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eigen/test/product.h

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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 LhsType, typename RhsType>
typename internal::enable_if<RhsType::SizeAtCompileTime==Dynamic,void>::type
check_mismatched_product(LhsType& lhs, const RhsType& rhs) {
VERIFY_RAISES_ASSERT(lhs = rhs*rhs);
}
template <typename LhsType, typename RhsType>
typename internal::enable_if<RhsType::SizeAtCompileTime!=Dynamic,void>::type
check_mismatched_product(LhsType& /*unused*/, const RhsType& /*unused*/) {
}
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) {
check_mismatched_product(m3, 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 scaled products
res = square;
res.noalias() = s1 * m1 * m2.transpose();
VERIFY_IS_APPROX(res, ((s1*m1).eval() * m2.transpose()));
res = square;
res.noalias() += s1 * m1 * m2.transpose();
VERIFY_IS_APPROX(res, square + ((s1*m1).eval() * m2.transpose()));
res = square;
res.noalias() -= s1 * m1 * m2.transpose();
VERIFY_IS_APPROX(res, square - ((s1*m1).eval() * m2.transpose()));
// 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());
// 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());
// vector at runtime (see bug 1166)
{
RowSquareMatrixType ref(square);
ColSquareMatrixType ref2(square2);
ref = res = square;
VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.col(0).transpose() * square.transpose(), (ref.row(0) = m1.col(0).transpose() * square.transpose()));
VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.block(0,0,rows,1).transpose() * square.transpose(), (ref.row(0) = m1.col(0).transpose() * square.transpose()));
VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.col(0).transpose() * square, (ref.row(0) = m1.col(0).transpose() * square));
VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.block(0,0,rows,1).transpose() * square, (ref.row(0) = m1.col(0).transpose() * square));
ref2 = res2 = square2;
VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.row(0) * square2.transpose(), (ref2.row(0) = m1.row(0) * square2.transpose()));
VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.block(0,0,1,cols) * square2.transpose(), (ref2.row(0) = m1.row(0) * square2.transpose()));
VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.row(0) * square2, (ref2.row(0) = m1.row(0) * square2));
VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.block(0,0,1,cols) * square2, (ref2.row(0) = m1.row(0) * square2));
}
// vector.block() (see bug 1283)
{
RowVectorType w1(rows);
VERIFY_IS_APPROX(square * v1.block(0,0,rows,1), square * v1);
VERIFY_IS_APPROX(w1.noalias() = square * v1.block(0,0,rows,1), square * v1);
VERIFY_IS_APPROX(w1.block(0,0,rows,1).noalias() = square * v1.block(0,0,rows,1), square * v1);
Matrix<Scalar,1,MatrixType::ColsAtCompileTime> w2(cols);
VERIFY_IS_APPROX(vc2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);
VERIFY_IS_APPROX(w2.noalias() = vc2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);
VERIFY_IS_APPROX(w2.block(0,0,1,cols).noalias() = vc2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);
vc2 = square2.block(0,0,1,cols).transpose();
VERIFY_IS_APPROX(square2.block(0,0,1,cols) * square2, vc2.transpose() * square2);
VERIFY_IS_APPROX(w2.noalias() = square2.block(0,0,1,cols) * square2, vc2.transpose() * square2);
VERIFY_IS_APPROX(w2.block(0,0,1,cols).noalias() = square2.block(0,0,1,cols) * square2, vc2.transpose() * square2);
vc2 = square2.block(0,0,cols,1);
VERIFY_IS_APPROX(square2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);
VERIFY_IS_APPROX(w2.noalias() = square2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);
VERIFY_IS_APPROX(w2.block(0,0,1,cols).noalias() = square2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2);
}
// 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));
}
// Aliasing
{
ColVectorType x(cols); x.setRandom();
ColVectorType z(x);
ColVectorType y(cols); y.setZero();
ColSquareMatrixType A(cols,cols); A.setRandom();
// CwiseBinaryOp
VERIFY_IS_APPROX(x = y + A*x, A*z);
x = z;
VERIFY_IS_APPROX(x = y - A*x, A*(-z));
x = z;
// CwiseUnaryOp
VERIFY_IS_APPROX(x = Scalar(1.)*(A*x), A*z);
}
// regression for blas_trais
{
VERIFY_IS_APPROX(square * (square*square).transpose(), square * square.transpose() * square.transpose());
VERIFY_IS_APPROX(square * (-(square*square)), -square * square * square);
VERIFY_IS_APPROX(square * (s1*(square*square)), s1 * square * square * square);
VERIFY_IS_APPROX(square * (square*square).conjugate(), square * square.conjugate() * square.conjugate());
}
// destination with a non-default inner-stride
// see bug 1741
if(!MatrixType::IsRowMajor)
{
typedef Matrix<Scalar,Dynamic,Dynamic> MatrixX;
MatrixX buffer(2*rows,2*rows);
Map<RowSquareMatrixType,0,Stride<Dynamic,2> > map1(buffer.data(),rows,rows,Stride<Dynamic,2>(2*rows,2));
buffer.setZero();
VERIFY_IS_APPROX(map1 = m1 * m2.transpose(), (m1 * m2.transpose()).eval());
buffer.setZero();
VERIFY_IS_APPROX(map1.noalias() = m1 * m2.transpose(), (m1 * m2.transpose()).eval());
buffer.setZero();
VERIFY_IS_APPROX(map1.noalias() += m1 * m2.transpose(), (m1 * m2.transpose()).eval());
}
}
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