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randpencil
random pencil
Syntax
F=randpencil(eps,infi,fin,eta)
Arguments
- eps
vector of integers
- infi
vector of integers
- fin
real vector, or monic polynomial, or vector of monic polynomial
- eta
vector of integers
- F
real matrix pencil
F=s*E-A
(s=poly(0,'s')
)
Description
Utility function.
F=randpencil(eps,infi,fin,eta)
returns a random pencil F
with given Kronecker structure. The structure is given by:
eps=[eps1,...,epsk]
: structure of epsilon blocks (size eps1x(eps1+1),....)
fin=[l1,...,ln]
set of finite eigenvalues (assumed real) (possibly [])
infi=[k1,...,kp]
size of J-blocks at infinity
ki>=1
(infi=[] if no J blocks).
eta=[eta1,...,etap]
: structure ofeta blocks (size eta1+1)xeta1,...)
epsi
's should be >=0, etai
's should be >=0, infi
's should
be >=1.
If fin
is a (monic) polynomial, the finite block admits the roots of
fin
as eigenvalues.
If fin
is a vector of polynomial, they are the finite elementary
divisors of F
i.e. the roots of p(i)
are finite
eigenvalues of F
.
Examples
See also
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