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Central Difference Derivative Approximation

Syntax	cendiff(function f, x, h)
See Also	fordiff

Description
Returns the central difference approximation for the Jacobian of f at x. The real or double-precision vector x specifies the point at which to approximate the Jacobian. The real or double-precision vector h specifies the step size for approximating the partials of f, and h has the same length as x. If h(j) is 0, partials with respect to x(j) are not approximated and 0 is returned in the corresponding column of the Jacobian.

A matrix function J(x) is the Jacobian of a column vector function f(x) if the (i,j) element of J(x) is the partial of the ith element of f(x) with respect to the jth element of x.

Given a real or double precision vector with the same dimension as x, the function f returns a real, double-precision, or complex column vector. The return value of cendiff has the type that results from coercion between the type of x, h and f(x). It has the same number of rows as f(x) and its column dimension is equal to the length of x.

The functions cendiff and fordiff can be used to approximate derivatives for an optimization or zero-finding algorithm. The cendiff function is more accurate, but it requires more function evaluations.

Example
     function f(x) begin
          return x^2
     end
     x = 1.
     h = .1
     cendiff(function f, x, h)
returns
     2