Developer Reference for Intel® oneAPI Math Kernel Library for Fortran
?lasyf_rook
Computes a partial factorization of a complex symmetric matrix, using the bounded Bunch-Kaufman diagonal pivoting method.
Syntax
call slasyf_rook ( uplo , n , nb , kb , a , lda , ipiv , w , ldw , info )
call dlasyf_rook ( uplo , n , nb , kb , a , lda , ipiv , w , ldw , info )
call clasyf_rook ( uplo , n , nb , kb , a , lda , ipiv , w , ldw , info )
call zlasyf_rook ( uplo , n , nb , kb , a , lda , ipiv , w , ldw , info )
Include Files
mkl.fi
Description
slasyf_rook dlasyf_rook clasyf_rook zlasyf_rook
The routine ? lasyf_rook computes a partial factorization of a complex symmetric matrix A using the bounded Bunch-Kaufman (“rook”) diagonal pivoting method. The partial factorization has the form:
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 .
This is an auxiliary routine called by ?sytrf_rook (Computes the bounded Bunch-Kaufman factorization of a symmetric matrix.) . It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if uplo = 'U' ) or A22 (if uplo = 'L' ).
Input Parameters
- uplo
-
CHARACTER*1 . Specifies whether the upper or lower triangular part of the symmetric matrix A is stored: = ‘U’ : Upper triangular = ‘L’ : Lower triangular
- n
-
INTEGER . The order of the matrix A . n≥ 0 .
- nb
-
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.
- a
-
REAL for slasyf_rook DOUBLE PRECISION for dlasyf_rook COMPLEX for clasyf_rook DOUBLE COMPLEX for zlasyf_rook . Array, DIMENSION ( lda , n ). 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.
- lda
-
INTEGER . The leading dimension of the array a . lda≥ max(1,n) .
- w
-
REAL for slasyf_rook DOUBLE PRECISION for dlasyf_rook COMPLEX for clasyf_rook DOUBLE COMPLEX for zlasyf_rook . Workspace array, DIMENSION ( ldw , nb ).
- ldw
-
INTEGER . The leading dimension of the array w . ldw≥ max(1,n) .
Output Parameters
- kb
-
INTEGER . The number of columns of A that were actually factored kb is either nb -1 or nb , or n if n ≤ nb .
- a
-
On exit, a contains details of the partial factorization.
- ipiv
-
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 Dk, k is a 1-by-1 diagonal block. If uplo = 'U' and ipiv(k) < 0 and ipiv(k - 1) < 0 , then rows and columns k and - ipiv(k) were interchanged, rows and columns k - 1 and - ipiv(k-1) were interchanged, and D_{k-1:k, k-1:k} is a 2-by-2 diagonal block. If uplo = 'L' and ipiv(k) < 0 and ipiv(k + 1) < 0 , then rows and columns k and -ipiv ( k ) were interchanged, rows and columns k + 1 and -ipiv ( k + 1) were interchanged, and D_{k:k+1, k:k+1} is a 2-by-2 diagonal block.
info
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.