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

```
ZLAHQR(3F)							    ZLAHQR(3F)

```

### NAME[Toc][Back]

```     ZLAHQR - i	an auxiliary routine called by ZHSEQR to update	the
eigenvalues and Schur decomposition already computed by ZHSEQR, by
dealing with the Hessenberg submatrix in rows and columns ILO to IHI
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	ZLAHQR(	WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, IHIZ, Z,
LDZ, INFO )

LOGICAL	WANTT, WANTZ

INTEGER	IHI, IHIZ, ILO,	ILOZ, INFO, LDH, LDZ, N

COMPLEX*16	H( LDH,	* ), W(	* ), Z(	LDZ, * )
```

### PURPOSE[Toc][Back]

```     ZLAHQR is an auxiliary routine called by ZHSEQR to	update the eigenvalues
and Schur decomposition already computed by ZHSEQR, by dealing with the
Hessenberg	submatrix in rows and columns ILO to IHI.

```

### ARGUMENTS[Toc][Back]

```     WANTT   (input) LOGICAL
= .TRUE. :	the full Schur form T is required;
= .FALSE.:	only eigenvalues are required.

WANTZ   (input) LOGICAL
= .TRUE. :	the matrix of Schur vectors Z is required;
= .FALSE.:	Schur vectors are not required.

N	     (input) INTEGER
The order of the matrix H.	 N >= 0.

ILO     (input) INTEGER
IHI     (input) INTEGER It	is assumed that	H is already upper
triangular	in rows	and columns IHI+1:N, and that H(ILO,ILO-1) = 0
(unless ILO = 1).	ZLAHQR works primarily with the	Hessenberg
submatrix in rows and columns ILO to IHI, but applies
transformations to	all of H if WANTT is .TRUE..  1	<= ILO <=
max(1,IHI); IHI <=	N.

H	     (input/output) COMPLEX*16 array, dimension	(LDH,N)
On	entry, the upper Hessenberg matrix H.  On exit,	if WANTT is
.TRUE., H is upper	triangular in rows and columns ILO:IHI,	with
any 2-by-2	diagonal blocks	in standard form. If WANTT is .FALSE.,
the contents of H are unspecified on exit.

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

Page 1

ZLAHQR(3F)							    ZLAHQR(3F)

W	     (output) COMPLEX*16 array,	dimension (N)
The computed eigenvalues ILO to IHI are stored in the
corresponding elements of W. If WANTT is .TRUE., the eigenvalues
are stored	in the same order as on	the diagonal of	the Schur form
returned in H, with W(i) =	H(i,i).

ILOZ    (input) INTEGER
IHIZ    (input) INTEGER Specify the rows of Z to which
transformations must be applied if	WANTZ is .TRUE..  1 <= ILOZ <=
ILO; IHI <= IHIZ <= N.

Z	     (input/output) COMPLEX*16 array, dimension	(LDZ,N)
If	WANTZ is .TRUE., on entry Z must contain the current matrix Z
of	transformations	accumulated by ZHSEQR, and on exit Z has been
updated; transformations are applied only to the submatrix
Z(ILOZ:IHIZ,ILO:IHI).  If WANTZ is	.FALSE., Z is not referenced.

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

INFO    (output) INTEGER
= 0: successful exit
> 0: if INFO = i, ZLAHQR failed to	compute	all the	eigenvalues
ILO to IHI	in a total of 30*(IHI-ILO+1) iterations; elements
i+1:ihi of	W contain those	eigenvalues which have been
successfully computed.
ZLAHQR(3F)							    ZLAHQR(3F)

```

### NAME[Toc][Back]

```     ZLAHQR - i	an auxiliary routine called by ZHSEQR to update	the
eigenvalues and Schur decomposition already computed by ZHSEQR, by
dealing with the Hessenberg submatrix in rows and columns ILO to IHI
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	ZLAHQR(	WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, IHIZ, Z,
LDZ, INFO )

LOGICAL	WANTT, WANTZ

INTEGER	IHI, IHIZ, ILO,	ILOZ, INFO, LDH, LDZ, N

COMPLEX*16	H( LDH,	* ), W(	* ), Z(	LDZ, * )
```

### PURPOSE[Toc][Back]

```     ZLAHQR is an auxiliary routine called by ZHSEQR to	update the eigenvalues
and Schur decomposition already computed by ZHSEQR, by dealing with the
Hessenberg	submatrix in rows and columns ILO to IHI.

```

### ARGUMENTS[Toc][Back]

```     WANTT   (input) LOGICAL
= .TRUE. :	the full Schur form T is required;
= .FALSE.:	only eigenvalues are required.

WANTZ   (input) LOGICAL
= .TRUE. :	the matrix of Schur vectors Z is required;
= .FALSE.:	Schur vectors are not required.

N	     (input) INTEGER
The order of the matrix H.	 N >= 0.

ILO     (input) INTEGER
IHI     (input) INTEGER It	is assumed that	H is already upper
triangular	in rows	and columns IHI+1:N, and that H(ILO,ILO-1) = 0
(unless ILO = 1).	ZLAHQR works primarily with the	Hessenberg
submatrix in rows and columns ILO to IHI, but applies
transformations to	all of H if WANTT is .TRUE..  1	<= ILO <=
max(1,IHI); IHI <=	N.

H	     (input/output) COMPLEX*16 array, dimension	(LDH,N)
On	entry, the upper Hessenberg matrix H.  On exit,	if WANTT is
.TRUE., H is upper	triangular in rows and columns ILO:IHI,	with
any 2-by-2	diagonal blocks	in standard form. If WANTT is .FALSE.,
the contents of H are unspecified on exit.

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

Page 1

ZLAHQR(3F)							    ZLAHQR(3F)

W	     (output) COMPLEX*16 array,	dimension (N)
The computed eigenvalues ILO to IHI are stored in the
corresponding elements of W. If WANTT is .TRUE., the eigenvalues
are stored	in the same order as on	the diagonal of	the Schur form
returned in H, with W(i) =	H(i,i).

ILOZ    (input) INTEGER
IHIZ    (input) INTEGER Specify the rows of Z to which
transformations must be applied if	WANTZ is .TRUE..  1 <= ILOZ <=
ILO; IHI <= IHIZ <= N.

Z	     (input/output) COMPLEX*16 array, dimension	(LDZ,N)
If	WANTZ is .TRUE., on entry Z must contain the current matrix Z
of	transformations	accumulated by ZHSEQR, and on exit Z has been
updated; transformations are applied only to the submatrix
Z(ILOZ:IHIZ,ILO:IHI).  If WANTZ is	.FALSE., Z is not referenced.

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

INFO    (output) INTEGER
= 0: successful exit
> 0: if INFO = i, ZLAHQR failed to	compute	all the	eigenvalues
ILO to IHI	in a total of 30*(IHI-ILO+1) iterations; elements
i+1:ihi of	W contain those	eigenvalues which have been
successfully computed.

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