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Diffstat (limited to 'test/array_cwise.cpp')
| -rw-r--r-- | test/array_cwise.cpp | 710 |
1 files changed, 710 insertions, 0 deletions
diff --git a/test/array_cwise.cpp b/test/array_cwise.cpp new file mode 100644 index 000000000..0cc438b39 --- /dev/null +++ b/test/array_cwise.cpp @@ -0,0 +1,710 @@ +// 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" + + +// Test the corner cases of pow(x, y) for real types. +template<typename Scalar> +void pow_test() { + const Scalar zero = Scalar(0); + const Scalar eps = Eigen::NumTraits<Scalar>::epsilon(); + const Scalar one = Scalar(1); + const Scalar two = Scalar(2); + const Scalar three = Scalar(3); + const Scalar sqrt_half = Scalar(std::sqrt(0.5)); + const Scalar sqrt2 = Scalar(std::sqrt(2)); + const Scalar inf = Eigen::NumTraits<Scalar>::infinity(); + const Scalar nan = Eigen::NumTraits<Scalar>::quiet_NaN(); + const Scalar denorm_min = std::numeric_limits<Scalar>::denorm_min(); + const Scalar min = (std::numeric_limits<Scalar>::min)(); + const Scalar max = (std::numeric_limits<Scalar>::max)(); + const Scalar max_exp = (static_cast<Scalar>(int(Eigen::NumTraits<Scalar>::max_exponent())) * Scalar(EIGEN_LN2)) / eps; + + const static Scalar abs_vals[] = {zero, + denorm_min, + min, + eps, + sqrt_half, + one, + sqrt2, + two, + three, + max_exp, + max, + inf, + nan}; + const int abs_cases = 13; + const int num_cases = 2*abs_cases * 2*abs_cases; + // Repeat the same value to make sure we hit the vectorized path. + const int num_repeats = 32; + Array<Scalar, Dynamic, Dynamic> x(num_repeats, num_cases); + Array<Scalar, Dynamic, Dynamic> y(num_repeats, num_cases); + int count = 0; + for (int i = 0; i < abs_cases; ++i) { + const Scalar abs_x = abs_vals[i]; + for (int sign_x = 0; sign_x < 2; ++sign_x) { + Scalar x_case = sign_x == 0 ? -abs_x : abs_x; + for (int j = 0; j < abs_cases; ++j) { + const Scalar abs_y = abs_vals[j]; + for (int sign_y = 0; sign_y < 2; ++sign_y) { + Scalar y_case = sign_y == 0 ? -abs_y : abs_y; + for (int repeat = 0; repeat < num_repeats; ++repeat) { + x(repeat, count) = x_case; + y(repeat, count) = y_case; + } + ++count; + } + } + } + } + + Array<Scalar, Dynamic, Dynamic> actual = x.pow(y); + const Scalar tol = test_precision<Scalar>(); + bool all_pass = true; + for (int i = 0; i < 1; ++i) { + for (int j = 0; j < num_cases; ++j) { + Scalar e = static_cast<Scalar>(std::pow(x(i,j), y(i,j))); + Scalar a = actual(i, j); + bool fail = !(a==e) && !internal::isApprox(a, e, tol) && !((numext::isnan)(a) && (numext::isnan)(e)); + all_pass &= !fail; + if (fail) { + std::cout << "pow(" << x(i,j) << "," << y(i,j) << ") = " << a << " != " << e << std::endl; + } + } + } + VERIFY(all_pass); +} + +template<typename ArrayType> void array(const ArrayType& m) +{ + 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); + } + #if EIGEN_HAS_CXX11 + { + 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); + } + #endif + + // 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(Eigen::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 o2(static_cast<int>(rows)); + VERIFY(o2.size()==rows); + } + #if EIGEN_HAS_CXX11 + { + OneDArrayType o1{rows}; + VERIFY(o1.size()==rows); + OneDArrayType o4{int(rows)}; + VERIFY(o4.size()==rows); + } + #endif + // Check possible conflicts with 2D ctor + typedef Array<Scalar, Dynamic, Dynamic> TwoDArrayType; + typedef Array<Scalar, 2, 1> ArrayType2; + { + TwoDArrayType o1(rows,cols); + VERIFY(o1.rows()==rows); + VERIFY(o1.cols()==cols); + TwoDArrayType o2(static_cast<int>(rows),static_cast<int>(cols)); + VERIFY(o2.rows()==rows); + VERIFY(o2.cols()==cols); + + ArrayType2 o3(rows,cols); + VERIFY(o3(0)==Scalar(rows) && o3(1)==Scalar(cols)); + ArrayType2 o4(static_cast<int>(rows),static_cast<int>(cols)); + VERIFY(o4(0)==Scalar(rows) && o4(1)==Scalar(cols)); + } + #if EIGEN_HAS_CXX11 + { + TwoDArrayType o1{rows,cols}; + VERIFY(o1.rows()==rows); + VERIFY(o1.cols()==cols); + TwoDArrayType o2{int(rows),int(cols)}; + VERIFY(o2.rows()==rows); + VERIFY(o2.cols()==cols); + + ArrayType2 o3{rows,cols}; + VERIFY(o3(0)==Scalar(rows) && o3(1)==Scalar(cols)); + ArrayType2 o4{int(rows),int(cols)}; + VERIFY(o4(0)==Scalar(rows) && o4(1)==Scalar(cols)); + } + #endif +} + +template<typename ArrayType> void comparisons(const ArrayType& m) +{ + using std::abs; + 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<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::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(Scalar(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_CXX11_MATH + VERIFY_IS_APPROX(m1.tanh().atanh(), atanh(tanh(m1))); + VERIFY_IS_APPROX(m1.sinh().asinh(), asinh(sinh(m1))); + VERIFY_IS_APPROX(m1.cosh().acosh(), acosh(cosh(m1))); +#endif + VERIFY_IS_APPROX(m1.logistic(), logistic(m1)); + + VERIFY_IS_APPROX(m1.arg(), arg(m1)); + VERIFY_IS_APPROX(m1.round(), round(m1)); + VERIFY_IS_APPROX(m1.rint(), rint(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(m4.inverse(), inverse(m4)); + 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)); + VERIFY((m1.sqrt().sign().isNaN() == (Eigen::isnan)(sign(sqrt(m1)))).all()); + + // avoid inf and NaNs so verification doesn't fail + m3 = m4.abs(); + VERIFY_IS_APPROX(m3.sqrt(), sqrt(abs(m3))); + VERIFY_IS_APPROX(m3.rsqrt(), Scalar(1)/sqrt(abs(m3))); + VERIFY_IS_APPROX(rsqrt(m3), Scalar(1)/sqrt(abs(m3))); + VERIFY_IS_APPROX(m3.log(), log(m3)); + VERIFY_IS_APPROX(m3.log1p(), log1p(m3)); + VERIFY_IS_APPROX(m3.log10(), log10(m3)); + VERIFY_IS_APPROX(m3.log2(), log2(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), Scalar(0.5)*(exp(m1)-exp(-m1))); + VERIFY_IS_APPROX(cosh(m1), Scalar(0.5)*(exp(m1)+exp(-m1))); + VERIFY_IS_APPROX(tanh(m1), (Scalar(0.5)*(exp(m1)-exp(-m1)))/(Scalar(0.5)*(exp(m1)+exp(-m1)))); + VERIFY_IS_APPROX(logistic(m1), (Scalar(1)/(Scalar(1)+exp(-m1)))); + VERIFY_IS_APPROX(arg(m1), ((m1<Scalar(0)).template cast<Scalar>())*Scalar(std::acos(Scalar(-1)))); + VERIFY((round(m1) <= ceil(m1) && round(m1) >= floor(m1)).all()); + VERIFY((rint(m1) <= ceil(m1) && rint(m1) >= floor(m1)).all()); + VERIFY(((ceil(m1) - round(m1)) <= Scalar(0.5) || (round(m1) - floor(m1)) <= Scalar(0.5)).all()); + VERIFY(((ceil(m1) - round(m1)) <= Scalar(1.0) && (round(m1) - floor(m1)) <= Scalar(1.0)).all()); + VERIFY(((ceil(m1) - rint(m1)) <= Scalar(0.5) || (rint(m1) - floor(m1)) <= Scalar(0.5)).all()); + VERIFY(((ceil(m1) - rint(m1)) <= Scalar(1.0) && (rint(m1) - floor(m1)) <= Scalar(1.0)).all()); + VERIFY((Eigen::isnan)((m1*Scalar(0))/Scalar(0)).all()); + VERIFY((Eigen::isinf)(m4/Scalar(0)).all()); + VERIFY(((Eigen::isfinite)(m1) && (!(Eigen::isfinite)(m1*Scalar(0)/Scalar(0))) && (!(Eigen::isfinite)(m4/Scalar(0)))).all()); + VERIFY_IS_APPROX(inverse(inverse(m4)),m4); + VERIFY((abs(m1) == m1 || abs(m1) == -m1).all()); + VERIFY_IS_APPROX(m3, sqrt(abs2(m3))); + VERIFY_IS_APPROX(m1.absolute_difference(m2), (m1 > m2).select(m1 - m2, m2 - 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(Eigen::real(m1)) + numext::abs2(Eigen::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(m3) + smallNumber)); + VERIFY_IS_APPROX((m3 + smallNumber + Scalar(1)).log() , log1p(abs(m3) + 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.expm1(), expm1(m1)); + VERIFY_IS_APPROX((m3 + smallNumber).exp() - Scalar(1), expm1(abs(m3) + smallNumber)); + + 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()); + + // Avoid inf and NaN. + m3 = (m1.square()<NumTraits<Scalar>::epsilon()).select(Scalar(1),m3); + VERIFY_IS_APPROX(m3.pow(RealScalar(-2)), m3.square().inverse()); + pow_test<Scalar>(); + + VERIFY_IS_APPROX(log10(m3), log(m3)/numext::log(Scalar(10))); + VERIFY_IS_APPROX(log2(m3), log(m3)/numext::log(Scalar(2))); + + // 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 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::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.logistic(), logistic(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(m4.inverse(), inverse(m4)); + VERIFY_IS_APPROX(m1.log(), log(m1)); + VERIFY_IS_APPROX(m1.log10(), log10(m1)); + VERIFY_IS_APPROX(m1.log2(), log2(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(m1.expm1(), expm1(m1)); + VERIFY_IS_APPROX(expm1(m1), exp(m1) - 1.); + // Check for larger magnitude complex numbers that expm1 matches exp - 1. + VERIFY_IS_APPROX(expm1(10. * m1), exp(10. * m1) - 1.); + + 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(logistic(m1), (1.0/(1.0 + exp(-m1)))); + + for (Index i = 0; i < m.rows(); ++i) + for (Index j = 0; j < m.cols(); ++j) + m3(i,j) = std::atan2(m1(i,j).imag(), m1(i,j).real()); + 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(m4)),m4); + VERIFY_IS_APPROX(conj(m1.conjugate()), m1); + VERIFY_IS_APPROX(abs(m1), sqrt(square(m1.real())+square(m1.imag()))); + VERIFY_IS_APPROX(abs(m1), sqrt(abs2(m1))); + VERIFY_IS_APPROX(log10(m1), log(m1)/log(10)); + VERIFY_IS_APPROX(log2(m1), log(m1)/log(2)); + + 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); + // Check vectorized inplace transpose. + ArrayType m5 = ArrayType::Random(131, 131); + ArrayType m6 = m5; + m6.transposeInPlace(); + VERIFY_IS_APPROX(m6, m5.transpose()); +} + +template<typename ArrayType> void min_max(const ArrayType& m) +{ + 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)); + + + // min/max with various NaN propagation options. + if (m1.size() > 1 && !NumTraits<Scalar>::IsInteger) { + m1(0,0) = NumTraits<Scalar>::quiet_NaN(); + maxM1 = m1.template maxCoeff<PropagateNaN>(); + minM1 = m1.template minCoeff<PropagateNaN>(); + VERIFY((numext::isnan)(maxM1)); + VERIFY((numext::isnan)(minM1)); + + maxM1 = m1.template maxCoeff<PropagateNumbers>(); + minM1 = m1.template minCoeff<PropagateNumbers>(); + VERIFY(!(numext::isnan)(maxM1)); + VERIFY(!(numext::isnan)(minM1)); + } +} + +template<int N> +struct shift_left { + template<typename Scalar> + Scalar operator()(const Scalar& v) const { + return v << N; + } +}; + +template<int N> +struct arithmetic_shift_right { + template<typename Scalar> + Scalar operator()(const Scalar& v) const { + return v >> N; + } +}; + +template<typename ArrayType> void array_integer(const ArrayType& m) +{ + Index rows = m.rows(); + Index cols = m.cols(); + + ArrayType m1 = ArrayType::Random(rows, cols), + m2(rows, cols); + + m2 = m1.template shiftLeft<2>(); + VERIFY( (m2 == m1.unaryExpr(shift_left<2>())).all() ); + m2 = m1.template shiftLeft<9>(); + VERIFY( (m2 == m1.unaryExpr(shift_left<9>())).all() ); + + m2 = m1.template shiftRight<2>(); + VERIFY( (m2 == m1.unaryExpr(arithmetic_shift_right<2>())).all() ); + m2 = m1.template shiftRight<9>(); + VERIFY( (m2 == m1.unaryExpr(arithmetic_shift_right<9>())).all() ); +} + +EIGEN_DECLARE_TEST(array_cwise) +{ + 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))) ); + CALL_SUBTEST_6( array(Array<Index,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_6( array_integer(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) ); + CALL_SUBTEST_6( array_integer(Array<Index,Dynamic,Dynamic>(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))) ); + CALL_SUBTEST_7( array_real(Array<Eigen::half, 32, 32>()) ); + CALL_SUBTEST_8( array_real(Array<Eigen::bfloat16, 32, 32>()) ); + } + 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)); +} |