?sytf2_rook

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?sytf2_rook

Computes the factorization of a real/complex symmetric indefinite matrix, using the bounded Bunch-Kaufman diagonal pivoting method (unblocked algorithm).

Syntax

call ssytf2_rook ( uplo , n , a , lda , ipiv , info )

call dsytf2_rook ( uplo , n , a , lda , ipiv , info )

call csytf2_rook ( uplo , n , a , lda , ipiv , info )

call zsytf2_rook ( uplo , n , a , lda , ipiv , info )

Include Files

mkl.fi

Description

The routine ?sytf2_rook computes the factorization of a real/complex symmetric matrix A using the bounded Bunch-Kaufman (“rook”) diagonal pivoting method:

A = U*D*U^{T} , or A = L*D*L^{T} ,

where U (or L ) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

This is the unblocked version of the algorithm, calling BLAS Level 2 Routines .

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 .
a: REAL for ssytf2_rook DOUBLE PRECISION for dsytf2_rook COMPLEX for csytf2_rook DOUBLE COMPLEX for zsytf2_rook . 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.
lda: INTEGER . The leading dimension of the array a . lda≥ max(1,n) .

Output Parameters

a: On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L .
ipiv: INTEGER . Array, DIMENSION ( n ). Details of the interchanges and the block structure of D 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) < 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 , the k- th argument has an illegal value
> 0: if info = k , D ( k , k ) is exactly zero. The factorization are completed, but the block diagonal matrix D is exactly singular, and division by zero will occur if it is used to solve a system of equations.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?sytf2_rook

Syntax

Include Files

Description

Input Parameters

Output Parameters