711 lines
27 KiB
C++
711 lines
27 KiB
C++
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#include "main.h"
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// Test the corner cases of pow(x, y) for real types.
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template<typename Scalar>
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void pow_test() {
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const Scalar zero = Scalar(0);
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const Scalar eps = Eigen::NumTraits<Scalar>::epsilon();
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const Scalar one = Scalar(1);
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const Scalar two = Scalar(2);
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const Scalar three = Scalar(3);
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const Scalar sqrt_half = Scalar(std::sqrt(0.5));
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const Scalar sqrt2 = Scalar(std::sqrt(2));
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const Scalar inf = Eigen::NumTraits<Scalar>::infinity();
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const Scalar nan = Eigen::NumTraits<Scalar>::quiet_NaN();
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const Scalar denorm_min = std::numeric_limits<Scalar>::denorm_min();
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const Scalar min = (std::numeric_limits<Scalar>::min)();
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const Scalar max = (std::numeric_limits<Scalar>::max)();
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const Scalar max_exp = (static_cast<Scalar>(int(Eigen::NumTraits<Scalar>::max_exponent())) * Scalar(EIGEN_LN2)) / eps;
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const static Scalar abs_vals[] = {zero,
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denorm_min,
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min,
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eps,
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sqrt_half,
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one,
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sqrt2,
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two,
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three,
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max_exp,
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max,
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inf,
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nan};
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const int abs_cases = 13;
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const int num_cases = 2*abs_cases * 2*abs_cases;
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// Repeat the same value to make sure we hit the vectorized path.
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const int num_repeats = 32;
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Array<Scalar, Dynamic, Dynamic> x(num_repeats, num_cases);
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Array<Scalar, Dynamic, Dynamic> y(num_repeats, num_cases);
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int count = 0;
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for (int i = 0; i < abs_cases; ++i) {
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const Scalar abs_x = abs_vals[i];
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for (int sign_x = 0; sign_x < 2; ++sign_x) {
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Scalar x_case = sign_x == 0 ? -abs_x : abs_x;
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for (int j = 0; j < abs_cases; ++j) {
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const Scalar abs_y = abs_vals[j];
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for (int sign_y = 0; sign_y < 2; ++sign_y) {
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Scalar y_case = sign_y == 0 ? -abs_y : abs_y;
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for (int repeat = 0; repeat < num_repeats; ++repeat) {
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x(repeat, count) = x_case;
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y(repeat, count) = y_case;
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}
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++count;
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}
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}
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}
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}
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Array<Scalar, Dynamic, Dynamic> actual = x.pow(y);
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const Scalar tol = test_precision<Scalar>();
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bool all_pass = true;
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for (int i = 0; i < 1; ++i) {
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for (int j = 0; j < num_cases; ++j) {
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Scalar e = static_cast<Scalar>(std::pow(x(i,j), y(i,j)));
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Scalar a = actual(i, j);
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bool fail = !(a==e) && !internal::isApprox(a, e, tol) && !((numext::isnan)(a) && (numext::isnan)(e));
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all_pass &= !fail;
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if (fail) {
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std::cout << "pow(" << x(i,j) << "," << y(i,j) << ") = " << a << " != " << e << std::endl;
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}
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}
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}
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VERIFY(all_pass);
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}
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template<typename ArrayType> void array(const ArrayType& m)
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{
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typedef typename ArrayType::Scalar Scalar;
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typedef typename ArrayType::RealScalar RealScalar;
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typedef Array<Scalar, ArrayType::RowsAtCompileTime, 1> ColVectorType;
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typedef Array<Scalar, 1, ArrayType::ColsAtCompileTime> RowVectorType;
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Index rows = m.rows();
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Index cols = m.cols();
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ArrayType m1 = ArrayType::Random(rows, cols),
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m2 = ArrayType::Random(rows, cols),
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m3(rows, cols);
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ArrayType m4 = m1; // copy constructor
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VERIFY_IS_APPROX(m1, m4);
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ColVectorType cv1 = ColVectorType::Random(rows);
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RowVectorType rv1 = RowVectorType::Random(cols);
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Scalar s1 = internal::random<Scalar>(),
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s2 = internal::random<Scalar>();
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// scalar addition
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VERIFY_IS_APPROX(m1 + s1, s1 + m1);
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VERIFY_IS_APPROX(m1 + s1, ArrayType::Constant(rows,cols,s1) + m1);
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VERIFY_IS_APPROX(s1 - m1, (-m1)+s1 );
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VERIFY_IS_APPROX(m1 - s1, m1 - ArrayType::Constant(rows,cols,s1));
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VERIFY_IS_APPROX(s1 - m1, ArrayType::Constant(rows,cols,s1) - m1);
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VERIFY_IS_APPROX((m1*Scalar(2)) - s2, (m1+m1) - ArrayType::Constant(rows,cols,s2) );
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m3 = m1;
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m3 += s2;
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VERIFY_IS_APPROX(m3, m1 + s2);
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m3 = m1;
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m3 -= s1;
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VERIFY_IS_APPROX(m3, m1 - s1);
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// scalar operators via Maps
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m3 = m1;
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ArrayType::Map(m1.data(), m1.rows(), m1.cols()) -= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
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VERIFY_IS_APPROX(m1, m3 - m2);
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m3 = m1;
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ArrayType::Map(m1.data(), m1.rows(), m1.cols()) += ArrayType::Map(m2.data(), m2.rows(), m2.cols());
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VERIFY_IS_APPROX(m1, m3 + m2);
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m3 = m1;
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ArrayType::Map(m1.data(), m1.rows(), m1.cols()) *= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
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VERIFY_IS_APPROX(m1, m3 * m2);
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m3 = m1;
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m2 = ArrayType::Random(rows,cols);
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m2 = (m2==0).select(1,m2);
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ArrayType::Map(m1.data(), m1.rows(), m1.cols()) /= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
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VERIFY_IS_APPROX(m1, m3 / m2);
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// reductions
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VERIFY_IS_APPROX(m1.abs().colwise().sum().sum(), m1.abs().sum());
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VERIFY_IS_APPROX(m1.abs().rowwise().sum().sum(), m1.abs().sum());
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using std::abs;
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VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.colwise().sum().sum() - m1.sum()), m1.abs().sum());
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VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.rowwise().sum().sum() - m1.sum()), m1.abs().sum());
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if (!internal::isMuchSmallerThan(abs(m1.sum() - (m1+m2).sum()), m1.abs().sum(), test_precision<Scalar>()))
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VERIFY_IS_NOT_APPROX(((m1+m2).rowwise().sum()).sum(), m1.sum());
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VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(internal::scalar_sum_op<Scalar,Scalar>()));
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// vector-wise ops
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m3 = m1;
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VERIFY_IS_APPROX(m3.colwise() += cv1, m1.colwise() + cv1);
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m3 = m1;
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VERIFY_IS_APPROX(m3.colwise() -= cv1, m1.colwise() - cv1);
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m3 = m1;
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VERIFY_IS_APPROX(m3.rowwise() += rv1, m1.rowwise() + rv1);
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m3 = m1;
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VERIFY_IS_APPROX(m3.rowwise() -= rv1, m1.rowwise() - rv1);
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// Conversion from scalar
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VERIFY_IS_APPROX((m3 = s1), ArrayType::Constant(rows,cols,s1));
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VERIFY_IS_APPROX((m3 = 1), ArrayType::Constant(rows,cols,1));
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VERIFY_IS_APPROX((m3.topLeftCorner(rows,cols) = 1), ArrayType::Constant(rows,cols,1));
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typedef Array<Scalar,
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ArrayType::RowsAtCompileTime==Dynamic?2:ArrayType::RowsAtCompileTime,
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ArrayType::ColsAtCompileTime==Dynamic?2:ArrayType::ColsAtCompileTime,
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ArrayType::Options> FixedArrayType;
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{
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FixedArrayType f1(s1);
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VERIFY_IS_APPROX(f1, FixedArrayType::Constant(s1));
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FixedArrayType f2(numext::real(s1));
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VERIFY_IS_APPROX(f2, FixedArrayType::Constant(numext::real(s1)));
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FixedArrayType f3((int)100*numext::real(s1));
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VERIFY_IS_APPROX(f3, FixedArrayType::Constant((int)100*numext::real(s1)));
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f1.setRandom();
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FixedArrayType f4(f1.data());
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VERIFY_IS_APPROX(f4, f1);
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}
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#if EIGEN_HAS_CXX11
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{
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FixedArrayType f1{s1};
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VERIFY_IS_APPROX(f1, FixedArrayType::Constant(s1));
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FixedArrayType f2{numext::real(s1)};
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VERIFY_IS_APPROX(f2, FixedArrayType::Constant(numext::real(s1)));
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FixedArrayType f3{(int)100*numext::real(s1)};
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VERIFY_IS_APPROX(f3, FixedArrayType::Constant((int)100*numext::real(s1)));
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f1.setRandom();
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FixedArrayType f4{f1.data()};
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VERIFY_IS_APPROX(f4, f1);
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}
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#endif
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// pow
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VERIFY_IS_APPROX(m1.pow(2), m1.square());
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VERIFY_IS_APPROX(pow(m1,2), m1.square());
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VERIFY_IS_APPROX(m1.pow(3), m1.cube());
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VERIFY_IS_APPROX(pow(m1,3), m1.cube());
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VERIFY_IS_APPROX((-m1).pow(3), -m1.cube());
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VERIFY_IS_APPROX(pow(2*m1,3), 8*m1.cube());
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ArrayType exponents = ArrayType::Constant(rows, cols, RealScalar(2));
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VERIFY_IS_APPROX(Eigen::pow(m1,exponents), m1.square());
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VERIFY_IS_APPROX(m1.pow(exponents), m1.square());
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VERIFY_IS_APPROX(Eigen::pow(2*m1,exponents), 4*m1.square());
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VERIFY_IS_APPROX((2*m1).pow(exponents), 4*m1.square());
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VERIFY_IS_APPROX(Eigen::pow(m1,2*exponents), m1.square().square());
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VERIFY_IS_APPROX(m1.pow(2*exponents), m1.square().square());
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VERIFY_IS_APPROX(Eigen::pow(m1(0,0), exponents), ArrayType::Constant(rows,cols,m1(0,0)*m1(0,0)));
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// Check possible conflicts with 1D ctor
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typedef Array<Scalar, Dynamic, 1> OneDArrayType;
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{
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OneDArrayType o1(rows);
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VERIFY(o1.size()==rows);
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OneDArrayType o2(static_cast<int>(rows));
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VERIFY(o2.size()==rows);
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}
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#if EIGEN_HAS_CXX11
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{
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OneDArrayType o1{rows};
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VERIFY(o1.size()==rows);
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OneDArrayType o4{int(rows)};
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VERIFY(o4.size()==rows);
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}
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#endif
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// Check possible conflicts with 2D ctor
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typedef Array<Scalar, Dynamic, Dynamic> TwoDArrayType;
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typedef Array<Scalar, 2, 1> ArrayType2;
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{
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TwoDArrayType o1(rows,cols);
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VERIFY(o1.rows()==rows);
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VERIFY(o1.cols()==cols);
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TwoDArrayType o2(static_cast<int>(rows),static_cast<int>(cols));
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VERIFY(o2.rows()==rows);
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VERIFY(o2.cols()==cols);
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ArrayType2 o3(rows,cols);
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VERIFY(o3(0)==Scalar(rows) && o3(1)==Scalar(cols));
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ArrayType2 o4(static_cast<int>(rows),static_cast<int>(cols));
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VERIFY(o4(0)==Scalar(rows) && o4(1)==Scalar(cols));
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}
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#if EIGEN_HAS_CXX11
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{
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TwoDArrayType o1{rows,cols};
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VERIFY(o1.rows()==rows);
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VERIFY(o1.cols()==cols);
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TwoDArrayType o2{int(rows),int(cols)};
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VERIFY(o2.rows()==rows);
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VERIFY(o2.cols()==cols);
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ArrayType2 o3{rows,cols};
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VERIFY(o3(0)==Scalar(rows) && o3(1)==Scalar(cols));
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ArrayType2 o4{int(rows),int(cols)};
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VERIFY(o4(0)==Scalar(rows) && o4(1)==Scalar(cols));
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}
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#endif
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}
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template<typename ArrayType> void comparisons(const ArrayType& m)
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{
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using std::abs;
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typedef typename ArrayType::Scalar Scalar;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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Index rows = m.rows();
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Index cols = m.cols();
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Index r = internal::random<Index>(0, rows-1),
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c = internal::random<Index>(0, cols-1);
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ArrayType m1 = ArrayType::Random(rows, cols),
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m2 = ArrayType::Random(rows, cols),
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m3(rows, cols),
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m4 = m1;
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m4 = (m4.abs()==Scalar(0)).select(1,m4);
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VERIFY(((m1 + Scalar(1)) > m1).all());
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VERIFY(((m1 - Scalar(1)) < m1).all());
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if (rows*cols>1)
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{
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m3 = m1;
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m3(r,c) += 1;
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VERIFY(! (m1 < m3).all() );
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VERIFY(! (m1 > m3).all() );
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}
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VERIFY(!(m1 > m2 && m1 < m2).any());
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VERIFY((m1 <= m2 || m1 >= m2).all());
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// comparisons array to scalar
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VERIFY( (m1 != (m1(r,c)+1) ).any() );
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VERIFY( (m1 > (m1(r,c)-1) ).any() );
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VERIFY( (m1 < (m1(r,c)+1) ).any() );
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VERIFY( (m1 == m1(r,c) ).any() );
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// comparisons scalar to array
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VERIFY( ( (m1(r,c)+1) != m1).any() );
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VERIFY( ( (m1(r,c)-1) < m1).any() );
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VERIFY( ( (m1(r,c)+1) > m1).any() );
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VERIFY( ( m1(r,c) == m1).any() );
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// test Select
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VERIFY_IS_APPROX( (m1<m2).select(m1,m2), m1.cwiseMin(m2) );
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VERIFY_IS_APPROX( (m1>m2).select(m1,m2), m1.cwiseMax(m2) );
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Scalar mid = (m1.cwiseAbs().minCoeff() + m1.cwiseAbs().maxCoeff())/Scalar(2);
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for (int j=0; j<cols; ++j)
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for (int i=0; i<rows; ++i)
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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));
|
||
|
|
}
|