/usr/include/fflas-ffpack/utils/fflas_randommatrix.h is in fflas-ffpack-common 2.2.2-5.
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* Copyright (C) FFLAS-FFPACK
* Written by Brice Boyer (briceboyer) <boyer.brice@gmail.com>
* This file is Free Software and part of FFLAS-FFPACK.
*
* ========LICENCE========
* This file is part of the library FFLAS-FFPACK.
*
* FFLAS-FFPACK 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========
*.
*/
/*! @file utils/fflas_randommatrix.h
* @ingroup tests
* @brief Utilities to create matrices with prescribed shapes, properties,...
* To be used in benchmarks/tests
*/
#ifndef __FFLASFFPACK_randommatrix_H
#define __FFLASFFPACK_randommatrix_H
#include "fflas-ffpack/fflas-ffpack-config.h"
#include "fflas-ffpack/utils/debug.h"
#include "fflas-ffpack/ffpack/ffpack.h"
#include <givaro/givinteger.h>
#include <givaro/givintprime.h>
#include <givaro/givranditer.h>
#include <chrono>
#include <random>
namespace FFPACK {
/*! @brief Random Matrix.
* Creates a \c m x \c n matrix with random entries.
* @param F field
* @param A pointer to the matrix (preallocated to at least \c m x \c lda field elements)
* @param m number of rows in \p A
* @param n number of cols in \p A
* @param lda leading dimension of \p A
* @return pointer to \c A.
*/
template<class Field>
typename Field::Element * RandomMatrix(const Field & F,
typename Field::Element * A,
size_t m, size_t n, size_t lda, size_t b=0)
{
typedef typename Field::RandIter Randiter ;
Randiter R(F, b);
for (size_t i=0 ; i<m ; ++i)
for (size_t j= 0; j<n ;++j)
R.random( A[i*lda+j] );
return A;
}
/*! Random integer in range.
* @param a min bound
* @param b max bound
* @return a random integer in [a,b[ */
size_t RandInt(size_t a, size_t b)
{
size_t x = a ;
x += (size_t)rand()%(b-a);
FFLASFFPACK_check(x<b && x>=a);
return x ;
}
/*! @brief Random Matrix with prescribed rank.
* Creates an \c m x \c n matrix with random entries and rank \c r.
* @param F field
* @param A pointer to the matrix (preallocated to at least \c m x \c lda field elements)
* @param r rank of the matrix to build
* @param m number of rows in \p A
* @param n number of cols in \p A
* @param lda leading dimension of \p A
* @return pointer to \c A.
*/
template<class Field>
typename Field::Element_ptr RandomMatrixWithRank (const Field & F,
typename Field::Element_ptr A, size_t lda,
size_t r, size_t m, size_t n)
{
FFLASFFPACK_check(r <= std::min(m,n));
FFLASFFPACK_check(n <= lda);
typedef typename Field::RandIter Randiter ;
typedef typename Field::Element_ptr Element_ptr;
Randiter R(F);
Givaro::GeneralRingNonZeroRandIter<Field,Randiter> nzR(R);
size_t * P = FFLAS::fflas_new<size_t>(n);
size_t * Q = FFLAS::fflas_new<size_t>(m);
for (size_t i = 0 ; i < m ; ++i ) Q[i] = 0;
for (size_t i = 0 ; i < n ; ++i ) P[i] = 0;
Element_ptr U = FFLAS::fflas_new(F,m,n);
Element_ptr L = FFLAS::fflas_new(F,m,m);
/* Create L, lower invertible */
for (size_t i=0 ; i<m ; ++i){
for (size_t j= 0; j<i ;++j) R.random( L[i*m+j] );
nzR.random( L[i*m+i] );
for (size_t j= i+1; j<m ;++j) F.init(L[i*m+j],F.zero);
}
/* Create U, upper or rank r */
for (size_t i=0 ; i<r ; ++i){
for (size_t j= 0 ; j<i ;++j) F.init(U[i*n+j],0U);
nzR.random( U[i*n+i] );
for (size_t j= i+1; j<n ;++j) R.random( U[i*n+j] );
}
for (size_t i=r ; i<m ; ++i)
for (size_t j= 0 ; j<n ;++j)
F.init(U[i*n+j],F.zero);
/* Create a random P,Q */
for (size_t i = 0 ; i < n ; ++i)
P[i] = i + RandInt(0U,n-i);
for (size_t i = 0 ; i < m ; ++i)
Q[i] = i + RandInt(0U,m-i);
/* compute product */
FFPACK::applyP (F, FFLAS::FflasRight, FFLAS::FflasNoTrans,
m,0,(int)n, U, n, P);
FFPACK::applyP (F, FFLAS::FflasLeft, FFLAS::FflasNoTrans,
m,0,(int)m, L, m, Q);
FFLAS::fgemm (F, FFLAS::FflasNoTrans, FFLAS::FflasNoTrans,
m, n, m, F.one, L, m, U, n, F.zero, A, lda);
//! @todo compute LU with ftrtr
FFLAS::fflas_delete(P);
FFLAS::fflas_delete(L);
FFLAS::fflas_delete(U);
FFLAS::fflas_delete(Q);
return A;
}
void RandomRankProfile (size_t N, size_t R, size_t* rkp){
size_t curr = 0;
std::vector<bool> rows(N,false);
while (curr<R){
size_t i;
while (rows [i = rand() % N]);
rows[i] = true;
rkp [curr] = i;
curr++;
}
}
template<class Field>
void RandomMatrixWithRankandRPM (const Field& F, typename Field::Element_ptr A, size_t lda,
size_t R, size_t M, size_t N,
const size_t * RRP, const size_t * CRP){
typedef typename Field::RandIter Randiter ;
Randiter RI(F);
Givaro::GeneralRingNonZeroRandIter<Field,Randiter> nzR(RI);
typename Field::Element_ptr L= FFLAS::fflas_new(F,M,N);
FFLAS::pfzero(F, M, N, L, N);
FFLAS::ParSeqHelper::Parallel<FFLAS::CuttingStrategy::Block,FFLAS::StrategyParameter::Threads> H;
SYNCH_GROUP ( FOR1D(k, R, H,
{
size_t i = RRP[k];
size_t j = CRP[k];
nzR.random (L [i*N+j]);
for (size_t l=i+1; l < M; ++l)
RI.random (L [l*N+j]);
}));
typename Field::Element_ptr U= FFLAS::fflas_new(F,N,N);
FFLAS::pfzero(F, N, N, U, N);
SYNCH_GROUP ( FOR1D(i, N, H,
{
nzR.random (U [i*N+i]);
for (size_t j=i+1; j < N; ++j)
RI.random (U [i*N+j]);
}));
typename Field::Element alpha, beta;
F.init(alpha,1.0);
F.init(beta,0.0);
// auto sp=SPLITTER(); //CP: broken with Modular<Integer>. Need to reorganize the helper behaviour with ParSeq and ModeTraits
auto sp=NOSPLIT();
FFLAS::fgemm (F, FFLAS::FflasNoTrans, FFLAS::FflasNoTrans, M,N,N, alpha, L, N, U, N, beta, A, lda, sp);
FFLAS::fflas_delete(L);
FFLAS::fflas_delete(U);
}
/*! @brief Random Matrix with prescribed rank, with random rank profile matrix
* Creates an \c m x \c n matrix with random entries, rank \c r and with a rank profile matrix
* chosen uniformly at random.
* @param F field
* @param A pointer to the matrix (preallocated to at least \c m x \c lda field elements)
* @param r rank of the matrix to build
* @param m number of rows in \p A
* @param n number of cols in \p A
* @param lda leading dimension of \p A
* @return pointer to \c A.
*/
template<class Field>
void RandomMatrixWithRankandRandomRPM (const Field& F, typename Field::Element_ptr A, size_t lda,
size_t R, size_t M, size_t N){
// generate the r pivots in the rank profile matrix E
size_t pivot_r[R];
size_t pivot_c[R];
RandomRankProfile (M, R, pivot_r);
RandomRankProfile (N, R, pivot_c);
RandomMatrixWithRankandRPM (F, A, lda, R, M, N, pivot_r, pivot_c);
}
/*! @brief Random Matrix with prescribed det.
* @bug duplicate with linbox
* Creates a \c m x \c n matrix with random entries and rank \c r.
* @param F field
* @param A pointer to the matrix (preallocated to at least \c m x \c lda field elements)
* @param r rank of the matrix to build
* @param m number of rows in \p A
* @param n number of cols in \p A
* @param lda leading dimension of \p A
* @return pointer to \c A.
*/
template<class Field>
typename Field::Element * RandomMatrixWithDet(const Field & F,
typename Field::Element * A,
typename Field::Element d,
size_t n, size_t lda)
{
FFLASFFPACK_check(n <= lda);
typedef typename Field::RandIter Randiter ;
typedef typename Field::Element Element ;
Randiter R(F);
Givaro::GeneralRingNonZeroRandIter<Field,Randiter> nzR(R);
size_t * P = FFLAS::fflas_new<size_t>(n);
size_t * Q = FFLAS::fflas_new<size_t>(n);
for (size_t i = 0 ; i < n ; ++i ) Q[i] = 0;
for (size_t i = 0 ; i < n ; ++i ) P[i] = 0;
Element * U = FFLAS::fflas_new<Element>(n*lda);
Element * L = FFLAS::fflas_new<Element>(n*n);
/* Create a random P,Q */
for (size_t i = 0 ; i < n ; ++i)
P[i] = i + RandInt(0U,n-i);
for (size_t i = 0 ; i < n ; ++i)
Q[i] = i + RandInt(0U,n-i);
/* det of P,Q */
int d1 =1 ;
for (size_t i = 0 ; i < n ; ++i)
if (P[i] != i)
d1 = -d1;
for (size_t i = 0 ; i < n ; ++i)
if (Q[i] != i)
d1 = -d1;
/* Create L, lower det d */
for (size_t i=0 ; i<n ; ++i)
for (size_t j= 0; j<i ;++j)
R.random( L[i*n+j] );
Element dd = F.one;
for (size_t i=0 ; i<n-1 ; ++i) {
nzR.random( L[i*n+i] );
F.mulin(dd,L[i*n+i]);
}
F.div(dd,d,dd);
if (d1<0) F.negin(dd);
L[n*n-1] = dd ;
for (size_t i=0 ; i<n ; ++i)
for (size_t j= i+1; j<n ;++j)
F.init(L[i*n+j],0U);
/* Create U, upper or rank r */
for (size_t i=0 ; i<n ; ++i) {
for (size_t j= 0; j<i ;++j)
U[i*lda+j] = F.zero;
U[i*lda+i] = F.one;
for (size_t j= i+1; j<n ;++j)
R.random( U[i*lda+j] );
}
/* compute product */
FFPACK::applyP (F, FFLAS::FflasRight, FFLAS::FflasNoTrans,
n,0,(int)n, U, lda, P);
FFPACK::applyP (F, FFLAS::FflasLeft, FFLAS::FflasNoTrans,
n,0,(int)n, L, n, Q);
FFLAS::fgemm (F, FFLAS::FflasNoTrans, FFLAS::FflasNoTrans,
n,n,n, 1.0, L,n, U,lda, 0.0, A,lda);
//! @todo compute LU with ftrtr
FFLAS::fflas_delete( P);
FFLAS::fflas_delete( L);
FFLAS::fflas_delete( U);
FFLAS::fflas_delete( Q);
return A;
}
} // FFPACK
#endif
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