# ?hetf2

Computes the factorization of a complex Hermitian matrix, using the diagonal pivoting method (unblocked algorithm).

## Syntax

call chetf2( uplo, n, a, lda, ipiv, info )

call zhetf2( uplo, n, a, lda, ipiv, info )

## Description

The routine computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method:

`A = U*D*U'` or `A = L*D*L'`

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, U' is the conjugate transpose of U, and D is Hermitian 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 Hermitian matrix A is stored:

  = 'U': Upper triangular

  = 'L': Lower triangular

n

  INTEGER. The order of the matrix A. `n ≥ 0`.

A

  COMPLEX for chetf2

  COMPLEX*16 for zhetf2.

  Array, DIMENSION (lda, n).

  On entry, the Hermitian 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) = 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`, the k-th argument had an illegal value

  > 0: if `info = k`, D(k,k) is exactly zero. The factorization has been 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