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/* linbox/algorithms/gauss.inl
* Copyright (C) 1999 Jean-Guillaume Dumas
*
* Written by Jean-Guillaume Dumas <Jean-Guillaume.Dumas@imag.fr>
* Time-stamp: <09 Feb 07 11:25:51 Jean-Guillaume.Dumas@imag.fr>
*
* -----------------------------------------------------------
* 2003-02-02 Bradford Hovinen <bghovinen@math.uwaterloo.ca>
*
* Ported to new matrix archetype; update interface to meet current
* standards. Rename gauss_foo as foo and gauss_Uin as upperin
*
* Move function definitions to gauss.inl
* -----------------------------------------------------------
*
* See COPYING for license information.
*/
// ========================================================================= //
// (C) The Linbox Group 1999
// Calcul de rang par la méthode de Gauss pivot par ligne, sur matrice creuse
// ========================================================================= //
#ifndef __GAUSS_INL
#define __GAUSS_INL
#include "linbox/algorithms/gauss.h"
#include "linbox/util/commentator.h"
#ifdef __LINBOX_ALL__
#define __LINBOX_COUNT__
#define __LINBOX_OFTEN__
#define __LINBOX_FILLIN__
#endif
namespace LinBox
{
template <class _Field>
template <class Vector, class D>
void GaussDomain<_Field>::eliminate (Vector &lignecourante,
const Vector &lignepivot,
const unsigned long &indcol,
const long &indpermut,
D &columns)
{
typedef typename Vector::value_type E;
unsigned long k = indcol - 1;
unsigned long nj = lignecourante.size () ;
// std::cerr << "BEGIN ELIMINATE, k: " << k << ", nj: " << nj << ", indpermut: " << indpermut << ", indcol: " << indcol << std::endl;
// std::cerr << "lignepivot: [";
// for(typename Vector::const_iterator refs = lignepivot.begin();
// refs != lignepivot.end() ;
// ++refs )
// std::cerr << '(' << refs->first << ';' << refs->second << ')';
// std::cerr << "], lignecour: [";
// for(typename Vector::const_iterator refs = lignecourante.begin();
// refs != lignecourante.end() ;
// ++refs )
// std::cerr << '(' << refs->first << ';' << refs->second << ')';
// std::cerr << ']' << std::endl;
if (nj > 0) {
unsigned long j_head = 0;
for (; j_head < nj; ++j_head)
if (static_cast<long>(lignecourante[j_head].first) >= indpermut) break;
// std::cerr << "ELIMINATE, j_head: " << j_head << std::endl;
if (j_head < nj) {
if (static_cast<long>(lignecourante[j_head].first) == indpermut) {
// -------------------------------------------
// Permutation
if ( indpermut != static_cast<long>(k)) {
if (lignecourante[0].first == k) {
// non zero <--> non zero
Element tmp;
_F.assign (tmp, lignecourante[0].second);
_F.assign (lignecourante[0].second,
lignecourante[j_head].second);
_F.assign (lignecourante[j_head].second, tmp);
} else {
// zero <--> non zero
E tmp = lignecourante[j_head];
--columns[tmp.first];
++columns[k];
tmp.first = k;
for (long l = j_head; l > 0; l--)
lignecourante[l] = lignecourante[l-1];
lignecourante[0] = tmp;
}
j_head = 0;
}
// -------------------------------------------
// Elimination
unsigned long npiv = lignepivot.size ();
Vector construit (nj + npiv);
// construit : <-- j
// courante : <-- m
// pivot : <-- l
unsigned long j = 0;
unsigned long m = j_head + 1;
// A[i,k] <-- - A[i,k] / A[k,k]
Element headcoeff;
_F.divin (_F.neg (headcoeff, lignecourante[j_head].second),
lignepivot[0].second);
--columns[lignecourante[j_head].first];
// if A[k,j]=0, then A[i,j] <-- A[i,j]
while (j < j_head) {
construit[j] = lignecourante[j];
j++;
}
unsigned long j_piv;
unsigned long l = 0;
for (; l < npiv; l++)
if (lignepivot[l].first > k) break;
// for all j such that (j>k) and A[k,j]!=0
while (l < npiv) {
j_piv = lignepivot[l].first;
// if A[k,j]=0, then A[i,j] <-- A[i,j]
while ((m < nj) && (lignecourante[m].first < j_piv))
construit[j++] = lignecourante[m++];
// if A[i,j]!=0, then A[i,j] <-- A[i,j] - A[i,k]*A[k,j]
if ((m < nj) && (lignecourante[m].first == j_piv)) {
Element tmp;
_F.axpy (tmp, headcoeff, lignepivot[l].second,
lignecourante[m].second);
if (! _F.isZero (tmp)) {
_F.assign (lignecourante[m].second, tmp);
construit[j++] = lignecourante[m++];
} else
--columns[lignecourante[m++].first];
} else {
Element tmp;
_F.mul (tmp, headcoeff, lignepivot[l].second);
if (! _F.isZero (tmp)) {
++columns[j_piv];
construit[j++] = E (j_piv, tmp);
}
}
l++;
}
// if A[k,j]=0, then A[i,j] <-- A[i,j]
while (m<nj)
construit[j++] = lignecourante[m++];
construit.resize (j);
lignecourante = construit;
} else {
// -------------------------------------------
// j_head < nj but nothing under the pivot
// Permutation
// std::cerr << "----------------------------------------------------------" << std::endl;
// std::cerr << "j_head < nj" << std::endl;
// std::cerr << "j_head: " << j_head << ", nj: " << nj << ", k:" << k
// // // << "lignepivot: " << lignepivot
// // // << ", lignecour: " << lignecourante
// << std::endl;
// std::cerr << "----------------------------------------------------------" << std::endl;
if (indpermut != static_cast<long>(k)) {
if (j_head>0) {
unsigned long l = 0;
for (; l < nj; ++l)
if (lignecourante[l].first >= k) break;
if ((l < nj) && (lignecourante[l].first == k)) {
// non zero <--> zero
E tmp = lignecourante[l];
--columns[k];
++columns[indpermut];
tmp.first = indpermut;
unsigned long bjh = j_head-1;
for (; l < bjh; ++l)
lignecourante[l] = lignecourante[l + 1];
lignecourante[bjh] = tmp;
} // else // zero <--> zero
} // else // zero <--> zero
}
}
} else {
// -------------------------------------------
// j_head >= nj > 0
// std::cerr << "----------------------------------------------------------" << std::endl;
// std::cerr << "j_head >= nj > 0" << std::endl;
// std::cerr << "j_head: " << j_head << ", nj: " << nj << ", k:" << k
// // // << "lignepivot: " << lignepivot
// // // << ", lignecour: " << lignecourante
// << std::endl;
// std::cerr << "----------------------------------------------------------" << std::endl;
if (indpermut != static_cast<long>(k)) {
unsigned long l = 0;
for (; l < nj; ++l)
if (lignecourante[l].first >= k) break;
if ((l < nj) && (lignecourante[l].first == k)) {
// non zero <--> zero
E tmp = lignecourante[l];
--columns[k];
++columns[indpermut];
tmp.first = indpermut;
unsigned long bjh = nj - 1;
for (; l < bjh; ++l)
lignecourante[l] = lignecourante[l + 1];
lignecourante[bjh] = tmp;
} // else
// zero <--> zero
}
}
}
// std::cerr << "END ELIMINATE, k: " << k << ", nj: " << nj << ", indpermut: " << indpermut << ", indcol: " << indcol << std::endl;
// std::cerr << "lignepivot: [";
// for(typename Vector::const_iterator refs = lignepivot.begin();
// refs != lignepivot.end() ;
// ++refs )
// std::cerr << '(' << refs->first << ';' << refs->second << ')';
// std::cerr << "], lignecour: [";
// for(typename Vector::const_iterator refs = lignecourante.begin();
// refs != lignecourante.end() ;
// ++refs )
// std::cerr << '(' << refs->first << ';' << refs->second << ')';
// std::cerr << ']' << std::endl;
}
template <class _Field>
template <class Vector>
void GaussDomain<_Field>::eliminate (Vector &lignecourante,
const Vector &lignepivot,
const unsigned long &indcol,
const long &indpermut)
{
typedef typename Vector::value_type E;
unsigned long k = indcol - 1;
unsigned long nj = lignecourante.size () ;
if (nj > 0) {
unsigned long j_head = 0;
for (; j_head < nj; ++j_head)
if (static_cast<long>(lignecourante[j_head].first) >= indpermut) break;
if (j_head < nj) {
if (static_cast<long>(lignecourante[j_head].first) == indpermut) {
// -------------------------------------------
// Permutation
if (indpermut != static_cast<long>(k)) {
if (lignecourante[0].first == k) {
// non zero <--> non zero
Element tmp;
_F.assign (tmp, lignecourante[0].second) ;
_F.assign (lignecourante[0].second,
lignecourante[j_head].second);
_F.assign (lignecourante[j_head].second, tmp);
} else {
// zero <--> non zero
E tmp = lignecourante[j_head];
tmp.first = k;
for (long l = j_head; l > 0; l--)
lignecourante[l] = lignecourante[l-1];
lignecourante[0] = tmp;
}
j_head = 0;
}
// -------------------------------------------
// Elimination
unsigned long npiv = lignepivot.size ();
Vector construit (nj + npiv);
// construit : <-- j
// courante : <-- m
// pivot : <-- l
unsigned long j = 0;
unsigned long m = j_head + 1;
// A[i,k] <-- - A[i,k] / A[k,k]
Element headcoeff;
_F.divin (_F.neg (headcoeff, lignecourante[j_head].second),
lignepivot[0].second);
// if A[k,j]=0, then A[i,j] <-- A[i,j]
while (j < j_head) {
construit[j] = lignecourante[j];
j++;
}
unsigned long j_piv;
unsigned long l = 0;
for (; l < npiv; l++)
if (lignepivot[l].first > k) break;
// for all j such that (j>k) and A[k,j]!=0
while (l < npiv) {
j_piv = lignepivot[l].first;
// if A[k,j]=0, then A[i,j] <-- A[i,j]
while ((m < nj) && (lignecourante[m].first < j_piv))
construit[j++] = lignecourante[m++];
// if A[i,j]!=0, then A[i,j] <-- A[i,j] - A[i,k]*A[k,j]
if ((m < nj) && (lignecourante[m].first == j_piv)) {
Element tmp;
_F.axpy (tmp, headcoeff, lignepivot[l].second,
lignecourante[m].second);
if (! _F.isZero (tmp)) {
_F.assign (lignecourante[m].second, tmp);
construit[j++] = lignecourante[m++];
} else
++m;
} else {
Element tmp;
_F.mul (tmp, headcoeff, lignepivot[l].second);
if (! _F.isZero (tmp))
construit[j++] = E (j_piv, tmp);
}
l++;
}
// if A[k,j]=0, then A[i,j] <-- A[i,j]
while (m < nj)
construit[j++] = lignecourante[m++];
construit.resize (j);
lignecourante = construit;
} else {
// -------------------------------------------
// j_head < nj but nothing under the pivot
// Permutation
if (indpermut != static_cast<long>(k)) {
if (j_head > 0) {
unsigned long l = 0;
for (; l < nj; ++l)
if (lignecourante[l].first >= k) break;
if ((l < nj) && (lignecourante[l].first == k)) {
// non zero <--> zero
E tmp = lignecourante[l];
tmp.first = indpermut;
unsigned long bjh = j_head -1;
for (; l < bjh; l++)
lignecourante[l] = lignecourante[l + 1];
lignecourante[bjh] = tmp;
} // else // zero <--> zero
} // else // zero <--> zero
}
}
} else {
// -------------------------------------------
// -------------------------------------------
// j_head >= nj > 0
// std::cerr << "----------------------------------------------------------" << std::endl;
// std::cerr << "j_head >= nj > 0" << std::endl;
// std::cerr << "j_head: " << j_head << ", nj: " << nj << ", k:" << k
// // << "lignepivot: " << lignepivot
// // << ", lignecour: " << lignecourante
// << std::endl;
// std::cerr << "----------------------------------------------------------" << std::endl;
if (indpermut != static_cast<long>(k)) {
unsigned long l = 0;
for (; l < nj; ++l)
if (lignecourante[l].first >= k) break;
if ((l < nj) && (lignecourante[l].first == k)) {
// non zero <--> zero
E tmp = lignecourante[l];
tmp.first = indpermut;
unsigned long bjh = nj - 1;
for (; l < bjh; l++)
lignecourante[l] = lignecourante[l + 1];
lignecourante[bjh] = tmp;
} // else
// zero <--> zero
}
}
}
}
template <class _Field>
template<class Vector>
void GaussDomain<_Field>::Upper (Vector &lignecur,
const Vector &lignepivot,
unsigned long indcol,
long indpermut)
{
static typename _Field::Element zero = _F.init(zero);
long n = lignecur.size () ;
long k = indcol - 1 ;
// permutation if one has been performed to compute the pivot
if (indpermut != k) {
typename Vector::value_type tmp = lignecur[k];
lignecur[k] = lignecur[indpermut];
lignecur[indpermut] = tmp;
}
typename Vector::value_type headcoeff;
_F.divin (_F.neg (headcoeff, lignecur[k]), lignepivot[k]);
// LU in place
_F.assign (lignecur[k], zero);
for (long j = k; ++j < n;)
_F.axpyin (lignecur[j], headcoeff, lignepivot[j]) ;
}
template <class _Field>
template <class Vector>
void GaussDomain<_Field>::LU (Vector &lignecur,
const Vector &lignepivot,
unsigned long indcol,
long indpermut)
{
long n = lignecur.size ();
long k = indcol - 1;
// permutation if one has been performed to compute the pivot
if (indpermut != k) {
typename Vector::value_type tmp = lignecur[k];
lignecur[k] = lignecur[indpermut];
lignecur[indpermut] = tmp;
}
typename Vector::value_type headcoeff;
// LU in place
_F.div (headcoeff, lignecur[k], lignepivot[k]);
_F.assign (lignecur[k], headcoeff);
_F.negin (headcoeff);
for (long j = k; ++j < n;)
_F.axpyin (lignecur[j],headcoeff,lignepivot[j]);
}
template <class _Field>
template <class Vector, class D>
void GaussDomain<_Field>::SparseFindPivot (Vector &lignepivot,
unsigned long &indcol,
long &indpermut,
D &columns,
Element &determinant)
{
// std::cerr << "SFP BEG : lignepivot: [";
// for(typename Vector::const_iterator refs = lignepivot.begin();
// refs != lignepivot.end() ;
// ++refs )
// std::cerr << '(' << refs->first << ';' << refs->second << ')';
// std::cerr << "]" << std::endl;
typedef typename Vector::value_type E;
long nj = lignepivot.size ();
bool pivoting = false;
if (nj > 0) {
indpermut = lignepivot[0].first;
long ds = --columns[indpermut], dl, p = 0;
for (long j = 1; j < nj; ++j) {
if ((dl = --columns[lignepivot[j].first]) < ds) {
ds = dl;
p = j;
}
}
if (p != 0) {
pivoting = true;
if (indpermut == static_cast<long>(indcol)) {
Element ttm;
_F.assign (ttm, lignepivot[p].second);
indpermut = lignepivot[p].first;
_F.assign (lignepivot[p].second, lignepivot[0].second);
_F.assign (lignepivot[0].second, ttm);
} else {
E ttm = lignepivot[p];
indpermut = ttm.first;
for (long m = p; m; --m)
lignepivot[m] = lignepivot[m-1];
lignepivot[0] = ttm;
}
}
_F.mulin(determinant, lignepivot[0].second);
if (indpermut != static_cast<long>(indcol)) {
// no need to decrement/increment, already done during the search
lignepivot[0].first = indcol;
pivoting = true;
}
if (pivoting) _F.negin(determinant);
++indcol;
} else
indpermut = -1;
// std::cerr << "SFP END : lignepivot: [";
// for(typename Vector::const_iterator refs = lignepivot.begin();
// refs != lignepivot.end() ;
// ++refs )
// std::cerr << '(' << refs->first << ';' << refs->second << ')';
// std::cerr << "]" << std::endl;
}
template <class _Field>
template <class Vector>
void GaussDomain<_Field>::SparseFindPivot (Vector &lignepivot, unsigned long &indcol, long &indpermut, Element& determinant)
{
long nj = lignepivot.size ();
if (nj > 0) {
indpermut = lignepivot[0].first;
_F.mulin(determinant, lignepivot[0].second);
if (indpermut != static_cast<long>(indcol)){
lignepivot[0].first = indcol;
_F.negin(determinant);
}
++indcol;
} else
indpermut = -1;
}
template <class _Field>
template <class Vector>
void GaussDomain<_Field>::FindPivot (Vector &lignepivot, unsigned long &k, long &indpermut)
{
// Dense lignepivot
long n = lignepivot.size ();
long j = k;
for (; j < n ; ++j )
if (!_F.isZero (lignepivot[j])) break ;
if (j == n )
indpermut = -1 ;
else {
indpermut = j ;
if (indpermut != k) {
typename Vector::value_type tmp = lignepivot[k] ;
lignepivot[k] = lignepivot[j] ;
lignepivot[j] = tmp ;
}
++k;
}
}
template <class _Field>
template <class Matrix>
unsigned long& GaussDomain<_Field>::InPlaceLinearPivoting (unsigned long &res,
Element &determinant,
Matrix &LigneA,
unsigned long Ni,
unsigned long Nj)
{
typedef typename Matrix::Row Vector;
typedef typename Vector::value_type E;
// Requirements : LigneA is an array of sparse rows
// In place (LigneA is modified)
// With reordering (D is a density type. Density is allocated here)
// long Ni = LigneA.n_row (), Nj = LigneA.n_col ();
commentator.start ("Gaussian elimination with reordering",
"IPLR", Ni);
commentator.report (Commentator::LEVEL_NORMAL, INTERNAL_DESCRIPTION)
<< "Gaussian elimination on " << Ni << " x " << Nj << " matrix" << std::endl;
#ifdef __LINBOX_COUNT__
long long nbelem = 0;
#endif
_F.init(determinant,1UL);
Vector Vzer (0);
// allocation of the column density
std::vector<size_t> col_density (Nj);
// assignment of LigneA with the domain object
for (unsigned long jj = 0; jj < Ni; ++jj)
for (unsigned long k = 0; k < LigneA[jj].size (); k++)
++col_density[LigneA[jj][k].first];
long last = Ni - 1;
long c;
unsigned long indcol = 0;
#ifdef __LINBOX_OFTEN__
long sstep = last/40;
if (sstep > 1000) sstep = 1000;
#else
long sstep = 1000;
#endif
// Elimination steps with reordering
for (long k = 0; k < last; ++k) {
unsigned long l;
long p = k, s = LigneA[k].size (), sl;
#ifdef __LINBOX_FILLIN__
if ( ! (k % 100) ) {
#else
if ( ! (k % sstep) ) {
#endif
commentator.progress (k);
#ifdef __LINBOX_FILLIN__
for (sl = 0, l = 0; l < Ni; ++l)
sl += LigneA[l].size ();
commentator.report (Commentator::LEVEL_IMPORTANT, PARTIAL_RESULT)
<< "Fillin (" << indcol << "/" << Ni << ") = "
<< sl << std::endl;
#endif
}
if (s) {
for (l = k + 1; l < Ni; ++l)
if (((sl = LigneA[l].size ()) < s) && (sl)) {
s = sl;
p = l;
}
if (p != k) {
_F.negin(determinant);
Vector vtm = LigneA[k];
LigneA[k] = LigneA[p];
LigneA[p] = vtm;
}
// LigneA.write(std::cerr << "BEF, k:" << k << ", indcol:" << indcol << ", c:" << c)<<std::endl;
SparseFindPivot (LigneA[k], indcol, c, col_density, determinant);
// LigneA.write(std::cerr << "PIV, k:" << k << ", indcol:" << indcol << ", c:" << c)<<std::endl;
if (c != -1)
for (l = k + 1; l < Ni; ++l)
eliminate (LigneA[l], LigneA[k], indcol, c, col_density);
// LigneA.write(std::cerr << "AFT " )<<std::endl;
#ifdef __LINBOX_COUNT__
nbelem += LigneA[k].size ();
#endif
LigneA[k] = Vzer;
}
}//for k
SparseFindPivot (LigneA[last], indcol, c, determinant);
#ifdef __LINBOX_COUNT__
nbelem += LigneA[last].size ();
commentator.report (Commentator::LEVEL_NORMAL, PARTIAL_RESULT)
<< "Left elements : " << nbelem << std::endl;
#endif
#ifdef __LINBOX_FILLIN__
long sl = 0, l = 0;
for (; l < Ni; ++l)
sl += LigneA[l].size ();
commentator.report (Commentator::LEVEL_IMPORTANT, PARTIAL_RESULT)
<< "Fillin (" << indcol << "/" << Ni << ") = " << sl << std::endl;
#endif
res = indcol;
integer card;
if ((res < Ni) || (res < Nj))
_F.init(determinant,0UL);
_F.write(commentator.report (Commentator::LEVEL_NORMAL, PARTIAL_RESULT)
<< "Determinant : ", determinant)
<< " over GF (" << _F.cardinality (card) << ")" << std::endl;
commentator.report (Commentator::LEVEL_NORMAL, PARTIAL_RESULT)
<< "Rank : " << res
<< " over GF (" << card << ")" << std::endl;
commentator.stop ("done", 0, "IPLR");
return res;
}
template <class _Field>
template <class Matrix>
unsigned long& GaussDomain<_Field>::NoReordering (unsigned long &res,
Element &determinant,
Matrix &LigneA,
unsigned long Ni,
unsigned long Nj)
{
// Requirements : SLA is an array of sparse rows
// IN PLACE.
// Without reordering (Pivot is first non-zero in row)
// long Ni = SLA.n_row (), Nj = SLA.n_col ();
// long Ni = LigneA.n_row (), Nj = LigneA.n_col ();
commentator.start ("Gaussian elimination (no reordering)",
"NoRe", Ni);
commentator.report (Commentator::LEVEL_NORMAL, INTERNAL_DESCRIPTION)
<< "Gaussian elimination on " << Ni << " x " << Nj << " matrix" << std::endl;
typedef typename Matrix::Row Vector;
typedef typename Vector::value_type E;
typedef typename Matrix::Element Element;
#ifdef __LINBOX_COUNT__
long long nbelem = 0;
#endif
Vector Vzer (0);
_F.init(determinant,1UL);
long last = Ni - 1;
long c;
unsigned long indcol (0);
for (long k = 0; k < last; ++k) {
if (!(k % 1000))
commentator.progress (k);
unsigned long l;
if (!LigneA[k].empty ()) {
SparseFindPivot (LigneA[k], indcol, c, determinant);
if (c != -1)
for (l = k + 1; l < Ni; ++l)
eliminate (LigneA[l], LigneA[k], indcol, c);
#ifdef __LINBOX_COUNT__
nbelem += LigneA[k].size ();
#endif
LigneA[k] = Vzer;
}
}
SparseFindPivot ( LigneA[last], indcol, c, determinant);
#ifdef __LINBOX_COUNT__
nbelem += LigneA[last].size ();
commentator.report (Commentator::LEVEL_NORMAL, PARTIAL_RESULT)
<< "Left elements : " << nbelem << std::endl;
#endif
res = indcol;
if ((res < Ni) || (res < Nj))
_F.init(determinant,0UL);
integer card;
_F.write(commentator.report (Commentator::LEVEL_NORMAL, PARTIAL_RESULT)
<< "Determinant : ", determinant)
<< " over GF (" << _F.cardinality (card) << ")" << std::endl;
commentator.report (Commentator::LEVEL_NORMAL, PARTIAL_RESULT)
<< "Rank : " << res
<< " over GF (" << card << ")" << std::endl;
commentator.stop ("done", 0, "NoRe");
return res;
}
template <class _Field>
template <class Matrix>
unsigned long &GaussDomain<_Field>::upperin (unsigned long &res, Matrix &A)
{
// Requirements : A is an array of rows
// In place (A is modified)
// Without reordering (Pivot is first non-zero in row)
long Ni = A.rowdim ();
long last = Ni - 1;
long c;
unsigned long indcol = 0;
for (long k = 0; k < last; ++k) {
FindPivot (A[k], indcol, c);
if (c != -1)
for (long l = k + 1; l < Ni; ++l)
Upper (A[l], A[k], indcol, c);
}
FindPivot (A[last], indcol, c);
return res = indcol;
}
template <class _Field>
template <class Matrix>
unsigned long &GaussDomain<_Field>::LUin (unsigned long &res, Matrix &A)
{
// Requirements : A is an array of rows
// In place (A is modified)
// Without reordering (Pivot is first non-zero in row)
long Ni = A.rowdim ();
long last = Ni - 1;
long c;
unsigned long indcol = 0;
for (long k = 0; k < last; ++k) {
FindPivot (A[k], indcol, c);
if (c != -1)
for (long l = k + 1; l < Ni; ++l)
LU (A[l], A[k], indcol, c);
}
FindPivot (A[last], indcol, c);
return res = indcol;
}
template <class _Field>
template <class Matrix> unsigned long& GaussDomain<_Field>::rankin(unsigned long &rank,
Matrix &A,
unsigned long Ni,
unsigned long Nj,
SparseEliminationTraits::PivotStrategy reord)
{
Element determinant;
if (reord == SparseEliminationTraits::PIVOT_NONE)
return NoReordering(rank, determinant, A, Ni, Nj);
else
return InPlaceLinearPivoting(rank, determinant, A, Ni, Nj);
}
template <class _Field>
template <class Matrix> unsigned long& GaussDomain<_Field>::rankin(unsigned long &rank,
Matrix &A,
SparseEliminationTraits::PivotStrategy reord)
{
return rankin(rank, A, A.rowdim (), A.coldim (), reord);
}
template <class _Field>
template <class Matrix> unsigned long& GaussDomain<_Field>::rank(unsigned long &rank,
const Matrix &A,
SparseEliminationTraits::PivotStrategy reord)
{
return rank(rank, A, A.rowdim (), A.coldim (), reord);
}
template <class _Field>
template <class Matrix> unsigned long& GaussDomain<_Field>::rank(unsigned long &rank,
const Matrix &A,
unsigned long Ni,
unsigned long Nj,
SparseEliminationTraits::PivotStrategy reord)
{
Matrix CopyA(Ni);
for(unsigned long i = 0; i < Ni; ++i)
CopyA[i] = A[i];
Element determinant;
if (reord == SparseEliminationTraits::PIVOT_NONE)
return NoReordering(rank, determinant, CopyA, Ni, Nj);
else {
return InPlaceLinearPivoting(rank, determinant, CopyA, Ni, Nj);
}
}
template <class _Field>
template <class Matrix> typename GaussDomain<_Field>::Element& GaussDomain<_Field>::detin(Element &determinant,
Matrix &A,
unsigned long Ni,
unsigned long Nj,
SparseEliminationTraits::PivotStrategy reord)
{
unsigned long rank;
if (reord == SparseEliminationTraits::PIVOT_NONE)
NoReordering(rank, determinant, A, Ni, Nj);
else
InPlaceLinearPivoting(rank, determinant, A, Ni, Nj);
return determinant;
}
template <class _Field>
template <class Matrix> typename GaussDomain<_Field>::Element& GaussDomain<_Field>::detin(Element &determinant,
Matrix &A,
SparseEliminationTraits::PivotStrategy reord)
{
return detin(determinant, A, A.rowdim (), A.coldim (), reord);
}
template <class _Field>
template <class Matrix> typename GaussDomain<_Field>::Element& GaussDomain<_Field>::det(Element &determinant,
const Matrix &A,
SparseEliminationTraits::PivotStrategy reord)
{
return det(determinant, A, A.rowdim (), A.coldim (), reord);
}
template <class _Field>
template <class Matrix> typename GaussDomain<_Field>::Element& GaussDomain<_Field>::det(Element &determinant,
const Matrix &A,
unsigned long Ni,
unsigned long Nj,
SparseEliminationTraits::PivotStrategy reord)
{
Matrix CopyA(Ni);
for(unsigned long i = 0; i < Ni; ++i)
CopyA[i] = A[i];
unsigned long rank;
if (reord == SparseEliminationTraits::PIVOT_NONE)
NoReordering(rank, determinant, CopyA, Ni, Nj);
else {
InPlaceLinearPivoting(rank, determinant, CopyA, Ni, Nj);
}
return determinant;
}
} // namespace LinBox
#endif // __GAUSS_INL
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