# cdrvev.f - Man Page

TESTING/EIG/cdrvev.f

## Synopsis

### Functions/Subroutines

subroutine cdrvev (nsizes, nn, ntypes, dotype, iseed, thresh, nounit, a, lda, h, w, w1, vl, ldvl, vr, ldvr, lre, ldlre, result, work, nwork, rwork, iwork, info)
CDRVEV

## Function/Subroutine Documentation

### subroutine cdrvev (integer nsizes, integer, dimension( * ) nn, integer ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed, real thresh, integer nounit, complex, dimension( lda, * ) a, integer lda, complex, dimension( lda, * ) h, complex, dimension( * ) w, complex, dimension( * ) w1, complex, dimension( ldvl, * ) vl, integer ldvl, complex, dimension( ldvr, * ) vr, integer ldvr, complex, dimension( ldlre, * ) lre, integer ldlre, real, dimension( 7 ) result, complex, dimension( * ) work, integer nwork, real, dimension( * ) rwork, integer, dimension( * ) iwork, integer info)

CDRVEV

Purpose:

```    CDRVEV  checks the nonsymmetric eigenvalue problem driver CGEEV.

When CDRVEV is called, a number of matrix 'sizes' ('n's') and a
number of matrix 'types' are specified.  For each size ('n')
and each type of matrix, one matrix will be generated and used
to test the nonsymmetric eigenroutines.  For each matrix, 7
tests will be performed:

(1)     | A * VR - VR * W | / ( n |A| ulp )

Here VR is the matrix of unit right eigenvectors.
W is a diagonal matrix with diagonal entries W(j).

(2)     | A**H * VL - VL * W**H | / ( n |A| ulp )

Here VL is the matrix of unit left eigenvectors, A**H is the
conjugate-transpose of A, and W is as above.

(3)     | |VR(i)| - 1 | / ulp and whether largest component real

VR(i) denotes the i-th column of VR.

(4)     | |VL(i)| - 1 | / ulp and whether largest component real

VL(i) denotes the i-th column of VL.

(5)     W(full) = W(partial)

W(full) denotes the eigenvalues computed when both VR and VL
are also computed, and W(partial) denotes the eigenvalues
computed when only W, only W and VR, or only W and VL are
computed.

(6)     VR(full) = VR(partial)

VR(full) denotes the right eigenvectors computed when both VR
and VL are computed, and VR(partial) denotes the result
when only VR is computed.

(7)     VL(full) = VL(partial)

VL(full) denotes the left eigenvectors computed when both VR
and VL are also computed, and VL(partial) denotes the result
when only VL is computed.

The 'sizes' are specified by an array NN(1:NSIZES); the value of
each element NN(j) specifies one size.
The 'types' are specified by a logical array DOTYPE( 1:NTYPES );
if DOTYPE(j) is .TRUE., then matrix type 'j' will be generated.
Currently, the list of possible types is:

(1)  The zero matrix.
(2)  The identity matrix.
(3)  A (transposed) Jordan block, with 1's on the diagonal.

(4)  A diagonal matrix with evenly spaced entries
1, ..., ULP  and random complex angles.
(ULP = (first number larger than 1) - 1 )
(5)  A diagonal matrix with geometrically spaced entries
1, ..., ULP  and random complex angles.
(6)  A diagonal matrix with 'clustered' entries 1, ULP, ..., ULP
and random complex angles.

(7)  Same as (4), but multiplied by a constant near
the overflow threshold
(8)  Same as (4), but multiplied by a constant near
the underflow threshold

(9)  A matrix of the form  U' T U, where U is unitary and
T has evenly spaced entries 1, ..., ULP with random complex
angles on the diagonal and random O(1) entries in the upper
triangle.

(10) A matrix of the form  U' T U, where U is unitary and
T has geometrically spaced entries 1, ..., ULP with random
complex angles on the diagonal and random O(1) entries in
the upper triangle.

(11) A matrix of the form  U' T U, where U is unitary and
T has 'clustered' entries 1, ULP,..., ULP with random
complex angles on the diagonal and random O(1) entries in
the upper triangle.

(12) A matrix of the form  U' T U, where U is unitary and
T has complex eigenvalues randomly chosen from
ULP < |z| < 1   and random O(1) entries in the upper
triangle.

(13) A matrix of the form  X' T X, where X has condition
SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP
with random complex angles on the diagonal and random O(1)
entries in the upper triangle.

(14) A matrix of the form  X' T X, where X has condition
SQRT( ULP ) and T has geometrically spaced entries
1, ..., ULP with random complex angles on the diagonal
and random O(1) entries in the upper triangle.

(15) A matrix of the form  X' T X, where X has condition
SQRT( ULP ) and T has 'clustered' entries 1, ULP,..., ULP
with random complex angles on the diagonal and random O(1)
entries in the upper triangle.

(16) A matrix of the form  X' T X, where X has condition
SQRT( ULP ) and T has complex eigenvalues randomly chosen
from ULP < |z| < 1 and random O(1) entries in the upper
triangle.

(17) Same as (16), but multiplied by a constant
near the overflow threshold
(18) Same as (16), but multiplied by a constant
near the underflow threshold

(19) Nonsymmetric matrix with random entries chosen from |z| < 1
If N is at least 4, all entries in first two rows and last
row, and first column and last two columns are zero.
(20) Same as (19), but multiplied by a constant
near the overflow threshold
(21) Same as (19), but multiplied by a constant
near the underflow threshold```
Parameters

NSIZES

```          NSIZES is INTEGER
The number of sizes of matrices to use.  If it is zero,
CDRVEV does nothing.  It must be at least zero.```

NN

```          NN is INTEGER array, dimension (NSIZES)
An array containing the sizes to be used for the matrices.
Zero values will be skipped.  The values must be at least
zero.```

NTYPES

```          NTYPES is INTEGER
The number of elements in DOTYPE.   If it is zero, CDRVEV
does nothing.  It must be at least zero.  If it is MAXTYP+1
and NSIZES is 1, then an additional type, MAXTYP+1 is
defined, which is to use whatever matrix is in A.  This
is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
DOTYPE(MAXTYP+1) is .TRUE. .```

DOTYPE

```          DOTYPE is LOGICAL array, dimension (NTYPES)
If DOTYPE(j) is .TRUE., then for each size in NN a
matrix of that size and of type j will be generated.
If NTYPES is smaller than the maximum number of types
defined (PARAMETER MAXTYP), then types NTYPES+1 through
MAXTYP will not be generated.  If NTYPES is larger
than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
will be ignored.```

ISEED

```          ISEED is INTEGER array, dimension (4)
On entry ISEED specifies the seed of the random number
generator. The array elements should be between 0 and 4095;
if not they will be reduced mod 4096.  Also, ISEED(4) must
be odd.  The random number generator uses a linear
congruential sequence limited to small integers, and so
should produce machine independent random numbers. The
values of ISEED are changed on exit, and can be used in the
next call to CDRVEV to continue the same random number
sequence.```

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.```

NOUNIT

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

A

```          A is COMPLEX array, dimension (LDA, max(NN))
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, and H. LDA must be at
least 1 and at least max(NN).```

H

```          H is COMPLEX array, dimension (LDA, max(NN))
Another copy of the test matrix A, modified by CGEEV.```

W

```          W is COMPLEX array, dimension (max(NN))
The eigenvalues of A. On exit, W are the eigenvalues of
the matrix in A.```

W1

```          W1 is COMPLEX array, dimension (max(NN))
Like W, this array contains the eigenvalues of A,
but those computed when CGEEV only computes a partial
eigendecomposition, i.e. not the eigenvalues and left
and right eigenvectors.```

VL

```          VL is COMPLEX array, dimension (LDVL, max(NN))
VL holds the computed left eigenvectors.```

LDVL

```          LDVL is INTEGER
Leading dimension of VL. Must be at least max(1,max(NN)).```

VR

```          VR is COMPLEX array, dimension (LDVR, max(NN))
VR holds the computed right eigenvectors.```

LDVR

```          LDVR is INTEGER
Leading dimension of VR. Must be at least max(1,max(NN)).```

LRE

```          LRE is COMPLEX array, dimension (LDLRE, max(NN))
LRE holds the computed right or left eigenvectors.```

LDLRE

```          LDLRE is INTEGER
Leading dimension of LRE. Must be at least max(1,max(NN)).```

RESULT

```          RESULT is REAL array, dimension (7)
The values computed by the seven tests described above.
The values are currently limited to 1/ulp, to avoid
overflow.```

WORK

`          WORK is COMPLEX array, dimension (NWORK)`

NWORK

```          NWORK is INTEGER
The number of entries in WORK.  This must be at least
5*NN(j)+2*NN(j)**2 for all j.```

RWORK

`          RWORK is REAL array, dimension (2*max(NN))`

IWORK

`          IWORK is INTEGER array, dimension (max(NN))`

INFO

```          INFO is INTEGER
If 0, then everything ran OK.
-1: NSIZES < 0
-2: Some NN(j) < 0
-3: NTYPES < 0
-6: THRESH < 0
-9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).
-14: LDVL < 1 or LDVL < NMAX, where NMAX is max( NN(j) ).
-16: LDVR < 1 or LDVR < NMAX, where NMAX is max( NN(j) ).
-18: LDLRE < 1 or LDLRE < NMAX, where NMAX is max( NN(j) ).
-21: NWORK too small.
If  CLATMR, CLATMS, CLATME or CGEEV returns an error code,
the absolute value of it is returned.

-----------------------------------------------------------------------

Some Local Variables and Parameters:
---- ----- --------- --- ----------

ZERO, ONE       Real 0 and 1.
MAXTYP          The number of types defined.
NMAX            Largest value in NN.
NERRS           The number of tests which have exceeded THRESH
COND, CONDS,
IMODE           Values to be passed to the matrix generators.
ANORM           Norm of A; passed to matrix generators.

OVFL, UNFL      Overflow and underflow thresholds.
ULP, ULPINV     Finest relative precision and its inverse.
RTULP, RTULPI   Square roots of the previous 4 values.

The following four arrays decode JTYPE:
KTYPE(j)        The general type (1-10) for type 'j'.
KMODE(j)        The MODE value to be passed to the matrix
generator for type 'j'.
KMAGN(j)        The order of magnitude ( O(1),
O(overflow^(1/2) ), O(underflow^(1/2) )
KCONDS(j)       Selectw whether CONDS is to be 1 or
1/sqrt(ulp).  (0 means irrelevant.)```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 387 of file cdrvev.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

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