# sdrvsg2stg.f - Man Page

TESTING/EIG/sdrvsg2stg.f

## Synopsis

### Functions/Subroutines

subroutine sdrvsg2stg (nsizes, nn, ntypes, dotype, iseed, thresh, nounit, a, lda, b, ldb, d, d2, z, ldz, ab, bb, ap, bp, work, nwork, iwork, liwork, result, info)
SDRVSG2STG

## Function/Subroutine Documentation

### subroutine sdrvsg2stg (integer nsizes, integer, dimension( * ) nn, integer ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed, real thresh, integer nounit, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) d, real, dimension( * ) d2, real, dimension( ldz, * ) z, integer ldz, real, dimension( lda, * ) ab, real, dimension( ldb, * ) bb, real, dimension( * ) ap, real, dimension( * ) bp, real, dimension( * ) work, integer nwork, integer, dimension( * ) iwork, integer liwork, real, dimension( * ) result, integer info)

SDRVSG2STG

Purpose:

SDRVSG2STG checks the real symmetric generalized eigenproblem
drivers.

SSYGV computes all eigenvalues and, optionally,
eigenvectors of a real symmetric-definite generalized
eigenproblem.

SSYGVD computes all eigenvalues and, optionally,
eigenvectors of a real symmetric-definite generalized
eigenproblem using a divide and conquer algorithm.

SSYGVX computes selected eigenvalues and, optionally,
eigenvectors of a real symmetric-definite generalized
eigenproblem.

SSPGV computes all eigenvalues and, optionally,
eigenvectors of a real symmetric-definite generalized
eigenproblem in packed storage.

SSPGVD computes all eigenvalues and, optionally,
eigenvectors of a real symmetric-definite generalized
eigenproblem in packed storage using a divide and
conquer algorithm.

SSPGVX computes selected eigenvalues and, optionally,
eigenvectors of a real symmetric-definite generalized
eigenproblem in packed storage.

SSBGV computes all eigenvalues and, optionally,
eigenvectors of a real symmetric-definite banded
generalized eigenproblem.

SSBGVD computes all eigenvalues and, optionally,
eigenvectors of a real symmetric-definite banded
generalized eigenproblem using a divide and conquer
algorithm.

SSBGVX computes selected eigenvalues and, optionally,
eigenvectors of a real symmetric-definite banded
generalized eigenproblem.

When SDRVSG2STG 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 A of the given type will be
generated; a random well-conditioned matrix B is also generated
and the pair (A,B) is used to test the drivers.

For each pair (A,B), the following tests are performed:

(1) SSYGV with ITYPE = 1 and UPLO ='U':

| A Z - B Z D | / ( |A| |Z| n ulp )
| D - D2 | / ( |D| ulp )   where D is computed by
SSYGV and  D2 is computed by
SSYGV_2STAGE. This test is
only performed for SSYGV

(2) as (1) but calling SSPGV
(3) as (1) but calling SSBGV
(4) as (1) but with UPLO = 'L'
(5) as (4) but calling SSPGV
(6) as (4) but calling SSBGV

(7) SSYGV with ITYPE = 2 and UPLO ='U':

| A B Z - Z D | / ( |A| |Z| n ulp )

(8) as (7) but calling SSPGV
(9) as (7) but with UPLO = 'L'
(10) as (9) but calling SSPGV

(11) SSYGV with ITYPE = 3 and UPLO ='U':

| B A Z - Z D | / ( |A| |Z| n ulp )

(12) as (11) but calling SSPGV
(13) as (11) but with UPLO = 'L'
(14) as (13) but calling SSPGV

SSYGVD, SSPGVD and SSBGVD performed the same 14 tests.

SSYGVX, SSPGVX and SSBGVX performed the above 14 tests with
the parameter RANGE = 'A', 'N' and 'I', respectively.

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.
This type is used for the matrix A which has half-bandwidth KA.
B is generated as a well-conditioned positive definite matrix
with half-bandwidth KB (<= KA).
Currently, the list of possible types for A is:

(1)  The zero matrix.
(2)  The identity matrix.

(3)  A diagonal matrix with evenly spaced entries
1, ..., ULP  and random signs.
(ULP = (first number larger than 1) - 1 )
(4)  A diagonal matrix with geometrically spaced entries
1, ..., ULP  and random signs.
(5)  A diagonal matrix with 'clustered' entries
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) Same as (8), but with KA = 1 and KB = 1
(17) Same as (8), but with KA = 2 and KB = 1
(18) Same as (8), but with KA = 2 and KB = 2
(19) Same as (8), but with KA = 3 and KB = 1
(20) Same as (8), but with KA = 3 and KB = 2
(21) Same as (8), but with KA = 3 and KB = 3
NSIZES  INTEGER
The number of sizes of matrices to use.  If it is zero,
SDRVSG2STG 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, SDRVSG2STG
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 SDRVSG2STG to continue the same random number
sequence.
Modified.

THRESH  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. real)
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       REAL             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 and AB.  It must be at
least 1 and at least max( NN ).
Not modified.

B       REAL             array, dimension (LDB , max(NN))
Used to hold the symmetric positive definite matrix for
the generalized problem.
On exit, B contains the last matrix actually
used.
Modified.

LDB     INTEGER
The leading dimension of B and BB.  It must be at
least 1 and at least max( NN ).
Not modified.

D       REAL             array, dimension (max(NN))
The eigenvalues of A. On exit, the eigenvalues in D
correspond with the matrix in A.
Modified.

Z       REAL             array, dimension (LDZ, max(NN))
The matrix of eigenvectors.
Modified.

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

AB      REAL             array, dimension (LDA, max(NN))
Workspace.
Modified.

BB      REAL             array, dimension (LDB, max(NN))
Workspace.
Modified.

AP      REAL             array, dimension (max(NN)**2)
Workspace.
Modified.

BP      REAL             array, dimension (max(NN)**2)
Workspace.
Modified.

WORK    REAL array, dimension (NWORK)
Workspace.
Modified.

NWORK   INTEGER
The number of entries in WORK.  This must be at least
1+5*N+2*N*lg(N)+3*N**2 where N = max( NN(j) ) and
lg( N ) = smallest integer k such that 2**k >= N.
Not modified.

IWORK   INTEGER array, dimension (LIWORK)
Workspace.
Modified.

LIWORK  INTEGER
The number of entries in WORK.  This must be at least 6*N.
Not modified.

RESULT  REAL array, dimension (70)
The values computed by the 70 tests described above.
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: LDZ < 1 or LDZ < NMAX.
-21: NWORK too small.
-23: LIWORK too small.
If  SLATMR, SLATMS, SSYGV, SSPGV, SSBGV, SSYGVD, SSPGVD,
SSBGVD, SSYGVX, SSPGVX or SSBGVX 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 that have been run
on this matrix.
NTESTT          The total number of tests for this call.
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 SLAFTS).
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) )
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 358 of file sdrvsg2stg.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sdrvsg2stg(3) is an alias of sdrvsg2stg.f(3).

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