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306 lines
14 KiB
C++
306 lines
14 KiB
C++
// 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) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
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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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#include <Eigen/QR>
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template <typename Derived1, typename Derived2>
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bool areNotApprox(const MatrixBase<Derived1>& m1, const MatrixBase<Derived2>& m2,
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typename Derived1::RealScalar epsilon = NumTraits<typename Derived1::RealScalar>::dummy_precision()) {
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return !((m1 - m2).cwiseAbs2().maxCoeff() <
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epsilon * epsilon * (std::max)(m1.cwiseAbs2().maxCoeff(), m2.cwiseAbs2().maxCoeff()));
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}
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// Allow specifying tolerance for verifying error.
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template <typename Type1, typename Type2, typename Tol>
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inline bool verifyIsApprox(const Type1& a, const Type2& b, Tol tol) {
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bool ret = a.isApprox(b, tol);
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if (!ret) {
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std::cerr << "Difference too large wrt tolerance " << tol << ", relative error is: " << test_relative_error(a, b)
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<< std::endl;
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}
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return ret;
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}
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template <typename LhsType, typename RhsType>
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std::enable_if_t<RhsType::SizeAtCompileTime == Dynamic, void> check_mismatched_product(LhsType& lhs,
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const RhsType& rhs) {
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VERIFY_RAISES_ASSERT(lhs = rhs * rhs);
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}
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template <typename LhsType, typename RhsType>
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std::enable_if_t<RhsType::SizeAtCompileTime != Dynamic, void> check_mismatched_product(LhsType& /*unused*/,
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const RhsType& /*unused*/) {}
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template <typename MatrixType>
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void product(const MatrixType& m) {
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/* this test covers the following files:
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Identity.h Product.h
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*/
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typedef typename MatrixType::Scalar Scalar;
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typedef typename MatrixType::RealScalar RealScalar;
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typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> RowVectorType;
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typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> ColVectorType;
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typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> RowSquareMatrixType;
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typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> ColSquareMatrixType;
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typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime,
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MatrixType::Flags & RowMajorBit ? ColMajor : RowMajor>
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OtherMajorMatrixType;
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// We want a tighter epsilon for not-approx tests. Otherwise, for certain
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// low-precision types (e.g. bfloat16), the bound ends up being relatively large
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// (e.g. 0.12), causing flaky tests.
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RealScalar not_approx_epsilon = RealScalar(0.1) * NumTraits<RealScalar>::dummy_precision();
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Index rows = m.rows();
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Index cols = m.cols();
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// this test relies a lot on Random.h, and there's not much more that we can do
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// to test it, hence I consider that we will have tested Random.h
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MatrixType m1 = MatrixType::Random(rows, cols), m2 = MatrixType::Random(rows, cols), m3(rows, cols);
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RowSquareMatrixType identity = RowSquareMatrixType::Identity(rows, rows),
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square = RowSquareMatrixType::Random(rows, rows), res = RowSquareMatrixType::Random(rows, rows);
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ColSquareMatrixType square2 = ColSquareMatrixType::Random(cols, cols), res2 = ColSquareMatrixType::Random(cols, cols);
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RowVectorType v1 = RowVectorType::Random(rows);
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ColVectorType vc2 = ColVectorType::Random(cols), vcres(cols);
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// Prevent overflows for integer types.
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if (Eigen::NumTraits<Scalar>::IsInteger) {
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Scalar kMaxVal = Scalar(10000);
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m1.array() = m1.array() - kMaxVal * (m1.array() / kMaxVal);
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m2.array() = m2.array() - kMaxVal * (m2.array() / kMaxVal);
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v1.array() = v1.array() - kMaxVal * (v1.array() / kMaxVal);
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}
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OtherMajorMatrixType tm1 = m1;
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Scalar s1 = internal::random<Scalar>();
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Index r = internal::random<Index>(0, rows - 1), c = internal::random<Index>(0, cols - 1),
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c2 = internal::random<Index>(0, cols - 1);
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// begin testing Product.h: only associativity for now
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// (we use Transpose.h but this doesn't count as a test for it)
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{
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// Increase tolerance, since coefficients here can get relatively large.
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RealScalar tol = RealScalar(2) * get_test_precision(m1);
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VERIFY(verifyIsApprox((m1 * m1.transpose()) * m2, m1 * (m1.transpose() * m2), tol));
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}
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m3 = m1;
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m3 *= m1.transpose() * m2;
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VERIFY_IS_APPROX(m3, m1 * (m1.transpose() * m2));
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VERIFY_IS_APPROX(m3, m1 * (m1.transpose() * m2));
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// continue testing Product.h: distributivity
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VERIFY_IS_APPROX(square * (m1 + m2), square * m1 + square * m2);
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VERIFY_IS_APPROX(square * (m1 - m2), square * m1 - square * m2);
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// continue testing Product.h: compatibility with ScalarMultiple.h
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VERIFY_IS_APPROX(s1 * (square * m1), (s1 * square) * m1);
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VERIFY_IS_APPROX(s1 * (square * m1), square * (m1 * s1));
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// test Product.h together with Identity.h
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VERIFY_IS_APPROX(v1, identity * v1);
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VERIFY_IS_APPROX(v1.transpose(), v1.transpose() * identity);
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// again, test operator() to check const-qualification
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VERIFY_IS_APPROX(MatrixType::Identity(rows, cols)(r, c), static_cast<Scalar>(r == c));
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if (rows != cols) {
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check_mismatched_product(m3, m1);
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}
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// test the previous tests were not screwed up because operator* returns 0
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// (we use the more accurate default epsilon)
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if (!NumTraits<Scalar>::IsInteger && (std::min)(rows, cols) > 1) {
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VERIFY(areNotApprox(m1.transpose() * m2, m2.transpose() * m1, not_approx_epsilon));
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}
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// test optimized operator+= path
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res = square;
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res.noalias() += m1 * m2.transpose();
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VERIFY_IS_APPROX(res, square + m1 * m2.transpose());
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if (!NumTraits<Scalar>::IsInteger && (std::min)(rows, cols) > 1) {
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VERIFY(areNotApprox(res, square + m2 * m1.transpose(), not_approx_epsilon));
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}
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vcres = vc2;
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vcres.noalias() += m1.transpose() * v1;
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VERIFY_IS_APPROX(vcres, vc2 + m1.transpose() * v1);
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// test optimized operator-= path
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res = square;
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res.noalias() -= m1 * m2.transpose();
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VERIFY_IS_APPROX(res, square - (m1 * m2.transpose()));
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if (!NumTraits<Scalar>::IsInteger && (std::min)(rows, cols) > 1) {
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VERIFY(areNotApprox(res, square - m2 * m1.transpose(), not_approx_epsilon));
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}
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vcres = vc2;
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vcres.noalias() -= m1.transpose() * v1;
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VERIFY_IS_APPROX(vcres, vc2 - m1.transpose() * v1);
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// test scaled products
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res = square;
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res.noalias() = s1 * m1 * m2.transpose();
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VERIFY_IS_APPROX(res, ((s1 * m1).eval() * m2.transpose()));
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res = square;
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res.noalias() += s1 * m1 * m2.transpose();
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VERIFY_IS_APPROX(res, square + ((s1 * m1).eval() * m2.transpose()));
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res = square;
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res.noalias() -= s1 * m1 * m2.transpose();
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VERIFY_IS_APPROX(res, square - ((s1 * m1).eval() * m2.transpose()));
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// test d ?= a+b*c rules
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res.noalias() = square + m1 * m2.transpose();
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VERIFY_IS_APPROX(res, square + m1 * m2.transpose());
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res.noalias() += square + m1 * m2.transpose();
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VERIFY_IS_APPROX(res, Scalar(2) * (square + m1 * m2.transpose()));
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res.noalias() -= square + m1 * m2.transpose();
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VERIFY_IS_APPROX(res, square + m1 * m2.transpose());
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// test d ?= a-b*c rules
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res.noalias() = square - m1 * m2.transpose();
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VERIFY_IS_APPROX(res, square - m1 * m2.transpose());
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res.noalias() += square - m1 * m2.transpose();
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VERIFY_IS_APPROX(res, Scalar(2) * (square - m1 * m2.transpose()));
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res.noalias() -= square - m1 * m2.transpose();
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VERIFY_IS_APPROX(res, square - m1 * m2.transpose());
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tm1 = m1;
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VERIFY_IS_APPROX(tm1.transpose() * v1, m1.transpose() * v1);
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VERIFY_IS_APPROX(v1.transpose() * tm1, v1.transpose() * m1);
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// test submatrix and matrix/vector product
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for (int i = 0; i < rows; ++i) res.row(i) = m1.row(i) * m2.transpose();
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VERIFY_IS_APPROX(res, m1 * m2.transpose());
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// the other way round:
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for (int i = 0; i < rows; ++i) res.col(i) = m1 * m2.transpose().col(i);
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VERIFY_IS_APPROX(res, m1 * m2.transpose());
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res2 = square2;
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res2.noalias() += m1.transpose() * m2;
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VERIFY_IS_APPROX(res2, square2 + m1.transpose() * m2);
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if (!NumTraits<Scalar>::IsInteger && (std::min)(rows, cols) > 1) {
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VERIFY(areNotApprox(res2, square2 + m2.transpose() * m1, not_approx_epsilon));
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}
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res.col(r).noalias() = square.adjoint() * square.col(r);
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VERIFY_IS_APPROX(res.col(r), (square.adjoint() * square.col(r)).eval());
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res.col(r).noalias() = square * square.col(r);
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VERIFY_IS_APPROX(res.col(r), (square * square.col(r)).eval());
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// vector at runtime (see bug 1166)
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{
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RowSquareMatrixType ref(square);
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ColSquareMatrixType ref2(square2);
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ref = res = square;
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VERIFY_IS_APPROX(res.block(0, 0, 1, rows).noalias() = m1.col(0).transpose() * square.transpose(),
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(ref.row(0) = m1.col(0).transpose() * square.transpose()));
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VERIFY_IS_APPROX(res.block(0, 0, 1, rows).noalias() = m1.block(0, 0, rows, 1).transpose() * square.transpose(),
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(ref.row(0) = m1.col(0).transpose() * square.transpose()));
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VERIFY_IS_APPROX(res.block(0, 0, 1, rows).noalias() = m1.col(0).transpose() * square,
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(ref.row(0) = m1.col(0).transpose() * square));
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VERIFY_IS_APPROX(res.block(0, 0, 1, rows).noalias() = m1.block(0, 0, rows, 1).transpose() * square,
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(ref.row(0) = m1.col(0).transpose() * square));
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ref2 = res2 = square2;
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VERIFY_IS_APPROX(res2.block(0, 0, 1, cols).noalias() = m1.row(0) * square2.transpose(),
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(ref2.row(0) = m1.row(0) * square2.transpose()));
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VERIFY_IS_APPROX(res2.block(0, 0, 1, cols).noalias() = m1.block(0, 0, 1, cols) * square2.transpose(),
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(ref2.row(0) = m1.row(0) * square2.transpose()));
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VERIFY_IS_APPROX(res2.block(0, 0, 1, cols).noalias() = m1.row(0) * square2, (ref2.row(0) = m1.row(0) * square2));
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VERIFY_IS_APPROX(res2.block(0, 0, 1, cols).noalias() = m1.block(0, 0, 1, cols) * square2,
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(ref2.row(0) = m1.row(0) * square2));
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}
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// vector.block() (see bug 1283)
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{
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RowVectorType w1(rows);
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VERIFY_IS_APPROX(square * v1.block(0, 0, rows, 1), square * v1);
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VERIFY_IS_APPROX(w1.noalias() = square * v1.block(0, 0, rows, 1), square * v1);
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VERIFY_IS_APPROX(w1.block(0, 0, rows, 1).noalias() = square * v1.block(0, 0, rows, 1), square * v1);
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Matrix<Scalar, 1, MatrixType::ColsAtCompileTime> w2(cols);
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VERIFY_IS_APPROX(vc2.block(0, 0, cols, 1).transpose() * square2, vc2.transpose() * square2);
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VERIFY_IS_APPROX(w2.noalias() = vc2.block(0, 0, cols, 1).transpose() * square2, vc2.transpose() * square2);
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VERIFY_IS_APPROX(w2.block(0, 0, 1, cols).noalias() = vc2.block(0, 0, cols, 1).transpose() * square2,
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vc2.transpose() * square2);
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vc2 = square2.block(0, 0, 1, cols).transpose();
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VERIFY_IS_APPROX(square2.block(0, 0, 1, cols) * square2, vc2.transpose() * square2);
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VERIFY_IS_APPROX(w2.noalias() = square2.block(0, 0, 1, cols) * square2, vc2.transpose() * square2);
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VERIFY_IS_APPROX(w2.block(0, 0, 1, cols).noalias() = square2.block(0, 0, 1, cols) * square2,
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vc2.transpose() * square2);
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vc2 = square2.block(0, 0, cols, 1);
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VERIFY_IS_APPROX(square2.block(0, 0, cols, 1).transpose() * square2, vc2.transpose() * square2);
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VERIFY_IS_APPROX(w2.noalias() = square2.block(0, 0, cols, 1).transpose() * square2, vc2.transpose() * square2);
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VERIFY_IS_APPROX(w2.block(0, 0, 1, cols).noalias() = square2.block(0, 0, cols, 1).transpose() * square2,
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vc2.transpose() * square2);
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}
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// inner product
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{
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Scalar x = square2.row(c) * square2.col(c2);
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VERIFY_IS_APPROX(x, square2.row(c).transpose().cwiseProduct(square2.col(c2)).sum());
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}
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// outer product
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{
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VERIFY_IS_APPROX(m1.col(c) * m1.row(r), m1.block(0, c, rows, 1) * m1.block(r, 0, 1, cols));
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VERIFY_IS_APPROX(m1.row(r).transpose() * m1.col(c).transpose(),
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m1.block(r, 0, 1, cols).transpose() * m1.block(0, c, rows, 1).transpose());
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VERIFY_IS_APPROX(m1.block(0, c, rows, 1) * m1.row(r), m1.block(0, c, rows, 1) * m1.block(r, 0, 1, cols));
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VERIFY_IS_APPROX(m1.col(c) * m1.block(r, 0, 1, cols), m1.block(0, c, rows, 1) * m1.block(r, 0, 1, cols));
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VERIFY_IS_APPROX(m1.leftCols(1) * m1.row(r), m1.block(0, 0, rows, 1) * m1.block(r, 0, 1, cols));
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VERIFY_IS_APPROX(m1.col(c) * m1.topRows(1), m1.block(0, c, rows, 1) * m1.block(0, 0, 1, cols));
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}
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// Aliasing
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{
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ColVectorType x(cols);
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x.setRandom();
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ColVectorType z(x);
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ColVectorType y(cols);
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y.setZero();
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ColSquareMatrixType A(cols, cols);
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A.setRandom();
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// CwiseBinaryOp
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VERIFY_IS_APPROX(x = y + A * x, A * z);
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x = z;
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VERIFY_IS_APPROX(x = y - A * x, A * (-z));
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x = z;
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// CwiseUnaryOp
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VERIFY_IS_APPROX(x = Scalar(1.) * (A * x), A * z);
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}
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// regression for blas_trais
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{
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// Increase test tolerance, since coefficients can get relatively large.
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RealScalar tol = RealScalar(2) * get_test_precision(square);
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VERIFY(
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verifyIsApprox(square * (square * square).transpose(), square * square.transpose() * square.transpose(), tol));
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VERIFY(verifyIsApprox(square * (-(square * square)), -square * square * square, tol));
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VERIFY(verifyIsApprox(square * (s1 * (square * square)), s1 * square * square * square, tol));
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VERIFY(
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verifyIsApprox(square * (square * square).conjugate(), square * square.conjugate() * square.conjugate(), tol));
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}
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// destination with a non-default inner-stride
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// see bug 1741
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if (!MatrixType::IsRowMajor) {
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typedef Matrix<Scalar, Dynamic, Dynamic> MatrixX;
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MatrixX buffer(2 * rows, 2 * rows);
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Map<RowSquareMatrixType, 0, Stride<Dynamic, 2> > map1(buffer.data(), rows, rows, Stride<Dynamic, 2>(2 * rows, 2));
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buffer.setZero();
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VERIFY_IS_APPROX(map1 = m1 * m2.transpose(), (m1 * m2.transpose()).eval());
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buffer.setZero();
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VERIFY_IS_APPROX(map1.noalias() = m1 * m2.transpose(), (m1 * m2.transpose()).eval());
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buffer.setZero();
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VERIFY_IS_APPROX(map1.noalias() += m1 * m2.transpose(), (m1 * m2.transpose()).eval());
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}
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}
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