numdiff - numerical gradient estimation

Calling Sequence

g=numdiff(fun,x [,dx])

Parameters

• fun : an external, Scilab function or list. See below for calling sequence, see also external for details about external functions.
• x : vector, the argument of the function fun
• dx : vector, the finite difference step. Default value is dx=sqrt(%eps)*(1+1d-3*abs(x))
• g : vector, the estimated gradient

Description

given a function fun(x) from R^n to R^p computes the matrix g such as

    [   d f    ]
    [      i   ]
g = [   ----   ]
 ij [   d x    ]
    [      j   ]
   

using finite difference methods.

The function fun calling sequence must be y=fun(x,p1,p2,..pn).If parameters p1,p2,..pn exist then numdiff can be called as follow g=numdiff(list(fun,p1,p2,..pn),x).

Examples

function  f=myfun(x,y,z,t)
f=(x+y)^t+z
endfunction

y=3;z=4;t=2;
g=numdiff(list(myfun,3,4,2),1)

x=1;
exact=t*(x+y)^(t-1)
 

See Also

optim