# -*- coding: utf-8 -*-
from . import Filter
import numpy as np
from math import pi
[docs]class Papadakis(Filter):
r"""
Papadakis Filterbank
Inherits its methods from Filters
This function create a parseval filterbank of :math:`2`.
The low-pass filter is defined by a function :math:`f_l(x)`
.. math:: f_{l}=\begin{cases} 1 & \mbox{if }x\leq a\\ \sqrt{1-\frac{\sin\left(\frac{3\pi}{2a}x\right)}{2}} & \mbox{if }a<x\leq \frac{5a}{3} \\ 0 & \mbox{if }x>\frac{5a}{3} \end{cases}
The high pass filter is adaptated to obtain a tight frame.
Parameters
----------
G : Graph
a : float
See equation above for this parameter
The spectrum is scaled between 0 and 2 (default = 3/4)
Returns
-------
out : Papadakis
Examples
--------
>>> from pygsp import graphs, filters
>>> G = graphs.Logo()
>>> F = filters.Papadakis(G)
"""
def __init__(self, G, a=0.75, **kwargs):
super(Papadakis, self).__init__(G, **kwargs)
g = [lambda x: papadakis(x * (2./G.lmax), a)]
g.append(lambda x: np.real(np.sqrt(1 - (papadakis(x*(2./G.lmax), a)) **
2)))
self.g = g
def papadakis(val, a):
y = np.empty(np.shape(val))
l1 = a
l2 = a*5./3
r1ind = (val >= 0) * (val < l1)
r2ind = (val >= l1) * (val < l2)
r3ind = val >= l2
y[r1ind] = 1
y[r2ind] = np.sqrt((1 - np.sin(3*pi/(2*a) * val[r2ind]))/2.)
y[r3ind] = 0
return y