DLASYF
Purpose
DLASYF computes a partial factorization of a real symmetric 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**T U22**T )
A = ( L11 0 ) ( D 0 ) ( L11**T L21**T ) 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.
DLASYF is an auxiliary routine called by DSYTRF. It uses blocked code
(calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
A22 (if UPLO = 'L').
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**T U22**T )
A = ( L11 0 ) ( D 0 ) ( L11**T L21**T ) 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.
DLASYF is an auxiliary routine called by DSYTRF. It uses blocked code
(calling Level 3 BLAS) to update the submatrix 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. |
| 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. |
| A |
(input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the symmetric 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 |
(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 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. |
| W |
(workspace) DOUBLE PRECISION 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. |