| // 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 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>())); |
| |
| // 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); |
| |
| // 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)); |
| #ifdef 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.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(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(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))); |
| |
| 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)); |
| |
| // Smoke test to check any compilation issues |
| ArrayType m1_abs_p1 = m1.abs() + 1; |
| ArrayType m2_abs_p1 = m2.abs() + 1; |
| VERIFY_IS_APPROX(Eigen::igamma(m1_abs_p1, m2_abs_p1), Eigen::igamma(m1_abs_p1, m2_abs_p1)); |
| VERIFY_IS_APPROX(Eigen::igammac(m1_abs_p1, m2_abs_p1), Eigen::igammac(m1_abs_p1, m2_abs_p1)); |
| VERIFY_IS_APPROX(Eigen::igamma(m2_abs_p1, m1_abs_p1), Eigen::igamma(m2_abs_p1, m1_abs_p1)); |
| VERIFY_IS_APPROX(Eigen::igammac(m2_abs_p1, m1_abs_p1), Eigen::igammac(m2_abs_p1, m1_abs_p1)); |
| |
| // 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()); |
| |
| // check special functions (comparing against numpy implementation) |
| #ifdef EIGEN_HAS_C99_MATH |
| if (!NumTraits<Scalar>::IsComplex) { |
| VERIFY_IS_APPROX(numext::digamma(Scalar(1)), RealScalar(-0.5772156649015329)); |
| VERIFY_IS_APPROX(numext::digamma(Scalar(1.5)), RealScalar(0.03648997397857645)); |
| VERIFY_IS_APPROX(numext::digamma(Scalar(4)), RealScalar(1.2561176684318)); |
| VERIFY_IS_APPROX(numext::digamma(Scalar(-10.5)), RealScalar(2.398239129535781)); |
| VERIFY_IS_APPROX(numext::digamma(Scalar(10000.5)), RealScalar(9.210340372392849)); |
| VERIFY_IS_EQUAL(numext::digamma(Scalar(0)), |
| std::numeric_limits<RealScalar>::infinity()); |
| VERIFY_IS_EQUAL(numext::digamma(Scalar(-1)), |
| std::numeric_limits<RealScalar>::infinity()); |
| |
| Scalar a_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(10000.5)}; |
| Scalar x_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(10000.5)}; |
| |
| // 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, 0.0, 0.0, 0.0, 0.0, 0.0}, |
| {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, 0.5013297751014064}}; |
| Scalar igammac_s[][6] = { |
| {1.0, 1.0, 1.0, 1.0, 1.0, 1.0}, |
| {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, 0.49867022490946517}}; |
| for (int i = 0; i < 6; ++i) { |
| for (int j = 0; j < 6; ++j) { |
| //std::cout << numext::igamma(a_s[i], x_s[j]) << " vs. " << igamma_s[i][j] << std::endl; |
| //std::cout << numext::igammac(a_s[i], x_s[j]) << " c.vs. " << |
| //igammac_s[i][j] << std::endl; |
| std::cout << a_s[i] << ", " << x_s[j] << std::endl; |
| VERIFY_IS_APPROX(numext::igamma(a_s[i], x_s[j]), igamma_s[i][j]); |
| 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 = 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)); |
| |
| } |
| |
| void test_array() |
| { |
| 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_multiple_op<double>, ArrayXd > Xpr; |
| VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Xpr>::type, |
| ArrayBase<Xpr> |
| >::value)); |
| } |