Visible to Intel only — GUID: GUID-E6F56A4E-0F5E-46E8-A937-8AC4993E7446
Visible to Intel only — GUID: GUID-E6F56A4E-0F5E-46E8-A937-8AC4993E7446
?hetf2
Computes the factorization of a complex Hermitian matrix, using the diagonal pivoting method (unblocked algorithm).
Syntax
call chetf2( uplo, n, a, lda, ipiv, info )
call zhetf2( uplo, n, a, lda, ipiv, info )
Include Files
- mkl.fi
Description
The routine computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman 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
DOUBLE COMPLEX for zhetf2.
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) = ipiv( k-1) < 0, then rows and columns k-1 and -ipiv(k) were interchanged and D(k-1:k,k-1:k ) is a 2-by-2 diagonal block.
If uplo = 'L' and ipiv(k) = ipiv( k+1) < 0, then rows and columns k+1 and -ipiv(k) were interchanged and D(k: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.