sme_contrib.optimize.hessian
- sme_contrib.optimize.hessian(f, x0, rel_eps=0.01, processes=None)
Approximate Hessian of function
f
at pointx0
Uses a finite difference approximation where the step size used for each element
i
ofx0
isrel_eps * x[i]
.Requires \(N^2 + N + 1\) evalulations of
f
, where \(N\) is the number of elements ofx0
The evaluations of
f
are done in parallel, sof
must be a thread-safe function that can safely be called from multiple threads at the same time.Note
This choice of step size allows the different elements of x0 to have vastly different scales without causing numerical instabilities, but it will fail if an element of
x0
is equal to 0.- Parameters
f – The function to evaluate, it should be callable as f(x0) and return a scalar
x0 – The point at which to evaluate the function, a flot or list of floats.
rel_eps – The relative step size to use
processes – The number of processes to use (the default
None
means use all available cpu cores)
- Returns
The Hessian as a 2d numpy array of floats
- Return type
np.array