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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// 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"
#include <Eigen/QR>
template<typename Derived1, typename Derived2>bool areNotApprox(const MatrixBase<Derived1>& m1, const MatrixBase<Derived2>& m2, typename Derived1::RealScalar epsilon = NumTraits<typename Derived1::RealScalar>::dummy_precision()){ return !((m1-m2).cwiseAbs2().maxCoeff() < epsilon * epsilon * (std::max)(m1.cwiseAbs2().maxCoeff(), m2.cwiseAbs2().maxCoeff()));}
template<typename MatrixType> void product(const MatrixType& m){ /* this test covers the following files:
Identity.h Product.h */ typedef typename MatrixType::Scalar Scalar; typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> RowVectorType; typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> ColVectorType; typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> RowSquareMatrixType; typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> ColSquareMatrixType; typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime, MatrixType::Flags&RowMajorBit?ColMajor:RowMajor> OtherMajorMatrixType;
Index rows = m.rows(); Index cols = m.cols();
// this test relies a lot on Random.h, and there's not much more that we can do
// to test it, hence I consider that we will have tested Random.h
MatrixType m1 = MatrixType::Random(rows, cols), m2 = MatrixType::Random(rows, cols), m3(rows, cols); RowSquareMatrixType identity = RowSquareMatrixType::Identity(rows, rows), square = RowSquareMatrixType::Random(rows, rows), res = RowSquareMatrixType::Random(rows, rows); ColSquareMatrixType square2 = ColSquareMatrixType::Random(cols, cols), res2 = ColSquareMatrixType::Random(cols, cols); RowVectorType v1 = RowVectorType::Random(rows); ColVectorType vc2 = ColVectorType::Random(cols), vcres(cols); OtherMajorMatrixType tm1 = m1;
Scalar s1 = internal::random<Scalar>();
Index r = internal::random<Index>(0, rows-1), c = internal::random<Index>(0, cols-1), c2 = internal::random<Index>(0, cols-1);
// begin testing Product.h: only associativity for now
// (we use Transpose.h but this doesn't count as a test for it)
VERIFY_IS_APPROX((m1*m1.transpose())*m2, m1*(m1.transpose()*m2)); m3 = m1; m3 *= m1.transpose() * m2; VERIFY_IS_APPROX(m3, m1 * (m1.transpose()*m2)); VERIFY_IS_APPROX(m3, m1 * (m1.transpose()*m2));
// continue testing Product.h: distributivity
VERIFY_IS_APPROX(square*(m1 + m2), square*m1+square*m2); VERIFY_IS_APPROX(square*(m1 - m2), square*m1-square*m2);
// continue testing Product.h: compatibility with ScalarMultiple.h
VERIFY_IS_APPROX(s1*(square*m1), (s1*square)*m1); VERIFY_IS_APPROX(s1*(square*m1), square*(m1*s1));
// test Product.h together with Identity.h
VERIFY_IS_APPROX(v1, identity*v1); VERIFY_IS_APPROX(v1.transpose(), v1.transpose() * identity); // again, test operator() to check const-qualification
VERIFY_IS_APPROX(MatrixType::Identity(rows, cols)(r,c), static_cast<Scalar>(r==c));
if (rows!=cols) VERIFY_RAISES_ASSERT(m3 = m1*m1);
// test the previous tests were not screwed up because operator* returns 0
// (we use the more accurate default epsilon)
if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1) { VERIFY(areNotApprox(m1.transpose()*m2,m2.transpose()*m1)); }
// test optimized operator+= path
res = square; res.noalias() += m1 * m2.transpose(); VERIFY_IS_APPROX(res, square + m1 * m2.transpose()); if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1) { VERIFY(areNotApprox(res,square + m2 * m1.transpose())); } vcres = vc2; vcres.noalias() += m1.transpose() * v1; VERIFY_IS_APPROX(vcres, vc2 + m1.transpose() * v1);
// test optimized operator-= path
res = square; res.noalias() -= m1 * m2.transpose(); VERIFY_IS_APPROX(res, square - (m1 * m2.transpose())); if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1) { VERIFY(areNotApprox(res,square - m2 * m1.transpose())); } vcres = vc2; vcres.noalias() -= m1.transpose() * v1; VERIFY_IS_APPROX(vcres, vc2 - m1.transpose() * v1);
// test d ?= a+b*c rules
res.noalias() = square + m1 * m2.transpose(); VERIFY_IS_APPROX(res, square + m1 * m2.transpose()); res.noalias() += square + m1 * m2.transpose(); VERIFY_IS_APPROX(res, 2*(square + m1 * m2.transpose())); res.noalias() -= square + m1 * m2.transpose(); VERIFY_IS_APPROX(res, square + m1 * m2.transpose());
tm1 = m1; VERIFY_IS_APPROX(tm1.transpose() * v1, m1.transpose() * v1); VERIFY_IS_APPROX(v1.transpose() * tm1, v1.transpose() * m1);
// test submatrix and matrix/vector product
for (int i=0; i<rows; ++i) res.row(i) = m1.row(i) * m2.transpose(); VERIFY_IS_APPROX(res, m1 * m2.transpose()); // the other way round:
for (int i=0; i<rows; ++i) res.col(i) = m1 * m2.transpose().col(i); VERIFY_IS_APPROX(res, m1 * m2.transpose());
res2 = square2; res2.noalias() += m1.transpose() * m2; VERIFY_IS_APPROX(res2, square2 + m1.transpose() * m2); if (!NumTraits<Scalar>::IsInteger && (std::min)(rows,cols)>1) { VERIFY(areNotApprox(res2,square2 + m2.transpose() * m1)); }
VERIFY_IS_APPROX(res.col(r).noalias() = square.adjoint() * square.col(r), (square.adjoint() * square.col(r)).eval()); VERIFY_IS_APPROX(res.col(r).noalias() = square * square.col(r), (square * square.col(r)).eval());
// inner product
Scalar x = square2.row(c) * square2.col(c2); VERIFY_IS_APPROX(x, square2.row(c).transpose().cwiseProduct(square2.col(c2)).sum()); // outer product
VERIFY_IS_APPROX(m1.col(c) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols)); VERIFY_IS_APPROX(m1.row(r).transpose() * m1.col(c).transpose(), m1.block(r,0,1,cols).transpose() * m1.block(0,c,rows,1).transpose()); VERIFY_IS_APPROX(m1.block(0,c,rows,1) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols)); VERIFY_IS_APPROX(m1.col(c) * m1.block(r,0,1,cols), m1.block(0,c,rows,1) * m1.block(r,0,1,cols)); VERIFY_IS_APPROX(m1.leftCols(1) * m1.row(r), m1.block(0,0,rows,1) * m1.block(r,0,1,cols)); 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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