?lasyf

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?lasyf

Computes a partial factorization of a symmetric matrix, using the diagonal pivoting method.

Syntax

call slasyf ( uplo , n , nb , kb , a , lda , ipiv , w , ldw , info )

call dlasyf ( uplo , n , nb , kb , a , lda , ipiv , w , ldw , info )

call clasyf ( uplo , n , nb , kb , a , lda , ipiv , w , ldw , info )

call zlasyf ( uplo , n , nb , kb , a , lda , ipiv , w , ldw , info )

Include Files

mkl.fi

Description

slasyf dlasyf clasyf zlasyf

The routine ? lasyf computes a partial factorization of a symmetric matrix A using the Bunch-Kaufman diagonal pivoting method. The partial factorization has the form:

If uplo = 'U' :
If uplo = ‘L’ :

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 (Computes the 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 DOUBLE PRECISION for dlasyf COMPLEX for clasyf DOUBLE COMPLEX for zlasyf . 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 DOUBLE PRECISION for dlasyf COMPLEX for clasyf DOUBLE COMPLEX for zlasyf . 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 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.

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.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?lasyf

Syntax

Include Files

Description

Input Parameters

Output Parameters