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man pages->IRIX man pages -> complib/zhegs2 (3)
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### Contents

```
ZHEGS2(3F)							    ZHEGS2(3F)

```

### NAME[Toc][Back]

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

### SYNOPSIS[Toc][Back]

```     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[Toc][Back]

```     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[Toc][Back]

```     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 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.

Page 1

ZHEGS2(3F)							    ZHEGS2(3F)

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.
ZHEGS2(3F)							    ZHEGS2(3F)

```

### NAME[Toc][Back]

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

### SYNOPSIS[Toc][Back]

```     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[Toc][Back]

```     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[Toc][Back]

```     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 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.

Page 1

ZHEGS2(3F)							    ZHEGS2(3F)

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.

PPPPaaaaggggeeee 2222```
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