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

```
_QZVAL(3F)							    _QZVAL(3F)

```

### NAME[Toc][Back]

```     QZVAL, SQZVAL   -	EISPACK	routine.  This subroutine is the third step of
the QZ algorithm for solving generalized matrix eigenvalue	problems,

```

### SYNOPSYS[Toc][Back]

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

subroutine sqzval(nm,	n, a, b, alfr, alfi, beta, matz, z)
integer	   nm, n
real		   a(nm,n),b(nm,n),alfr(n),alfi(n),beta(n),z(nm,n)
logical	   matz

```

### DESCRIPTION[Toc][Back]

```     On	Input This subroutine accepts a	pair of	REAL matrices, one of them in
quasi-triangular form and the other in upper triangular form.  It reduces
the quasi-triangular matrix further, so that any remaining	2-by-2 blocks
correspond	to pairs of complex eigenvalues, and returns quantities	whose
ratios give the generalized eigenvalues.  It is usually preceded by
QZHES and	QZIT  and may be followed by  QZVEC.

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.

MATZ should be set	to .TRUE. If the right hand transformations are	to be
accumulated for later use in computing eigenvectors, and to .FALSE.
otherwise.

Z contains, if MATZ has been set to .TRUE., the transformation matrix
produced in the reductions	by QZHES and QZIT, if performed, or else the
identity matrix.  If MATZ has been	set to .FALSE.,	Z is not referenced.
On	Output

A has been	reduced	further	to a quasi-triangular matrix in	which all
nonzero subdiagonal elements correspond to	pairs of complex eigenvalues.

B is still	in upper triangular form, although its elements	have been
altered.  B(N,1) is unaltered.

ALFR and ALFI contain the real and	imaginary parts	of the diagonal

Page 1

_QZVAL(3F)							    _QZVAL(3F)

elements of the triangular	matrix that would be obtained if a were
reduced completely	to triangular form by unitary transformations.	Nonzero
values of ALFI occur in pairs, the first member positive and the
second negative.

BETA contains the diagonal	elements of the	corresponding B, normalized to
be	real and non-negative.	The generalized	eigenvalues are	then the
ratios ((ALFR+I*ALFI)/BETA).

Z contains	the product of the right hand transformations (for all three
steps) if MATZ has	been set to .TRUE.  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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