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

```
_QZVEC(3F)							    _QZVEC(3F)

```

### NAME[Toc][Back]

```     QZVEC, ZQZVEC   -	EISPACK	routine.  This subroutine is the optional
fourth step of the	QZ algorithm for solving generalized matrix eigenvalue
problems,

```

### SYNOPSYS[Toc][Back]

```	  subroutine  qzvec(nm,	n, a, b, alfr, alfi, beta, z)
integer	   nm, n
double precision a(nm,n),b(nm,n),alfr(n),alfi(n),beta(n),z(nm,n)

subroutine sqzvec(nm,	n, a, b, alfr, alfi, beta, z)
integer	   nm, n
real		   a(nm,n),b(nm,n),alfr(n),alfi(n),beta(n),z(nm,n)

```

### DESCRIPTION[Toc][Back]

```     This subroutine accepts a pair of REAL matrices, one of them in quasitriangular
form (in which each 2-by-2 block corresponds to	a pair of
complex eigenvalues) and the other	in upper triangular form.  It computes
the eigenvectors of the triangular	problem	and transforms the results
back to the original coordinate system.  It is usually preceded by
QZHES,  QZIT, and	QZVAL.

On	Input

NM	must be	set to the row dimension of two-dimensional array parameters
as	declared in the	calling	program	dimension statement.

N is the order of the matrices.

A contains	a real upper quasi-triangular matrix.

B contains	a real upper triangular	matrix.	 In addition, location B(N,1)
contains the tolerance quantity (EPSB) computed and saved in  QZIT.

ALFR , ALFI, and BETA  are	vectors	with components	whose ratios
((ALFR+I*ALFI)/BETA) are the generalized eigenvalues.  They are usually
obtained from  QZVAL.

Z contains	the transformation matrix produced in the reductions by
QZHES,  QZIT, and	QZVAL, if performed.  If the eigenvectors of the
triangular	problem	are desired, Z must contain the	identity matrix.  On
Output

A is unaltered.  Its subdiagonal elements provide information
about the storage of the complex eigenvectors.

B has been	destroyed.

ALFR , ALFI, and BETA are unaltered.

Page 1

_QZVEC(3F)							    _QZVEC(3F)

Z contains	the real and imaginary parts of	the eigenvectors. If ALFI(I)
.EQ. 0.0, the I-th	eigenvalue is real and
the I-th column	of Z contains its eigenvector.	If ALFI(I) .NE.	0.0,
the I-th eigenvalue is complex.
If ALFI(I) .GT.	0.0, the eigenvalue is the first of
a complex pair and the I-th and	(I+1)-th columns
of Z contain its eigenvector.
If ALFI(I) .LT.	0.0, the eigenvalue is the second of
a complex pair and the (I-1)-th	and I-th columns
of Z contain the conjugate of its eigenvector.	Each eigenvector is
normalized	so that	the modulus of its largest component is	1.0 .
Questions and comments should be directed to B. S.	Garbow,	APPLIED
MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY

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