391 lines
15 KiB
C++
391 lines
15 KiB
C++
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// 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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template<typename MatrixType> void product_extra(const MatrixType& m)
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{
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typedef typename MatrixType::Scalar Scalar;
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typedef Matrix<Scalar, 1, Dynamic> RowVectorType;
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typedef Matrix<Scalar, Dynamic, 1> ColVectorType;
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typedef Matrix<Scalar, Dynamic, Dynamic,
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MatrixType::Flags&RowMajorBit> OtherMajorMatrixType;
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Index rows = m.rows();
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Index cols = m.cols();
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MatrixType m1 = MatrixType::Random(rows, cols),
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m2 = MatrixType::Random(rows, cols),
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m3(rows, cols),
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mzero = MatrixType::Zero(rows, cols),
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identity = MatrixType::Identity(rows, rows),
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square = MatrixType::Random(rows, rows),
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res = MatrixType::Random(rows, rows),
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square2 = MatrixType::Random(cols, cols),
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res2 = MatrixType::Random(cols, cols);
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RowVectorType v1 = RowVectorType::Random(rows), vrres(rows);
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ColVectorType vc2 = ColVectorType::Random(cols), vcres(cols);
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OtherMajorMatrixType tm1 = m1;
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Scalar s1 = internal::random<Scalar>(),
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s2 = internal::random<Scalar>(),
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s3 = internal::random<Scalar>();
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VERIFY_IS_APPROX(m3.noalias() = m1 * m2.adjoint(), m1 * m2.adjoint().eval());
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VERIFY_IS_APPROX(m3.noalias() = m1.adjoint() * square.adjoint(), m1.adjoint().eval() * square.adjoint().eval());
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VERIFY_IS_APPROX(m3.noalias() = m1.adjoint() * m2, m1.adjoint().eval() * m2);
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VERIFY_IS_APPROX(m3.noalias() = (s1 * m1.adjoint()) * m2, (s1 * m1.adjoint()).eval() * m2);
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VERIFY_IS_APPROX(m3.noalias() = ((s1 * m1).adjoint()) * m2, (numext::conj(s1) * m1.adjoint()).eval() * m2);
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VERIFY_IS_APPROX(m3.noalias() = (- m1.adjoint() * s1) * (s3 * m2), (- m1.adjoint() * s1).eval() * (s3 * m2).eval());
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VERIFY_IS_APPROX(m3.noalias() = (s2 * m1.adjoint() * s1) * m2, (s2 * m1.adjoint() * s1).eval() * m2);
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VERIFY_IS_APPROX(m3.noalias() = (-m1*s2) * s1*m2.adjoint(), (-m1*s2).eval() * (s1*m2.adjoint()).eval());
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// a very tricky case where a scale factor has to be automatically conjugated:
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VERIFY_IS_APPROX( m1.adjoint() * (s1*m2).conjugate(), (m1.adjoint()).eval() * ((s1*m2).conjugate()).eval());
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// test all possible conjugate combinations for the four matrix-vector product cases:
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VERIFY_IS_APPROX((-m1.conjugate() * s2) * (s1 * vc2),
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(-m1.conjugate()*s2).eval() * (s1 * vc2).eval());
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VERIFY_IS_APPROX((-m1 * s2) * (s1 * vc2.conjugate()),
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(-m1*s2).eval() * (s1 * vc2.conjugate()).eval());
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VERIFY_IS_APPROX((-m1.conjugate() * s2) * (s1 * vc2.conjugate()),
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(-m1.conjugate()*s2).eval() * (s1 * vc2.conjugate()).eval());
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VERIFY_IS_APPROX((s1 * vc2.transpose()) * (-m1.adjoint() * s2),
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(s1 * vc2.transpose()).eval() * (-m1.adjoint()*s2).eval());
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VERIFY_IS_APPROX((s1 * vc2.adjoint()) * (-m1.transpose() * s2),
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(s1 * vc2.adjoint()).eval() * (-m1.transpose()*s2).eval());
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VERIFY_IS_APPROX((s1 * vc2.adjoint()) * (-m1.adjoint() * s2),
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(s1 * vc2.adjoint()).eval() * (-m1.adjoint()*s2).eval());
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VERIFY_IS_APPROX((-m1.adjoint() * s2) * (s1 * v1.transpose()),
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(-m1.adjoint()*s2).eval() * (s1 * v1.transpose()).eval());
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VERIFY_IS_APPROX((-m1.transpose() * s2) * (s1 * v1.adjoint()),
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(-m1.transpose()*s2).eval() * (s1 * v1.adjoint()).eval());
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VERIFY_IS_APPROX((-m1.adjoint() * s2) * (s1 * v1.adjoint()),
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(-m1.adjoint()*s2).eval() * (s1 * v1.adjoint()).eval());
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VERIFY_IS_APPROX((s1 * v1) * (-m1.conjugate() * s2),
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(s1 * v1).eval() * (-m1.conjugate()*s2).eval());
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VERIFY_IS_APPROX((s1 * v1.conjugate()) * (-m1 * s2),
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(s1 * v1.conjugate()).eval() * (-m1*s2).eval());
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VERIFY_IS_APPROX((s1 * v1.conjugate()) * (-m1.conjugate() * s2),
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(s1 * v1.conjugate()).eval() * (-m1.conjugate()*s2).eval());
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VERIFY_IS_APPROX((-m1.adjoint() * s2) * (s1 * v1.adjoint()),
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(-m1.adjoint()*s2).eval() * (s1 * v1.adjoint()).eval());
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// test the vector-matrix product with non aligned starts
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Index i = internal::random<Index>(0,m1.rows()-2);
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Index j = internal::random<Index>(0,m1.cols()-2);
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Index r = internal::random<Index>(1,m1.rows()-i);
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Index c = internal::random<Index>(1,m1.cols()-j);
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Index i2 = internal::random<Index>(0,m1.rows()-1);
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Index j2 = internal::random<Index>(0,m1.cols()-1);
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VERIFY_IS_APPROX(m1.col(j2).adjoint() * m1.block(0,j,m1.rows(),c), m1.col(j2).adjoint().eval() * m1.block(0,j,m1.rows(),c).eval());
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VERIFY_IS_APPROX(m1.block(i,0,r,m1.cols()) * m1.row(i2).adjoint(), m1.block(i,0,r,m1.cols()).eval() * m1.row(i2).adjoint().eval());
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// test negative strides
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{
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Map<MatrixType,Unaligned,Stride<Dynamic,Dynamic> > map1(&m1(rows-1,cols-1), rows, cols, Stride<Dynamic,Dynamic>(-m1.outerStride(),-1));
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Map<MatrixType,Unaligned,Stride<Dynamic,Dynamic> > map2(&m2(rows-1,cols-1), rows, cols, Stride<Dynamic,Dynamic>(-m2.outerStride(),-1));
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Map<RowVectorType,Unaligned,InnerStride<-1> > mapv1(&v1(v1.size()-1), v1.size(), InnerStride<-1>(-1));
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Map<ColVectorType,Unaligned,InnerStride<-1> > mapvc2(&vc2(vc2.size()-1), vc2.size(), InnerStride<-1>(-1));
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VERIFY_IS_APPROX(MatrixType(map1), m1.reverse());
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VERIFY_IS_APPROX(MatrixType(map2), m2.reverse());
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VERIFY_IS_APPROX(m3.noalias() = MatrixType(map1) * MatrixType(map2).adjoint(), m1.reverse() * m2.reverse().adjoint());
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VERIFY_IS_APPROX(m3.noalias() = map1 * map2.adjoint(), m1.reverse() * m2.reverse().adjoint());
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VERIFY_IS_APPROX(map1 * vc2, m1.reverse() * vc2);
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VERIFY_IS_APPROX(m1 * mapvc2, m1 * mapvc2);
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VERIFY_IS_APPROX(map1.adjoint() * v1.transpose(), m1.adjoint().reverse() * v1.transpose());
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VERIFY_IS_APPROX(m1.adjoint() * mapv1.transpose(), m1.adjoint() * v1.reverse().transpose());
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}
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// regression test
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MatrixType tmp = m1 * m1.adjoint() * s1;
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VERIFY_IS_APPROX(tmp, m1 * m1.adjoint() * s1);
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// regression test for bug 1343, assignment to arrays
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Array<Scalar,Dynamic,1> a1 = m1 * vc2;
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VERIFY_IS_APPROX(a1.matrix(),m1*vc2);
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Array<Scalar,Dynamic,1> a2 = s1 * (m1 * vc2);
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VERIFY_IS_APPROX(a2.matrix(),s1*m1*vc2);
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Array<Scalar,1,Dynamic> a3 = v1 * m1;
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VERIFY_IS_APPROX(a3.matrix(),v1*m1);
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Array<Scalar,Dynamic,Dynamic> a4 = m1 * m2.adjoint();
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VERIFY_IS_APPROX(a4.matrix(),m1*m2.adjoint());
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}
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// Regression test for bug reported at http://forum.kde.org/viewtopic.php?f=74&t=96947
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void mat_mat_scalar_scalar_product()
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{
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Eigen::Matrix2Xd dNdxy(2, 3);
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dNdxy << -0.5, 0.5, 0,
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-0.3, 0, 0.3;
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double det = 6.0, wt = 0.5;
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VERIFY_IS_APPROX(dNdxy.transpose()*dNdxy*det*wt, det*wt*dNdxy.transpose()*dNdxy);
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}
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template <typename MatrixType>
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void zero_sized_objects(const MatrixType& m)
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{
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typedef typename MatrixType::Scalar Scalar;
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const int PacketSize = internal::packet_traits<Scalar>::size;
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const int PacketSize1 = PacketSize>1 ? PacketSize-1 : 1;
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Index rows = m.rows();
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Index cols = m.cols();
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{
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MatrixType res, a(rows,0), b(0,cols);
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VERIFY_IS_APPROX( (res=a*b), MatrixType::Zero(rows,cols) );
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VERIFY_IS_APPROX( (res=a*a.transpose()), MatrixType::Zero(rows,rows) );
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VERIFY_IS_APPROX( (res=b.transpose()*b), MatrixType::Zero(cols,cols) );
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VERIFY_IS_APPROX( (res=b.transpose()*a.transpose()), MatrixType::Zero(cols,rows) );
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}
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{
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MatrixType res, a(rows,cols), b(cols,0);
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res = a*b;
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VERIFY(res.rows()==rows && res.cols()==0);
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b.resize(0,rows);
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res = b*a;
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VERIFY(res.rows()==0 && res.cols()==cols);
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}
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{
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Matrix<Scalar,PacketSize,0> a;
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Matrix<Scalar,0,1> b;
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Matrix<Scalar,PacketSize,1> res;
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VERIFY_IS_APPROX( (res=a*b), MatrixType::Zero(PacketSize,1) );
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VERIFY_IS_APPROX( (res=a.lazyProduct(b)), MatrixType::Zero(PacketSize,1) );
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}
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{
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Matrix<Scalar,PacketSize1,0> a;
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Matrix<Scalar,0,1> b;
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Matrix<Scalar,PacketSize1,1> res;
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VERIFY_IS_APPROX( (res=a*b), MatrixType::Zero(PacketSize1,1) );
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VERIFY_IS_APPROX( (res=a.lazyProduct(b)), MatrixType::Zero(PacketSize1,1) );
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}
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{
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Matrix<Scalar,PacketSize,Dynamic> a(PacketSize,0);
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Matrix<Scalar,Dynamic,1> b(0,1);
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Matrix<Scalar,PacketSize,1> res;
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VERIFY_IS_APPROX( (res=a*b), MatrixType::Zero(PacketSize,1) );
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VERIFY_IS_APPROX( (res=a.lazyProduct(b)), MatrixType::Zero(PacketSize,1) );
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}
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{
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Matrix<Scalar,PacketSize1,Dynamic> a(PacketSize1,0);
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Matrix<Scalar,Dynamic,1> b(0,1);
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Matrix<Scalar,PacketSize1,1> res;
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VERIFY_IS_APPROX( (res=a*b), MatrixType::Zero(PacketSize1,1) );
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VERIFY_IS_APPROX( (res=a.lazyProduct(b)), MatrixType::Zero(PacketSize1,1) );
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}
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}
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template<int>
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void bug_127()
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{
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// Bug 127
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//
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// a product of the form lhs*rhs with
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//
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// lhs:
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// rows = 1, cols = 4
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// RowsAtCompileTime = 1, ColsAtCompileTime = -1
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// MaxRowsAtCompileTime = 1, MaxColsAtCompileTime = 5
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//
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// rhs:
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// rows = 4, cols = 0
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// RowsAtCompileTime = -1, ColsAtCompileTime = -1
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// MaxRowsAtCompileTime = 5, MaxColsAtCompileTime = 1
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//
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// was failing on a runtime assertion, because it had been mis-compiled as a dot product because Product.h was using the
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// max-sizes to detect size 1 indicating vectors, and that didn't account for 0-sized object with max-size 1.
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Matrix<float,1,Dynamic,RowMajor,1,5> a(1,4);
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Matrix<float,Dynamic,Dynamic,ColMajor,5,1> b(4,0);
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a*b;
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}
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template<int> void bug_817()
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{
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ArrayXXf B = ArrayXXf::Random(10,10), C;
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VectorXf x = VectorXf::Random(10);
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C = (x.transpose()*B.matrix());
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B = (x.transpose()*B.matrix());
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VERIFY_IS_APPROX(B,C);
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}
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template<int>
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void unaligned_objects()
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{
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// Regression test for the bug reported here:
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// http://forum.kde.org/viewtopic.php?f=74&t=107541
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// Recall the matrix*vector kernel avoid unaligned loads by loading two packets and then reassemble then.
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// There was a mistake in the computation of the valid range for fully unaligned objects: in some rare cases,
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// memory was read outside the allocated matrix memory. Though the values were not used, this might raise segfault.
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for(int m=450;m<460;++m)
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{
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for(int n=8;n<12;++n)
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{
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MatrixXf M(m, n);
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VectorXf v1(n), r1(500);
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RowVectorXf v2(m), r2(16);
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M.setRandom();
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v1.setRandom();
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v2.setRandom();
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for(int o=0; o<4; ++o)
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{
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r1.segment(o,m).noalias() = M * v1;
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VERIFY_IS_APPROX(r1.segment(o,m), M * MatrixXf(v1));
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r2.segment(o,n).noalias() = v2 * M;
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VERIFY_IS_APPROX(r2.segment(o,n), MatrixXf(v2) * M);
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}
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}
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}
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}
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template<typename T>
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EIGEN_DONT_INLINE
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Index test_compute_block_size(Index m, Index n, Index k)
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{
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Index mc(m), nc(n), kc(k);
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internal::computeProductBlockingSizes<T,T>(kc, mc, nc);
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return kc+mc+nc;
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}
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template<typename T>
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Index compute_block_size()
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{
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Index ret = 0;
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ret += test_compute_block_size<T>(0,1,1);
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ret += test_compute_block_size<T>(1,0,1);
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ret += test_compute_block_size<T>(1,1,0);
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ret += test_compute_block_size<T>(0,0,1);
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ret += test_compute_block_size<T>(0,1,0);
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ret += test_compute_block_size<T>(1,0,0);
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ret += test_compute_block_size<T>(0,0,0);
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return ret;
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}
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template<typename>
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void aliasing_with_resize()
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{
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Index m = internal::random<Index>(10,50);
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Index n = internal::random<Index>(10,50);
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MatrixXd A, B, C(m,n), D(m,m);
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VectorXd a, b, c(n);
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|
|
C.setRandom();
|
||
|
|
D.setRandom();
|
||
|
|
c.setRandom();
|
||
|
|
double s = internal::random<double>(1,10);
|
||
|
|
|
||
|
|
A = C;
|
||
|
|
B = A * A.transpose();
|
||
|
|
A = A * A.transpose();
|
||
|
|
VERIFY_IS_APPROX(A,B);
|
||
|
|
|
||
|
|
A = C;
|
||
|
|
B = (A * A.transpose())/s;
|
||
|
|
A = (A * A.transpose())/s;
|
||
|
|
VERIFY_IS_APPROX(A,B);
|
||
|
|
|
||
|
|
A = C;
|
||
|
|
B = (A * A.transpose()) + D;
|
||
|
|
A = (A * A.transpose()) + D;
|
||
|
|
VERIFY_IS_APPROX(A,B);
|
||
|
|
|
||
|
|
A = C;
|
||
|
|
B = D + (A * A.transpose());
|
||
|
|
A = D + (A * A.transpose());
|
||
|
|
VERIFY_IS_APPROX(A,B);
|
||
|
|
|
||
|
|
A = C;
|
||
|
|
B = s * (A * A.transpose());
|
||
|
|
A = s * (A * A.transpose());
|
||
|
|
VERIFY_IS_APPROX(A,B);
|
||
|
|
|
||
|
|
A = C;
|
||
|
|
a = c;
|
||
|
|
b = (A * a)/s;
|
||
|
|
a = (A * a)/s;
|
||
|
|
VERIFY_IS_APPROX(a,b);
|
||
|
|
}
|
||
|
|
|
||
|
|
template<int>
|
||
|
|
void bug_1308()
|
||
|
|
{
|
||
|
|
int n = 10;
|
||
|
|
MatrixXd r(n,n);
|
||
|
|
VectorXd v = VectorXd::Random(n);
|
||
|
|
r = v * RowVectorXd::Ones(n);
|
||
|
|
VERIFY_IS_APPROX(r, v.rowwise().replicate(n));
|
||
|
|
r = VectorXd::Ones(n) * v.transpose();
|
||
|
|
VERIFY_IS_APPROX(r, v.rowwise().replicate(n).transpose());
|
||
|
|
|
||
|
|
Matrix4d ones44 = Matrix4d::Ones();
|
||
|
|
Matrix4d m44 = Matrix4d::Ones() * Matrix4d::Ones();
|
||
|
|
VERIFY_IS_APPROX(m44,Matrix4d::Constant(4));
|
||
|
|
VERIFY_IS_APPROX(m44.noalias()=ones44*Matrix4d::Ones(), Matrix4d::Constant(4));
|
||
|
|
VERIFY_IS_APPROX(m44.noalias()=ones44.transpose()*Matrix4d::Ones(), Matrix4d::Constant(4));
|
||
|
|
VERIFY_IS_APPROX(m44.noalias()=Matrix4d::Ones()*ones44, Matrix4d::Constant(4));
|
||
|
|
VERIFY_IS_APPROX(m44.noalias()=Matrix4d::Ones()*ones44.transpose(), Matrix4d::Constant(4));
|
||
|
|
|
||
|
|
typedef Matrix<double,4,4,RowMajor> RMatrix4d;
|
||
|
|
RMatrix4d r44 = Matrix4d::Ones() * Matrix4d::Ones();
|
||
|
|
VERIFY_IS_APPROX(r44,Matrix4d::Constant(4));
|
||
|
|
VERIFY_IS_APPROX(r44.noalias()=ones44*Matrix4d::Ones(), Matrix4d::Constant(4));
|
||
|
|
VERIFY_IS_APPROX(r44.noalias()=ones44.transpose()*Matrix4d::Ones(), Matrix4d::Constant(4));
|
||
|
|
VERIFY_IS_APPROX(r44.noalias()=Matrix4d::Ones()*ones44, Matrix4d::Constant(4));
|
||
|
|
VERIFY_IS_APPROX(r44.noalias()=Matrix4d::Ones()*ones44.transpose(), Matrix4d::Constant(4));
|
||
|
|
VERIFY_IS_APPROX(r44.noalias()=ones44*RMatrix4d::Ones(), Matrix4d::Constant(4));
|
||
|
|
VERIFY_IS_APPROX(r44.noalias()=ones44.transpose()*RMatrix4d::Ones(), Matrix4d::Constant(4));
|
||
|
|
VERIFY_IS_APPROX(r44.noalias()=RMatrix4d::Ones()*ones44, Matrix4d::Constant(4));
|
||
|
|
VERIFY_IS_APPROX(r44.noalias()=RMatrix4d::Ones()*ones44.transpose(), Matrix4d::Constant(4));
|
||
|
|
|
||
|
|
// RowVector4d r4;
|
||
|
|
m44.setOnes();
|
||
|
|
r44.setZero();
|
||
|
|
VERIFY_IS_APPROX(r44.noalias() += m44.row(0).transpose() * RowVector4d::Ones(), ones44);
|
||
|
|
r44.setZero();
|
||
|
|
VERIFY_IS_APPROX(r44.noalias() += m44.col(0) * RowVector4d::Ones(), ones44);
|
||
|
|
r44.setZero();
|
||
|
|
VERIFY_IS_APPROX(r44.noalias() += Vector4d::Ones() * m44.row(0), ones44);
|
||
|
|
r44.setZero();
|
||
|
|
VERIFY_IS_APPROX(r44.noalias() += Vector4d::Ones() * m44.col(0).transpose(), ones44);
|
||
|
|
}
|
||
|
|
|
||
|
|
EIGEN_DECLARE_TEST(product_extra)
|
||
|
|
{
|
||
|
|
for(int i = 0; i < g_repeat; i++) {
|
||
|
|
CALL_SUBTEST_1( product_extra(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
|
||
|
|
CALL_SUBTEST_2( product_extra(MatrixXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
|
||
|
|
CALL_SUBTEST_2( mat_mat_scalar_scalar_product() );
|
||
|
|
CALL_SUBTEST_3( product_extra(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2), internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );
|
||
|
|
CALL_SUBTEST_4( product_extra(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2), internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );
|
||
|
|
CALL_SUBTEST_1( zero_sized_objects(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
|
||
|
|
}
|
||
|
|
CALL_SUBTEST_5( bug_127<0>() );
|
||
|
|
CALL_SUBTEST_5( bug_817<0>() );
|
||
|
|
CALL_SUBTEST_5( bug_1308<0>() );
|
||
|
|
CALL_SUBTEST_6( unaligned_objects<0>() );
|
||
|
|
CALL_SUBTEST_7( compute_block_size<float>() );
|
||
|
|
CALL_SUBTEST_7( compute_block_size<double>() );
|
||
|
|
CALL_SUBTEST_7( compute_block_size<std::complex<double> >() );
|
||
|
|
CALL_SUBTEST_8( aliasing_with_resize<void>() );
|
||
|
|
|
||
|
|
}
|