mirror of
https://gitlab.com/libeigen/eigen.git
synced 2024-12-15 07:10:37 +08:00
245 lines
11 KiB
C++
245 lines
11 KiB
C++
// 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 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());
|
|
}
|
|
|
|
}
|