| | | Scilab Reference Manual | |
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randpencil — random pencil
F=randpencil(eps,infi,fin,eta)
| 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')) |
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.
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)
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