zlahef_rook (3) - Linux Manuals
subroutine zlahef_rook (characterUPLO, integerN, integerNB, integerKB, complex*16, dimension( lda, * )A, integerLDA, integer, dimension( * )IPIV, complex*16, dimension( ldw, * )W, integerLDW, integerINFO)
ZLAHEF_ROOK computes a partial factorization of a complex Hermitian matrix A using the bounded Bunch-Kaufman ("rook") 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. ZLAHEF_ROOK is an auxiliary routine called by ZHETRF_ROOK. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or A22 (if UPLO = 'L').
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
N is INTEGER The order of the matrix A. N >= 0.
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.
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.
A is COMPLEX*16 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.
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
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 1-by-1 diagonal block. If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k-1 and -IPIV(k-1) were inerchaged, D(k-1:k,k-1:k) is a 2-by-2 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 1-by-1 diagonal block. If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k+1 and -IPIV(k+1) were inerchaged, D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
W is COMPLEX*16 array, dimension (LDW,NB)
LDW is INTEGER The leading dimension of the array W. LDW >= max(1,N).
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
- November 2013
November 2013, Igor Kozachenko, Computer Science Division, University of California, Berkeley September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester
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