test_GNumerics.cpp
23 KB
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/***************************************************************************
* test_GNumerics.cpp - test numerics modules *
* ----------------------------------------------------------------------- *
* copyright (C) 2010-2020 by Jurgen Knodlseder *
* ----------------------------------------------------------------------- *
* *
* This program is free software: you can redistribute it and/or modify *
* it under the terms of the GNU General Public License as published by *
* the Free Software Foundation, either version 3 of the License, or *
* (at your option) any later version. *
* *
* This program is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
* GNU General Public License for more details. *
* *
* You should have received a copy of the GNU General Public License *
* along with this program. If not, see <http://www.gnu.org/licenses/>. *
* *
***************************************************************************/
/**
* @file test_GNumerics.cpp
* @brief Unit tests implementation for numerics module
* @author Juergen Knoedlseder
*/
/* __ Includes ___________________________________________________________ */
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <ostream>
#include <stdexcept>
#include <stdlib.h>
#include "test_GNumerics.hpp"
/* __ Namespaces _________________________________________________________ */
/* __ Globals ____________________________________________________________ */
/***********************************************************************//**
* @brief Set tests
***************************************************************************/
void TestGNumerics::set(void)
{
//set name
name("GNumerics");
// Set parameters
m_sigma = 2.5;
// Append tests
append(static_cast<pfunction>(&TestGNumerics::test_math),
"Test GMath");
append(static_cast<pfunction>(&TestGNumerics::test_ndarray),
"Test GNdarray");
append(static_cast<pfunction>(&TestGNumerics::test_fft),
"Test GFft");
append(static_cast<pfunction>(&TestGNumerics::test_function),
"Test GFunction");
append(static_cast<pfunction>(&TestGNumerics::test_functions),
"Test GFunctions");
append(static_cast<pfunction>(&TestGNumerics::test_integral),
"Test GIntegral");
append(static_cast<pfunction>(&TestGNumerics::test_integrals),
"Test GIntegrals");
append(static_cast<pfunction>(&TestGNumerics::test_romberg_integration),
"Test Romberg integration");
append(static_cast<pfunction>(&TestGNumerics::test_adaptive_simpson_integration),
"Test adaptive Simpson integration");
append(static_cast<pfunction>(&TestGNumerics::test_gauss_kronrod_integration),
"Test Gauss-Kronrod integration");
// Return
return;
}
/***********************************************************************//**
* @brief Clone test suite
*
* @return Pointer to deep copy of test suite.
***************************************************************************/
TestGNumerics* TestGNumerics::clone(void) const
{
// Clone test suite
return new TestGNumerics(*this);
}
/***********************************************************************//**
* @brief Test mathematics functions
***************************************************************************/
void TestGNumerics::test_math(void)
{
// Test acos function
test_value(gammalib::acos(0.0), 1.57079633);
test_value(gammalib::acos(0.37), 1.19178731);
// Test atan2 function
test_value(gammalib::atan2( 1.0, 2.0), 0.463647609001);
test_value(gammalib::atan2( 1.0,-3.0), 2.819842099193);
test_value(gammalib::atan2(-2.0,-3.0), -2.553590050042);
test_value(gammalib::atan2(-2.0, 1.0), -1.107148717794);
// Test cosd function
test_value(gammalib::cosd( 0.0), 1.0);
test_value(gammalib::cosd( 33.0), 0.83867057);
test_value(gammalib::cosd(178.1), -0.99945022);
// Test sind function
test_value(gammalib::sind( 0.0), 0.0);
test_value(gammalib::sind( 33.0), 0.54463904);
test_value(gammalib::sind(178.1), 0.03315518);
// Test tand function
test_value(gammalib::tand(-10.0), -0.176326980708);
test_value(gammalib::tand( 12.0), 0.21255656167);
test_value(gammalib::tand(178.1), -0.0331734166041);
// Test asind function
test_value(gammalib::asind(0.0), 0.0);
test_value(gammalib::asind(0.37), 21.7156172833);
// Test acosd function
test_value(gammalib::acosd(0.0), 90.0);
test_value(gammalib::acosd(0.37), 68.28438272);
// Test atan2d function
test_value(gammalib::atan2d( 1.0, 2.0), 26.5650511771);
test_value(gammalib::atan2d( 1.0,-3.0), 161.565051177);
test_value(gammalib::atan2d(-2.0,-3.0), -146.309932474);
test_value(gammalib::atan2d(-2.0, 1.0), -63.4349488229);
// Test sincosd function
double s;
double c;
gammalib::sincosd(33.0, &s, &c);
test_value(s, 0.54463904);
test_value(c, 0.83867057);
// Test logarithm of gamma function
test_value(gammalib::gammln(0.5), 0.572364942925);
test_value(gammalib::gammln(1.5), -0.120782237635);
// Test error function
test_value(gammalib::erf(0.0), 0.0);
test_value(gammalib::erf(1.0), 0.8427008);
test_value(gammalib::erf(2.0), 0.9953223);
// Test complementary error function
test_value(gammalib::erfc(0.0), 1.0);
test_value(gammalib::erfc(0.1), 0.887537084);
test_value(gammalib::erfc(0.8), 0.257899035);
// Test inverse error function
test_value(gammalib::erfinv(0.3), 0.2724627147);
test_value(gammalib::erfinv(0.9), 1.1630871537);
// Test modulo function
test_value(gammalib::modulo(3.1, 2.8), 0.3);
test_value(gammalib::modulo(-5.7, 1.37), 1.15);
// Test power law integration
test_value(gammalib::plaw_integral(2.0, 3.0, 9.0, 5.0), 29.112577);
test_value(gammalib::plaw_integral(2.0, 9.0, 9.0, 2.0), 27.073393);
test_value(gammalib::plaw_integral(2.0, 9.0, 5.0, 2.0), 12.471065);
// Test Gaussian integration
test_value(gammalib::gauss_integral(0.0, 1.0), 0.341344746069);
test_value(gammalib::gauss_integral(-1.0, 1.0), 0.682689492137086);
test_value(gammalib::gauss_integral(-2.0, 2.0), 0.954499736103642);
test_value(gammalib::gauss_integral(-3.0, 3.0), 0.997300203936740);
// Exit test
return;
}
/***********************************************************************//**
* @brief Test n-dimensional array
***************************************************************************/
void TestGNumerics::test_ndarray(void)
{
// Test void constructor
GNdarray nd0;
test_value(nd0.size(), 0);
test_value(nd0.dim(), 0);
// Test 1-dimensional array
GNdarray nd1(3);
test_value(nd1.size(), 3);
test_value(nd1.dim(), 1);
test_value(nd1.shape()[0], 3);
for (int i = 0; i < 3; ++i) {
nd1(i) = double(i);
test_value(nd1.at(i), double(i));
}
// Test 2-dimensional array
GNdarray nd2(3,2);
test_value(nd2.size(), 6);
test_value(nd2.dim(), 2);
test_value(nd2.shape()[0], 3);
test_value(nd2.shape()[1], 2);
for (int ix = 0; ix < 3; ++ix) {
for (int iy = 0; iy < 2; ++iy) {
double ref = double(ix)+double(iy);
nd2(ix,iy) = ref;
test_value(nd2.at(ix,iy), ref);
}
}
// Test 3-dimensional array
GNdarray nd3(2,2,2);
test_value(nd3.size(), 8);
test_value(nd3.dim(), 3);
test_value(nd3.shape()[0], 2);
test_value(nd3.shape()[1], 2);
test_value(nd3.shape()[2], 2);
for (int ix = 0; ix < 2; ++ix) {
for (int iy = 0; iy < 2; ++iy) {
for (int iz = 0; iz < 2; ++iz) {
double ref = double(ix)+double(iy)+double(iz);
nd3(ix,iy,iz) = ref;
test_value(nd3.at(ix,iy,iz), ref);
}
}
}
// Test n-dimensional array
std::vector<int> n(5,2);
GNdarray ndn(n);
test_value(ndn.size(), 32);
test_value(ndn.dim(), 5);
for (int i = 0; i < 5; ++i) {
test_value(ndn.shape()[i], 2);
}
std::vector<int> itest(5,1);
ndn(itest) = 3.1415;
test_value(ndn.at(itest), 3.1415);
// Setup arrays for operator tests
GNdarray nda(1,2);
nda(0,0) = 3.0;
nda(0,1) = 5.5;
GNdarray ndb = nda;
GNdarray ndc = nda + ndb;
// Test operator=
test_value(ndb(0,0), 3.0);
test_value(ndb(0,1), 5.5);
// Test operator== and operator!=
test_assert(nda == ndb, "Test operator==");
test_assert(nda != ndc, "Test operator!=");
// Test array operator+=
nda += ndb;
test_value(nda(0,0), 6.0);
test_value(nda(0,1), 11.0);
// Test array operator-=
nda -= ndb;
test_value(nda(0,0), 3.0);
test_value(nda(0,1), 5.5);
// Test value operator+=
nda += 1.5;
test_value(nda(0,0), 4.5);
test_value(nda(0,1), 7.0);
// Test value operator-=
nda -= 1.5;
test_value(nda(0,0), 3.0);
test_value(nda(0,1), 5.5);
// Test value operator*=
nda *= 3.0;
test_value(nda(0,0), 9.0);
test_value(nda(0,1), 16.5);
// Test value operator/=
nda /= 3.0;
test_value(nda(0,0), 3.0);
test_value(nda(0,1), 5.5);
// Test operator-
GNdarray ndd = -nda;
test_value(ndd(0,0), -3.0);
test_value(ndd(0,1), -5.5);
// Test operator+(GNdarray,GNdarray)
ndd = nda + ndb;
test_value(ndd(0,0), 6.0);
test_value(ndd(0,1), 11.0);
// Test operator+(GNdarray,double) and operator+(double,GNdarray)
ndd = nda + 1.5;
test_value(ndd(0,0), 4.5);
test_value(ndd(0,1), 7.0);
ndd = 1.5 + nda;
test_value(ndd(0,0), 4.5);
test_value(ndd(0,1), 7.0);
// Test operator-(GNdarray,GNdarray)
ndd = nda - ndb;
test_value(ndd(0,0), 0.0);
test_value(ndd(0,1), 0.0);
// Test operator-(GNdarray,double) and operator-(double,GNdarray)
ndd = nda - 1.5;
test_value(ndd(0,0), 1.5);
test_value(ndd(0,1), 4.0);
ndd = 1.5 - nda;
test_value(ndd(0,0), -1.5);
test_value(ndd(0,1), -4.0);
// Test operator*(GNdarray,double) and operator*(double,GNdarray)
ndd = nda * 3.0;
test_value(ndd(0,0), 9.0);
test_value(ndd(0,1), 16.5);
ndd = 3.0 * nda;
test_value(ndd(0,0), 9.0);
test_value(ndd(0,1), 16.5);
// Test operator/(GNdarray,double)
ndd = nda / 3.0;
test_value(ndd(0,0), 1.0);
test_value(ndd(0,1), 5.5/3.0);
// Test friend functions
test_value(min(nda), 3.0);
test_value(max(nda), 5.5);
test_value(sum(nda), 8.5);
test_value(acos(nda)(0,0), std::acos(3.0));
test_value(acos(nda)(0,1), std::acos(5.5));
test_value(acosh(nda)(0,0), acosh(3.0));
test_value(acosh(nda)(0,1), acosh(5.5));
test_value(asin(nda)(0,0), std::asin(3.0));
test_value(asin(nda)(0,1), std::asin(5.5));
test_value(asinh(nda)(0,0), asinh(3.0));
test_value(asinh(nda)(0,1), asinh(5.5));
test_value(atan(nda)(0,0), std::atan(3.0));
test_value(atan(nda)(0,1), std::atan(5.5));
test_value(atanh(nda)(0,0), atanh(3.0));
test_value(atanh(nda)(0,1), atanh(5.5));
test_value(cos(nda)(0,0), std::cos(3.0));
test_value(cos(nda)(0,1), std::cos(5.5));
test_value(cosh(nda)(0,0), std::cosh(3.0));
test_value(cosh(nda)(0,1), std::cosh(5.5));
test_value(exp(nda)(0,0), std::exp(3.0));
test_value(exp(nda)(0,1), std::exp(5.5));
test_value(abs(nda)(0,0), std::abs(3.0));
test_value(abs(nda)(0,1), std::abs(5.5));
test_value(log(nda)(0,0), std::log(3.0));
test_value(log(nda)(0,1), std::log(5.5));
test_value(log10(nda)(0,0), std::log10(3.0));
test_value(log10(nda)(0,1), std::log10(5.5));
test_value(sin(nda)(0,0), std::sin(3.0));
test_value(sin(nda)(0,1), std::sin(5.5));
test_value(sinh(nda)(0,0), std::sinh(3.0));
test_value(sinh(nda)(0,1), std::sinh(5.5));
test_value(sqrt(nda)(0,0), std::sqrt(3.0));
test_value(sqrt(nda)(0,1), std::sqrt(5.5));
test_value(tan(nda)(0,0), std::tan(3.0));
test_value(tan(nda)(0,1), std::tan(5.5));
test_value(tanh(nda)(0,0), std::tanh(3.0));
test_value(tanh(nda)(0,1), std::tanh(5.5));
test_value(pow(nda,3.0)(0,0), std::pow(3.0,3.0));
test_value(pow(nda,3.0)(0,1), std::pow(5.5,3.0));
// Exit test
return;
}
/***********************************************************************//**
* @brief Test Fast Fourier Transform
***************************************************************************/
void TestGNumerics::test_fft(void)
{
// Test 1-dimensional FFT
for (int n = 2; n < 12; ++n) {
// Skip n=8,9,10 since they can be factorised
if (n > 7 && n < 11) {
continue;
}
// Allocate 1-dimensional array
GNdarray array(n);
// Set one elements
array(n/2) = 1.0;
// Allocate FFT
GFft fft(array);
// Backward transformation
GNdarray back = fft.backward();
// Check FFT results
check_fft1(array, fft, back);
} // endfor: looped over array lengths
// Test 2-dimensional FFT
GNdarray array2(8,9);
array2(4,4) = 1.0;
GFft fft2(array2);
GNdarray back2 = fft2.backward();
check_fft2(array2, fft2, back2);
// Exit test
return;
}
/***********************************************************************//**
* @brief Check 1-dimensional Fast Fourier Transform
*
* @param[in] array Input array.
* @param[in] fft Fast Fourier Transform of input array.
* @param[in] back Backward transform of FFT (should be equal to input array)
***************************************************************************/
void TestGNumerics::check_fft1(const GNdarray& array,
const GFft& fft,
const GNdarray& back)
{
// Get normalisation factor
double norm = 1.0 / double(array.size());
// Compute reference value and compare with FFT result
for (int k = 0; k < array.size(); ++k) {
double ref_real = 0.0;
double ref_imag = 0.0;
for (int n = 0; n < array.size(); ++n) {
double x = -gammalib::twopi * k * n * norm;
ref_real += array(n) * std::cos(x);
ref_imag += array(n) * std::sin(x);
}
std::complex<double> ref(ref_real, ref_imag);
test_value(fft(k), ref);
}
// Test backward transformation
for (int k = 0; k < array.size(); ++k) {
test_value(back(k), array(k));
}
// Exit test
return;
}
/***********************************************************************//**
* @brief Check 2-dimensional Fast Fourier Transform
*
* @param[in] array Input array.
* @param[in] fft Fast Fourier Transform of input array.
* @param[in] back Backward transform of FFT (should be equal to input array)
***************************************************************************/
void TestGNumerics::check_fft2(const GNdarray& array,
const GFft& fft,
const GNdarray& back)
{
// Get normalisation factor
double normM = 1.0 / double(array.shape()[0]);
double normN = 1.0 / double(array.shape()[1]);
// Compute reference value and compare with FFT result
for (int k = 0; k < array.shape()[0]; ++k) {
for (int l = 0; l < array.shape()[1]; ++l) {
double ref_real = 0.0;
double ref_imag = 0.0;
for (int n = 0; n < array.shape()[1]; ++n) {
double sum_real = 0.0;
double sum_imag = 0.0;
for (int m = 0; m < array.shape()[0]; ++m) {
double x = -gammalib::twopi * m * k * normM;
sum_real += array(m,n) * std::cos(x);
sum_imag += array(m,n) * std::sin(x);
}
double y = -gammalib::twopi * n * l * normN;
ref_real += (sum_real * std::cos(y) - sum_imag * std::sin(y));
ref_imag += (sum_real * std::sin(y) + sum_imag * std::cos(y));
}
std::complex<double> ref(ref_real, ref_imag);
test_value(fft(k,l), ref);
}
}
// Test backward transformation
for (int k = 0; k < array.size(); ++k) {
test_value(back(k), array(k));
}
// Exit test
return;
}
/***********************************************************************//**
* @brief Test GFunction class
***************************************************************************/
void TestGNumerics::test_function(void)
{
// Allocate function
Gauss function(m_sigma);
// Test function value
test_value(function.eval(0.0), 0.159576912, "Check function value at x=0");
test_value(function.eval(1.0), 0.147308056, "Check function value at x=1");
// Exit test
return;
}
/***********************************************************************//**
* @brief Test GFunctions class
***************************************************************************/
void TestGNumerics::test_functions(void)
{
// Set sigma array
GVector sigma(3);
sigma[0] = 1.0;
sigma[1] = 2.0;
sigma[2] = 4.0;
// Allocate functions
GaussArray functions(sigma);
// Evaluate functions for x=0
GVector result = functions.eval(0.0);
// Test function values
test_value(result[0], 0.39894228, "Check function[0] value at x=0");
test_value(result[1], 0.19947114, "Check function[1] value at x=0");
test_value(result[2], 0.09973557, "Check function[2] value at x=0");
// Evaluate functions for x=1
result = functions.eval(1.0);
// Test function values
test_value(result[0], 0.24197072, "Check function[0] value at x=1");
test_value(result[1], 0.17603266, "Check function[1] value at x=1");
test_value(result[2], 0.09666703, "Check function[2] value at x=1");
// Exit test
return;
}
/***********************************************************************//**
* @brief Test GIntegral class
***************************************************************************/
void TestGNumerics::test_integral(void)
{
// Test integral and integrand allocation
Gauss integrand(m_sigma);
GIntegral integral(&integrand);
// Exit test
return;
}
/***********************************************************************//**
* @brief Test GIntegrals class
***************************************************************************/
void TestGNumerics::test_integrals(void)
{
// Set sigma array
GVector sigma(3);
sigma[0] = 1.0;
sigma[1] = 2.0;
sigma[2] = 4.0;
// Test kernels and integrals allocation
GaussArray kernels(sigma);
GIntegrals integrals(&kernels);
test_value(integrals.iter(), 0, "Check initial iterations");
test_value(integrals.calls(), 0, "Check initial calls");
// Integrate over the entire Gaussian
GVector result = integrals.romberg(-40.0, 40.0);
test_value(result[0], 1.0, 1.0e-6, "Check full integration result for (0,0)");
test_value(result[1], 1.0, 1.0e-6, "Check full integration result for (0,1)");
test_value(result[2], 1.0, 1.0e-6, "Check full integration result for (0,2)");
// Test [-1,1] integration
result = integrals.romberg(-1.0, 1.0);
test_value(result[0], 0.68268948, 1.0e-6,
"Check [-1,1] integration result for (0,0)");
test_value(result[1], 0.38292492, 1.0e-6,
"Check [-1,1] integration result for (0,1)");
test_value(result[2], 0.19741265, 1.0e-6,
"Check [-1,1] integration result for (0,2)");
// Exit test
return;
}
/***********************************************************************//**
* @brief Test Romberg integration
***************************************************************************/
void TestGNumerics::test_romberg_integration(void)
{
// Set-up integral
Gauss integrand(m_sigma);
GIntegral integral(&integrand);
// Integrate over the entire Gaussian
double result = integral.romberg(-10.0*m_sigma, 10.0*m_sigma);
test_value(result, 1.0, 1.0e-6, "Check full integration result");
// Test [-1sigma, 1sigma]
result = integral.romberg(-m_sigma, m_sigma);
test_value(result, 0.68268948, 1.0e-6,
"Check [-1sigma, 1sigma] integration results");
// Test [0.0, 1sigma]
result = integral.romberg(0.0, m_sigma);
test_value(result, 0.34134475, 1.0e-6,
"Check [0, 1sigma] integration results");
// Return
return;
}
/***********************************************************************//**
* @brief Test adaptive Simpson integration
***************************************************************************/
void TestGNumerics::test_adaptive_simpson_integration(void)
{
// Set-up integral
Gauss integrand(m_sigma);
GIntegral integral(&integrand);
// Integrate over the entire Gaussian
double result = integral.adaptive_simpson(-10.0*m_sigma, 10.0*m_sigma);
test_value(result, 1.0, 1.0e-6, "Check full integration result");
// Test [-1sigma, 1sigma]
result = integral.adaptive_simpson(-m_sigma, m_sigma);
test_value(result, 0.68268948, 1.0e-6,
"Check [-1sigma, 1sigma] integration results");
// Test [0.0, 1sigma]
result = integral.adaptive_simpson(0.0, m_sigma);
test_value(result, 0.34134475, 1.0e-6,
"Check [0, 1sigma] integration results");
// Return
return;
}
/***********************************************************************//**
* @brief Test Gauss-Kronrod integration
***************************************************************************/
void TestGNumerics::test_gauss_kronrod_integration(void)
{
// Set-up integral
Gauss integrand(m_sigma);
GIntegral integral(&integrand);
// Integrate over the entire Gaussian
double result = integral.gauss_kronrod(-10.0*m_sigma, 10.0*m_sigma);
test_value(result, 1.0, 1.0e-6, "Check full integration result");
// Test [-1sigma, 1sigma]
result = integral.gauss_kronrod(-m_sigma, m_sigma);
test_value(result, 0.68268948, 1.0e-6,
"Check [-1sigma, 1sigma] integration results");
// Test [0.0, 1sigma]
result = integral.gauss_kronrod(0.0, m_sigma);
test_value(result, 0.34134475, 1.0e-6,
"Check [0, 1sigma] integration results");
// Return
return;
}
/***********************************************************************//**
* @brief Main test function
***************************************************************************/
int main(void)
{
GTestSuites testsuite("GNumerics");
// Create a test suite
TestGNumerics test;
// Append to the container
testsuite.append(test);
// Run
bool success = testsuite.run();
// save xml report
testsuite.save("reports/GNumerics.xml");
// Return
return (success ? 0:1);
}