/usr/include/linbox/algorithms/eliminator.h is in liblinbox-dev 1.3.2-1.1build2.
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* Copyright (C) 2002 Bradford Hovinen
*
* Written by Bradford Hovinen <bghovinen@math.waterloo.ca>
*
* --------------------------------------------
*
* ========LICENCE========
* This file is part of the library LinBox.
*
* LinBox is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
* ========LICENCE========
* Elimination code for lookahead block Lanczos
*/
#ifndef __LINBOX_eliminator_H
#define __LINBOX_eliminator_H
#include "linbox/linbox-config.h"
#include <vector>
#include "linbox/field/archetype.h"
#include "linbox/vector/vector-domain.h"
#include "linbox/blackbox/archetype.h"
#include "linbox/solutions/methods.h"
namespace LinBox
{
/** Elimination system
*
* This is the supporting elimination system for a lookahead-based
* variant of block Lanczos.
*/
template <class Field, class Matrix = BlasMatrix<Field> >
class Eliminator {
public:
typedef typename Field::Element Element;
/** Permutation.
*
* A permutation is represented as a vector of pairs, each
* pair representing a transposition. Thus a permutation
* requires \p O(n log n) storage and \p O(n log n) application
* time, as opposed to the lower bound of \p O(n) for
* both. However, this allows us to decompose a permutation
* easily into its factors, thus eliminating the need for
* additional auxillary storage in each level of the
* Gauss-Jordan transform recursion. Additionally, we expect
* to use this with dense matrices that are "close to
* generic", meaning that the rank should be high and there
* should be relatively little need for transpositions. In
* practice, we therefore expect this to beat the vector
* representation. The use of this representation does not
* affect the analysis of the Gauss-Jordan transform, since
* each step where a permutation is applied also requires
* matrix multiplication, which is strictly more expensive.
*/
typedef std::pair<unsigned int, unsigned int> Transposition;
typedef std::vector<Transposition> Permutation;
/** Constructor
* @param F Field over which to operate
* @param N
*/
Eliminator (const Field &F, unsigned int N);
/** Destructor
*/
~Eliminator ();
/** Two-sided Gauss-Jordan transform
*
* @param Ainv Inverse of nonsingular part of A
* @param Tu Row dependencies
* @param Tv Column dependencies
* @param P Row permutation
* @param Q Column permutation
* @param A Input matrix
* @param rank Rank of A
*/
template <class Matrix1, class Matrix2, class Matrix3, class Matrix4>
void twoSidedGaussJordan (Matrix1 &Ainv,
Permutation &P,
Matrix2 &Tu,
Permutation &Q,
Matrix3 &Tv,
const Matrix4 &A,
unsigned int &rank);
/** Permute the input and invert it.
*
* Compute the pseudoinverse of the input matrix A and return
* it. First apply the permutation given by the lists leftPriorityIdx
* and rightPriorityIdx to the input matrix so that independent
* columns and rows are more likely to be found on the first indices
* in those lists. Zero out the rows and columns of the inverse
* corresponding to dependent rows and columns of the input. Set S and
* T to boolean vectors such that S^T A T is invertible and of maximal
* size.
*
* @param W Output inverse
* @param S Output vector S
* @param T Output vector T
* @param rightPriorityIdx Priority indices on the right
* @param Qp
* @param rank
* @param A Input matrix A
* @return Reference to inverse matrix
*/
Matrix &permuteAndInvert (Matrix &W,
std::vector<bool> &S,
std::vector<bool> &T,
std::list<unsigned int> &rightPriorityIdx,
Permutation &Qp,
unsigned int &rank,
const Matrix &A);
/** Perform a Gauss-Jordan transform using a recursive algorithm.
*
* Upon completion, we have UPA = R, where R is of reduced row
* echelon form
*
* @param U Output matrix U
* @param P Output permutation P
* @param A Input matrix A
* @param profile
* @param Tu
* @param Q
* @param Tv
* @param rank
* @param det
* @return Reference to U
*/
template <class Matrix1, class Matrix2, class Matrix3, class Matrix4>
Matrix1 &gaussJordan (Matrix1 &U,
std::vector<unsigned int> &profile,
Permutation &P,
Matrix2 &Tu,
Permutation &Q,
Matrix3 &Tv,
unsigned int &rank,
typename Field::Element &det,
const Matrix4 &A);
/**
* Retrieve the total user time spent permuting and inverting.
*/
double getTotalTime () const { return _total_time; }
/**
* Retrieve the total user time spent inverting only.
*/
double getInvertTime () const { return _invert_time; }
/**
* Write the filter vector to the given output stream
*/
std::ostream &writeFilter (std::ostream &out, const std::vector<bool> &v) const;
/**
* Write the given permutation to the output stream
*/
std::ostream &writePermutation (std::ostream &out, const Permutation &P) const;
private:
// Compute the kth indexed Gauss-Jordan transform of the input
Matrix &kthGaussJordan (unsigned int &r,
typename Field::Element &d,
unsigned int k,
unsigned int s,
unsigned int m,
const typename Field::Element &d0);
// Set the given matrix to the identity
template <class Matrix1>
Matrix1 &setIN (Matrix1 &A) const;
// Add d * I_N to A
template <class Matrix1>
Matrix1 &adddIN (Matrix1 &A,
const typename Field::Element &d) const;
// Clean out the given priority index list and add new elements as needed
void cleanPriorityIndexList (std::list<unsigned int> &list,
std::vector<bool> &S,
std::vector<bool> &old_S) const;
// Permute the given bit vector
template <class Iterator>
std::vector<bool> &permute (std::vector<bool> &v,
Iterator P_start,
Iterator P_end) const;
// Construct a permutation from the given priority list
Permutation &buildPermutation (Permutation &P, const std::list<unsigned int> &pidx) const;
// Prepare a minimal permutation based on the given permutation
Permutation &buildMinimalPermutation (Permutation &P, unsigned int rank,
unsigned int dim, const Permutation &Pold);
Permutation &buildMinimalPermutationFromProfile (Permutation &P, unsigned int rank,
unsigned int dim, const std::vector<unsigned int> &profile);
// Private variables
const Field &_field;
VectorDomain<Field> _VD;
MatrixDomain<Field> _MD;
unsigned int _number;
typename Field::Element _one;
// Temporaries used in the computation
mutable Permutation _perm;
mutable BlasMatrix<Field> _matA; // Variable
mutable BlasMatrix<Field> _matU; // Variable
mutable BlasMatrix<Field> _tmp;
// These record the independent rows and columns found during the
// elimination process
mutable std::vector<bool> _indepRows; // Independent rows
mutable std::vector<bool> _indepCols; // Independent columns
std::vector<unsigned int> _profile;
unsigned int _profile_idx;
// Timer information
double _total_time;
double _invert_time;
// Priority indices for rows
std::vector<unsigned int> _indices;
};
} // namespace LinBox
#include "eliminator.inl"
#endif // __LINBOX_eliminator_H
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