CLASYF - compute a partial factorization of a complex sym
metric matrix A using the Bunch-Kaufman diagonal pivoting
method
SYNOPSIS
SUBROUTINE CLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW,
INFO )
CHARACTER UPLO
INTEGER INFO, KB, LDA, LDW, N, NB
INTEGER IPIV( * )
COMPLEX A( LDA, * ), W( LDW, * )
PURPOSE
CLASYF computes a partial factorization of a complex sym
metric 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' U22' )
A = ( L11 0 ) ( D 0 ) ( L11' L21' ) 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' denotes the transpose of U.
CLASYF is an auxiliary routine called by CSYTRF. It uses
blocked code (calling Level 3 BLAS) to update the subma
trix A11 (if UPLO = 'U') or A22 (if UPLO = 'L').
ARGUMENTS
UPLO (input) CHARACTER*1
Specifies whether the upper or lower triangular
part of the symmetric matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular
N (input) INTEGER
The order of the matrix A. N >= 0.
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.
The number of columns of A that were actually fac
tored. KB is either NB-1 or NB, or N if N <= NB.
A (input/output) COMPLEX array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = 'U',
the leading n-by-n upper triangular part of A con
tains 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 tri
angular part of the matrix A, and the strictly
upper triangular part of A is not referenced. On
exit, A contains details of the partial factoriza
tion.
LDA (input) INTEGER
The leading dimension of the array A. LDA >=
max(1,N).
IPIV (output) INTEGER array, dimension (N)
Details of the interchanges and the block struc
ture of D. If UPLO = 'U', only the last KB ele
ments 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.
W (workspace) COMPLEX array, dimension (LDW,NB)
LDW (input) INTEGER
The leading dimension of the array W. LDW >=
max(1,N).
INFO (output) 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.
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