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.TH derivative 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
derivative- approximate derivative
.SH CALLING SEQUENCE
.nf
J=derivative(f,x0,h)
[J,J2]=derivative(f,x0,h)
.fi
.SH PARAMETERS
.TP 10
f
: Scilab function \fVf: R^n --> R^p\fR
.TP
x0
: real column vector (of dimension n)
.TP
h
: (small) positive real number (default is 1.d-7)
.TP
J
: real p x n Jacobian matrix
.TP
J2
: real p x (p*n) matrix
.SH DESCRIPTION
Approximate derivatives of a function f: \fVR^n --> R^p\fR.
.nf
f(x) = f(x0) + D1f(x0) *dx + 1/2* D2f(x0) *(dx.*.dx) +...
J = D1f(x0) ; J2=D2f(x0)
.fi
Derivatives are evaluated by finite difference:f_i(x+h)-f_i(x))/h.
Caution: h should be carefully chosen...
.SH EXAMPLE
.nf
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)]
.fi
.SH SEE ALSO
mtlb_diff, derivat
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