lahef_rook#

Functions

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
);
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

in
uplo

  • 'U': Upper triangular

  • 'L': Lower triangular

in
n

The order of the matrix A. n>=0.

in
nb

The 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.

out
kb

The number of columns of A that were actually factored. kb is either nb-1 or nb, or n if n<=nb.

inout
A

Single complex array of dimension (lda,n). On entry, the Hermitian matrix A. If uplo='U', the leading n-by-n upper triangular part contains the upper triangular part of A and the strictly lower triangular part is not referenced. If uplo='L', the leading n-by-n lower triangular part contains the lower triangular part of A and the strictly upper triangular part is not referenced. On exit, A contains details of the partial factorization.

in
lda

The leading dimension of A. lda>=max(1,n).

out
ipiv

Integer array of dimension n. Details of the interchanges and the block structure of D. If uplo='U', only the last kb elements are set. A positive entry denotes a 1-by-1 diagonal block. Two consecutive negative entries denote a 2-by-2 block and identify the two interchanges. If uplo='L', only the first kb elements are set, with the corresponding positive and consecutive-negative conventions.

out
W

Single complex array of dimension (ldw,nb).

in
ldw

The leading dimension of W. ldw>=max(1,n).

out
info

  • info=0: successful exit

  • info>0: if info=k, D(k,k) is exactly zero. The factorization has been completed, but D is exactly singular.

Functions

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
);
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

in
uplo

  • 'U': Upper triangular

  • 'L': Lower triangular

in
n

The order of the matrix A. n>=0.

in
nb

The 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.

out
kb

The number of columns of A that were actually factored. kb is either nb-1 or nb, or n if n<=nb.

inout
A

Double complex array of dimension (lda,n). On entry, the Hermitian matrix A. If uplo='U', the leading n-by-n upper triangular part contains the upper triangular part of A and the strictly lower triangular part is not referenced. If uplo='L', the leading n-by-n lower triangular part contains the lower triangular part of A and the strictly upper triangular part is not referenced. On exit, A contains details of the partial factorization.

in
lda

The leading dimension of A. lda>=max(1,n).

out
ipiv

Integer array of dimension n. Details of the interchanges and the block structure of D. If uplo='U', only the last kb elements are set. A positive entry denotes a 1-by-1 diagonal block. Two consecutive negative entries denote a 2-by-2 block and identify the two interchanges. If uplo='L', only the first kb elements are set, with the corresponding positive and consecutive-negative conventions.

out
W

Double complex array of dimension (ldw,nb).

in
ldw

The leading dimension of W. ldw>=max(1,n).

out
info

  • info=0: successful exit

  • info>0: if info=k, D(k,k) is exactly zero. The factorization has been completed, but D is exactly singular.