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LAPACK
3.4.2
LAPACK: Linear Algebra PACKage
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Functions/Subroutines | |
| subroutine | clahef (UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO) |
| CLAHEF computes a partial factorization of a complex Hermitian indefinite matrix, using the diagonal pivoting method. | |
| subroutine clahef | ( | character | UPLO, |
| integer | N, | ||
| integer | NB, | ||
| integer | KB, | ||
| complex, dimension( lda, * ) | A, | ||
| integer | LDA, | ||
| integer, dimension( * ) | IPIV, | ||
| complex, dimension( ldw, * ) | W, | ||
| integer | LDW, | ||
| integer | INFO | ||
| ) |
CLAHEF computes a partial factorization of a complex Hermitian indefinite matrix, using the diagonal pivoting method.
Download CLAHEF + dependencies [TGZ] [ZIP] [TXT]
CLAHEF computes a partial factorization of a complex Hermitian
matrix A using the Bunch-Kaufman 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.
Note that U**H denotes the conjugate transpose of U.
CLAHEF is an auxiliary routine called by CHETRF. It uses blocked code
(calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
A22 (if UPLO = 'L'). | [in] | UPLO | UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular |
| [in] | N | N is INTEGER
The order of the matrix A. N >= 0. |
| [in] | NB | NB is 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. |
| [out] | KB | KB is INTEGER
The number of columns of A that were actually factored.
KB is either NB-1 or NB, or N if N <= NB. |
| [in,out] | A | A is COMPLEX 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.
On exit, A contains details of the partial factorization. |
| [in] | LDA | LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N). |
| [out] | IPIV | IPIV is 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 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. |
| [out] | W | W is COMPLEX array, dimension (LDW,NB) |
| [in] | LDW | LDW is INTEGER
The leading dimension of the array W. LDW >= max(1,N). |
| [out] | INFO | INFO is 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. |
Definition at line 158 of file clahef.f.
1.8.1.1