
NAMEzlahef.f SYNOPSISFunctions/Subroutinessubroutine zlahef (UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO) Function/Subroutine Documentationsubroutine zlahef (characterUPLO, integerN, integerNB, integerKB, complex*16, dimension( lda, * )A, integerLDA, integer, dimension( * )IPIV, complex*16, dimension( ldw, * )W, integerLDW, integerINFO)ZLAHEF computes a partial factorization of a complex Hermitian indefinite matrix using the BunchKaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS). Purpose:ZLAHEF computes a partial factorization of a complex Hermitian matrix A using the BunchKaufman 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 NB1, or N if N <= NB. Note that U**H denotes the conjugate transpose of U. ZLAHEF is an auxiliary routine called by ZHETRF. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or A22 (if UPLO = 'L'). UPLO
Author:
UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored: = 'U': Upper triangular = 'L': Lower triangularN N is INTEGER The order of the matrix A. N >= 0.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 2by2 pivot blocks.KB KB is INTEGER The number of columns of A that were actually factored. KB is either NB1 or NB, or N if N <= NB.A A is COMPLEX*16 array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = 'U', the leading nbyn 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 nbyn 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.LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).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 IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1by1 diagonal block. If IPIV(k) = IPIV(k1) < 0, then rows and columns k1 and IPIV(k) were interchanged and D(k1:k,k1:k) is a 2by2 diagonal block. If UPLO = 'L': Only the first KB elements of IPIV are set. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1by1 diagonal block. If 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 2by2 diagonal block.W W is COMPLEX*16 array, dimension (LDW,NB)LDW LDW is INTEGER The leading dimension of the array W. LDW >= max(1,N).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. Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2013
Contributors:
November 2013, Igor Kozachenko, Computer Science Division, University of California, Berkeley AuthorGenerated automatically by Doxygen for LAPACK from the source code.
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