# ?sytf2

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

## Syntax

call ssytf2( uplo, n, a, lda, ipiv, info )

call dsytf2( uplo, n, a, lda, ipiv, info )

call csytf2( uplo, n, a, lda, ipiv, info )

call zsytf2( uplo, n, a, lda, ipiv, info )

## Description

The routine ?sytf2 computes the factorization of a real/complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method:

`A = U*D*UT`(`A = U*D*UH`), or `A = L*D*LT` (`A = L*D*LH`),

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

  DOUBLE PRECISION for dsytf2

  COMPLEX for csytf2

  COMPLEX*16 for zsytf2.

  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) are 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) are interchanged and D(k,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, 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: Auxiliary Routines