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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/util/lin.sci
 
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function [a,b,c,d]=lin(sim,x0,u0)
 
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//Syntaxes : sl=lin(sim,x0,u0)    or
 
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//           [a,b,c,d]=lin(sim,x0,u0)
 
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//
 
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//linearization of the non-linear differential system [y,xdot]=sim(x,u)
 
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//around x0 , u0. (sim is a scilab macro which computes y and xdot).
 
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//output:
 
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//- linear system sl (syslin list)
 
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//- (a,b,c,d)
 
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//
 
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//  Example : Let ftz be the function passed to ode e.g.
 
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//            [zd]=ftz(t,z,u), and let us assume y=x.
 
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//            [z]=ode(x0,t0,tf,list(ftz,u) compute x(tf)
 
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//            Let simula be the followinf function:
 
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//            function [y,xd]=simula(x,u)
 
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//            xd=ftz(tf,x,u); y=x;
 
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//
 
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//            The tangent linear system sl is obtained by:
 
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//               [a,b,c,d]=lin(simula,z,u)
 
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//                sl = syslin('c',a,b,c,d,x0)
 
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//!
 
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// Copyright INRIA
 
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[lhs,rhs]=argn(0)
 
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[n,w]=size(x0);[m,w]=size(u0);mpn=m+n
 
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nrm=norm([x0;u0]);if nrm<1 then nrm=1,end;
 
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[zz,nu]=colcomp(rand(mpn,mpn));
 
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d=10*%eps*nrm*zz(:,1:nu); [y,xd]=sim(x0,u0); y0=[xd;y];
 
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ab=[];for v=d,[y,xd]=sim(x0+v(1:n),u0+v(n+1:mpn)),
 
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     ab=[ab,([xd;y]-y0)],end
 
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[p,w]=size(y);
 
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ab=ab/d;a=ab(1:n,1:n);b=ab(1:n,n+1:mpn)
 
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c=ab(n+1:n+p,1:n);d=ab(n+1:n+p,n+1:mpn)
 
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if lhs==1 then a=syslin('c',a,b,c,d,x0),end
 
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