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template<class Field > |
void | applyP (const Field &F, const FFLAS::FFLAS_SIDE Side, const FFLAS::FFLAS_TRANSPOSE Trans, const size_t M, const int ibeg, const int iend, typename Field::Element *A, const size_t lda, const size_t *P) |
| Apply a permutation submatrix of P (between ibeg and iend) to a matrix to (iend-ibeg) vectors of size M stored in A (as column for NoTrans and rows for Trans). More...
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template<class Field > |
size_t | Rank (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda) |
| Computes the rank of the given matrix using a LQUP factorization. More...
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template<class Field > |
bool | IsSingular (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda) |
| Returns true if the given matrix is singular. More...
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template<class Field > |
Field::Element | Det (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda) |
| Returns the determinant of the given matrix. More...
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template<class Field > |
void | solveLB2 (const Field &F, const FFLAS::FFLAS_SIDE Side, const size_t M, const size_t N, const size_t R, typename Field::Element *L, const size_t ldl, const size_t *Q, typename Field::Element *B, const size_t ldb) |
| Solve L X = B in place. More...
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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 *A, const size_t lda, const size_t *P, const size_t *Q, typename Field::Element *B, const size_t ldb, int *info) |
| Solve the system or . More...
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template<class Field > |
Field::Element * | 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 *A, const size_t lda, const size_t *P, const size_t *Q, typename Field::Element *X, const size_t ldx, const typename Field::Element *B, const size_t ldb, int *info) |
| Solve the system A X = B or X A = B. More...
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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 *A, const size_t lda, typename Field::Element *B, const size_t ldb, int *info) |
| Square system solver. More...
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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 *A, const size_t lda, typename Field::Element *X, const size_t ldx, const typename Field::Element *B, const size_t ldb, int *info) |
| Rectangular system solver. More...
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template<class Field > |
Field::Element * | Solve (const Field &F, const size_t M, typename Field::Element *A, const size_t lda, typename Field::Element *x, const int incx, const typename Field::Element *b, const int incb) |
| Solve the system Ax=b. More...
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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 *A, const size_t lda, typename Field::Element *&NS, size_t &ldn, size_t &NSdim) |
| Computes a basis of the Left/Right nullspace of the matrix A. More...
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template<class Field > |
size_t | RowRankProfile (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *&rkprofile) |
| Computes the row rank profile of A. More...
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template<class Field > |
size_t | ColumnRankProfile (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *&rkprofile) |
| Computes the column rank profile of A. More...
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template<class Field > |
size_t | RowRankProfileSubmatrixIndices (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *&rowindices, size_t *&colindices, size_t &R) |
| RowRankProfileSubmatrixIndices. More...
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template<class Field > |
size_t | ColRankProfileSubmatrixIndices (const Field &F, const size_t M, const size_t N, typename Field::Element *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...
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template<class Field > |
size_t | RowRankProfileSubmatrix (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, typename Field::Element *&X, size_t &R) |
| Compute the r*r submatrix X of A, by picking the row rank profile rows of A. More...
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template<class Field > |
size_t | ColRankProfileSubmatrix (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, typename Field::Element *&X, size_t &R) |
| Compute the submatrix X of A, by picking the row rank profile rows of A. More...
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template<class Field > |
Field::Element * | LQUPtoInverseOfFullRankMinor (const Field &F, const size_t rank, typename Field::Element *A_factors, const size_t lda, const size_t *QtPointer, typename Field::Element *X, const size_t ldx) |
| LQUPtoInverseOfFullRankMinor. More...
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template<class Field > |
size_t | TURBO (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 cutoff) |
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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 *A, const size_t lda, size_t *P, size_t *Qt, const FFPACK_LUDIVINE_TAG LuTag=FfpackLQUP, const size_t cutoff=__FFPACK_LUDIVINE_CUTOFF) |
| Compute the LQUP factorization of the given matrix. More...
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template<class Field > |
size_t | LUpdate (const Field &F, const FFLAS::FFLAS_DIAG Diag, const FFLAS::FFLAS_TRANSPOSE trans, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, const size_t R, const size_t K, typename Field::Element *B, const size_t ldb, size_t *P, size_t *Q, const FFPACK::FFPACK_LUDIVINE_TAG LuTag=FFPACK::FfpackLQUP, const size_t cutoff=__FFPACK_LUDIVINE_CUTOFF) |
| LUpdate. More...
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template<class Field > |
size_t | LUdivine_small (const Field &F, const FFLAS::FFLAS_DIAG Diag, const FFLAS::FFLAS_TRANSPOSE trans, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *P, size_t *Q, const FFPACK_LUDIVINE_TAG LuTag=FfpackLQUP) |
| LUdivine small case. More...
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template<class Field > |
size_t | LUdivine_gauss (const Field &F, const FFLAS::FFLAS_DIAG Diag, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *P, size_t *Q, const FFPACK_LUDIVINE_TAG LuTag=FfpackLQUP) |
| LUdivine gauss. More...
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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 *A, const size_t lda) |
| Compute the inverse of a triangular matrix. More...
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template<class Field > |
void | ftrtrm (const Field &F, const FFLAS::FFLAS_DIAG diag, const size_t N, typename Field::Element *A, const size_t lda) |
| Compute the product UL. More...
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template<class Field > |
size_t | ColumnEchelonForm (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *P, size_t *Qt, bool transform=true) |
| Compute the Column Echelon form of the input matrix in-place. More...
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template<class Field > |
size_t | RowEchelonForm (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *P, size_t *Qt, const bool transform=false) |
| Compute the Row Echelon form of the input matrix in-place. More...
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template<class Field > |
size_t | ReducedColumnEchelonForm (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *P, size_t *Qt, const bool transform=true) |
| Compute the Reduced Column Echelon form of the input matrix in-place. More...
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template<class Field > |
size_t | ReducedRowEchelonForm (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *P, size_t *Qt, const bool transform=true) |
| Compute the Reduced Row Echelon form of the input matrix in-place. More...
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template<class Field > |
size_t | ReducedRowEchelonForm2 (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *P, size_t *Qt, const bool transform=true) |
| Variant by the block recursive algorithm. More...
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template<class Field > |
size_t | REF (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, const size_t colbeg, const size_t rowbeg, const size_t colsize, size_t *Qt, size_t *P) |
| REF. More...
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template<class Field > |
Field::Element * | Invert (const Field &F, const size_t M, typename Field::Element *A, const size_t lda, int &nullity) |
| Invert the given matrix in place or computes its nullity if it is singular. More...
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template<class Field > |
Field::Element * | Invert (const Field &F, const size_t M, const typename Field::Element *A, const size_t lda, typename Field::Element *X, const size_t ldx, int &nullity) |
| Invert the given matrix in place or computes its nullity if it is singular. More...
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template<class Field > |
Field::Element * | Invert2 (const Field &F, const size_t M, typename Field::Element *A, const size_t lda, typename Field::Element *X, const size_t ldx, int &nullity) |
| Invert the given matrix or computes its nullity if it is singular. More...
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template<class Field , class Polynomial > |
std::list< Polynomial > & | CharPoly (const Field &F, std::list< Polynomial > &charp, const size_t N, typename Field::Element *A, const size_t lda, const FFPACK_CHARPOLY_TAG CharpTag=FfpackArithProg) |
| Compute the characteristic polynomial of A using Krylov Method, and LUP factorization of the Krylov matrix. More...
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template<class Polynomial , class Field > |
Polynomial & | mulpoly (const Field &F, Polynomial &res, const Polynomial &P1, const Polynomial &P2) |
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template<class Field , class Polynomial > |
std::list< Polynomial > & | CharPoly (const Field &F, Polynomial &charp, const size_t N, typename Field::Element *A, const size_t lda, const FFPACK_CHARPOLY_TAG CharpTag=FfpackArithProg) |
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template<class Field , class Polynomial > |
Polynomial & | MinPoly (const Field &F, Polynomial &minP, const size_t N, const typename Field::Element *A, const size_t lda, typename Field::Element *X, const size_t ldx, size_t *P, const FFPACK::FFPACK_MINPOLY_TAG MinTag=FFPACK::FfpackDense, const size_t kg_mc=0, const size_t kg_mb=0, const size_t kg_j=0) |
| Compute the minimal polynomial. More...
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template<class Field > |
void | solveLB (const Field &F, const FFLAS::FFLAS_SIDE Side, const size_t M, const size_t N, const size_t R, typename Field::Element *L, const size_t ldl, const size_t *Q, typename Field::Element *B, const size_t ldb) |
| Solve L X = B or X L = B in place. More...
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template<class Field > |
void | trinv_left (const Field &F, const size_t N, const typename Field::Element *L, const size_t ldl, typename Field::Element *X, const size_t ldx) |
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template<class Field > |
size_t | 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, const size_t maxit, size_t virt) |
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template<class Field > |
size_t | 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) |
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template<class Field , class Polynomial > |
std::list< Polynomial > & | CharpolyArithProg (const Field &F, std::list< Polynomial > &frobeniusForm, const size_t N, typename Field::Element *A, const size_t lda, const size_t c) |
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template<class Field > |
void | CompressRows (Field &F, const size_t M, typename Field::Element *A, const size_t lda, typename Field::Element *tmp, const size_t ldtmp, const size_t *d, const size_t nb_blocs) |
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template<class Field > |
void | CompressRowsQK (Field &F, const size_t M, typename Field::Element *A, const size_t lda, typename Field::Element *tmp, const size_t ldtmp, const size_t *d, const size_t deg, const size_t nb_blocs) |
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template<class Field > |
void | DeCompressRows (Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, typename Field::Element *tmp, const size_t ldtmp, const size_t *d, const size_t nb_blocs) |
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template<class Field > |
void | DeCompressRowsQK (Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, typename Field::Element *tmp, const size_t ldtmp, const size_t *d, const size_t deg, const size_t nb_blocs) |
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template<class Field > |
void | CompressRowsQA (Field &F, const size_t M, typename Field::Element *A, const size_t lda, typename Field::Element *tmp, const size_t ldtmp, const size_t *d, const size_t nb_blocs) |
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template<class Field > |
void | DeCompressRowsQA (Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, typename Field::Element *tmp, const size_t ldtmp, const size_t *d, const size_t nb_blocs) |
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template<class Field > |
size_t | newD (const Field &F, size_t *d, bool &KeepOn, const size_t l, const size_t N, typename Field::Element *X, const size_t *Q, std::vector< std::vector< typename Field::Element > > &minpt) |
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template<class Field > |
size_t | updateD (const Field &F, size_t *d, size_t k, std::vector< std::vector< typename Field::Element > > &minpt) |
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template<class Field > |
void | RectangleCopyTURBO (const Field &F, const size_t M, const size_t N, const size_t dist2pivot, const size_t rank, typename Field::Element *T, const size_t ldt, const typename Field::Element *A, const size_t lda) |
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template<class Field > |
size_t | LUdivine_construct (const Field &F, const FFLAS::FFLAS_DIAG Diag, const size_t M, const size_t N, const typename Field::Element *A, const size_t lda, typename Field::Element *X, const size_t ldx, typename Field::Element *u, size_t *P, bool computeX, const FFPACK_MINPOLY_TAG MinTag=FFPACK::FfpackDense, const size_t kg_mc=0, const size_t kg_mb=0, const size_t kg_j=0) |
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template<class Field , class Polynomial > |
std::list< Polynomial > & | KellerGehrig (const Field &F, std::list< Polynomial > &charp, const size_t N, const typename Field::Element *A, const size_t lda) |
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template<class Field , class Polynomial > |
int | KGFast (const Field &F, std::list< Polynomial > &charp, const size_t N, typename Field::Element *A, const size_t lda, size_t *kg_mc, size_t *kg_mb, size_t *kg_j) |
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template<class Field , class Polynomial > |
std::list< Polynomial > & | KGFast_generalized (const Field &F, std::list< Polynomial > &charp, const size_t N, typename Field::Element *A, const size_t lda) |
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template<class Field > |
void | fgemv_kgf (const Field &F, const size_t N, const typename Field::Element *A, const size_t lda, const typename Field::Element *X, const size_t incX, typename Field::Element *Y, const size_t incY, const size_t kg_mc, const size_t kg_mb, const size_t kg_j) |
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template<class Field , class Polynomial > |
std::list< Polynomial > & | LUKrylov (const Field &F, std::list< Polynomial > &charp, const size_t N, typename Field::Element *A, const size_t lda, typename Field::Element *U, const size_t ldu) |
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template<class Field , class Polynomial > |
std::list< Polynomial > & | Danilevski (const Field &F, std::list< Polynomial > &charp, const size_t N, typename Field::Element *A, const size_t lda) |
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template<class Field , class Polynomial > |
std::list< Polynomial > & | LUKrylov_KGFast (const Field &F, std::list< Polynomial > &charp, const size_t N, typename Field::Element *A, const size_t lda, typename Field::Element *X, const size_t ldx) |
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