Visible to Intel only — GUID: GUID-D449985A-C504-43DE-924A-4FA3F2DAEFD2
Visible to Intel only — GUID: GUID-D449985A-C504-43DE-924A-4FA3F2DAEFD2
?hetf2_rook
Computes the factorization of a complex Hermitian matrix, using the bounded Bunch-Kaufman diagonal pivoting method (unblocked algorithm).
Syntax
call chetf2_rook( uplo, n, a, lda, ipiv, info )
call zhetf2_rook( uplo, n, a, lda, ipiv, info )
Include Files
- mkl.fi
Description
The routine computes the factorization of a complex Hermitian matrix A using the bounded Bunch-Kaufman ("rook") diagonal pivoting method:
A = U*D*UH or A = L*D*LH
where U (or L) is a product of permutation and unit upper (lower) triangular matrices, UH is the conjugate transpose of U, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
This is the unblocked version of the algorithm, calling BLAS Level 2 Routines.
Input Parameters
- uplo
-
CHARACTER*1.
Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular
- n
-
INTEGER. The order of the matrix A. n≥ 0.
- a
-
COMPLEX for chetf2_rook
DOUBLE COMPLEX for zhetf2_rook.
Array, DIMENSION (lda, n).
On entry, the Hermitian matrix A.
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).
Output Parameters
- a
-
On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L.
- ipiv
-
INTEGER. Array, DIMENSION (n).
Details of the interchanges and the block structure of D.
If ipiv(k) > 0, then rows and columns k and ipiv(k) were interchanged and D(k,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, the k-th argument had an illegal value
> 0: if info = k, D(k,k) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, and division by zero will occur if it is used to solve a system of equations.