// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// 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/.
// this hack is needed to make this file compiles with -pedantic (gcc)
#ifdef __GNUC__
#define throw(X)
#endif
#ifdef __INTEL_COMPILER
// disable "warning #76: argument to macro is empty" produced by the above hack
#pragma warning disable 76
#endif
// discard stack allocation as that too bypasses malloc
#define EIGEN_STACK_ALLOCATION_LIMIT 0
// any heap allocation will raise an assert
#define EIGEN_NO_MALLOC
#include "main.h"
#include <Eigen/Cholesky>
#include <Eigen/Eigenvalues>
#include <Eigen/LU>
#include <Eigen/QR>
#include <Eigen/SVD>
template<typename MatrixType> void nomalloc(const MatrixType& m)
{
/* this test check no dynamic memory allocation are issued with fixed-size matrices
*/
typedef typename MatrixType::Index Index;
typedef typename MatrixType::Scalar Scalar;
Index rows = m.rows();
Index cols = m.cols();
MatrixType m1 = MatrixType::Random(rows, cols),
m2 = MatrixType::Random(rows, cols),
m3(rows, cols);
Scalar s1 = internal::random<Scalar>();
Index r = internal::random<Index>(0, rows-1),
c = internal::random<Index>(0, cols-1);
VERIFY_IS_APPROX((m1+m2)*s1, s1*m1+s1*m2);
VERIFY_IS_APPROX((m1+m2)(r,c), (m1(r,c))+(m2(r,c)));
VERIFY_IS_APPROX(m1.cwiseProduct(m1.block(0,0,rows,cols)), (m1.array()*m1.array()).matrix());
VERIFY_IS_APPROX((m1*m1.transpose())*m2, m1*(m1.transpose()*m2));
m2.col(0).noalias() = m1 * m1.col(0);
m2.col(0).noalias() -= m1.adjoint() * m1.col(0);
m2.col(0).noalias() -= m1 * m1.row(0).adjoint();
m2.col(0).noalias() -= m1.adjoint() * m1.row(0).adjoint();
m2.row(0).noalias() = m1.row(0) * m1;
m2.row(0).noalias() -= m1.row(0) * m1.adjoint();
m2.row(0).noalias() -= m1.col(0).adjoint() * m1;
m2.row(0).noalias() -= m1.col(0).adjoint() * m1.adjoint();
VERIFY_IS_APPROX(m2,m2);
m2.col(0).noalias() = m1.template triangularView<Upper>() * m1.col(0);
m2.col(0).noalias() -= m1.adjoint().template triangularView<Upper>() * m1.col(0);
m2.col(0).noalias() -= m1.template triangularView<Upper>() * m1.row(0).adjoint();
m2.col(0).noalias() -= m1.adjoint().template triangularView<Upper>() * m1.row(0).adjoint();
m2.row(0).noalias() = m1.row(0) * m1.template triangularView<Upper>();
m2.row(0).noalias() -= m1.row(0) * m1.adjoint().template triangularView<Upper>();
m2.row(0).noalias() -= m1.col(0).adjoint() * m1.template triangularView<Upper>();
m2.row(0).noalias() -= m1.col(0).adjoint() * m1.adjoint().template triangularView<Upper>();
VERIFY_IS_APPROX(m2,m2);
m2.col(0).noalias() = m1.template selfadjointView<Upper>() * m1.col(0);
m2.col(0).noalias() -= m1.adjoint().template selfadjointView<Upper>() * m1.col(0);
m2.col(0).noalias() -= m1.template selfadjointView<Upper>() * m1.row(0).adjoint();
m2.col(0).noalias() -= m1.adjoint().template selfadjointView<Upper>() * m1.row(0).adjoint();
m2.row(0).noalias() = m1.row(0) * m1.template selfadjointView<Upper>();
m2.row(0).noalias() -= m1.row(0) * m1.adjoint().template selfadjointView<Upper>();
m2.row(0).noalias() -= m1.col(0).adjoint() * m1.template selfadjointView<Upper>();
m2.row(0).noalias() -= m1.col(0).adjoint() * m1.adjoint().template selfadjointView<Upper>();
VERIFY_IS_APPROX(m2,m2);
m2.template selfadjointView<Lower>().rankUpdate(m1.col(0),-1);
m2.template selfadjointView<Lower>().rankUpdate(m1.row(0),-1);
// The following fancy matrix-matrix products are not safe yet regarding static allocation
// m1 += m1.template triangularView<Upper>() * m2.col(;
// m1.template selfadjointView<Lower>().rankUpdate(m2);
// m1 += m1.template triangularView<Upper>() * m2;
// m1 += m1.template selfadjointView<Lower>() * m2;
// VERIFY_IS_APPROX(m1,m1);
}
template<typename Scalar>
void ctms_decompositions()
{
const int maxSize = 16;
const int size = 12;
typedef Eigen::Matrix<Scalar,
Eigen::Dynamic, Eigen::Dynamic,
0,
maxSize, maxSize> Matrix;
typedef Eigen::Matrix<Scalar,
Eigen::Dynamic, 1,
0,
maxSize, 1> Vector;
typedef Eigen::Matrix<std::complex<Scalar>,
Eigen::Dynamic, Eigen::Dynamic,
0,
maxSize, maxSize> ComplexMatrix;
const Matrix A(Matrix::Random(size, size)), B(Matrix::Random(size, size));
Matrix X(size,size);
const ComplexMatrix complexA(ComplexMatrix::Random(size, size));
const Matrix saA = A.adjoint() * A;
const Vector b(Vector::Random(size));
Vector x(size);
// Cholesky module
Eigen::LLT<Matrix> LLT; LLT.compute(A);
X = LLT.solve(B);
x = LLT.solve(b);
Eigen::LDLT<Matrix> LDLT; LDLT.compute(A);
X = LDLT.solve(B);
x = LDLT.solve(b);
// Eigenvalues module
Eigen::HessenbergDecomposition<ComplexMatrix> hessDecomp; hessDecomp.compute(complexA);
Eigen::ComplexSchur<ComplexMatrix> cSchur(size); cSchur.compute(complexA);
Eigen::ComplexEigenSolver<ComplexMatrix> cEigSolver; cEigSolver.compute(complexA);
Eigen::EigenSolver<Matrix> eigSolver; eigSolver.compute(A);
Eigen::SelfAdjointEigenSolver<Matrix> saEigSolver(size); saEigSolver.compute(saA);
Eigen::Tridiagonalization<Matrix> tridiag; tridiag.compute(saA);
// LU module
Eigen::PartialPivLU<Matrix> ppLU; ppLU.compute(A);
X = ppLU.solve(B);
x = ppLU.solve(b);
Eigen::FullPivLU<Matrix> fpLU; fpLU.compute(A);
X = fpLU.solve(B);
x = fpLU.solve(b);
// QR module
Eigen::HouseholderQR<Matrix> hQR; hQR.compute(A);
X = hQR.solve(B);
x = hQR.solve(b);
Eigen::ColPivHouseholderQR<Matrix> cpQR; cpQR.compute(A);
X = cpQR.solve(B);
x = cpQR.solve(b);
Eigen::FullPivHouseholderQR<Matrix> fpQR; fpQR.compute(A);
// FIXME X = fpQR.solve(B);
x = fpQR.solve(b);
// SVD module
Eigen::JacobiSVD<Matrix> jSVD; jSVD.compute(A, ComputeFullU | ComputeFullV);
}
void test_zerosized() {
// default constructors:
Eigen::MatrixXd A;
Eigen::VectorXd v;
// explicit zero-sized:
Eigen::ArrayXXd A0(0,0);
Eigen::ArrayXd v0(std::ptrdiff_t(0)); // FIXME ArrayXd(0) is ambiguous
// assigning empty objects to each other:
A=A0;
v=v0;
}
template<typename MatrixType> void test_reference(const MatrixType& m) {
typedef typename MatrixType::Scalar Scalar;
enum { Flag = MatrixType::IsRowMajor ? Eigen::RowMajor : Eigen::ColMajor};
enum { TransposeFlag = !MatrixType::IsRowMajor ? Eigen::RowMajor : Eigen::ColMajor};
typename MatrixType::Index rows = m.rows(), cols=m.cols();
// Dynamic reference:
typedef Eigen::Ref<const Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, Flag > > Ref;
typedef Eigen::Ref<const Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, TransposeFlag> > RefT;
Ref r1(m);
Ref r2(m.block(rows/3, cols/4, rows/2, cols/2));
RefT r3(m.transpose());
RefT r4(m.topLeftCorner(rows/2, cols/2).transpose());
VERIFY_RAISES_ASSERT(RefT r5(m));
VERIFY_RAISES_ASSERT(Ref r6(m.transpose()));
VERIFY_RAISES_ASSERT(Ref r7(Scalar(2) * m));
}
void test_nomalloc()
{
// check that our operator new is indeed called:
VERIFY_RAISES_ASSERT(MatrixXd dummy(MatrixXd::Random(3,3)));
CALL_SUBTEST_1(nomalloc(Matrix<float, 1, 1>()) );
CALL_SUBTEST_2(nomalloc(Matrix4d()) );
CALL_SUBTEST_3(nomalloc(Matrix<float,32,32>()) );
// Check decomposition modules with dynamic matrices that have a known compile-time max size (ctms)
CALL_SUBTEST_4(ctms_decompositions<float>());
CALL_SUBTEST_5(test_zerosized());
CALL_SUBTEST_6(test_reference(Matrix<float,32,32>()));
}