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Aide Scilab >> Calcul différentiel, Intégration > numdiff

# numdiff

### Calling Sequence

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

### 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

### 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)```

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