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huangweifeng
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third_party/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::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());
// test negative strides
{
Map<MatrixType, Unaligned, Stride<Dynamic, Dynamic> > map1(&m1(rows - 1, cols - 1), rows, cols,
Stride<Dynamic, Dynamic>(-m1.outerStride(), -1));
Map<MatrixType, Unaligned, Stride<Dynamic, Dynamic> > map2(&m2(rows - 1, cols - 1), rows, cols,
Stride<Dynamic, Dynamic>(-m2.outerStride(), -1));
Map<RowVectorType, Unaligned, InnerStride<-1> > mapv1(&v1(v1.size() - 1), v1.size(), InnerStride<-1>(-1));
Map<ColVectorType, Unaligned, InnerStride<-1> > mapvc2(&vc2(vc2.size() - 1), vc2.size(), InnerStride<-1>(-1));
VERIFY_IS_APPROX(MatrixType(map1), m1.reverse());
VERIFY_IS_APPROX(MatrixType(map2), m2.reverse());
VERIFY_IS_APPROX(m3.noalias() = MatrixType(map1) * MatrixType(map2).adjoint(),
m1.reverse() * m2.reverse().adjoint());
VERIFY_IS_APPROX(m3.noalias() = map1 * map2.adjoint(), m1.reverse() * m2.reverse().adjoint());
VERIFY_IS_APPROX(map1 * vc2, m1.reverse() * vc2);
VERIFY_IS_APPROX(m1 * mapvc2, m1 * mapvc2);
VERIFY_IS_APPROX(map1.adjoint() * v1.transpose(), m1.adjoint().reverse() * v1.transpose());
VERIFY_IS_APPROX(m1.adjoint() * mapv1.transpose(), m1.adjoint() * v1.reverse().transpose());
}
// regression test
MatrixType tmp = m1 * m1.adjoint() * s1;
VERIFY_IS_APPROX(tmp, m1 * m1.adjoint() * s1);
// regression test for bug 1343, assignment to arrays
Array<Scalar, Dynamic, 1> a1 = m1 * vc2;
VERIFY_IS_APPROX(a1.matrix(), m1 * vc2);
Array<Scalar, Dynamic, 1> a2 = s1 * (m1 * vc2);
VERIFY_IS_APPROX(a2.matrix(), s1 * m1 * vc2);
Array<Scalar, 1, Dynamic> a3 = v1 * m1;
VERIFY_IS_APPROX(a3.matrix(), v1 * m1);
Array<Scalar, Dynamic, Dynamic> a4 = m1 * m2.adjoint();
VERIFY_IS_APPROX(a4.matrix(), m1 * m2.adjoint());
}
// 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);
}
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>());
}