numdiff — numerical gradient estimation
g=numdiff(fun,x [,dx])
an external, Scilab function or list. See below for calling sequence, see also external for details about external functions.
vector, the argument of the function
fun
vector, the finite difference step. Default value is
dx=sqrt(%eps)*(1+1d-3*abs(x))
vector, the estimated gradient
given a function fun(x) from
R^n to R^p computes the matrix
g such as
g(i,j) = (df_i)/(dx_j)
using finite difference methods.
Without parameters, the function fun calling sequence is
y=fun(x), and numdiff can be called as
g=numdiff(fun,x). Else the function fun calling
sequence must be y=fun(x,param_1,pararm_2,..,param_q).
If parameters param_1,param_2,..param_q exist then
numdiff can be called as follow
g=numdiff(list(fun,param_1,param_2,..param_q),x).
See the derivative with respect to numerical accuracy issues and comparison between the two algorithms.
// example 1 (without parameters) // myfun is a function from R^2 to R : (x(1),x(2)) |--> myfun(x) function f=myfun(x) f=x(1)*x(1)+x(1)*x(2) endfunction x=[5 8] g=numdiff(myfun,x) // The exact gradient (i.e derivate belong x(1) :first component and derivate belong x(2): second component) is exact=[2*x(1)+x(2) x(1)] //example 2 (with parameters) // myfun is a function from R to R: x(1) |--> myfun(x) // myfun contains 3 parameters, a, b, c function f=myfun(x,a,b,c) f=(x+a)^c+b endfunction a=3; b=4; c=2; x=1 g2=numdiff(list(myfun,a,b,c),x) // The exact gradient, i.e derivate belong x(1), is : exact2=c*(x+a)^(c-1)