arsimul
=======

armax simulation



Calling Sequence
~~~~~~~~~~~~~~~~


::

    [z]=arsimul(a,b,d,sig,u,[up,yp,ep])
    [z]=arsimul(ar,u,[up,yp,ep])




Arguments
~~~~~~~~~

:ar an armax process. See armac.
: :a is the matrix `[Id,a1,...,a_r]` of dimension (n,(r+1)*n)
: :b is the matrix `[b0,......,b_s]` of dimension (n,(s+1)*m)
: :d is the matrix `[Id,d_1,......,d_t]` of dimension (n,(t+1)*n)
: :u is a matrix (m,N), which gives the entry u(:,j)=u_j
: :sig is a (n,n) matrix e_{k} is an n-dimensional Gaussian process
  with variance I
: :up, yp optional parameter which describe the past. `up=[
  u_0,u_{-1},...,u_{s-1}]`; `yp=[ y_0,y_{-1},...,y_{r-1}];` `ep=[
  e_0,e_{-1},...,e_{r-1}]`; if they are omitted, the past value are
  supposed to be zero
: :z `z=[y(1),....,y(N)]`
:



Description
~~~~~~~~~~~

simulation of an n-dimensional armax process `A(z^-1) z(k)=
B(z^-1)u(k) + D(z^-1)*sig*e(k)`


::

    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)=[])
    D(z)= Id+d1*z+...+d_t z^t;  ( t=0  => D(z)=Id)


z et e are in `R^n` et u in `R^m`



Method
~~~~~~

a state-space representation is constructed and ode with the option
"discr" is used to compute z