LASYF_ROOK - 5.2 English - 68552

LASYF_ROOK computes a partial factorization of a real symmetric

matrix using the bounded Bunch-Kaufman (“rook”) diagonal pivoting method.

Purpose:

   LASYF_ROOK computes a partial factorization of a real symmetric
   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**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.

   SLASYF_ROOK is an auxiliary routine called by SSYTRF_ROOK. It uses
   blocked code (calling Level 3 BLAS) to update the submatrix
   A11 (if UPLO = 'U') or A22 (if UPLO = 'L').

Parameters:

• UPLO – [in]

  UPLO is CHARACTER*1

  Specifies whether the upper or lower triangular part of the symmetric matrix A is stored:

  = ‘U’: Upper triangular

  = ‘L’: Lower triangular

• N – [in]

  N is INTEGER

  The order of the matrix A. N >= 0.

• NB – [in]

  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 – [out]

  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 – [inout]

  A is REAL 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 – [in]

  LDA is INTEGER

  The leading dimension of the array A. LDA >= fla_max(1,N).

• IPIV – [out]

  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 – [out] W is REAL array, dimension (LDW,NB)

• LDW – [in]

  LDW is INTEGER

  The leading dimension of the array W. LDW >= fla_max(1,N).

• INFO – [out]

  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.