/usr/include/linbox/algorithms/smith-form-sparseelim-poweroftwo.h is in liblinbox-dev 1.3.2-1.1build2.
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* Copyright (C) LinBox
* Written by JG Dumas
* Time-stamp: <06 Apr 12 11:50:12 Jean-Guillaume.Dumas@imag.fr>
* ========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========
*/
#ifndef __LINBOX_pp_gauss_poweroftwo_H
#define __LINBOX_pp_gauss_poweroftwo_H
#include <map>
#include <givaro/givconfig.h> // for Signed_Trait
#include "linbox/algorithms/smith-form-sparseelim-local.h"
// LINBOX_pp_gauss_steps_OUT outputs elimination steps
#ifdef LINBOX_pp_gauss_steps_OUT
// LINBOX_PRANK_OUT outputs intermediate ranks
# ifndef LINBOX_PRANK_OUT
# define LINBOX_PRANK_OUT
# endif
#endif
namespace LinBox
{
/** \brief Repository of functions for rank modulo a prime power by elimination
* on sparse matrices.
*/
template<typename UnsignedIntType>
class PowerGaussDomainPowerOfTwo {
typedef UnsignedIntType UInt_t;
typedef UnsignedIntType Element;
const Element zero;
const Element one;
public:
/** \brief The field parameter is the domain
* over which to perform computations
*/
PowerGaussDomainPowerOfTwo () : zero(0U), one(1U) {}
//Copy constructor
///
PowerGaussDomainPowerOfTwo (const PowerGaussDomainPowerOfTwo &M) {}
// --------------------------------------------
// Modulo operators
bool isNZero(const UInt_t& a ) const { return (bool)a ;}
bool isZero(const UInt_t& a ) const { return a == 0U;}
bool isOne(const UInt_t& a ) const { return a == 1U;}
bool isOdd(const UInt_t& b) const {
return (bool)(b & 1U);
}
bool MY_divides(const UInt_t& a, const UInt_t& b) const {
return (!(b%a));
}
UInt_t& MY_Zpz_inv (UInt_t& u1, const UInt_t& a, const size_t exponent, const UInt_t& TWOTOEXPMONE) const {
static const UInt_t ttep2(TWOTOEXPMONE+3);
if (this->isOne(a)) return u1=this->one;
REQUIRE( (one<<exponent) == (TWOTOEXPMONE+1) );
REQUIRE( a <= TWOTOEXPMONE );
REQUIRE( (a & 1) );
u1=ttep2-a; // 2-a
UInt_t xmone(a-1);
for(size_t i=2; i<exponent; i<<=1) {
xmone *= xmone;
xmone &= TWOTOEXPMONE;
u1 *= ++xmone; --xmone;
u1 &= TWOTOEXPMONE;
}
ENSURE( ((a * u1) & TWOTOEXPMONE) == 1 );
return u1;
}
// UInt_t& MY_Zpz_inv (UInt_t& u1, const UInt_t a, const UInt_t _p) const {
// u1 = 1UL;
// UInt_t r0(_p), r1(a);
// UInt_t q(r0/r1);
// r0 -= q * r1;
// if ( this->isZero(r0) ) return u1;
// UInt_t u0 = q;
// q = r1/r0;
// r1 -= q * r0;
// while ( this->isNZero(r1) ) {
// u1 += q * u0;
// q = r0/r1;
// r0 -= q * r1;
// if ( this->isZero(r0) ) return u1;
// u0 += q * u1;
// q = r1/r0;
// r1 -= q * r0;
// }
// return u1=_p-u0;
// }
// UInt_t MY_Zpz_inv (const UInt_t a, const UInt_t _p) const {
// UInt_t u1; return MY_Zpz_inv(u1,a,_p);
// }
// ------------------------------------------------
// Pivot Searchers and column strategy
// ------------------------------------------------
template<class Vecteur>
void SameColumnPivoting(const Vecteur& lignepivot, unsigned long& indcol, long& indpermut, Boolean_Trait<false>::BooleanType ) {}
template<class Vecteur>
void SameColumnPivoting(const Vecteur& lignepivot, unsigned long& indcol, long& indpermut, Boolean_Trait<true>::BooleanType ) {
// Try first in the same column
unsigned long nj = lignepivot.size() ;
if (nj && (indcol == lignepivot[0].first) && (this->isOdd(lignepivot[0].second) ) ) {
indpermut = indcol;
++indcol;
}
}
template<class BB, class Mmap>
bool SameColumnPivotingTrait(unsigned long& p, const BB& LigneA, const Mmap& psizes, unsigned long& indcol, long& indpermut, Boolean_Trait<false>::BooleanType ) {
// Do not try first in the same column
return false;
}
template<class BB, class Mmap>
bool SameColumnPivotingTrait(unsigned long& p, const BB& LigneA, const Mmap& psizes, unsigned long& indcol, long& c, Boolean_Trait<true>::BooleanType truetrait) {
c=-2;
for( typename Mmap::const_iterator iter = psizes.begin(); iter != psizes.end(); ++iter) {
p = (*iter).second;
SameColumnPivoting(LigneA[p], indcol, c, truetrait ) ;
if (c > -2 ) break;
}
if (c > -2)
return true;
else
return false;
}
template<class Vecteur>
void CherchePivot( Vecteur& lignepivot, unsigned long& indcol , long& indpermut ) {
unsigned long nj = lignepivot.size() ;
if (nj) {
indpermut= lignepivot[0].first;
if (indpermut != indcol)
lignepivot[0].first = (indcol);
++indcol;
}
else
indpermut = -1;
}
template<class Vecteur, class D>
void CherchePivot(Vecteur& lignepivot, unsigned long& indcol , long& indpermut, D& columns ) {
typedef typename Vecteur::value_type E;
long nj = lignepivot.size() ;
if (nj) {
indpermut = lignepivot[0].first;
long pp=0;
for(;pp<nj;++pp)
if (this->isOdd(lignepivot[pp].second) ) break;
if (pp < nj) {
long ds = columns[ lignepivot[pp].first ],dl,p=pp,j=pp;
for(++j;j<nj;++j)
if ( ( (dl=columns[lignepivot[j].first] ) < ds ) && (this->isOdd(lignepivot[j].second) ) ) {
ds = dl;
p = j;
}
if (p != 0) {
if (indpermut == (long)indcol) {
UInt_t ttm = lignepivot[p].second;
indpermut = lignepivot[p].first;
lignepivot[p].second = (lignepivot[0].second);
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;
}
}
if (indpermut != (long)indcol)
lignepivot[0].first = (indcol);
indcol++ ;
for(j=nj;j--;)
--columns[ lignepivot[j].first ];
}
else
indpermut = -2;
}
else
indpermut = -1;
}
template<class Vecteur>
void PreserveUpperMatrixRow(Vecteur& ligne, Boolean_Trait<true>::BooleanType ) {}
template<class Vecteur>
void PreserveUpperMatrixRow(Vecteur& ligne, Boolean_Trait<false>::BooleanType ) {
ligne = Vecteur(0);
}
template<class Vecteur, class De>
void FaireElimination( const size_t EXPONENT, const UInt_t& TWOK, const UInt_t& TWOKMONE,
Vecteur& lignecourante,
const Vecteur& lignepivot,
const long& indcol,
const long& indpermut,
De& columns) {
// typedef typename Vecteur::coefficientSpace F;
// typedef typename Vecteur::value_types E;
typedef typename Vecteur::value_type E;
unsigned long k = indcol - 1;
unsigned long nj = lignecourante.size() ;
if (nj) {
unsigned long j_head(0);
for(; j_head<nj; ++j_head)
if (long(lignecourante[j_head].first) >= indpermut) break;
unsigned long bjh(j_head-1);
if ((j_head<nj) && (long(lignecourante[j_head].first) == indpermut)) {
// -------------------------------------------
// Permutation
if (indpermut != (long)k) {
if (lignecourante[0].first == k) {
// non zero <--> non zero
UInt_t tmp = lignecourante[0].second ;
lignecourante[0].second = (lignecourante[j_head].second );
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();
Vecteur construit(nj + npiv);
// construit : <-- ci
// courante : <-- m
// pivot : <-- l
typedef typename Vecteur::iterator Viter;
Viter ci = construit.begin();
unsigned long m=1;
unsigned long l(0);
// A[i,k] <-- A[i,k] / A[k,k]
UInt_t headcoeff = TWOK-(lignecourante[0].second);
// UInt_t invpiv; MY_Zpz_inv(invpiv, lignepivot[0].second, TWOK);
UInt_t invpiv; MY_Zpz_inv(invpiv, lignepivot[0].second, EXPONENT, TWOKMONE);
headcoeff *= invpiv;
headcoeff &= TWOKMONE ;
// lignecourante[0].second = ( ((UModulo)( ( MOD-(lignecourante[0].second) ) * ( MY_Zpz_inv( lignepivot[0].second, MOD) ) ) ) % (UModulo)MOD ) ;
// UInt_t headcoeff = lignecourante[0].second ;
--columns[ lignecourante[0].first ];
unsigned long j_piv;
for(;l<npiv;++l)
if (lignepivot[l].first > k) break;
// for all j such that (j>k) and A[k,j]!=0
for(;l<npiv;++l) {
j_piv = lignepivot[l].first;
// if A[k,j]=0, then A[i,j] <-- A[i,j]
for (;(m<nj) && (lignecourante[m].first < j_piv);)
*ci++ = 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)) {
// lignecourante[m].second = ( ((UModulo)( headcoeff * lignepivot[l].second + lignecourante[m].second ) ) % (UModulo)MOD );
lignecourante[m].second += ( headcoeff * lignepivot[l].second );
lignecourante[m].second &= TWOKMONE;
if (isNZero(lignecourante[m].second))
*ci++ = lignecourante[m++];
else
--columns[ lignecourante[m++].first ];
// m++;
}
else {
UInt_t tmp(headcoeff);
tmp *= lignepivot[l].second;
tmp &= TWOKMONE;
if (isNZero(tmp)) {
++columns[j_piv];
*ci++ = E(j_piv, tmp );
}
}
}
// if A[k,j]=0, then A[i,j] <-- A[i,j]
for (;m<nj;)
*ci++ = lignecourante[m++];
construit.erase(ci,construit.end());
lignecourante = construit;
}
else
// -------------------------------------------
// Permutation
if (indpermut != (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[tmp.first ];
++columns[indpermut];
tmp.first = (indpermut);
for(;l<bjh;l++)
lignecourante[l] = lignecourante[l+1];
lignecourante[bjh] = tmp;
} // else
// zero <--> zero
}
}
}
// ------------------------------------------------------
// Rank calculators, defining row strategy
// ------------------------------------------------------
template<class BB, class D, class Container, bool PrivilegiateNoColumnPivoting, bool PreserveUpperMatrix>
void gauss_rankin(size_t EXPONENTMAX, Container& ranks, BB& LigneA, const size_t Ni, const size_t Nj, const D& density_trait)
{
commentator().start ("Gaussian elimination with reordering modulo a prime power of 2",
"PRGEPo2", Ni);
ranks.resize(0);
typedef typename BB::Row Vecteur;
size_t EXPONENT = EXPONENTMAX;
UInt_t TWOK(1UL); TWOK <<= EXPONENT;
UInt_t TWOKMONE(TWOK); --TWOKMONE;
#ifdef LINBOX_PRANK_OUT
std::cerr << "Elimination mod " << TWOK << std::endl;
#endif
D col_density(Nj);
// assignment of LigneA with the domain object
size_t jj;
for(jj=0; jj<Ni; ++jj) {
Vecteur tmp = LigneA[jj];
Vecteur toto(tmp.size());
unsigned long k=0,rs=0;
for(; k<tmp.size(); ++k) {
UInt_t r = tmp[k].second;
// if (r <0) r %= TWOK ;
// if (r <0) r += TWOK ;
if (r >= TWOK) r &= TWOKMONE;
if (isNZero(r)) {
++col_density[ tmp[k].first ];
toto[rs] =tmp[k];
toto[rs].second = ( r );
++rs;
}
}
toto.resize(rs);
LigneA[jj] = toto;
// LigneA[jj].reactualsize(Nj);
}
unsigned long last = Ni-1;
long c(0);
unsigned long indcol(0);
unsigned long ind_pow = 1;
unsigned long maxout = Ni/100; maxout = (maxout<10 ? 10 : (maxout>1000 ? 1000 : maxout) );
unsigned long thres = Ni/maxout; thres = (thres >0 ? thres : 1);
for (unsigned long k=0; k<last;++k) {
if ( ! (k % maxout) ) commentator().progress (k);
unsigned long p=k;
for(;;) {
std::multimap< long, long > psizes;
for(p=k; p<Ni; ++p)
psizes.insert( psizes.end(), std::pair<long,long>( LigneA[p].size(), p) );
#ifdef LINBOX_pp_gauss_steps_OUT
std::cerr << "------------ ordered rows " << k << " -----------" << std::endl;
for( std::multimap< long, long >::const_iterator iter = psizes.begin(); iter != psizes.end(); ++iter)
{
std::cerr << (*iter).second << " : #" << (*iter).first << std::endl;
}
std::cerr << "---------------------------------------" << std::endl;
#endif
if ( SameColumnPivotingTrait(p, LigneA, psizes, indcol, c, typename Boolean_Trait<PrivilegiateNoColumnPivoting>::BooleanType() ) )
break;
for( typename std::multimap< long, long >::const_iterator iter = psizes.begin(); iter != psizes.end(); ++iter) {
p = (*iter).second;
CherchePivot( LigneA[p], indcol, c , col_density) ;
if (c > -2 ) break;
}
if (c > -2) break;
for(unsigned long ii=k;ii<Ni;++ii)
for(unsigned long jjj=LigneA[ii].size();jjj--;)
LigneA[ii][jjj].second >>= 1;
--EXPONENT;
TWOK >>= 1;
TWOKMONE >>=1;
ranks.push_back( indcol );
++ind_pow;
#ifdef LINBOX_PRANK_OUT
std::cerr << "Rank mod 2^" << ind_pow << " : " << indcol << std::endl;
if (TWOK == 1) std::cerr << "wattadayada inhere ?" << std::endl;
#endif
}
if (p != k) {
#ifdef LINBOX_pp_gauss_steps_OUT
std::cerr << "------------ permuting rows " << p << " and " << k << " ---" << std::endl;
#endif
Vecteur vtm = LigneA[k];
LigneA[k] = LigneA[p];
LigneA[p] = vtm;
}
#ifdef LINBOX_pp_gauss_steps_OUT
if (c != (long(indcol)-1L))
std::cerr << "------------ permuting cols " << (indcol-1) << " and " << c << " ---" << std::endl;
#endif
if (c != -1)
for(unsigned long l=k + 1; l < Ni; ++l)
FaireElimination(EXPONENT, TWOK, TWOKMONE, LigneA[l], LigneA[k], indcol, c, col_density);
#ifdef LINBOX_pp_gauss_steps_OUT
LigneA.write(cerr << "step[" << k << "], pivot: " << c << std::endl) << endl;
#endif
PreserveUpperMatrixRow(LigneA[k], typename Boolean_Trait<PreserveUpperMatrix>::BooleanType());
}
c = -2;
SameColumnPivoting(LigneA[last], indcol, c, typename Boolean_Trait<PrivilegiateNoColumnPivoting>::BooleanType() );
if (c == -2) CherchePivot( LigneA[last], indcol, c, col_density );
while( c == -2) {
ranks.push_back( indcol );
for(long jjj=LigneA[last].size();jjj--;)
LigneA[last][jjj].second >>= 1;
TWOK >>= 1;
CherchePivot( LigneA[last], indcol, c, col_density );
}
while( TWOK > 1) {
TWOK >>= 1;
ranks.push_back( indcol );
}
// ranks.push_back(indcol);
#ifdef LINBOX_pp_gauss_steps_OUT
LigneA.write(cerr << "step[" << Ni-1 << "], pivot: " << c << std::endl) << endl;
#endif
#ifdef LINBOX_PRANK_OUT
std::cerr << "Rank mod 2^" << EXPONENT << " : " << indcol << std::endl;
#endif
commentator().stop ("done", 0, "PRGEPo2");
}
template<class BB, class D, class Container>
void prime_power_rankin (size_t EXPONENT, Container& ranks, BB& SLA, const size_t Ni, const size_t Nj, const D& density_trait, int StaticParameters=0) {
if (PRIVILEGIATE_NO_COLUMN_PIVOTING & StaticParameters) {
if (PRESERVE_UPPER_MATRIX & StaticParameters) {
gauss_rankin<BB,D,Container,true,true>(EXPONENT,ranks, SLA, Ni, Nj, density_trait);
} else {
gauss_rankin<BB,D,Container,true,false>(EXPONENT,ranks, SLA, Ni, Nj, density_trait);
}
} else {
if (PRESERVE_UPPER_MATRIX & StaticParameters) {
gauss_rankin<BB,D,Container,false,true>(EXPONENT,ranks, SLA, Ni, Nj, density_trait);
} else {
gauss_rankin<BB,D,Container,false,false>(EXPONENT,ranks, SLA, Ni, Nj, density_trait);
}
}
}
template<class Matrix, template<class, class> class Container, template<class> class Alloc>
Container<std::pair<size_t,UInt_t>, Alloc<std::pair<size_t,UInt_t> > >& operator()(Container<std::pair<size_t,UInt_t>, Alloc<std::pair<size_t,UInt_t> > >& L, Matrix& A, size_t EXPONENT, int StaticParameters=0) {
Container<size_t, Alloc<size_t> > ranks;
prime_power_rankin( EXPONENT, ranks, A, A.rowdim(), A.coldim(), std::vector<size_t>(),StaticParameters);
L.resize( 0 ) ;
UInt_t MOD(1);
size_t num = 0, diff;
for( typename Container<size_t, Alloc<size_t> >::const_iterator it = ranks.begin(); it != ranks.end(); ++it) {
diff = *it-num;
if (diff > 0)
L.push_back( std::pair<size_t,UInt_t>(*it-num,MOD) );
MOD <<= 1;
num = *it;
}
return L;
}
};
} // end of LinBox namespace
#endif //__LINBOX_pp_gauss_poweroftwo_H
// vim:sts=8:sw=8:ts=8:noet:sr:cino=>s,f0,{0,g0,(0,:0,t0,+0,=s
// Local Variables:
// mode: C++
// tab-width: 8
// indent-tabs-mode: nil
// c-basic-offset: 8
// End:
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