/usr/include/linbox/algorithms/dense-nullspace.h is in liblinbox-dev 1.3.2-1.1.
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* Written by <brice.boyer@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
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* ========LICENCE========
*/
/** \file algorithms/dense-nullspace.h
* @ingroup algorithm
*
* @brief We provide the right or left nullspace (kernel or cokernel) of a dense matrix.
* @details Provides :
* - the nullspace of a matrix \p A
* - (soon) a random vector within the nullspace of \p A
* @todo random nullspace vector
*/
#ifndef __LINBOX_dense_nullspace_H
#define __LINBOX_dense_nullspace_H
#include "linbox/algorithms/linbox-tags.h"
#include "linbox/matrix/blas-matrix.h"
namespace LinBox
{
/** Computes the kernel of a dense matrix using \c LQUP.
*
* Acccording to the dimensions of the input matrix, we chose different methods.
* @warning timings may vary and these choices were made on an experimental basis.
*
* @param F Field
* @param Side left or right from \c LinBox::SideTag
* @param m rows
* @param n cols
* @param A input matrix
* @param lda leading dimension of A
* @param Ker Kernel. \c NULL if \c kerdim==0
* @param ldk leading dimension of the kernel.
* @param kerdim dimension of the kernel.
* @return dimension of the kernel.
*
* @warning A is modified.
*/
template<class Field>
size_t
NullSpaceBasis (const Field& F, const LinBoxTag::Side Side,
const size_t & m, const size_t & n,
typename Field::Element * A, const size_t & lda,
typename Field::Element *& Ker, size_t& ldk,
size_t & kerdim) ;
/*! Nullspace of a dense matrix on a finite field.
* A is modified.
* @param F field
* @param Side \c SideTag::Left or \c SideTag::Right nullspace.
* @param[in,out] A Input matrix
* @param[out] Ker Nullspace of the matrix (Allocated in the routine)
* @param[out] kerdim rank of the kernel
* @return \p kerdim
*/
template<class Field>
size_t&
NullSpaceBasis (const Field& F, const LinBoxTag::Side Side,
BlasMatrix<typename Field::Element> & A,
BlasMatrix<typename Field::Element> & Ker,
size_t & kerdim) ;
/*! Nullspace of a dense matrix on a finite field.
* A is preserved.
* @param F field
* @param Side \c SideTag::Left or \c SideTag::Right nullspace.
* @param[in] A Input matrix
* @param[out] Ker Nullspace of the matrix (Allocated in the routine)
* @param[out] kerdim rank of the kernel
* @return \p kerdim
*/
template<class Field>
size_t&
NullSpaceBasis (const Field& F, const LinBoxTag::Side Side,
const BlasMatrix<typename Field::Element> & A,
BlasMatrix<typename Field::Element> & Ker,
size_t & kerdim)
{
BlasMatrix<typename Field::Element> B (A);
return NullSpaceBasis<Field>(F,Side,B,Ker,kerdim);
}
} // LinBox
#include "dense-nullspace.inl"
#endif // __LINBOX_dense_nullspace_H
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