Squashed 'third_party/eigen/' changes from 61d72f6..cf794d3
Change-Id: I9b814151b01f49af6337a8605d0c42a3a1ed4c72
git-subtree-dir: third_party/eigen
git-subtree-split: cf794d3b741a6278df169e58461f8529f43bce5d
diff --git a/test/svd_common.h b/test/svd_common.h
new file mode 100644
index 0000000..cba0665
--- /dev/null
+++ b/test/svd_common.h
@@ -0,0 +1,478 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2014 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/.
+
+#ifndef SVD_DEFAULT
+#error a macro SVD_DEFAULT(MatrixType) must be defined prior to including svd_common.h
+#endif
+
+#ifndef SVD_FOR_MIN_NORM
+#error a macro SVD_FOR_MIN_NORM(MatrixType) must be defined prior to including svd_common.h
+#endif
+
+#include "svd_fill.h"
+
+// Check that the matrix m is properly reconstructed and that the U and V factors are unitary
+// The SVD must have already been computed.
+template<typename SvdType, typename MatrixType>
+void svd_check_full(const MatrixType& m, const SvdType& svd)
+{
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime
+ };
+
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ 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();
+ RealScalar scaling = m.cwiseAbs().maxCoeff();
+ if(scaling<(std::numeric_limits<RealScalar>::min)())
+ {
+ VERIFY(sigma.cwiseAbs().maxCoeff() <= (std::numeric_limits<RealScalar>::min)());
+ }
+ else
+ {
+ VERIFY_IS_APPROX(m/scaling, u * (sigma/scaling) * v.adjoint());
+ }
+ VERIFY_IS_UNITARY(u);
+ VERIFY_IS_UNITARY(v);
+}
+
+// Compare partial SVD defined by computationOptions to a full SVD referenceSvd
+template<typename SvdType, typename MatrixType>
+void svd_compare_to_full(const MatrixType& m,
+ unsigned int computationOptions,
+ const SvdType& referenceSvd)
+{
+ typedef typename MatrixType::RealScalar RealScalar;
+ Index rows = m.rows();
+ Index cols = m.cols();
+ Index diagSize = (std::min)(rows, cols);
+ RealScalar prec = test_precision<RealScalar>();
+
+ SvdType svd(m, computationOptions);
+
+ VERIFY_IS_APPROX(svd.singularValues(), referenceSvd.singularValues());
+
+ if(computationOptions & (ComputeFullV|ComputeThinV))
+ {
+ VERIFY( (svd.matrixV().adjoint()*svd.matrixV()).isIdentity(prec) );
+ VERIFY_IS_APPROX( svd.matrixV().leftCols(diagSize) * svd.singularValues().asDiagonal() * svd.matrixV().leftCols(diagSize).adjoint(),
+ referenceSvd.matrixV().leftCols(diagSize) * referenceSvd.singularValues().asDiagonal() * referenceSvd.matrixV().leftCols(diagSize).adjoint());
+ }
+
+ if(computationOptions & (ComputeFullU|ComputeThinU))
+ {
+ VERIFY( (svd.matrixU().adjoint()*svd.matrixU()).isIdentity(prec) );
+ VERIFY_IS_APPROX( svd.matrixU().leftCols(diagSize) * svd.singularValues().cwiseAbs2().asDiagonal() * svd.matrixU().leftCols(diagSize).adjoint(),
+ referenceSvd.matrixU().leftCols(diagSize) * referenceSvd.singularValues().cwiseAbs2().asDiagonal() * referenceSvd.matrixU().leftCols(diagSize).adjoint());
+ }
+
+ // The following checks are not critical.
+ // For instance, with Dived&Conquer SVD, if only the factor 'V' is computedt then different matrix-matrix product implementation will be used
+ // and the resulting 'V' factor might be significantly different when the SVD decomposition is not unique, especially with single precision float.
+ ++g_test_level;
+ 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().cwiseAbs(), referenceSvd.matrixV().cwiseAbs());
+ if(computationOptions & ComputeThinV) VERIFY_IS_APPROX(svd.matrixV(), referenceSvd.matrixV().leftCols(diagSize));
+ --g_test_level;
+}
+
+//
+template<typename SvdType, typename MatrixType>
+void svd_least_square(const MatrixType& m, unsigned int computationOptions)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ typedef typename MatrixType::RealScalar RealScalar;
+ 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));
+ SvdType svd(m, computationOptions);
+
+ if(internal::is_same<RealScalar,double>::value) svd.setThreshold(1e-8);
+ else if(internal::is_same<RealScalar,float>::value) svd.setThreshold(2e-4);
+
+ SolutionType x = svd.solve(rhs);
+
+ RealScalar residual = (m*x-rhs).norm();
+ RealScalar rhs_norm = rhs.norm();
+ if(!test_isMuchSmallerThan(residual,rhs.norm()))
+ {
+ // ^^^ If the residual is very small, then we have an exact solution, so we are already good.
+
+ // evaluate normal equation which works also for least-squares solutions
+ if(internal::is_same<RealScalar,double>::value || svd.rank()==m.diagonal().size())
+ {
+ using std::sqrt;
+ // This test is not stable with single precision.
+ // This is probably because squaring m signicantly affects the precision.
+ if(internal::is_same<RealScalar,float>::value) ++g_test_level;
+
+ VERIFY_IS_APPROX(m.adjoint()*(m*x),m.adjoint()*rhs);
+
+ if(internal::is_same<RealScalar,float>::value) --g_test_level;
+ }
+
+ // Check that there is no significantly better solution in the neighborhood of x
+ for(Index k=0;k<x.rows();++k)
+ {
+ using std::abs;
+
+ SolutionType y(x);
+ y.row(k) = (RealScalar(1)+2*NumTraits<RealScalar>::epsilon())*x.row(k);
+ RealScalar residual_y = (m*y-rhs).norm();
+ VERIFY( test_isMuchSmallerThan(abs(residual_y-residual), rhs_norm) || residual < residual_y );
+ if(internal::is_same<RealScalar,float>::value) ++g_test_level;
+ VERIFY( test_isApprox(residual_y,residual) || residual < residual_y );
+ if(internal::is_same<RealScalar,float>::value) --g_test_level;
+
+ y.row(k) = (RealScalar(1)-2*NumTraits<RealScalar>::epsilon())*x.row(k);
+ residual_y = (m*y-rhs).norm();
+ VERIFY( test_isMuchSmallerThan(abs(residual_y-residual), rhs_norm) || residual < residual_y );
+ if(internal::is_same<RealScalar,float>::value) ++g_test_level;
+ VERIFY( test_isApprox(residual_y,residual) || residual < residual_y );
+ if(internal::is_same<RealScalar,float>::value) --g_test_level;
+ }
+ }
+}
+
+// check minimal norm solutions, the inoput matrix m is only used to recover problem size
+template<typename MatrixType>
+void svd_min_norm(const MatrixType& m, unsigned int computationOptions)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ Index cols = m.cols();
+
+ enum {
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime
+ };
+
+ typedef Matrix<Scalar, ColsAtCompileTime, Dynamic> SolutionType;
+
+ // generate a full-rank m x n problem with m<n
+ enum {
+ RankAtCompileTime2 = ColsAtCompileTime==Dynamic ? Dynamic : (ColsAtCompileTime)/2+1,
+ RowsAtCompileTime3 = ColsAtCompileTime==Dynamic ? Dynamic : ColsAtCompileTime+1
+ };
+ typedef Matrix<Scalar, RankAtCompileTime2, ColsAtCompileTime> MatrixType2;
+ typedef Matrix<Scalar, RankAtCompileTime2, 1> RhsType2;
+ typedef Matrix<Scalar, ColsAtCompileTime, RankAtCompileTime2> MatrixType2T;
+ Index rank = RankAtCompileTime2==Dynamic ? internal::random<Index>(1,cols) : Index(RankAtCompileTime2);
+ MatrixType2 m2(rank,cols);
+ int guard = 0;
+ do {
+ m2.setRandom();
+ } while(SVD_FOR_MIN_NORM(MatrixType2)(m2).setThreshold(test_precision<Scalar>()).rank()!=rank && (++guard)<10);
+ VERIFY(guard<10);
+
+ RhsType2 rhs2 = RhsType2::Random(rank);
+ // use QR to find a reference minimal norm solution
+ HouseholderQR<MatrixType2T> qr(m2.adjoint());
+ Matrix<Scalar,Dynamic,1> tmp = qr.matrixQR().topLeftCorner(rank,rank).template triangularView<Upper>().adjoint().solve(rhs2);
+ tmp.conservativeResize(cols);
+ tmp.tail(cols-rank).setZero();
+ SolutionType x21 = qr.householderQ() * tmp;
+ // now check with SVD
+ SVD_FOR_MIN_NORM(MatrixType2) svd2(m2, computationOptions);
+ SolutionType x22 = svd2.solve(rhs2);
+ VERIFY_IS_APPROX(m2*x21, rhs2);
+ VERIFY_IS_APPROX(m2*x22, rhs2);
+ VERIFY_IS_APPROX(x21, x22);
+
+ // Now check with a rank deficient matrix
+ typedef Matrix<Scalar, RowsAtCompileTime3, ColsAtCompileTime> MatrixType3;
+ typedef Matrix<Scalar, RowsAtCompileTime3, 1> RhsType3;
+ Index rows3 = RowsAtCompileTime3==Dynamic ? internal::random<Index>(rank+1,2*cols) : Index(RowsAtCompileTime3);
+ Matrix<Scalar,RowsAtCompileTime3,Dynamic> C = Matrix<Scalar,RowsAtCompileTime3,Dynamic>::Random(rows3,rank);
+ MatrixType3 m3 = C * m2;
+ RhsType3 rhs3 = C * rhs2;
+ SVD_FOR_MIN_NORM(MatrixType3) svd3(m3, computationOptions);
+ SolutionType x3 = svd3.solve(rhs3);
+ VERIFY_IS_APPROX(m3*x3, rhs3);
+ VERIFY_IS_APPROX(m3*x21, rhs3);
+ VERIFY_IS_APPROX(m2*x3, rhs2);
+ VERIFY_IS_APPROX(x21, x3);
+}
+
+// Check full, compare_to_full, least_square, and min_norm for all possible compute-options
+template<typename SvdType, typename MatrixType>
+void svd_test_all_computation_options(const MatrixType& m, bool full_only)
+{
+// if (QRPreconditioner == NoQRPreconditioner && m.rows() != m.cols())
+// return;
+ SvdType fullSvd(m, ComputeFullU|ComputeFullV);
+ CALL_SUBTEST(( svd_check_full(m, fullSvd) ));
+ CALL_SUBTEST(( svd_least_square<SvdType>(m, ComputeFullU | ComputeFullV) ));
+ CALL_SUBTEST(( svd_min_norm(m, ComputeFullU | ComputeFullV) ));
+
+ #if defined __INTEL_COMPILER
+ // remark #111: statement is unreachable
+ #pragma warning disable 111
+ #endif
+ if(full_only)
+ return;
+
+ CALL_SUBTEST(( svd_compare_to_full(m, ComputeFullU, fullSvd) ));
+ CALL_SUBTEST(( svd_compare_to_full(m, ComputeFullV, fullSvd) ));
+ CALL_SUBTEST(( svd_compare_to_full(m, 0, fullSvd) ));
+
+ if (MatrixType::ColsAtCompileTime == Dynamic) {
+ // thin U/V are only available with dynamic number of columns
+ CALL_SUBTEST(( svd_compare_to_full(m, ComputeFullU|ComputeThinV, fullSvd) ));
+ CALL_SUBTEST(( svd_compare_to_full(m, ComputeThinV, fullSvd) ));
+ CALL_SUBTEST(( svd_compare_to_full(m, ComputeThinU|ComputeFullV, fullSvd) ));
+ CALL_SUBTEST(( svd_compare_to_full(m, ComputeThinU , fullSvd) ));
+ CALL_SUBTEST(( svd_compare_to_full(m, ComputeThinU|ComputeThinV, fullSvd) ));
+
+ CALL_SUBTEST(( svd_least_square<SvdType>(m, ComputeFullU | ComputeThinV) ));
+ CALL_SUBTEST(( svd_least_square<SvdType>(m, ComputeThinU | ComputeFullV) ));
+ CALL_SUBTEST(( svd_least_square<SvdType>(m, ComputeThinU | ComputeThinV) ));
+
+ CALL_SUBTEST(( svd_min_norm(m, ComputeFullU | ComputeThinV) ));
+ CALL_SUBTEST(( svd_min_norm(m, ComputeThinU | ComputeFullV) ));
+ CALL_SUBTEST(( svd_min_norm(m, ComputeThinU | ComputeThinV) ));
+
+ // test reconstruction
+ Index diagSize = (std::min)(m.rows(), m.cols());
+ SvdType svd(m, ComputeThinU | ComputeThinV);
+ VERIFY_IS_APPROX(m, svd.matrixU().leftCols(diagSize) * svd.singularValues().asDiagonal() * svd.matrixV().leftCols(diagSize).adjoint());
+ }
+}
+
+
+// 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; }
+
+// all this function does is verify we don't iterate infinitely on nan/inf values
+template<typename SvdType, typename MatrixType>
+void svd_inf_nan()
+{
+ SvdType 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 nan = std::numeric_limits<Scalar>::quiet_NaN();
+ VERIFY(nan != nan);
+ svd.compute(MatrixType::Constant(10,10,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)) = nan;
+ svd.compute(m, ComputeFullU | ComputeFullV);
+
+ // regression test for bug 791
+ m.resize(3,3);
+ m << 0, 2*NumTraits<Scalar>::epsilon(), 0.5,
+ 0, -0.5, 0,
+ nan, 0, 0;
+ svd.compute(m, ComputeFullU | ComputeFullV);
+
+ m.resize(4,4);
+ m << 1, 0, 0, 0,
+ 0, 3, 1, 2e-308,
+ 1, 0, 1, nan,
+ 0, nan, nan, 0;
+ svd.compute(m, ComputeFullU | ComputeFullV);
+}
+
+// Regression test for bug 286: JacobiSVD loops indefinitely with some
+// matrices containing denormal numbers.
+template<typename>
+void svd_underoverflow()
+{
+#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;
+ SVD_DEFAULT(Matrix2d) svd;
+ svd.compute(M,ComputeFullU|ComputeFullV);
+ CALL_SUBTEST( svd_check_full(M,svd) );
+
+ // Check all 2x2 matrices made with the following coefficients:
+ VectorXd value_set(9);
+ value_set << 0, 1, -1, 5.60844e-313, -5.60844e-313, 4.94e-324, -4.94e-324, -4.94e-223, 4.94e-223;
+ Array4i id(0,0,0,0);
+ int k = 0;
+ do
+ {
+ M << value_set(id(0)), value_set(id(1)), value_set(id(2)), value_set(id(3));
+ svd.compute(M,ComputeFullU|ComputeFullV);
+ CALL_SUBTEST( svd_check_full(M,svd) );
+
+ id(k)++;
+ if(id(k)>=value_set.size())
+ {
+ while(k<3 && id(k)>=value_set.size()) id(++k)++;
+ id.head(k).setZero();
+ k=0;
+ }
+
+ } while((id<int(value_set.size())).all());
+
+#if defined __INTEL_COMPILER
+#pragma warning pop
+#endif
+
+ // Check for overflow:
+ Matrix3d M3;
+ M3 << 4.4331978442502944e+307, -5.8585363752028680e+307, 6.4527017443412964e+307,
+ 3.7841695601406358e+307, 2.4331702789740617e+306, -3.5235707140272905e+307,
+ -8.7190887618028355e+307, -7.3453213709232193e+307, -2.4367363684472105e+307;
+
+ SVD_DEFAULT(Matrix3d) svd3;
+ svd3.compute(M3,ComputeFullU|ComputeFullV); // just check we don't loop indefinitely
+ CALL_SUBTEST( svd_check_full(M3,svd3) );
+}
+
+// void jacobisvd(const MatrixType& a = MatrixType(), bool pickrandom = true)
+
+template<typename MatrixType>
+void svd_all_trivial_2x2( void (*cb)(const MatrixType&,bool) )
+{
+ MatrixType M;
+ VectorXd value_set(3);
+ value_set << 0, 1, -1;
+ Array4i id(0,0,0,0);
+ int k = 0;
+ do
+ {
+ M << value_set(id(0)), value_set(id(1)), value_set(id(2)), value_set(id(3));
+
+ cb(M,false);
+
+ id(k)++;
+ if(id(k)>=value_set.size())
+ {
+ while(k<3 && id(k)>=value_set.size()) id(++k)++;
+ id.head(k).setZero();
+ k=0;
+ }
+
+ } while((id<int(value_set.size())).all());
+}
+
+template<typename>
+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 tmp(10);)
+ SVD_DEFAULT(MatrixXf) svd;
+ internal::set_is_malloc_allowed(true);
+ svd.compute(m);
+ VERIFY_IS_APPROX(svd.singularValues(), v);
+
+ SVD_DEFAULT(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);
+
+ SVD_DEFAULT(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);
+}
+
+template<typename SvdType,typename MatrixType>
+void svd_verify_assert(const MatrixType& m)
+{
+ typedef typename MatrixType::Scalar Scalar;
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ enum {
+ RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+ ColsAtCompileTime = MatrixType::ColsAtCompileTime
+ };
+
+ typedef Matrix<Scalar, RowsAtCompileTime, 1> RhsType;
+ RhsType rhs(rows);
+ SvdType 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))
+ }
+}
+
+#undef SVD_DEFAULT
+#undef SVD_FOR_MIN_NORM