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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: reduces a complex Hermitian-definite generalized eigenproblem to standard form

```NAME
LAPACK-3   -   reduces   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*1
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 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.
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 factorization 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.

LAPACK routine (version 3.2)     March 2011                       LAPACK-3(3)
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