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derivative Scilab Group Scilab Function derivative
NAME
derivative- approximate derivative
CALLING SEQUENCE
J=derivative(f,x0,h)
[J,J2]=derivative(f,x0,h)
PARAMETERS
f : Scilab function f: R^n --> R^p
x0 : real column vector (of dimension n)
h : (small) positive real number (default is 1.d-7)
J : real p x n Jacobian matrix
J2 : real p x (p*n) matrix
DESCRIPTION
Approximate derivatives of a function f: R^n --> R^p.
f(x) = f(x0) + D1f(x0) *dx + 1/2* D2f(x0) *(dx.*.dx) +...
J = D1f(x0) ; J2=D2f(x0)
Derivatives are evaluated by finite difference:f_i(x+h)-f_i(x))/h.
Caution: h should be carefully chosen...
EXAMPLE
deff('y=f(x)','y=[sin(x(1))*cos(x(2));x(1)^2*x(2)^2;1+x(1)*x(2)^2]')
x0=[1;2];eps=0.001;h=eps*[2;5];
[J,J2]=derivative(f,x0);
[f(x0+h)-f(x0)-J*h ,0.5*J2*(h.*.h)]
SEE ALSO
mtlb_diff, derivat
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