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Reafctoring in D&C SVD unsupported module: clean and merge the SVDBase class to Eigen/SVD, rm copy/pasted JacobiSVD.h file
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@ -21,6 +21,7 @@
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*/
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#include "src/misc/Solve.h"
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#include "src/SVD/SVDBase.h"
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#include "src/SVD/JacobiSVD.h"
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#if defined(EIGEN_USE_LAPACKE) && !defined(EIGEN_USE_LAPACKE_STRICT)
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#include "src/SVD/JacobiSVD_MKL.h"
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@ -2,6 +2,7 @@
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// for linear algebra.
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//
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// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
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// Copyright (C) 2013-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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@ -442,6 +443,12 @@ void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
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*j_left = rot1 * j_right->transpose();
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}
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template<typename _MatrixType, int QRPreconditioner>
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struct traits<JacobiSVD<_MatrixType,QRPreconditioner> >
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{
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typedef _MatrixType MatrixType;
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};
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} // end namespace internal
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/** \ingroup SVD_Module
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@ -498,7 +505,9 @@ void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
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* \sa MatrixBase::jacobiSvd()
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*/
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template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
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: public SVDBase<JacobiSVD<_MatrixType,QRPreconditioner> >
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{
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typedef SVDBase<JacobiSVD> Base;
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public:
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typedef _MatrixType MatrixType;
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@ -515,13 +524,10 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
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MatrixOptions = MatrixType::Options
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};
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typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime,
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MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime>
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MatrixUType;
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typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime,
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MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime>
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MatrixVType;
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typedef typename internal::plain_diag_type<MatrixType, RealScalar>::type SingularValuesType;
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typedef typename Base::MatrixUType MatrixUType;
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typedef typename Base::MatrixVType MatrixVType;
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typedef typename Base::SingularValuesType SingularValuesType;
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typedef typename internal::plain_row_type<MatrixType>::type RowType;
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typedef typename internal::plain_col_type<MatrixType>::type ColType;
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typedef Matrix<Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime,
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@ -534,11 +540,6 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
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* perform decompositions via JacobiSVD::compute(const MatrixType&).
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*/
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JacobiSVD()
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: m_isInitialized(false),
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m_isAllocated(false),
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m_usePrescribedThreshold(false),
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m_computationOptions(0),
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m_rows(-1), m_cols(-1), m_diagSize(0)
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{}
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@ -549,11 +550,6 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
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* \sa JacobiSVD()
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*/
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JacobiSVD(Index rows, Index cols, unsigned int computationOptions = 0)
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: m_isInitialized(false),
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m_isAllocated(false),
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m_usePrescribedThreshold(false),
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m_computationOptions(0),
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m_rows(-1), m_cols(-1)
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{
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allocate(rows, cols, computationOptions);
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}
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@ -569,11 +565,6 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
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* available with the (non-default) FullPivHouseholderQR preconditioner.
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*/
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JacobiSVD(const MatrixType& matrix, unsigned int computationOptions = 0)
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: m_isInitialized(false),
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m_isAllocated(false),
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m_usePrescribedThreshold(false),
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m_computationOptions(0),
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m_rows(-1), m_cols(-1)
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{
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compute(matrix, computationOptions);
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}
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@ -601,54 +592,6 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
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return compute(matrix, m_computationOptions);
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}
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/** \returns the \a U matrix.
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*
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* For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
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* the U matrix is n-by-n if you asked for #ComputeFullU, and is n-by-m if you asked for #ComputeThinU.
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*
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* The \a m first columns of \a U are the left singular vectors of the matrix being decomposed.
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*
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* This method asserts that you asked for \a U to be computed.
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*/
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const MatrixUType& matrixU() const
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{
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eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
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eigen_assert(computeU() && "This JacobiSVD decomposition didn't compute U. Did you ask for it?");
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return m_matrixU;
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}
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/** \returns the \a V matrix.
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*
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* For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
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* the V matrix is p-by-p if you asked for #ComputeFullV, and is p-by-m if you asked for ComputeThinV.
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*
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* The \a m first columns of \a V are the right singular vectors of the matrix being decomposed.
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*
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* This method asserts that you asked for \a V to be computed.
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*/
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const MatrixVType& matrixV() const
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{
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eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
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eigen_assert(computeV() && "This JacobiSVD decomposition didn't compute V. Did you ask for it?");
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return m_matrixV;
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}
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/** \returns the vector of singular values.
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*
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* For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p, the
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* returned vector has size \a m. Singular values are always sorted in decreasing order.
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*/
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const SingularValuesType& singularValues() const
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{
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eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
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return m_singularValues;
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}
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/** \returns true if \a U (full or thin) is asked for in this SVD decomposition */
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inline bool computeU() const { return m_computeFullU || m_computeThinU; }
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/** \returns true if \a V (full or thin) is asked for in this SVD decomposition */
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inline bool computeV() const { return m_computeFullV || m_computeThinV; }
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/** \returns a (least squares) solution of \f$ A x = b \f$ using the current SVD decomposition of A.
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*
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* \param b the right-hand-side of the equation to solve.
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@ -666,94 +609,31 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
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eigen_assert(computeU() && computeV() && "JacobiSVD::solve() requires both unitaries U and V to be computed (thin unitaries suffice).");
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return internal::solve_retval<JacobiSVD, Rhs>(*this, b.derived());
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}
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/** \returns the number of singular values that are not exactly 0 */
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Index nonzeroSingularValues() const
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{
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eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
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return m_nonzeroSingularValues;
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}
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/** \returns the rank of the matrix of which \c *this is the SVD.
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*
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* \note This method has to determine which singular values should be considered nonzero.
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* For that, it uses the threshold value that you can control by calling
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* setThreshold(const RealScalar&).
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*/
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inline Index rank() const
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{
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using std::abs;
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eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
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if(m_singularValues.size()==0) return 0;
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RealScalar premultiplied_threshold = m_singularValues.coeff(0) * threshold();
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Index i = m_nonzeroSingularValues-1;
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while(i>=0 && m_singularValues.coeff(i) < premultiplied_threshold) --i;
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return i+1;
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}
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using Base::computeU;
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using Base::computeV;
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/** Allows to prescribe a threshold to be used by certain methods, such as rank() and solve(),
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* which need to determine when singular values are to be considered nonzero.
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* This is not used for the SVD decomposition itself.
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*
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* When it needs to get the threshold value, Eigen calls threshold().
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* The default is \c NumTraits<Scalar>::epsilon()
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*
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* \param threshold The new value to use as the threshold.
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*
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* A singular value will be considered nonzero if its value is strictly greater than
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* \f$ \vert singular value \vert \leqslant threshold \times \vert max singular value \vert \f$.
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*
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* If you want to come back to the default behavior, call setThreshold(Default_t)
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*/
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JacobiSVD& setThreshold(const RealScalar& threshold)
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{
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m_usePrescribedThreshold = true;
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m_prescribedThreshold = threshold;
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return *this;
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}
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/** Allows to come back to the default behavior, letting Eigen use its default formula for
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* determining the threshold.
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*
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* You should pass the special object Eigen::Default as parameter here.
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* \code svd.setThreshold(Eigen::Default); \endcode
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*
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* See the documentation of setThreshold(const RealScalar&).
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*/
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JacobiSVD& setThreshold(Default_t)
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{
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m_usePrescribedThreshold = false;
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return *this;
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}
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/** Returns the threshold that will be used by certain methods such as rank().
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*
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* See the documentation of setThreshold(const RealScalar&).
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*/
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RealScalar threshold() const
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{
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eigen_assert(m_isInitialized || m_usePrescribedThreshold);
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return m_usePrescribedThreshold ? m_prescribedThreshold
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: (std::max<Index>)(1,m_diagSize)*NumTraits<Scalar>::epsilon();
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}
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inline Index rows() const { return m_rows; }
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inline Index cols() const { return m_cols; }
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private:
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void allocate(Index rows, Index cols, unsigned int computationOptions);
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protected:
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MatrixUType m_matrixU;
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MatrixVType m_matrixV;
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SingularValuesType m_singularValues;
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using Base::m_matrixU;
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using Base::m_matrixV;
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using Base::m_singularValues;
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using Base::m_isInitialized;
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using Base::m_isAllocated;
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using Base::m_usePrescribedThreshold;
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using Base::m_computeFullU;
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using Base::m_computeThinU;
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using Base::m_computeFullV;
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using Base::m_computeThinV;
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using Base::m_computationOptions;
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using Base::m_nonzeroSingularValues;
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using Base::m_rows;
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using Base::m_cols;
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using Base::m_diagSize;
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using Base::m_prescribedThreshold;
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WorkMatrixType m_workMatrix;
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bool m_isInitialized, m_isAllocated, m_usePrescribedThreshold;
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bool m_computeFullU, m_computeThinU;
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bool m_computeFullV, m_computeThinV;
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unsigned int m_computationOptions;
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Index m_nonzeroSingularValues, m_rows, m_cols, m_diagSize;
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RealScalar m_prescribedThreshold;
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template<typename __MatrixType, int _QRPreconditioner, bool _IsComplex>
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friend struct internal::svd_precondition_2x2_block_to_be_real;
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@ -2,6 +2,7 @@
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// for linear algebra.
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//
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// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
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// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>
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//
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// Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com>
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// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr>
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@ -12,8 +13,8 @@
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#ifndef EIGEN_SVD_H
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#define EIGEN_SVD_H
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#ifndef EIGEN_SVDBASE_H
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#define EIGEN_SVDBASE_H
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namespace Eigen {
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/** \ingroup SVD_Module
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@ -21,9 +22,10 @@ namespace Eigen {
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*
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* \class SVDBase
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*
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* \brief Mother class of SVD classes algorithms
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* \brief Base class of SVD algorithms
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*
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* \tparam Derived the type of the actual SVD decomposition
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*
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* \param MatrixType the type of the matrix of which we are computing the SVD decomposition
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* SVD decomposition consists in decomposing any n-by-p matrix \a A as a product
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* \f[ A = U S V^* \f]
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* where \a U is a n-by-n unitary, \a V is a p-by-p unitary, and \a S is a n-by-p real positive matrix which is zero outside of its main diagonal;
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@ -42,12 +44,12 @@ namespace Eigen {
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* terminate in finite (and reasonable) time.
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* \sa MatrixBase::genericSvd()
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*/
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template<typename _MatrixType>
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template<typename Derived>
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class SVDBase
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{
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public:
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typedef _MatrixType MatrixType;
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typedef typename internal::traits<Derived>::MatrixType MatrixType;
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typedef typename MatrixType::Scalar Scalar;
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typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
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typedef typename MatrixType::Index Index;
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@ -61,46 +63,16 @@ public:
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MatrixOptions = MatrixType::Options
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};
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typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime,
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MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime>
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MatrixUType;
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typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime,
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MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime>
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MatrixVType;
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typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime> MatrixUType;
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typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime, MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime> MatrixVType;
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typedef typename internal::plain_diag_type<MatrixType, RealScalar>::type SingularValuesType;
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typedef typename internal::plain_row_type<MatrixType>::type RowType;
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typedef typename internal::plain_col_type<MatrixType>::type ColType;
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typedef Matrix<Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime,
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MatrixOptions, MaxDiagSizeAtCompileTime, MaxDiagSizeAtCompileTime>
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WorkMatrixType;
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/** \brief Method performing the decomposition of given matrix using custom options.
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*
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* \param matrix the matrix to decompose
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* \param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed.
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* By default, none is computed. This is a bit-field, the possible bits are #ComputeFullU, #ComputeThinU,
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* #ComputeFullV, #ComputeThinV.
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*
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* Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not
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* available with the (non-default) FullPivHouseholderQR preconditioner.
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*/
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SVDBase& compute(const MatrixType& matrix, unsigned int computationOptions);
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/** \brief Method performing the decomposition of given matrix using current options.
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*
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* \param matrix the matrix to decompose
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*
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* This method uses the current \a computationOptions, as already passed to the constructor or to compute(const MatrixType&, unsigned int).
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*/
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//virtual SVDBase& compute(const MatrixType& matrix) = 0;
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SVDBase& compute(const MatrixType& matrix);
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Derived& derived() { return *static_cast<Derived*>(this); }
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const Derived& derived() const { return *static_cast<const Derived*>(this); }
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/** \returns the \a U matrix.
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*
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* For the SVDBase decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
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* For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
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* the U matrix is n-by-n if you asked for #ComputeFullU, and is n-by-m if you asked for #ComputeThinU.
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*
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* The \a m first columns of \a U are the left singular vectors of the matrix being decomposed.
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@ -141,26 +113,84 @@ public:
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return m_singularValues;
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}
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/** \returns the number of singular values that are not exactly 0 */
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Index nonzeroSingularValues() const
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{
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eigen_assert(m_isInitialized && "SVD is not initialized.");
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return m_nonzeroSingularValues;
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}
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/** \returns the rank of the matrix of which \c *this is the SVD.
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*
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* \note This method has to determine which singular values should be considered nonzero.
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* For that, it uses the threshold value that you can control by calling
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* setThreshold(const RealScalar&).
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*/
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inline Index rank() const
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{
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using std::abs;
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eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
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if(m_singularValues.size()==0) return 0;
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RealScalar premultiplied_threshold = m_singularValues.coeff(0) * threshold();
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Index i = m_nonzeroSingularValues-1;
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while(i>=0 && m_singularValues.coeff(i) < premultiplied_threshold) --i;
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return i+1;
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}
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/** Allows to prescribe a threshold to be used by certain methods, such as rank() and solve(),
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* which need to determine when singular values are to be considered nonzero.
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* This is not used for the SVD decomposition itself.
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*
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* When it needs to get the threshold value, Eigen calls threshold().
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* The default is \c NumTraits<Scalar>::epsilon()
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*
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* \param threshold The new value to use as the threshold.
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*
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* A singular value will be considered nonzero if its value is strictly greater than
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* \f$ \vert singular value \vert \leqslant threshold \times \vert max singular value \vert \f$.
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*
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* If you want to come back to the default behavior, call setThreshold(Default_t)
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*/
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Derived& setThreshold(const RealScalar& threshold)
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{
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m_usePrescribedThreshold = true;
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m_prescribedThreshold = threshold;
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return derived();
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}
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/** Allows to come back to the default behavior, letting Eigen use its default formula for
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* determining the threshold.
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*
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* You should pass the special object Eigen::Default as parameter here.
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* \code svd.setThreshold(Eigen::Default); \endcode
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*
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* See the documentation of setThreshold(const RealScalar&).
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*/
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Derived& setThreshold(Default_t)
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{
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m_usePrescribedThreshold = false;
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||||
return derived();
|
||||
}
|
||||
|
||||
/** Returns the threshold that will be used by certain methods such as rank().
|
||||
*
|
||||
* See the documentation of setThreshold(const RealScalar&).
|
||||
*/
|
||||
RealScalar threshold() const
|
||||
{
|
||||
eigen_assert(m_isInitialized || m_usePrescribedThreshold);
|
||||
return m_usePrescribedThreshold ? m_prescribedThreshold
|
||||
: (std::max<Index>)(1,m_diagSize)*NumTraits<Scalar>::epsilon();
|
||||
}
|
||||
|
||||
/** \returns true if \a U (full or thin) is asked for in this SVD decomposition */
|
||||
inline bool computeU() const { return m_computeFullU || m_computeThinU; }
|
||||
/** \returns true if \a V (full or thin) is asked for in this SVD decomposition */
|
||||
inline bool computeV() const { return m_computeFullV || m_computeThinV; }
|
||||
|
||||
|
||||
inline Index rows() const { return m_rows; }
|
||||
inline Index cols() const { return m_cols; }
|
||||
|
||||
|
||||
protected:
|
||||
// return true if already allocated
|
||||
bool allocate(Index rows, Index cols, unsigned int computationOptions) ;
|
||||
@ -168,12 +198,12 @@ protected:
|
||||
MatrixUType m_matrixU;
|
||||
MatrixVType m_matrixV;
|
||||
SingularValuesType m_singularValues;
|
||||
bool m_isInitialized, m_isAllocated;
|
||||
bool m_isInitialized, m_isAllocated, m_usePrescribedThreshold;
|
||||
bool m_computeFullU, m_computeThinU;
|
||||
bool m_computeFullV, m_computeThinV;
|
||||
unsigned int m_computationOptions;
|
||||
Index m_nonzeroSingularValues, m_rows, m_cols, m_diagSize;
|
||||
|
||||
RealScalar m_prescribedThreshold;
|
||||
|
||||
/** \brief Default Constructor.
|
||||
*
|
||||
@ -182,8 +212,9 @@ protected:
|
||||
SVDBase()
|
||||
: m_isInitialized(false),
|
||||
m_isAllocated(false),
|
||||
m_usePrescribedThreshold(false),
|
||||
m_computationOptions(0),
|
||||
m_rows(-1), m_cols(-1)
|
||||
m_rows(-1), m_cols(-1), m_diagSize(0)
|
||||
{}
|
||||
|
||||
|
||||
@ -220,17 +251,13 @@ bool SVDBase<MatrixType>::allocate(Index rows, Index cols, unsigned int computat
|
||||
m_diagSize = (std::min)(m_rows, m_cols);
|
||||
m_singularValues.resize(m_diagSize);
|
||||
if(RowsAtCompileTime==Dynamic)
|
||||
m_matrixU.resize(m_rows, m_computeFullU ? m_rows
|
||||
: m_computeThinU ? m_diagSize
|
||||
: 0);
|
||||
m_matrixU.resize(m_rows, m_computeFullU ? m_rows : m_computeThinU ? m_diagSize : 0);
|
||||
if(ColsAtCompileTime==Dynamic)
|
||||
m_matrixV.resize(m_cols, m_computeFullV ? m_cols
|
||||
: m_computeThinV ? m_diagSize
|
||||
: 0);
|
||||
m_matrixV.resize(m_cols, m_computeFullV ? m_cols : m_computeThinV ? m_diagSize : 0);
|
||||
|
||||
return false;
|
||||
}
|
||||
|
||||
}// end namespace
|
||||
|
||||
#endif // EIGEN_SVD_H
|
||||
#endif // EIGEN_SVDBASE_H
|
@ -2,6 +2,7 @@
|
||||
// for linear algebra.
|
||||
//
|
||||
// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
|
||||
// Copyright (C) 2013-2014 Gael Guennebaud <gael.guennebaud@inria.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
|
||||
|
26
unsupported/Eigen/BDCSVD
Normal file
26
unsupported/Eigen/BDCSVD
Normal file
@ -0,0 +1,26 @@
|
||||
#ifndef EIGEN_BDCSVD_MODULE_H
|
||||
#define EIGEN_BDCSVD_MODULE_H
|
||||
|
||||
#include <Eigen/SVD>
|
||||
|
||||
#include "../../Eigen/src/Core/util/DisableStupidWarnings.h"
|
||||
|
||||
/** \defgroup BDCSVD_Module BDCSVD module
|
||||
*
|
||||
*
|
||||
*
|
||||
* This module provides Divide & Conquer SVD decomposition for matrices (both real and complex).
|
||||
* This decomposition is accessible via the following MatrixBase method:
|
||||
* - MatrixBase::bdcSvd()
|
||||
*
|
||||
* \code
|
||||
* #include <Eigen/BDCSVD>
|
||||
* \endcode
|
||||
*/
|
||||
|
||||
#include "src/BDCSVD/BDCSVD.h"
|
||||
|
||||
#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h"
|
||||
|
||||
#endif // EIGEN_BDCSVD_MODULE_H
|
||||
/* vim: set filetype=cpp et sw=2 ts=2 ai: */
|
@ -1,35 +0,0 @@
|
||||
#ifndef EIGEN_SVD_MODULE_H
|
||||
#define EIGEN_SVD_MODULE_H
|
||||
|
||||
#include <Eigen/QR>
|
||||
#include <Eigen/Householder>
|
||||
#include <Eigen/Jacobi>
|
||||
|
||||
#include "../../Eigen/src/Core/util/DisableStupidWarnings.h"
|
||||
|
||||
/** \defgroup SVD_Module SVD module
|
||||
*
|
||||
*
|
||||
*
|
||||
* This module provides SVD decomposition for matrices (both real and complex).
|
||||
* This decomposition is accessible via the following MatrixBase method:
|
||||
* - MatrixBase::jacobiSvd()
|
||||
*
|
||||
* \code
|
||||
* #include <Eigen/SVD>
|
||||
* \endcode
|
||||
*/
|
||||
|
||||
#include "../../Eigen/src/misc/Solve.h"
|
||||
#include "../../Eigen/src/SVD/UpperBidiagonalization.h"
|
||||
#include "src/SVD/SVDBase.h"
|
||||
#include "src/SVD/JacobiSVD.h"
|
||||
#include "src/SVD/BDCSVD.h"
|
||||
#if defined(EIGEN_USE_LAPACKE) && !defined(EIGEN_USE_LAPACKE_STRICT)
|
||||
#include "../../Eigen/src/SVD/JacobiSVD_MKL.h"
|
||||
#endif
|
||||
|
||||
#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h"
|
||||
|
||||
#endif // EIGEN_SVD_MODULE_H
|
||||
/* vim: set filetype=cpp et sw=2 ts=2 ai: */
|
@ -24,6 +24,20 @@
|
||||
#define ALGOSWAP 16
|
||||
|
||||
namespace Eigen {
|
||||
|
||||
template<typename _MatrixType> class BDCSVD;
|
||||
|
||||
namespace internal {
|
||||
|
||||
template<typename _MatrixType>
|
||||
struct traits<BDCSVD<_MatrixType> >
|
||||
{
|
||||
typedef _MatrixType MatrixType;
|
||||
};
|
||||
|
||||
} // end namespace internal
|
||||
|
||||
|
||||
/** \ingroup SVD_Module
|
||||
*
|
||||
*
|
||||
@ -36,9 +50,9 @@ namespace Eigen {
|
||||
* It should be used to speed up the calcul of SVD for big matrices.
|
||||
*/
|
||||
template<typename _MatrixType>
|
||||
class BDCSVD : public SVDBase<_MatrixType>
|
||||
class BDCSVD : public SVDBase<BDCSVD<_MatrixType> >
|
||||
{
|
||||
typedef SVDBase<_MatrixType> Base;
|
||||
typedef SVDBase<BDCSVD> Base;
|
||||
|
||||
public:
|
||||
using Base::rows;
|
||||
@ -77,9 +91,7 @@ public:
|
||||
* The default constructor is useful in cases in which the user intends to
|
||||
* perform decompositions via BDCSVD::compute(const MatrixType&).
|
||||
*/
|
||||
BDCSVD()
|
||||
: SVDBase<_MatrixType>::SVDBase(),
|
||||
algoswap(ALGOSWAP), m_numIters(0)
|
||||
BDCSVD() : algoswap(ALGOSWAP), m_numIters(0)
|
||||
{}
|
||||
|
||||
|
||||
@ -90,8 +102,7 @@ public:
|
||||
* \sa BDCSVD()
|
||||
*/
|
||||
BDCSVD(Index rows, Index cols, unsigned int computationOptions = 0)
|
||||
: SVDBase<_MatrixType>::SVDBase(),
|
||||
algoswap(ALGOSWAP), m_numIters(0)
|
||||
: algoswap(ALGOSWAP), m_numIters(0)
|
||||
{
|
||||
allocate(rows, cols, computationOptions);
|
||||
}
|
||||
@ -107,8 +118,7 @@ public:
|
||||
* available with the (non - default) FullPivHouseholderQR preconditioner.
|
||||
*/
|
||||
BDCSVD(const MatrixType& matrix, unsigned int computationOptions = 0)
|
||||
: SVDBase<_MatrixType>::SVDBase(),
|
||||
algoswap(ALGOSWAP), m_numIters(0)
|
||||
: algoswap(ALGOSWAP), m_numIters(0)
|
||||
{
|
||||
compute(matrix, computationOptions);
|
||||
}
|
||||
@ -116,6 +126,7 @@ public:
|
||||
~BDCSVD()
|
||||
{
|
||||
}
|
||||
|
||||
/** \brief Method performing the decomposition of given matrix using custom options.
|
||||
*
|
||||
* \param matrix the matrix to decompose
|
||||
@ -126,7 +137,7 @@ public:
|
||||
* Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not
|
||||
* available with the (non - default) FullPivHouseholderQR preconditioner.
|
||||
*/
|
||||
SVDBase<MatrixType>& compute(const MatrixType& matrix, unsigned int computationOptions);
|
||||
BDCSVD& compute(const MatrixType& matrix, unsigned int computationOptions);
|
||||
|
||||
/** \brief Method performing the decomposition of given matrix using current options.
|
||||
*
|
||||
@ -134,7 +145,7 @@ public:
|
||||
*
|
||||
* This method uses the current \a computationOptions, as already passed to the constructor or to compute(const MatrixType&, unsigned int).
|
||||
*/
|
||||
SVDBase<MatrixType>& compute(const MatrixType& matrix)
|
||||
BDCSVD& compute(const MatrixType& matrix)
|
||||
{
|
||||
return compute(matrix, this->m_computationOptions);
|
||||
}
|
||||
@ -160,8 +171,8 @@ public:
|
||||
solve(const MatrixBase<Rhs>& b) const
|
||||
{
|
||||
eigen_assert(this->m_isInitialized && "BDCSVD is not initialized.");
|
||||
eigen_assert(SVDBase<_MatrixType>::computeU() && SVDBase<_MatrixType>::computeV() &&
|
||||
"BDCSVD::solve() requires both unitaries U and V to be computed (thin unitaries suffice).");
|
||||
eigen_assert(computeU() && computeV() &&
|
||||
"BDCSVD::solve() requires both unitaries U and V to be computed (thin unitaries suffice).");
|
||||
return internal::solve_retval<BDCSVD, Rhs>(*this, b.derived());
|
||||
}
|
||||
|
||||
@ -195,6 +206,9 @@ public:
|
||||
return this->m_matrixV;
|
||||
}
|
||||
}
|
||||
|
||||
using Base::computeU;
|
||||
using Base::computeV;
|
||||
|
||||
private:
|
||||
void allocate(Index rows, Index cols, unsigned int computationOptions);
|
||||
@ -229,7 +243,7 @@ template<typename MatrixType>
|
||||
void BDCSVD<MatrixType>::allocate(Index rows, Index cols, unsigned int computationOptions)
|
||||
{
|
||||
isTranspose = (cols > rows);
|
||||
if (SVDBase<MatrixType>::allocate(rows, cols, computationOptions)) return;
|
||||
if (Base::allocate(rows, cols, computationOptions)) return;
|
||||
m_computed = MatrixXr::Zero(this->m_diagSize + 1, this->m_diagSize );
|
||||
if (isTranspose){
|
||||
compU = this->computeU();
|
||||
@ -262,8 +276,7 @@ void BDCSVD<MatrixType>::allocate(Index rows, Index cols, unsigned int computati
|
||||
|
||||
// Methode which compute the BDCSVD for the int
|
||||
template<>
|
||||
SVDBase<Matrix<int, Dynamic, Dynamic> >&
|
||||
BDCSVD<Matrix<int, Dynamic, Dynamic> >::compute(const MatrixType& matrix, unsigned int computationOptions) {
|
||||
BDCSVD<Matrix<int, Dynamic, Dynamic> >& BDCSVD<Matrix<int, Dynamic, Dynamic> >::compute(const MatrixType& matrix, unsigned int computationOptions) {
|
||||
allocate(matrix.rows(), matrix.cols(), computationOptions);
|
||||
this->m_nonzeroSingularValues = 0;
|
||||
m_computed = Matrix<int, Dynamic, Dynamic>::Zero(rows(), cols());
|
||||
@ -279,8 +292,7 @@ BDCSVD<Matrix<int, Dynamic, Dynamic> >::compute(const MatrixType& matrix, unsign
|
||||
|
||||
// Methode which compute the BDCSVD
|
||||
template<typename MatrixType>
|
||||
SVDBase<MatrixType>&
|
||||
BDCSVD<MatrixType>::compute(const MatrixType& matrix, unsigned int computationOptions)
|
||||
BDCSVD<MatrixType>& BDCSVD<MatrixType>::compute(const MatrixType& matrix, unsigned int computationOptions)
|
||||
{
|
||||
allocate(matrix.rows(), matrix.cols(), computationOptions);
|
||||
using std::abs;
|
6
unsupported/Eigen/src/BDCSVD/CMakeLists.txt
Normal file
6
unsupported/Eigen/src/BDCSVD/CMakeLists.txt
Normal file
@ -0,0 +1,6 @@
|
||||
FILE(GLOB Eigen_BDCSVD_SRCS "*.h")
|
||||
|
||||
INSTALL(FILES
|
||||
${Eigen_BDCSVD_SRCS}
|
||||
DESTINATION ${INCLUDE_INSTALL_DIR}unsupported/Eigen/src/BDCSVD COMPONENT Devel
|
||||
)
|
@ -12,3 +12,4 @@ ADD_SUBDIRECTORY(Skyline)
|
||||
ADD_SUBDIRECTORY(SparseExtra)
|
||||
ADD_SUBDIRECTORY(KroneckerProduct)
|
||||
ADD_SUBDIRECTORY(Splines)
|
||||
ADD_SUBDIRECTORY(BDCSVD)
|
||||
|
@ -1,6 +0,0 @@
|
||||
FILE(GLOB Eigen_SVD_SRCS "*.h")
|
||||
|
||||
INSTALL(FILES
|
||||
${Eigen_SVD_SRCS}
|
||||
DESTINATION ${INCLUDE_INSTALL_DIR}unsupported/Eigen/src/SVD COMPONENT Devel
|
||||
)
|
@ -1,782 +0,0 @@
|
||||
// This file is part of Eigen, a lightweight C++ template library
|
||||
// for linear algebra.
|
||||
//
|
||||
// Copyright (C) 2009-2010 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 EIGEN_JACOBISVD_H
|
||||
#define EIGEN_JACOBISVD_H
|
||||
|
||||
namespace Eigen {
|
||||
|
||||
namespace internal {
|
||||
// forward declaration (needed by ICC)
|
||||
// the empty body is required by MSVC
|
||||
template<typename MatrixType, int QRPreconditioner,
|
||||
bool IsComplex = NumTraits<typename MatrixType::Scalar>::IsComplex>
|
||||
struct svd_precondition_2x2_block_to_be_real {};
|
||||
|
||||
/*** QR preconditioners (R-SVD)
|
||||
***
|
||||
*** Their role is to reduce the problem of computing the SVD to the case of a square matrix.
|
||||
*** This approach, known as R-SVD, is an optimization for rectangular-enough matrices, and is a requirement for
|
||||
*** JacobiSVD which by itself is only able to work on square matrices.
|
||||
***/
|
||||
|
||||
enum { PreconditionIfMoreColsThanRows, PreconditionIfMoreRowsThanCols };
|
||||
|
||||
template<typename MatrixType, int QRPreconditioner, int Case>
|
||||
struct qr_preconditioner_should_do_anything
|
||||
{
|
||||
enum { a = MatrixType::RowsAtCompileTime != Dynamic &&
|
||||
MatrixType::ColsAtCompileTime != Dynamic &&
|
||||
MatrixType::ColsAtCompileTime <= MatrixType::RowsAtCompileTime,
|
||||
b = MatrixType::RowsAtCompileTime != Dynamic &&
|
||||
MatrixType::ColsAtCompileTime != Dynamic &&
|
||||
MatrixType::RowsAtCompileTime <= MatrixType::ColsAtCompileTime,
|
||||
ret = !( (QRPreconditioner == NoQRPreconditioner) ||
|
||||
(Case == PreconditionIfMoreColsThanRows && bool(a)) ||
|
||||
(Case == PreconditionIfMoreRowsThanCols && bool(b)) )
|
||||
};
|
||||
};
|
||||
|
||||
template<typename MatrixType, int QRPreconditioner, int Case,
|
||||
bool DoAnything = qr_preconditioner_should_do_anything<MatrixType, QRPreconditioner, Case>::ret
|
||||
> struct qr_preconditioner_impl {};
|
||||
|
||||
template<typename MatrixType, int QRPreconditioner, int Case>
|
||||
class qr_preconditioner_impl<MatrixType, QRPreconditioner, Case, false>
|
||||
{
|
||||
public:
|
||||
typedef typename MatrixType::Index Index;
|
||||
void allocate(const JacobiSVD<MatrixType, QRPreconditioner>&) {}
|
||||
bool run(JacobiSVD<MatrixType, QRPreconditioner>&, const MatrixType&)
|
||||
{
|
||||
return false;
|
||||
}
|
||||
};
|
||||
|
||||
/*** preconditioner using FullPivHouseholderQR ***/
|
||||
|
||||
template<typename MatrixType>
|
||||
class qr_preconditioner_impl<MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true>
|
||||
{
|
||||
public:
|
||||
typedef typename MatrixType::Index Index;
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
enum
|
||||
{
|
||||
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
||||
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime
|
||||
};
|
||||
typedef Matrix<Scalar, 1, RowsAtCompileTime, RowMajor, 1, MaxRowsAtCompileTime> WorkspaceType;
|
||||
|
||||
void allocate(const JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd)
|
||||
{
|
||||
if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())
|
||||
{
|
||||
m_qr.~QRType();
|
||||
::new (&m_qr) QRType(svd.rows(), svd.cols());
|
||||
}
|
||||
if (svd.m_computeFullU) m_workspace.resize(svd.rows());
|
||||
}
|
||||
|
||||
bool run(JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)
|
||||
{
|
||||
if(matrix.rows() > matrix.cols())
|
||||
{
|
||||
m_qr.compute(matrix);
|
||||
svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView<Upper>();
|
||||
if(svd.m_computeFullU) m_qr.matrixQ().evalTo(svd.m_matrixU, m_workspace);
|
||||
if(svd.computeV()) svd.m_matrixV = m_qr.colsPermutation();
|
||||
return true;
|
||||
}
|
||||
return false;
|
||||
}
|
||||
private:
|
||||
typedef FullPivHouseholderQR<MatrixType> QRType;
|
||||
QRType m_qr;
|
||||
WorkspaceType m_workspace;
|
||||
};
|
||||
|
||||
template<typename MatrixType>
|
||||
class qr_preconditioner_impl<MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true>
|
||||
{
|
||||
public:
|
||||
typedef typename MatrixType::Index Index;
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
enum
|
||||
{
|
||||
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
||||
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
|
||||
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
|
||||
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
|
||||
Options = MatrixType::Options
|
||||
};
|
||||
typedef Matrix<Scalar, ColsAtCompileTime, RowsAtCompileTime, Options, MaxColsAtCompileTime, MaxRowsAtCompileTime>
|
||||
TransposeTypeWithSameStorageOrder;
|
||||
|
||||
void allocate(const JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd)
|
||||
{
|
||||
if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())
|
||||
{
|
||||
m_qr.~QRType();
|
||||
::new (&m_qr) QRType(svd.cols(), svd.rows());
|
||||
}
|
||||
m_adjoint.resize(svd.cols(), svd.rows());
|
||||
if (svd.m_computeFullV) m_workspace.resize(svd.cols());
|
||||
}
|
||||
|
||||
bool run(JacobiSVD<MatrixType, FullPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)
|
||||
{
|
||||
if(matrix.cols() > matrix.rows())
|
||||
{
|
||||
m_adjoint = matrix.adjoint();
|
||||
m_qr.compute(m_adjoint);
|
||||
svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();
|
||||
if(svd.m_computeFullV) m_qr.matrixQ().evalTo(svd.m_matrixV, m_workspace);
|
||||
if(svd.computeU()) svd.m_matrixU = m_qr.colsPermutation();
|
||||
return true;
|
||||
}
|
||||
else return false;
|
||||
}
|
||||
private:
|
||||
typedef FullPivHouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
|
||||
QRType m_qr;
|
||||
TransposeTypeWithSameStorageOrder m_adjoint;
|
||||
typename internal::plain_row_type<MatrixType>::type m_workspace;
|
||||
};
|
||||
|
||||
/*** preconditioner using ColPivHouseholderQR ***/
|
||||
|
||||
template<typename MatrixType>
|
||||
class qr_preconditioner_impl<MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true>
|
||||
{
|
||||
public:
|
||||
typedef typename MatrixType::Index Index;
|
||||
|
||||
void allocate(const JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd)
|
||||
{
|
||||
if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())
|
||||
{
|
||||
m_qr.~QRType();
|
||||
::new (&m_qr) QRType(svd.rows(), svd.cols());
|
||||
}
|
||||
if (svd.m_computeFullU) m_workspace.resize(svd.rows());
|
||||
else if (svd.m_computeThinU) m_workspace.resize(svd.cols());
|
||||
}
|
||||
|
||||
bool run(JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)
|
||||
{
|
||||
if(matrix.rows() > matrix.cols())
|
||||
{
|
||||
m_qr.compute(matrix);
|
||||
svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView<Upper>();
|
||||
if(svd.m_computeFullU) m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace);
|
||||
else if(svd.m_computeThinU)
|
||||
{
|
||||
svd.m_matrixU.setIdentity(matrix.rows(), matrix.cols());
|
||||
m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixU, m_workspace);
|
||||
}
|
||||
if(svd.computeV()) svd.m_matrixV = m_qr.colsPermutation();
|
||||
return true;
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
||||
private:
|
||||
typedef ColPivHouseholderQR<MatrixType> QRType;
|
||||
QRType m_qr;
|
||||
typename internal::plain_col_type<MatrixType>::type m_workspace;
|
||||
};
|
||||
|
||||
template<typename MatrixType>
|
||||
class qr_preconditioner_impl<MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true>
|
||||
{
|
||||
public:
|
||||
typedef typename MatrixType::Index Index;
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
enum
|
||||
{
|
||||
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
||||
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
|
||||
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
|
||||
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
|
||||
Options = MatrixType::Options
|
||||
};
|
||||
|
||||
typedef Matrix<Scalar, ColsAtCompileTime, RowsAtCompileTime, Options, MaxColsAtCompileTime, MaxRowsAtCompileTime>
|
||||
TransposeTypeWithSameStorageOrder;
|
||||
|
||||
void allocate(const JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd)
|
||||
{
|
||||
if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())
|
||||
{
|
||||
m_qr.~QRType();
|
||||
::new (&m_qr) QRType(svd.cols(), svd.rows());
|
||||
}
|
||||
if (svd.m_computeFullV) m_workspace.resize(svd.cols());
|
||||
else if (svd.m_computeThinV) m_workspace.resize(svd.rows());
|
||||
m_adjoint.resize(svd.cols(), svd.rows());
|
||||
}
|
||||
|
||||
bool run(JacobiSVD<MatrixType, ColPivHouseholderQRPreconditioner>& svd, const MatrixType& matrix)
|
||||
{
|
||||
if(matrix.cols() > matrix.rows())
|
||||
{
|
||||
m_adjoint = matrix.adjoint();
|
||||
m_qr.compute(m_adjoint);
|
||||
|
||||
svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();
|
||||
if(svd.m_computeFullV) m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace);
|
||||
else if(svd.m_computeThinV)
|
||||
{
|
||||
svd.m_matrixV.setIdentity(matrix.cols(), matrix.rows());
|
||||
m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixV, m_workspace);
|
||||
}
|
||||
if(svd.computeU()) svd.m_matrixU = m_qr.colsPermutation();
|
||||
return true;
|
||||
}
|
||||
else return false;
|
||||
}
|
||||
|
||||
private:
|
||||
typedef ColPivHouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
|
||||
QRType m_qr;
|
||||
TransposeTypeWithSameStorageOrder m_adjoint;
|
||||
typename internal::plain_row_type<MatrixType>::type m_workspace;
|
||||
};
|
||||
|
||||
/*** preconditioner using HouseholderQR ***/
|
||||
|
||||
template<typename MatrixType>
|
||||
class qr_preconditioner_impl<MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true>
|
||||
{
|
||||
public:
|
||||
typedef typename MatrixType::Index Index;
|
||||
|
||||
void allocate(const JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd)
|
||||
{
|
||||
if (svd.rows() != m_qr.rows() || svd.cols() != m_qr.cols())
|
||||
{
|
||||
m_qr.~QRType();
|
||||
::new (&m_qr) QRType(svd.rows(), svd.cols());
|
||||
}
|
||||
if (svd.m_computeFullU) m_workspace.resize(svd.rows());
|
||||
else if (svd.m_computeThinU) m_workspace.resize(svd.cols());
|
||||
}
|
||||
|
||||
bool run(JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd, const MatrixType& matrix)
|
||||
{
|
||||
if(matrix.rows() > matrix.cols())
|
||||
{
|
||||
m_qr.compute(matrix);
|
||||
svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.cols(),matrix.cols()).template triangularView<Upper>();
|
||||
if(svd.m_computeFullU) m_qr.householderQ().evalTo(svd.m_matrixU, m_workspace);
|
||||
else if(svd.m_computeThinU)
|
||||
{
|
||||
svd.m_matrixU.setIdentity(matrix.rows(), matrix.cols());
|
||||
m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixU, m_workspace);
|
||||
}
|
||||
if(svd.computeV()) svd.m_matrixV.setIdentity(matrix.cols(), matrix.cols());
|
||||
return true;
|
||||
}
|
||||
return false;
|
||||
}
|
||||
private:
|
||||
typedef HouseholderQR<MatrixType> QRType;
|
||||
QRType m_qr;
|
||||
typename internal::plain_col_type<MatrixType>::type m_workspace;
|
||||
};
|
||||
|
||||
template<typename MatrixType>
|
||||
class qr_preconditioner_impl<MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true>
|
||||
{
|
||||
public:
|
||||
typedef typename MatrixType::Index Index;
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
enum
|
||||
{
|
||||
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
||||
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
|
||||
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
|
||||
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
|
||||
Options = MatrixType::Options
|
||||
};
|
||||
|
||||
typedef Matrix<Scalar, ColsAtCompileTime, RowsAtCompileTime, Options, MaxColsAtCompileTime, MaxRowsAtCompileTime>
|
||||
TransposeTypeWithSameStorageOrder;
|
||||
|
||||
void allocate(const JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd)
|
||||
{
|
||||
if (svd.cols() != m_qr.rows() || svd.rows() != m_qr.cols())
|
||||
{
|
||||
m_qr.~QRType();
|
||||
::new (&m_qr) QRType(svd.cols(), svd.rows());
|
||||
}
|
||||
if (svd.m_computeFullV) m_workspace.resize(svd.cols());
|
||||
else if (svd.m_computeThinV) m_workspace.resize(svd.rows());
|
||||
m_adjoint.resize(svd.cols(), svd.rows());
|
||||
}
|
||||
|
||||
bool run(JacobiSVD<MatrixType, HouseholderQRPreconditioner>& svd, const MatrixType& matrix)
|
||||
{
|
||||
if(matrix.cols() > matrix.rows())
|
||||
{
|
||||
m_adjoint = matrix.adjoint();
|
||||
m_qr.compute(m_adjoint);
|
||||
|
||||
svd.m_workMatrix = m_qr.matrixQR().block(0,0,matrix.rows(),matrix.rows()).template triangularView<Upper>().adjoint();
|
||||
if(svd.m_computeFullV) m_qr.householderQ().evalTo(svd.m_matrixV, m_workspace);
|
||||
else if(svd.m_computeThinV)
|
||||
{
|
||||
svd.m_matrixV.setIdentity(matrix.cols(), matrix.rows());
|
||||
m_qr.householderQ().applyThisOnTheLeft(svd.m_matrixV, m_workspace);
|
||||
}
|
||||
if(svd.computeU()) svd.m_matrixU.setIdentity(matrix.rows(), matrix.rows());
|
||||
return true;
|
||||
}
|
||||
else return false;
|
||||
}
|
||||
|
||||
private:
|
||||
typedef HouseholderQR<TransposeTypeWithSameStorageOrder> QRType;
|
||||
QRType m_qr;
|
||||
TransposeTypeWithSameStorageOrder m_adjoint;
|
||||
typename internal::plain_row_type<MatrixType>::type m_workspace;
|
||||
};
|
||||
|
||||
/*** 2x2 SVD implementation
|
||||
***
|
||||
*** JacobiSVD consists in performing a series of 2x2 SVD subproblems
|
||||
***/
|
||||
|
||||
template<typename MatrixType, int QRPreconditioner>
|
||||
struct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, false>
|
||||
{
|
||||
typedef JacobiSVD<MatrixType, QRPreconditioner> SVD;
|
||||
typedef typename SVD::Index Index;
|
||||
static void run(typename SVD::WorkMatrixType&, SVD&, Index, Index) {}
|
||||
};
|
||||
|
||||
template<typename MatrixType, int QRPreconditioner>
|
||||
struct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, true>
|
||||
{
|
||||
typedef JacobiSVD<MatrixType, QRPreconditioner> SVD;
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename MatrixType::RealScalar RealScalar;
|
||||
typedef typename SVD::Index Index;
|
||||
static void run(typename SVD::WorkMatrixType& work_matrix, SVD& svd, Index p, Index q)
|
||||
{
|
||||
using std::sqrt;
|
||||
Scalar z;
|
||||
JacobiRotation<Scalar> rot;
|
||||
RealScalar n = sqrt(numext::abs2(work_matrix.coeff(p,p)) + numext::abs2(work_matrix.coeff(q,p)));
|
||||
if(n==0)
|
||||
{
|
||||
z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
|
||||
work_matrix.row(p) *= z;
|
||||
if(svd.computeU()) svd.m_matrixU.col(p) *= conj(z);
|
||||
z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
|
||||
work_matrix.row(q) *= z;
|
||||
if(svd.computeU()) svd.m_matrixU.col(q) *= conj(z);
|
||||
}
|
||||
else
|
||||
{
|
||||
rot.c() = conj(work_matrix.coeff(p,p)) / n;
|
||||
rot.s() = work_matrix.coeff(q,p) / n;
|
||||
work_matrix.applyOnTheLeft(p,q,rot);
|
||||
if(svd.computeU()) svd.m_matrixU.applyOnTheRight(p,q,rot.adjoint());
|
||||
if(work_matrix.coeff(p,q) != Scalar(0))
|
||||
{
|
||||
Scalar z = abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
|
||||
work_matrix.col(q) *= z;
|
||||
if(svd.computeV()) svd.m_matrixV.col(q) *= z;
|
||||
}
|
||||
if(work_matrix.coeff(q,q) != Scalar(0))
|
||||
{
|
||||
z = abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
|
||||
work_matrix.row(q) *= z;
|
||||
if(svd.computeU()) svd.m_matrixU.col(q) *= conj(z);
|
||||
}
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
template<typename MatrixType, typename RealScalar, typename Index>
|
||||
void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
|
||||
JacobiRotation<RealScalar> *j_left,
|
||||
JacobiRotation<RealScalar> *j_right)
|
||||
{
|
||||
using std::sqrt;
|
||||
Matrix<RealScalar,2,2> m;
|
||||
m << numext::real(matrix.coeff(p,p)), numext::real(matrix.coeff(p,q)),
|
||||
numext::real(matrix.coeff(q,p)), numext::real(matrix.coeff(q,q));
|
||||
JacobiRotation<RealScalar> rot1;
|
||||
RealScalar t = m.coeff(0,0) + m.coeff(1,1);
|
||||
RealScalar d = m.coeff(1,0) - m.coeff(0,1);
|
||||
if(t == RealScalar(0))
|
||||
{
|
||||
rot1.c() = RealScalar(0);
|
||||
rot1.s() = d > RealScalar(0) ? RealScalar(1) : RealScalar(-1);
|
||||
}
|
||||
else
|
||||
{
|
||||
RealScalar u = d / t;
|
||||
rot1.c() = RealScalar(1) / sqrt(RealScalar(1) + numext::abs2(u));
|
||||
rot1.s() = rot1.c() * u;
|
||||
}
|
||||
m.applyOnTheLeft(0,1,rot1);
|
||||
j_right->makeJacobi(m,0,1);
|
||||
*j_left = rot1 * j_right->transpose();
|
||||
}
|
||||
|
||||
} // end namespace internal
|
||||
|
||||
/** \ingroup SVD_Module
|
||||
*
|
||||
*
|
||||
* \class JacobiSVD
|
||||
*
|
||||
* \brief Two-sided Jacobi SVD decomposition of a rectangular matrix
|
||||
*
|
||||
* \param MatrixType the type of the matrix of which we are computing the SVD decomposition
|
||||
* \param QRPreconditioner this optional parameter allows to specify the type of QR decomposition that will be used internally
|
||||
* for the R-SVD step for non-square matrices. See discussion of possible values below.
|
||||
*
|
||||
* SVD decomposition consists in decomposing any n-by-p matrix \a A as a product
|
||||
* \f[ A = U S V^* \f]
|
||||
* where \a U is a n-by-n unitary, \a V is a p-by-p unitary, and \a S is a n-by-p real positive matrix which is zero outside of its main diagonal;
|
||||
* the diagonal entries of S are known as the \em singular \em values of \a A and the columns of \a U and \a V are known as the left
|
||||
* and right \em singular \em vectors of \a A respectively.
|
||||
*
|
||||
* Singular values are always sorted in decreasing order.
|
||||
*
|
||||
* This JacobiSVD decomposition computes only the singular values by default. If you want \a U or \a V, you need to ask for them explicitly.
|
||||
*
|
||||
* You can ask for only \em thin \a U or \a V to be computed, meaning the following. In case of a rectangular n-by-p matrix, letting \a m be the
|
||||
* smaller value among \a n and \a p, there are only \a m singular vectors; the remaining columns of \a U and \a V do not correspond to actual
|
||||
* singular vectors. Asking for \em thin \a U or \a V means asking for only their \a m first columns to be formed. So \a U is then a n-by-m matrix,
|
||||
* and \a V is then a p-by-m matrix. Notice that thin \a U and \a V are all you need for (least squares) solving.
|
||||
*
|
||||
* Here's an example demonstrating basic usage:
|
||||
* \include JacobiSVD_basic.cpp
|
||||
* Output: \verbinclude JacobiSVD_basic.out
|
||||
*
|
||||
* This JacobiSVD class is a two-sided Jacobi R-SVD decomposition, ensuring optimal reliability and accuracy. The downside is that it's slower than
|
||||
* bidiagonalizing SVD algorithms for large square matrices; however its complexity is still \f$ O(n^2p) \f$ where \a n is the smaller dimension and
|
||||
* \a p is the greater dimension, meaning that it is still of the same order of complexity as the faster bidiagonalizing R-SVD algorithms.
|
||||
* In particular, like any R-SVD, it takes advantage of non-squareness in that its complexity is only linear in the greater dimension.
|
||||
*
|
||||
* If the input matrix has inf or nan coefficients, the result of the computation is undefined, but the computation is guaranteed to
|
||||
* terminate in finite (and reasonable) time.
|
||||
*
|
||||
* The possible values for QRPreconditioner are:
|
||||
* \li ColPivHouseholderQRPreconditioner is the default. In practice it's very safe. It uses column-pivoting QR.
|
||||
* \li FullPivHouseholderQRPreconditioner, is the safest and slowest. It uses full-pivoting QR.
|
||||
* Contrary to other QRs, it doesn't allow computing thin unitaries.
|
||||
* \li HouseholderQRPreconditioner is the fastest, and less safe and accurate than the pivoting variants. It uses non-pivoting QR.
|
||||
* This is very similar in safety and accuracy to the bidiagonalization process used by bidiagonalizing SVD algorithms (since bidiagonalization
|
||||
* is inherently non-pivoting). However the resulting SVD is still more reliable than bidiagonalizing SVDs because the Jacobi-based iterarive
|
||||
* process is more reliable than the optimized bidiagonal SVD iterations.
|
||||
* \li NoQRPreconditioner allows not to use a QR preconditioner at all. This is useful if you know that you will only be computing
|
||||
* JacobiSVD decompositions of square matrices. Non-square matrices require a QR preconditioner. Using this option will result in
|
||||
* faster compilation and smaller executable code. It won't significantly speed up computation, since JacobiSVD is always checking
|
||||
* if QR preconditioning is needed before applying it anyway.
|
||||
*
|
||||
* \sa MatrixBase::jacobiSvd()
|
||||
*/
|
||||
template<typename _MatrixType, int QRPreconditioner>
|
||||
class JacobiSVD : public SVDBase<_MatrixType>
|
||||
{
|
||||
public:
|
||||
|
||||
typedef _MatrixType MatrixType;
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
|
||||
typedef typename MatrixType::Index Index;
|
||||
enum {
|
||||
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
||||
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
|
||||
DiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime),
|
||||
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
|
||||
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
|
||||
MaxDiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(MaxRowsAtCompileTime,MaxColsAtCompileTime),
|
||||
MatrixOptions = MatrixType::Options
|
||||
};
|
||||
|
||||
typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime,
|
||||
MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime>
|
||||
MatrixUType;
|
||||
typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime,
|
||||
MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime>
|
||||
MatrixVType;
|
||||
typedef typename internal::plain_diag_type<MatrixType, RealScalar>::type SingularValuesType;
|
||||
typedef typename internal::plain_row_type<MatrixType>::type RowType;
|
||||
typedef typename internal::plain_col_type<MatrixType>::type ColType;
|
||||
typedef Matrix<Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime,
|
||||
MatrixOptions, MaxDiagSizeAtCompileTime, MaxDiagSizeAtCompileTime>
|
||||
WorkMatrixType;
|
||||
|
||||
/** \brief Default Constructor.
|
||||
*
|
||||
* The default constructor is useful in cases in which the user intends to
|
||||
* perform decompositions via JacobiSVD::compute(const MatrixType&).
|
||||
*/
|
||||
JacobiSVD()
|
||||
: SVDBase<_MatrixType>::SVDBase()
|
||||
{}
|
||||
|
||||
|
||||
/** \brief Default Constructor with memory preallocation
|
||||
*
|
||||
* Like the default constructor but with preallocation of the internal data
|
||||
* according to the specified problem size.
|
||||
* \sa JacobiSVD()
|
||||
*/
|
||||
JacobiSVD(Index rows, Index cols, unsigned int computationOptions = 0)
|
||||
: SVDBase<_MatrixType>::SVDBase()
|
||||
{
|
||||
allocate(rows, cols, computationOptions);
|
||||
}
|
||||
|
||||
/** \brief Constructor performing the decomposition of given matrix.
|
||||
*
|
||||
* \param matrix the matrix to decompose
|
||||
* \param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed.
|
||||
* By default, none is computed. This is a bit-field, the possible bits are #ComputeFullU, #ComputeThinU,
|
||||
* #ComputeFullV, #ComputeThinV.
|
||||
*
|
||||
* Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not
|
||||
* available with the (non-default) FullPivHouseholderQR preconditioner.
|
||||
*/
|
||||
JacobiSVD(const MatrixType& matrix, unsigned int computationOptions = 0)
|
||||
: SVDBase<_MatrixType>::SVDBase()
|
||||
{
|
||||
compute(matrix, computationOptions);
|
||||
}
|
||||
|
||||
/** \brief Method performing the decomposition of given matrix using custom options.
|
||||
*
|
||||
* \param matrix the matrix to decompose
|
||||
* \param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed.
|
||||
* By default, none is computed. This is a bit-field, the possible bits are #ComputeFullU, #ComputeThinU,
|
||||
* #ComputeFullV, #ComputeThinV.
|
||||
*
|
||||
* Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not
|
||||
* available with the (non-default) FullPivHouseholderQR preconditioner.
|
||||
*/
|
||||
SVDBase<MatrixType>& compute(const MatrixType& matrix, unsigned int computationOptions);
|
||||
|
||||
/** \brief Method performing the decomposition of given matrix using current options.
|
||||
*
|
||||
* \param matrix the matrix to decompose
|
||||
*
|
||||
* This method uses the current \a computationOptions, as already passed to the constructor or to compute(const MatrixType&, unsigned int).
|
||||
*/
|
||||
SVDBase<MatrixType>& compute(const MatrixType& matrix)
|
||||
{
|
||||
return compute(matrix, this->m_computationOptions);
|
||||
}
|
||||
|
||||
/** \returns a (least squares) solution of \f$ A x = b \f$ using the current SVD decomposition of A.
|
||||
*
|
||||
* \param b the right-hand-side of the equation to solve.
|
||||
*
|
||||
* \note Solving requires both U and V to be computed. Thin U and V are enough, there is no need for full U or V.
|
||||
*
|
||||
* \note SVD solving is implicitly least-squares. Thus, this method serves both purposes of exact solving and least-squares solving.
|
||||
* In other words, the returned solution is guaranteed to minimize the Euclidean norm \f$ \Vert A x - b \Vert \f$.
|
||||
*/
|
||||
template<typename Rhs>
|
||||
inline const internal::solve_retval<JacobiSVD, Rhs>
|
||||
solve(const MatrixBase<Rhs>& b) const
|
||||
{
|
||||
eigen_assert(this->m_isInitialized && "JacobiSVD is not initialized.");
|
||||
eigen_assert(SVDBase<MatrixType>::computeU() && SVDBase<MatrixType>::computeV() && "JacobiSVD::solve() requires both unitaries U and V to be computed (thin unitaries suffice).");
|
||||
return internal::solve_retval<JacobiSVD, Rhs>(*this, b.derived());
|
||||
}
|
||||
|
||||
|
||||
|
||||
private:
|
||||
void allocate(Index rows, Index cols, unsigned int computationOptions);
|
||||
|
||||
protected:
|
||||
WorkMatrixType m_workMatrix;
|
||||
|
||||
template<typename __MatrixType, int _QRPreconditioner, bool _IsComplex>
|
||||
friend struct internal::svd_precondition_2x2_block_to_be_real;
|
||||
template<typename __MatrixType, int _QRPreconditioner, int _Case, bool _DoAnything>
|
||||
friend struct internal::qr_preconditioner_impl;
|
||||
|
||||
internal::qr_preconditioner_impl<MatrixType, QRPreconditioner, internal::PreconditionIfMoreColsThanRows> m_qr_precond_morecols;
|
||||
internal::qr_preconditioner_impl<MatrixType, QRPreconditioner, internal::PreconditionIfMoreRowsThanCols> m_qr_precond_morerows;
|
||||
};
|
||||
|
||||
template<typename MatrixType, int QRPreconditioner>
|
||||
void JacobiSVD<MatrixType, QRPreconditioner>::allocate(Index rows, Index cols, unsigned int computationOptions)
|
||||
{
|
||||
if (SVDBase<MatrixType>::allocate(rows, cols, computationOptions)) return;
|
||||
|
||||
if (QRPreconditioner == FullPivHouseholderQRPreconditioner)
|
||||
{
|
||||
eigen_assert(!(this->m_computeThinU || this->m_computeThinV) &&
|
||||
"JacobiSVD: can't compute thin U or thin V with the FullPivHouseholderQR preconditioner. "
|
||||
"Use the ColPivHouseholderQR preconditioner instead.");
|
||||
}
|
||||
|
||||
m_workMatrix.resize(this->m_diagSize, this->m_diagSize);
|
||||
|
||||
if(this->m_cols>this->m_rows) m_qr_precond_morecols.allocate(*this);
|
||||
if(this->m_rows>this->m_cols) m_qr_precond_morerows.allocate(*this);
|
||||
}
|
||||
|
||||
template<typename MatrixType, int QRPreconditioner>
|
||||
SVDBase<MatrixType>&
|
||||
JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsigned int computationOptions)
|
||||
{
|
||||
using std::abs;
|
||||
allocate(matrix.rows(), matrix.cols(), computationOptions);
|
||||
|
||||
// currently we stop when we reach precision 2*epsilon as the last bit of precision can require an unreasonable number of iterations,
|
||||
// only worsening the precision of U and V as we accumulate more rotations
|
||||
const RealScalar precision = RealScalar(2) * NumTraits<Scalar>::epsilon();
|
||||
|
||||
// limit for very small denormal numbers to be considered zero in order to avoid infinite loops (see bug 286)
|
||||
const RealScalar considerAsZero = RealScalar(2) * std::numeric_limits<RealScalar>::denorm_min();
|
||||
|
||||
/*** step 1. The R-SVD step: we use a QR decomposition to reduce to the case of a square matrix */
|
||||
|
||||
if(!m_qr_precond_morecols.run(*this, matrix) && !m_qr_precond_morerows.run(*this, matrix))
|
||||
{
|
||||
m_workMatrix = matrix.block(0,0,this->m_diagSize,this->m_diagSize);
|
||||
if(this->m_computeFullU) this->m_matrixU.setIdentity(this->m_rows,this->m_rows);
|
||||
if(this->m_computeThinU) this->m_matrixU.setIdentity(this->m_rows,this->m_diagSize);
|
||||
if(this->m_computeFullV) this->m_matrixV.setIdentity(this->m_cols,this->m_cols);
|
||||
if(this->m_computeThinV) this->m_matrixV.setIdentity(this->m_cols, this->m_diagSize);
|
||||
}
|
||||
|
||||
/*** step 2. The main Jacobi SVD iteration. ***/
|
||||
|
||||
bool finished = false;
|
||||
while(!finished)
|
||||
{
|
||||
finished = true;
|
||||
|
||||
// do a sweep: for all index pairs (p,q), perform SVD of the corresponding 2x2 sub-matrix
|
||||
|
||||
for(Index p = 1; p < this->m_diagSize; ++p)
|
||||
{
|
||||
for(Index q = 0; q < p; ++q)
|
||||
{
|
||||
// if this 2x2 sub-matrix is not diagonal already...
|
||||
// notice that this comparison will evaluate to false if any NaN is involved, ensuring that NaN's don't
|
||||
// keep us iterating forever. Similarly, small denormal numbers are considered zero.
|
||||
using std::max;
|
||||
RealScalar threshold = (max)(considerAsZero, precision * (max)(abs(m_workMatrix.coeff(p,p)),
|
||||
abs(m_workMatrix.coeff(q,q))));
|
||||
if((max)(abs(m_workMatrix.coeff(p,q)),abs(m_workMatrix.coeff(q,p))) > threshold)
|
||||
{
|
||||
finished = false;
|
||||
|
||||
// perform SVD decomposition of 2x2 sub-matrix corresponding to indices p,q to make it diagonal
|
||||
internal::svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner>::run(m_workMatrix, *this, p, q);
|
||||
JacobiRotation<RealScalar> j_left, j_right;
|
||||
internal::real_2x2_jacobi_svd(m_workMatrix, p, q, &j_left, &j_right);
|
||||
|
||||
// accumulate resulting Jacobi rotations
|
||||
m_workMatrix.applyOnTheLeft(p,q,j_left);
|
||||
if(SVDBase<MatrixType>::computeU()) this->m_matrixU.applyOnTheRight(p,q,j_left.transpose());
|
||||
|
||||
m_workMatrix.applyOnTheRight(p,q,j_right);
|
||||
if(SVDBase<MatrixType>::computeV()) this->m_matrixV.applyOnTheRight(p,q,j_right);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/*** step 3. The work matrix is now diagonal, so ensure it's positive so its diagonal entries are the singular values ***/
|
||||
|
||||
for(Index i = 0; i < this->m_diagSize; ++i)
|
||||
{
|
||||
RealScalar a = abs(m_workMatrix.coeff(i,i));
|
||||
this->m_singularValues.coeffRef(i) = a;
|
||||
if(SVDBase<MatrixType>::computeU() && (a!=RealScalar(0))) this->m_matrixU.col(i) *= this->m_workMatrix.coeff(i,i)/a;
|
||||
}
|
||||
|
||||
/*** step 4. Sort singular values in descending order and compute the number of nonzero singular values ***/
|
||||
|
||||
this->m_nonzeroSingularValues = this->m_diagSize;
|
||||
for(Index i = 0; i < this->m_diagSize; i++)
|
||||
{
|
||||
Index pos;
|
||||
RealScalar maxRemainingSingularValue = this->m_singularValues.tail(this->m_diagSize-i).maxCoeff(&pos);
|
||||
if(maxRemainingSingularValue == RealScalar(0))
|
||||
{
|
||||
this->m_nonzeroSingularValues = i;
|
||||
break;
|
||||
}
|
||||
if(pos)
|
||||
{
|
||||
pos += i;
|
||||
std::swap(this->m_singularValues.coeffRef(i), this->m_singularValues.coeffRef(pos));
|
||||
if(SVDBase<MatrixType>::computeU()) this->m_matrixU.col(pos).swap(this->m_matrixU.col(i));
|
||||
if(SVDBase<MatrixType>::computeV()) this->m_matrixV.col(pos).swap(this->m_matrixV.col(i));
|
||||
}
|
||||
}
|
||||
|
||||
this->m_isInitialized = true;
|
||||
return *this;
|
||||
}
|
||||
|
||||
namespace internal {
|
||||
template<typename _MatrixType, int QRPreconditioner, typename Rhs>
|
||||
struct solve_retval<JacobiSVD<_MatrixType, QRPreconditioner>, Rhs>
|
||||
: solve_retval_base<JacobiSVD<_MatrixType, QRPreconditioner>, Rhs>
|
||||
{
|
||||
typedef JacobiSVD<_MatrixType, QRPreconditioner> JacobiSVDType;
|
||||
EIGEN_MAKE_SOLVE_HELPERS(JacobiSVDType,Rhs)
|
||||
|
||||
template<typename Dest> void evalTo(Dest& dst) const
|
||||
{
|
||||
eigen_assert(rhs().rows() == dec().rows());
|
||||
|
||||
// A = U S V^*
|
||||
// So A^{-1} = V S^{-1} U^*
|
||||
|
||||
Index diagSize = (std::min)(dec().rows(), dec().cols());
|
||||
typename JacobiSVDType::SingularValuesType invertedSingVals(diagSize);
|
||||
|
||||
Index nonzeroSingVals = dec().nonzeroSingularValues();
|
||||
invertedSingVals.head(nonzeroSingVals) = dec().singularValues().head(nonzeroSingVals).array().inverse();
|
||||
invertedSingVals.tail(diagSize - nonzeroSingVals).setZero();
|
||||
|
||||
dst = dec().matrixV().leftCols(diagSize)
|
||||
* invertedSingVals.asDiagonal()
|
||||
* dec().matrixU().leftCols(diagSize).adjoint()
|
||||
* rhs();
|
||||
}
|
||||
};
|
||||
} // end namespace internal
|
||||
|
||||
/** \svd_module
|
||||
*
|
||||
* \return the singular value decomposition of \c *this computed by two-sided
|
||||
* Jacobi transformations.
|
||||
*
|
||||
* \sa class JacobiSVD
|
||||
*/
|
||||
template<typename Derived>
|
||||
JacobiSVD<typename MatrixBase<Derived>::PlainObject>
|
||||
MatrixBase<Derived>::jacobiSvd(unsigned int computationOptions) const
|
||||
{
|
||||
return JacobiSVD<PlainObject>(*this, computationOptions);
|
||||
}
|
||||
|
||||
} // end namespace Eigen
|
||||
|
||||
#endif // EIGEN_JACOBISVD_H
|
@ -18,7 +18,7 @@
|
||||
#define EIGEN_RUNTIME_NO_MALLOC
|
||||
|
||||
#include "main.h"
|
||||
#include <unsupported/Eigen/SVD>
|
||||
#include <unsupported/Eigen/BDCSVD>
|
||||
#include <Eigen/LU>
|
||||
|
||||
|
||||
|
Loading…
Reference in New Issue
Block a user