Visible to Intel only — GUID: GUID-1ADFA5B0-62CF-4044-8717-8E60EF31092F
Visible to Intel only — GUID: GUID-1ADFA5B0-62CF-4044-8717-8E60EF31092F
?lasyf_rook
Computes a partial factorization of a complex symmetric matrix, using the bounded Bunch-Kaufman diagonal pivoting method.
Syntax
call slasyf_rook( uplo, n, nb, kb, a, lda, ipiv, w, ldw, info )
call dlasyf_rook( uplo, n, nb, kb, a, lda, ipiv, w, ldw, info )
call clasyf_rook( uplo, n, nb, kb, a, lda, ipiv, w, ldw, info )
call zlasyf_rook( uplo, n, nb, kb, a, lda, ipiv, w, ldw, info )
Include Files
- mkl.fi
Description
The routine ?lasyf_rook computes a partial factorization of a complex symmetric matrix A using the bounded Bunch-Kaufman ("rook") diagonal pivoting method. The partial factorization has the form:
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.
This is an auxiliary routine called by ?sytrf_rook. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if uplo = 'U') or A22 (if uplo = 'L').
Input Parameters
- uplo
-
CHARACTER*1.
Specifies whether the upper or lower triangular part of the symmetric matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular
- n
-
INTEGER. The order of the matrix A. n≥ 0.
- nb
-
INTEGER. 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.
- a
-
REAL for slasyf_rook
DOUBLE PRECISION for dlasyf_rook
COMPLEX for clasyf_rook
DOUBLE COMPLEX for zlasyf_rook.
Array, DIMENSION (lda, n). If uplo = 'U', the leading n-by-n upper triangular part of a contains the upper triangular part of the matrix A, and the strictly lower triangular part of a is not referenced. If uplo = 'L', the leading n-by-n lower triangular part of a contains the lower triangular part of the matrix A, and the strictly upper triangular part of a is not referenced.
- lda
-
INTEGER. The leading dimension of the array a. lda≥ max(1,n).
- w
-
REAL for slasyf_rook
DOUBLE PRECISION for dlasyf_rook
COMPLEX for clasyf_rook
DOUBLE COMPLEX for zlasyf_rook.
Workspace array, DIMENSION (ldw, nb).
- ldw
-
INTEGER. The leading dimension of the array w. ldw≥ max(1,n).
Output Parameters
- kb
-
INTEGER. The number of columns of A that were actually factored kb is either nb-1 or nb, or n if n ≤ nb.
- a
-
On exit, a contains details of the partial factorization.
- ipiv
-
INTEGER. Array, DIMENSION (n ). Details of the interchanges and the block structure of D.
If uplo = 'U', only the last kb elements of ipiv are set;
if uplo = 'L', only the first kb elements are set.
If ipiv(k) > 0, then rows and columns k and ipiv(k) were interchanged and Dk, k is a 1-by-1 diagonal block.
If uplo = 'U' and ipiv(k) < 0 and ipiv(k - 1) < 0, then rows and columns k and -ipiv(k) were interchanged, rows and columns k - 1 and -ipiv(k - 1) were interchanged, and Dk-1:k, k-1:k is a 2-by-2 diagonal block.
If uplo = 'L' and ipiv(k) < 0 and ipiv(k + 1) < 0, then rows and columns k and -ipiv(k) were interchanged, rows and columns k + 1 and -ipiv(k + 1) were interchanged, and Dk:k+1, k:k+1 is a 2-by-2 diagonal block.
- info
-
INTEGER.
= 0: successful exit
> 0: if info = k, D(k, k) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular.