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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>
  <TITLE>arsimul</TITLE>
  <TYPE>Scilab Function</TYPE>
  <DATE>April 1993</DATE>
  <SHORT_DESCRIPTION name="arsimul"> armax simulation</SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>[z]=arsimul(a,b,d,sig,u,[up,yp,ep])  </CALLING_SEQUENCE_ITEM>
    <CALLING_SEQUENCE_ITEM>[z]=arsimul(ar,u,[up,yp,ep])  </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
    <PARAM_INDENT>
      <PARAM_ITEM>
        <PARAM_NAME>ar</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: an armax process. See armac.</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>a</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: is the matrix  <VERB>[Id,a1,...,a_r]</VERB>     of dimension (n,(r+1)*n)</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>b</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: is the matrix <VERB>[b0,......,b_s]</VERB>      of dimension (n,(s+1)*m)</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>d</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: is the matrix <VERB>[Id,d_1,......,d_t]</VERB>  of dimension (n,(t+1)*n)</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>u</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: is a matrix  (m,N), which gives the entry u(:,j)=u_j</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>sig</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: is a  (n,n) matrix  e_{k} is an n-dimensional Gaussian process with variance I</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>up, yp</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: optional parameter which describe the past.  <VERB>up=[ u_0,u_{-1},...,u_{s-1}]</VERB>; 
          <VERB>yp=[ y_0,y_{-1},...,y_{r-1}];</VERB>   <VERB>ep=[ e_0,e_{-1},...,e_{r-1}]</VERB>; 
          if they are omitted, the past value are supposed to be zero</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>z</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: <VERB>z=[y(1),....,y(N)]</VERB></SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
    <P>
    simulation of an n-dimensional armax process 
    <VERB>A(z^-1) z(k)= B(z^-1)u(k) + D(z^-1)*sig*e(k)</VERB>
    </P>
    <VERBATIM>
       A(z)= Id+a1*z+...+a_r*z^r;  ( r=0  =&gt; A(z)=Id)
       B(z)= b0+b1*z+...+b_s z^s;  ( s=-1 =&gt; B(z)=[])
       D(z)= Id+d1*z+...+d_t z^t;  ( t=0  =&gt; D(z)=Id)
    </VERBATIM>
    <P>
    z et e are in  <VERB>R^n</VERB> et u in <VERB>R^m</VERB></P>
  </DESCRIPTION>
  <SECTION label="Method">
    <P>
    a state-space representation is constructed and ode with the option  &quot;discr&quot; is used to compute z</P>
  </SECTION>
  <AUTHOR>J-Ph.C.</AUTHOR>
</MAN>
