# cchkhb2stg.f - Man Page

TESTING/EIG/cchkhb2stg.f

## Synopsis

### Functions/Subroutines

subroutine cchkhb2stg (nsizes, nn, nwdths, kk, ntypes, dotype, iseed, thresh, nounit, a, lda, sd, se, d1, d2, d3, u, ldu, work, lwork, rwork, result, info)
CCHKHB2STG

## Function/Subroutine Documentation

### subroutine cchkhb2stg (integer nsizes, integer, dimension( * ) nn, integer nwdths, integer, dimension( * ) kk, integer ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed, real thresh, integer nounit, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) sd, real, dimension( * ) se, real, dimension( * ) d1, real, dimension( * ) d2, real, dimension( * ) d3, complex, dimension( ldu, * ) u, integer ldu, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, real, dimension( * ) result, integer info)

CCHKHB2STG

Purpose:

``` CCHKHB2STG tests the reduction of a Hermitian band matrix to tridiagonal
from, used with the Hermitian eigenvalue problem.

CHBTRD factors a Hermitian band matrix A as  U S U* , where * means
conjugate transpose, S is symmetric tridiagonal, and U is unitary.
CHBTRD can use either just the lower or just the upper triangle
of A; CCHKHB2STG checks both cases.

CHETRD_HB2ST factors a Hermitian band matrix A as  U S U* ,
where * means conjugate transpose, S is symmetric tridiagonal, and U is
unitary. CHETRD_HB2ST can use either just the lower or just
the upper triangle of A; CCHKHB2STG checks both cases.

DSTEQR factors S as  Z D1 Z'.
D1 is the matrix of eigenvalues computed when Z is not computed
and from the S resulting of DSBTRD 'U' (used as reference for DSYTRD_SB2ST)
D2 is the matrix of eigenvalues computed when Z is not computed
and from the S resulting of DSYTRD_SB2ST 'U'.
D3 is the matrix of eigenvalues computed when Z is not computed
and from the S resulting of DSYTRD_SB2ST 'L'.

When CCHKHB2STG is called, a number of matrix 'sizes' ('n's'), a number
of bandwidths ('k's'), and a number of matrix 'types' are
specified.  For each size ('n'), each bandwidth ('k') less than or
equal to 'n', and each type of matrix, one matrix will be generated
and used to test the hermitian banded reduction routine.  For each
matrix, a number of tests will be performed:

(1)     | A - V S V* | / ( |A| n ulp )  computed by CHBTRD with
UPLO='U'

(2)     | I - UU* | / ( n ulp )

(3)     | A - V S V* | / ( |A| n ulp )  computed by CHBTRD with
UPLO='L'

(4)     | I - UU* | / ( n ulp )

(5)     | D1 - D2 | / ( |D1| ulp )      where D1 is computed by
DSBTRD with UPLO='U' and
D2 is computed by
CHETRD_HB2ST with UPLO='U'

(6)     | D1 - D3 | / ( |D1| ulp )      where D1 is computed by
DSBTRD with UPLO='U' and
D3 is computed by
CHETRD_HB2ST with UPLO='L'

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 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 unitary 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 unitary 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 unitary 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) Hermitian 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 )```
Parameters

NSIZES

```          NSIZES is INTEGER
The number of sizes of matrices to use.  If it is zero,
CCHKHB2STG 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.```

NWDTHS

```          NWDTHS is INTEGER
The number of bandwidths to use.  If it is zero,
CCHKHB2STG does nothing.  It must be at least zero.```

KK

```          KK is INTEGER array, dimension (NWDTHS)
An array containing the bandwidths to be used for the band
matrices.  The values must be at least zero.```

NTYPES

```          NTYPES is INTEGER
The number of elements in DOTYPE.   If it is zero, CCHKHB2STG
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 CCHKHB2STG 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 IINFO not equal to 0.)```

A

```          A is COMPLEX array, dimension
(LDA, max(NN))
Used to hold the matrix whose eigenvalues are to be
computed.```

LDA

```          LDA is INTEGER
The leading dimension of A.  It must be at least 2 (not 1!)
and at least max( KK )+1.```

SD

```          SD is REAL array, dimension (max(NN))
Used to hold the diagonal of the tridiagonal matrix computed
by CHBTRD.```

SE

```          SE is REAL array, dimension (max(NN))
Used to hold the off-diagonal of the tridiagonal matrix
computed by CHBTRD.```

D1

```          D1 is REAL array, dimension (max(NN))
Used store eigenvalues resulting from the tridiagonal
form using the DSBTRD.```

D2

`          D2 is REAL array, dimension (max(NN))`

D3

`          D3 is REAL array, dimension (max(NN))`

U

```          U is COMPLEX array, dimension (LDU, max(NN))
Used to hold the unitary matrix computed by CHBTRD.```

LDU

```          LDU is INTEGER
The leading dimension of U.  It must be at least 1
and at least max( NN ).```

WORK

`          WORK is COMPLEX array, dimension (LWORK)`

LWORK

```          LWORK is INTEGER
The number of entries in WORK.  This must be at least
max( LDA+1, max(NN)+1 )*max(NN).```

RWORK

`          RWORK is REAL array`

RESULT

```          RESULT is REAL array, dimension (4)
The values computed by the tests described above.
The values are currently limited to 1/ulp, to avoid
overflow.```

INFO

```          INFO is INTEGER
If 0, then everything ran OK.

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

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.
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 337 of file cchkhb2stg.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cchkhb2stg(3) is an alias of cchkhb2stg.f(3).

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