numdiff

Arguments

fun

an external, Scilab function or list. See below for calling sequence, see also external for details about external functions.

x

a vector, the argument of the function fun.

dx

a vector, the finite difference step. Default value is dx=sqrt(%eps)*(1+1d-3*abs(x)).

g

a vector, the estimated gradient.

Description

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. Uses an order 1 formula.

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.

Examples

// 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)

See Also

• optim — non-linear optimization routine
• derivative — approximate derivatives of a function
• external — Objet Scilab, fonction externe ou routine