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test.cxx
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/************************************************************************/
/* */
/* Copyright 2004-2011 by Ullrich Koethe */
/* */
/* This file is part of the VIGRA computer vision library. */
/* The VIGRA Website is */
/* http://hci.iwr.uni-heidelberg.de/vigra/ */
/* Please direct questions, bug reports, and contributions to */
/* ullrich.koethe@iwr.uni-heidelberg.de or */
/* vigra@informatik.uni-hamburg.de */
/* obtaining a copy of this software and associated documentation */
/* files (the "Software"), to deal in the Software without */
/* restriction, including without limitation the rights to use, */
/* copy, modify, merge, publish, distribute, sublicense, and/or */
/* sell copies of the Software, and to permit persons to whom the */
/* Software is furnished to do so, subject to the following */
/* conditions: */
/* */
/* The above copyright notice and this permission notice shall be */
/* included in all copies or substantial portions of the */
/* Software. */
/* */
/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND */
/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES */
/* OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND */
/* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT */
/* HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, */
/* WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING */
/* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR */
/* OTHER DEALINGS IN THE SOFTWARE. */
/* */
/************************************************************************/
#if defined(__GNUC__) && __GNUC__ == 2 && __GNUC_MINOR__ == 95
// deactivate broken std::relops
# define __SGI_STL_INTERNAL_RELOPS
#endif // __GNUC__
#include <typeinfo>
#include <iostream>
#include <iomanip>
#include <algorithm>
#include <sstream>
#include <cstdlib>
#include "vigra/unittest.hxx"
#include "vigra/mathutil.hxx"
#include "vigra/algorithm.hxx"
#include "vigra/functorexpression.hxx"
#include "vigra/polynomial.hxx"
#include "vigra/array_vector.hxx"
#include "vigra/splines.hxx"
#include "vigra/gaussians.hxx"
#include "vigra/rational.hxx"
#include "vigra/fixedpoint.hxx"
#include "vigra/autodiff.hxx"
#include "vigra/linear_algebra.hxx"
#include "vigra/singular_value_decomposition.hxx"
#include "vigra/regression.hxx"
#include "vigra/random.hxx"
#include "vigra/tinyvector.hxx"
#include "vigra/quaternion.hxx"
#include "vigra/clebsch-gordan.hxx"
#include "vigra/bessel.hxx"
#include "vigra/timing.hxx"
#define VIGRA_TOLERANCE_MESSAGE "If this test fails, please adjust the tolerance threshold and report\n" \
"your findings (including compiler information etc.) to the VIGRA mailing list:"
#define NegativeShift(i, s)\
(vigra::Int32)((vigra::UInt32) i << s)
static double coefficients[][12] =
{
{ 5.0, -416.0, 720.0, -464.0, 136.0, -18.0, 1.0 },
{ 8.0, 40320.0, -109584.0, 118124.0, -67284.0, 22449.0, -4536.0, 546.0, -36.0, 1.0},
{ 3.0, 1e10, -1e10, -1e-10, 1e-10},
{ 3.0, 1e-10, -1e-10, -1e10, 1e10},
{ 10.0, 2.88e-8, -1.848e-6, 0.00005204, -0.0008458, 0.008777,
-0.06072, 0.2835, -0.882, 1.75, -2.0, 1.0},
{ 5.0, 0.3411268890719874, 0.48265610836623374, 0.29941395284477745,
0.13065520631476124, 0.68342489290545338, 0.0017437185812028133 },
{ 3.0, -1.0, 1000001000001.0 / 1e6, -1000001000001.0 / 1e6, 1.0},
{ 8.0, 36.0, 0.0, 85.0, 0.0, 63.0, 0.0, 15.0, 0.0, 1.0 }
};
typedef std::complex<double> C;
static C reference[][12] =
{
{ C(1e-12), C(2.0), C(2.0), C(2.0), C(6.0, -4.0), C(6.0, 4.0) },
{ C(1e-11), C(1.0), C(2.0), C(3.0), C(4.0), C(5.0), C(6.0), C(7.0), C(8.0) },
{ C(1e-12), C(-1e10), C(1.0), C(1e10) },
{ C(1e-12), C(-1e-10), C(1e-10), C(1.0) },
{ C(1e-5), C(0.1), C(0.1), C(0.1), C(0.1), C(0.2), C(0.2), C(0.2),
C(0.3), C(0.3), C(0.4) },
{ C(1e-12), C(-391.74516023901123),
C(-0.56839260551055271, -0.4046562986541693), C(-0.56839260551055271, 0.4046562986541693),
C(0.47331479192572767, -0.89542786425410759), C(0.47331479192572767, 0.89542786425410759) },
{ C(1e-12), C(1e-6), C(1.0), C(1e6) },
{ C(1e-12), C(0.0, -3.0), C(0.0, -2.0), C(0.0, -1.0), C(0.0, -1.0),
C(0.0, 1.0), C(0.0, 1.0), C(0.0, 2.0), C(0.0, 3.0) }
};
#if 0
#undef should
#define should(v) (std::cerr << #v << ": " << (v) << std::endl)
#undef shouldEqual
#define shouldEqual(v1, v2) \
(std::cerr << #v1 << " == " << #v2 << ": " << (v1) << " " << (v2) << std::endl)
#undef shouldEqualTolerance
#define shouldEqualTolerance(v1, v2, e) \
(std::cerr << #v1 << " == " << #v2 << ": " << (v1) << " " << (v2) << " " << (v1 - v2) << std::endl)
#endif
template <unsigned int N, class POLYNOMIAL>
struct PolynomialTest
{
void testPolynomial()
{
double epsilon = reference[N][0].real();
unsigned int order = (unsigned int)(coefficients[N][0] + 0.5);
POLYNOMIAL p(coefficients[N]+1, order);
vigra::ArrayVector<std::complex<double> > roots;
should(polynomialRoots(p, roots));
shouldEqual(roots.size(), order);
for(unsigned int i = 0; i<roots.size(); ++i)
{
shouldEqualTolerance(roots[i].real(), reference[N][i+1].real(), epsilon);
shouldEqualTolerance(roots[i].imag(), reference[N][i+1].imag(), epsilon);
}
}
void testPolynomialEigenvalueMethod()
{
double epsilon = 1e-7;
unsigned int order = (unsigned int)(coefficients[N][0] + 0.5);
POLYNOMIAL p(coefficients[N]+1, order);
p.setEpsilon(epsilon);
vigra::ArrayVector<std::complex<double> > roots;
should(polynomialRootsEigenvalueMethod(p, roots));
shouldEqual(roots.size(), order);
for(unsigned int i = 0; i<roots.size(); ++i)
{
shouldEqualTolerance(roots[i].real(), reference[N][i+1].real(), epsilon);
shouldEqualTolerance(roots[i].imag(), reference[N][i+1].imag(), epsilon);
}
}
};
struct HighOrderPolynomialTest
{
void testPolynomial()
{
unsigned int order = 80;
double epsilon = 1e-12;
vigra::ArrayVector<double> coeffs(order+1, 0.0);
coeffs[0] = -1.0;
coeffs[order] = 1.0;
vigra::Polynomial<double> p(coeffs.begin(), order);
vigra::ArrayVector<std::complex<double> > roots;
should(vigra::polynomialRoots(p, roots));
shouldEqual(roots.size(), order);
for(unsigned int i = 0; i<roots.size(); ++i)
{
shouldEqualTolerance(std::abs(roots[i]), 1.0, epsilon);
C r = p(roots[i]);
shouldEqualTolerance(r.real(), 0.0, epsilon);
shouldEqualTolerance(r.imag(), 0.0, epsilon);
}
vigra::ArrayVector<double> rroots;
should(polynomialRealRoots(p, rroots));
shouldEqual(rroots.size(), 2u);
shouldEqualTolerance(rroots[0], -1.0, epsilon);
shouldEqualTolerance(rroots[1], 1.0, epsilon);
}
void testPolynomialEigenvalueMethod()
{
unsigned int order = 80;
double epsilon = 1e-12;
vigra::ArrayVector<double> coeffs(order+1, 0.0);
coeffs[0] = -1.0;
coeffs[order] = 1.0;
vigra::Polynomial<double> p(coeffs.begin(), order);
vigra::ArrayVector<std::complex<double> > roots;
should(vigra::polynomialRootsEigenvalueMethod(p, roots));
shouldEqual(roots.size(), order);
for(unsigned int i = 0; i<roots.size(); ++i)
{
shouldEqualTolerance(std::abs(roots[i]), 1.0, epsilon);
C r = p(roots[i]);
shouldEqualTolerance(r.real(), 0.0, epsilon);
shouldEqualTolerance(r.imag(), 0.0, epsilon);
}
vigra::ArrayVector<double> rroots;
should(polynomialRealRootsEigenvalueMethod(p, rroots));
shouldEqual(rroots.size(), 2u);
shouldEqualTolerance(rroots[0], -1.0, epsilon);
shouldEqualTolerance(rroots[1], 1.0, epsilon);
}
};
template <int ORDER>
struct SplineTest
{
typedef vigra::BSpline<ORDER, double> BS;
typedef vigra::BSplineBase<ORDER, double> BSB;
BS spline;
BSB splineBase;
void testValues()
{
double r = spline.radius();
shouldEqual(r, splineBase.radius());
for(int d = 0; d <= ORDER+1; ++d)
{
for(double x = -r-0.5; x <= r+0.5; x += 0.5)
shouldEqualTolerance(spline(x, d), splineBase(x, d), 1e-15);
}
}
void testFixedPointValues()
{
double r = spline.radius();
shouldEqual(r, splineBase.radius());
for(double x = -r-0.5; x <= r+0.5; x += 0.5)
{
vigra::FixedPoint<11,20> fpx20(x);
vigra::FixedPoint<11,15> fpx15(x);
should(vigra::abs(vigra::fixed_point_cast<double>(spline(fpx20)) - spline(x)) < 1e-6);
should(vigra::abs(vigra::fixed_point_cast<double>(spline(fpx15)) - spline(x)) < 4e-5);
}
}
void testPrefilterCoefficients()
{
int n = ORDER / 2;
vigra::ArrayVector<double> const & ps = spline.prefilterCoefficients();
vigra::ArrayVector<double> const & psb = splineBase.prefilterCoefficients();
if(n == 0)
{
shouldEqual(ps.size(), 0u);
shouldEqual(psb.size(), 0u);
}
else
{
vigra::ArrayVector<double> & psb1 =
const_cast<vigra::ArrayVector<double> &>(psb);
std::sort(psb1.begin(), psb1.end());
for(int i = 0; i < n; ++i)
shouldEqualTolerance(ps[i], psb[i], 1e-14);
}
}
void testWeightMatrix()
{
int n = ORDER + 1;
typename BS::WeightMatrix const & ws = BS::weights();
typename BSB::WeightMatrix const & wsb = BSB::weights();
for(int d = 0; d < n; ++d)
for(int i = 0; i < n; ++i)
shouldEqualTolerance(ws[d][i], wsb[d][i], 1e-14);
}
};
struct FunctionsTest
{
void testGaussians()
{
vigra::Gaussian<double> g,
g1(2.0, 1),
g2(1.0, 2),
g3(2.0, 3),
g4(2.0, 4),
g5(2.0, 5);
double epsilon = 1e-15;
shouldEqual(g.derivativeOrder(), 0u);
shouldEqual(g.sigma(), 1.0);
shouldEqualTolerance(g(0.0), 0.3989422804014327, epsilon);
shouldEqualTolerance(g(0.5), 0.35206532676429952, epsilon);
shouldEqualTolerance(g(1.0), 0.24197072451914337, epsilon);
shouldEqualTolerance(g(-1.0), 0.24197072451914337, epsilon);
shouldEqual(g1.derivativeOrder(), 1u);
shouldEqual(g1.sigma(), 2.0);
shouldEqualTolerance(g1(0.0), 0, epsilon);
shouldEqualTolerance(g1(0.5), -0.024166757300178077, epsilon);
shouldEqualTolerance(g1(1.0), -0.044008165845537441, epsilon);
shouldEqualTolerance(g1(-1.0), 0.044008165845537441, epsilon);
shouldEqual(g2.derivativeOrder(), 2u);
shouldEqual(g2.sigma(), 1.0);
shouldEqualTolerance(g2(0.0), -0.3989422804014327, epsilon);
shouldEqualTolerance(g2(0.5), -0.26404899507322466, epsilon);
shouldEqualTolerance(g2(1.0), 0, epsilon);
shouldEqualTolerance(g2(-1.0), 0, epsilon);
shouldEqualTolerance(g2(1.5), 0.16189699458236467, epsilon);
shouldEqualTolerance(g2(-1.5), 0.16189699458236467, epsilon);
shouldEqual(g3.derivativeOrder(), 3u);
shouldEqual(g3.sigma(), 2.0);
shouldEqualTolerance(g3(0.0), 0, epsilon);
shouldEqualTolerance(g3(0.5), 0.017747462392318277, epsilon);
shouldEqualTolerance(g3(1.0), 0.030255614018806987, epsilon);
shouldEqualTolerance(g3(-1.0), -0.030255614018806987, epsilon);
shouldEqualTolerance(g3(2.0*VIGRA_CSTD::sqrt(3.0)), 0, epsilon);
shouldEqualTolerance(g3(-2.0*VIGRA_CSTD::sqrt(3.0)), 0, epsilon);
shouldEqualTolerance(g4(0.0), 0.037400838787634318, epsilon);
shouldEqualTolerance(g4(1.0), 0.017190689783413062, epsilon);
shouldEqualTolerance(g4(-1.0), 0.017190689783413062, epsilon);
shouldEqualTolerance(g4(1.483927568605452), 0, epsilon);
shouldEqualTolerance(g4(4.668828436677955), 0, epsilon);
shouldEqualTolerance(g5(0.0), 0, epsilon);
shouldEqualTolerance(g5(1.0), -0.034553286464660257, epsilon);
shouldEqualTolerance(g5(-1.0), 0.034553286464660257, epsilon);
shouldEqualTolerance(g5(2.711252359948531), 0, epsilon);
shouldEqualTolerance(g5(5.713940027745611), 0, epsilon);
}
void testSpecialIntegerFunctions()
{
for(vigra::Int32 i = 0; i < 1024; ++i)
{
shouldEqual(vigra::sqrti(i), (vigra::Int32)vigra::floor(vigra::sqrt((double)i)));
}
shouldEqual(vigra::roundi(0.0), 0);
shouldEqual(vigra::roundi(1.0), 1);
shouldEqual(vigra::roundi(1.1), 1);
shouldEqual(vigra::roundi(1.6), 2);
shouldEqual(vigra::roundi(-1.0), -1);
shouldEqual(vigra::roundi(-1.1), -1);
shouldEqual(vigra::roundi(-1.6), -2);
vigra::UInt32 roundPower2[] = {0, 1, 2, 3, 4, 5, 7, 8, 9, 15, 16, 0xffff, 0x7fffffff, 0x80000000, 0x80000001, 0xffffffff};
vigra::UInt32 floorResult[] = {0, 1, 2, 2, 4, 4, 4, 8, 8, 8, 16, 0x8000, 0x40000000, 0x80000000, 0x80000000, 0x80000000};
vigra::UInt32 ceilResult[] = {0, 1, 2, 4, 4, 8, 8, 8, 16, 16, 16, 0x10000, 0x80000000, 0x80000000, 0, 0};
for(unsigned int i = 0; i < sizeof(roundPower2) / sizeof(vigra::UInt32); ++i)
{
shouldEqual(vigra::floorPower2(roundPower2[i]), floorResult[i]);
shouldEqual(vigra::ceilPower2(roundPower2[i]), ceilResult[i]);
}
for(vigra::Int32 k=0; k<32; ++k)
{
shouldEqual(vigra::log2i(1 << k), k);
shouldEqual(vigra::log2i((1 << k) + 1), k == 0 ? 1 : k);
shouldEqual(vigra::log2i((1 << k) - 1), k-1);
}
should(vigra::even(0));
should(!vigra::odd(0));
should(!vigra::even(1));
should(vigra::odd(1));
should(vigra::even(2));
should(!vigra::odd(2));
should(!vigra::even(-1));
should(vigra::odd(-1));
should(vigra::even(-2));
should(!vigra::odd(-2));
}
void testSpecialFunctions()
{
shouldEqualTolerance(vigra::ellipticIntegralE(M_PI / 2.0, 0.0), M_PI / 2.0, 1e-14);
shouldEqualTolerance(vigra::ellipticIntegralF(0.3, 0.3), 0.30039919311549118, 1e-14);
shouldEqualTolerance(vigra::ellipticIntegralE(0.3, 0.3), 0.29960175507025716, 1e-14);
shouldEqualTolerance(vigra::erf(0.3), 0.32862675945912745, 1e-7);
should(vigra::noncentralChi2CDFApprox(200, 0.0, 200.0) > 0.5);
should(vigra::noncentralChi2CDFApprox(200, 0.0, 199.0) < 0.5);
should(vigra::noncentralChi2CDF(200, 0.0, 200.0) > 0.5);
should(vigra::noncentralChi2CDF(200, 0.0, 199.0) < 0.5);
shouldEqualTolerance(vigra::noncentralChi2CDF(2, 2.0, 2.0), 0.34574583872316456, 1e-7);
shouldEqualTolerance(vigra::noncentralChi2(2, 2.0, 2.0), 0.154254161276835, 1e-7);
shouldEqualTolerance(vigra::noncentralChi2CDF(3, 2.0, 2.0), 0.22073308707450343, 1e-7);
shouldEqualTolerance(vigra::noncentralChi2(3, 2.0, 2.0), 0.13846402271767755, 1e-7);
shouldEqualTolerance(vigra::noncentralChi2CDFApprox(2, 2.0, 2.0), 0.34574583872316456, 1e-1);
shouldEqualTolerance(vigra::noncentralChi2CDFApprox(3, 2.0, 2.0), 0.22073308707450343, 1e-1);
for(double x = -4.0; x <= 4.0; x += 1.0)
{
shouldEqual(vigra::sin_pi(x), 0.0);
shouldEqual(vigra::cos_pi(x+0.5), 0.0);
}
for(double x = -4.5; x <= 4.5; x += 2.0)
{
shouldEqual(vigra::sin_pi(x), -1.0);
shouldEqual(vigra::cos_pi(x+0.5), 1.0);
}
for(double x = -3.5; x <= 4.5; x += 2.0)
{
shouldEqual(vigra::sin_pi(x), 1.0);
shouldEqual(vigra::cos_pi(x+0.5), -1.0);
}
for(double x = -4.0; x <= 4.0; x += 0.0625)
{
shouldEqualTolerance(vigra::sin_pi(x), std::sin(M_PI*x), 1e-14);
shouldEqualTolerance(vigra::cos_pi(x), std::cos(M_PI*x), 1e-14);
}
shouldEqualTolerance(vigra::sin_pi(0.25), 0.5*M_SQRT2, 2e-16);
shouldEqualTolerance(vigra::cos_pi(0.25), 0.5*M_SQRT2, 2e-16);
shouldEqual(vigra::gamma(4.0), 6.0);
shouldEqualTolerance(vigra::gamma(0.1), 9.5135076986687306, 1e-15);
shouldEqualTolerance(vigra::gamma(3.2), 2.4239654799353683, 1e-15);
shouldEqualTolerance(vigra::gamma(170.2), 1.1918411166366696e+305, 1e-15);
shouldEqualTolerance(vigra::gamma(-0.1), -10.686287021193193, 1e-14);
shouldEqualTolerance(vigra::gamma(-3.2), 0.689056412005979, 1e-14);
shouldEqualTolerance(vigra::gamma(-170.2), -2.6348340538196879e-307, 1e-14);
try { vigra::gamma(0.0); failTest("No exception thrown"); } catch(vigra::PreconditionViolation &) {}
try { vigra::gamma(-1.0); failTest("No exception thrown"); } catch(vigra::PreconditionViolation &) {}
shouldEqual(vigra::loggamma(1.0), 0.0);
shouldEqual(vigra::loggamma(2.0), 0.0);
shouldEqualTolerance(vigra::loggamma(4.0e-22), 49.2705776847491144296, 1e-15);
shouldEqualTolerance(vigra::loggamma(0.1), 2.2527126517342055401, 1e-15);
shouldEqualTolerance(vigra::loggamma(0.3), 1.0957979948180756047, 1e-15);
shouldEqualTolerance(vigra::loggamma(0.8), 0.15205967839983755563, 1e-15);
shouldEqualTolerance(vigra::loggamma(1.1), -0.049872441259839757344, 1e-15);
shouldEqualTolerance(vigra::loggamma(1.3), -0.10817480950786048655, 1e-15);
shouldEqualTolerance(vigra::loggamma(1.8), -0.071083872914372153717, 1e-15);
shouldEqualTolerance(vigra::loggamma(3.0), 0.69314718055994528623, 1e-15);
shouldEqualTolerance(vigra::loggamma(3.1), 0.78737508327386251938, 1e-15);
shouldEqualTolerance(vigra::loggamma(4.0), 1.79175946922805500081, 1e-15);
shouldEqualTolerance(vigra::loggamma(8.0), 8.5251613610654143002, 1e-15);
shouldEqualTolerance(vigra::loggamma(1000.0), 5905.2204232091812118261, 1e-15);
shouldEqualTolerance(vigra::loggamma(1000.2), 5906.6018942569799037, 1e-15);
shouldEqualTolerance(vigra::loggamma(2.8e+17), 1.096859847946237952e+19, 1e-15);
shouldEqualTolerance(vigra::loggamma(2.9e+17), 1.1370510622188449792e+19, 1e-15);
shouldEqualTolerance(vigra::loggamma(5.7646075230342349e+17), 2.2998295812288974848e+19, 1e-15);
try { vigra::loggamma(0.0); failTest("No exception thrown"); } catch(vigra::PreconditionViolation &) {}
try { vigra::loggamma(-1.0); failTest("No exception thrown"); } catch(vigra::PreconditionViolation &) {}
double args[5] = {0.0, 1.0, 0.7, -0.7, -1.0};
for(int i=0; i<5; ++i)
{
double x = args[i], x2 = x*x;
shouldEqualTolerance(vigra::legendre(0, x), 1.0, 1e-15);
shouldEqualTolerance(vigra::legendre(1, x), x, 1e-15);
shouldEqualTolerance(vigra::legendre(2, x), 0.5*(3.0*x2-1.0), 1e-15);
shouldEqualTolerance(vigra::legendre(3, x), 0.5*x*(5.0*x2-3.0), 1e-15);
shouldEqualTolerance(vigra::legendre(0, 0, x), 1.0, 1e-15);
shouldEqualTolerance(vigra::legendre(1, 0, x), x, 1e-15);
shouldEqualTolerance(vigra::legendre(1, 1, x), -std::sqrt(1.0-x2), 1e-15);
shouldEqualTolerance(vigra::legendre(2, 0, x), 0.5*(3.0*x2-1.0), 1e-15);
shouldEqualTolerance(vigra::legendre(2, 1, x), -3.0*x*std::sqrt(1.0-x2), 1e-15);
shouldEqualTolerance(vigra::legendre(2, 2, x), 3.0*(1.0-x2), 1e-15);
shouldEqualTolerance(vigra::legendre(4, 2, x), 7.5*(7.0*x2-1.0)*(1.0-x2), 1e-15);
shouldEqualTolerance(vigra::legendre(1, -1, x), -vigra::legendre(1, 1, x) / 2.0, 1e-15);
shouldEqualTolerance(vigra::legendre(2, -1, x), -vigra::legendre(2, 1, x) / 6.0, 1e-15);
shouldEqualTolerance(vigra::legendre(2, -2, x), vigra::legendre(2, 2, x) / 24.0, 1e-15);
}
}
void testBessel()
{
// Reference values computed to 16 digits with Python.mpmath.
// Casual comparison showed no difference to Mathematica's results.
double x[] = { 1.0, 4.0, 6.0 };
double besseljnref[] = {
7.6519768655796649e-01, -3.9714980986384740e-01, 1.5064525725099692e-01,
5.7672480775687329e-01, -3.2757913759146523e-01, -4.6828234823458334e-03,
4.8609126058589103e-01, -2.4287320996018547e-01, -1.1299172042407525e-01,
4.3017147387562193e-01, -1.6755558799533424e-01, -1.8093519033665686e-01,
3.9123236045864818e-01, -1.0535743487538894e-01, -2.1960268610200856e-01,
3.6208707488717234e-01, -5.5038855669513713e-02, -2.3828585178317879e-01,
3.3919660498317961e-01, -1.4458842084785106e-02, -2.4372476722886663e-01,
3.2058907797982628e-01, 1.8376032647858614e-02, -2.4057094958616052e-01,
3.0506707225300012e-01, 4.5095329080457235e-02, -2.3197310306707983e-01,
2.9185568526512001e-01, 6.6976198673670620e-02, -2.2004622511384700e-01,
2.8042823052537585e-01, 8.5006705446061023e-02, -2.0620569442259729e-01,
2.7041248255096445e-01, 9.9950477050301592e-02, -1.9139539469541733e-01,
2.6153687541034509e-01, 1.1240023492610679e-01, -1.7624117645477547e-01,
2.5359797330294920e-01, 1.2281915265293869e-01, -1.6115376768165826e-01,
2.4643993656993257e-01, 1.3157198580936999e-01, -1.4639794400255970e-01
};
double besselynref[] = {
8.8256964215676956e-02, -1.6940739325064992e-02, -2.8819468398157916e-01,
-1.0703243154093754e-01, 1.4786314339122683e-01, -3.0266723702418485e-01,
-1.6040039348492374e-01, 2.2985790254811306e-01, -2.6303660482037811e-01,
-1.8202211595348500e-01, 2.6808060304231507e-01, -2.0509487811877961e-01,
-1.9214228737369318e-01, 2.8294322431117191e-01, -1.4494951186809379e-01,
-1.9706088806443733e-01, 2.8511777841103764e-01, -8.9252841434580163e-02,
-1.9930679029227036e-01, 2.8035255955745608e-01, -4.0297251103395833e-02,
-2.0006390460040860e-01, 2.7184139484930947e-01, 1.5698795407253514e-03,
-1.9994686666043449e-01, 2.6140472921203017e-01, 3.6815736940746704e-02,
-1.9929926580524435e-01, 2.5009898312668521e-01, 6.6197858895869655e-02,
-1.9832403085028555e-01, 2.3854272714494473e-01, 9.0526604143921052e-02,
-1.9714613354518651e-01, 2.2709735924007149e-01, 1.1056356972736049e-01,
-1.9584504763522584e-01, 2.1597027298252575e-01, 1.2698414345087472e-01,
-1.9447256680104227e-01, 2.0527533641239212e-01, 1.4036965442780550e-01,
-1.9306306446008192e-01, 1.9506914688206353e-01, 1.5121244335755843e-01
};
for(int n = 0; n < 15; ++n)
{
if(n == 0)
shouldEqual(vigra::besselJ(n, 0.0), 1.0);
else
shouldEqual(vigra::besselJ(n, 0.0), 0.0);
should(vigra::besselY(n, 0.0) == -std::numeric_limits<double>::infinity());
for(int k=0; k<3; ++k)
{
double f = vigra::odd(n) ? -1.0 : 1.0;
double eps = 1e-14;
shouldEqualTolerance(vigra::besselJ(n, x[k]+n) - besseljnref[k+3*n], 0.0, eps);
shouldEqualTolerance(vigra::besselJ(-n, x[k]+n) - f*besseljnref[k+3*n], 0.0, eps);
shouldEqualTolerance(vigra::besselY(n, x[k]+n) - besselynref[k+3*n], 0.0, eps);
shouldEqualTolerance(vigra::besselY(-n, x[k]+n) - f*besselynref[k+3*n], 0.0, eps);
}
}
}
void closeAtToleranceTest()
{
double a = 0.0, b = vigra::NumericTraits<double>::epsilon(), c = 1000.0, d = 1000.1;
using namespace vigra;
should(closeAtTolerance(a, b));
should(closeAtTolerance(c, c + b));
should(!closeAtTolerance(c, d));
should(closeAtTolerance(c, d, 0.01));
should(closeAtTolerance(-a, -b));
should(closeAtTolerance(-c, -c + b));
should(!closeAtTolerance(-c, -d));
should(closeAtTolerance(-c, -d, 0.01));
should(!closeAtTolerance(c, -c));
should(!closeAtTolerance(a, c));
should(!closeAtTolerance(c, d));
should(!closeAtTolerance(-a, -c));
should(!closeAtTolerance(-c, -d));
should(lessEqualAtTolerance(a, c));
should(lessEqualAtTolerance(c, c));
should(lessEqualAtTolerance(c, c-b));
should(lessEqualAtTolerance(c, d));
should(!lessEqualAtTolerance(d, c));
should(lessEqualAtTolerance(d, c, 0.01));
should(greaterEqualAtTolerance(c, a));
should(greaterEqualAtTolerance(c, c));
should(greaterEqualAtTolerance(c-b, c));
should(greaterEqualAtTolerance(d, c));
should(!greaterEqualAtTolerance(c, d));
should(greaterEqualAtTolerance(c, d, 0.01));
}
void testArgMinMax()
{
using namespace vigra;
using namespace vigra::functor;
double data[] = {1.0, 5.0,
3.0, 2.0,
-2.0, 4.0};
double *end = data + 6;
shouldEqual(argMin(data, end), data+4);
shouldEqual(argMax(data, end), data+1);
shouldEqual(argMinIf(data, end, Arg1() > Param(0.0)), data);
shouldEqual(argMinIf(data, end, Arg1() > Param(5.0)), end);
shouldEqual(argMaxIf(data, end, Arg1() < Param(5.0)), data+5);
shouldEqual(argMaxIf(data, end, Arg1() < Param(-2.0)), end);
}
void testAlgorithms()
{
static const int size = 6;
int index[size];
vigra::linearSequence(index, index+size);
int indexref[size] = {0, 1, 2, 3, 4, 5};
shouldEqualSequence(index, index+size, indexref);
vigra::linearSequence(index, index+size, 5, 5);
int indexref2[size] = {5, 10, 15, 20, 25, 30};
shouldEqualSequence(index, index+size, indexref2);
double data[size] = {1.0, 5.0,
3.0, 2.0,
-2.0, 4.0};
vigra::indexSort(data, data+size, index, std::greater<double>());
int sortref[size] = {1, 5, 2, 3, 0, 4};
shouldEqualSequence(index, index+size, sortref);
vigra::indexSort(data, data+size, index);
int sortref2[size] = {4, 0, 3, 2, 5, 1};
shouldEqualSequence(index, index+size, sortref2);
double res[size];
vigra::applyPermutation(index, index+size, data, res);
double ref[size] = {-2.0, 1.0, 2.0, 3.0, 4.0, 5.0 };
shouldEqualSequence(res, res+size, ref);
int inverse[size];
vigra::inversePermutation(index, index+size, inverse);
int inverseref[size] = {1, 5, 3, 2, 0, 4};
shouldEqualSequence(inverse, inverse+size, inverseref);
vigra::applyPermutation(inverse, inverse+size, ref, res);
shouldEqualSequence(res, res+size, data);
}
void testChecksum()
{
std::string s("");
vigra::UInt32 crc = vigra::checksum(s.c_str(), s.size());
shouldEqual(crc, 0u);
s = "hello world";
crc = vigra::checksum(s.c_str(), s.size());
shouldEqual(crc, 222957957u);
s = "hallo world";
crc = vigra::checksum(s.c_str(), s.size());
shouldEqual(crc, 77705727u);
int split = 5;
std::string s1 = s.substr(0, split), s2 = s.substr(split);
crc = vigra::checksum(s1.c_str(), s1.size());
crc = vigra::concatenateChecksum(crc, s2.c_str(), s2.size());
shouldEqual(crc, 77705727u);
const int size = 446;
char t[size+1] =
"Lorem ipsum dolor sit amet, consectetur adipisicing elit, "
"sed do eiusmod tempor incididunt ut labore et dolore magna "
"aliqua. Ut enim ad minim veniam, quis nostrud exercitation "
"ullamco laboris nisi ut aliquip ex ea commodo consequat. "
"Duis aute irure dolor in reprehenderit in voluptate velit "
"esse cillum dolore eu fugiat nulla pariatur. Excepteur "
"sint occaecat cupidatat non proident, sunt in culpa qui "
"officia deserunt mollit anim id est laborum.";
crc = vigra::checksum(t, size);
shouldEqual(crc, 2408722991u);
for(split = 64; split < 80; ++split) // check alignment
{
crc = vigra::checksum(t, split);
crc = vigra::concatenateChecksum(crc, t+split, size-split);
shouldEqual(crc, 2408722991u);
}
}
void testClebschGordan()
{
using vigra::clebschGordan;
shouldEqualTolerance(clebschGordan(0.5, 0.5, 0.5, 0.5, 1.0, 1.0), std::sqrt(1.0), 1e-15);
shouldEqualTolerance(clebschGordan(0.5, 0.5, 0.5, -0.5, 1.0, 0.0), std::sqrt(0.5), 1e-15);
shouldEqualTolerance(clebschGordan(0.5, -0.5, 0.5, 0.5, 1.0, 0.0), std::sqrt(0.5), 1e-15);
shouldEqualTolerance(clebschGordan(0.5, 0.5, 0.5, -0.5, 0.0, 0.0), std::sqrt(0.5), 1e-15);
shouldEqualTolerance(clebschGordan(0.5, -0.5, 0.5, 0.5, 0.0, 0.0), -std::sqrt(0.5), 1e-15);
shouldEqualTolerance(clebschGordan(2.0, 2.0, 0.5, 0.5, 2.5, 2.5), std::sqrt(1.0), 1e-15);
shouldEqualTolerance(clebschGordan(2.0, 2.0, 0.5, -0.5, 2.5, 1.5), std::sqrt(0.2), 1e-15);
shouldEqualTolerance(clebschGordan(2.0, 1.0, 0.5, 0.5, 2.5, 1.5), std::sqrt(0.8), 1e-15);
shouldEqualTolerance(clebschGordan(2.0, 2.0, 0.5, -0.5, 1.5, 1.5), std::sqrt(0.8), 1e-15);
shouldEqualTolerance(clebschGordan(2.0, 1.0, 0.5, 0.5, 1.5, 1.5), -std::sqrt(0.2), 1e-15);
}
};
struct RationalTest
{
typedef vigra::Rational<int> R;
void testGcdLcm()
{
shouldEqual(vigra::gcd(24, 18), 6);
shouldEqual(vigra::lcm(6, 4), 12);
shouldEqual(vigra::gcd(18, 24), 6);
shouldEqual(vigra::lcm(4, 6), 12);
}
void testOStreamShifting()
{
std::ostringstream out;
out << R(1,2);
out << "Testing.." << R(42,23) << 3.141592653589793238 << std::endl;
}
void testOperators()
{
shouldEqual(R(3,4), R(3,4));
shouldEqual(-R(3,4), R(-3,4));
shouldEqual(R(3,4) + R(12,6), R(11,4));
shouldEqual(R(3,4) - R(12,6), R(-5,4));
shouldEqual(R(3,4) * R(12,6), R(3,2));
shouldEqual(R(3,4) / R(12,6), R(3,8));
shouldEqual(abs(R(-3,4)), R(3,4));
shouldEqual(norm(R(-3,4)), R(3,4));
shouldEqual(squaredNorm(R(-3,4)), R(9,16));
should(R(3,4) == R(9,12));
should(R(3,4) != R(12,6));
should(R(3,4) < R(12,6));
should(R(19,4) > R(12,6));
should(R(3,4) <= R(12,6));
should(R(19,4) >= R(12,6));
shouldEqual(R(3,4) + 2, R(11,4));
shouldEqual(R(3,4) - 2, R(-5,4));
shouldEqual(R(3,4) * 2, R(3,2));
shouldEqual(R(3,4) / 2, R(3,8));
should(!(R(3,4) == 2));
should(R(3,4) != 2);
should(R(3,4) < 2);
should(R(19,4) > 2);
should(R(3,4) <= 2);
should(R(19,4) >= 2);
shouldEqual(2 + R(3,4), R(11,4));
shouldEqual(2 - R(3,4), R(5,4));
shouldEqual(2 * R(3,4), R(3,2));
shouldEqual(2 / R(3,4), R(8, 3));
should(!(2 == R(3,4)));
should(2 != R(3,4));
should(2 > R(3,4));
should(2 < R(19,4));
should(2 >= R(3,4));
should(2 <= R(19,4));
}
void testConversion()
{
shouldEqual(vigra::rational_cast<R>(R(3,2)), R(3,2));
shouldEqual(vigra::rational_cast<int>(R(3,2)), 1);
shouldEqual(vigra::rational_cast<double>(R(3,2)), 1.5);
shouldEqual(vigra::rational_cast<double>(1.5), 1.5);
shouldEqual(R(vigra::Rational<short>((short)-2, (short)-4)), R(1,2));
shouldEqual(R(3.5, 1e-4), R(7,2));
shouldEqual(R(-3.5, 1e-4), R(-7,2));
shouldEqual(R(0.123, 1e-4), R(123,1000));
shouldEqual(R(-0.123, 1e-4), R(-123,1000));
shouldEqual(R(0.123456, 1e-4), R(1235,10000));
shouldEqual(R(0.123432, 1e-4), R(1234,10000));
shouldEqual(R(-0.123456, 1e-4), R(-1235,10000));
shouldEqual(R(-0.123432, 1e-4), R(-1234,10000));
}
void testFunctions()
{
shouldEqual(pow(R(1,2),2), R(1,4));
shouldEqual(pow(R(2),-2), R(1,4));
shouldEqual(pow(R(-1,2),2), R(1,4));
shouldEqual(pow(R(-2),-2), R(1,4));
shouldEqual(pow(R(-1,2),3), R(-1,8));
shouldEqual(pow(R(-2),-3), R(-1,8));
shouldEqual(pow(R(3),0), R(1));
shouldEqual(pow(R(0),3), R(0));
shouldEqual(pow(R(0),0), R(1));
should(pow(R(0),-3).is_pinf());
should(pow(R(1,0, false), 1).is_pinf());
should(pow(R(-1,0, false), 1).is_ninf());
shouldEqual(pow(R(1,0, false), -1), R(0));
shouldEqual(pow(R(-1,0, false), -1), R(0));
try { pow(R(1,0, false), 0); failTest("No exception thrown"); } catch(vigra::bad_rational &) {}
try { pow(R(-1,0, false), 0); failTest("No exception thrown"); } catch(vigra::bad_rational &) {}
shouldEqual(floor(R(2)), R(2));
shouldEqual(floor(R(3,2)), R(1));
shouldEqual(floor(R(1,2)), R(0));
shouldEqual(floor(R(-1,2)), R(-1));
shouldEqual(floor(R(1,-2)), R(-1));
shouldEqual(floor(R(-3,2)), R(-2));
shouldEqual(floor(R(-2)), R(-2));
shouldEqual(floor(R(1,0,false)), R(1,0,false));
shouldEqual(floor(R(-1,0,false)), R(-1,0,false));
shouldEqual(ceil(R(2)), R(2));
shouldEqual(ceil(R(3,2)), R(2));
shouldEqual(ceil(R(1,2)), R(1));
shouldEqual(ceil(R(-1,2)), R(0));
shouldEqual(ceil(R(1,-2)), R(0));
shouldEqual(ceil(R(-3,2)), R(-1));
shouldEqual(ceil(R(-2)), R(-2));
shouldEqual(ceil(R(1,0,false)), R(1,0,false));
shouldEqual(ceil(R(-1,0,false)), R(-1,0,false));
}
void testInf()
{
R inf(2,0);
R ninf(-2,0);
should(inf.is_inf());
should(inf.is_pinf());
should(!inf.is_ninf());
should(ninf.is_inf());
should(ninf.is_ninf());
should(!ninf.is_pinf());
shouldEqual(inf.numerator(), 1);
shouldEqual(ninf.numerator(), -1);
should((inf + R(1)).is_pinf());
should((inf + R(0)).is_pinf());
should((inf + R(-1)).is_pinf());
should((ninf + R(1)).is_ninf());
should((ninf + R(0)).is_ninf());
should((ninf + R(-1)).is_ninf());
should((inf + 1).is_pinf());
should((inf + 0).is_pinf());
should((inf + (-1)).is_pinf());
should((ninf + 1).is_ninf());
should((ninf + 0).is_ninf());
should((ninf + (-1)).is_ninf());
should((inf + inf).is_pinf());
should((ninf + ninf).is_ninf());
shouldEqual((inf + R(3)).numerator(), 1);
shouldEqual((ninf + R(3)).numerator(), -1);
should((inf - R(1)).is_pinf());
should((inf - R(0)).is_pinf());
should((inf - R(-1)).is_pinf());
should((ninf - R(1)).is_ninf());
should((ninf - R(0)).is_ninf());
should((ninf - R(-1)).is_ninf());
should((inf - 1).is_pinf());
should((inf - 0).is_pinf());
should((inf - (-1)).is_pinf());
should((ninf - 1).is_ninf());
should((ninf - 0).is_ninf());
should((ninf - (-1)).is_ninf());
should((inf - ninf).is_pinf());
should((ninf - inf).is_ninf());
shouldEqual((inf - R(3)).numerator(), 1);
shouldEqual((ninf - R(3)).numerator(), -1);
should((inf * R(1)).is_pinf());
should((inf * R(-1)).is_ninf());
should((ninf * R(1)).is_ninf());
should((ninf * R(-1)).is_pinf());
should((inf * 1).is_pinf());
should((inf * (-1)).is_ninf());
should((ninf * 1).is_ninf());
should((ninf * (-1)).is_pinf());
should((inf * inf).is_pinf());
should((inf * ninf).is_ninf());
should((ninf * inf).is_ninf());
should((ninf * ninf).is_pinf());
shouldEqual((inf * R(3)).numerator(), 1);
shouldEqual((ninf * R(3)).numerator(), -1);
shouldEqual((inf * R(-3)).numerator(), -1);
shouldEqual((ninf * R(-3)).numerator(), 1);
should((inf / R(1)).is_pinf());
should((inf / R(0)).is_pinf());
should((inf / R(-1)).is_ninf());
should((ninf / R(1)).is_ninf());
should((ninf / R(0)).is_ninf());
should((ninf / R(-1)).is_pinf());
shouldEqual(R(1) / inf, R(0));
shouldEqual(R(-1) / inf, R(0));
shouldEqual(R(1) / ninf, R(0));
shouldEqual(R(-1) / ninf, R(0));
should((inf / 1).is_pinf());
should((inf / 0).is_pinf());
should((inf / (-1)).is_ninf());
should((ninf / 1).is_ninf());
should((ninf / 0).is_ninf());
should((ninf / (-1)).is_pinf());
shouldEqual(2 / inf, R(0));
shouldEqual((-2) / inf, R(0));
shouldEqual(2 / ninf, R(0));
shouldEqual((-2) / ninf, R(0));
shouldEqual((2 / inf).denominator(), 1);
shouldEqual(((-2) / inf).denominator(), 1);
shouldEqual((2 / ninf).denominator(), 1);
shouldEqual(((-2) / ninf).denominator(), 1);
shouldEqual((inf / R(3)).numerator(), 1);
shouldEqual((ninf / R(3)).numerator(), -1);
shouldEqual((inf / R(-3)).numerator(), -1);
shouldEqual((ninf / R(-3)).numerator(), 1);
should(inf == inf);
should(!(inf != inf));
should(!(inf < inf));
should(inf <= inf);
should(!(inf > inf));
should(inf >= inf);
should(ninf == ninf);
should(!(ninf != ninf));
should(!(ninf < ninf));
should(ninf <= ninf);
should(!(ninf > ninf));
should(ninf >= ninf);
should(inf != ninf);
should(ninf != inf);
should(inf > ninf);
should(ninf < inf);
should(!(inf < ninf));
should(!(ninf > inf));
should(inf != 0);
should(ninf != 0);
should(inf > 0);
should(inf >= 0);
should(ninf < 0);
should(ninf <= 0);
should(!(0 < ninf));
should(!(0 > inf));
should(!(0 <= ninf));
should(!(0 >= inf));
should(inf != R(1));
should(ninf != R(1));
should(inf > R(1));
should(inf >= R(1));
should(ninf < R(1));
should(ninf <= R(1));
should(!(R(1) < ninf));
should(!(R(1) > inf));
should(!(R(1) <= ninf));
should(!(R(1) >= inf));
try { inf + ninf; failTest("No exception thrown"); } catch(vigra::bad_rational &) {}
try { ninf + inf; failTest("No exception thrown"); } catch(vigra::bad_rational &) {}
try { inf - inf; failTest("No exception thrown"); } catch(vigra::bad_rational &) {}
try { ninf - ninf; failTest("No exception thrown"); } catch(vigra::bad_rational &) {}
try { inf * R(0); failTest("No exception thrown"); } catch(vigra::bad_rational &) {}
try { ninf * R(0); failTest("No exception thrown"); } catch(vigra::bad_rational &) {}
try { R(0) * inf; failTest("No exception thrown"); } catch(vigra::bad_rational &) {}
try { R(0) * ninf; failTest("No exception thrown"); } catch(vigra::bad_rational &) {}
try { inf * 0; failTest("No exception thrown"); } catch(vigra::bad_rational &) {}
try { ninf * 0; failTest("No exception thrown"); } catch(vigra::bad_rational &) {}
try { 0 * inf; failTest("No exception thrown"); } catch(vigra::bad_rational &) {}
try { 0 * ninf; failTest("No exception thrown"); } catch(vigra::bad_rational &) {}
try { inf / inf; failTest("No exception thrown"); } catch(vigra::bad_rational &) {}
try { inf / ninf; failTest("No exception thrown"); } catch(vigra::bad_rational &) {}
try { ninf / inf; failTest("No exception thrown"); } catch(vigra::bad_rational &) {}
try { R(0) / R(0); failTest("No exception thrown"); } catch(vigra::bad_rational &) {}
try { R(0) / 0; failTest("No exception thrown"); } catch(vigra::bad_rational &) {}
try { 0 / R(0); failTest("No exception thrown"); } catch(vigra::bad_rational &) {}
}
};
struct AutodiffTest
{
typedef vigra::autodiff::DualVector<double, 1> N1;
typedef vigra::autodiff::DualVector<double, 2> N2;
void testOStreamShifting()
{
std::ostringstream out;
out << N1(1.0,2.0);
out << "Testing.." << N1(42.0,23.0) << 3.141592653589793238 << std::endl;
}
void testOperators()
{
should(N2(3.0,4.0,5.0).value() == 3.0);
should(N2(3.0,4.0,5.0).gradient() == N2::Gradient(4.0,5.0));
should(N2(3.0,4.0,5.0) == N2(3.0, N2::Gradient(4.0,5.0)));
should(N1(3.0,4.0) == N1(3.0,4.0));
should(!(N1(3.0,4.0) == N1(2.0,4.0)));
should(!(N1(3.0,4.0) == N1(3.0,2.0)));
should(!(N1(3.0,4.0) != N1(3.0,4.0)));
should(N1(3.0,4.0) != N1(2.0,4.0));
should(N1(3.0,4.0) != N1(3.0,2.0));
should(closeAtTolerance(N1(3.0,4.0), N1(3.0,4.0)));
should(!closeAtTolerance(N1(3.0,4.0), N1(2.0,4.0)));
should(!closeAtTolerance(N1(3.0,4.0), N1(3.0,2.0)));