FFLAS-FFPACK
Namespaces | Functions
ffpack.h File Reference

Set of elimination based routines for dense linear algebra. More...

#include "givaro/givpoly1.h"
#include <fflas-ffpack/fflas-ffpack-config.h>
#include "fflas-ffpack/fflas/fflas.h"
#include "fflas-ffpack/fflas/fflas_helpers.inl"
#include <list>
#include <vector>
#include <iostream>
#include <algorithm>
#include "fflas-ffpack/checkers/checkers_ffpack.h"
#include "ffpack_fgesv.inl"
#include "ffpack_fgetrs.inl"
#include "fflas-ffpack/checkers/checkers_ffpack.inl"
#include "ffpack_pluq.inl"
#include "ffpack_pluq_mp.inl"
#include "ffpack_ppluq.inl"
#include "ffpack_ludivine.inl"
#include "ffpack_ludivine_mp.inl"
#include "ffpack_echelonforms.inl"
#include "ffpack_fsytrf.inl"
#include "ffpack_invert.inl"
#include "ffpack_ftrtr.inl"
#include "ffpack_ftrstr.inl"
#include "ffpack_ftrssyr2k.inl"
#include "ffpack_charpoly_kglu.inl"
#include "ffpack_charpoly_kgfast.inl"
#include "ffpack_charpoly_kgfastgeneralized.inl"
#include "ffpack_charpoly_danilevski.inl"
#include "ffpack_charpoly.inl"
#include "ffpack_frobenius.inl"
#include "ffpack_minpoly.inl"
#include "ffpack_krylovelim.inl"
#include "ffpack_permutation.inl"
#include "ffpack_rankprofiles.inl"
#include "ffpack_det_mp.inl"
#include "ffpack_bruhatgen.inl"
#include "ffpack.inl"

Namespaces

namespace  FFPACK
 Finite Field PACK Set of elimination based routines for dense linear algebra.
 

Functions

void LAPACKPerm2MathPerm (size_t *MathP, const size_t *LapackP, const size_t N)
 Conversion of a permutation from LAPACK format to Math format.
 
void MathPerm2LAPACKPerm (size_t *LapackP, const size_t *MathP, const size_t N)
 Conversion of a permutation from Maths format to LAPACK format.
 
template<class Field >
void applyP (const Field &F, const FFLAS::FFLAS_SIDE Side, const FFLAS::FFLAS_TRANSPOSE Trans, const size_t M, const size_t ibeg, const size_t iend, typename Field::Element_ptr A, const size_t lda, const size_t *P)
 Computes P1 x Diag (I_R, P2) where P1 is a LAPACK and P2 a LAPACK permutation and store the result in P1 as a LAPACK permutation. More...
 
template<class Field >
void MonotonicApplyP (const Field &F, const FFLAS::FFLAS_SIDE Side, const FFLAS::FFLAS_TRANSPOSE Trans, const size_t M, const size_t ibeg, const size_t iend, typename Field::Element_ptr A, const size_t lda, const size_t *P, const size_t R)
 Apply a R-monotonically increasing permutation P, to the matrix A. More...
 
template<class Field >
void fgetrs (const Field &F, const FFLAS::FFLAS_SIDE Side, const size_t M, const size_t N, const size_t R, typename Field::Element_ptr A, const size_t lda, const size_t *P, const size_t *Q, typename Field::Element_ptr B, const size_t ldb, int *info)
 Solve the system $A X = B$ or $X A = B$. More...
 
template<class Field >
Field::Element_ptr fgetrs (const Field &F, const FFLAS::FFLAS_SIDE Side, const size_t M, const size_t N, const size_t NRHS, const size_t R, typename Field::Element_ptr A, const size_t lda, const size_t *P, const size_t *Q, typename Field::Element_ptr X, const size_t ldx, typename Field::ConstElement_ptr B, const size_t ldb, int *info)
 Solve the system A X = B or X A = B. More...
 
template<class Field >
size_t fgesv (const Field &F, const FFLAS::FFLAS_SIDE Side, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr B, const size_t ldb, int *info)
 Square system solver. More...
 
template<class Field >
size_t fgesv (const Field &F, const FFLAS::FFLAS_SIDE Side, const size_t M, const size_t N, const size_t NRHS, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr X, const size_t ldx, typename Field::ConstElement_ptr B, const size_t ldb, int *info)
 Rectangular system solver. More...
 
template<class Field >
void ftrtri (const Field &F, const FFLAS::FFLAS_UPLO Uplo, const FFLAS::FFLAS_DIAG Diag, const size_t N, typename Field::Element_ptr A, const size_t lda, const size_t threshold=__FFLASFFPACK_FTRTRI_THRESHOLD)
 Compute the inverse of a triangular matrix. More...
 
template<class Field >
void ftrtrm (const Field &F, const FFLAS::FFLAS_SIDE side, const FFLAS::FFLAS_DIAG diag, const size_t N, typename Field::Element_ptr A, const size_t lda)
 Compute the product of two triangular matrices of opposite shape. More...
 
template<class Field >
void ftrstr (const Field &F, const FFLAS::FFLAS_SIDE side, const FFLAS::FFLAS_UPLO Uplo, const FFLAS::FFLAS_DIAG diagA, const FFLAS::FFLAS_DIAG diagB, const size_t N, typename Field::ConstElement_ptr A, const size_t lda, typename Field::Element_ptr B, const size_t ldb, const size_t threshold=64)
 Solve a triangular system with a triangular right hand side of the same shape. More...
 
template<class Field >
void ftrssyr2k (const Field &F, const FFLAS::FFLAS_UPLO Uplo, const FFLAS::FFLAS_DIAG diagA, const size_t N, typename Field::ConstElement_ptr A, const size_t lda, typename Field::Element_ptr B, const size_t ldb, const size_t threshold=64)
 Solve a triangular system in a symmetric sum: find B upper/lower triangular such that A^T B + B^T A = C where C is symmetric. More...
 
template<class Field >
bool fsytrf (const Field &F, const FFLAS::FFLAS_UPLO UpLo, const size_t N, typename Field::Element_ptr A, const size_t lda, const size_t threshold=__FFLASFFPACK_FSYTRF_THRESHOLD)
 Triangular factorization of symmetric matrices. More...
 
template<class Field >
bool fsytrf_nonunit (const Field &F, const FFLAS::FFLAS_UPLO UpLo, const size_t N, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr D, const size_t incD, const size_t threshold=__FFLASFFPACK_FSYTRF_THRESHOLD)
 Triangular factorization of symmetric matrices. More...
 
template<class Field >
size_t PLUQ (const Field &F, const FFLAS::FFLAS_DIAG Diag, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t *P, size_t *Q)
 Compute a PLUQ factorization of the given matrix. More...
 
template<class Field >
size_t LUdivine (const Field &F, const FFLAS::FFLAS_DIAG Diag, const FFLAS::FFLAS_TRANSPOSE trans, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t *P, size_t *Qt, const FFPACK_LU_TAG LuTag=FfpackSlabRecursive, const size_t cutoff=__FFLASFFPACK_LUDIVINE_THRESHOLD)
 Compute the CUP or PLE factorization of the given matrix. More...
 
template<class Field >
size_t ColumnEchelonForm (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t *P, size_t *Qt, bool transform=false, const FFPACK_LU_TAG LuTag=FfpackSlabRecursive)
 Compute the Column Echelon form of the input matrix in-place. More...
 
template<class Field >
size_t RowEchelonForm (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t *P, size_t *Qt, const bool transform=false, const FFPACK_LU_TAG LuTag=FfpackSlabRecursive)
 Compute the Row Echelon form of the input matrix in-place. More...
 
template<class Field >
size_t ReducedColumnEchelonForm (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t *P, size_t *Qt, const bool transform=false, const FFPACK_LU_TAG LuTag=FfpackSlabRecursive)
 Compute the Reduced Column Echelon form of the input matrix in-place. More...
 
template<class Field >
size_t ReducedRowEchelonForm (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t *P, size_t *Qt, const bool transform=false, const FFPACK_LU_TAG LuTag=FfpackSlabRecursive)
 Compute the Reduced Row Echelon form of the input matrix in-place. More...
 
template<class Field >
size_t GaussJordan (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, const size_t colbeg, const size_t rowbeg, const size_t colsize, size_t *P, size_t *Q, const FFPACK::FFPACK_LU_TAG LuTag)
 Gauss-Jordan algorithm computing the Reduced Row echelon form and its transform matrix. More...
 
template<class Field >
Field::Element_ptr Invert (const Field &F, const size_t M, typename Field::Element_ptr A, const size_t lda, int &nullity)
 Invert the given matrix in place or computes its nullity if it is singular. More...
 
template<class Field >
Field::Element_ptr Invert (const Field &F, const size_t M, typename Field::ConstElement_ptr A, const size_t lda, typename Field::Element_ptr X, const size_t ldx, int &nullity)
 Invert the given matrix or computes its nullity if it is singular. More...
 
template<class Field >
Field::Element_ptr Invert2 (const Field &F, const size_t M, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr X, const size_t ldx, int &nullity)
 Invert the given matrix or computes its nullity if it is singular. More...
 
template<class PolRing >
std::list< typename PolRing::Element > & CharPoly (const PolRing &R, std::list< typename PolRing::Element > &charp, const size_t N, typename PolRing::Domain_t::Element_ptr A, const size_t lda, typename PolRing::Domain_t::RandIter &G, const FFPACK_CHARPOLY_TAG CharpTag=FfpackAuto, const size_t degree=__FFLASFFPACK_ARITHPROG_THRESHOLD)
 Compute the characteristic polynomial of the matrix A. More...
 
template<class PolRing >
PolRing::Element & CharPoly (const PolRing &R, typename PolRing::Element &charp, const size_t N, typename PolRing::Domain_t::Element_ptr A, const size_t lda, typename PolRing::Domain_t::RandIter &G, const FFPACK_CHARPOLY_TAG CharpTag=FfpackAuto, const size_t degree=__FFLASFFPACK_ARITHPROG_THRESHOLD)
 Compute the characteristic polynomial of the matrix A. More...
 
template<class PolRing >
PolRing::Element & CharPoly (const PolRing &R, typename PolRing::Element &charp, const size_t N, typename PolRing::Domain_t::Element_ptr A, const size_t lda, const FFPACK_CHARPOLY_TAG CharpTag=FfpackAuto, const size_t degree=__FFLASFFPACK_ARITHPROG_THRESHOLD)
 Compute the characteristic polynomial of the matrix A. More...
 
template<class PolRing >
void RandomKrylovPrecond (const PolRing &PR, std::list< typename PolRing::Element > &completedFactors, const size_t N, typename PolRing::Domain_t::Element_ptr A, const size_t lda, size_t &Nb, typename PolRing::Domain_t::Element_ptr &B, size_t &ldb, typename PolRing::Domain_t::RandIter &g, const size_t degree=__FFLASFFPACK_ARITHPROG_THRESHOLD)
 
template<class Field , class Polynomial >
Polynomial & MinPoly (const Field &F, Polynomial &minP, const size_t N, typename Field::ConstElement_ptr A, const size_t lda)
 Compute the minimal polynomial of the matrix A. More...
 
template<class Field , class Polynomial , class RandIter >
Polynomial & MinPoly (const Field &F, Polynomial &minP, const size_t N, typename Field::ConstElement_ptr A, const size_t lda, RandIter &G)
 Compute the minimal polynomial of the matrix A. More...
 
template<class Field , class Polynomial >
Polynomial & MatVecMinPoly (const Field &F, Polynomial &minP, const size_t N, typename Field::ConstElement_ptr A, const size_t lda, typename Field::ConstElement_ptr v, const size_t incv)
 Compute the minimal polynomial of the matrix A and a vector v, namely the first linear dependency relation in the Krylov basis $(v,Av, ..., A^Nv)$. More...
 
template<class Field >
size_t Rank (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda)
 Computes the rank of the given matrix using a PLUQ factorization. More...
 
template<class Field >
bool IsSingular (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda)
 Returns true if the given matrix is singular. More...
 
template<class Field >
Field::Element & Det (const Field &F, typename Field::Element &det, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t *P=NULL, size_t *Q=NULL)
 Returns the determinant of the given square matrix. More...
 
template<class Field >
Field::Element_ptr Solve (const Field &F, const size_t M, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr x, const int incx, typename Field::ConstElement_ptr b, const int incb)
 Solves a linear system AX = b using PLUQ factorization. More...
 
template<class Field >
*void RandomNullSpaceVector (const Field &F, const FFLAS::FFLAS_SIDE Side, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr X, const size_t incX)
 Solve L X = B or X L = B in place. More...
 
template<class Field >
size_t NullSpaceBasis (const Field &F, const FFLAS::FFLAS_SIDE Side, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr &NS, size_t &ldn, size_t &NSdim)
 Computes a basis of the Left/Right nullspace of the matrix A. More...
 
template<class Field >
size_t RowRankProfile (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t *&rkprofile, const FFPACK_LU_TAG LuTag=FfpackSlabRecursive)
 Computes the row rank profile of A. More...
 
template<class Field >
size_t ColumnRankProfile (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t *&rkprofile, const FFPACK_LU_TAG LuTag=FfpackSlabRecursive)
 Computes the column rank profile of A. More...
 
void RankProfileFromLU (const size_t *P, const size_t N, const size_t R, size_t *rkprofile, const FFPACK_LU_TAG LuTag)
 Recovers the column/row rank profile from the permutation of an LU decomposition. More...
 
size_t LeadingSubmatrixRankProfiles (const size_t M, const size_t N, const size_t R, const size_t LSm, const size_t LSn, const size_t *P, const size_t *Q, size_t *RRP, size_t *CRP)
 Recovers the row and column rank profiles of any leading submatrix from the PLUQ decomposition. More...
 
template<class Field >
size_t RowRankProfileSubmatrixIndices (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t *&rowindices, size_t *&colindices, size_t &R)
 RowRankProfileSubmatrixIndices. More...
 
template<class Field >
size_t ColRankProfileSubmatrixIndices (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t *&rowindices, size_t *&colindices, size_t &R)
 Computes the indices of the submatrix r*r X of A whose columns correspond to the column rank profile of A. More...
 
template<class Field >
size_t RowRankProfileSubmatrix (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr &X, size_t &R)
 Computes the r*r submatrix X of A, by picking the row rank profile rows of A. More...
 
template<class Field >
size_t ColRankProfileSubmatrix (const Field &F, const size_t M, const size_t N, typename Field::Element_ptr A, const size_t lda, typename Field::Element_ptr &X, size_t &R)
 Compute the $ r\times r$ submatrix X of A, by picking the row rank profile rows of A. More...
 
template<class Field >
void getTriangular (const Field &F, const FFLAS::FFLAS_UPLO Uplo, const FFLAS::FFLAS_DIAG diag, const size_t M, const size_t N, const size_t R, typename Field::ConstElement_ptr A, const size_t lda, typename Field::Element_ptr T, const size_t ldt, const bool OnlyNonZeroVectors=false)
 Extracts a triangular matrix from a compact storage A=L\U of rank R. More...
 
template<class Field >
void getTriangular (const Field &F, const FFLAS::FFLAS_UPLO Uplo, const FFLAS::FFLAS_DIAG diag, const size_t M, const size_t N, const size_t R, typename Field::Element_ptr A, const size_t lda)
 Cleans up a compact storage A=L\U to reveal a triangular matrix of rank R. More...
 
template<class Field >
void getEchelonForm (const Field &F, const FFLAS::FFLAS_UPLO Uplo, const FFLAS::FFLAS_DIAG diag, const size_t M, const size_t N, const size_t R, const size_t *P, typename Field::ConstElement_ptr A, const size_t lda, typename Field::Element_ptr T, const size_t ldt, const bool OnlyNonZeroVectors=false, const FFPACK_LU_TAG LuTag=FfpackSlabRecursive)
 Extracts a matrix in echelon form from a compact storage A=L\U of rank R obtained by RowEchelonForm or ColumnEchelonForm. More...
 
template<class Field >
void getEchelonForm (const Field &F, const FFLAS::FFLAS_UPLO Uplo, const FFLAS::FFLAS_DIAG diag, const size_t M, const size_t N, const size_t R, const size_t *P, typename Field::Element_ptr A, const size_t lda, const FFPACK_LU_TAG LuTag=FfpackSlabRecursive)
 Cleans up a compact storage A=L\U obtained by RowEchelonForm or ColumnEchelonForm to reveal an echelon form of rank R. More...
 
template<class Field >
void getEchelonTransform (const Field &F, const FFLAS::FFLAS_UPLO Uplo, const FFLAS::FFLAS_DIAG diag, const size_t M, const size_t N, const size_t R, const size_t *P, const size_t *Q, typename Field::ConstElement_ptr A, const size_t lda, typename Field::Element_ptr T, const size_t ldt, const FFPACK_LU_TAG LuTag=FfpackSlabRecursive)
 Extracts a transformation matrix to echelon form from a compact storage A=L\U of rank R obtained by RowEchelonForm or ColumnEchelonForm. More...
 
template<class Field >
void getReducedEchelonForm (const Field &F, const FFLAS::FFLAS_UPLO Uplo, const size_t M, const size_t N, const size_t R, const size_t *P, typename Field::ConstElement_ptr A, const size_t lda, typename Field::Element_ptr T, const size_t ldt, const bool OnlyNonZeroVectors=false, const FFPACK_LU_TAG LuTag=FfpackSlabRecursive)
 Extracts a matrix in echelon form from a compact storage A=L\U of rank R obtained by ReducedRowEchelonForm or ReducedColumnEchelonForm with transform = true. More...
 
template<class Field >
void getReducedEchelonForm (const Field &F, const FFLAS::FFLAS_UPLO Uplo, const size_t M, const size_t N, const size_t R, const size_t *P, typename Field::Element_ptr A, const size_t lda, const FFPACK_LU_TAG LuTag=FfpackSlabRecursive)
 Cleans up a compact storage A=L\U of rank R obtained by ReducedRowEchelonForm or ReducedColumnEchelonForm with transform = true. More...
 
template<class Field >
void getReducedEchelonTransform (const Field &F, const FFLAS::FFLAS_UPLO Uplo, const size_t M, const size_t N, const size_t R, const size_t *P, const size_t *Q, typename Field::ConstElement_ptr A, const size_t lda, typename Field::Element_ptr T, const size_t ldt, const FFPACK_LU_TAG LuTag=FfpackSlabRecursive)
 Extracts a transformation matrix to echelon form from a compact storage A=L\U of rank R obtained by RowEchelonForm or ColumnEchelonForm. More...
 
void PLUQtoEchelonPermutation (const size_t N, const size_t R, const size_t *P, size_t *outPerm)
 Auxiliary routine: determines the permutation that changes a PLUQ decomposition into a echelon form revealing PLUQ decomposition.
 
template<class Field >
size_t LTBruhatGen (const Field &Fi, const FFLAS::FFLAS_DIAG diag, const size_t N, typename Field::Element_ptr A, const size_t lda, size_t *P, size_t *Q)
 LTBruhatGen Suppose A is Left Triangular Matrix This procedure computes the Bruhat Representation of A and return the rank of A. More...
 
template<class Field >
void getLTBruhatGen (const Field &Fi, const size_t N, const size_t r, const size_t *P, const size_t *Q, typename Field::Element_ptr R, const size_t ldr)
 GetLTBruhatGen This procedure Computes the Rank Revealing Matrix based on the Bruhta representation of a Matrix. More...
 
template<class Field >
void getLTBruhatGen (const Field &Fi, const FFLAS::FFLAS_UPLO Uplo, const FFLAS::FFLAS_DIAG diag, const size_t N, const size_t r, const size_t *P, const size_t *Q, typename Field::ConstElement_ptr A, const size_t lda, typename Field::Element_ptr T, const size_t ldt)
 GetLTBruhatGen This procedure computes the matrix L or U f the Bruhat Representation Suppose that A is the bruhat representation of a matrix. More...
 
size_t LTQSorder (const size_t N, const size_t r, const size_t *P, const size_t *Q)
 LTQSorder This procedure computes the order of quasiseparability of a matrix. More...
 
template<class Field >
size_t CompressToBlockBiDiagonal (const Field &Fi, const FFLAS::FFLAS_UPLO Uplo, size_t N, size_t s, size_t r, const size_t *P, const size_t *Q, typename Field::Element_ptr A, size_t lda, typename Field::Element_ptr X, size_t ldx, size_t *K, size_t *M, size_t *T)
 CompressToBlockBiDiagonal This procedure compress a compact representation of a row echelon form or column echelon form. More...
 
template<class Field >
void ExpandBlockBiDiagonalToBruhat (const Field &Fi, const FFLAS::FFLAS_UPLO Uplo, size_t N, size_t s, size_t r, typename Field::Element_ptr A, size_t lda, typename Field::Element_ptr X, size_t ldx, size_t NbBlocks, size_t *K, size_t *M, size_t *T)
 ExpandBlockBiDiagonal This procedure expand a compact representation of a row echelon form or column echelon form. More...
 
void Bruhat2EchelonPermutation (size_t N, size_t R, const size_t *P, const size_t *Q, size_t *M)
 Bruhat2EchelonPermutation (N,R,P,Q) Compute M such that LM or MU is in echelon form where L or U are factors of the Bruhat Rpresentation. More...
 
template<class Field >
void productBruhatxTS (const Field &Fi, size_t N, size_t s, size_t r, const size_t *P, const size_t *Q, const typename Field::Element_ptr Xu, size_t ldu, size_t NbBlocksU, size_t *Ku, size_t *Tu, size_t *MU, const typename Field::Element_ptr Xl, size_t ldl, size_t NbBlocksL, size_t *Kl, size_t *Tl, size_t *ML, typename Field::Element_ptr B, size_t t, size_t ldb, typename Field::Element_ptr C, size_t ldc)
 productBruhatxTS Comput the product between the CRE compact representation of a matrix A and B a tall matrix
 
template<class Field >
Field::Element_ptr LQUPtoInverseOfFullRankMinor (const Field &F, const size_t rank, typename Field::Element_ptr A_factors, const size_t lda, const size_t *QtPointer, typename Field::Element_ptr X, const size_t ldx)
 LQUPtoInverseOfFullRankMinor. More...
 

Detailed Description

Set of elimination based routines for dense linear algebra.

Matrices are supposed over finite prime field of characteristic less than 2^26.

Function Documentation

◆ GaussJordan()

size_t GaussJordan ( const Field &  F,
const size_t  M,
const size_t  N,
typename Field::Element_ptr  A,
const size_t  lda,
const size_t  colbeg,
const size_t  rowbeg,
const size_t  colsize,
size_t *  P,
size_t *  Q,
const FFPACK::FFPACK_LU_TAG  LuTag 
)
inline

Gauss-Jordan algorithm computing the Reduced Row echelon form and its transform matrix.

Bibliography:
  • Algorithm 2.8 of A. Storjohann Thesis 2000,
  • Algorithm 11 of Jeannerod C-P., Pernet, C. and Storjohann, A. Rank-profile revealing Gaussian elimination and the CUP matrix decomposition , J. of Symbolic Comp., 2013
Parameters
Mrow dimension of A
Ncolumn dimension of A
[in,out]Aan m x n matrix
ldaleading dimension of A
Prow permutation
Qcolumn permutation
LuTagset the base case to a Tile (FfpackGaussJordanTile) or Slab (FfpackGaussJordanSlab) recursive RedEchelon

| I | A11 | A12 | | |-—|--—|--—|-—| | |I | *| A22 | | | |0 | 0| A22 | | |-—|--—|--—|-—| | | 0 | A32 | | |-—|--—|--—|-—|

where the transformation matrix is stored at the pivot column position

◆ RandomKrylovPrecond()

void RandomKrylovPrecond ( const PolRing &  PR,
std::list< typename PolRing::Element > &  completedFactors,
const size_t  N,
typename PolRing::Domain_t::Element_ptr  A,
const size_t  lda,
size_t &  Nb,
typename PolRing::Domain_t::Element_ptr &  B,
size_t &  ldb,
typename PolRing::Domain_t::RandIter &  g,
const size_t  degree = __FFLASFFPACK_ARITHPROG_THRESHOLD 
)
inline
Todo:
swap to save space ??
Todo:
Todo:
don't assing K2 c*noc x N but only mas (c,noc) x N and store each one after the other
Todo:
swap to save space ??
Todo:
Todo:
don't assing K2 c*noc x N but only mas (c,noc) x N and store each one after the other
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