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# arsimul

armax simulation

### Syntax

[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 an ode with the option
`"discrete"`

is used to compute `z`

.

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