lahef_rk#

clahef_rk

Functions

void clahef_rk(
    const char*          uplo,
    const INT            n,
    const INT            nb,
          INT*           kb,
          c64*  restrict A,
    const INT            lda,
          c64*  restrict E,
          INT*  restrict ipiv,
          c64*  restrict W,
    const INT            ldw,
          INT*           info
);

void clahef_rk(const char *uplo, const INT n, const INT nb, INT *kb, c64 *restrict A, const INT lda, c64 *restrict E, INT *restrict ipiv, c64 *restrict W, const INT ldw, INT *info)#

CLAHEF_RK 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.

CLAHEF_RK is an auxiliary routine called by CHETRF_RK. 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, contains: a) Only diagonal elements of the Hermitian block diagonal matrix D on the diagonal of A, i.e. D(k,k)=A(k,k); (superdiagonal (or subdiagonal) elements of D are stored on exit in array E), and b) If uplo='U': factor U in the superdiagonal part of A. If uplo='L': factor L in the subdiagonal part of A.

in

lda

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

out

E

Single complex array of dimension n. On exit, contains the superdiagonal (or subdiagonal) elements of the Hermitian block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks. If uplo='U', E[i] is D(i-1,i) for 1<=i<n and E[0] is zero. If uplo='L', E[i] is D(i+1,i) for 0<=i<n-1 and E[n-1] is zero. E[k] is zero for a 1-by-1 block D(k).

out

ipiv

Integer array of dimension n. Describes the permutation matrix P and the block structure of D. A non-negative ipiv[k] denotes a 1-by-1 block; a pair of consecutive negative values denotes a 2-by-2 block. For a negative entry, the exchanged 0-based index is -ipiv[k]-1. For uplo='U', factorization proceeds from n-1 to 0 and the recovered index is at most k. For uplo='L', factorization proceeds from 0 to n-1 and the recovered index is at least k.

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, the k-th argument had an illegal value
info>0: if info=k, the matrix A is singular because the corresponding diagonal block is zero.

zlahef_rk

Functions

void zlahef_rk(
    const char*          uplo,
    const INT            n,
    const INT            nb,
          INT*           kb,
          c128* restrict A,
    const INT            lda,
          c128* restrict E,
          INT*  restrict ipiv,
          c128* restrict W,
    const INT            ldw,
          INT*           info
);

void zlahef_rk(const char *uplo, const INT n, const INT nb, INT *kb, c128 *restrict A, const INT lda, c128 *restrict E, INT *restrict ipiv, c128 *restrict W, const INT ldw, INT *info)#

ZLAHEF_RK 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.

ZLAHEF_RK is an auxiliary routine called by ZHETRF_RK. 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, contains: a) Only diagonal elements of the Hermitian block diagonal matrix D on the diagonal of A, i.e. D(k,k)=A(k,k); (superdiagonal (or subdiagonal) elements of D are stored on exit in array E), and b) If uplo='U': factor U in the superdiagonal part of A. If uplo='L': factor L in the subdiagonal part of A.

in

lda

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

out

E

Double complex array of dimension n. On exit, contains the superdiagonal (or subdiagonal) elements of the Hermitian block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks. If uplo='U', E[i] is D(i-1,i) for 1<=i<n and E[0] is zero. If uplo='L', E[i] is D(i+1,i) for 0<=i<n-1 and E[n-1] is zero. E[k] is zero for a 1-by-1 block D(k).

out

ipiv

Integer array of dimension n. Describes the permutation matrix P and the block structure of D. A non-negative ipiv[k] denotes a 1-by-1 block; a pair of consecutive negative values denotes a 2-by-2 block. For a negative entry, the exchanged 0-based index is -ipiv[k]-1. For uplo='U', factorization proceeds from n-1 to 0 and the recovered index is at most k. For uplo='L', factorization proceeds from 0 to n-1 and the recovered index is at least k.

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, the k-th argument had an illegal value
info>0: if info=k, the matrix A is singular because the corresponding diagonal block is zero.