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eigen/test/product_extra.cpp

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