.TH ZLASYF 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME ZLASYF - a partial factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method .SH SYNOPSIS .TP 19 SUBROUTINE ZLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO ) .TP 19 .ti +4 CHARACTER UPLO .TP 19 .ti +4 INTEGER INFO, KB, LDA, LDW, N, NB .TP 19 .ti +4 INTEGER IPIV( * ) .TP 19 .ti +4 COMPLEX*16 A( LDA, * ), W( LDW, * ) .SH PURPOSE ZLASYF computes a partial factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method. The partial factorization has the form: .br A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = \(aqU\(aq, or: ( 0 U22 ) ( 0 D ) ( U12\(aq U22\(aq ) .br A = ( L11 0 ) ( D 0 ) ( L11\(aq L21\(aq ) if UPLO = \(aqL\(aq ( L21 I ) ( 0 A22 ) ( 0 I ) .br 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\(aq denotes the transpose of U. .br ZLASYF is an auxiliary routine called by ZSYTRF. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = \(aqU\(aq) or A22 (if UPLO = \(aqL\(aq). .br .SH ARGUMENTS .TP 8 UPLO (input) CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored: .br = \(aqU\(aq: Upper triangular .br = \(aqL\(aq: Lower triangular .TP 8 N (input) INTEGER The order of the matrix A. N >= 0. .TP 8 NB (input) 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. .TP 8 KB (output) INTEGER The number of columns of A that were actually factored. KB is either NB-1 or NB, or N if N <= NB. .TP 8 A (input/output) COMPLEX*16 array, dimension (LDA,N) On entry, the symmetric matrix A. If UPLO = \(aqU\(aq, 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 = \(aqL\(aq, 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. .TP 8 LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). .TP 8 IPIV (output) INTEGER array, dimension (N) Details of the interchanges and the block structure of D. If UPLO = \(aqU\(aq, only the last KB elements of IPIV are set; if UPLO = \(aqL\(aq, 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 = \(aqU\(aq 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 = \(aqL\(aq 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. .TP 8 W (workspace) COMPLEX*16 array, dimension (LDW,NB) .TP 8 LDW (input) INTEGER The leading dimension of the array W. LDW >= max(1,N). .TP 8 INFO (output) INTEGER = 0: successful exit .br > 0: if INFO = k, D(k,k) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular.