<reponame>naspert/pygsp<gh_stars>0
# -*- coding: utf-8 -*-

import numpy as np

from pygsp import utils
from . import Filter  # prevent circular import in Python < 3.5


_logger = utils.build_logger(__name__)


class Meyer(Filter):
    r"""Design a filter bank of Meyer wavelets (tight frame).

    Parameters
    ----------
    G : graph
    Nf : int
        Number of filters from 0 to lmax (default = 6).
    scales : ndarray
        Vector of scales to be used (default: log scale).

    References
    ----------
    Use of this kernel for SGWT proposed by <NAME> and <NAME> in :cite:`leonardi2011wavelet`.

    Examples
    --------

    Filter bank's representation in Fourier and time (ring graph) domains.

    >>> import matplotlib.pyplot as plt
    >>> G = graphs.Ring(N=20)
    >>> G.estimate_lmax()
    >>> G.set_coordinates('line1D')
    >>> g = filters.Meyer(G)
    >>> s = g.localize(G.N // 2)
    >>> fig, axes = plt.subplots(1, 2)
    >>> g.plot(ax=axes[0])
    >>> G.plot_signal(s, ax=axes[1])

    """

    def __init__(self, G, Nf=6, scales=None):

        if scales is None:
            scales = (4./(3 * G.lmax)) * np.power(2., np.arange(Nf-2, -1, -1))

        if len(scales) != Nf - 1:
            raise ValueError('len(scales) should be Nf-1.')

        g = [lambda x: kernel(scales[0] * x, 'scaling_function')]

        for i in range(Nf - 1):
            g.append(lambda x, i=i: kernel(scales[i] * x, 'wavelet'))

        def kernel(x, kernel_type):
            r"""
            Evaluates Meyer function and scaling function

            * meyer wavelet kernel: supported on [2/3,8/3]
            * meyer scaling function kernel: supported on [0,4/3]
            """

            x = np.asarray(x)

            l1 = 2/3.
            l2 = 4/3.  # 2*l1
            l3 = 8/3.  # 4*l1

            def v(x):
                return x**4 * (35 - 84*x + 70*x**2 - 20*x**3)

            r1ind = (x < l1)
            r2ind = (x >= l1) * (x < l2)
            r3ind = (x >= l2) * (x < l3)

            # as we initialize r with zero, computed function will implicitly
            # be zero for all x not in one of the three regions defined above
            r = np.zeros(x.shape)
            if kernel_type == 'scaling_function':
                r[r1ind] = 1
                r[r2ind] = np.cos((np.pi/2) * v(np.abs(x[r2ind])/l1 - 1))
            elif kernel_type == 'wavelet':
                r[r2ind] = np.sin((np.pi/2) * v(np.abs(x[r2ind])/l1 - 1))
                r[r3ind] = np.cos((np.pi/2) * v(np.abs(x[r3ind])/l2 - 1))
            else:
                raise ValueError('Unknown kernel type {}'.format(kernel_type))

            return r

        super(Meyer, self).__init__(G, g)

# -*- coding: utf-8 -*-

import numpy as np

from pygsp import utils
from . import Filter  # prevent circular import in Python < 3.5


_logger = utils.build_logger(__name__)


class Meyer(Filter):
    r"""Design a filter bank of Meyer wavelets (tight frame).

    Parameters
    ----------
    G : graph
    Nf : int
        Number of filters from 0 to lmax (default = 6).
    scales : ndarray
        Vector of scales to be used (default: log scale).

    References
    ----------
    Use of this kernel for SGWT proposed by <NAME> and <NAME> in :cite:`leonardi2011wavelet`.

    Examples
    --------

    Filter bank's representation in Fourier and time (ring graph) domains.

    >>> import matplotlib.pyplot as plt
    >>> G = graphs.Ring(N=20)
    >>> G.estimate_lmax()
    >>> G.set_coordinates('line1D')
    >>> g = filters.Meyer(G)
    >>> s = g.localize(G.N // 2)
    >>> fig, axes = plt.subplots(1, 2)
    >>> g.plot(ax=axes[0])
    >>> G.plot_signal(s, ax=axes[1])

    """

    def __init__(self, G, Nf=6, scales=None):

        if scales is None:
            scales = (4./(3 * G.lmax)) * np.power(2., np.arange(Nf-2, -1, -1))

        if len(scales) != Nf - 1:
            raise ValueError('len(scales) should be Nf-1.')

        g = [lambda x: kernel(scales[0] * x, 'scaling_function')]

        for i in range(Nf - 1):
            g.append(lambda x, i=i: kernel(scales[i] * x, 'wavelet'))

        def kernel(x, kernel_type):
            r"""
            Evaluates Meyer function and scaling function

            * meyer wavelet kernel: supported on [2/3,8/3]
            * meyer scaling function kernel: supported on [0,4/3]
            """

            x = np.asarray(x)

            l1 = 2/3.
            l2 = 4/3.  # 2*l1
            l3 = 8/3.  # 4*l1

            def v(x):
                return x**4 * (35 - 84*x + 70*x**2 - 20*x**3)

            r1ind = (x < l1)
            r2ind = (x >= l1) * (x < l2)
            r3ind = (x >= l2) * (x < l3)

            # as we initialize r with zero, computed function will implicitly
            # be zero for all x not in one of the three regions defined above
            r = np.zeros(x.shape)
            if kernel_type == 'scaling_function':
                r[r1ind] = 1
                r[r2ind] = np.cos((np.pi/2) * v(np.abs(x[r2ind])/l1 - 1))
            elif kernel_type == 'wavelet':
                r[r2ind] = np.sin((np.pi/2) * v(np.abs(x[r2ind])/l1 - 1))
                r[r3ind] = np.cos((np.pi/2) * v(np.abs(x[r3ind])/l2 - 1))
            else:
                raise ValueError('Unknown kernel type {}'.format(kernel_type))

            return r

        super(Meyer, self).__init__(G, g)
# -*- coding: utf-8 -*- # prevent circular import in Python < 3.5 Design a filter bank of Meyer wavelets (tight frame).      Parameters     ----------     G : graph     Nf : int         Number of filters from 0 to lmax (default = 6).     scales : ndarray         Vector of scales to be used (default: log scale).      References     ----------     Use of this kernel for SGWT proposed by <NAME> and <NAME> in :cite:`leonardi2011wavelet`.      Examples     --------      Filter bank's representation in Fourier and time (ring graph) domains.      >>> import matplotlib.pyplot as plt     >>> G = graphs.Ring(N=20)     >>> G.estimate_lmax()     >>> G.set_coordinates('line1D')     >>> g = filters.Meyer(G)     >>> s = g.localize(G.N // 2)     >>> fig, axes = plt.subplots(1, 2)     >>> g.plot(ax=axes[0])     >>> G.plot_signal(s, ax=axes[1]) Evaluates Meyer function and scaling function              * meyer wavelet kernel: supported on [2/3,8/3]             * meyer scaling function kernel: supported on [0,4/3] # 2*l1 # 4*l1 # as we initialize r with zero, computed function will implicitly # be zero for all x not in one of the three regions defined above