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// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) ENPC -
//
// 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 z=narsimul(x1,x2,x3,x4,x5,x6,x7,x8)
//function z=narsimul(a,b,d,sig,u,up,yp,ep)
// or
// function z=arsimul(ar,u,up,yp,ep)
//
// Armax simulation using rtitr
// A(z)= Id+a1*z+...+a_r*z^r; ( r=0 => A(z)=Id)
// B(z)= b0+b1*z+...+b_s z^s; ( s=-1 => B(z)=0)
// D(z)= Id+d1*z+...+d_t z^t; ( t=0 => D(z)=Id)
// z et e sont a valeurs dans dans R^n et u dans R^m
// Auteur : J-Ph. Chancelier ENPC Cergrene
//
// Copyright Enpc
[lhs,rhs]=argn(0)
// switch to ar representation
if type(x1)==1 then
if rhs < 5 then
error(msprintf(gettext("%s: Wrong number of input arguments: %d to %d expected.\n"),"narsimul",5,8));
end;
ar=armac(x1,x2,x3,size(x1,"r"),size(x5,"r"),x4);
select rhs
case 5 then
z=narsimul(ar,x5);
case 6 then
z=narsimul(ar,x5,x6);
case 7 then
z=narsimul(ar,x5,x6,x7);
case 8 then
z=narsimul(ar,x5,x6,x7,x8);
end
elseif typeof(x1)== "ar" then // Here the call is always arsimul(ar,....)
if rhs < 2|rhs>5 then
error(msprintf(gettext("%s: Wrong number of input arguments: %d to %d expected.\n"),"narsimul",2,5));
end;
a=x1("a");b=x1("b");d=x1("d");sig=x1("sig");
u=x2;
[mmu,Nu]=size(u);
if mmu<>x1("nu") then
error(msprintf(gettext("%s: Incompatible input arguments #%d and #%d: "+..
"Number of rows of #%d are incompatible with #%d argument.\n"),..
"narsimul",1,2,2,1));
end;
// dimensions
[al,ac]=size(a);adeg=int(ac/al);
[dl,dc]=size(d);ddeg=int(dc/dl);
[bl,bc]=size(b);[mmu,Nu]=size(u);bdeg=int(bc/mmu);
// quelques tests a faire : bl=al=dl,
// <i>deg*<i>l=<i>c, pour i=a,b,d
//
// On genere d'abord y(k) solution de : A(z^-1)y(k)=B^(z-1)u(k)
s=poly(0,"s");
// Build polynomial matrix A(s)
mata= a*((s.^[adeg-1:-1:0]).*.eye(al,al))';
// Build polynomial matrix B(s)
matb= b*((s.^[bdeg-1:-1:0]).*.eye(mmu,mmu))';
//
num=matb*s**(adeg-1)
den=mata*s**(bdeg-1);
// Using past values
// yp doit etre de taille (al,(adeg-1))
// up doit etre de taille (al,(bdeg-1))
// ep doit etre de taille (al,(adeg-1))
//
if rhs <=3 then
up=0*ones(mmu,(bdeg-1));
else
up=x3
if size(up,1)<>mmu then
error(msprintf(gettext("%s: Incompatible input arguments #%d and #%d: Same row dimensions expected.\n"),"narsimul",2,3))
end
if size(up,2)<>bdeg-1,
error(msprintf(gettext("%s: Incompatible input arguments #%d and #%d: "+..
"Number of columns of #%d are incompatible with #%d argument.\n"),..
"narsimul",1,3,3,1));
end
end
if rhs <=4 then
yp=0*ones(al,(adeg-1));
else
yp=x4
if size(yp,1)<>al then
error(msprintf(gettext("%s: Incompatible input arguments #%d and #%d: "+..
"Number of rows of #%d are incompatible with #%d argument.\n"),..
"narsimul",1,4,4,1));
end
if size(yp,2)<>(adeg-1) then
error(msprintf(gettext("%s: Incompatible input arguments #%d and #%d: "+..
"Number of columns of #%d are incompatible with #%d argument.\n"),..
"narsimul",1,4,4,1));
end
end
if rhs <=5,
ep=0*ones(al,(ddeg-1));
else
ep=x5
if size(ep,1)<>al then
error(msprintf(gettext("%s: Incompatible input arguments #%d and #%d: "+..
"Number of rows of #%d are incompatible with #%d argument.\n"),..
"narsimul",1,5,5,1));
end
if size(ep,2)<>(adeg-1) then
error(msprintf(gettext("%s: Incompatible input arguments #%d and #%d: "+..
"Number of columns of #%d are incompatible with #%d argument.\n"),..
"narsimul",1,5,5,1));
end
end;
//
degnum=max(degree(den));
yp=[0*ones(al,degnum+1-adeg),yp(:,(adeg-1):-1:1)];
up=[0*ones(mmu,degnum+1-bdeg),up(:,(bdeg-1):-1:1)];
y=rtitr(num,den,u,up,yp);
// truncate the solution to only keep y_1,..y_Nu
// (if b0=0 rtitr computes y_{Nu+1})
y=y(:,1:Nu);
// Generate bru such that A(z^-1)bru= D(z^-1) sig*e(t)
// Build polynomial matrix D(s)
matd= d*((s.^[ddeg-1:-1:0]).*.eye(al,al))';
num=matd*s**(adeg-1)
den=mata*s**(ddeg-1);
degnum=max(degree(den));
ep=[0*ones(al,degnum+1-ddeg),ep(:,(ddeg-1):-1:1)];
// Normal noise
br=sig*rand(al,Nu,"normal")
bru=rtitr(num,den,br,ep,0*ones(ep));
// z(k) = y(k) + bru(k)
z=y+bru(:,1:Nu);
else
error(msprintf(gettext("%s: Wrong type for input argument #%d: %s data structure expected.\n"),"narsimul",1,"arma"));
end;
endfunction
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