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eigen/test/array.cpp

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#include "main.h"
template<typename ArrayType> void array(const ArrayType& m)
{
typedef typename ArrayType::Index Index;
typedef typename ArrayType::Scalar Scalar;
typedef typename ArrayType::RealScalar RealScalar;
typedef Array<Scalar, ArrayType::RowsAtCompileTime, 1> ColVectorType;
typedef Array<Scalar, 1, ArrayType::ColsAtCompileTime> RowVectorType;
Index rows = m.rows();
Index cols = m.cols();
ArrayType m1 = ArrayType::Random(rows, cols),
m2 = ArrayType::Random(rows, cols),
m3(rows, cols);
ArrayType m4 = m1; // copy constructor
VERIFY_IS_APPROX(m1, m4);
ColVectorType cv1 = ColVectorType::Random(rows);
RowVectorType rv1 = RowVectorType::Random(cols);
Scalar s1 = internal::random<Scalar>(),
s2 = internal::random<Scalar>();
// scalar addition
VERIFY_IS_APPROX(m1 + s1, s1 + m1);
VERIFY_IS_APPROX(m1 + s1, ArrayType::Constant(rows,cols,s1) + m1);
VERIFY_IS_APPROX(s1 - m1, (-m1)+s1 );
VERIFY_IS_APPROX(m1 - s1, m1 - ArrayType::Constant(rows,cols,s1));
VERIFY_IS_APPROX(s1 - m1, ArrayType::Constant(rows,cols,s1) - m1);
VERIFY_IS_APPROX((m1*Scalar(2)) - s2, (m1+m1) - ArrayType::Constant(rows,cols,s2) );
m3 = m1;
m3 += s2;
VERIFY_IS_APPROX(m3, m1 + s2);
m3 = m1;
m3 -= s1;
VERIFY_IS_APPROX(m3, m1 - s1);
// scalar operators via Maps
m3 = m1;
ArrayType::Map(m1.data(), m1.rows(), m1.cols()) -= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
VERIFY_IS_APPROX(m1, m3 - m2);
m3 = m1;
ArrayType::Map(m1.data(), m1.rows(), m1.cols()) += ArrayType::Map(m2.data(), m2.rows(), m2.cols());
VERIFY_IS_APPROX(m1, m3 + m2);
m3 = m1;
ArrayType::Map(m1.data(), m1.rows(), m1.cols()) *= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
VERIFY_IS_APPROX(m1, m3 * m2);
m3 = m1;
m2 = ArrayType::Random(rows,cols);
m2 = (m2==0).select(1,m2);
ArrayType::Map(m1.data(), m1.rows(), m1.cols()) /= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
VERIFY_IS_APPROX(m1, m3 / m2);
// reductions
VERIFY_IS_APPROX(m1.abs().colwise().sum().sum(), m1.abs().sum());
VERIFY_IS_APPROX(m1.abs().rowwise().sum().sum(), m1.abs().sum());
using std::abs;
VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.colwise().sum().sum() - m1.sum()), m1.abs().sum());
VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.rowwise().sum().sum() - m1.sum()), m1.abs().sum());
if (!internal::isMuchSmallerThan(abs(m1.sum() - (m1+m2).sum()), m1.abs().sum(), test_precision<Scalar>()))
VERIFY_IS_NOT_APPROX(((m1+m2).rowwise().sum()).sum(), m1.sum());
VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(internal::scalar_sum_op<Scalar,Scalar>()));
// vector-wise ops
m3 = m1;
VERIFY_IS_APPROX(m3.colwise() += cv1, m1.colwise() + cv1);
m3 = m1;
VERIFY_IS_APPROX(m3.colwise() -= cv1, m1.colwise() - cv1);
m3 = m1;
VERIFY_IS_APPROX(m3.rowwise() += rv1, m1.rowwise() + rv1);
m3 = m1;
VERIFY_IS_APPROX(m3.rowwise() -= rv1, m1.rowwise() - rv1);
// Conversion from scalar
VERIFY_IS_APPROX((m3 = s1), ArrayType::Constant(rows,cols,s1));
VERIFY_IS_APPROX((m3 = 1), ArrayType::Constant(rows,cols,1));
VERIFY_IS_APPROX((m3.topLeftCorner(rows,cols) = 1), ArrayType::Constant(rows,cols,1));
typedef Array<Scalar,
ArrayType::RowsAtCompileTime==Dynamic?2:ArrayType::RowsAtCompileTime,
ArrayType::ColsAtCompileTime==Dynamic?2:ArrayType::ColsAtCompileTime,
ArrayType::Options> FixedArrayType;
FixedArrayType f1(s1);
VERIFY_IS_APPROX(f1, FixedArrayType::Constant(s1));
FixedArrayType f2(numext::real(s1));
VERIFY_IS_APPROX(f2, FixedArrayType::Constant(numext::real(s1)));
FixedArrayType f3((int)100*numext::real(s1));
VERIFY_IS_APPROX(f3, FixedArrayType::Constant((int)100*numext::real(s1)));
f1.setRandom();
FixedArrayType f4(f1.data());
VERIFY_IS_APPROX(f4, f1);
// pow
VERIFY_IS_APPROX(m1.pow(2), m1.square());
VERIFY_IS_APPROX(pow(m1,2), m1.square());
VERIFY_IS_APPROX(m1.pow(3), m1.cube());
VERIFY_IS_APPROX(pow(m1,3), m1.cube());
VERIFY_IS_APPROX((-m1).pow(3), -m1.cube());
VERIFY_IS_APPROX(pow(2*m1,3), 8*m1.cube());
ArrayType exponents = ArrayType::Constant(rows, cols, RealScalar(2));
VERIFY_IS_APPROX(Eigen::pow(m1,exponents), m1.square());
VERIFY_IS_APPROX(m1.pow(exponents), m1.square());
VERIFY_IS_APPROX(Eigen::pow(2*m1,exponents), 4*m1.square());
VERIFY_IS_APPROX((2*m1).pow(exponents), 4*m1.square());
VERIFY_IS_APPROX(Eigen::pow(m1,2*exponents), m1.square().square());
VERIFY_IS_APPROX(m1.pow(2*exponents), m1.square().square());
VERIFY_IS_APPROX(pow(m1(0,0), exponents), ArrayType::Constant(rows,cols,m1(0,0)*m1(0,0)));
// Check possible conflicts with 1D ctor
typedef Array<Scalar, Dynamic, 1> OneDArrayType;
OneDArrayType o1(rows);
VERIFY(o1.size()==rows);
OneDArrayType o4((int)rows);
VERIFY(o4.size()==rows);
}
template<typename ArrayType> void comparisons(const ArrayType& m)
{
using std::abs;
typedef typename ArrayType::Index Index;
typedef typename ArrayType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
Index rows = m.rows();
Index cols = m.cols();
Index r = internal::random<Index>(0, rows-1),
c = internal::random<Index>(0, cols-1);
ArrayType m1 = ArrayType::Random(rows, cols),
m2 = ArrayType::Random(rows, cols),
m3(rows, cols),
m4 = m1;
m4 = (m4.abs()==Scalar(0)).select(1,m4);
VERIFY(((m1 + Scalar(1)) > m1).all());
VERIFY(((m1 - Scalar(1)) < m1).all());
if (rows*cols>1)
{
m3 = m1;
m3(r,c) += 1;
VERIFY(! (m1 < m3).all() );
VERIFY(! (m1 > m3).all() );
}
VERIFY(!(m1 > m2 && m1 < m2).any());
VERIFY((m1 <= m2 || m1 >= m2).all());
// comparisons array to scalar
VERIFY( (m1 != (m1(r,c)+1) ).any() );
VERIFY( (m1 > (m1(r,c)-1) ).any() );
VERIFY( (m1 < (m1(r,c)+1) ).any() );
VERIFY( (m1 == m1(r,c) ).any() );
// comparisons scalar to array
VERIFY( ( (m1(r,c)+1) != m1).any() );
VERIFY( ( (m1(r,c)-1) < m1).any() );
VERIFY( ( (m1(r,c)+1) > m1).any() );
VERIFY( ( m1(r,c) == m1).any() );
// test Select
VERIFY_IS_APPROX( (m1<m2).select(m1,m2), m1.cwiseMin(m2) );
VERIFY_IS_APPROX( (m1>m2).select(m1,m2), m1.cwiseMax(m2) );
Scalar mid = (m1.cwiseAbs().minCoeff() + m1.cwiseAbs().maxCoeff())/Scalar(2);
for (int j=0; j<cols; ++j)
for (int i=0; i<rows; ++i)
m3(i,j) = abs(m1(i,j))<mid ? 0 : m1(i,j);
VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid))
.select(ArrayType::Zero(rows,cols),m1), m3);
// shorter versions:
VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid))
.select(0,m1), m3);
VERIFY_IS_APPROX( (m1.abs()>=ArrayType::Constant(rows,cols,mid))
.select(m1,0), m3);
// even shorter version:
VERIFY_IS_APPROX( (m1.abs()<mid).select(0,m1), m3);
// count
VERIFY(((m1.abs()+1)>RealScalar(0.1)).count() == rows*cols);
// and/or
VERIFY( (m1<RealScalar(0) && m1>RealScalar(0)).count() == 0);
VERIFY( (m1<RealScalar(0) || m1>=RealScalar(0)).count() == rows*cols);
RealScalar a = m1.abs().mean();
VERIFY( (m1<-a || m1>a).count() == (m1.abs()>a).count());
typedef Array<typename ArrayType::Index, Dynamic, 1> ArrayOfIndices;
// TODO allows colwise/rowwise for array
VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).colwise().count(), ArrayOfIndices::Constant(cols,rows).transpose());
VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).rowwise().count(), ArrayOfIndices::Constant(rows, cols));
}
template<typename ArrayType> void array_real(const ArrayType& m)
{
using std::abs;
using std::sqrt;
typedef typename ArrayType::Index Index;
typedef typename ArrayType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
Index rows = m.rows();
Index cols = m.cols();
ArrayType m1 = ArrayType::Random(rows, cols),
m2 = ArrayType::Random(rows, cols),
m3(rows, cols),
m4 = m1;
m4 = (m4.abs()==Scalar(0)).select(1,m4);
Scalar s1 = internal::random<Scalar>();
// these tests are mostly to check possible compilation issues with free-functions.
VERIFY_IS_APPROX(m1.sin(), sin(m1));
VERIFY_IS_APPROX(m1.cos(), cos(m1));
VERIFY_IS_APPROX(m1.tan(), tan(m1));
VERIFY_IS_APPROX(m1.asin(), asin(m1));
VERIFY_IS_APPROX(m1.acos(), acos(m1));
VERIFY_IS_APPROX(m1.atan(), atan(m1));
VERIFY_IS_APPROX(m1.sinh(), sinh(m1));
VERIFY_IS_APPROX(m1.cosh(), cosh(m1));
VERIFY_IS_APPROX(m1.tanh(), tanh(m1));
#if EIGEN_HAS_C99_MATH
VERIFY_IS_APPROX(m1.lgamma(), lgamma(m1));
VERIFY_IS_APPROX(m1.digamma(), digamma(m1));
VERIFY_IS_APPROX(m1.erf(), erf(m1));
VERIFY_IS_APPROX(m1.erfc(), erfc(m1));
#endif // EIGEN_HAS_C99_MATH
VERIFY_IS_APPROX(m1.arg(), arg(m1));
VERIFY_IS_APPROX(m1.round(), round(m1));
VERIFY_IS_APPROX(m1.floor(), floor(m1));
VERIFY_IS_APPROX(m1.ceil(), ceil(m1));
VERIFY((m1.isNaN() == (Eigen::isnan)(m1)).all());
VERIFY((m1.isInf() == (Eigen::isinf)(m1)).all());
VERIFY((m1.isFinite() == (Eigen::isfinite)(m1)).all());
VERIFY_IS_APPROX(m1.inverse(), inverse(m1));
VERIFY_IS_APPROX(m1.abs(), abs(m1));
VERIFY_IS_APPROX(m1.abs2(), abs2(m1));
VERIFY_IS_APPROX(m1.square(), square(m1));
VERIFY_IS_APPROX(m1.cube(), cube(m1));
VERIFY_IS_APPROX(cos(m1+RealScalar(3)*m2), cos((m1+RealScalar(3)*m2).eval()));
VERIFY_IS_APPROX(m1.sign(), sign(m1));
// avoid NaNs with abs() so verification doesn't fail
m3 = m1.abs();
VERIFY_IS_APPROX(m3.sqrt(), sqrt(abs(m1)));
VERIFY_IS_APPROX(m3.rsqrt(), Scalar(1)/sqrt(abs(m1)));
VERIFY_IS_APPROX(m3.log(), log(m3));
VERIFY_IS_APPROX(m3.log1p(), log1p(m3));
VERIFY_IS_APPROX(m3.log10(), log10(m3));
VERIFY((!(m1>m2) == (m1<=m2)).all());
VERIFY_IS_APPROX(sin(m1.asin()), m1);
VERIFY_IS_APPROX(cos(m1.acos()), m1);
VERIFY_IS_APPROX(tan(m1.atan()), m1);
VERIFY_IS_APPROX(sinh(m1), 0.5*(exp(m1)-exp(-m1)));
VERIFY_IS_APPROX(cosh(m1), 0.5*(exp(m1)+exp(-m1)));
VERIFY_IS_APPROX(tanh(m1), (0.5*(exp(m1)-exp(-m1)))/(0.5*(exp(m1)+exp(-m1))));
VERIFY_IS_APPROX(arg(m1), ((m1<0).template cast<Scalar>())*std::acos(-1.0));
VERIFY((round(m1) <= ceil(m1) && round(m1) >= floor(m1)).all());
VERIFY((Eigen::isnan)((m1*0.0)/0.0).all());
VERIFY((Eigen::isinf)(m4/0.0).all());
VERIFY(((Eigen::isfinite)(m1) && (!(Eigen::isfinite)(m1*0.0/0.0)) && (!(Eigen::isfinite)(m4/0.0))).all());
VERIFY_IS_APPROX(inverse(inverse(m1)),m1);
VERIFY((abs(m1) == m1 || abs(m1) == -m1).all());
VERIFY_IS_APPROX(m3, sqrt(abs2(m1)));
VERIFY_IS_APPROX( m1.sign(), -(-m1).sign() );
VERIFY_IS_APPROX( m1*m1.sign(),m1.abs());
VERIFY_IS_APPROX(m1.sign() * m1.abs(), m1);
VERIFY_IS_APPROX(numext::abs2(numext::real(m1)) + numext::abs2(numext::imag(m1)), numext::abs2(m1));
VERIFY_IS_APPROX(numext::abs2(real(m1)) + numext::abs2(imag(m1)), numext::abs2(m1));
if(!NumTraits<Scalar>::IsComplex)
VERIFY_IS_APPROX(numext::real(m1), m1);
// shift argument of logarithm so that it is not zero
Scalar smallNumber = NumTraits<Scalar>::dummy_precision();
VERIFY_IS_APPROX((m3 + smallNumber).log() , log(abs(m1) + smallNumber));
VERIFY_IS_APPROX((m3 + smallNumber + 1).log() , log1p(abs(m1) + smallNumber));
VERIFY_IS_APPROX(m1.exp() * m2.exp(), exp(m1+m2));
VERIFY_IS_APPROX(m1.exp(), exp(m1));
VERIFY_IS_APPROX(m1.exp() / m2.exp(),(m1-m2).exp());
VERIFY_IS_APPROX(m3.pow(RealScalar(0.5)), m3.sqrt());
VERIFY_IS_APPROX(pow(m3,RealScalar(0.5)), m3.sqrt());
VERIFY_IS_APPROX(m3.pow(RealScalar(-0.5)), m3.rsqrt());
VERIFY_IS_APPROX(pow(m3,RealScalar(-0.5)), m3.rsqrt());
VERIFY_IS_APPROX(log10(m3), log(m3)/log(10));
// scalar by array division
const RealScalar tiny = sqrt(std::numeric_limits<RealScalar>::epsilon());
s1 += Scalar(tiny);
m1 += ArrayType::Constant(rows,cols,Scalar(tiny));
VERIFY_IS_APPROX(s1/m1, s1 * m1.inverse());
#if EIGEN_HAS_C99_MATH
// check special functions (comparing against numpy implementation)
if (!NumTraits<Scalar>::IsComplex)
{
{
// Test various propreties of igamma & igammac. These are normalized
// gamma integrals where
// igammac(a, x) = Gamma(a, x) / Gamma(a)
// igamma(a, x) = gamma(a, x) / Gamma(a)
// where Gamma and gamma are considered the standard unnormalized
// upper and lower incomplete gamma functions, respectively.
ArrayType a = m1.abs() + 2;
ArrayType x = m2.abs() + 2;
ArrayType zero = ArrayType::Zero(rows, cols);
ArrayType one = ArrayType::Constant(rows, cols, Scalar(1.0));
ArrayType a_m1 = a - one;
ArrayType Gamma_a_x = Eigen::igammac(a, x) * a.lgamma().exp();
ArrayType Gamma_a_m1_x = Eigen::igammac(a_m1, x) * a_m1.lgamma().exp();
ArrayType gamma_a_x = Eigen::igamma(a, x) * a.lgamma().exp();
ArrayType gamma_a_m1_x = Eigen::igamma(a_m1, x) * a_m1.lgamma().exp();
// Gamma(a, 0) == Gamma(a)
VERIFY_IS_APPROX(Eigen::igammac(a, zero), one);
// Gamma(a, x) + gamma(a, x) == Gamma(a)
VERIFY_IS_APPROX(Gamma_a_x + gamma_a_x, a.lgamma().exp());
// Gamma(a, x) == (a - 1) * Gamma(a-1, x) + x^(a-1) * exp(-x)
VERIFY_IS_APPROX(Gamma_a_x, (a - 1) * Gamma_a_m1_x + x.pow(a-1) * (-x).exp());
// gamma(a, x) == (a - 1) * gamma(a-1, x) - x^(a-1) * exp(-x)
VERIFY_IS_APPROX(gamma_a_x, (a - 1) * gamma_a_m1_x - x.pow(a-1) * (-x).exp());
}
// Check exact values of igamma and igammac against a third party calculation.
Scalar a_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)};
Scalar x_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)};
// location i*6+j corresponds to a_s[i], x_s[j].
Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();
Scalar igamma_s[][6] = {{0.0, nan, nan, nan, nan, nan},
{0.0, 0.6321205588285578, 0.7768698398515702,
0.9816843611112658, 9.999500016666262e-05, 1.0},
{0.0, 0.4275932955291202, 0.608374823728911,
0.9539882943107686, 7.522076445089201e-07, 1.0},
{0.0, 0.01898815687615381, 0.06564245437845008,
0.5665298796332909, 4.166333347221828e-18, 1.0},
{0.0, 0.9999780593618628, 0.9999899967080838,
0.9999996219837988, 0.9991370418689945, 1.0},
{0.0, 0.0, 0.0, 0.0, 0.0, 0.5042041932513908}};
Scalar igammac_s[][6] = {{nan, nan, nan, nan, nan, nan},
{1.0, 0.36787944117144233, 0.22313016014842982,
0.018315638888734182, 0.9999000049998333, 0.0},
{1.0, 0.5724067044708798, 0.3916251762710878,
0.04601170568923136, 0.9999992477923555, 0.0},
{1.0, 0.9810118431238462, 0.9343575456215499,
0.4334701203667089, 1.0, 0.0},
{1.0, 2.1940638138146658e-05, 1.0003291916285e-05,
3.7801620118431334e-07, 0.0008629581310054535,
0.0},
{1.0, 1.0, 1.0, 1.0, 1.0, 0.49579580674813944}};
for (int i = 0; i < 6; ++i) {
for (int j = 0; j < 6; ++j) {
if ((std::isnan)(igamma_s[i][j])) {
VERIFY((std::isnan)(numext::igamma(a_s[i], x_s[j])));
} else {
VERIFY_IS_APPROX(numext::igamma(a_s[i], x_s[j]), igamma_s[i][j]);
}
if ((std::isnan)(igammac_s[i][j])) {
VERIFY((std::isnan)(numext::igammac(a_s[i], x_s[j])));
} else {
VERIFY_IS_APPROX(numext::igammac(a_s[i], x_s[j]), igammac_s[i][j]);
}
}
}
}
#endif // EIGEN_HAS_C99_MATH
// check inplace transpose
m3 = m1;
m3.transposeInPlace();
VERIFY_IS_APPROX(m3, m1.transpose());
m3.transposeInPlace();
VERIFY_IS_APPROX(m3, m1);
}
template<typename ArrayType> void array_complex(const ArrayType& m)
{
typedef typename ArrayType::Index Index;
typedef typename ArrayType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
Index rows = m.rows();
Index cols = m.cols();
ArrayType m1 = ArrayType::Random(rows, cols),
m2(rows, cols),
m4 = m1;
m4.real() = (m4.real().abs()==RealScalar(0)).select(RealScalar(1),m4.real());
m4.imag() = (m4.imag().abs()==RealScalar(0)).select(RealScalar(1),m4.imag());
Array<RealScalar, -1, -1> m3(rows, cols);
for (Index i = 0; i < m.rows(); ++i)
for (Index j = 0; j < m.cols(); ++j)
m2(i,j) = sqrt(m1(i,j));
// these tests are mostly to check possible compilation issues with free-functions.
VERIFY_IS_APPROX(m1.sin(), sin(m1));
VERIFY_IS_APPROX(m1.cos(), cos(m1));
VERIFY_IS_APPROX(m1.tan(), tan(m1));
VERIFY_IS_APPROX(m1.sinh(), sinh(m1));
VERIFY_IS_APPROX(m1.cosh(), cosh(m1));
VERIFY_IS_APPROX(m1.tanh(), tanh(m1));
VERIFY_IS_APPROX(m1.arg(), arg(m1));
VERIFY((m1.isNaN() == (Eigen::isnan)(m1)).all());
VERIFY((m1.isInf() == (Eigen::isinf)(m1)).all());
VERIFY((m1.isFinite() == (Eigen::isfinite)(m1)).all());
VERIFY_IS_APPROX(m1.inverse(), inverse(m1));
VERIFY_IS_APPROX(m1.log(), log(m1));
VERIFY_IS_APPROX(m1.log10(), log10(m1));
VERIFY_IS_APPROX(m1.abs(), abs(m1));
VERIFY_IS_APPROX(m1.abs2(), abs2(m1));
VERIFY_IS_APPROX(m1.sqrt(), sqrt(m1));
VERIFY_IS_APPROX(m1.square(), square(m1));
VERIFY_IS_APPROX(m1.cube(), cube(m1));
VERIFY_IS_APPROX(cos(m1+RealScalar(3)*m2), cos((m1+RealScalar(3)*m2).eval()));
VERIFY_IS_APPROX(m1.sign(), sign(m1));
VERIFY_IS_APPROX(m1.exp() * m2.exp(), exp(m1+m2));
VERIFY_IS_APPROX(m1.exp(), exp(m1));
VERIFY_IS_APPROX(m1.exp() / m2.exp(),(m1-m2).exp());
VERIFY_IS_APPROX(sinh(m1), 0.5*(exp(m1)-exp(-m1)));
VERIFY_IS_APPROX(cosh(m1), 0.5*(exp(m1)+exp(-m1)));
VERIFY_IS_APPROX(tanh(m1), (0.5*(exp(m1)-exp(-m1)))/(0.5*(exp(m1)+exp(-m1))));
for (Index i = 0; i < m.rows(); ++i)
for (Index j = 0; j < m.cols(); ++j)
m3(i,j) = std::atan2(imag(m1(i,j)), real(m1(i,j)));
VERIFY_IS_APPROX(arg(m1), m3);
std::complex<RealScalar> zero(0.0,0.0);
VERIFY((Eigen::isnan)(m1*zero/zero).all());
#if EIGEN_COMP_MSVC
// msvc complex division is not robust
VERIFY((Eigen::isinf)(m4/RealScalar(0)).all());
#else
#if EIGEN_COMP_CLANG
// clang's complex division is notoriously broken too
if((numext::isinf)(m4(0,0)/RealScalar(0))) {
#endif
VERIFY((Eigen::isinf)(m4/zero).all());
#if EIGEN_COMP_CLANG
}
else
{
VERIFY((Eigen::isinf)(m4.real()/zero.real()).all());
}
#endif
#endif // MSVC
VERIFY(((Eigen::isfinite)(m1) && (!(Eigen::isfinite)(m1*zero/zero)) && (!(Eigen::isfinite)(m1/zero))).all());
VERIFY_IS_APPROX(inverse(inverse(m1)),m1);
VERIFY_IS_APPROX(conj(m1.conjugate()), m1);
VERIFY_IS_APPROX(abs(m1), sqrt(square(real(m1))+square(imag(m1))));
VERIFY_IS_APPROX(abs(m1), sqrt(abs2(m1)));
VERIFY_IS_APPROX(log10(m1), log(m1)/log(10));
VERIFY_IS_APPROX( m1.sign(), -(-m1).sign() );
VERIFY_IS_APPROX( m1.sign() * m1.abs(), m1);
// scalar by array division
Scalar s1 = internal::random<Scalar>();
const RealScalar tiny = std::sqrt(std::numeric_limits<RealScalar>::epsilon());
s1 += Scalar(tiny);
m1 += ArrayType::Constant(rows,cols,Scalar(tiny));
VERIFY_IS_APPROX(s1/m1, s1 * m1.inverse());
// check inplace transpose
m2 = m1;
m2.transposeInPlace();
VERIFY_IS_APPROX(m2, m1.transpose());
m2.transposeInPlace();
VERIFY_IS_APPROX(m2, m1);
}
template<typename ArrayType> void min_max(const ArrayType& m)
{
typedef typename ArrayType::Index Index;
typedef typename ArrayType::Scalar Scalar;
Index rows = m.rows();
Index cols = m.cols();
ArrayType m1 = ArrayType::Random(rows, cols);
// min/max with array
Scalar maxM1 = m1.maxCoeff();
Scalar minM1 = m1.minCoeff();
VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, minM1), (m1.min)(ArrayType::Constant(rows,cols, minM1)));
VERIFY_IS_APPROX(m1, (m1.min)(ArrayType::Constant(rows,cols, maxM1)));
VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, maxM1), (m1.max)(ArrayType::Constant(rows,cols, maxM1)));
VERIFY_IS_APPROX(m1, (m1.max)(ArrayType::Constant(rows,cols, minM1)));
// min/max with scalar input
VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, minM1), (m1.min)( minM1));
VERIFY_IS_APPROX(m1, (m1.min)( maxM1));
VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, maxM1), (m1.max)( maxM1));
VERIFY_IS_APPROX(m1, (m1.max)( minM1));
}
template<typename X, typename Y>
void verify_component_wise(const X& x, const Y& y)
{
for(Index i=0; i<x.size(); ++i)
{
if((numext::isfinite)(y(i)))
VERIFY_IS_APPROX( x(i), y(i) );
else if((numext::isnan)(y(i)))
VERIFY((numext::isnan)(x(i)));
else
VERIFY_IS_EQUAL( x(i), y(i) );
}
}
// check special functions (comparing against numpy implementation)
template<typename ArrayType> void array_special_functions()
{
using std::abs;
using std::sqrt;
typedef typename ArrayType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
Scalar plusinf = std::numeric_limits<Scalar>::infinity();
Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();
// Check the zeta function against scipy.special.zeta
{
ArrayType x(7), q(7), res(7), ref(7);
x << 1.5, 4, 10.5, 10000.5, 3, 1, 0.9;
q << 2, 1.5, 3, 1.0001, -2.5, 1.2345, 1.2345;
ref << 1.61237534869, 0.234848505667, 1.03086757337e-5, 0.367879440865, 0.054102025820864097, plusinf, nan;
CALL_SUBTEST( verify_component_wise(ref, ref); );
CALL_SUBTEST( res = x.zeta(q); verify_component_wise(res, ref); );
CALL_SUBTEST( res = zeta(x,q); verify_component_wise(res, ref); );
}
// digamma
{
ArrayType x(7), res(7), ref(7);
x << 1, 1.5, 4, -10.5, 10000.5, 0, -1;
ref << -0.5772156649015329, 0.03648997397857645, 1.2561176684318, 2.398239129535781, 9.210340372392849, plusinf, plusinf;
CALL_SUBTEST( verify_component_wise(ref, ref); );
CALL_SUBTEST( res = x.digamma(); verify_component_wise(res, ref); );
CALL_SUBTEST( res = digamma(x); verify_component_wise(res, ref); );
}
#if EIGEN_HAS_C99_MATH
{
ArrayType n(11), x(11), res(11), ref(11);
n << 1, 1, 1, 1.5, 17, 31, 28, 8, 42, 147, 170;
x << 2, 3, 25.5, 1.5, 4.7, 11.8, 17.7, 30.2, 15.8, 54.1, 64;
ref << 0.644934066848, 0.394934066848, 0.0399946696496, nan, 293.334565435, 0.445487887616, -2.47810300902e-07, -8.29668781082e-09, -0.434562276666, 0.567742190178, -0.0108615497927;
CALL_SUBTEST( verify_component_wise(ref, ref); );
if(sizeof(RealScalar)>=8) { // double
// Reason for commented line: http://eigen.tuxfamily.org/bz/show_bug.cgi?id=1232
// CALL_SUBTEST( res = x.polygamma(n); verify_component_wise(res, ref); );
CALL_SUBTEST( res = polygamma(n,x); verify_component_wise(res, ref); );
}
else {
// CALL_SUBTEST( res = x.polygamma(n); verify_component_wise(res.head(8), ref.head(8)); );
CALL_SUBTEST( res = polygamma(n,x); verify_component_wise(res.head(8), ref.head(8)); );
}
}
#endif
#if EIGEN_HAS_C99_MATH
{
// Inputs and ground truth generated with scipy via:
// a = np.logspace(-3, 3, 5) - 1e-3
// b = np.logspace(-3, 3, 5) - 1e-3
// x = np.linspace(-0.1, 1.1, 5)
// (full_a, full_b, full_x) = np.vectorize(lambda a, b, x: (a, b, x))(*np.ix_(a, b, x))
// full_a = full_a.flatten().tolist() # same for full_b, full_x
// v = scipy.special.betainc(full_a, full_b, full_x).flatten().tolist()
//
// Note in Eigen, we call betainc with arguments in the order (x, a, b).
ArrayType a(125);
ArrayType b(125);
ArrayType x(125);
ArrayType v(125);
ArrayType res(125);
a << 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999,
0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999,
0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999,
31.62177660168379, 31.62177660168379, 31.62177660168379,
31.62177660168379, 31.62177660168379, 31.62177660168379,
31.62177660168379, 31.62177660168379, 31.62177660168379,
31.62177660168379, 31.62177660168379, 31.62177660168379,
31.62177660168379, 31.62177660168379, 31.62177660168379,
31.62177660168379, 31.62177660168379, 31.62177660168379,
31.62177660168379, 31.62177660168379, 31.62177660168379,
31.62177660168379, 31.62177660168379, 31.62177660168379,
31.62177660168379, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999,
999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999,
999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999,
999.999, 999.999, 999.999;
b << 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379, 0.03062277660168379,
0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.999,
0.999, 0.999, 0.999, 0.999, 31.62177660168379, 31.62177660168379,
31.62177660168379, 31.62177660168379, 31.62177660168379, 999.999,
999.999, 999.999, 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0,
0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
0.03062277660168379, 0.03062277660168379, 0.999, 0.999, 0.999, 0.999,
0.999, 31.62177660168379, 31.62177660168379, 31.62177660168379,
31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999,
999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379,
0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999,
31.62177660168379, 31.62177660168379, 31.62177660168379,
31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999,
999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379,
0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999,
31.62177660168379, 31.62177660168379, 31.62177660168379,
31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999,
999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379,
0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999,
31.62177660168379, 31.62177660168379, 31.62177660168379,
31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999,
999.999, 999.999;
x << -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5,
0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2,
0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1,
0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1,
-0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8,
1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5,
0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2,
0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1,
0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5,
0.8, 1.1;
v << nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
nan, nan, nan, 0.47972119876364683, 0.5, 0.5202788012363533, nan, nan,
0.9518683957740043, 0.9789663010413743, 0.9931729188073435, nan, nan,
0.999995949033062, 0.9999999999993698, 0.9999999999999999, nan, nan,
0.9999999999999999, 0.9999999999999999, 0.9999999999999999, nan, nan,
nan, nan, nan, nan, nan, 0.006827081192655869, 0.0210336989586256,
0.04813160422599567, nan, nan, 0.20014344256217678, 0.5000000000000001,
0.7998565574378232, nan, nan, 0.9991401428435834, 0.999999999698403,
0.9999999999999999, nan, nan, 0.9999999999999999, 0.9999999999999999,
0.9999999999999999, nan, nan, nan, nan, nan, nan, nan,
1.0646600232370887e-25, 6.301722877826246e-13, 4.050966937974938e-06,
nan, nan, 7.864342668429763e-23, 3.015969667594166e-10,
0.0008598571564165444, nan, nan, 6.031987710123844e-08,
0.5000000000000007, 0.9999999396801229, nan, nan, 0.9999999999999999,
0.9999999999999999, 0.9999999999999999, nan, nan, nan, nan, nan, nan,
nan, 0.0, 7.029920380986636e-306, 2.2450728208591345e-101, nan, nan,
0.0, 9.275871147869727e-302, 1.2232913026152827e-97, nan, nan, 0.0,
3.0891393081932924e-252, 2.9303043666183996e-60, nan, nan,
2.248913486879199e-196, 0.5000000000004947, 0.9999999999999999, nan;
CALL_SUBTEST(res = betainc(a, b, x);
verify_component_wise(res, v););
}
// Test various properties of betainc
{
ArrayType m1 = ArrayType::Random(32);
ArrayType m2 = ArrayType::Random(32);
ArrayType m3 = ArrayType::Random(32);
ArrayType one = ArrayType::Constant(32, Scalar(1.0));
const Scalar eps = std::numeric_limits<Scalar>::epsilon();
ArrayType a = (m1 * 4.0).exp();
ArrayType b = (m2 * 4.0).exp();
ArrayType x = m3.abs();
// betainc(a, 1, x) == x**a
CALL_SUBTEST(
ArrayType test = betainc(a, one, x);
ArrayType expected = x.pow(a);
verify_component_wise(test, expected););
// betainc(1, b, x) == 1 - (1 - x)**b
CALL_SUBTEST(
ArrayType test = betainc(one, b, x);
ArrayType expected = one - (one - x).pow(b);
verify_component_wise(test, expected););
// betainc(a, b, x) == 1 - betainc(b, a, 1-x)
CALL_SUBTEST(
ArrayType test = betainc(a, b, x) + betainc(b, a, one - x);
ArrayType expected = one;
verify_component_wise(test, expected););
// betainc(a+1, b, x) = betainc(a, b, x) - x**a * (1 - x)**b / (a * beta(a, b))
CALL_SUBTEST(
ArrayType num = x.pow(a) * (one - x).pow(b);
ArrayType denom = a * (a.lgamma() + b.lgamma() - (a + b).lgamma()).exp();
// Add eps to rhs and lhs so that component-wise test doesn't result in
// nans when both outputs are zeros.
ArrayType expected = betainc(a, b, x) - num / denom + eps;
ArrayType test = betainc(a + one, b, x) + eps;
if (sizeof(Scalar) >= 8) { // double
verify_component_wise(test, expected);
} else {
// Reason for limited test: http://eigen.tuxfamily.org/bz/show_bug.cgi?id=1232
verify_component_wise(test.head(8), expected.head(8));
});
// betainc(a, b+1, x) = betainc(a, b, x) + x**a * (1 - x)**b / (b * beta(a, b))
CALL_SUBTEST(
// Add eps to rhs and lhs so that component-wise test doesn't result in
// nans when both outputs are zeros.
ArrayType num = x.pow(a) * (one - x).pow(b);
ArrayType denom = b * (a.lgamma() + b.lgamma() - (a + b).lgamma()).exp();
ArrayType expected = betainc(a, b, x) + num / denom + eps;
ArrayType test = betainc(a, b + one, x) + eps;
verify_component_wise(test, expected););
}
#endif
}
void test_array()
{
#ifndef EIGEN_HAS_C99_MATH
std::cerr << "WARNING: testing of special math functions disabled" << std::endl;
#endif
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( array(Array<float, 1, 1>()) );
CALL_SUBTEST_2( array(Array22f()) );
CALL_SUBTEST_3( array(Array44d()) );
CALL_SUBTEST_4( array(ArrayXXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_5( array(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_6( array(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
}
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( comparisons(Array<float, 1, 1>()) );
CALL_SUBTEST_2( comparisons(Array22f()) );
CALL_SUBTEST_3( comparisons(Array44d()) );
CALL_SUBTEST_5( comparisons(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_6( comparisons(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
}
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( min_max(Array<float, 1, 1>()) );
CALL_SUBTEST_2( min_max(Array22f()) );
CALL_SUBTEST_3( min_max(Array44d()) );
CALL_SUBTEST_5( min_max(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_6( min_max(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
}
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( array_real(Array<float, 1, 1>()) );
CALL_SUBTEST_2( array_real(Array22f()) );
CALL_SUBTEST_3( array_real(Array44d()) );
CALL_SUBTEST_5( array_real(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
}
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_4( array_complex(ArrayXXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
}
VERIFY((internal::is_same< internal::global_math_functions_filtering_base<int>::type, int >::value));
VERIFY((internal::is_same< internal::global_math_functions_filtering_base<float>::type, float >::value));
VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Array2i>::type, ArrayBase<Array2i> >::value));
typedef CwiseUnaryOp<internal::scalar_abs_op<double>, ArrayXd > Xpr;
VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Xpr>::type,
ArrayBase<Xpr>
>::value));
CALL_SUBTEST_7(array_special_functions<ArrayXf>());
CALL_SUBTEST_7(array_special_functions<ArrayXd>());
}
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