arsimul(1)

NAME
arsimul - armax simulation

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

PARAMETERS

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-diensional 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)=0)
   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 "discret" is used to compute z

AUTHOR
J-Ph.C.