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####

MATLAB Interface to GUPTRI.

An interface to MATLAB in terms of a MEX-file is available for
the routine GUPTRI. In the following we give a brief description of the
arguments and output of the `guptri` function
and demonstrate its usage on a small numerical example.

The most general call,

stores the transformation matrices in `P` and
`Q` and and in `S` and `T`,
respectively.
The computed Kronecker structure is revealed by `kstr`, as
described in the example discussed later in this section.
The `guptri` function reduces an pencil
to generalized upper triangular form
as in
(8.34)-(8.35):
S=
ccccc
A_r & * & * & * & *

0 &A_z & * & * & *

0 & 0 &A_f & * & *

0 & 0 & 0 &A_i& *

0 & 0 & 0 & 0 & A_l
,
T=
ccccc
B_r & * & * & * & *

0 &B_z & * & * & *

0 &0 &B_f& * & *

0 &0 &0 &B_i & *

0 &0 &0 & 0 &B_l
,
where the diagonal blocks of and in staircase forms
describe the Kronecker structure of
(see §8.7.6).

Besides , the user can optionally provide three input parameters
(`EPSU`, `GAP`, and `ZERO`) that control the computation of
the GUPTRI form.
`EPSU` (relative uncertainty in data) and `GAP`
(should be at least 1 and nominally 1000) are used
to make rank decisions in order
to determine the Kronecker structure of an input pencil
(see p. ).
The default value is
, but other values may be necessary for certain examples.
`ZERO` is used as a logical variable, which when set to true
(`ZERO` = nonzero value) forces `guptri` to zero out
small singular values during the reduction process
so that the returned pencil really has the computed GUPTRI form
(see p. ).
Otherwise, the returned pencil is a true equivalence
transformation of the input pencil and all zero blocks in the
GUPTRI form will contain small entries (normally of size `EPSU`
at most).

** Next:** Example in MATLAB.
** Up:** More on GUPTRI and
** Previous:** Arithmetic and Space Complexity.
** Contents**
** Index**
Susan Blackford
2000-11-20