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Calculate the jacobian of a function using the complex step method.
Let f be a user-supplied function. Given a point x at
which we seek for the Jacobian, the function jacobs returns
the Jacobian matrix d(f(1), …, df(end))/d(x(1), …,
x(n)). The function uses the complex step method and thus can be
applied to real analytic functions.
The optional argument hook is a structure with additional options. hook can have the following fields:
h - can be used to define the magnitude of the complex step and defaults
to 1e-20; steps larger than 1e-3 are not allowed.
fixed - is a logical vector internally usable by some optimization
functions; it indicates for which elements of x no gradient should be
computed, but zero should be returned.
For example:
f = @(x) [x(1)^2 + x(2); x(2)*exp(x(1))]; Df = jacobs ([1, 2], f)