lahef_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

Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored: = ‘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, dimension (lda, n). On entry, the Hermitian matrix A. 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 the array A. lda >= max(1, n).

out
E

Single complex array, 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.

out
ipiv

Integer array, dimension (n). IPIV describes the permutation matrix P in the factorization.

out
W

Single complex array, dimension (ldw, nb).

in
ldw

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

out
info

  • = 0: successful exit

  • < 0: If info = -k, the k-th argument had an illegal value

  • > 0: If info = k, the matrix A is singular.

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

Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored: = ‘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, dimension (lda, n). On entry, the Hermitian matrix A. 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 the array A. lda >= max(1, n).

out
E

Double complex array, 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.

out
ipiv

Integer array, dimension (n). IPIV describes the permutation matrix P in the factorization.

out
W

Double complex array, dimension (ldw, nb).

in
ldw

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

out
info

  • = 0: successful exit

  • < 0: If info = -k, the k-th argument had an illegal value

  • > 0: If info = k, the matrix A is singular.

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