# cdrgvx.f - Man Page

TESTING/EIG/cdrgvx.f

## Synopsis

### Functions/Subroutines

subroutine cdrgvx (nsize, thresh, nin, nout, a, lda, b, ai, bi, alpha, beta, vl, vr, ilo, ihi, lscale, rscale, s, stru, dif, diftru, work, lwork, rwork, iwork, liwork, result, bwork, info)
CDRGVX

## Function/Subroutine Documentation

### subroutine cdrgvx (integer nsize, real thresh, integer nin, integer nout, complex, dimension( lda, * ) a, integer lda, complex, dimension( lda, * ) b, complex, dimension( lda, * ) ai, complex, dimension( lda, * ) bi, complex, dimension( * ) alpha, complex, dimension( * ) beta, complex, dimension( lda, * ) vl, complex, dimension( lda, * ) vr, integer ilo, integer ihi, real, dimension( * ) lscale, real, dimension( * ) rscale, real, dimension( * ) s, real, dimension( * ) stru, real, dimension( * ) dif, real, dimension( * ) diftru, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer, dimension( * ) iwork, integer liwork, real, dimension( 4 ) result, logical, dimension( * ) bwork, integer info)

CDRGVX

Purpose:

``` CDRGVX checks the nonsymmetric generalized eigenvalue problem
expert driver CGGEVX.

CGGEVX computes the generalized eigenvalues, (optionally) the left
and/or right eigenvectors, (optionally) computes a balancing
transformation to improve the conditioning, and (optionally)
reciprocal condition numbers for the eigenvalues and eigenvectors.

When CDRGVX is called with NSIZE > 0, two types of test matrix pairs
are generated by the subroutine SLATM6 and test the driver CGGEVX.
The test matrices have the known exact condition numbers for
eigenvalues. For the condition numbers of the eigenvectors
corresponding the first and last eigenvalues are also know
“exactly” (see CLATM6).
For each matrix pair, the following tests will be performed and
compared with the threshold THRESH.

(1) max over all left eigenvalue/-vector pairs (beta/alpha,l) of

| l**H * (beta A - alpha B) | / ( ulp max( |beta A|, |alpha B| ) )

where l**H is the conjugate transpose of l.

(2) max over all right eigenvalue/-vector pairs (beta/alpha,r) of

| (beta A - alpha B) r | / ( ulp max( |beta A|, |alpha B| ) )

(3) The condition number S(i) of eigenvalues computed by CGGEVX
differs less than a factor THRESH from the exact S(i) (see
CLATM6).

(4) DIF(i) computed by CTGSNA differs less than a factor 10*THRESH
from the exact value (for the 1st and 5th vectors only).

Test Matrices
=============

Two kinds of test matrix pairs
(A, B) = inverse(YH) * (Da, Db) * inverse(X)
are used in the tests:

1: Da = 1+a   0    0    0    0    Db = 1   0   0   0   0
0   2+a   0    0    0         0   1   0   0   0
0    0   3+a   0    0         0   0   1   0   0
0    0    0   4+a   0         0   0   0   1   0
0    0    0    0   5+a ,      0   0   0   0   1 , and

2: Da =  1   -1    0    0    0    Db = 1   0   0   0   0
1    1    0    0    0         0   1   0   0   0
0    0    1    0    0         0   0   1   0   0
0    0    0   1+a  1+b        0   0   0   1   0
0    0    0  -1-b  1+a ,      0   0   0   0   1 .

In both cases the same inverse(YH) and inverse(X) are used to compute
(A, B), giving the exact eigenvectors to (A,B) as (YH, X):

YH:  =  1    0   -y    y   -y    X =  1   0  -x  -x   x
0    1   -y    y   -y         0   1   x  -x  -x
0    0    1    0    0         0   0   1   0   0
0    0    0    1    0         0   0   0   1   0
0    0    0    0    1,        0   0   0   0   1 , where

a, b, x and y will have all values independently of each other from
{ sqrt(sqrt(ULP)),  0.1,  1,  10,  1/sqrt(sqrt(ULP)) }.```
Parameters

NSIZE

```          NSIZE is INTEGER
The number of sizes of matrices to use.  NSIZE must be at
least zero. If it is zero, no randomly generated matrices
are tested, but any test matrices read from NIN will be
tested.  If it is not zero, then N = 5.```

THRESH

```          THRESH is REAL
A test will count as 'failed' if the 'error', computed as
described above, exceeds THRESH.  Note that the error
is scaled to be O(1), so THRESH should be a reasonably
small multiple of 1, e.g., 10 or 100.  In particular,
it should not depend on the precision (single vs. double)
or the size of the matrix.  It must be at least zero.```

NIN

```          NIN is INTEGER
The FORTRAN unit number for reading in the data file of
problems to solve.```

NOUT

```          NOUT is INTEGER
The FORTRAN unit number for printing out error messages
(e.g., if a routine returns IINFO not equal to 0.)```

A

```          A is COMPLEX array, dimension (LDA, NSIZE)
Used to hold the matrix whose eigenvalues are to be
computed.  On exit, A contains the last matrix actually used.```

LDA

```          LDA is INTEGER
The leading dimension of A, B, AI, BI, Ao, and Bo.
It must be at least 1 and at least NSIZE.```

B

```          B is COMPLEX array, dimension (LDA, NSIZE)
Used to hold the matrix whose eigenvalues are to be
computed.  On exit, B contains the last matrix actually used.```

AI

```          AI is COMPLEX array, dimension (LDA, NSIZE)
Copy of A, modified by CGGEVX.```

BI

```          BI is COMPLEX array, dimension (LDA, NSIZE)
Copy of B, modified by CGGEVX.```

ALPHA

`          ALPHA is COMPLEX array, dimension (NSIZE)`

BETA

```          BETA is COMPLEX array, dimension (NSIZE)

On exit, ALPHA/BETA are the eigenvalues.```

VL

```          VL is COMPLEX array, dimension (LDA, NSIZE)
VL holds the left eigenvectors computed by CGGEVX.```

VR

```          VR is COMPLEX array, dimension (LDA, NSIZE)
VR holds the right eigenvectors computed by CGGEVX.```

ILO

`                ILO is INTEGER`

IHI

`                IHI is INTEGER`

LSCALE

`                LSCALE is REAL array, dimension (N)`

RSCALE

`                RSCALE is REAL array, dimension (N)`

S

`                S is REAL array, dimension (N)`

STRU

`                STRU is REAL array, dimension (N)`

DIF

`                DIF is REAL array, dimension (N)`

DIFTRU

`                DIFTRU is REAL array, dimension (N)`

WORK

`          WORK is COMPLEX array, dimension (LWORK)`

LWORK

```          LWORK is INTEGER
Leading dimension of WORK.  LWORK >= 2*N*N + 2*N```

RWORK

`          RWORK is REAL array, dimension (6*N)`

IWORK

`          IWORK is INTEGER array, dimension (LIWORK)`

LIWORK

```          LIWORK is INTEGER
Leading dimension of IWORK.  LIWORK >= N+2.```

RESULT

`                RESULT is REAL array, dimension (4)`

BWORK

`          BWORK is LOGICAL array, dimension (N)`

INFO

```          INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value.
> 0:  A routine returned an error code.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 294 of file cdrgvx.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cdrgvx(3) is an alias of cdrgvx.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK