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-rw-r--r--test/jacobisvd.cpp350
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diff --git a/test/jacobisvd.cpp b/test/jacobisvd.cpp
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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>
+//
+// 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 <Eigen/SVD>
+
+template<typename MatrixType, int QRPreconditioner>
+void jacobisvd_check_full(const MatrixType& m, const JacobiSVD<MatrixType, QRPreconditioner>& 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 typename NumTraits<Scalar>::Real RealScalar;
+ typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime> MatrixUType;
+ typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime> MatrixVType;
+ typedef Matrix<Scalar, RowsAtCompileTime, 1> ColVectorType;
+ typedef Matrix<Scalar, ColsAtCompileTime, 1> InputVectorType;
+
+ 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);
+}
+
+template<typename MatrixType, int QRPreconditioner>
+void jacobisvd_compare_to_full(const MatrixType& m,
+ unsigned int computationOptions,
+ const JacobiSVD<MatrixType, QRPreconditioner>& referenceSvd)
+{
+ typedef typename MatrixType::Index Index;
+ Index rows = m.rows();
+ Index cols = m.cols();
+ Index diagSize = (std::min)(rows, cols);
+
+ JacobiSVD<MatrixType, QRPreconditioner> 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));
+}
+
+template<typename MatrixType, int QRPreconditioner>
+void jacobisvd_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));
+ JacobiSVD<MatrixType, QRPreconditioner> 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);
+}
+
+template<typename MatrixType, int QRPreconditioner>
+void jacobisvd_test_all_computation_options(const MatrixType& m)
+{
+ if (QRPreconditioner == NoQRPreconditioner && m.rows() != m.cols())
+ return;
+ JacobiSVD<MatrixType, QRPreconditioner> fullSvd(m, ComputeFullU|ComputeFullV);
+
+ jacobisvd_check_full(m, fullSvd);
+ jacobisvd_solve<MatrixType, QRPreconditioner>(m, ComputeFullU | ComputeFullV);
+
+ if(QRPreconditioner == FullPivHouseholderQRPreconditioner)
+ return;
+
+ jacobisvd_compare_to_full(m, ComputeFullU, fullSvd);
+ jacobisvd_compare_to_full(m, ComputeFullV, fullSvd);
+ jacobisvd_compare_to_full(m, 0, fullSvd);
+
+ if (MatrixType::ColsAtCompileTime == Dynamic) {
+ // thin U/V are only available with dynamic number of columns
+ jacobisvd_compare_to_full(m, ComputeFullU|ComputeThinV, fullSvd);
+ jacobisvd_compare_to_full(m, ComputeThinV, fullSvd);
+ jacobisvd_compare_to_full(m, ComputeThinU|ComputeFullV, fullSvd);
+ jacobisvd_compare_to_full(m, ComputeThinU , fullSvd);
+ jacobisvd_compare_to_full(m, ComputeThinU|ComputeThinV, fullSvd);
+ jacobisvd_solve<MatrixType, QRPreconditioner>(m, ComputeFullU | ComputeThinV);
+ jacobisvd_solve<MatrixType, QRPreconditioner>(m, ComputeThinU | ComputeFullV);
+ jacobisvd_solve<MatrixType, QRPreconditioner>(m, ComputeThinU | ComputeThinV);
+
+ // test reconstruction
+ typedef typename MatrixType::Index Index;
+ Index diagSize = (std::min)(m.rows(), m.cols());
+ JacobiSVD<MatrixType, QRPreconditioner> svd(m, ComputeThinU | ComputeThinV);
+ VERIFY_IS_APPROX(m, svd.matrixU().leftCols(diagSize) * svd.singularValues().asDiagonal() * svd.matrixV().leftCols(diagSize).adjoint());
+ }
+}
+
+template<typename MatrixType>
+void jacobisvd(const MatrixType& a = MatrixType(), bool pickrandom = true)
+{
+ MatrixType m = pickrandom ? MatrixType::Random(a.rows(), a.cols()) : a;
+
+ jacobisvd_test_all_computation_options<MatrixType, FullPivHouseholderQRPreconditioner>(m);
+ jacobisvd_test_all_computation_options<MatrixType, ColPivHouseholderQRPreconditioner>(m);
+ jacobisvd_test_all_computation_options<MatrixType, HouseholderQRPreconditioner>(m);
+ jacobisvd_test_all_computation_options<MatrixType, NoQRPreconditioner>(m);
+}
+
+template<typename MatrixType> void jacobisvd_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);
+
+ JacobiSVD<MatrixType> 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))
+
+ JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner> svd_fullqr;
+ VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeFullU|ComputeThinV))
+ VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeThinU|ComputeThinV))
+ VERIFY_RAISES_ASSERT(svd_fullqr.compute(a, ComputeThinU|ComputeFullV))
+ }
+ else
+ {
+ VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinU))
+ VERIFY_RAISES_ASSERT(svd.compute(a, ComputeThinV))
+ }
+}
+
+template<typename MatrixType>
+void jacobisvd_method()
+{
+ enum { Size = MatrixType::RowsAtCompileTime };
+ typedef typename MatrixType::RealScalar RealScalar;
+ typedef Matrix<RealScalar, Size, 1> RealVecType;
+ MatrixType m = MatrixType::Identity();
+ VERIFY_IS_APPROX(m.jacobiSvd().singularValues(), RealVecType::Ones());
+ VERIFY_RAISES_ASSERT(m.jacobiSvd().matrixU());
+ VERIFY_RAISES_ASSERT(m.jacobiSvd().matrixV());
+ VERIFY_IS_APPROX(m.jacobiSvd(ComputeFullU|ComputeFullV).solve(m), m);
+}
+
+// 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>
+void jacobisvd_inf_nan()
+{
+ // all this function does is verify we don't iterate infinitely on nan/inf values
+
+ JacobiSVD<MatrixType> 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);
+}
+
+// Regression test for bug 286: JacobiSVD loops indefinitely with some
+// matrices containing denormal numbers.
+void jacobisvd_bug286()
+{
+#if defined __INTEL_COMPILER
+// shut up warning #239: floating point underflow
+#pragma warning push
+#pragma warning disable 239
+#endif
+ Matrix2d M;
+ M << -7.90884e-313, -4.94e-324,
+ 0, 5.60844e-313;
+#if defined __INTEL_COMPILER
+#pragma warning pop
+#endif
+ JacobiSVD<Matrix2d> svd;
+ svd.compute(M); // just check we don't loop indefinitely
+}
+
+void jacobisvd_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);)
+ JacobiSVD<MatrixXf> svd;
+ internal::set_is_malloc_allowed(true);
+ svd.compute(m);
+ VERIFY_IS_APPROX(svd.singularValues(), v);
+
+ JacobiSVD<MatrixXf> 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);
+
+ JacobiSVD<MatrixXf> 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);
+}
+
+void test_jacobisvd()
+{
+ CALL_SUBTEST_3(( jacobisvd_verify_assert(Matrix3f()) ));
+ CALL_SUBTEST_4(( jacobisvd_verify_assert(Matrix4d()) ));
+ CALL_SUBTEST_7(( jacobisvd_verify_assert(MatrixXf(10,12)) ));
+ CALL_SUBTEST_8(( jacobisvd_verify_assert(MatrixXcd(7,5)) ));
+
+ for(int i = 0; i < g_repeat; i++) {
+ Matrix2cd m;
+ m << 0, 1,
+ 0, 1;
+ CALL_SUBTEST_1(( jacobisvd(m, false) ));
+ m << 1, 0,
+ 1, 0;
+ CALL_SUBTEST_1(( jacobisvd(m, false) ));
+
+ Matrix2d n;
+ n << 0, 0,
+ 0, 0;
+ CALL_SUBTEST_2(( jacobisvd(n, false) ));
+ n << 0, 0,
+ 0, 1;
+ CALL_SUBTEST_2(( jacobisvd(n, false) ));
+
+ CALL_SUBTEST_3(( jacobisvd<Matrix3f>() ));
+ CALL_SUBTEST_4(( jacobisvd<Matrix4d>() ));
+ CALL_SUBTEST_5(( jacobisvd<Matrix<float,3,5> >() ));
+ CALL_SUBTEST_6(( jacobisvd<Matrix<double,Dynamic,2> >(Matrix<double,Dynamic,2>(10,2)) ));
+
+ int r = internal::random<int>(1, 30),
+ c = internal::random<int>(1, 30);
+ CALL_SUBTEST_7(( jacobisvd<MatrixXf>(MatrixXf(r,c)) ));
+ CALL_SUBTEST_8(( jacobisvd<MatrixXcd>(MatrixXcd(r,c)) ));
+ (void) r;
+ (void) c;
+
+ // Test on inf/nan matrix
+ CALL_SUBTEST_7( jacobisvd_inf_nan<MatrixXf>() );
+ }
+
+ CALL_SUBTEST_7(( jacobisvd<MatrixXf>(MatrixXf(internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2), internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/2))) ));
+ CALL_SUBTEST_8(( jacobisvd<MatrixXcd>(MatrixXcd(internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/3), internal::random<int>(EIGEN_TEST_MAX_SIZE/4, EIGEN_TEST_MAX_SIZE/3))) ));
+
+ // test matrixbase method
+ CALL_SUBTEST_1(( jacobisvd_method<Matrix2cd>() ));
+ CALL_SUBTEST_3(( jacobisvd_method<Matrix3f>() ));
+
+ // Test problem size constructors
+ CALL_SUBTEST_7( JacobiSVD<MatrixXf>(10,10) );
+
+ // Check that preallocation avoids subsequent mallocs
+ CALL_SUBTEST_9( jacobisvd_preallocate() );
+
+ // Regression check for bug 286
+ CALL_SUBTEST_2( jacobisvd_bug286() );
+}
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