/usr/include/linbox/ffpack/ffpack_krylovelim.inl is in liblinbox-dev 1.1.6~rc0-4.1.
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/* ffpack/ffpack_krylovelim.inl
* Copyright (C) 2006 Clement Pernet
*
* Written by Clement Pernet <Clement.Pernet@imag.fr>
*
* See COPYING for license information.
*/
#ifndef MIN
#define MIN(a,b) (a<b)?a:b
#endif
#ifndef MAX
#define MAX(a,b) (a<b)?b:a
#endif
// A is m x n with m <= n
// Ensures : rankprof is the row rankprofil of the matrix k x n matrix B formed as follows (k = sum d_i):
// for d_i < j < d_{i+1} the jth row B_j = is e_j
// B_{d_i} = A_i
// iterates must be initialized by [1, 2, ...]
// inviterates is the inverse finction of iterates
template <class Field>
inline size_t
FFPACK::KrylovElim( const Field& F, const size_t M, const size_t N,
typename Field::Element * A, const size_t lda, size_t*P,
size_t *Q, const size_t deg, size_t *iterates, size_t * inviterates,size_t maxit,
size_t virt){
if ( !(M && N) ) return 0;
typedef typename Field::Element elt;
static elt Mone, one, zero;
F.init(Mone, -1.0);
F.init(one,1.0);
F.init(zero,0.0);
if (M == 1){
virt += deg;
for (size_t i=0; i<virt; ++i)
if (iterates[i]){
// cerr<<"A["<<N-i-1<<"]=0"<<endl;
F.assign (A [N-iterates[i]], zero);
}
size_t ip=0;
//while (ip<N && !F.isUnit(*(A+ip)))ip++;
while (ip<N && F.isZero (*(A+ip))) {
// cout<<(*(A+ip))<<" ";
ip++;
}
//cout<<endl;
*Q=0;
//cerr<<"ip = "<<ip<<endl;
if (ip==N){ // current row is zero
*P=0;
//cerr<<"return 0"<<endl;
return 0;
}
*P = ip;
// cerr<<"iterates = ";
// cerr<<"iterates avant"<<endl;
// for (size_t i=0; i<N; ++i)
// cerr<<iterates[i]<<" ";
// cerr<<endl;
// cerr<<"inviterates["<<N<<"-"<<ip<<"] ="<<inviterates[N-ip]<<endl;
// cerr<<"iterates[inviterates[N-ip]] ="<<iterates[inviterates[N-ip]]<<endl;
iterates [inviterates[N-ip] -1 ] = 0;
if (ip >0){
iterates [inviterates[N] -1 ] = N-ip;
inviterates[N-ip] = inviterates[N];
}
// cerr<<"iterates apres"<<endl;
// for (size_t i=0; i<N; ++i)
// cerr<<iterates[i]<<" ";
// cerr<<endl;
//cout<<"iterates ["<<N<<"-1-"<<ip<<"] = 0"<<endl;
if (ip!=0){
// swap the pivot
typename Field::Element tmp=*A;
*A = *(A+ip);
*(A+ip) = tmp;
}
return 1;
} else { // MN>1
size_t Nup = M>>1;
size_t Ndown = M - Nup;
// Recursive call on NW
size_t R = KrylovElim (F, Nup, N, A, lda, P, Q, deg, iterates, inviterates, maxit, virt);
typename Field::Element *Ar = A + Nup*lda; // SW
typename Field::Element *Ac = A + R; // NE
typename Field::Element *An = Ar + R; // SE
if (R){
// Ar <- Ar.P
applyP (F, FflasRight, FflasTrans, Ndown, 0, R, Ar, lda, P);
// Ar <- Ar.U1^-1
ftrsm( F, FflasRight, FflasUpper,
FflasNoTrans, FFLAS::FflasNonUnit, Ndown, R,
one, A, lda, Ar, lda);
// An <- An - Ar*Ac
fgemm( F, FflasNoTrans, FflasNoTrans, Ndown, N-R, R,
Mone, Ar, lda, Ac, lda, one, An, lda);
}
// Recursive call on SE
size_t R2 = KrylovElim (F, Ndown, N-R, An, lda,P+R, Q+Nup, deg, iterates, inviterates, maxit, MIN(maxit-deg,(virt+Nup*deg)));
for (size_t i = R; i < R + R2; ++i)
P[i] += R;
if (R2)
// An <- An.P2
applyP (F, FflasRight, FflasTrans, Nup, R, R+R2, A, lda, P);
// Non zero row permutations
for (size_t i = Nup; i < M; i++)
Q[i] += Nup;
if (R < Nup){
// Permutation of the 0 rows
for ( size_t i = Nup, j = R ; i < Nup + R2; ++i, ++j){
fcopy( F, N - j, A + j*(lda + 1), 1, A + i*lda + j, 1);
for (typename Field::Element *Ai = A + i*lda + j;
Ai != A + i*lda + N; ++Ai)
F.assign (*Ai, zero);
size_t t = Q[j];
Q[j]=Q[i];
Q[i] = t;
}
}
return R + R2;
}
}
template <class Field>
size_t
FFPACK::SpecRankProfile (const Field& F, const size_t M, const size_t N,
typename Field::Element * A, const size_t lda, const size_t deg,
size_t *rankProfile){
//size_t deg = (N-1)/M+1; // Number of trivial iterates per blocs
size_t * Q = new size_t[M];
size_t * P = new size_t[N];
size_t * iterates = new size_t[N];
size_t * inviterates = new size_t[N+1];
for (size_t i=0; i < N; ++i)
inviterates[i+1] = iterates[i] = i+1;
size_t R = KrylovElim (F, M, N, A, lda, P, Q, deg, iterates, inviterates, N,0);
//cerr<<"Apres tout iterates = "<<endl;
// for (size_t i=0; i<N; ++i)
// cerr<<iterates[i]<<" ";
// cerr<<endl;
size_t curr_row = 0;
size_t it_idx = 0;
size_t bk_idx = 0;
size_t rp_idx = 0;
bool dependent = false;
for (size_t i=0; i<M; ++i){
// cerr<<"Block "<<i<<endl;
for (size_t j=0; j<deg; ++j){
if (curr_row < N+M -1){
if (iterates[it_idx++]){
rankProfile [rp_idx++] = curr_row;
if (dependent){
#if DEBUG
std::cerr<<"FAIL itere dependant intercale"<<std::endl;
#endif
throw CharpolyFailed();
}
#if DEBUG
std::cerr<<"X";
#endif
}
else{
dependent = true;
#if DEBUG
std::cerr<<"O";
#endif
}
curr_row++;
}
}
dependent = false;
if ((Q [bk_idx] == i)&&(i<R)){
rankProfile [rp_idx++] = curr_row;
#if DEBUG
std::cerr<<"V"<<std::endl;
#endif
bk_idx++;
}
#if DEBUG
else
std::cerr<<"W"<<std::endl;
#endif
curr_row++;
}
delete[] P;
delete[] Q;
delete[] inviterates;
delete[] iterates;
return rp_idx;
}
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