hankel.hankel.get_h

hankel.hankel.get_h(f, nu, K=None, cls=<class 'hankel.hankel.HankelTransform'>, hstart=0.05, hdecrement=2, atol=0.001, rtol=0.001, maxiter=15, inverse=False)

Determine the largest value of h which gives a converged solution.

Parameters:

f : callable

The function to be integrated/transformed.

nu : float

Either the order of the transformation, or the number of dimensions (if cls is a SymmetricFourierTransform)

K : float or array-like, optional

The scale(s) of the transformation. If None, assumes an integration over f(x)J_nu(x) is desired. It is recommended to use a down-sampled K for this routine for efficiency. Often a min/max is enough.

cls : HankelTransform subclass, optional

Either HankelTransform or a subclass, specifying the type of transformation to do on f.

hstart : float, optional

The starting value of h.

hdecrement : float, optional

How much to divide h by on each iteration.

atol, rtol : float, optional

The tolerance parameters, passed to np.isclose, defining the stopping condition.

maxiter : int, optional

Maximum number of iterations to perform.

inverse : bool, optional

Whether to treat as an inverse transformation.

Returns:

h : float

The h value at which the solution converges.

res : scalar or tuple

The value of the integral/transformation using the returned h – if a transformation, returns results at K.

N : int

The number of nodes necessary in the final calculation. While each iteration uses N=3.2/h, the returned N checks whether nodes are numerically zero above some threshold.

Notes

This function is not completely general. The function f is assumed to be reasonably smooth and non-oscillatory.