Documentation of rotvar

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Function Synopsis

zv=rotvar(pol,covm)

Help text

ROTVAR computes the standard deviations of roots to polynomials

   ZV = rotvar(POL,COVM)

   POL is the entered polynomial and
   COVM is the covariance matrix of its coefficients
   ZV is returned as the roots of POL and their standard deviations.
   The first column of ZV contains the roots and the corresponding
   elements in the second column give the standard deviations.
   For complex conjugate pairs the second entry is the correlation
   coefficient between the real and imaginary parts.

   The routine is primarily a help subroutine to th2zp.

Cross-Reference Information

Listing of function rotvar

function zv=rotvar(pol,covm)

%   L. Ljung 87-7-2, 94-08-27
%   Copyright (c) 1986-98 by The MathWorks, Inc.
%   $Revision: 2.3 $  $Date: 1997/12/02 03:43:56 $

[dr,dc]=size(covm);lp=length(pol);
r=roots(pol);
zv(:,1)=r;lr=length(r);
if isempty(covm),zv(:,2)=zeros(lr,1);return,end
k=1;
while k<lr+1
        if imag(r(k))==0
                D(k,:)=real(-poly(r([1:k-1,k+1:lr])));
                k=k+1;
        else

                D(k,:)=real(-2*poly([r([1:k-1,k+2:lr]);real(r(k))]));
                D(k+1,:)=real([0, 2*imag(r(k))*poly(r([1:k-1,k+2:lr]))]);
                k=k+2;
        end
end
D=inv(D)';
if lr~=dr,
     DZ(:,2:lp)=D/pol(1);
     DZ(:,1)=-D*pol(2:lp)'/(pol(1)^2);
else
     DZ=D;
end
PV=DZ*covm*DZ';
k=1;l=1;i=sqrt(-1);
while k<lp
     if imag(r(k))==0,
        zv(k,2)=sqrt(PV(l,l));k=k+1;l=l+1;
     else
        zv(k,2)=sqrt(PV(l,l))+i*sqrt(PV(l+1,l+1));
        zv(k+1,2)=PV(l,l+1)/sqrt(PV(l,l)*PV(l+1,l+1));
        k=k+2;l=l+2;
     end
end