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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()));
}
// Allow specifying tolerance for verifying error.
template <typename Type1, typename Type2, typename Tol>
inline bool verifyIsApprox(const Type1& a, const Type2& b, Tol tol) {
bool ret = a.isApprox(b, tol);
if (!ret) {
std::cerr << "Difference too large wrt tolerance " << tol << ", relative error is: " << test_relative_error(a, b)
<< std::endl;
}
return ret;
}
template <typename LhsType, typename RhsType>
std::enable_if_t<RhsType::SizeAtCompileTime == Dynamic, void> check_mismatched_product(LhsType& lhs,
const RhsType& rhs) {
VERIFY_RAISES_ASSERT(lhs = rhs * rhs);
}
template <typename LhsType, typename RhsType>
std::enable_if_t<RhsType::SizeAtCompileTime != Dynamic, void> 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 typename MatrixType::RealScalar RealScalar;
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;
// Wwe want a tighter epsilon for not-approx tests. Otherwise, for certain
// low-precision types (e.g. bfloat16), the bound ends up being relatively large
// (e.g. 0.12), causing flaky tests.
RealScalar not_approx_epsilon = RealScalar(0.1) * NumTraits<RealScalar>::dummy_precision();
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)
{
// Increase tolerance, since coefficients here can get relatively large.
RealScalar tol = RealScalar(2) * get_test_precision(m1);
VERIFY(verifyIsApprox((m1 * m1.transpose()) * m2, m1 * (m1.transpose() * m2), tol));
}
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, not_approx_epsilon));
}
// 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(), not_approx_epsilon));
}
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(), not_approx_epsilon));
}
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, Scalar(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, Scalar(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, not_approx_epsilon));
}
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
{
// Increase test tolerance, since coefficients can get relatively large.
RealScalar tol = RealScalar(2) * get_test_precision(square);
VERIFY(
verifyIsApprox(square * (square * square).transpose(), square * square.transpose() * square.transpose(), tol));
VERIFY(verifyIsApprox(square * (-(square * square)), -square * square * square, tol));
VERIFY(verifyIsApprox(square * (s1 * (square * square)), s1 * square * square * square, tol));
VERIFY(
verifyIsApprox(square * (square * square).conjugate(), square * square.conjugate() * square.conjugate(), tol));
}
// 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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