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# zhegs2

```
NAME
ZHEGS2 - reduce a complex Hermitian-definite generalized
eigenproblem to standard form

SYNOPSIS
SUBROUTINE ZHEGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )

CHARACTER      UPLO

INTEGER        INFO, ITYPE, LDA, LDB, N

COMPLEX*16     A( LDA, * ), B( LDB, * )

PURPOSE
ZHEGS2 reduces a complex Hermitian-definite generalized
eigenproblem to standard form.

If ITYPE = 1, the problem is A*x = lambda*B*x,
and A is overwritten by inv(U')*A*inv(U) or inv(L)*A*inv(L')

If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
B*A*x = lambda*x, and A is overwritten by U*A*U` or L'*A*L.

B must have been previously factorized as U'*U or L*L' by
ZPOTRF.

ARGUMENTS
ITYPE   (input) INTEGER
= 1: compute inv(U')*A*inv(U) or inv(L)*A*inv(L');
= 2 or 3: compute U*A*U' or L'*A*L.

UPLO    (input) CHARACTER
Specifies whether the upper or lower triangular part
of the Hermitian matrix A is stored, and how B has
been factorized.  = 'U':  Upper triangular
= 'L':  Lower triangular

N       (input) INTEGER
The order of the matrices A and B.  N >= 0.

A       (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the Hermitian matrix A.  If UPLO = 'U',
the leading n by n upper triangular part of A con-
tains 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 tri-
angular part of A is not referenced.

On exit, if INFO = 0, the transformed matrix, stored

in the same format as A.

LDA     (input) INTEGER
The leading dimension of the array A.  LDA >=
max(1,N).

B       (input) COMPLEX*16 array, dimension (LDB,N)
The triangular factor from the Cholesky factoriza-
tion of B, as returned by ZPOTRF.

LDB     (input) INTEGER
The leading dimension of the array B.  LDB >=
max(1,N).

INFO    (output) INTEGER
= 0:  successful exit.
< 0:  if INFO = -i, the i-th argument had an illegal
value.
```