# ddrves.f - Man Page

TESTING/EIG/ddrves.f

## Synopsis

### Functions/Subroutines

subroutine ddrves (nsizes, nn, ntypes, dotype, iseed, thresh, nounit, a, lda, h, ht, wr, wi, wrt, wit, vs, ldvs, result, work, nwork, iwork, bwork, info)
DDRVES

## Function/Subroutine Documentation

### subroutine ddrves (integer nsizes, integer, dimension( * ) nn, integer ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed, double precision thresh, integer nounit, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( lda, * ) h, double precision, dimension( lda, * ) ht, double precision, dimension( * ) wr, double precision, dimension( * ) wi, double precision, dimension( * ) wrt, double precision, dimension( * ) wit, double precision, dimension( ldvs, * ) vs, integer ldvs, double precision, dimension( 13 ) result, double precision, dimension( * ) work, integer nwork, integer, dimension( * ) iwork, logical, dimension( * ) bwork, integer info)

DDRVES

Purpose:

```    DDRVES checks the nonsymmetric eigenvalue (Schur form) problem
driver DGEES.

When DDRVES 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, 13
tests will be performed:

(1)     0 if T is in Schur form, 1/ulp otherwise
(no sorting of eigenvalues)

(2)     | A - VS T VS' | / ( n |A| ulp )

Here VS is the matrix of Schur eigenvectors, and T is in Schur
form  (no sorting of eigenvalues).

(3)     | I - VS VS' | / ( n ulp ) (no sorting of eigenvalues).

(4)     0     if WR+sqrt(-1)*WI are eigenvalues of T
1/ulp otherwise
(no sorting of eigenvalues)

(5)     0     if T(with VS) = T(without VS),
1/ulp otherwise
(no sorting of eigenvalues)

(6)     0     if eigenvalues(with VS) = eigenvalues(without VS),
1/ulp otherwise
(no sorting of eigenvalues)

(7)     0 if T is in Schur form, 1/ulp otherwise
(with sorting of eigenvalues)

(8)     | A - VS T VS' | / ( n |A| ulp )

Here VS is the matrix of Schur eigenvectors, and T is in Schur
form  (with sorting of eigenvalues).

(9)     | I - VS VS' | / ( n ulp ) (with sorting of eigenvalues).

(10)    0     if WR+sqrt(-1)*WI are eigenvalues of T
1/ulp otherwise
(with sorting of eigenvalues)

(11)    0     if T(with VS) = T(without VS),
1/ulp otherwise
(with sorting of eigenvalues)

(12)    0     if eigenvalues(with VS) = eigenvalues(without VS),
1/ulp otherwise
(with sorting of eigenvalues)

(13)    if sorting worked and SDIM is the number of
eigenvalues which were SELECTed

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

(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 orthogonal and
T has evenly spaced entries 1, ..., ULP with random signs
on the diagonal and random O(1) entries in the upper
triangle.

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

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

(12) A matrix of the form  U' T U, where U is orthogonal and
T has real or complex conjugate paired eigenvalues randomly
chosen from ( ULP, 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 signs 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 signs 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 signs 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 real or complex conjugate paired
eigenvalues randomly chosen from ( ULP, 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 (-1,1).
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,
DDRVES 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, DDRVES
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 DDRVES to continue the same random number
sequence.```

THRESH

```          THRESH is DOUBLE PRECISION
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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDA, max(NN))
Another copy of the test matrix A, modified by DGEES.```

HT

```          HT is DOUBLE PRECISION array, dimension (LDA, max(NN))
Yet another copy of the test matrix A, modified by DGEES.```

WR

`          WR is DOUBLE PRECISION array, dimension (max(NN))`

WI

```          WI is DOUBLE PRECISION array, dimension (max(NN))

The real and imaginary parts of the eigenvalues of A.
On exit, WR + WI*i are the eigenvalues of the matrix in A.```

WRT

`          WRT is DOUBLE PRECISION array, dimension (max(NN))`

WIT

```          WIT is DOUBLE PRECISION array, dimension (max(NN))

Like WR, WI, these arrays contain the eigenvalues of A,
but those computed when DGEES only computes a partial
eigendecomposition, i.e. not Schur vectors```

VS

```          VS is DOUBLE PRECISION array, dimension (LDVS, max(NN))
VS holds the computed Schur vectors.```

LDVS

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

RESULT

```          RESULT is DOUBLE PRECISION array, dimension (13)
The values computed by the 13 tests described above.
The values are currently limited to 1/ulp, to avoid overflow.```

WORK

`          WORK is DOUBLE PRECISION 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.```

IWORK

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

BWORK

`          BWORK is LOGICAL 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) ).
-17: LDVS < 1 or LDVS < NMAX, where NMAX is max( NN(j) ).
-20: NWORK too small.
If  DLATMR, SLATMS, SLATME or DGEES 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 385 of file ddrves.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

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