0;
|
| 621 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 622 |
|
|
max_abs_diff = std::abs(diff);
|
| 623 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 624 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 625 |
|
|
{
|
| 626 |
|
|
const Tp frac = diff / f0;
|
| 627 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 628 |
|
|
max_abs_frac = std::abs(frac);
|
| 629 |
|
|
}
|
| 630 |
|
|
}
|
| 631 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 632 |
|
|
}
|
| 633 |
|
|
|
| 634 |
|
|
// Test data for l=5, m=2.
|
| 635 |
|
|
testcase_sph_legendre<double> data009[] = {
|
| 636 |
|
|
{ 0.0000000000000000, 5, 2,
|
| 637 |
|
|
0.0000000000000000 },
|
| 638 |
|
|
{ 0.078919441745546146, 5, 2,
|
| 639 |
|
|
0.15707963267948966 },
|
| 640 |
|
|
{ 0.26373799140437981, 5, 2,
|
| 641 |
|
|
0.31415926535897931 },
|
| 642 |
|
|
{ 0.43002359842080096, 5, 2,
|
| 643 |
|
|
0.47123889803846897 },
|
| 644 |
|
|
{ 0.45642486439050994, 5, 2,
|
| 645 |
|
|
0.62831853071795862 },
|
| 646 |
|
|
{ 0.29959604906083276, 5, 2,
|
| 647 |
|
|
0.78539816339744828 },
|
| 648 |
|
|
{ 0.023781239849532242, 5, 2,
|
| 649 |
|
|
0.94247779607693793 },
|
| 650 |
|
|
{ -0.23313989334673815, 5, 2,
|
| 651 |
|
|
1.0995574287564276 },
|
| 652 |
|
|
{ -0.33799912776303714, 5, 2,
|
| 653 |
|
|
1.2566370614359172 },
|
| 654 |
|
|
{ -0.23964508489529743, 5, 2,
|
| 655 |
|
|
1.4137166941154069 },
|
| 656 |
|
|
{ -1.0377480524338170e-16, 5, 2,
|
| 657 |
|
|
1.5707963267948966 },
|
| 658 |
|
|
{ 0.23964508489529704, 5, 2,
|
| 659 |
|
|
1.7278759594743860 },
|
| 660 |
|
|
{ 0.33799912776303714, 5, 2,
|
| 661 |
|
|
1.8849555921538759 },
|
| 662 |
|
|
{ 0.23313989334673837, 5, 2,
|
| 663 |
|
|
2.0420352248333655 },
|
| 664 |
|
|
{ -0.023781239849532242, 5, 2,
|
| 665 |
|
|
2.1991148575128552 },
|
| 666 |
|
|
{ -0.29959604906083276, 5, 2,
|
| 667 |
|
|
2.3561944901923448 },
|
| 668 |
|
|
{ -0.45642486439050978, 5, 2,
|
| 669 |
|
|
2.5132741228718345 },
|
| 670 |
|
|
{ -0.43002359842080118, 5, 2,
|
| 671 |
|
|
2.6703537555513241 },
|
| 672 |
|
|
{ -0.26373799140437981, 5, 2,
|
| 673 |
|
|
2.8274333882308138 },
|
| 674 |
|
|
{ -0.078919441745546867, 5, 2,
|
| 675 |
|
|
2.9845130209103035 },
|
| 676 |
|
|
{ 0.0000000000000000, 5, 2,
|
| 677 |
|
|
3.1415926535897931 },
|
| 678 |
|
|
};
|
| 679 |
|
|
|
| 680 |
|
|
// Test function for l=5, m=2.
|
| 681 |
|
|
template <typename Tp>
|
| 682 |
|
|
void test009()
|
| 683 |
|
|
{
|
| 684 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 685 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 686 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 687 |
|
|
unsigned int num_datum = sizeof(data009)
|
| 688 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 689 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 690 |
|
|
{
|
| 691 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data009[i].l), Tp(data009[i].m),
|
| 692 |
|
|
Tp(data009[i].theta));
|
| 693 |
|
|
const Tp f0 = data009[i].f0;
|
| 694 |
|
|
const Tp diff = f - f0;
|
| 695 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 696 |
|
|
max_abs_diff = std::abs(diff);
|
| 697 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 698 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 699 |
|
|
{
|
| 700 |
|
|
const Tp frac = diff / f0;
|
| 701 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 702 |
|
|
max_abs_frac = std::abs(frac);
|
| 703 |
|
|
}
|
| 704 |
|
|
}
|
| 705 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 706 |
|
|
}
|
| 707 |
|
|
|
| 708 |
|
|
// Test data for l=5, m=5.
|
| 709 |
|
|
testcase_sph_legendre<double> data010[] = {
|
| 710 |
|
|
{ 0.0000000000000000, 5, 5,
|
| 711 |
|
|
0.0000000000000000 },
|
| 712 |
|
|
{ -4.3481439097909148e-05, 5, 5,
|
| 713 |
|
|
0.15707963267948966 },
|
| 714 |
|
|
{ -0.0013078367086431812, 5, 5,
|
| 715 |
|
|
0.31415926535897931 },
|
| 716 |
|
|
{ -0.0089510818191922761, 5, 5,
|
| 717 |
|
|
0.47123889803846897 },
|
| 718 |
|
|
{ -0.032563803777573896, 5, 5,
|
| 719 |
|
|
0.62831853071795862 },
|
| 720 |
|
|
{ -0.082047757105021310, 5, 5,
|
| 721 |
|
|
0.78539816339744828 },
|
| 722 |
|
|
{ -0.16085328164143819, 5, 5,
|
| 723 |
|
|
0.94247779607693793 },
|
| 724 |
|
|
{ -0.26064303436645375, 5, 5,
|
| 725 |
|
|
1.0995574287564276 },
|
| 726 |
|
|
{ -0.36113811790820566, 5, 5,
|
| 727 |
|
|
1.2566370614359172 },
|
| 728 |
|
|
{ -0.43625592459446139, 5, 5,
|
| 729 |
|
|
1.4137166941154069 },
|
| 730 |
|
|
{ -0.46413220344085809, 5, 5,
|
| 731 |
|
|
1.5707963267948966 },
|
| 732 |
|
|
{ -0.43625592459446155, 5, 5,
|
| 733 |
|
|
1.7278759594743860 },
|
| 734 |
|
|
{ -0.36113811790820577, 5, 5,
|
| 735 |
|
|
1.8849555921538759 },
|
| 736 |
|
|
{ -0.26064303436645381, 5, 5,
|
| 737 |
|
|
2.0420352248333655 },
|
| 738 |
|
|
{ -0.16085328164143819, 5, 5,
|
| 739 |
|
|
2.1991148575128552 },
|
| 740 |
|
|
{ -0.082047757105021310, 5, 5,
|
| 741 |
|
|
2.3561944901923448 },
|
| 742 |
|
|
{ -0.032563803777573924, 5, 5,
|
| 743 |
|
|
2.5132741228718345 },
|
| 744 |
|
|
{ -0.0089510818191923004, 5, 5,
|
| 745 |
|
|
2.6703537555513241 },
|
| 746 |
|
|
{ -0.0013078367086431812, 5, 5,
|
| 747 |
|
|
2.8274333882308138 },
|
| 748 |
|
|
{ -4.3481439097910151e-05, 5, 5,
|
| 749 |
|
|
2.9845130209103035 },
|
| 750 |
|
|
{ 0.0000000000000000, 5, 5,
|
| 751 |
|
|
3.1415926535897931 },
|
| 752 |
|
|
};
|
| 753 |
|
|
|
| 754 |
|
|
// Test function for l=5, m=5.
|
| 755 |
|
|
template <typename Tp>
|
| 756 |
|
|
void test010()
|
| 757 |
|
|
{
|
| 758 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 759 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 760 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 761 |
|
|
unsigned int num_datum = sizeof(data010)
|
| 762 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 763 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 764 |
|
|
{
|
| 765 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data010[i].l), Tp(data010[i].m),
|
| 766 |
|
|
Tp(data010[i].theta));
|
| 767 |
|
|
const Tp f0 = data010[i].f0;
|
| 768 |
|
|
const Tp diff = f - f0;
|
| 769 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 770 |
|
|
max_abs_diff = std::abs(diff);
|
| 771 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 772 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 773 |
|
|
{
|
| 774 |
|
|
const Tp frac = diff / f0;
|
| 775 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 776 |
|
|
max_abs_frac = std::abs(frac);
|
| 777 |
|
|
}
|
| 778 |
|
|
}
|
| 779 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 780 |
|
|
}
|
| 781 |
|
|
|
| 782 |
|
|
// Test data for l=10, m=0.
|
| 783 |
|
|
testcase_sph_legendre<double> data011[] = {
|
| 784 |
|
|
{ 1.2927207364566027, 10, 0,
|
| 785 |
|
|
0.0000000000000000 },
|
| 786 |
|
|
{ 0.55288895150522632, 10, 0,
|
| 787 |
|
|
0.15707963267948966 },
|
| 788 |
|
|
{ -0.44874428379711506, 10, 0,
|
| 789 |
|
|
0.31415926535897931 },
|
| 790 |
|
|
{ -0.25532095827149692, 10, 0,
|
| 791 |
|
|
0.47123889803846897 },
|
| 792 |
|
|
{ 0.36625249688013967, 10, 0,
|
| 793 |
|
|
0.62831853071795862 },
|
| 794 |
|
|
{ 0.14880806329084145, 10, 0,
|
| 795 |
|
|
0.78539816339744828 },
|
| 796 |
|
|
{ -0.33533356797848746, 10, 0,
|
| 797 |
|
|
0.94247779607693793 },
|
| 798 |
|
|
{ -0.080639967662335818, 10, 0,
|
| 799 |
|
|
1.0995574287564276 },
|
| 800 |
|
|
{ 0.32197986450174521, 10, 0,
|
| 801 |
|
|
1.2566370614359172 },
|
| 802 |
|
|
{ 0.025713542103667848, 10, 0,
|
| 803 |
|
|
1.4137166941154069 },
|
| 804 |
|
|
{ -0.31813049373736707, 10, 0,
|
| 805 |
|
|
1.5707963267948966 },
|
| 806 |
|
|
{ 0.025713542103666668, 10, 0,
|
| 807 |
|
|
1.7278759594743860 },
|
| 808 |
|
|
{ 0.32197986450174532, 10, 0,
|
| 809 |
|
|
1.8849555921538759 },
|
| 810 |
|
|
{ -0.080639967662335416, 10, 0,
|
| 811 |
|
|
2.0420352248333655 },
|
| 812 |
|
|
{ -0.33533356797848746, 10, 0,
|
| 813 |
|
|
2.1991148575128552 },
|
| 814 |
|
|
{ 0.14880806329084145, 10, 0,
|
| 815 |
|
|
2.3561944901923448 },
|
| 816 |
|
|
{ 0.36625249688013994, 10, 0,
|
| 817 |
|
|
2.5132741228718345 },
|
| 818 |
|
|
{ -0.25532095827149576, 10, 0,
|
| 819 |
|
|
2.6703537555513241 },
|
| 820 |
|
|
{ -0.44874428379711506, 10, 0,
|
| 821 |
|
|
2.8274333882308138 },
|
| 822 |
|
|
{ 0.55288895150521977, 10, 0,
|
| 823 |
|
|
2.9845130209103035 },
|
| 824 |
|
|
{ 1.2927207364566027, 10, 0,
|
| 825 |
|
|
3.1415926535897931 },
|
| 826 |
|
|
};
|
| 827 |
|
|
|
| 828 |
|
|
// Test function for l=10, m=0.
|
| 829 |
|
|
template <typename Tp>
|
| 830 |
|
|
void test011()
|
| 831 |
|
|
{
|
| 832 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 833 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 834 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 835 |
|
|
unsigned int num_datum = sizeof(data011)
|
| 836 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 837 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 838 |
|
|
{
|
| 839 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data011[i].l), Tp(data011[i].m),
|
| 840 |
|
|
Tp(data011[i].theta));
|
| 841 |
|
|
const Tp f0 = data011[i].f0;
|
| 842 |
|
|
const Tp diff = f - f0;
|
| 843 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 844 |
|
|
max_abs_diff = std::abs(diff);
|
| 845 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 846 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 847 |
|
|
{
|
| 848 |
|
|
const Tp frac = diff / f0;
|
| 849 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 850 |
|
|
max_abs_frac = std::abs(frac);
|
| 851 |
|
|
}
|
| 852 |
|
|
}
|
| 853 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 854 |
|
|
}
|
| 855 |
|
|
|
| 856 |
|
|
// Test data for l=10, m=1.
|
| 857 |
|
|
testcase_sph_legendre<double> data012[] = {
|
| 858 |
|
|
{ 0.0000000000000000, 10, 1,
|
| 859 |
|
|
0.0000000000000000 },
|
| 860 |
|
|
{ -0.74373723919063905, 10, 1,
|
| 861 |
|
|
0.15707963267948966 },
|
| 862 |
|
|
{ -0.29035110456209551, 10, 1,
|
| 863 |
|
|
0.31415926535897931 },
|
| 864 |
|
|
{ 0.42219282075271497, 10, 1,
|
| 865 |
|
|
0.47123889803846897 },
|
| 866 |
|
|
{ 0.17109256898931269, 10, 1,
|
| 867 |
|
|
0.62831853071795862 },
|
| 868 |
|
|
{ -0.35583574648544292, 10, 1,
|
| 869 |
|
|
0.78539816339744828 },
|
| 870 |
|
|
{ -0.10089212303543979, 10, 1,
|
| 871 |
|
|
0.94247779607693793 },
|
| 872 |
|
|
{ 0.32997652649321085, 10, 1,
|
| 873 |
|
|
1.0995574287564276 },
|
| 874 |
|
|
{ 0.047416376890033113, 10, 1,
|
| 875 |
|
|
1.2566370614359172 },
|
| 876 |
|
|
{ -0.31999356750295654, 10, 1,
|
| 877 |
|
|
1.4137166941154069 },
|
| 878 |
|
|
{ -2.0430664782290766e-16, 10, 1,
|
| 879 |
|
|
1.5707963267948966 },
|
| 880 |
|
|
{ 0.31999356750295660, 10, 1,
|
| 881 |
|
|
1.7278759594743860 },
|
| 882 |
|
|
{ -0.047416376890032523, 10, 1,
|
| 883 |
|
|
1.8849555921538759 },
|
| 884 |
|
|
{ -0.32997652649321102, 10, 1,
|
| 885 |
|
|
2.0420352248333655 },
|
| 886 |
|
|
{ 0.10089212303543979, 10, 1,
|
| 887 |
|
|
2.1991148575128552 },
|
| 888 |
|
|
{ 0.35583574648544292, 10, 1,
|
| 889 |
|
|
2.3561944901923448 },
|
| 890 |
|
|
{ -0.17109256898931186, 10, 1,
|
| 891 |
|
|
2.5132741228718345 },
|
| 892 |
|
|
{ -0.42219282075271553, 10, 1,
|
| 893 |
|
|
2.6703537555513241 },
|
| 894 |
|
|
{ 0.29035110456209551, 10, 1,
|
| 895 |
|
|
2.8274333882308138 },
|
| 896 |
|
|
{ 0.74373723919064028, 10, 1,
|
| 897 |
|
|
2.9845130209103035 },
|
| 898 |
|
|
{ 0.0000000000000000, 10, 1,
|
| 899 |
|
|
3.1415926535897931 },
|
| 900 |
|
|
};
|
| 901 |
|
|
|
| 902 |
|
|
// Test function for l=10, m=1.
|
| 903 |
|
|
template <typename Tp>
|
| 904 |
|
|
void test012()
|
| 905 |
|
|
{
|
| 906 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 907 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 908 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 909 |
|
|
unsigned int num_datum = sizeof(data012)
|
| 910 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 911 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 912 |
|
|
{
|
| 913 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data012[i].l), Tp(data012[i].m),
|
| 914 |
|
|
Tp(data012[i].theta));
|
| 915 |
|
|
const Tp f0 = data012[i].f0;
|
| 916 |
|
|
const Tp diff = f - f0;
|
| 917 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 918 |
|
|
max_abs_diff = std::abs(diff);
|
| 919 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 920 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 921 |
|
|
{
|
| 922 |
|
|
const Tp frac = diff / f0;
|
| 923 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 924 |
|
|
max_abs_frac = std::abs(frac);
|
| 925 |
|
|
}
|
| 926 |
|
|
}
|
| 927 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 928 |
|
|
}
|
| 929 |
|
|
|
| 930 |
|
|
// Test data for l=10, m=2.
|
| 931 |
|
|
testcase_sph_legendre<double> data013[] = {
|
| 932 |
|
|
{ 0.0000000000000000, 10, 2,
|
| 933 |
|
|
0.0000000000000000 },
|
| 934 |
|
|
{ 0.34571695599980284, 10, 2,
|
| 935 |
|
|
0.15707963267948966 },
|
| 936 |
|
|
{ 0.62485535978198059, 10, 2,
|
| 937 |
|
|
0.31415926535897931 },
|
| 938 |
|
|
{ 0.098210039644716363, 10, 2,
|
| 939 |
|
|
0.47123889803846897 },
|
| 940 |
|
|
{ -0.41494799233049656, 10, 2,
|
| 941 |
|
|
0.62831853071795862 },
|
| 942 |
|
|
{ -0.081698973831472149, 10, 2,
|
| 943 |
|
|
0.78539816339744828 },
|
| 944 |
|
|
{ 0.35253132222271272, 10, 2,
|
| 945 |
|
|
0.94247779607693793 },
|
| 946 |
|
|
{ 0.049026298555981063, 10, 2,
|
| 947 |
|
|
1.0995574287564276 },
|
| 948 |
|
|
{ -0.32791246874130797, 10, 2,
|
| 949 |
|
|
1.2566370614359172 },
|
| 950 |
|
|
{ -0.016196782433946910, 10, 2,
|
| 951 |
|
|
1.4137166941154069 },
|
| 952 |
|
|
{ 0.32106263400438328, 10, 2,
|
| 953 |
|
|
1.5707963267948966 },
|
| 954 |
|
|
{ -0.016196782433945765, 10, 2,
|
| 955 |
|
|
1.7278759594743860 },
|
| 956 |
|
|
{ -0.32791246874130797, 10, 2,
|
| 957 |
|
|
1.8849555921538759 },
|
| 958 |
|
|
{ 0.049026298555980702, 10, 2,
|
| 959 |
|
|
2.0420352248333655 },
|
| 960 |
|
|
{ 0.35253132222271272, 10, 2,
|
| 961 |
|
|
2.1991148575128552 },
|
| 962 |
|
|
{ -0.081698973831472149, 10, 2,
|
| 963 |
|
|
2.3561944901923448 },
|
| 964 |
|
|
{ -0.41494799233049667, 10, 2,
|
| 965 |
|
|
2.5132741228718345 },
|
| 966 |
|
|
{ 0.098210039644714753, 10, 2,
|
| 967 |
|
|
2.6703537555513241 },
|
| 968 |
|
|
{ 0.62485535978198059, 10, 2,
|
| 969 |
|
|
2.8274333882308138 },
|
| 970 |
|
|
{ 0.34571695599980551, 10, 2,
|
| 971 |
|
|
2.9845130209103035 },
|
| 972 |
|
|
{ 0.0000000000000000, 10, 2,
|
| 973 |
|
|
3.1415926535897931 },
|
| 974 |
|
|
};
|
| 975 |
|
|
|
| 976 |
|
|
// Test function for l=10, m=2.
|
| 977 |
|
|
template <typename Tp>
|
| 978 |
|
|
void test013()
|
| 979 |
|
|
{
|
| 980 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 981 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 982 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 983 |
|
|
unsigned int num_datum = sizeof(data013)
|
| 984 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 985 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 986 |
|
|
{
|
| 987 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data013[i].l), Tp(data013[i].m),
|
| 988 |
|
|
Tp(data013[i].theta));
|
| 989 |
|
|
const Tp f0 = data013[i].f0;
|
| 990 |
|
|
const Tp diff = f - f0;
|
| 991 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 992 |
|
|
max_abs_diff = std::abs(diff);
|
| 993 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 994 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 995 |
|
|
{
|
| 996 |
|
|
const Tp frac = diff / f0;
|
| 997 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 998 |
|
|
max_abs_frac = std::abs(frac);
|
| 999 |
|
|
}
|
| 1000 |
|
|
}
|
| 1001 |
|
|
VERIFY(max_abs_frac < Tp(5.0000000000000039e-13));
|
| 1002 |
|
|
}
|
| 1003 |
|
|
|
| 1004 |
|
|
// Test data for l=10, m=5.
|
| 1005 |
|
|
testcase_sph_legendre<double> data014[] = {
|
| 1006 |
|
|
{ 0.0000000000000000, 10, 5,
|
| 1007 |
|
|
0.0000000000000000 },
|
| 1008 |
|
|
{ -0.0030300124052750187, 10, 5,
|
| 1009 |
|
|
0.15707963267948966 },
|
| 1010 |
|
|
{ -0.070348585248056830, 10, 5,
|
| 1011 |
|
|
0.31415926535897931 },
|
| 1012 |
|
|
{ -0.30055029290703639, 10, 5,
|
| 1013 |
|
|
0.47123889803846897 },
|
| 1014 |
|
|
{ -0.49987818144009166, 10, 5,
|
| 1015 |
|
|
0.62831853071795862 },
|
| 1016 |
|
|
{ -0.28108771757150086, 10, 5,
|
| 1017 |
|
|
0.78539816339744828 },
|
| 1018 |
|
|
{ 0.22068081187249308, 10, 5,
|
| 1019 |
|
|
0.94247779607693793 },
|
| 1020 |
|
|
{ 0.33689502212592115, 10, 5,
|
| 1021 |
|
|
1.0995574287564276 },
|
| 1022 |
|
|
{ -0.086095515520763985, 10, 5,
|
| 1023 |
|
|
1.2566370614359172 },
|
| 1024 |
|
|
{ -0.33935827318511558, 10, 5,
|
| 1025 |
|
|
1.4137166941154069 },
|
| 1026 |
|
|
{ -1.9213014340664578e-16, 10, 5,
|
| 1027 |
|
|
1.5707963267948966 },
|
| 1028 |
|
|
{ 0.33935827318511552, 10, 5,
|
| 1029 |
|
|
1.7278759594743860 },
|
| 1030 |
|
|
{ 0.086095515520764526, 10, 5,
|
| 1031 |
|
|
1.8849555921538759 },
|
| 1032 |
|
|
{ -0.33689502212592098, 10, 5,
|
| 1033 |
|
|
2.0420352248333655 },
|
| 1034 |
|
|
{ -0.22068081187249308, 10, 5,
|
| 1035 |
|
|
2.1991148575128552 },
|
| 1036 |
|
|
{ 0.28108771757150086, 10, 5,
|
| 1037 |
|
|
2.3561944901923448 },
|
| 1038 |
|
|
{ 0.49987818144009155, 10, 5,
|
| 1039 |
|
|
2.5132741228718345 },
|
| 1040 |
|
|
{ 0.30055029290703678, 10, 5,
|
| 1041 |
|
|
2.6703537555513241 },
|
| 1042 |
|
|
{ 0.070348585248056830, 10, 5,
|
| 1043 |
|
|
2.8274333882308138 },
|
| 1044 |
|
|
{ 0.0030300124052750855, 10, 5,
|
| 1045 |
|
|
2.9845130209103035 },
|
| 1046 |
|
|
{ 0.0000000000000000, 10, 5,
|
| 1047 |
|
|
3.1415926535897931 },
|
| 1048 |
|
|
};
|
| 1049 |
|
|
|
| 1050 |
|
|
// Test function for l=10, m=5.
|
| 1051 |
|
|
template <typename Tp>
|
| 1052 |
|
|
void test014()
|
| 1053 |
|
|
{
|
| 1054 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1055 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1056 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1057 |
|
|
unsigned int num_datum = sizeof(data014)
|
| 1058 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 1059 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1060 |
|
|
{
|
| 1061 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data014[i].l), Tp(data014[i].m),
|
| 1062 |
|
|
Tp(data014[i].theta));
|
| 1063 |
|
|
const Tp f0 = data014[i].f0;
|
| 1064 |
|
|
const Tp diff = f - f0;
|
| 1065 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1066 |
|
|
max_abs_diff = std::abs(diff);
|
| 1067 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1068 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1069 |
|
|
{
|
| 1070 |
|
|
const Tp frac = diff / f0;
|
| 1071 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1072 |
|
|
max_abs_frac = std::abs(frac);
|
| 1073 |
|
|
}
|
| 1074 |
|
|
}
|
| 1075 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 1076 |
|
|
}
|
| 1077 |
|
|
|
| 1078 |
|
|
// Test data for l=10, m=10.
|
| 1079 |
|
|
testcase_sph_legendre<double> data015[] = {
|
| 1080 |
|
|
{ 0.0000000000000000, 10, 10,
|
| 1081 |
|
|
0.0000000000000000 },
|
| 1082 |
|
|
{ 4.7624282733343473e-09, 10, 10,
|
| 1083 |
|
|
0.15707963267948966 },
|
| 1084 |
|
|
{ 4.3085156534549772e-06, 10, 10,
|
| 1085 |
|
|
0.31415926535897931 },
|
| 1086 |
|
|
{ 0.00020182347649472368, 10, 10,
|
| 1087 |
|
|
0.47123889803846897 },
|
| 1088 |
|
|
{ 0.0026711045506511684, 10, 10,
|
| 1089 |
|
|
0.62831853071795862 },
|
| 1090 |
|
|
{ 0.016957196623256943, 10, 10,
|
| 1091 |
|
|
0.78539816339744828 },
|
| 1092 |
|
|
{ 0.065174916004990341, 10, 10,
|
| 1093 |
|
|
0.94247779607693793 },
|
| 1094 |
|
|
{ 0.17112476903017843, 10, 10,
|
| 1095 |
|
|
1.0995574287564276 },
|
| 1096 |
|
|
{ 0.32852414199733548, 10, 10,
|
| 1097 |
|
|
1.2566370614359172 },
|
| 1098 |
|
|
{ 0.47940582314838287, 10, 10,
|
| 1099 |
|
|
1.4137166941154069 },
|
| 1100 |
|
|
{ 0.54263029194422152, 10, 10,
|
| 1101 |
|
|
1.5707963267948966 },
|
| 1102 |
|
|
{ 0.47940582314838309, 10, 10,
|
| 1103 |
|
|
1.7278759594743860 },
|
| 1104 |
|
|
{ 0.32852414199733571, 10, 10,
|
| 1105 |
|
|
1.8849555921538759 },
|
| 1106 |
|
|
{ 0.17112476903017854, 10, 10,
|
| 1107 |
|
|
2.0420352248333655 },
|
| 1108 |
|
|
{ 0.065174916004990341, 10, 10,
|
| 1109 |
|
|
2.1991148575128552 },
|
| 1110 |
|
|
{ 0.016957196623256943, 10, 10,
|
| 1111 |
|
|
2.3561944901923448 },
|
| 1112 |
|
|
{ 0.0026711045506511706, 10, 10,
|
| 1113 |
|
|
2.5132741228718345 },
|
| 1114 |
|
|
{ 0.00020182347649472493, 10, 10,
|
| 1115 |
|
|
2.6703537555513241 },
|
| 1116 |
|
|
{ 4.3085156534549772e-06, 10, 10,
|
| 1117 |
|
|
2.8274333882308138 },
|
| 1118 |
|
|
{ 4.7624282733345673e-09, 10, 10,
|
| 1119 |
|
|
2.9845130209103035 },
|
| 1120 |
|
|
{ 0.0000000000000000, 10, 10,
|
| 1121 |
|
|
3.1415926535897931 },
|
| 1122 |
|
|
};
|
| 1123 |
|
|
|
| 1124 |
|
|
// Test function for l=10, m=10.
|
| 1125 |
|
|
template <typename Tp>
|
| 1126 |
|
|
void test015()
|
| 1127 |
|
|
{
|
| 1128 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1129 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1130 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1131 |
|
|
unsigned int num_datum = sizeof(data015)
|
| 1132 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 1133 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1134 |
|
|
{
|
| 1135 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data015[i].l), Tp(data015[i].m),
|
| 1136 |
|
|
Tp(data015[i].theta));
|
| 1137 |
|
|
const Tp f0 = data015[i].f0;
|
| 1138 |
|
|
const Tp diff = f - f0;
|
| 1139 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1140 |
|
|
max_abs_diff = std::abs(diff);
|
| 1141 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1142 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1143 |
|
|
{
|
| 1144 |
|
|
const Tp frac = diff / f0;
|
| 1145 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1146 |
|
|
max_abs_frac = std::abs(frac);
|
| 1147 |
|
|
}
|
| 1148 |
|
|
}
|
| 1149 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 1150 |
|
|
}
|
| 1151 |
|
|
|
| 1152 |
|
|
// Test data for l=20, m=0.
|
| 1153 |
|
|
testcase_sph_legendre<double> data016[] = {
|
| 1154 |
|
|
{ 1.8062879984608917, 20, 0,
|
| 1155 |
|
|
0.0000000000000000 },
|
| 1156 |
|
|
{ -0.58906549291415966, 20, 0,
|
| 1157 |
|
|
0.15707963267948966 },
|
| 1158 |
|
|
{ 0.45624611402342408, 20, 0,
|
| 1159 |
|
|
0.31415926535897931 },
|
| 1160 |
|
|
{ -0.39955402700466724, 20, 0,
|
| 1161 |
|
|
0.47123889803846897 },
|
| 1162 |
|
|
{ 0.36818552901640750, 20, 0,
|
| 1163 |
|
|
0.62831853071795862 },
|
| 1164 |
|
|
{ -0.34873131330857787, 20, 0,
|
| 1165 |
|
|
0.78539816339744828 },
|
| 1166 |
|
|
{ 0.33600882829186501, 20, 0,
|
| 1167 |
|
|
0.94247779607693793 },
|
| 1168 |
|
|
{ -0.32759286308122904, 20, 0,
|
| 1169 |
|
|
1.0995574287564276 },
|
| 1170 |
|
|
{ 0.32222458068091320, 20, 0,
|
| 1171 |
|
|
1.2566370614359172 },
|
| 1172 |
|
|
{ -0.31922731037135960, 20, 0,
|
| 1173 |
|
|
1.4137166941154069 },
|
| 1174 |
|
|
{ 0.31826262039531755, 20, 0,
|
| 1175 |
|
|
1.5707963267948966 },
|
| 1176 |
|
|
{ -0.31922731037135965, 20, 0,
|
| 1177 |
|
|
1.7278759594743860 },
|
| 1178 |
|
|
{ 0.32222458068091336, 20, 0,
|
| 1179 |
|
|
1.8849555921538759 },
|
| 1180 |
|
|
{ -0.32759286308122937, 20, 0,
|
| 1181 |
|
|
2.0420352248333655 },
|
| 1182 |
|
|
{ 0.33600882829186501, 20, 0,
|
| 1183 |
|
|
2.1991148575128552 },
|
| 1184 |
|
|
{ -0.34873131330857787, 20, 0,
|
| 1185 |
|
|
2.3561944901923448 },
|
| 1186 |
|
|
{ 0.36818552901640839, 20, 0,
|
| 1187 |
|
|
2.5132741228718345 },
|
| 1188 |
|
|
{ -0.39955402700466852, 20, 0,
|
| 1189 |
|
|
2.6703537555513241 },
|
| 1190 |
|
|
{ 0.45624611402342408, 20, 0,
|
| 1191 |
|
|
2.8274333882308138 },
|
| 1192 |
|
|
{ -0.58906549291416699, 20, 0,
|
| 1193 |
|
|
2.9845130209103035 },
|
| 1194 |
|
|
{ 1.8062879984608917, 20, 0,
|
| 1195 |
|
|
3.1415926535897931 },
|
| 1196 |
|
|
};
|
| 1197 |
|
|
|
| 1198 |
|
|
// Test function for l=20, m=0.
|
| 1199 |
|
|
template <typename Tp>
|
| 1200 |
|
|
void test016()
|
| 1201 |
|
|
{
|
| 1202 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1203 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1204 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1205 |
|
|
unsigned int num_datum = sizeof(data016)
|
| 1206 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 1207 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1208 |
|
|
{
|
| 1209 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data016[i].l), Tp(data016[i].m),
|
| 1210 |
|
|
Tp(data016[i].theta));
|
| 1211 |
|
|
const Tp f0 = data016[i].f0;
|
| 1212 |
|
|
const Tp diff = f - f0;
|
| 1213 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1214 |
|
|
max_abs_diff = std::abs(diff);
|
| 1215 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1216 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1217 |
|
|
{
|
| 1218 |
|
|
const Tp frac = diff / f0;
|
| 1219 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1220 |
|
|
max_abs_frac = std::abs(frac);
|
| 1221 |
|
|
}
|
| 1222 |
|
|
}
|
| 1223 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 1224 |
|
|
}
|
| 1225 |
|
|
|
| 1226 |
|
|
// Test data for l=20, m=1.
|
| 1227 |
|
|
testcase_sph_legendre<double> data017[] = {
|
| 1228 |
|
|
{ 0.0000000000000000, 20, 1,
|
| 1229 |
|
|
0.0000000000000000 },
|
| 1230 |
|
|
{ -0.45905213045060206, 20, 1,
|
| 1231 |
|
|
0.15707963267948966 },
|
| 1232 |
|
|
{ 0.31166370423309170, 20, 1,
|
| 1233 |
|
|
0.31415926535897931 },
|
| 1234 |
|
|
{ -0.23278757741246814, 20, 1,
|
| 1235 |
|
|
0.47123889803846897 },
|
| 1236 |
|
|
{ 0.17937240823504183, 20, 1,
|
| 1237 |
|
|
0.62831853071795862 },
|
| 1238 |
|
|
{ -0.13857299972299736, 20, 1,
|
| 1239 |
|
|
0.78539816339744828 },
|
| 1240 |
|
|
{ 0.10495324841927710, 20, 1,
|
| 1241 |
|
|
0.94247779607693793 },
|
| 1242 |
|
|
{ -0.075707774352164178, 20, 1,
|
| 1243 |
|
|
1.0995574287564276 },
|
| 1244 |
|
|
{ 0.049168697683476620, 20, 1,
|
| 1245 |
|
|
1.2566370614359172 },
|
| 1246 |
|
|
{ -0.024216050551253254, 20, 1,
|
| 1247 |
|
|
1.4137166941154069 },
|
| 1248 |
|
|
{ 3.9938443510694349e-16, 20, 1,
|
| 1249 |
|
|
1.5707963267948966 },
|
| 1250 |
|
|
{ 0.024216050551250898, 20, 1,
|
| 1251 |
|
|
1.7278759594743860 },
|
| 1252 |
|
|
{ -0.049168697683475482, 20, 1,
|
| 1253 |
|
|
1.8849555921538759 },
|
| 1254 |
|
|
{ 0.075707774352163332, 20, 1,
|
| 1255 |
|
|
2.0420352248333655 },
|
| 1256 |
|
|
{ -0.10495324841927710, 20, 1,
|
| 1257 |
|
|
2.1991148575128552 },
|
| 1258 |
|
|
{ 0.13857299972299736, 20, 1,
|
| 1259 |
|
|
2.3561944901923448 },
|
| 1260 |
|
|
{ -0.17937240823504039, 20, 1,
|
| 1261 |
|
|
2.5132741228718345 },
|
| 1262 |
|
|
{ 0.23278757741246658, 20, 1,
|
| 1263 |
|
|
2.6703537555513241 },
|
| 1264 |
|
|
{ -0.31166370423309170, 20, 1,
|
| 1265 |
|
|
2.8274333882308138 },
|
| 1266 |
|
|
{ 0.45905213045059318, 20, 1,
|
| 1267 |
|
|
2.9845130209103035 },
|
| 1268 |
|
|
{ 0.0000000000000000, 20, 1,
|
| 1269 |
|
|
3.1415926535897931 },
|
| 1270 |
|
|
};
|
| 1271 |
|
|
|
| 1272 |
|
|
// Test function for l=20, m=1.
|
| 1273 |
|
|
template <typename Tp>
|
| 1274 |
|
|
void test017()
|
| 1275 |
|
|
{
|
| 1276 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1277 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1278 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1279 |
|
|
unsigned int num_datum = sizeof(data017)
|
| 1280 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 1281 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1282 |
|
|
{
|
| 1283 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data017[i].l), Tp(data017[i].m),
|
| 1284 |
|
|
Tp(data017[i].theta));
|
| 1285 |
|
|
const Tp f0 = data017[i].f0;
|
| 1286 |
|
|
const Tp diff = f - f0;
|
| 1287 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1288 |
|
|
max_abs_diff = std::abs(diff);
|
| 1289 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1290 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1291 |
|
|
{
|
| 1292 |
|
|
const Tp frac = diff / f0;
|
| 1293 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1294 |
|
|
max_abs_frac = std::abs(frac);
|
| 1295 |
|
|
}
|
| 1296 |
|
|
}
|
| 1297 |
|
|
VERIFY(max_abs_frac < Tp(5.0000000000000039e-13));
|
| 1298 |
|
|
}
|
| 1299 |
|
|
|
| 1300 |
|
|
// Test data for l=20, m=2.
|
| 1301 |
|
|
testcase_sph_legendre<double> data018[] = {
|
| 1302 |
|
|
{ 0.0000000000000000, 20, 2,
|
| 1303 |
|
|
0.0000000000000000 },
|
| 1304 |
|
|
{ 0.87399805141574682, 20, 2,
|
| 1305 |
|
|
0.15707963267948966 },
|
| 1306 |
|
|
{ -0.55116854080894984, 20, 2,
|
| 1307 |
|
|
0.31415926535897931 },
|
| 1308 |
|
|
{ 0.44520137308557534, 20, 2,
|
| 1309 |
|
|
0.47123889803846897 },
|
| 1310 |
|
|
{ -0.39321637877908228, 20, 2,
|
| 1311 |
|
|
0.62831853071795862 },
|
| 1312 |
|
|
{ 0.36312025711350970, 20, 2,
|
| 1313 |
|
|
0.78539816339744828 },
|
| 1314 |
|
|
{ -0.34427103004873094, 20, 2,
|
| 1315 |
|
|
0.94247779607693793 },
|
| 1316 |
|
|
{ 0.33214917638387625, 20, 2,
|
| 1317 |
|
|
1.0995574287564276 },
|
| 1318 |
|
|
{ -0.32455734448839091, 20, 2,
|
| 1319 |
|
|
1.2566370614359172 },
|
| 1320 |
|
|
{ 0.32036529628513238, 20, 2,
|
| 1321 |
|
|
1.4137166941154069 },
|
| 1322 |
|
|
{ -0.31902310563819986, 20, 2,
|
| 1323 |
|
|
1.5707963267948966 },
|
| 1324 |
|
|
{ 0.32036529628513266, 20, 2,
|
| 1325 |
|
|
1.7278759594743860 },
|
| 1326 |
|
|
{ -0.32455734448839102, 20, 2,
|
| 1327 |
|
|
1.8849555921538759 },
|
| 1328 |
|
|
{ 0.33214917638387670, 20, 2,
|
| 1329 |
|
|
2.0420352248333655 },
|
| 1330 |
|
|
{ -0.34427103004873094, 20, 2,
|
| 1331 |
|
|
2.1991148575128552 },
|
| 1332 |
|
|
{ 0.36312025711350970, 20, 2,
|
| 1333 |
|
|
2.3561944901923448 },
|
| 1334 |
|
|
{ -0.39321637877908278, 20, 2,
|
| 1335 |
|
|
2.5132741228718345 },
|
| 1336 |
|
|
{ 0.44520137308557639, 20, 2,
|
| 1337 |
|
|
2.6703537555513241 },
|
| 1338 |
|
|
{ -0.55116854080894984, 20, 2,
|
| 1339 |
|
|
2.8274333882308138 },
|
| 1340 |
|
|
{ 0.87399805141574360, 20, 2,
|
| 1341 |
|
|
2.9845130209103035 },
|
| 1342 |
|
|
{ 0.0000000000000000, 20, 2,
|
| 1343 |
|
|
3.1415926535897931 },
|
| 1344 |
|
|
};
|
| 1345 |
|
|
|
| 1346 |
|
|
// Test function for l=20, m=2.
|
| 1347 |
|
|
template <typename Tp>
|
| 1348 |
|
|
void test018()
|
| 1349 |
|
|
{
|
| 1350 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1351 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1352 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1353 |
|
|
unsigned int num_datum = sizeof(data018)
|
| 1354 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 1355 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1356 |
|
|
{
|
| 1357 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data018[i].l), Tp(data018[i].m),
|
| 1358 |
|
|
Tp(data018[i].theta));
|
| 1359 |
|
|
const Tp f0 = data018[i].f0;
|
| 1360 |
|
|
const Tp diff = f - f0;
|
| 1361 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1362 |
|
|
max_abs_diff = std::abs(diff);
|
| 1363 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1364 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1365 |
|
|
{
|
| 1366 |
|
|
const Tp frac = diff / f0;
|
| 1367 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1368 |
|
|
max_abs_frac = std::abs(frac);
|
| 1369 |
|
|
}
|
| 1370 |
|
|
}
|
| 1371 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 1372 |
|
|
}
|
| 1373 |
|
|
|
| 1374 |
|
|
// Test data for l=20, m=5.
|
| 1375 |
|
|
testcase_sph_legendre<double> data019[] = {
|
| 1376 |
|
|
{ 0.0000000000000000, 20, 5,
|
| 1377 |
|
|
0.0000000000000000 },
|
| 1378 |
|
|
{ -0.10024848623504846, 20, 5,
|
| 1379 |
|
|
0.15707963267948966 },
|
| 1380 |
|
|
{ -0.68115361075940595, 20, 5,
|
| 1381 |
|
|
0.31415926535897931 },
|
| 1382 |
|
|
{ 0.31774532551156237, 20, 5,
|
| 1383 |
|
|
0.47123889803846897 },
|
| 1384 |
|
|
{ -0.16011868165390564, 20, 5,
|
| 1385 |
|
|
0.62831853071795862 },
|
| 1386 |
|
|
{ 0.085844143304116230, 20, 5,
|
| 1387 |
|
|
0.78539816339744828 },
|
| 1388 |
|
|
{ -0.047467540840864686, 20, 5,
|
| 1389 |
|
|
0.94247779607693793 },
|
| 1390 |
|
|
{ 0.026283575189471282, 20, 5,
|
| 1391 |
|
|
1.0995574287564276 },
|
| 1392 |
|
|
{ -0.013891104052597331, 20, 5,
|
| 1393 |
|
|
1.2566370614359172 },
|
| 1394 |
|
|
{ 0.0059873308239496931, 20, 5,
|
| 1395 |
|
|
1.4137166941154069 },
|
| 1396 |
|
|
{ 3.9355286582083095e-16, 20, 5,
|
| 1397 |
|
|
1.5707963267948966 },
|
| 1398 |
|
|
{ -0.0059873308239519040, 20, 5,
|
| 1399 |
|
|
1.7278759594743860 },
|
| 1400 |
|
|
{ 0.013891104052598531, 20, 5,
|
| 1401 |
|
|
1.8849555921538759 },
|
| 1402 |
|
|
{ -0.026283575189472212, 20, 5,
|
| 1403 |
|
|
2.0420352248333655 },
|
| 1404 |
|
|
{ 0.047467540840864686, 20, 5,
|
| 1405 |
|
|
2.1991148575128552 },
|
| 1406 |
|
|
{ -0.085844143304116230, 20, 5,
|
| 1407 |
|
|
2.3561944901923448 },
|
| 1408 |
|
|
{ 0.16011868165390636, 20, 5,
|
| 1409 |
|
|
2.5132741228718345 },
|
| 1410 |
|
|
{ -0.31774532551156448, 20, 5,
|
| 1411 |
|
|
2.6703537555513241 },
|
| 1412 |
|
|
{ 0.68115361075940595, 20, 5,
|
| 1413 |
|
|
2.8274333882308138 },
|
| 1414 |
|
|
{ 0.10024848623505037, 20, 5,
|
| 1415 |
|
|
2.9845130209103035 },
|
| 1416 |
|
|
{ 0.0000000000000000, 20, 5,
|
| 1417 |
|
|
3.1415926535897931 },
|
| 1418 |
|
|
};
|
| 1419 |
|
|
|
| 1420 |
|
|
// Test function for l=20, m=5.
|
| 1421 |
|
|
template <typename Tp>
|
| 1422 |
|
|
void test019()
|
| 1423 |
|
|
{
|
| 1424 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1425 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1426 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1427 |
|
|
unsigned int num_datum = sizeof(data019)
|
| 1428 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 1429 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1430 |
|
|
{
|
| 1431 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data019[i].l), Tp(data019[i].m),
|
| 1432 |
|
|
Tp(data019[i].theta));
|
| 1433 |
|
|
const Tp f0 = data019[i].f0;
|
| 1434 |
|
|
const Tp diff = f - f0;
|
| 1435 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1436 |
|
|
max_abs_diff = std::abs(diff);
|
| 1437 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1438 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1439 |
|
|
{
|
| 1440 |
|
|
const Tp frac = diff / f0;
|
| 1441 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1442 |
|
|
max_abs_frac = std::abs(frac);
|
| 1443 |
|
|
}
|
| 1444 |
|
|
}
|
| 1445 |
|
|
VERIFY(max_abs_frac < Tp(1.0000000000000008e-12));
|
| 1446 |
|
|
}
|
| 1447 |
|
|
|
| 1448 |
|
|
// Test data for l=20, m=10.
|
| 1449 |
|
|
testcase_sph_legendre<double> data020[] = {
|
| 1450 |
|
|
{ 0.0000000000000000, 20, 10,
|
| 1451 |
|
|
0.0000000000000000 },
|
| 1452 |
|
|
{ 3.0595797603706485e-05, 20, 10,
|
| 1453 |
|
|
0.15707963267948966 },
|
| 1454 |
|
|
{ 0.015924453916397008, 20, 10,
|
| 1455 |
|
|
0.31415926535897931 },
|
| 1456 |
|
|
{ 0.26588079118745700, 20, 10,
|
| 1457 |
|
|
0.47123889803846897 },
|
| 1458 |
|
|
{ 0.54045081420686825, 20, 10,
|
| 1459 |
|
|
0.62831853071795862 },
|
| 1460 |
|
|
{ -0.28215279394285597, 20, 10,
|
| 1461 |
|
|
0.78539816339744828 },
|
| 1462 |
|
|
{ 0.0085297337582246665, 20, 10,
|
| 1463 |
|
|
0.94247779607693793 },
|
| 1464 |
|
|
{ 0.16930127953533775, 20, 10,
|
| 1465 |
|
|
1.0995574287564276 },
|
| 1466 |
|
|
{ -0.27215134048018352, 20, 10,
|
| 1467 |
|
|
1.2566370614359172 },
|
| 1468 |
|
|
{ 0.32456597088029526, 20, 10,
|
| 1469 |
|
|
1.4137166941154069 },
|
| 1470 |
|
|
{ -0.34057893241353715, 20, 10,
|
| 1471 |
|
|
1.5707963267948966 },
|
| 1472 |
|
|
{ 0.32456597088029449, 20, 10,
|
| 1473 |
|
|
1.7278759594743860 },
|
| 1474 |
|
|
{ -0.27215134048018308, 20, 10,
|
| 1475 |
|
|
1.8849555921538759 },
|
| 1476 |
|
|
{ 0.16930127953533725, 20, 10,
|
| 1477 |
|
|
2.0420352248333655 },
|
| 1478 |
|
|
{ 0.0085297337582246665, 20, 10,
|
| 1479 |
|
|
2.1991148575128552 },
|
| 1480 |
|
|
{ -0.28215279394285597, 20, 10,
|
| 1481 |
|
|
2.3561944901923448 },
|
| 1482 |
|
|
{ 0.54045081420686658, 20, 10,
|
| 1483 |
|
|
2.5132741228718345 },
|
| 1484 |
|
|
{ 0.26588079118745822, 20, 10,
|
| 1485 |
|
|
2.6703537555513241 },
|
| 1486 |
|
|
{ 0.015924453916397008, 20, 10,
|
| 1487 |
|
|
2.8274333882308138 },
|
| 1488 |
|
|
{ 3.0595797603707854e-05, 20, 10,
|
| 1489 |
|
|
2.9845130209103035 },
|
| 1490 |
|
|
{ 0.0000000000000000, 20, 10,
|
| 1491 |
|
|
3.1415926535897931 },
|
| 1492 |
|
|
};
|
| 1493 |
|
|
|
| 1494 |
|
|
// Test function for l=20, m=10.
|
| 1495 |
|
|
template <typename Tp>
|
| 1496 |
|
|
void test020()
|
| 1497 |
|
|
{
|
| 1498 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1499 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1500 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1501 |
|
|
unsigned int num_datum = sizeof(data020)
|
| 1502 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 1503 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1504 |
|
|
{
|
| 1505 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data020[i].l), Tp(data020[i].m),
|
| 1506 |
|
|
Tp(data020[i].theta));
|
| 1507 |
|
|
const Tp f0 = data020[i].f0;
|
| 1508 |
|
|
const Tp diff = f - f0;
|
| 1509 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1510 |
|
|
max_abs_diff = std::abs(diff);
|
| 1511 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1512 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1513 |
|
|
{
|
| 1514 |
|
|
const Tp frac = diff / f0;
|
| 1515 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1516 |
|
|
max_abs_frac = std::abs(frac);
|
| 1517 |
|
|
}
|
| 1518 |
|
|
}
|
| 1519 |
|
|
VERIFY(max_abs_frac < Tp(5.0000000000000039e-13));
|
| 1520 |
|
|
}
|
| 1521 |
|
|
|
| 1522 |
|
|
// Test data for l=20, m=20.
|
| 1523 |
|
|
testcase_sph_legendre<double> data021[] = {
|
| 1524 |
|
|
{ 0.0000000000000000, 20, 20,
|
| 1525 |
|
|
0.0000000000000000 },
|
| 1526 |
|
|
{ 4.9264471419245886e-17, 20, 20,
|
| 1527 |
|
|
0.15707963267948966 },
|
| 1528 |
|
|
{ 4.0321091681531780e-11, 20, 20,
|
| 1529 |
|
|
0.31415926535897931 },
|
| 1530 |
|
|
{ 8.8474944184471664e-08, 20, 20,
|
| 1531 |
|
|
0.47123889803846897 },
|
| 1532 |
|
|
{ 1.5497395129387764e-05, 20, 20,
|
| 1533 |
|
|
0.62831853071795862 },
|
| 1534 |
|
|
{ 0.00062457564282984723, 20, 20,
|
| 1535 |
|
|
0.78539816339744828 },
|
| 1536 |
|
|
{ 0.0092265192458967603, 20, 20,
|
| 1537 |
|
|
0.94247779607693793 },
|
| 1538 |
|
|
{ 0.063606673236323269, 20, 20,
|
| 1539 |
|
|
1.0995574287564276 },
|
| 1540 |
|
|
{ 0.23442909509776308, 20, 20,
|
| 1541 |
|
|
1.2566370614359172 },
|
| 1542 |
|
|
{ 0.49921030481087009, 20, 20,
|
| 1543 |
|
|
1.4137166941154069 },
|
| 1544 |
|
|
{ 0.63956545825776223, 20, 20,
|
| 1545 |
|
|
1.5707963267948966 },
|
| 1546 |
|
|
{ 0.49921030481087064, 20, 20,
|
| 1547 |
|
|
1.7278759594743860 },
|
| 1548 |
|
|
{ 0.23442909509776344, 20, 20,
|
| 1549 |
|
|
1.8849555921538759 },
|
| 1550 |
|
|
{ 0.063606673236323352, 20, 20,
|
| 1551 |
|
|
2.0420352248333655 },
|
| 1552 |
|
|
{ 0.0092265192458967603, 20, 20,
|
| 1553 |
|
|
2.1991148575128552 },
|
| 1554 |
|
|
{ 0.00062457564282984723, 20, 20,
|
| 1555 |
|
|
2.3561944901923448 },
|
| 1556 |
|
|
{ 1.5497395129387818e-05, 20, 20,
|
| 1557 |
|
|
2.5132741228718345 },
|
| 1558 |
|
|
{ 8.8474944184472617e-08, 20, 20,
|
| 1559 |
|
|
2.6703537555513241 },
|
| 1560 |
|
|
{ 4.0321091681531780e-11, 20, 20,
|
| 1561 |
|
|
2.8274333882308138 },
|
| 1562 |
|
|
{ 4.9264471419250786e-17, 20, 20,
|
| 1563 |
|
|
2.9845130209103035 },
|
| 1564 |
|
|
{ 0.0000000000000000, 20, 20,
|
| 1565 |
|
|
3.1415926535897931 },
|
| 1566 |
|
|
};
|
| 1567 |
|
|
|
| 1568 |
|
|
// Test function for l=20, m=20.
|
| 1569 |
|
|
template <typename Tp>
|
| 1570 |
|
|
void test021()
|
| 1571 |
|
|
{
|
| 1572 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1573 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1574 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1575 |
|
|
unsigned int num_datum = sizeof(data021)
|
| 1576 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 1577 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1578 |
|
|
{
|
| 1579 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data021[i].l), Tp(data021[i].m),
|
| 1580 |
|
|
Tp(data021[i].theta));
|
| 1581 |
|
|
const Tp f0 = data021[i].f0;
|
| 1582 |
|
|
const Tp diff = f - f0;
|
| 1583 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1584 |
|
|
max_abs_diff = std::abs(diff);
|
| 1585 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1586 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1587 |
|
|
{
|
| 1588 |
|
|
const Tp frac = diff / f0;
|
| 1589 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1590 |
|
|
max_abs_frac = std::abs(frac);
|
| 1591 |
|
|
}
|
| 1592 |
|
|
}
|
| 1593 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 1594 |
|
|
}
|
| 1595 |
|
|
|
| 1596 |
|
|
// Test data for l=50, m=0.
|
| 1597 |
|
|
testcase_sph_legendre<double> data022[] = {
|
| 1598 |
|
|
{ 2.8350175706934717, 50, 0,
|
| 1599 |
|
|
0.0000000000000000 },
|
| 1600 |
|
|
{ 0.53157537495174845, 50, 0,
|
| 1601 |
|
|
0.15707963267948966 },
|
| 1602 |
|
|
{ -0.46056183476301349, 50, 0,
|
| 1603 |
|
|
0.31415926535897931 },
|
| 1604 |
|
|
{ -0.24876032079677909, 50, 0,
|
| 1605 |
|
|
0.47123889803846897 },
|
| 1606 |
|
|
{ 0.36926172901532522, 50, 0,
|
| 1607 |
|
|
0.62831853071795862 },
|
| 1608 |
|
|
{ 0.14571730283563306, 50, 0,
|
| 1609 |
|
|
0.78539816339744828 },
|
| 1610 |
|
|
{ -0.33636199170850811, 50, 0,
|
| 1611 |
|
|
0.94247779607693793 },
|
| 1612 |
|
|
{ -0.079132716267092035, 50, 0,
|
| 1613 |
|
|
1.0995574287564276 },
|
| 1614 |
|
|
{ 0.32232921941301440, 50, 0,
|
| 1615 |
|
|
1.2566370614359172 },
|
| 1616 |
|
|
{ 0.025253991969481446, 50, 0,
|
| 1617 |
|
|
1.4137166941154069 },
|
| 1618 |
|
|
{ -0.31830208724152359, 50, 0,
|
| 1619 |
|
|
1.5707963267948966 },
|
| 1620 |
|
|
{ 0.025253991969476128, 50, 0,
|
| 1621 |
|
|
1.7278759594743860 },
|
| 1622 |
|
|
{ 0.32232921941301479, 50, 0,
|
| 1623 |
|
|
1.8849555921538759 },
|
| 1624 |
|
|
{ -0.079132716267090078, 50, 0,
|
| 1625 |
|
|
2.0420352248333655 },
|
| 1626 |
|
|
{ -0.33636199170850811, 50, 0,
|
| 1627 |
|
|
2.1991148575128552 },
|
| 1628 |
|
|
{ 0.14571730283563306, 50, 0,
|
| 1629 |
|
|
2.3561944901923448 },
|
| 1630 |
|
|
{ 0.36926172901532717, 50, 0,
|
| 1631 |
|
|
2.5132741228718345 },
|
| 1632 |
|
|
{ -0.24876032079677393, 50, 0,
|
| 1633 |
|
|
2.6703537555513241 },
|
| 1634 |
|
|
{ -0.46056183476301349, 50, 0,
|
| 1635 |
|
|
2.8274333882308138 },
|
| 1636 |
|
|
{ 0.53157537495172380, 50, 0,
|
| 1637 |
|
|
2.9845130209103035 },
|
| 1638 |
|
|
{ 2.8350175706934717, 50, 0,
|
| 1639 |
|
|
3.1415926535897931 },
|
| 1640 |
|
|
};
|
| 1641 |
|
|
|
| 1642 |
|
|
// Test function for l=50, m=0.
|
| 1643 |
|
|
template <typename Tp>
|
| 1644 |
|
|
void test022()
|
| 1645 |
|
|
{
|
| 1646 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1647 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1648 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1649 |
|
|
unsigned int num_datum = sizeof(data022)
|
| 1650 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 1651 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1652 |
|
|
{
|
| 1653 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data022[i].l), Tp(data022[i].m),
|
| 1654 |
|
|
Tp(data022[i].theta));
|
| 1655 |
|
|
const Tp f0 = data022[i].f0;
|
| 1656 |
|
|
const Tp diff = f - f0;
|
| 1657 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1658 |
|
|
max_abs_diff = std::abs(diff);
|
| 1659 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1660 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1661 |
|
|
{
|
| 1662 |
|
|
const Tp frac = diff / f0;
|
| 1663 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1664 |
|
|
max_abs_frac = std::abs(frac);
|
| 1665 |
|
|
}
|
| 1666 |
|
|
}
|
| 1667 |
|
|
VERIFY(max_abs_frac < Tp(5.0000000000000039e-13));
|
| 1668 |
|
|
}
|
| 1669 |
|
|
|
| 1670 |
|
|
// Test data for l=50, m=1.
|
| 1671 |
|
|
testcase_sph_legendre<double> data023[] = {
|
| 1672 |
|
|
{ 0.0000000000000000, 50, 1,
|
| 1673 |
|
|
0.0000000000000000 },
|
| 1674 |
|
|
{ -0.63751752155226116, 50, 1,
|
| 1675 |
|
|
0.15707963267948966 },
|
| 1676 |
|
|
{ -0.32616619317604312, 50, 1,
|
| 1677 |
|
|
0.31415926535897931 },
|
| 1678 |
|
|
{ 0.40649930826162706, 50, 1,
|
| 1679 |
|
|
0.47123889803846897 },
|
| 1680 |
|
|
{ 0.18473991408344026, 50, 1,
|
| 1681 |
|
|
0.62831853071795862 },
|
| 1682 |
|
|
{ -0.35083930302013211, 50, 1,
|
| 1683 |
|
|
0.78539816339744828 },
|
| 1684 |
|
|
{ -0.10755382110947098, 50, 1,
|
| 1685 |
|
|
0.94247779607693793 },
|
| 1686 |
|
|
{ 0.32822568316499862, 50, 1,
|
| 1687 |
|
|
1.0995574287564276 },
|
| 1688 |
|
|
{ 0.050286056609798180, 50, 1,
|
| 1689 |
|
|
1.2566370614359172 },
|
| 1690 |
|
|
{ -0.31935368562159638, 50, 1,
|
| 1691 |
|
|
1.4137166941154069 },
|
| 1692 |
|
|
{ -9.8421602686195941e-16, 50, 1,
|
| 1693 |
|
|
1.5707963267948966 },
|
| 1694 |
|
|
{ 0.31935368562159705, 50, 1,
|
| 1695 |
|
|
1.7278759594743860 },
|
| 1696 |
|
|
{ -0.050286056609795383, 50, 1,
|
| 1697 |
|
|
1.8849555921538759 },
|
| 1698 |
|
|
{ -0.32822568316499923, 50, 1,
|
| 1699 |
|
|
2.0420352248333655 },
|
| 1700 |
|
|
{ 0.10755382110947098, 50, 1,
|
| 1701 |
|
|
2.1991148575128552 },
|
| 1702 |
|
|
{ 0.35083930302013211, 50, 1,
|
| 1703 |
|
|
2.3561944901923448 },
|
| 1704 |
|
|
{ -0.18473991408343632, 50, 1,
|
| 1705 |
|
|
2.5132741228718345 },
|
| 1706 |
|
|
{ -0.40649930826163039, 50, 1,
|
| 1707 |
|
|
2.6703537555513241 },
|
| 1708 |
|
|
{ 0.32616619317604312, 50, 1,
|
| 1709 |
|
|
2.8274333882308138 },
|
| 1710 |
|
|
{ 0.63751752155227837, 50, 1,
|
| 1711 |
|
|
2.9845130209103035 },
|
| 1712 |
|
|
{ 0.0000000000000000, 50, 1,
|
| 1713 |
|
|
3.1415926535897931 },
|
| 1714 |
|
|
};
|
| 1715 |
|
|
|
| 1716 |
|
|
// Test function for l=50, m=1.
|
| 1717 |
|
|
template <typename Tp>
|
| 1718 |
|
|
void test023()
|
| 1719 |
|
|
{
|
| 1720 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1721 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1722 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1723 |
|
|
unsigned int num_datum = sizeof(data023)
|
| 1724 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 1725 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1726 |
|
|
{
|
| 1727 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data023[i].l), Tp(data023[i].m),
|
| 1728 |
|
|
Tp(data023[i].theta));
|
| 1729 |
|
|
const Tp f0 = data023[i].f0;
|
| 1730 |
|
|
const Tp diff = f - f0;
|
| 1731 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1732 |
|
|
max_abs_diff = std::abs(diff);
|
| 1733 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1734 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1735 |
|
|
{
|
| 1736 |
|
|
const Tp frac = diff / f0;
|
| 1737 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1738 |
|
|
max_abs_frac = std::abs(frac);
|
| 1739 |
|
|
}
|
| 1740 |
|
|
}
|
| 1741 |
|
|
VERIFY(max_abs_frac < Tp(5.0000000000000039e-13));
|
| 1742 |
|
|
}
|
| 1743 |
|
|
|
| 1744 |
|
|
// Test data for l=50, m=2.
|
| 1745 |
|
|
testcase_sph_legendre<double> data024[] = {
|
| 1746 |
|
|
{ 0.0000000000000000, 50, 2,
|
| 1747 |
|
|
0.0000000000000000 },
|
| 1748 |
|
|
{ -0.37230261163839168, 50, 2,
|
| 1749 |
|
|
0.15707963267948966 },
|
| 1750 |
|
|
{ 0.50051599680315972, 50, 2,
|
| 1751 |
|
|
0.31415926535897931 },
|
| 1752 |
|
|
{ 0.21724795180329545, 50, 2,
|
| 1753 |
|
|
0.47123889803846897 },
|
| 1754 |
|
|
{ -0.37948127307610940, 50, 2,
|
| 1755 |
|
|
0.62831853071795862 },
|
| 1756 |
|
|
{ -0.13187372121003119, 50, 2,
|
| 1757 |
|
|
0.78539816339744828 },
|
| 1758 |
|
|
{ 0.33959009162400194, 50, 2,
|
| 1759 |
|
|
0.94247779607693793 },
|
| 1760 |
|
|
{ 0.072537503112490409, 50, 2,
|
| 1761 |
|
|
1.0995574287564276 },
|
| 1762 |
|
|
{ -0.32310306941855271, 50, 2,
|
| 1763 |
|
|
1.2566370614359172 },
|
| 1764 |
|
|
{ -0.023259822816436588, 50, 2,
|
| 1765 |
|
|
1.4137166941154069 },
|
| 1766 |
|
|
{ 0.31842698506357275, 50, 2,
|
| 1767 |
|
|
1.5707963267948966 },
|
| 1768 |
|
|
{ -0.023259822816431144, 50, 2,
|
| 1769 |
|
|
1.7278759594743860 },
|
| 1770 |
|
|
{ -0.32310306941855299, 50, 2,
|
| 1771 |
|
|
1.8849555921538759 },
|
| 1772 |
|
|
{ 0.072537503112488369, 50, 2,
|
| 1773 |
|
|
2.0420352248333655 },
|
| 1774 |
|
|
{ 0.33959009162400194, 50, 2,
|
| 1775 |
|
|
2.1991148575128552 },
|
| 1776 |
|
|
{ -0.13187372121003119, 50, 2,
|
| 1777 |
|
|
2.3561944901923448 },
|
| 1778 |
|
|
{ -0.37948127307611074, 50, 2,
|
| 1779 |
|
|
2.5132741228718345 },
|
| 1780 |
|
|
{ 0.21724795180328935, 50, 2,
|
| 1781 |
|
|
2.6703537555513241 },
|
| 1782 |
|
|
{ 0.50051599680315972, 50, 2,
|
| 1783 |
|
|
2.8274333882308138 },
|
| 1784 |
|
|
{ -0.37230261163836298, 50, 2,
|
| 1785 |
|
|
2.9845130209103035 },
|
| 1786 |
|
|
{ 0.0000000000000000, 50, 2,
|
| 1787 |
|
|
3.1415926535897931 },
|
| 1788 |
|
|
};
|
| 1789 |
|
|
|
| 1790 |
|
|
// Test function for l=50, m=2.
|
| 1791 |
|
|
template <typename Tp>
|
| 1792 |
|
|
void test024()
|
| 1793 |
|
|
{
|
| 1794 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1795 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1796 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1797 |
|
|
unsigned int num_datum = sizeof(data024)
|
| 1798 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 1799 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1800 |
|
|
{
|
| 1801 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data024[i].l), Tp(data024[i].m),
|
| 1802 |
|
|
Tp(data024[i].theta));
|
| 1803 |
|
|
const Tp f0 = data024[i].f0;
|
| 1804 |
|
|
const Tp diff = f - f0;
|
| 1805 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1806 |
|
|
max_abs_diff = std::abs(diff);
|
| 1807 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1808 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1809 |
|
|
{
|
| 1810 |
|
|
const Tp frac = diff / f0;
|
| 1811 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1812 |
|
|
max_abs_frac = std::abs(frac);
|
| 1813 |
|
|
}
|
| 1814 |
|
|
}
|
| 1815 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000015e-12));
|
| 1816 |
|
|
}
|
| 1817 |
|
|
|
| 1818 |
|
|
// Test data for l=50, m=5.
|
| 1819 |
|
|
testcase_sph_legendre<double> data025[] = {
|
| 1820 |
|
|
{ 0.0000000000000000, 50, 5,
|
| 1821 |
|
|
0.0000000000000000 },
|
| 1822 |
|
|
{ -0.57750385903193069, 50, 5,
|
| 1823 |
|
|
0.15707963267948966 },
|
| 1824 |
|
|
{ 0.077360497065584566, 50, 5,
|
| 1825 |
|
|
0.31415926535897931 },
|
| 1826 |
|
|
{ 0.47707267400540210, 50, 5,
|
| 1827 |
|
|
0.47123889803846897 },
|
| 1828 |
|
|
{ 0.055370615126630537, 50, 5,
|
| 1829 |
|
|
0.62831853071795862 },
|
| 1830 |
|
|
{ -0.37629451847202855, 50, 5,
|
| 1831 |
|
|
0.78539816339744828 },
|
| 1832 |
|
|
{ -0.048042277801960624, 50, 5,
|
| 1833 |
|
|
0.94247779607693793 },
|
| 1834 |
|
|
{ 0.33619379362228685, 50, 5,
|
| 1835 |
|
|
1.0995574287564276 },
|
| 1836 |
|
|
{ 0.025265227185719726, 50, 5,
|
| 1837 |
|
|
1.2566370614359172 },
|
| 1838 |
|
|
{ -0.32083679430964518, 50, 5,
|
| 1839 |
|
|
1.4137166941154069 },
|
| 1840 |
|
|
{ -9.8189201019751884e-16, 50, 5,
|
| 1841 |
|
|
1.5707963267948966 },
|
| 1842 |
|
|
{ 0.32083679430964590, 50, 5,
|
| 1843 |
|
|
1.7278759594743860 },
|
| 1844 |
|
|
{ -0.025265227185716856, 50, 5,
|
| 1845 |
|
|
1.8849555921538759 },
|
| 1846 |
|
|
{ -0.33619379362228730, 50, 5,
|
| 1847 |
|
|
2.0420352248333655 },
|
| 1848 |
|
|
{ 0.048042277801960624, 50, 5,
|
| 1849 |
|
|
2.1991148575128552 },
|
| 1850 |
|
|
{ 0.37629451847202855, 50, 5,
|
| 1851 |
|
|
2.3561944901923448 },
|
| 1852 |
|
|
{ -0.055370615126626936, 50, 5,
|
| 1853 |
|
|
2.5132741228718345 },
|
| 1854 |
|
|
{ -0.47707267400540210, 50, 5,
|
| 1855 |
|
|
2.6703537555513241 },
|
| 1856 |
|
|
{ -0.077360497065584566, 50, 5,
|
| 1857 |
|
|
2.8274333882308138 },
|
| 1858 |
|
|
{ 0.57750385903191004, 50, 5,
|
| 1859 |
|
|
2.9845130209103035 },
|
| 1860 |
|
|
{ 0.0000000000000000, 50, 5,
|
| 1861 |
|
|
3.1415926535897931 },
|
| 1862 |
|
|
};
|
| 1863 |
|
|
|
| 1864 |
|
|
// Test function for l=50, m=5.
|
| 1865 |
|
|
template <typename Tp>
|
| 1866 |
|
|
void test025()
|
| 1867 |
|
|
{
|
| 1868 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1869 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1870 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1871 |
|
|
unsigned int num_datum = sizeof(data025)
|
| 1872 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 1873 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1874 |
|
|
{
|
| 1875 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data025[i].l), Tp(data025[i].m),
|
| 1876 |
|
|
Tp(data025[i].theta));
|
| 1877 |
|
|
const Tp f0 = data025[i].f0;
|
| 1878 |
|
|
const Tp diff = f - f0;
|
| 1879 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1880 |
|
|
max_abs_diff = std::abs(diff);
|
| 1881 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1882 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1883 |
|
|
{
|
| 1884 |
|
|
const Tp frac = diff / f0;
|
| 1885 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1886 |
|
|
max_abs_frac = std::abs(frac);
|
| 1887 |
|
|
}
|
| 1888 |
|
|
}
|
| 1889 |
|
|
VERIFY(max_abs_frac < Tp(1.0000000000000008e-12));
|
| 1890 |
|
|
}
|
| 1891 |
|
|
|
| 1892 |
|
|
// Test data for l=50, m=10.
|
| 1893 |
|
|
testcase_sph_legendre<double> data026[] = {
|
| 1894 |
|
|
{ 0.0000000000000000, 50, 10,
|
| 1895 |
|
|
0.0000000000000000 },
|
| 1896 |
|
|
{ 0.15606941844800759, 50, 10,
|
| 1897 |
|
|
0.15707963267948966 },
|
| 1898 |
|
|
{ -0.53748868836814601, 50, 10,
|
| 1899 |
|
|
0.31415926535897931 },
|
| 1900 |
|
|
{ -0.49304919025183896, 50, 10,
|
| 1901 |
|
|
0.47123889803846897 },
|
| 1902 |
|
|
{ -0.26267582750428264, 50, 10,
|
| 1903 |
|
|
0.62831853071795862 },
|
| 1904 |
|
|
{ 0.22058983666314402, 50, 10,
|
| 1905 |
|
|
0.78539816339744828 },
|
| 1906 |
|
|
{ 0.32936725160671759, 50, 10,
|
| 1907 |
|
|
0.94247779607693793 },
|
| 1908 |
|
|
{ -0.092053311559446988, 50, 10,
|
| 1909 |
|
|
1.0995574287564276 },
|
| 1910 |
|
|
{ -0.32542913495935555, 50, 10,
|
| 1911 |
|
|
1.2566370614359172 },
|
| 1912 |
|
|
{ 0.025673223789103500, 50, 10,
|
| 1913 |
|
|
1.4137166941154069 },
|
| 1914 |
|
|
{ 0.32150019350255743, 50, 10,
|
| 1915 |
|
|
1.5707963267948966 },
|
| 1916 |
|
|
{ 0.025673223789108864, 50, 10,
|
| 1917 |
|
|
1.7278759594743860 },
|
| 1918 |
|
|
{ -0.32542913495935494, 50, 10,
|
| 1919 |
|
|
1.8849555921538759 },
|
| 1920 |
|
|
{ -0.092053311559448570, 50, 10,
|
| 1921 |
|
|
2.0420352248333655 },
|
| 1922 |
|
|
{ 0.32936725160671759, 50, 10,
|
| 1923 |
|
|
2.1991148575128552 },
|
| 1924 |
|
|
{ 0.22058983666314402, 50, 10,
|
| 1925 |
|
|
2.3561944901923448 },
|
| 1926 |
|
|
{ -0.26267582750427909, 50, 10,
|
| 1927 |
|
|
2.5132741228718345 },
|
| 1928 |
|
|
{ -0.49304919025184119, 50, 10,
|
| 1929 |
|
|
2.6703537555513241 },
|
| 1930 |
|
|
{ -0.53748868836814601, 50, 10,
|
| 1931 |
|
|
2.8274333882308138 },
|
| 1932 |
|
|
{ 0.15606941844801259, 50, 10,
|
| 1933 |
|
|
2.9845130209103035 },
|
| 1934 |
|
|
{ 0.0000000000000000, 50, 10,
|
| 1935 |
|
|
3.1415926535897931 },
|
| 1936 |
|
|
};
|
| 1937 |
|
|
|
| 1938 |
|
|
// Test function for l=50, m=10.
|
| 1939 |
|
|
template <typename Tp>
|
| 1940 |
|
|
void test026()
|
| 1941 |
|
|
{
|
| 1942 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 1943 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 1944 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 1945 |
|
|
unsigned int num_datum = sizeof(data026)
|
| 1946 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 1947 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 1948 |
|
|
{
|
| 1949 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data026[i].l), Tp(data026[i].m),
|
| 1950 |
|
|
Tp(data026[i].theta));
|
| 1951 |
|
|
const Tp f0 = data026[i].f0;
|
| 1952 |
|
|
const Tp diff = f - f0;
|
| 1953 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 1954 |
|
|
max_abs_diff = std::abs(diff);
|
| 1955 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 1956 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 1957 |
|
|
{
|
| 1958 |
|
|
const Tp frac = diff / f0;
|
| 1959 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 1960 |
|
|
max_abs_frac = std::abs(frac);
|
| 1961 |
|
|
}
|
| 1962 |
|
|
}
|
| 1963 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 1964 |
|
|
}
|
| 1965 |
|
|
|
| 1966 |
|
|
// Test data for l=50, m=20.
|
| 1967 |
|
|
testcase_sph_legendre<double> data027[] = {
|
| 1968 |
|
|
{ 0.0000000000000000, 50, 20,
|
| 1969 |
|
|
0.0000000000000000 },
|
| 1970 |
|
|
{ 3.0409598712833082e-07, 50, 20,
|
| 1971 |
|
|
0.15707963267948966 },
|
| 1972 |
|
|
{ 0.030940518122882305, 50, 20,
|
| 1973 |
|
|
0.31415926535897931 },
|
| 1974 |
|
|
{ 0.64134588721659935, 50, 20,
|
| 1975 |
|
|
0.47123889803846897 },
|
| 1976 |
|
|
{ 0.29895244392136394, 50, 20,
|
| 1977 |
|
|
0.62831853071795862 },
|
| 1978 |
|
|
{ 0.25309324781874065, 50, 20,
|
| 1979 |
|
|
0.78539816339744828 },
|
| 1980 |
|
|
{ 0.34368634714931712, 50, 20,
|
| 1981 |
|
|
0.94247779607693793 },
|
| 1982 |
|
|
{ 0.33996764360663956, 50, 20,
|
| 1983 |
|
|
1.0995574287564276 },
|
| 1984 |
|
|
{ 0.12866267745104118, 50, 20,
|
| 1985 |
|
|
1.2566370614359172 },
|
| 1986 |
|
|
{ -0.18201114398922874, 50, 20,
|
| 1987 |
|
|
1.4137166941154069 },
|
| 1988 |
|
|
{ -0.33216683431510857, 50, 20,
|
| 1989 |
|
|
1.5707963267948966 },
|
| 1990 |
|
|
{ -0.18201114398923304, 50, 20,
|
| 1991 |
|
|
1.7278759594743860 },
|
| 1992 |
|
|
{ 0.12866267745103846, 50, 20,
|
| 1993 |
|
|
1.8849555921538759 },
|
| 1994 |
|
|
{ 0.33996764360663906, 50, 20,
|
| 1995 |
|
|
2.0420352248333655 },
|
| 1996 |
|
|
{ 0.34368634714931712, 50, 20,
|
| 1997 |
|
|
2.1991148575128552 },
|
| 1998 |
|
|
{ 0.25309324781874065, 50, 20,
|
| 1999 |
|
|
2.3561944901923448 },
|
| 2000 |
|
|
{ 0.29895244392136738, 50, 20,
|
| 2001 |
|
|
2.5132741228718345 },
|
| 2002 |
|
|
{ 0.64134588721659791, 50, 20,
|
| 2003 |
|
|
2.6703537555513241 },
|
| 2004 |
|
|
{ 0.030940518122882305, 50, 20,
|
| 2005 |
|
|
2.8274333882308138 },
|
| 2006 |
|
|
{ 3.0409598712835877e-07, 50, 20,
|
| 2007 |
|
|
2.9845130209103035 },
|
| 2008 |
|
|
{ 0.0000000000000000, 50, 20,
|
| 2009 |
|
|
3.1415926535897931 },
|
| 2010 |
|
|
};
|
| 2011 |
|
|
|
| 2012 |
|
|
// Test function for l=50, m=20.
|
| 2013 |
|
|
template <typename Tp>
|
| 2014 |
|
|
void test027()
|
| 2015 |
|
|
{
|
| 2016 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2017 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2018 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2019 |
|
|
unsigned int num_datum = sizeof(data027)
|
| 2020 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 2021 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2022 |
|
|
{
|
| 2023 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data027[i].l), Tp(data027[i].m),
|
| 2024 |
|
|
Tp(data027[i].theta));
|
| 2025 |
|
|
const Tp f0 = data027[i].f0;
|
| 2026 |
|
|
const Tp diff = f - f0;
|
| 2027 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2028 |
|
|
max_abs_diff = std::abs(diff);
|
| 2029 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2030 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2031 |
|
|
{
|
| 2032 |
|
|
const Tp frac = diff / f0;
|
| 2033 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2034 |
|
|
max_abs_frac = std::abs(frac);
|
| 2035 |
|
|
}
|
| 2036 |
|
|
}
|
| 2037 |
|
|
VERIFY(max_abs_frac < Tp(5.0000000000000039e-13));
|
| 2038 |
|
|
}
|
| 2039 |
|
|
|
| 2040 |
|
|
// Test data for l=50, m=50.
|
| 2041 |
|
|
testcase_sph_legendre<double> data028[] = {
|
| 2042 |
|
|
{ 0.0000000000000000, 50, 50,
|
| 2043 |
|
|
0.0000000000000000 },
|
| 2044 |
|
|
{ 4.1649039898151844e-41, 50, 50,
|
| 2045 |
|
|
0.15707963267948966 },
|
| 2046 |
|
|
{ 2.5240684647724192e-26, 50, 50,
|
| 2047 |
|
|
0.31415926535897931 },
|
| 2048 |
|
|
{ 5.6927376423967334e-18, 50, 50,
|
| 2049 |
|
|
0.47123889803846897 },
|
| 2050 |
|
|
{ 2.3116239814797057e-12, 50, 50,
|
| 2051 |
|
|
0.62831853071795862 },
|
| 2052 |
|
|
{ 2.3835981241325311e-08, 50, 50,
|
| 2053 |
|
|
0.78539816339744828 },
|
| 2054 |
|
|
{ 1.9992410287270356e-05, 50, 50,
|
| 2055 |
|
|
0.94247779607693793 },
|
| 2056 |
|
|
{ 0.0024947505670829791, 50, 50,
|
| 2057 |
|
|
1.0995574287564276 },
|
| 2058 |
|
|
{ 0.065057774647971175, 50, 50,
|
| 2059 |
|
|
1.2566370614359172 },
|
| 2060 |
|
|
{ 0.43050607056732243, 50, 50,
|
| 2061 |
|
|
1.4137166941154069 },
|
| 2062 |
|
|
{ 0.79980281171531975, 50, 50,
|
| 2063 |
|
|
1.5707963267948966 },
|
| 2064 |
|
|
{ 0.43050607056732360, 50, 50,
|
| 2065 |
|
|
1.7278759594743860 },
|
| 2066 |
|
|
{ 0.065057774647971384, 50, 50,
|
| 2067 |
|
|
1.8849555921538759 },
|
| 2068 |
|
|
{ 0.0024947505670829856, 50, 50,
|
| 2069 |
|
|
2.0420352248333655 },
|
| 2070 |
|
|
{ 1.9992410287270356e-05, 50, 50,
|
| 2071 |
|
|
2.1991148575128552 },
|
| 2072 |
|
|
{ 2.3835981241325311e-08, 50, 50,
|
| 2073 |
|
|
2.3561944901923448 },
|
| 2074 |
|
|
{ 2.3116239814797222e-12, 50, 50,
|
| 2075 |
|
|
2.5132741228718345 },
|
| 2076 |
|
|
{ 5.6927376423968544e-18, 50, 50,
|
| 2077 |
|
|
2.6703537555513241 },
|
| 2078 |
|
|
{ 2.5240684647724192e-26, 50, 50,
|
| 2079 |
|
|
2.8274333882308138 },
|
| 2080 |
|
|
{ 4.1649039898161316e-41, 50, 50,
|
| 2081 |
|
|
2.9845130209103035 },
|
| 2082 |
|
|
{ 0.0000000000000000, 50, 50,
|
| 2083 |
|
|
3.1415926535897931 },
|
| 2084 |
|
|
};
|
| 2085 |
|
|
|
| 2086 |
|
|
// Test function for l=50, m=50.
|
| 2087 |
|
|
template <typename Tp>
|
| 2088 |
|
|
void test028()
|
| 2089 |
|
|
{
|
| 2090 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2091 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2092 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2093 |
|
|
unsigned int num_datum = sizeof(data028)
|
| 2094 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 2095 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2096 |
|
|
{
|
| 2097 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data028[i].l), Tp(data028[i].m),
|
| 2098 |
|
|
Tp(data028[i].theta));
|
| 2099 |
|
|
const Tp f0 = data028[i].f0;
|
| 2100 |
|
|
const Tp diff = f - f0;
|
| 2101 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2102 |
|
|
max_abs_diff = std::abs(diff);
|
| 2103 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2104 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2105 |
|
|
{
|
| 2106 |
|
|
const Tp frac = diff / f0;
|
| 2107 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2108 |
|
|
max_abs_frac = std::abs(frac);
|
| 2109 |
|
|
}
|
| 2110 |
|
|
}
|
| 2111 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 2112 |
|
|
}
|
| 2113 |
|
|
|
| 2114 |
|
|
// Test data for l=100, m=0.
|
| 2115 |
|
|
testcase_sph_legendre<double> data029[] = {
|
| 2116 |
|
|
{ 3.9993839251484076, 100, 0,
|
| 2117 |
|
|
0.0000000000000000 },
|
| 2118 |
|
|
{ -0.60770160285935471, 100, 0,
|
| 2119 |
|
|
0.15707963267948966 },
|
| 2120 |
|
|
{ 0.46193027883956100, 100, 0,
|
| 2121 |
|
|
0.31415926535897931 },
|
| 2122 |
|
|
{ -0.40218718869815234, 100, 0,
|
| 2123 |
|
|
0.47123889803846897 },
|
| 2124 |
|
|
{ 0.36960201406910737, 100, 0,
|
| 2125 |
|
|
0.62831853071795862 },
|
| 2126 |
|
|
{ -0.34953726547378611, 100, 0,
|
| 2127 |
|
|
0.78539816339744828 },
|
| 2128 |
|
|
{ 0.33646959352497846, 100, 0,
|
| 2129 |
|
|
0.94247779607693793 },
|
| 2130 |
|
|
{ -0.32784733067663169, 100, 0,
|
| 2131 |
|
|
1.0995574287564276 },
|
| 2132 |
|
|
{ 0.32235624474047936, 100, 0,
|
| 2133 |
|
|
1.2566370614359172 },
|
| 2134 |
|
|
{ -0.31929330706601283, 100, 0,
|
| 2135 |
|
|
1.4137166941154069 },
|
| 2136 |
|
|
{ 0.31830791662110325, 100, 0,
|
| 2137 |
|
|
1.5707963267948966 },
|
| 2138 |
|
|
{ -0.31929330706601389, 100, 0,
|
| 2139 |
|
|
1.7278759594743860 },
|
| 2140 |
|
|
{ 0.32235624474048052, 100, 0,
|
| 2141 |
|
|
1.8849555921538759 },
|
| 2142 |
|
|
{ -0.32784733067663291, 100, 0,
|
| 2143 |
|
|
2.0420352248333655 },
|
| 2144 |
|
|
{ 0.33646959352497846, 100, 0,
|
| 2145 |
|
|
2.1991148575128552 },
|
| 2146 |
|
|
{ -0.34953726547378611, 100, 0,
|
| 2147 |
|
|
2.3561944901923448 },
|
| 2148 |
|
|
{ 0.36960201406911114, 100, 0,
|
| 2149 |
|
|
2.5132741228718345 },
|
| 2150 |
|
|
{ -0.40218718869815695, 100, 0,
|
| 2151 |
|
|
2.6703537555513241 },
|
| 2152 |
|
|
{ 0.46193027883956100, 100, 0,
|
| 2153 |
|
|
2.8274333882308138 },
|
| 2154 |
|
|
{ -0.60770160285939478, 100, 0,
|
| 2155 |
|
|
2.9845130209103035 },
|
| 2156 |
|
|
{ 3.9993839251484076, 100, 0,
|
| 2157 |
|
|
3.1415926535897931 },
|
| 2158 |
|
|
};
|
| 2159 |
|
|
|
| 2160 |
|
|
// Test function for l=100, m=0.
|
| 2161 |
|
|
template <typename Tp>
|
| 2162 |
|
|
void test029()
|
| 2163 |
|
|
{
|
| 2164 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2165 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2166 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2167 |
|
|
unsigned int num_datum = sizeof(data029)
|
| 2168 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 2169 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2170 |
|
|
{
|
| 2171 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data029[i].l), Tp(data029[i].m),
|
| 2172 |
|
|
Tp(data029[i].theta));
|
| 2173 |
|
|
const Tp f0 = data029[i].f0;
|
| 2174 |
|
|
const Tp diff = f - f0;
|
| 2175 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2176 |
|
|
max_abs_diff = std::abs(diff);
|
| 2177 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2178 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2179 |
|
|
{
|
| 2180 |
|
|
const Tp frac = diff / f0;
|
| 2181 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2182 |
|
|
max_abs_frac = std::abs(frac);
|
| 2183 |
|
|
}
|
| 2184 |
|
|
}
|
| 2185 |
|
|
VERIFY(max_abs_frac < Tp(1.0000000000000008e-12));
|
| 2186 |
|
|
}
|
| 2187 |
|
|
|
| 2188 |
|
|
// Test data for l=100, m=1.
|
| 2189 |
|
|
testcase_sph_legendre<double> data030[] = {
|
| 2190 |
|
|
{ 0.0000000000000000, 100, 1,
|
| 2191 |
|
|
0.0000000000000000 },
|
| 2192 |
|
|
{ -0.50851949013719622, 100, 1,
|
| 2193 |
|
|
0.15707963267948966 },
|
| 2194 |
|
|
{ 0.33129641402221310, 100, 1,
|
| 2195 |
|
|
0.31415926535897931 },
|
| 2196 |
|
|
{ -0.24390405750942562, 100, 1,
|
| 2197 |
|
|
0.47123889803846897 },
|
| 2198 |
|
|
{ 0.18659755088414165, 100, 1,
|
| 2199 |
|
|
0.62831853071795862 },
|
| 2200 |
|
|
{ -0.14355908970516640, 100, 1,
|
| 2201 |
|
|
0.78539816339744828 },
|
| 2202 |
|
|
{ 0.10844906813251093, 100, 1,
|
| 2203 |
|
|
0.94247779607693793 },
|
| 2204 |
|
|
{ -0.078100088690859812, 100, 1,
|
| 2205 |
|
|
1.0995574287564276 },
|
| 2206 |
|
|
{ 0.050670002998304528, 100, 1,
|
| 2207 |
|
|
1.2566370614359172 },
|
| 2208 |
|
|
{ -0.024941251747138762, 100, 1,
|
| 2209 |
|
|
1.4137166941154069 },
|
| 2210 |
|
|
{ 1.9587949830851639e-15, 100, 1,
|
| 2211 |
|
|
1.5707963267948966 },
|
| 2212 |
|
|
{ 0.024941251747127649, 100, 1,
|
| 2213 |
|
|
1.7278759594743860 },
|
| 2214 |
|
|
{ -0.050670002998298595, 100, 1,
|
| 2215 |
|
|
1.8849555921538759 },
|
| 2216 |
|
|
{ 0.078100088690855676, 100, 1,
|
| 2217 |
|
|
2.0420352248333655 },
|
| 2218 |
|
|
{ -0.10844906813251093, 100, 1,
|
| 2219 |
|
|
2.1991148575128552 },
|
| 2220 |
|
|
{ 0.14355908970516640, 100, 1,
|
| 2221 |
|
|
2.3561944901923448 },
|
| 2222 |
|
|
{ -0.18659755088413349, 100, 1,
|
| 2223 |
|
|
2.5132741228718345 },
|
| 2224 |
|
|
{ 0.24390405750941485, 100, 1,
|
| 2225 |
|
|
2.6703537555513241 },
|
| 2226 |
|
|
{ -0.33129641402221310, 100, 1,
|
| 2227 |
|
|
2.8274333882308138 },
|
| 2228 |
|
|
{ 0.50851949013714548, 100, 1,
|
| 2229 |
|
|
2.9845130209103035 },
|
| 2230 |
|
|
{ 0.0000000000000000, 100, 1,
|
| 2231 |
|
|
3.1415926535897931 },
|
| 2232 |
|
|
};
|
| 2233 |
|
|
|
| 2234 |
|
|
// Test function for l=100, m=1.
|
| 2235 |
|
|
template <typename Tp>
|
| 2236 |
|
|
void test030()
|
| 2237 |
|
|
{
|
| 2238 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2239 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2240 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2241 |
|
|
unsigned int num_datum = sizeof(data030)
|
| 2242 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 2243 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2244 |
|
|
{
|
| 2245 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data030[i].l), Tp(data030[i].m),
|
| 2246 |
|
|
Tp(data030[i].theta));
|
| 2247 |
|
|
const Tp f0 = data030[i].f0;
|
| 2248 |
|
|
const Tp diff = f - f0;
|
| 2249 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2250 |
|
|
max_abs_diff = std::abs(diff);
|
| 2251 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2252 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2253 |
|
|
{
|
| 2254 |
|
|
const Tp frac = diff / f0;
|
| 2255 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2256 |
|
|
max_abs_frac = std::abs(frac);
|
| 2257 |
|
|
}
|
| 2258 |
|
|
}
|
| 2259 |
|
|
VERIFY(max_abs_frac < Tp(1.0000000000000008e-12));
|
| 2260 |
|
|
}
|
| 2261 |
|
|
|
| 2262 |
|
|
// Test data for l=100, m=2.
|
| 2263 |
|
|
testcase_sph_legendre<double> data031[] = {
|
| 2264 |
|
|
{ 0.0000000000000000, 100, 2,
|
| 2265 |
|
|
0.0000000000000000 },
|
| 2266 |
|
|
{ 0.67166274297194040, 100, 2,
|
| 2267 |
|
|
0.15707963267948966 },
|
| 2268 |
|
|
{ -0.48226933687995144, 100, 2,
|
| 2269 |
|
|
0.31415926535897931 },
|
| 2270 |
|
|
{ 0.41175421895715447, 100, 2,
|
| 2271 |
|
|
0.47123889803846897 },
|
| 2272 |
|
|
{ -0.37475021787822460, 100, 2,
|
| 2273 |
|
|
0.62831853071795862 },
|
| 2274 |
|
|
{ 0.35242909383605475, 100, 2,
|
| 2275 |
|
|
0.78539816339744828 },
|
| 2276 |
|
|
{ -0.33807110409160002, 100, 2,
|
| 2277 |
|
|
0.94247779607693793 },
|
| 2278 |
|
|
{ 0.32867180390709999, 100, 2,
|
| 2279 |
|
|
1.0995574287564276 },
|
| 2280 |
|
|
{ -0.32271583790278469, 100, 2,
|
| 2281 |
|
|
1.2566370614359172 },
|
| 2282 |
|
|
{ 0.31940354677687433, 100, 2,
|
| 2283 |
|
|
1.4137166941154069 },
|
| 2284 |
|
|
{ -0.31833943693772526, 100, 2,
|
| 2285 |
|
|
1.5707963267948966 },
|
| 2286 |
|
|
{ 0.31940354677687521, 100, 2,
|
| 2287 |
|
|
1.7278759594743860 },
|
| 2288 |
|
|
{ -0.32271583790278524, 100, 2,
|
| 2289 |
|
|
1.8849555921538759 },
|
| 2290 |
|
|
{ 0.32867180390710143, 100, 2,
|
| 2291 |
|
|
2.0420352248333655 },
|
| 2292 |
|
|
{ -0.33807110409160002, 100, 2,
|
| 2293 |
|
|
2.1991148575128552 },
|
| 2294 |
|
|
{ 0.35242909383605475, 100, 2,
|
| 2295 |
|
|
2.3561944901923448 },
|
| 2296 |
|
|
{ -0.37475021787822771, 100, 2,
|
| 2297 |
|
|
2.5132741228718345 },
|
| 2298 |
|
|
{ 0.41175421895716069, 100, 2,
|
| 2299 |
|
|
2.6703537555513241 },
|
| 2300 |
|
|
{ -0.48226933687995144, 100, 2,
|
| 2301 |
|
|
2.8274333882308138 },
|
| 2302 |
|
|
{ 0.67166274297196804, 100, 2,
|
| 2303 |
|
|
2.9845130209103035 },
|
| 2304 |
|
|
{ 0.0000000000000000, 100, 2,
|
| 2305 |
|
|
3.1415926535897931 },
|
| 2306 |
|
|
};
|
| 2307 |
|
|
|
| 2308 |
|
|
// Test function for l=100, m=2.
|
| 2309 |
|
|
template <typename Tp>
|
| 2310 |
|
|
void test031()
|
| 2311 |
|
|
{
|
| 2312 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2313 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2314 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2315 |
|
|
unsigned int num_datum = sizeof(data031)
|
| 2316 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 2317 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2318 |
|
|
{
|
| 2319 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data031[i].l), Tp(data031[i].m),
|
| 2320 |
|
|
Tp(data031[i].theta));
|
| 2321 |
|
|
const Tp f0 = data031[i].f0;
|
| 2322 |
|
|
const Tp diff = f - f0;
|
| 2323 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2324 |
|
|
max_abs_diff = std::abs(diff);
|
| 2325 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2326 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2327 |
|
|
{
|
| 2328 |
|
|
const Tp frac = diff / f0;
|
| 2329 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2330 |
|
|
max_abs_frac = std::abs(frac);
|
| 2331 |
|
|
}
|
| 2332 |
|
|
}
|
| 2333 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000020e-13));
|
| 2334 |
|
|
}
|
| 2335 |
|
|
|
| 2336 |
|
|
// Test data for l=100, m=5.
|
| 2337 |
|
|
testcase_sph_legendre<double> data032[] = {
|
| 2338 |
|
|
{ 0.0000000000000000, 100, 5,
|
| 2339 |
|
|
0.0000000000000000 },
|
| 2340 |
|
|
{ 0.062564361105907143, 100, 5,
|
| 2341 |
|
|
0.15707963267948966 },
|
| 2342 |
|
|
{ 0.14179554455880186, 100, 5,
|
| 2343 |
|
|
0.31415926535897931 },
|
| 2344 |
|
|
{ -0.14356866942906019, 100, 5,
|
| 2345 |
|
|
0.47123889803846897 },
|
| 2346 |
|
|
{ 0.12355483388448507, 100, 5,
|
| 2347 |
|
|
0.62831853071795862 },
|
| 2348 |
|
|
{ -0.10090029999681098, 100, 5,
|
| 2349 |
|
|
0.78539816339744828 },
|
| 2350 |
|
|
{ 0.078905134460230564, 100, 5,
|
| 2351 |
|
|
0.94247779607693793 },
|
| 2352 |
|
|
{ -0.058040182398187236, 100, 5,
|
| 2353 |
|
|
1.0995574287564276 },
|
| 2354 |
|
|
{ 0.038142759389484152, 100, 5,
|
| 2355 |
|
|
1.2566370614359172 },
|
| 2356 |
|
|
{ -0.018906264170660277, 100, 5,
|
| 2357 |
|
|
1.4137166941154069 },
|
| 2358 |
|
|
{ 1.9576303042914544e-15, 100, 5,
|
| 2359 |
|
|
1.5707963267948966 },
|
| 2360 |
|
|
{ 0.018906264170649747, 100, 5,
|
| 2361 |
|
|
1.7278759594743860 },
|
| 2362 |
|
|
{ -0.038142759389478524, 100, 5,
|
| 2363 |
|
|
1.8849555921538759 },
|
| 2364 |
|
|
{ 0.058040182398182996, 100, 5,
|
| 2365 |
|
|
2.0420352248333655 },
|
| 2366 |
|
|
{ -0.078905134460230564, 100, 5,
|
| 2367 |
|
|
2.1991148575128552 },
|
| 2368 |
|
|
{ 0.10090029999681098, 100, 5,
|
| 2369 |
|
|
2.3561944901923448 },
|
| 2370 |
|
|
{ -0.12355483388447780, 100, 5,
|
| 2371 |
|
|
2.5132741228718345 },
|
| 2372 |
|
|
{ 0.14356866942904903, 100, 5,
|
| 2373 |
|
|
2.6703537555513241 },
|
| 2374 |
|
|
{ -0.14179554455880186, 100, 5,
|
| 2375 |
|
|
2.8274333882308138 },
|
| 2376 |
|
|
{ -0.062564361105959004, 100, 5,
|
| 2377 |
|
|
2.9845130209103035 },
|
| 2378 |
|
|
{ 0.0000000000000000, 100, 5,
|
| 2379 |
|
|
3.1415926535897931 },
|
| 2380 |
|
|
};
|
| 2381 |
|
|
|
| 2382 |
|
|
// Test function for l=100, m=5.
|
| 2383 |
|
|
template <typename Tp>
|
| 2384 |
|
|
void test032()
|
| 2385 |
|
|
{
|
| 2386 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2387 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2388 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2389 |
|
|
unsigned int num_datum = sizeof(data032)
|
| 2390 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 2391 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2392 |
|
|
{
|
| 2393 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data032[i].l), Tp(data032[i].m),
|
| 2394 |
|
|
Tp(data032[i].theta));
|
| 2395 |
|
|
const Tp f0 = data032[i].f0;
|
| 2396 |
|
|
const Tp diff = f - f0;
|
| 2397 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2398 |
|
|
max_abs_diff = std::abs(diff);
|
| 2399 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2400 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2401 |
|
|
{
|
| 2402 |
|
|
const Tp frac = diff / f0;
|
| 2403 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2404 |
|
|
max_abs_frac = std::abs(frac);
|
| 2405 |
|
|
}
|
| 2406 |
|
|
}
|
| 2407 |
|
|
VERIFY(max_abs_frac < Tp(5.0000000000000029e-12));
|
| 2408 |
|
|
}
|
| 2409 |
|
|
|
| 2410 |
|
|
// Test data for l=100, m=10.
|
| 2411 |
|
|
testcase_sph_legendre<double> data033[] = {
|
| 2412 |
|
|
{ 0.0000000000000000, 100, 10,
|
| 2413 |
|
|
0.0000000000000000 },
|
| 2414 |
|
|
{ -0.75366545187995670, 100, 10,
|
| 2415 |
|
|
0.15707963267948966 },
|
| 2416 |
|
|
{ -0.35914570017277186, 100, 10,
|
| 2417 |
|
|
0.31415926535897931 },
|
| 2418 |
|
|
{ 0.43480692911578245, 100, 10,
|
| 2419 |
|
|
0.47123889803846897 },
|
| 2420 |
|
|
{ -0.40862111080315705, 100, 10,
|
| 2421 |
|
|
0.62831853071795862 },
|
| 2422 |
|
|
{ 0.37832688692909400, 100, 10,
|
| 2423 |
|
|
0.78539816339744828 },
|
| 2424 |
|
|
{ -0.35484056194773472, 100, 10,
|
| 2425 |
|
|
0.94247779607693793 },
|
| 2426 |
|
|
{ 0.33821981171196336, 100, 10,
|
| 2427 |
|
|
1.0995574287564276 },
|
| 2428 |
|
|
{ -0.32729120767830605, 100, 10,
|
| 2429 |
|
|
1.2566370614359172 },
|
| 2430 |
|
|
{ 0.32110336937091455, 100, 10,
|
| 2431 |
|
|
1.4137166941154069 },
|
| 2432 |
|
|
{ -0.31910064020036194, 100, 10,
|
| 2433 |
|
|
1.5707963267948966 },
|
| 2434 |
|
|
{ 0.32110336937091488, 100, 10,
|
| 2435 |
|
|
1.7278759594743860 },
|
| 2436 |
|
|
{ -0.32729120767830577, 100, 10,
|
| 2437 |
|
|
1.8849555921538759 },
|
| 2438 |
|
|
{ 0.33821981171196341, 100, 10,
|
| 2439 |
|
|
2.0420352248333655 },
|
| 2440 |
|
|
{ -0.35484056194773472, 100, 10,
|
| 2441 |
|
|
2.1991148575128552 },
|
| 2442 |
|
|
{ 0.37832688692909400, 100, 10,
|
| 2443 |
|
|
2.3561944901923448 },
|
| 2444 |
|
|
{ -0.40862111080315433, 100, 10,
|
| 2445 |
|
|
2.5132741228718345 },
|
| 2446 |
|
|
{ 0.43480692911577806, 100, 10,
|
| 2447 |
|
|
2.6703537555513241 },
|
| 2448 |
|
|
{ -0.35914570017277186, 100, 10,
|
| 2449 |
|
|
2.8274333882308138 },
|
| 2450 |
|
|
{ -0.75366545187998180, 100, 10,
|
| 2451 |
|
|
2.9845130209103035 },
|
| 2452 |
|
|
{ 0.0000000000000000, 100, 10,
|
| 2453 |
|
|
3.1415926535897931 },
|
| 2454 |
|
|
};
|
| 2455 |
|
|
|
| 2456 |
|
|
// Test function for l=100, m=10.
|
| 2457 |
|
|
template <typename Tp>
|
| 2458 |
|
|
void test033()
|
| 2459 |
|
|
{
|
| 2460 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2461 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2462 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2463 |
|
|
unsigned int num_datum = sizeof(data033)
|
| 2464 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 2465 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2466 |
|
|
{
|
| 2467 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data033[i].l), Tp(data033[i].m),
|
| 2468 |
|
|
Tp(data033[i].theta));
|
| 2469 |
|
|
const Tp f0 = data033[i].f0;
|
| 2470 |
|
|
const Tp diff = f - f0;
|
| 2471 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2472 |
|
|
max_abs_diff = std::abs(diff);
|
| 2473 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2474 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2475 |
|
|
{
|
| 2476 |
|
|
const Tp frac = diff / f0;
|
| 2477 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2478 |
|
|
max_abs_frac = std::abs(frac);
|
| 2479 |
|
|
}
|
| 2480 |
|
|
}
|
| 2481 |
|
|
VERIFY(max_abs_frac < Tp(1.0000000000000008e-12));
|
| 2482 |
|
|
}
|
| 2483 |
|
|
|
| 2484 |
|
|
// Test data for l=100, m=20.
|
| 2485 |
|
|
testcase_sph_legendre<double> data034[] = {
|
| 2486 |
|
|
{ 0.0000000000000000, 100, 20,
|
| 2487 |
|
|
0.0000000000000000 },
|
| 2488 |
|
|
{ 0.053569660841553138, 100, 20,
|
| 2489 |
|
|
0.15707963267948966 },
|
| 2490 |
|
|
{ 0.57154926874732426, 100, 20,
|
| 2491 |
|
|
0.31415926535897931 },
|
| 2492 |
|
|
{ 0.47536909969585828, 100, 20,
|
| 2493 |
|
|
0.47123889803846897 },
|
| 2494 |
|
|
{ -0.28882554564109014, 100, 20,
|
| 2495 |
|
|
0.62831853071795862 },
|
| 2496 |
|
|
{ 0.020116179014049645, 100, 20,
|
| 2497 |
|
|
0.78539816339744828 },
|
| 2498 |
|
|
{ 0.14752195931706580, 100, 20,
|
| 2499 |
|
|
0.94247779607693793 },
|
| 2500 |
|
|
{ -0.24069428588868527, 100, 20,
|
| 2501 |
|
|
1.0995574287564276 },
|
| 2502 |
|
|
{ 0.29031796025014395, 100, 20,
|
| 2503 |
|
|
1.2566370614359172 },
|
| 2504 |
|
|
{ -0.31437256851143475, 100, 20,
|
| 2505 |
|
|
1.4137166941154069 },
|
| 2506 |
|
|
{ 0.32153954851141792, 100, 20,
|
| 2507 |
|
|
1.5707963267948966 },
|
| 2508 |
|
|
{ -0.31437256851143192, 100, 20,
|
| 2509 |
|
|
1.7278759594743860 },
|
| 2510 |
|
|
{ 0.29031796025014112, 100, 20,
|
| 2511 |
|
|
1.8849555921538759 },
|
| 2512 |
|
|
{ -0.24069428588868211, 100, 20,
|
| 2513 |
|
|
2.0420352248333655 },
|
| 2514 |
|
|
{ 0.14752195931706580, 100, 20,
|
| 2515 |
|
|
2.1991148575128552 },
|
| 2516 |
|
|
{ 0.020116179014049645, 100, 20,
|
| 2517 |
|
|
2.3561944901923448 },
|
| 2518 |
|
|
{ -0.28882554564109658, 100, 20,
|
| 2519 |
|
|
2.5132741228718345 },
|
| 2520 |
|
|
{ 0.47536909969585378, 100, 20,
|
| 2521 |
|
|
2.6703537555513241 },
|
| 2522 |
|
|
{ 0.57154926874732426, 100, 20,
|
| 2523 |
|
|
2.8274333882308138 },
|
| 2524 |
|
|
{ 0.053569660841557065, 100, 20,
|
| 2525 |
|
|
2.9845130209103035 },
|
| 2526 |
|
|
{ 0.0000000000000000, 100, 20,
|
| 2527 |
|
|
3.1415926535897931 },
|
| 2528 |
|
|
};
|
| 2529 |
|
|
|
| 2530 |
|
|
// Test function for l=100, m=20.
|
| 2531 |
|
|
template <typename Tp>
|
| 2532 |
|
|
void test034()
|
| 2533 |
|
|
{
|
| 2534 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2535 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2536 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2537 |
|
|
unsigned int num_datum = sizeof(data034)
|
| 2538 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 2539 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2540 |
|
|
{
|
| 2541 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data034[i].l), Tp(data034[i].m),
|
| 2542 |
|
|
Tp(data034[i].theta));
|
| 2543 |
|
|
const Tp f0 = data034[i].f0;
|
| 2544 |
|
|
const Tp diff = f - f0;
|
| 2545 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2546 |
|
|
max_abs_diff = std::abs(diff);
|
| 2547 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2548 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2549 |
|
|
{
|
| 2550 |
|
|
const Tp frac = diff / f0;
|
| 2551 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2552 |
|
|
max_abs_frac = std::abs(frac);
|
| 2553 |
|
|
}
|
| 2554 |
|
|
}
|
| 2555 |
|
|
VERIFY(max_abs_frac < Tp(2.5000000000000015e-12));
|
| 2556 |
|
|
}
|
| 2557 |
|
|
|
| 2558 |
|
|
// Test data for l=100, m=50.
|
| 2559 |
|
|
testcase_sph_legendre<double> data035[] = {
|
| 2560 |
|
|
{ 0.0000000000000000, 100, 50,
|
| 2561 |
|
|
0.0000000000000000 },
|
| 2562 |
|
|
{ 3.3047910392590630e-21, 100, 50,
|
| 2563 |
|
|
0.15707963267948966 },
|
| 2564 |
|
|
{ 1.0592655372554983e-07, 100, 50,
|
| 2565 |
|
|
0.31415926535897931 },
|
| 2566 |
|
|
{ 0.080418744223952635, 100, 50,
|
| 2567 |
|
|
0.47123889803846897 },
|
| 2568 |
|
|
{ -0.56450600580393062, 100, 50,
|
| 2569 |
|
|
0.62831853071795862 },
|
| 2570 |
|
|
{ 0.33338739844741766, 100, 50,
|
| 2571 |
|
|
0.78539816339744828 },
|
| 2572 |
|
|
{ 0.39741714816514678, 100, 50,
|
| 2573 |
|
|
0.94247779607693793 },
|
| 2574 |
|
|
{ 0.35223993750972293, 100, 50,
|
| 2575 |
|
|
1.0995574287564276 },
|
| 2576 |
|
|
{ 0.17885891940721749, 100, 50,
|
| 2577 |
|
|
1.2566370614359172 },
|
| 2578 |
|
|
{ -0.15341660126461953, 100, 50,
|
| 2579 |
|
|
1.4137166941154069 },
|
| 2580 |
|
|
{ -0.34175924303503102, 100, 50,
|
| 2581 |
|
|
1.5707963267948966 },
|
| 2582 |
|
|
{ -0.15341660126462864, 100, 50,
|
| 2583 |
|
|
1.7278759594743860 },
|
| 2584 |
|
|
{ 0.17885891940721332, 100, 50,
|
| 2585 |
|
|
1.8849555921538759 },
|
| 2586 |
|
|
{ 0.35223993750972149, 100, 50,
|
| 2587 |
|
|
2.0420352248333655 },
|
| 2588 |
|
|
{ 0.39741714816514678, 100, 50,
|
| 2589 |
|
|
2.1991148575128552 },
|
| 2590 |
|
|
{ 0.33338739844741766, 100, 50,
|
| 2591 |
|
|
2.3561944901923448 },
|
| 2592 |
|
|
{ -0.56450600580392785, 100, 50,
|
| 2593 |
|
|
2.5132741228718345 },
|
| 2594 |
|
|
{ 0.080418744223953439, 100, 50,
|
| 2595 |
|
|
2.6703537555513241 },
|
| 2596 |
|
|
{ 1.0592655372554983e-07, 100, 50,
|
| 2597 |
|
|
2.8274333882308138 },
|
| 2598 |
|
|
{ 3.3047910392597871e-21, 100, 50,
|
| 2599 |
|
|
2.9845130209103035 },
|
| 2600 |
|
|
{ 0.0000000000000000, 100, 50,
|
| 2601 |
|
|
3.1415926535897931 },
|
| 2602 |
|
|
};
|
| 2603 |
|
|
|
| 2604 |
|
|
// Test function for l=100, m=50.
|
| 2605 |
|
|
template <typename Tp>
|
| 2606 |
|
|
void test035()
|
| 2607 |
|
|
{
|
| 2608 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2609 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2610 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2611 |
|
|
unsigned int num_datum = sizeof(data035)
|
| 2612 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 2613 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2614 |
|
|
{
|
| 2615 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data035[i].l), Tp(data035[i].m),
|
| 2616 |
|
|
Tp(data035[i].theta));
|
| 2617 |
|
|
const Tp f0 = data035[i].f0;
|
| 2618 |
|
|
const Tp diff = f - f0;
|
| 2619 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2620 |
|
|
max_abs_diff = std::abs(diff);
|
| 2621 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2622 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2623 |
|
|
{
|
| 2624 |
|
|
const Tp frac = diff / f0;
|
| 2625 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2626 |
|
|
max_abs_frac = std::abs(frac);
|
| 2627 |
|
|
}
|
| 2628 |
|
|
}
|
| 2629 |
|
|
VERIFY(max_abs_frac < Tp(5.0000000000000039e-13));
|
| 2630 |
|
|
}
|
| 2631 |
|
|
|
| 2632 |
|
|
// Test data for l=100, m=100.
|
| 2633 |
|
|
testcase_sph_legendre<double> data036[] = {
|
| 2634 |
|
|
{ 0.0000000000000000, 100, 100,
|
| 2635 |
|
|
0.0000000000000000 },
|
| 2636 |
|
|
{ 2.5744136608862186e-81, 100, 100,
|
| 2637 |
|
|
0.15707963267948966 },
|
| 2638 |
|
|
{ 9.4551974868956498e-52, 100, 100,
|
| 2639 |
|
|
0.31415926535897931 },
|
| 2640 |
|
|
{ 4.8096190703396912e-35, 100, 100,
|
| 2641 |
|
|
0.47123889803846897 },
|
| 2642 |
|
|
{ 7.9305393636343450e-24, 100, 100,
|
| 2643 |
|
|
0.62831853071795862 },
|
| 2644 |
|
|
{ 8.4320740610946652e-16, 100, 100,
|
| 2645 |
|
|
0.78539816339744828 },
|
| 2646 |
|
|
{ 5.9319660146027522e-10, 100, 100,
|
| 2647 |
|
|
0.94247779607693793 },
|
| 2648 |
|
|
{ 9.2368225946796921e-06, 100, 100,
|
| 2649 |
|
|
1.0995574287564276 },
|
| 2650 |
|
|
{ 0.0062815489742043982, 100, 100,
|
| 2651 |
|
|
1.2566370614359172 },
|
| 2652 |
|
|
{ 0.27505966018176986, 100, 100,
|
| 2653 |
|
|
1.4137166941154069 },
|
| 2654 |
|
|
{ 0.94936713998764621, 100, 100,
|
| 2655 |
|
|
1.5707963267948966 },
|
| 2656 |
|
|
{ 0.27505966018177136, 100, 100,
|
| 2657 |
|
|
1.7278759594743860 },
|
| 2658 |
|
|
{ 0.0062815489742044433, 100, 100,
|
| 2659 |
|
|
1.8849555921538759 },
|
| 2660 |
|
|
{ 9.2368225946797582e-06, 100, 100,
|
| 2661 |
|
|
2.0420352248333655 },
|
| 2662 |
|
|
{ 5.9319660146027522e-10, 100, 100,
|
| 2663 |
|
|
2.1991148575128552 },
|
| 2664 |
|
|
{ 8.4320740610946652e-16, 100, 100,
|
| 2665 |
|
|
2.3561944901923448 },
|
| 2666 |
|
|
{ 7.9305393636344581e-24, 100, 100,
|
| 2667 |
|
|
2.5132741228718345 },
|
| 2668 |
|
|
{ 4.8096190703399648e-35, 100, 100,
|
| 2669 |
|
|
2.6703537555513241 },
|
| 2670 |
|
|
{ 9.4551974868956498e-52, 100, 100,
|
| 2671 |
|
|
2.8274333882308138 },
|
| 2672 |
|
|
{ 2.5744136608873895e-81, 100, 100,
|
| 2673 |
|
|
2.9845130209103035 },
|
| 2674 |
|
|
{ 0.0000000000000000, 100, 100,
|
| 2675 |
|
|
3.1415926535897931 },
|
| 2676 |
|
|
};
|
| 2677 |
|
|
|
| 2678 |
|
|
// Test function for l=100, m=100.
|
| 2679 |
|
|
template <typename Tp>
|
| 2680 |
|
|
void test036()
|
| 2681 |
|
|
{
|
| 2682 |
|
|
const Tp eps = std::numeric_limits<Tp>::epsilon();
|
| 2683 |
|
|
Tp max_abs_diff = -Tp(1);
|
| 2684 |
|
|
Tp max_abs_frac = -Tp(1);
|
| 2685 |
|
|
unsigned int num_datum = sizeof(data036)
|
| 2686 |
|
|
/ sizeof(testcase_sph_legendre<double>);
|
| 2687 |
|
|
for (unsigned int i = 0; i < num_datum; ++i)
|
| 2688 |
|
|
{
|
| 2689 |
|
|
const Tp f = std::tr1::sph_legendre(Tp(data036[i].l), Tp(data036[i].m),
|
| 2690 |
|
|
Tp(data036[i].theta));
|
| 2691 |
|
|
const Tp f0 = data036[i].f0;
|
| 2692 |
|
|
const Tp diff = f - f0;
|
| 2693 |
|
|
if (std::abs(diff) > max_abs_diff)
|
| 2694 |
|
|
max_abs_diff = std::abs(diff);
|
| 2695 |
|
|
if (std::abs(f0) > Tp(10) * eps
|
| 2696 |
|
|
&& std::abs(f) > Tp(10) * eps)
|
| 2697 |
|
|
{
|
| 2698 |
|
|
const Tp frac = diff / f0;
|
| 2699 |
|
|
if (std::abs(frac) > max_abs_frac)
|
| 2700 |
|
|
max_abs_frac = std::abs(frac);
|
| 2701 |
|
|
}
|
| 2702 |
|
|
}
|
| 2703 |
|
|
VERIFY(max_abs_frac < Tp(5.0000000000000039e-13));
|
| 2704 |
|
|
}
|
| 2705 |
|
|
|
| 2706 |
|
|
int main(int, char**)
|
| 2707 |
|
|
{
|
| 2708 |
|
|
test001<double>();
|
| 2709 |
|
|
test002<double>();
|
| 2710 |
|
|
test003<double>();
|
| 2711 |
|
|
test004<double>();
|
| 2712 |
|
|
test005<double>();
|
| 2713 |
|
|
test006<double>();
|
| 2714 |
|
|
test007<double>();
|
| 2715 |
|
|
test008<double>();
|
| 2716 |
|
|
test009<double>();
|
| 2717 |
|
|
test010<double>();
|
| 2718 |
|
|
test011<double>();
|
| 2719 |
|
|
test012<double>();
|
| 2720 |
|
|
test013<double>();
|
| 2721 |
|
|
test014<double>();
|
| 2722 |
|
|
test015<double>();
|
| 2723 |
|
|
test016<double>();
|
| 2724 |
|
|
test017<double>();
|
| 2725 |
|
|
test018<double>();
|
| 2726 |
|
|
test019<double>();
|
| 2727 |
|
|
test020<double>();
|
| 2728 |
|
|
test021<double>();
|
| 2729 |
|
|
test022<double>();
|
| 2730 |
|
|
test023<double>();
|
| 2731 |
|
|
test024<double>();
|
| 2732 |
|
|
test025<double>();
|
| 2733 |
|
|
test026<double>();
|
| 2734 |
|
|
test027<double>();
|
| 2735 |
|
|
test028<double>();
|
| 2736 |
|
|
test029<double>();
|
| 2737 |
|
|
test030<double>();
|
| 2738 |
|
|
test031<double>();
|
| 2739 |
|
|
test032<double>();
|
| 2740 |
|
|
test033<double>();
|
| 2741 |
|
|
test034<double>();
|
| 2742 |
|
|
test035<double>();
|
| 2743 |
|
|
test036<double>();
|
| 2744 |
|
|
return 0;
|
| 2745 |
|
|
}
|
