# ddrvst2stg.f - Man Page

TESTING/EIG/ddrvst2stg.f

## Synopsis

### Functions/Subroutines

subroutine ddrvst2stg (nsizes, nn, ntypes, dotype, iseed, thresh, nounit, a, lda, d1, d2, d3, d4, eveigs, wa1, wa2, wa3, u, ldu, v, tau, z, work, lwork, iwork, liwork, result, info)
DDRVST2STG

## Function/Subroutine Documentation

### subroutine ddrvst2stg (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( * ) d1, double precision, dimension( * ) d2, double precision, dimension( * ) d3, double precision, dimension( * ) d4, double precision, dimension( * ) eveigs, double precision, dimension( * ) wa1, double precision, dimension( * ) wa2, double precision, dimension( * ) wa3, double precision, dimension( ldu, * ) u, integer ldu, double precision, dimension( ldu, * ) v, double precision, dimension( * ) tau, double precision, dimension( ldu, * ) z, double precision, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, double precision, dimension( * ) result, integer info)

DDRVST2STG

Purpose:

```      DDRVST2STG  checks the symmetric eigenvalue problem drivers.

DSTEV computes all eigenvalues and, optionally,
eigenvectors of a real symmetric tridiagonal matrix.

DSTEVX computes selected eigenvalues and, optionally,
eigenvectors of a real symmetric tridiagonal matrix.

DSTEVR computes selected eigenvalues and, optionally,
eigenvectors of a real symmetric tridiagonal matrix
using the Relatively Robust Representation where it can.

DSYEV computes all eigenvalues and, optionally,
eigenvectors of a real symmetric matrix.

DSYEVX computes selected eigenvalues and, optionally,
eigenvectors of a real symmetric matrix.

DSYEVR computes selected eigenvalues and, optionally,
eigenvectors of a real symmetric matrix
using the Relatively Robust Representation where it can.

DSPEV computes all eigenvalues and, optionally,
eigenvectors of a real symmetric matrix in packed
storage.

DSPEVX computes selected eigenvalues and, optionally,
eigenvectors of a real symmetric matrix in packed
storage.

DSBEV computes all eigenvalues and, optionally,
eigenvectors of a real symmetric band matrix.

DSBEVX computes selected eigenvalues and, optionally,
eigenvectors of a real symmetric band matrix.

DSYEVD computes all eigenvalues and, optionally,
eigenvectors of a real symmetric matrix using
a divide and conquer algorithm.

DSPEVD computes all eigenvalues and, optionally,
eigenvectors of a real symmetric matrix in packed
storage, using a divide and conquer algorithm.

DSBEVD computes all eigenvalues and, optionally,
eigenvectors of a real symmetric band matrix,
using a divide and conquer algorithm.

When DDRVST2STG 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 appropriate drivers.  For each matrix and each
driver routine called, the following tests will be performed:

(1)     | A - Z D Z' | / ( |A| n ulp )

(2)     | I - Z Z' | / ( n ulp )

(3)     | D1 - D2 | / ( |D1| ulp )

where Z is the matrix of eigenvectors returned when the
eigenvector option is given and D1 and D2 are the eigenvalues
returned with and without the eigenvector option.

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

(6)  Same as (4), but multiplied by SQRT( overflow threshold )
(7)  Same as (4), but multiplied by SQRT( underflow threshold )

(8)  A matrix of the form  U' D U, where U is orthogonal and
D has evenly spaced entries 1, ..., ULP with random signs
on the diagonal.

(9)  A matrix of the form  U' D U, where U is orthogonal and
D has geometrically spaced entries 1, ..., ULP with random
signs on the diagonal.

(10) A matrix of the form  U' D U, where U is orthogonal and
D has 'clustered' entries 1, ULP,..., ULP with random
signs on the diagonal.

(11) Same as (8), but multiplied by SQRT( overflow threshold )
(12) Same as (8), but multiplied by SQRT( underflow threshold )

(13) Symmetric matrix with random entries chosen from (-1,1).
(14) Same as (13), but multiplied by SQRT( overflow threshold )
(15) Same as (13), but multiplied by SQRT( underflow threshold )
(16) A band matrix with half bandwidth randomly chosen between
0 and N-1, with evenly spaced eigenvalues 1, ..., ULP
with random signs.
(17) Same as (16), but multiplied by SQRT( overflow threshold )
(18) Same as (16), but multiplied by SQRT( underflow threshold )```
```  NSIZES  INTEGER
The number of sizes of matrices to use.  If it is zero,
DDRVST2STG does nothing.  It must be at least zero.
Not modified.

NN      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.
Not modified.

NTYPES  INTEGER
The number of elements in DOTYPE.   If it is zero, DDRVST2STG
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. .
Not modified.

DOTYPE  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.
Not modified.

ISEED   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 DDRVST2STG to continue the same random number
sequence.
Modified.

THRESH  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.
Not modified.

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

A       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.
Modified.

LDA     INTEGER
The leading dimension of A.  It must be at
least 1 and at least max( NN ).
Not modified.

D1      DOUBLE PRECISION array, dimension (max(NN))
The eigenvalues of A, as computed by DSTEQR simultaneously
with Z.  On exit, the eigenvalues in D1 correspond with the
matrix in A.
Modified.

D2      DOUBLE PRECISION array, dimension (max(NN))
The eigenvalues of A, as computed by DSTEQR if Z is not
computed.  On exit, the eigenvalues in D2 correspond with
the matrix in A.
Modified.

D3      DOUBLE PRECISION array, dimension (max(NN))
The eigenvalues of A, as computed by DSTERF.  On exit, the
eigenvalues in D3 correspond with the matrix in A.
Modified.

D4      DOUBLE PRECISION array, dimension

EVEIGS  DOUBLE PRECISION array, dimension (max(NN))
The eigenvalues as computed by DSTEV('N', ... )
(I reserve the right to change this to the output of
whichever algorithm computes the most accurate eigenvalues).

WA1     DOUBLE PRECISION array, dimension

WA2     DOUBLE PRECISION array, dimension

WA3     DOUBLE PRECISION array, dimension

U       DOUBLE PRECISION array, dimension (LDU, max(NN))
The orthogonal matrix computed by DSYTRD + DORGTR.
Modified.

LDU     INTEGER
The leading dimension of U, Z, and V.  It must be at
least 1 and at least max( NN ).
Not modified.

V       DOUBLE PRECISION array, dimension (LDU, max(NN))
The Housholder vectors computed by DSYTRD in reducing A to
tridiagonal form.
Modified.

TAU     DOUBLE PRECISION array, dimension (max(NN))
The Householder factors computed by DSYTRD in reducing A
to tridiagonal form.
Modified.

Z       DOUBLE PRECISION array, dimension (LDU, max(NN))
The orthogonal matrix of eigenvectors computed by DSTEQR,
DPTEQR, and DSTEIN.
Modified.

WORK    DOUBLE PRECISION array, dimension (LWORK)
Workspace.
Modified.

LWORK   INTEGER
The number of entries in WORK.  This must be at least
1 + 4 * Nmax + 2 * Nmax * lg Nmax + 4 * Nmax**2
where Nmax = max( NN(j), 2 ) and lg = log base 2.
Not modified.

IWORK   INTEGER array,
dimension (6 + 6*Nmax + 5 * Nmax * lg Nmax )
where Nmax = max( NN(j), 2 ) and lg = log base 2.
Workspace.
Modified.

RESULT  DOUBLE PRECISION array, dimension (105)
The values computed by the tests described above.
The values are currently limited to 1/ulp, to avoid
overflow.
Modified.

INFO    INTEGER
If 0, then everything ran OK.
-1: NSIZES < 0
-2: Some NN(j) < 0
-3: NTYPES < 0
-5: THRESH < 0
-9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).
-16: LDU < 1 or LDU < NMAX.
-21: LWORK too small.
If  DLATMR, DLATMS, DSYTRD, DORGTR, DSTEQR, DSTERF,
or DORMTR returns an error code, the
absolute value of it is returned.
Modified.

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

Some Local Variables and Parameters:
---- ----- --------- --- ----------
ZERO, ONE       Real 0 and 1.
MAXTYP          The number of types defined.
NTEST           The number of tests performed, or which can
be performed so far, for the current matrix.
NTESTT          The total number of tests performed so far.
NMAX            Largest value in NN.
NMATS           The number of matrices generated so far.
NERRS           The number of tests which have exceeded THRESH
so far (computed by DLAFTS).
COND, 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.
RTOVFL, RTUNFL  Square roots of the previous 2 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) )

The tests performed are:                 Routine tested
1= | A - U S U' | / ( |A| n ulp )         DSTEV('V', ... )
2= | I - U U' | / ( n ulp )               DSTEV('V', ... )
3= |D(with Z) - D(w/o Z)| / (|D| ulp)     DSTEV('N', ... )
4= | A - U S U' | / ( |A| n ulp )         DSTEVX('V','A', ... )
5= | I - U U' | / ( n ulp )               DSTEVX('V','A', ... )
6= |D(with Z) - EVEIGS| / (|D| ulp)       DSTEVX('N','A', ... )
7= | A - U S U' | / ( |A| n ulp )         DSTEVR('V','A', ... )
8= | I - U U' | / ( n ulp )               DSTEVR('V','A', ... )
9= |D(with Z) - EVEIGS| / (|D| ulp)       DSTEVR('N','A', ... )
10= | A - U S U' | / ( |A| n ulp )        DSTEVX('V','I', ... )
11= | I - U U' | / ( n ulp )              DSTEVX('V','I', ... )
12= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSTEVX('N','I', ... )
13= | A - U S U' | / ( |A| n ulp )        DSTEVX('V','V', ... )
14= | I - U U' | / ( n ulp )              DSTEVX('V','V', ... )
15= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSTEVX('N','V', ... )
16= | A - U S U' | / ( |A| n ulp )        DSTEVD('V', ... )
17= | I - U U' | / ( n ulp )              DSTEVD('V', ... )
18= |D(with Z) - EVEIGS| / (|D| ulp)      DSTEVD('N', ... )
19= | A - U S U' | / ( |A| n ulp )        DSTEVR('V','I', ... )
20= | I - U U' | / ( n ulp )              DSTEVR('V','I', ... )
21= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSTEVR('N','I', ... )
22= | A - U S U' | / ( |A| n ulp )        DSTEVR('V','V', ... )
23= | I - U U' | / ( n ulp )              DSTEVR('V','V', ... )
24= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSTEVR('N','V', ... )

25= | A - U S U' | / ( |A| n ulp )        DSYEV('L','V', ... )
26= | I - U U' | / ( n ulp )              DSYEV('L','V', ... )
27= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSYEV_2STAGE('L','N', ... )
28= | A - U S U' | / ( |A| n ulp )        DSYEVX('L','V','A', ... )
29= | I - U U' | / ( n ulp )              DSYEVX('L','V','A', ... )
30= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSYEVX_2STAGE('L','N','A', ... )
31= | A - U S U' | / ( |A| n ulp )        DSYEVX('L','V','I', ... )
32= | I - U U' | / ( n ulp )              DSYEVX('L','V','I', ... )
33= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSYEVX_2STAGE('L','N','I', ... )
34= | A - U S U' | / ( |A| n ulp )        DSYEVX('L','V','V', ... )
35= | I - U U' | / ( n ulp )              DSYEVX('L','V','V', ... )
36= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSYEVX_2STAGE('L','N','V', ... )
37= | A - U S U' | / ( |A| n ulp )        DSPEV('L','V', ... )
38= | I - U U' | / ( n ulp )              DSPEV('L','V', ... )
39= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSPEV('L','N', ... )
40= | A - U S U' | / ( |A| n ulp )        DSPEVX('L','V','A', ... )
41= | I - U U' | / ( n ulp )              DSPEVX('L','V','A', ... )
42= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSPEVX('L','N','A', ... )
43= | A - U S U' | / ( |A| n ulp )        DSPEVX('L','V','I', ... )
44= | I - U U' | / ( n ulp )              DSPEVX('L','V','I', ... )
45= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSPEVX('L','N','I', ... )
46= | A - U S U' | / ( |A| n ulp )        DSPEVX('L','V','V', ... )
47= | I - U U' | / ( n ulp )              DSPEVX('L','V','V', ... )
48= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSPEVX('L','N','V', ... )
49= | A - U S U' | / ( |A| n ulp )        DSBEV('L','V', ... )
50= | I - U U' | / ( n ulp )              DSBEV('L','V', ... )
51= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSBEV_2STAGE('L','N', ... )
52= | A - U S U' | / ( |A| n ulp )        DSBEVX('L','V','A', ... )
53= | I - U U' | / ( n ulp )              DSBEVX('L','V','A', ... )
54= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSBEVX_2STAGE('L','N','A', ... )
55= | A - U S U' | / ( |A| n ulp )        DSBEVX('L','V','I', ... )
56= | I - U U' | / ( n ulp )              DSBEVX('L','V','I', ... )
57= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSBEVX_2STAGE('L','N','I', ... )
58= | A - U S U' | / ( |A| n ulp )        DSBEVX('L','V','V', ... )
59= | I - U U' | / ( n ulp )              DSBEVX('L','V','V', ... )
60= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSBEVX_2STAGE('L','N','V', ... )
61= | A - U S U' | / ( |A| n ulp )        DSYEVD('L','V', ... )
62= | I - U U' | / ( n ulp )              DSYEVD('L','V', ... )
63= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSYEVD_2STAGE('L','N', ... )
64= | A - U S U' | / ( |A| n ulp )        DSPEVD('L','V', ... )
65= | I - U U' | / ( n ulp )              DSPEVD('L','V', ... )
66= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSPEVD('L','N', ... )
67= | A - U S U' | / ( |A| n ulp )        DSBEVD('L','V', ... )
68= | I - U U' | / ( n ulp )              DSBEVD('L','V', ... )
69= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSBEVD_2STAGE('L','N', ... )
70= | A - U S U' | / ( |A| n ulp )        DSYEVR('L','V','A', ... )
71= | I - U U' | / ( n ulp )              DSYEVR('L','V','A', ... )
72= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSYEVR_2STAGE('L','N','A', ... )
73= | A - U S U' | / ( |A| n ulp )        DSYEVR('L','V','I', ... )
74= | I - U U' | / ( n ulp )              DSYEVR('L','V','I', ... )
75= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSYEVR_2STAGE('L','N','I', ... )
76= | A - U S U' | / ( |A| n ulp )        DSYEVR('L','V','V', ... )
77= | I - U U' | / ( n ulp )              DSYEVR('L','V','V', ... )
78= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSYEVR_2STAGE('L','N','V', ... )

Tests 25 through 78 are repeated (as tests 79 through 132)
with UPLO='U'

79= | A - U S U' | / ( |A| n ulp )        DSPEVR('L','V','A', ... )
80= | I - U U' | / ( n ulp )              DSPEVR('L','V','A', ... )
81= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSPEVR('L','N','A', ... )
82= | A - U S U' | / ( |A| n ulp )        DSPEVR('L','V','I', ... )
83= | I - U U' | / ( n ulp )              DSPEVR('L','V','I', ... )
84= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSPEVR('L','N','I', ... )
85= | A - U S U' | / ( |A| n ulp )        DSPEVR('L','V','V', ... )
86= | I - U U' | / ( n ulp )              DSPEVR('L','V','V', ... )
87= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSPEVR('L','N','V', ... )
88= | A - U S U' | / ( |A| n ulp )        DSBEVR('L','V','A', ... )
89= | I - U U' | / ( n ulp )              DSBEVR('L','V','A', ... )
90= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSBEVR('L','N','A', ... )
91= | A - U S U' | / ( |A| n ulp )        DSBEVR('L','V','I', ... )
92= | I - U U' | / ( n ulp )              DSBEVR('L','V','I', ... )
93= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSBEVR('L','N','I', ... )
94= | A - U S U' | / ( |A| n ulp )        DSBEVR('L','V','V', ... )
95= | I - U U' | / ( n ulp )              DSBEVR('L','V','V', ... )
96= |D(with Z) - D(w/o Z)| / (|D| ulp)    DSBEVR('L','N','V', ... )```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 449 of file ddrvst2stg.f.

## Author

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## Referenced By

The man page ddrvst2stg(3) is an alias of ddrvst2stg.f(3).

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