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+// 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>()));
+}