lahef_rook#
Functions
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void clahef_rook(const char *uplo, const INT n, const INT nb, INT *kb, c64 *restrict A, const INT lda, INT *restrict ipiv, c64 *restrict W, const INT ldw, INT *info)#
CLAHEF_ROOK computes a partial factorization of a complex Hermitian matrix A using the bounded Bunch-Kaufman (“rook”) diagonal pivoting method.
The partial factorization has the form:
A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = ‘U’, or: ( 0 U22 ) ( 0 D ) ( U12**H U22**H )
A = ( L11 0 ) ( D 0 ) ( L11**H L21**H ) if UPLO = ‘L’ ( L21 I ) ( 0 A22 ) ( 0 I )
where the order of D is at most NB. The actual order is returned in the argument KB, and is either NB or NB-1, or N if N <= NB. Note that U**H denotes the conjugate transpose of U.
CLAHEF_ROOK is an auxiliary routine called by CHETRF_ROOK. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = ‘U’) or A22 (if UPLO = ‘L’).
Parameters
inuploSpecifies whether the upper or lower triangular part of the Hermitian matrix A is stored: = ‘U’: Upper triangular = ‘L’: Lower triangular
innThe order of the matrix A. n >= 0.
innbThe maximum number of columns of the matrix A that should be factored. nb should be at least 2 to allow for 2-by-2 pivot blocks.
outkbThe number of columns of A that were actually factored. kb is either nb-1 or nb, or n if n <= nb.
inoutASingle complex array, dimension (lda, n). On entry, the Hermitian matrix A. On exit, details of the partial factorization.
inldaThe leading dimension of the array A. lda >= max(1, n).
outipivInteger array, dimension (n). Details of the interchanges and the block structure of D.
outWSingle complex array, dimension (ldw, nb).
inldwThe leading dimension of the array W. ldw >= max(1, n).
outinfo= 0: successful exit
> 0: if info = k, D(k,k) is exactly zero.
void clahef_rook(
const char* uplo,
const INT n,
const INT nb,
INT* kb,
c64* restrict A,
const INT lda,
INT* restrict ipiv,
c64* restrict W,
const INT ldw,
INT* info
);
Functions
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void zlahef_rook(const char *uplo, const INT n, const INT nb, INT *kb, c128 *restrict A, const INT lda, INT *restrict ipiv, c128 *restrict W, const INT ldw, INT *info)#
ZLAHEF_ROOK computes a partial factorization of a complex Hermitian matrix A using the bounded Bunch-Kaufman (“rook”) diagonal pivoting method.
The partial factorization has the form:
A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = ‘U’, or: ( 0 U22 ) ( 0 D ) ( U12**H U22**H )
A = ( L11 0 ) ( D 0 ) ( L11**H L21**H ) if UPLO = ‘L’ ( L21 I ) ( 0 A22 ) ( 0 I )
where the order of D is at most NB. The actual order is returned in the argument KB, and is either NB or NB-1, or N if N <= NB. Note that U**H denotes the conjugate transpose of U.
ZLAHEF_ROOK is an auxiliary routine called by ZHETRF_ROOK. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = ‘U’) or A22 (if UPLO = ‘L’).
Parameters
inuploSpecifies whether the upper or lower triangular part of the Hermitian matrix A is stored: = ‘U’: Upper triangular = ‘L’: Lower triangular
innThe order of the matrix A. n >= 0.
innbThe maximum number of columns of the matrix A that should be factored. nb should be at least 2 to allow for 2-by-2 pivot blocks.
outkbThe number of columns of A that were actually factored. kb is either nb-1 or nb, or n if n <= nb.
inoutADouble complex array, dimension (lda, n). On entry, the Hermitian matrix A. On exit, details of the partial factorization.
inldaThe leading dimension of the array A. lda >= max(1, n).
outipivInteger array, dimension (n). Details of the interchanges and the block structure of D.
outWDouble complex array, dimension (ldw, nb).
inldwThe leading dimension of the array W. ldw >= max(1, n).
outinfo= 0: successful exit
> 0: if info = k, D(k,k) is exactly zero.
void zlahef_rook(
const char* uplo,
const INT n,
const INT nb,
INT* kb,
c128* restrict A,
const INT lda,
INT* restrict ipiv,
c128* restrict W,
const INT ldw,
INT* info
);