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Diffstat (limited to 'modules/cacsd/macros/lin.sci')
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diff --git a/modules/cacsd/macros/lin.sci b/modules/cacsd/macros/lin.sci new file mode 100755 index 000000000..8231230d9 --- /dev/null +++ b/modules/cacsd/macros/lin.sci @@ -0,0 +1,43 @@ +// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab +// Copyright (C) INRIA - +// +// This file must be used under the terms of the CeCILL. +// This source file is licensed as described in the file COPYING, which +// you should have received as part of this distribution. The terms +// are also available at +// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt + +function [a,b,c,d]=lin(sim,x0,u0) + //Syntaxes : sl=lin(sim,x0,u0) or + // [a,b,c,d]=lin(sim,x0,u0) + // + //linearization of the non-linear differential system [y,xdot]=sim(x,u) + //around x0 , u0. (sim is a scilab macro which computes y and xdot). + //output: + //- linear system sl (syslin list) + //- (a,b,c,d) + // + // Example : Let ftz be the function passed to ode e.g. + // [zd]=ftz(t,z,u), and let us assume y=x. + // [z]=ode(x0,t0,tf,list(ftz,u) compute x(tf) + // Let simula be the following function: + // function [y,xd]=simula(x,u) + // xd=ftz(tf,x,u); y=x; + // + // The tangent linear system sl is obtained by: + // [a,b,c,d]=lin(simula,z,u) + // sl = syslin('c',a,b,c,d,x0) + //! + + [lhs,rhs]=argn(0) + [n,w]=size(x0);[m,w]=size(u0);mpn=m+n + nrm=norm([x0;u0]);if nrm<1 then nrm=1,end; + [zz,nu]=colcomp(rand(mpn,mpn)); + d=10*%eps*nrm*zz(:,1:nu); [y,xd]=sim(x0,u0); y0=[xd;y]; + ab=[];for v=d,[y,xd]=sim(x0+v(1:n),u0+v(n+1:mpn)), + ab=[ab,([xd;y]-y0)],end + [p,w]=size(y); + ab=ab/d;a=ab(1:n,1:n);b=ab(1:n,n+1:mpn) + c=ab(n+1:n+p,1:n);d=ab(n+1:n+p,n+1:mpn) + if lhs==1 then a=syslin("c",a,b,c,d,x0),end +endfunction |