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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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This commit is contained in:
Gael Guennebaud
2014-09-01 18:16:20 +02:00
parent b121eecf60
commit eb39296028
14 changed files with 180 additions and 1049 deletions
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1
Eigen/SVD
View File

@@ -21,6 +21,7 @@
*/
#include "src/misc/Solve.h"
#include "src/SVD/SVDBase.h"
#include "src/SVD/JacobiSVD.h"
#if defined(EIGEN_USE_LAPACKE) && !defined(EIGEN_USE_LAPACKE_STRICT)
#include "src/SVD/JacobiSVD_MKL.h"

182
Eigen/src/SVD/JacobiSVD.h
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@@ -2,6 +2,7 @@
// for linear algebra.
//
// Copyright (C) 2009-2010 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
@@ -442,6 +443,12 @@ void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
*j_left = rot1 * j_right->transpose();
}
template<typename _MatrixType, int QRPreconditioner>
struct traits<JacobiSVD<_MatrixType,QRPreconditioner> >
{
typedef _MatrixType MatrixType;
};
} // end namespace internal
/** \ingroup SVD_Module
@@ -498,7 +505,9 @@ void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
* \sa MatrixBase::jacobiSvd()
*/
template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
: public SVDBase<JacobiSVD<_MatrixType,QRPreconditioner> >
{
typedef SVDBase<JacobiSVD> Base;
public:
typedef _MatrixType MatrixType;
@@ -515,13 +524,10 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
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 Base::MatrixUType MatrixUType;
typedef typename Base::MatrixVType MatrixVType;
typedef typename Base::SingularValuesType SingularValuesType;
typedef typename internal::plain_row_type<MatrixType>::type RowType;
typedef typename internal::plain_col_type<MatrixType>::type ColType;
typedef Matrix<Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime,
@@ -534,11 +540,6 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
* perform decompositions via JacobiSVD::compute(const MatrixType&).
*/
JacobiSVD()
: m_isInitialized(false),
m_isAllocated(false),
m_usePrescribedThreshold(false),
m_computationOptions(0),
m_rows(-1), m_cols(-1), m_diagSize(0)
{}
@@ -549,11 +550,6 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
* \sa JacobiSVD()
*/
JacobiSVD(Index rows, Index cols, unsigned int computationOptions = 0)
: m_isInitialized(false),
m_isAllocated(false),
m_usePrescribedThreshold(false),
m_computationOptions(0),
m_rows(-1), m_cols(-1)
{
allocate(rows, cols, computationOptions);
}
@@ -569,11 +565,6 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
* available with the (non-default) FullPivHouseholderQR preconditioner.
*/
JacobiSVD(const MatrixType& matrix, unsigned int computationOptions = 0)
: m_isInitialized(false),
m_isAllocated(false),
m_usePrescribedThreshold(false),
m_computationOptions(0),
m_rows(-1), m_cols(-1)
{
compute(matrix, computationOptions);
}
@@ -601,54 +592,6 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
return compute(matrix, m_computationOptions);
}
/** \returns the \a U matrix.
*
* For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
* the U matrix is n-by-n if you asked for #ComputeFullU, and is n-by-m if you asked for #ComputeThinU.
*
* The \a m first columns of \a U are the left singular vectors of the matrix being decomposed.
*
* This method asserts that you asked for \a U to be computed.
*/
const MatrixUType& matrixU() const
{
eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
eigen_assert(computeU() && "This JacobiSVD decomposition didn't compute U. Did you ask for it?");
return m_matrixU;
}
/** \returns the \a V matrix.
*
* For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
* the V matrix is p-by-p if you asked for #ComputeFullV, and is p-by-m if you asked for ComputeThinV.
*
* The \a m first columns of \a V are the right singular vectors of the matrix being decomposed.
*
* This method asserts that you asked for \a V to be computed.
*/
const MatrixVType& matrixV() const
{
eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
eigen_assert(computeV() && "This JacobiSVD decomposition didn't compute V. Did you ask for it?");
return m_matrixV;
}
/** \returns the vector of singular values.
*
* For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p, the
* returned vector has size \a m. Singular values are always sorted in decreasing order.
*/
const SingularValuesType& singularValues() const
{
eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
return m_singularValues;
}
/** \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; }
/** \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.
@@ -666,94 +609,31 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
eigen_assert(computeU() && computeV() && "JacobiSVD::solve() requires both unitaries U and V to be computed (thin unitaries suffice).");
return internal::solve_retval<JacobiSVD, Rhs>(*this, b.derived());
}
/** \returns the number of singular values that are not exactly 0 */
Index nonzeroSingularValues() const
{
eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
return m_nonzeroSingularValues;
}
/** \returns the rank of the matrix of which \c *this is the SVD.
*
* \note This method has to determine which singular values should be considered nonzero.
* For that, it uses the threshold value that you can control by calling
* setThreshold(const RealScalar&).
*/
inline Index rank() const
{
using std::abs;
eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
if(m_singularValues.size()==0) return 0;
RealScalar premultiplied_threshold = m_singularValues.coeff(0) * threshold();
Index i = m_nonzeroSingularValues-1;
while(i>=0 && m_singularValues.coeff(i) < premultiplied_threshold) --i;
return i+1;
}
using Base::computeU;
using Base::computeV;
/** Allows to prescribe a threshold to be used by certain methods, such as rank() and solve(),
* which need to determine when singular values are to be considered nonzero.
* This is not used for the SVD decomposition itself.
*
* When it needs to get the threshold value, Eigen calls threshold().
* The default is \c NumTraits<Scalar>::epsilon()
*
* \param threshold The new value to use as the threshold.
*
* A singular value will be considered nonzero if its value is strictly greater than
* \f$ \vert singular value \vert \leqslant threshold \times \vert max singular value \vert \f$.
*
* If you want to come back to the default behavior, call setThreshold(Default_t)
*/
JacobiSVD& setThreshold(const RealScalar& threshold)
{
m_usePrescribedThreshold = true;
m_prescribedThreshold = threshold;
return *this;
}
/** Allows to come back to the default behavior, letting Eigen use its default formula for
* determining the threshold.
*
* You should pass the special object Eigen::Default as parameter here.
* \code svd.setThreshold(Eigen::Default); \endcode
*
* See the documentation of setThreshold(const RealScalar&).
*/
JacobiSVD& setThreshold(Default_t)
{
m_usePrescribedThreshold = false;
return *this;
}
/** 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();
}
inline Index rows() const { return m_rows; }
inline Index cols() const { return m_cols; }
private:
void allocate(Index rows, Index cols, unsigned int computationOptions);
protected:
MatrixUType m_matrixU;
MatrixVType m_matrixV;
SingularValuesType m_singularValues;
using Base::m_matrixU;
using Base::m_matrixV;
using Base::m_singularValues;
using Base::m_isInitialized;
using Base::m_isAllocated;
using Base::m_usePrescribedThreshold;
using Base::m_computeFullU;
using Base::m_computeThinU;
using Base::m_computeFullV;
using Base::m_computeThinV;
using Base::m_computationOptions;
using Base::m_nonzeroSingularValues;
using Base::m_rows;
using Base::m_cols;
using Base::m_diagSize;
using Base::m_prescribedThreshold;
WorkMatrixType m_workMatrix;
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;
template<typename __MatrixType, int _QRPreconditioner, bool _IsComplex>
friend struct internal::svd_precondition_2x2_block_to_be_real;

263
Eigen/src/SVD/SVDBase.h Normal file
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@@ -0,0 +1,263 @@
// 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>
// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com>
// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr>
// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr>
// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_SVDBASE_H
#define EIGEN_SVDBASE_H
namespace Eigen {
/** \ingroup SVD_Module
*
*
* \class SVDBase
*
* \brief Base class of SVD algorithms
*
* \tparam Derived the type of the actual SVD decomposition
*
* 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.
*
*
* 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.
*
* 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.
* \sa MatrixBase::genericSvd()
*/
template<typename Derived>
class SVDBase
{
public:
typedef typename internal::traits<Derived>::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;
Derived& derived() { return *static_cast<Derived*>(this); }
const Derived& derived() const { return *static_cast<const Derived*>(this); }
/** \returns the \a U matrix.
*
* For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
* the U matrix is n-by-n if you asked for #ComputeFullU, and is n-by-m if you asked for #ComputeThinU.
*
* The \a m first columns of \a U are the left singular vectors of the matrix being decomposed.
*
* This method asserts that you asked for \a U to be computed.
*/
const MatrixUType& matrixU() const
{
eigen_assert(m_isInitialized && "SVD is not initialized.");
eigen_assert(computeU() && "This SVD decomposition didn't compute U. Did you ask for it?");
return m_matrixU;
}
/** \returns the \a V matrix.
*
* For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
* the V matrix is p-by-p if you asked for #ComputeFullV, and is p-by-m if you asked for ComputeThinV.
*
* The \a m first columns of \a V are the right singular vectors of the matrix being decomposed.
*
* This method asserts that you asked for \a V to be computed.
*/
const MatrixVType& matrixV() const
{
eigen_assert(m_isInitialized && "SVD is not initialized.");
eigen_assert(computeV() && "This SVD decomposition didn't compute V. Did you ask for it?");
return m_matrixV;
}
/** \returns the vector of singular values.
*
* For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p, the
* returned vector has size \a m. Singular values are always sorted in decreasing order.
*/
const SingularValuesType& singularValues() const
{
eigen_assert(m_isInitialized && "SVD is not initialized.");
return m_singularValues;
}
/** \returns the number of singular values that are not exactly 0 */
Index nonzeroSingularValues() const
{
eigen_assert(m_isInitialized && "SVD is not initialized.");
return m_nonzeroSingularValues;
}
/** \returns the rank of the matrix of which \c *this is the SVD.
*
* \note This method has to determine which singular values should be considered nonzero.
* For that, it uses the threshold value that you can control by calling
* setThreshold(const RealScalar&).
*/
inline Index rank() const
{
using std::abs;
eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
if(m_singularValues.size()==0) return 0;
RealScalar premultiplied_threshold = m_singularValues.coeff(0) * threshold();
Index i = m_nonzeroSingularValues-1;
while(i>=0 && m_singularValues.coeff(i) < premultiplied_threshold) --i;
return i+1;
}
/** Allows to prescribe a threshold to be used by certain methods, such as rank() and solve(),
* which need to determine when singular values are to be considered nonzero.
* This is not used for the SVD decomposition itself.
*
* When it needs to get the threshold value, Eigen calls threshold().
* The default is \c NumTraits<Scalar>::epsilon()
*
* \param threshold The new value to use as the threshold.
*
* A singular value will be considered nonzero if its value is strictly greater than
* \f$ \vert singular value \vert \leqslant threshold \times \vert max singular value \vert \f$.
*
* If you want to come back to the default behavior, call setThreshold(Default_t)
*/
Derived& setThreshold(const RealScalar& threshold)
{
m_usePrescribedThreshold = true;
m_prescribedThreshold = threshold;
return derived();
}
/** Allows to come back to the default behavior, letting Eigen use its default formula for
* determining the threshold.
*
* You should pass the special object Eigen::Default as parameter here.
* \code svd.setThreshold(Eigen::Default); \endcode
*
* See the documentation of setThreshold(const RealScalar&).
*/
Derived& setThreshold(Default_t)
{
m_usePrescribedThreshold = false;
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) ;
MatrixUType m_matrixU;
MatrixVType m_matrixV;
SingularValuesType m_singularValues;
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.
*
* Default constructor of SVDBase
*/
SVDBase()
: m_isInitialized(false),
m_isAllocated(false),
m_usePrescribedThreshold(false),
m_computationOptions(0),
m_rows(-1), m_cols(-1), m_diagSize(0)
{}
};
template<typename MatrixType>
bool SVDBase<MatrixType>::allocate(Index rows, Index cols, unsigned int computationOptions)
{
eigen_assert(rows >= 0 && cols >= 0);
if (m_isAllocated &&
rows == m_rows &&
cols == m_cols &&
computationOptions == m_computationOptions)
{
return true;
}
m_rows = rows;
m_cols = cols;
m_isInitialized = false;
m_isAllocated = true;
m_computationOptions = computationOptions;
m_computeFullU = (computationOptions & ComputeFullU) != 0;
m_computeThinU = (computationOptions & ComputeThinU) != 0;
m_computeFullV = (computationOptions & ComputeFullV) != 0;
m_computeThinV = (computationOptions & ComputeThinV) != 0;
eigen_assert(!(m_computeFullU && m_computeThinU) && "SVDBase: you can't ask for both full and thin U");
eigen_assert(!(m_computeFullV && m_computeThinV) && "SVDBase: you can't ask for both full and thin V");
eigen_assert(EIGEN_IMPLIES(m_computeThinU || m_computeThinV, MatrixType::ColsAtCompileTime==Dynamic) &&
"SVDBase: thin U and V are only available when your matrix has a dynamic number of columns.");
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);
if(ColsAtCompileTime==Dynamic)
m_matrixV.resize(m_cols, m_computeFullV ? m_cols : m_computeThinV ? m_diagSize : 0);
return false;
}
}// end namespace
#endif // EIGEN_SVDBASE_H

1
Eigen/src/SVD/UpperBidiagonalization.h
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@@ -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