# schkbb.f - Man Page

TESTING/EIG/schkbb.f

## Synopsis

### Functions/Subroutines

subroutine schkbb (nsizes, mval, nval, nwdths, kk, ntypes, dotype, nrhs, iseed, thresh, nounit, a, lda, ab, ldab, bd, be, q, ldq, p, ldp, c, ldc, cc, work, lwork, result, info)
SCHKBB

## Function/Subroutine Documentation

### subroutine schkbb (integer nsizes, integer, dimension( * ) mval, integer, dimension( * ) nval, integer nwdths, integer, dimension( * ) kk, integer ntypes, logical, dimension( * ) dotype, integer nrhs, integer, dimension( 4 ) iseed, real thresh, integer nounit, real, dimension( lda, * ) a, integer lda, real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) bd, real, dimension( * ) be, real, dimension( ldq, * ) q, integer ldq, real, dimension( ldp, * ) p, integer ldp, real, dimension( ldc, * ) c, integer ldc, real, dimension( ldc, * ) cc, real, dimension( * ) work, integer lwork, real, dimension( * ) result, integer info)

SCHKBB

Purpose:

``` SCHKBB tests the reduction of a general real rectangular band
matrix to bidiagonal form.

SGBBRD factors a general band matrix A as  Q B P* , where * means
transpose, B is upper bidiagonal, and Q and P are orthogonal;
SGBBRD can also overwrite a given matrix C with Q* C .

For each pair of matrix dimensions (M,N) and each selected matrix
type, an M by N matrix A and an M by NRHS matrix C are generated.
The problem dimensions are as follows
A:          M x N
Q:          M x M
P:          N x N
B:          min(M,N) x min(M,N)
C:          M x NRHS

For each generated matrix, 4 tests are performed:

(1)   | A - Q B PT | / ( |A| max(M,N) ulp ), PT = P'

(2)   | I - Q' Q | / ( M ulp )

(3)   | I - PT PT' | / ( N ulp )

(4)   | Y - Q' C | / ( |Y| max(M,NRHS) ulp ), where Y = Q' C.

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:

The possible matrix types are

(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 (3), but multiplied by SQRT( overflow threshold )
(7)  Same as (3), but multiplied by SQRT( underflow threshold )

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

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

(10) A matrix of the form  U D V, where U and V are 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) Rectangular 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 values of M and N contained in the vectors
MVAL and NVAL.  The matrix sizes are used in pairs (M,N).
If NSIZES is zero, SCHKBB does nothing.  NSIZES must be at
least zero.```

MVAL

```          MVAL is INTEGER array, dimension (NSIZES)
The values of the matrix row dimension M.```

NVAL

```          NVAL is INTEGER array, dimension (NSIZES)
The values of the matrix column dimension N.```

NWDTHS

```          NWDTHS is INTEGER
The number of bandwidths to use.  If it is zero,
SCHKBB 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, SCHKBB
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.```

NRHS

```          NRHS is INTEGER
The number of columns in the 'right-hand side' matrix C.
If NRHS = 0, then the operations on the right-hand side will
not be tested. NRHS must be at least 0.```

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 SCHKBB 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 REAL array, dimension
(LDA, max(NN))
Used to hold the matrix A.```

LDA

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

AB

```          AB is REAL array, dimension (LDAB, max(NN))
Used to hold A in band storage format.```

LDAB

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

BD

```          BD is REAL array, dimension (max(NN))
Used to hold the diagonal of the bidiagonal matrix computed
by SGBBRD.```

BE

```          BE is REAL array, dimension (max(NN))
Used to hold the off-diagonal of the bidiagonal matrix
computed by SGBBRD.```

Q

```          Q is REAL array, dimension (LDQ, max(NN))
Used to hold the orthogonal matrix Q computed by SGBBRD.```

LDQ

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

P

```          P is REAL array, dimension (LDP, max(NN))
Used to hold the orthogonal matrix P computed by SGBBRD.```

LDP

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

C

```          C is REAL array, dimension (LDC, max(NN))
Used to hold the matrix C updated by SGBBRD.```

LDC

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

CC

```          CC is REAL array, dimension (LDC, max(NN))
Used to hold a copy of the matrix C.```

WORK

`          WORK is REAL 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).```

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 351 of file schkbb.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

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