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  • Committer: Bazaar Package Importer
  • Author(s): Torsten Werner
  • Date: 2002-03-21 16:57:43 UTC
  • Revision ID: james.westby@ubuntu.com-20020321165743-e9mv12c1tb1plztg
Tags: upstream-2.6
Import upstream version 2.6

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macros/percent/%choose.sci
 
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function [flag]=%choose(x)
 
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// Utility function for use with schur
 
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//     [U,dim]=schur(A,choose) returns orth. basis
 
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//     for eigenspace associated to selected polynomials
 
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//Needs two global variables : 
 
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//     %sel = list of selected polynomials (user defined)
 
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//     eps = threshold for polynomials selection (eps= 0.0001 as default value)
 
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//            see below 
 
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//     Example:
 
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//     A=...
 
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//     chis=poly(A,'s');  //Characteristic polynomial
 
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//     w=factors(chis);    //Factors of chis in a list
 
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//     %sel=list(w(2),w(3)); // two selected polynomials
 
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//     eps=0.01;     //Threshold (see almosteq below)
 
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//     [U,dim]=schur(A,%choose);     //Ordered Schur form
 
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//     U1=U(:,1:dim);chi1=poly(U1'*A*U1,'s')  //Check
 
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//     w1=factors(chi1)          // w1 = %sel ?
 
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//
 
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// Copyright INRIA
 
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eps=0.0001;         //modify eps here !
 
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// 
 
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ls=x(1);flag=0;s=poly(0,'s');
 
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select ls
 
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case 1 then
 
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  // ASSUME x(3) NOT ZERO   (for gev pb. x(3)=0 => eval @ infty)
 
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  vp=x(2)/x(3);pol=s-vp; //disp(pol);
 
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  for p=%sel; if almosteq(pol,p,eps) then flag=1;end;end
 
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case 2 then
 
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  pol=s^2-x(2)*s+x(3);  //disp(pol);
 
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  for p=%sel; if almosteq(pol,p,eps) then flag=1;end;end   
 
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end
 
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function trfa=almosteq(pol,p,eps)
 
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// returns %T if pol ~ p     %F if not
 
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if degree(pol)<>degree(p) then trfa=%F;return;end
 
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if norm((coeff(p)-coeff(pol)),1)<=eps then trfa=%T;return;end
 
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trfa=%F;
 
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