?sytf2_rook

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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?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.

Parent topic: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?sytf2_rook