# arsimul

armax simulation

### Syntax

```z = arsimul(ar, u)
z = arsimul(ar, u, up, yp, ep)
z = arsimul(a, b, d, sig, u)
z = arsimul(a, b, d, sig, 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 an ode with the option `"discrete"` is used to compute `z`.

### Examples

```a=[1,-2.851,2.717,-0.865].*.eye(2,2)
b=[0,1,1,1].*.[1;1];
d=[1,0.7,0.2].*.eye(2,2);
sig=eye(2,2);
ar=armac(a,b,d,2,1,sig)
u=rand(1,10,'normal');
y=arsimul(ar,u)```
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