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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
This commit is contained in:
Gael Guennebaud
263
Eigen/src/SVD/SVDBase.h
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263
Eigen/src/SVD/SVDBase.h
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// This file is part of Eigen, a lightweight C++ template library
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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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// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr>
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// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.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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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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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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*
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*
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* \class SVDBase
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*
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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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* 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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* 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
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* and right \em singular \em vectors of \a A respectively.
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*
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* Singular values are always sorted in decreasing order.
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*
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*
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* 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
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* 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
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* 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,
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* 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.
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*
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* If the input matrix has inf or nan coefficients, the result of the computation is undefined, but the computation is guaranteed to
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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 Derived>
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class SVDBase
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{
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public:
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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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enum {
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RowsAtCompileTime = MatrixType::RowsAtCompileTime,
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ColsAtCompileTime = MatrixType::ColsAtCompileTime,
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DiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime),
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MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
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MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
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MaxDiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(MaxRowsAtCompileTime,MaxColsAtCompileTime),
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MatrixOptions = MatrixType::Options
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};
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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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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 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 && "SVD is not initialized.");
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eigen_assert(computeU() && "This SVD 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 && "SVD is not initialized.");
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eigen_assert(computeV() && "This SVD 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 && "SVD is not initialized.");
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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();
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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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/** \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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inline Index rows() const { return m_rows; }
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inline Index cols() const { return m_cols; }
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protected:
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// return true if already allocated
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bool allocate(Index rows, Index cols, unsigned int computationOptions) ;
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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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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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/** \brief Default Constructor.
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*
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* Default constructor of SVDBase
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*/
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SVDBase()
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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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};
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template<typename MatrixType>
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bool SVDBase<MatrixType>::allocate(Index rows, Index cols, unsigned int computationOptions)
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{
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eigen_assert(rows >= 0 && cols >= 0);
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if (m_isAllocated &&
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rows == m_rows &&
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cols == m_cols &&
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computationOptions == m_computationOptions)
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{
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return true;
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}
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m_rows = rows;
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m_cols = cols;
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m_isInitialized = false;
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m_isAllocated = true;
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m_computationOptions = computationOptions;
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m_computeFullU = (computationOptions & ComputeFullU) != 0;
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m_computeThinU = (computationOptions & ComputeThinU) != 0;
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m_computeFullV = (computationOptions & ComputeFullV) != 0;
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m_computeThinV = (computationOptions & ComputeThinV) != 0;
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eigen_assert(!(m_computeFullU && m_computeThinU) && "SVDBase: you can't ask for both full and thin U");
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eigen_assert(!(m_computeFullV && m_computeThinV) && "SVDBase: you can't ask for both full and thin V");
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eigen_assert(EIGEN_IMPLIES(m_computeThinU || m_computeThinV, MatrixType::ColsAtCompileTime==Dynamic) &&
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"SVDBase: thin U and V are only available when your matrix has a dynamic number of columns.");
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m_diagSize = (std::min)(m_rows, m_cols);
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m_singularValues.resize(m_diagSize);
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if(RowsAtCompileTime==Dynamic)
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m_matrixU.resize(m_rows, m_computeFullU ? m_rows : m_computeThinU ? m_diagSize : 0);
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if(ColsAtCompileTime==Dynamic)
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m_matrixV.resize(m_cols, m_computeFullV ? m_cols : m_computeThinV ? m_diagSize : 0);
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return false;
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}
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}// end namespace
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#endif // EIGEN_SVDBASE_H
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