Perform zero-order Hankel Transform for an 1D array (float or real valued).

Related tags

Deep LearningHankel-transform-qDHT
Overview

Quais-discrete Hankel Transform

python3 algorithm that perform zero-order Hankel Transform for an 1D array (float or real valued). Such QDHT algorithm is especially suit for iterative codes, where energy-preserving is important -- as discrete form of Parseval theorem is guaranteed.

For more details, see: Li Yu, et.al, Quais-discrete Hankel transform, Optics Letters, 23, 409, 1998.

description

usage

import numpy as np 
import matplotlib.pyplot as plt 

N = 4096 # points 
ht = Hankel_qDHT(N) 
r_axis = ht.r   # the generated ratial axis, r is almost equally spaced, 
                # corresponding to the positive-zeros of 0-order Bessel 
                # function J_0(x) 
# field before 0-order Hankel Transform: 
field =  np.exp(-np.pi * r_axis**2 / (1.0 + 1.0J * 0.2)) 
# field after the transform, lives still on ht.r axis: 
field_H0 = ht.transform(field) # 

plt.plot(r_axis, np.abs(field), "b-") 
plt.plot(r_axis, np.abs(field_H0), "r--") 
plt.xlabel("r") 
plt.ylabel("abs. field") 
plt.show()

performance

78ms each transform for 1*4096 complex-valued array.

example

qDHT close to the precise of machine error: compare with the direct-sum result

requiremets

python>=3.0 site-packages: numpy, scipy, matplotlib

Owner
We collect codes that solve any specific scientific-computing probelms
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