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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) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com>
+// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr>
+// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr>
+// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr>
+//
+// 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/.
+
+// discard stack allocation as that too bypasses malloc
+#define EIGEN_STACK_ALLOCATION_LIMIT 0
+#define EIGEN_RUNTIME_NO_MALLOC
+
+#include "main.h"
+#include <unsupported/Eigen/SVD>
+#include <Eigen/LU>
+
+
+// check if "svd" is the good image of "m"
+template<typename MatrixType, typename SVD>
+void svd_check_full(const MatrixType& m, const SVD& svd)
+{
+ typedef typename MatrixType::Index Index;
+ Index rows = m.rows();
+ Index cols = m.cols();
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime
+ };
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime> MatrixUType;
+ typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime> MatrixVType;
+
+
+ MatrixType sigma = MatrixType::Zero(rows, cols);
+ sigma.diagonal() = svd.singularValues().template cast<Scalar>();
+ MatrixUType u = svd.matrixU();
+ MatrixVType v = svd.matrixV();
+ VERIFY_IS_APPROX(m, u * sigma * v.adjoint());
+ VERIFY_IS_UNITARY(u);
+ VERIFY_IS_UNITARY(v);
+} // end svd_check_full
+
+
+
+// Compare to a reference value
+template<typename MatrixType, typename SVD>
+void svd_compare_to_full(const MatrixType& m,
+ unsigned int computationOptions,
+ const SVD& referenceSvd)
+{
+ typedef typename MatrixType::Index Index;
+ Index rows = m.rows();
+ Index cols = m.cols();
+ Index diagSize = (std::min)(rows, cols);
+
+ SVD svd(m, computationOptions);
+
+ VERIFY_IS_APPROX(svd.singularValues(), referenceSvd.singularValues());
+ if(computationOptions & ComputeFullU)
+ VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU());
+ if(computationOptions & ComputeThinU)
+ VERIFY_IS_APPROX(svd.matrixU(), referenceSvd.matrixU().leftCols(diagSize));
+ if(computationOptions & ComputeFullV)
+ VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV());
+ if(computationOptions & ComputeThinV)
+ VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV().leftCols(diagSize));
+} // end svd_compare_to_full
+
+
+
+template<typename MatrixType, typename SVD>
+void svd_solve(const MatrixType& m, unsigned int computationOptions)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::Index Index;
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime
+ };
+
+ typedef Matrix<Scalar, RowsAtCompileTime, Dynamic> RhsType;
+ typedef Matrix<Scalar, ColsAtCompileTime, Dynamic> SolutionType;
+
+ RhsType rhs = RhsType::Random(rows, internal::random<Index>(1, cols));
+ SVD svd(m, computationOptions);
+ SolutionType x = svd.solve(rhs);
+ // evaluate normal equation which works also for least-squares solutions
+ VERIFY_IS_APPROX(m.adjoint()*m*x,m.adjoint()*rhs);
+} // end svd_solve
+
+
+// test computations options
+// 2 functions because Jacobisvd can return before the second function
+template<typename MatrixType, typename SVD>
+void svd_test_computation_options_1(const MatrixType& m, const SVD& fullSvd)
+{
+ svd_check_full< MatrixType, SVD >(m, fullSvd);
+ svd_solve< MatrixType, SVD >(m, ComputeFullU | ComputeFullV);
+}
+
+
+template<typename MatrixType, typename SVD>
+void svd_test_computation_options_2(const MatrixType& m, const SVD& fullSvd)
+{
+ svd_compare_to_full< MatrixType, SVD >(m, ComputeFullU, fullSvd);
+ svd_compare_to_full< MatrixType, SVD >(m, ComputeFullV, fullSvd);
+ svd_compare_to_full< MatrixType, SVD >(m, 0, fullSvd);
+
+ if (MatrixType::ColsAtCompileTime == Dynamic) {
+ // thin U/V are only available with dynamic number of columns
+
+ svd_compare_to_full< MatrixType, SVD >(m, ComputeFullU|ComputeThinV, fullSvd);
+ svd_compare_to_full< MatrixType, SVD >(m, ComputeThinV, fullSvd);
+ svd_compare_to_full< MatrixType, SVD >(m, ComputeThinU|ComputeFullV, fullSvd);
+ svd_compare_to_full< MatrixType, SVD >(m, ComputeThinU , fullSvd);
+ svd_compare_to_full< MatrixType, SVD >(m, ComputeThinU|ComputeThinV, fullSvd);
+ svd_solve<MatrixType, SVD>(m, ComputeFullU | ComputeThinV);
+ svd_solve<MatrixType, SVD>(m, ComputeThinU | ComputeFullV);
+ svd_solve<MatrixType, SVD>(m, ComputeThinU | ComputeThinV);
+
+ typedef typename MatrixType::Index Index;
+ Index diagSize = (std::min)(m.rows(), m.cols());
+ SVD svd(m, ComputeThinU | ComputeThinV);
+ VERIFY_IS_APPROX(m, svd.matrixU().leftCols(diagSize) * svd.singularValues().asDiagonal() * svd.matrixV().leftCols(diagSize).adjoint());
+ }
+}
+
+template<typename MatrixType, typename SVD>
+void svd_verify_assert(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::Index Index;
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime
+ };
+
+ typedef Matrix<Scalar, RowsAtCompileTime, 1> RhsType;
+ RhsType rhs(rows);
+ SVD svd;
+ VERIFY_RAISES_ASSERT(svd.matrixU())
+ VERIFY_RAISES_ASSERT(svd.singularValues())
+ VERIFY_RAISES_ASSERT(svd.matrixV())
+ VERIFY_RAISES_ASSERT(svd.solve(rhs))
+ MatrixType a = MatrixType::Zero(rows, cols);
+ a.setZero();
+ svd.compute(a, 0);
+ VERIFY_RAISES_ASSERT(svd.matrixU())
+ VERIFY_RAISES_ASSERT(svd.matrixV())
+ svd.singularValues();
+ VERIFY_RAISES_ASSERT(svd.solve(rhs))
+
+ if (ColsAtCompileTime == Dynamic)
+ {
+ svd.compute(a, ComputeThinU);
+ svd.matrixU();
+ VERIFY_RAISES_ASSERT(svd.matrixV())
+ VERIFY_RAISES_ASSERT(svd.solve(rhs))
+ svd.compute(a, ComputeThinV);
+ svd.matrixV();
+ VERIFY_RAISES_ASSERT(svd.matrixU())
+ VERIFY_RAISES_ASSERT(svd.solve(rhs))
+ }
+ else
+ {
+ VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinU))
+ VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinV))
+ }
+}
+
+// work around stupid msvc error when constructing at compile time an expression that involves
+// a division by zero, even if the numeric type has floating point
+template<typename Scalar>
+EIGEN_DONT_INLINE Scalar zero() { return Scalar(0); }
+
+// workaround aggressive optimization in ICC
+template<typename T> EIGEN_DONT_INLINE T sub(T a, T b) { return a - b; }
+
+
+template<typename MatrixType, typename SVD>
+void svd_inf_nan()
+{
+ // all this function does is verify we don't iterate infinitely on nan/inf values
+
+ SVD svd;
+ typedef typename MatrixType::Scalar Scalar;
+ Scalar some_inf = Scalar(1) / zero<Scalar>();
+ VERIFY(sub(some_inf, some_inf) != sub(some_inf, some_inf));
+ svd.compute(MatrixType::Constant(10,10,some_inf), ComputeFullU | ComputeFullV);
+
+ Scalar some_nan = zero<Scalar> () / zero<Scalar> ();
+ VERIFY(some_nan != some_nan);
+ svd.compute(MatrixType::Constant(10,10,some_nan), ComputeFullU | ComputeFullV);
+
+ MatrixType m = MatrixType::Zero(10,10);
+ m(internal::random<int>(0,9), internal::random<int>(0,9)) = some_inf;
+ svd.compute(m, ComputeFullU | ComputeFullV);
+
+ m = MatrixType::Zero(10,10);
+ m(internal::random<int>(0,9), internal::random<int>(0,9)) = some_nan;
+ svd.compute(m, ComputeFullU | ComputeFullV);
+}
+
+
+template<typename SVD>
+void svd_preallocate()
+{
+ Vector3f v(3.f, 2.f, 1.f);
+ MatrixXf m = v.asDiagonal();
+
+ internal::set_is_malloc_allowed(false);
+ VERIFY_RAISES_ASSERT(VectorXf v(10);)
+ SVD svd;
+ internal::set_is_malloc_allowed(true);
+ svd.compute(m);
+ VERIFY_IS_APPROX(svd.singularValues(), v);
+
+ SVD svd2(3,3);
+ internal::set_is_malloc_allowed(false);
+ svd2.compute(m);
+ internal::set_is_malloc_allowed(true);
+ VERIFY_IS_APPROX(svd2.singularValues(), v);
+ VERIFY_RAISES_ASSERT(svd2.matrixU());
+ VERIFY_RAISES_ASSERT(svd2.matrixV());
+ svd2.compute(m, ComputeFullU | ComputeFullV);
+ VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity());
+ VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity());
+ internal::set_is_malloc_allowed(false);
+ svd2.compute(m);
+ internal::set_is_malloc_allowed(true);
+
+ SVD svd3(3,3,ComputeFullU|ComputeFullV);
+ internal::set_is_malloc_allowed(false);
+ svd2.compute(m);
+ internal::set_is_malloc_allowed(true);
+ VERIFY_IS_APPROX(svd2.singularValues(), v);
+ VERIFY_IS_APPROX(svd2.matrixU(), Matrix3f::Identity());
+ VERIFY_IS_APPROX(svd2.matrixV(), Matrix3f::Identity());
+ internal::set_is_malloc_allowed(false);
+ svd2.compute(m, ComputeFullU|ComputeFullV);
+ internal::set_is_malloc_allowed(true);
+}
+
+
+
+
+