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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// 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/Array>
#include <Eigen/QR>
template<typename Derived1, typename Derived2>
bool areNotApprox(const MatrixBase<Derived1>& m1, const MatrixBase<Derived2>& m2, typename Derived1::RealScalar epsilon = precision<typename Derived1::RealScalar>())
{
return !((m1-m2).cwise().abs2().maxCoeff() < epsilon * epsilon
* std::max(m1.cwise().abs2().maxCoeff(), m2.cwise().abs2().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 typename NumTraits<Scalar>::FloatingPoint FloatingPoint;
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::Options^RowMajor> OtherMajorMatrixType;
int rows = m.rows();
int 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 = ei_random<Scalar>();
int r = ei_random<int>(0, rows-1),
c = ei_random<int>(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.lazy() * (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));
// again, test operator() to check const-qualification
s1 += (square.lazy() * m1)(r,c);
// 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>::HasFloatingPoint && std::min(rows,cols)>1)
{
VERIFY(areNotApprox(m1.transpose()*m2,m2.transpose()*m1));
}
// test optimized operator+= path
res = square;
res += (m1 * m2.transpose()).lazy();
VERIFY_IS_APPROX(res, square + m1 * m2.transpose());
if (NumTraits<Scalar>::HasFloatingPoint && std::min(rows,cols)>1)
{
VERIFY(areNotApprox(res,square + m2 * m1.transpose()));
}
vcres = vc2;
vcres += (m1.transpose() * v1).lazy();
VERIFY_IS_APPROX(vcres, vc2 + m1.transpose() * v1);
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 += (m1.transpose() * m2).lazy();
VERIFY_IS_APPROX(res2, square2 + m1.transpose() * m2);
if (NumTraits<Scalar>::HasFloatingPoint && std::min(rows,cols)>1)
{
VERIFY(areNotApprox(res2,square2 + m2.transpose() * m1));
}
}
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