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quaskro(1) Scilab Function quaskro(1)
NAME
randpencil - random pencil
CALLING SEQUENCE
F=randpencil(eps,infi,fin,eta)
PARAMETERS
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.
EXAMPLE
F=randpencil([0,1],[2],[-1,0,1],[3]);
[Q,Z,Qd,Zd,numbeps,numbeta]=kroneck(F);
Qd, Zd
s=poly(0,'s');
F=randpencil([],[1,2],s^3-2,[]); //regular pencil
det(F)
SEE ALSO
kroneck, pencan, penlaur
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