# -*- coding: utf-8 -*-
# ######### COPYRIGHT #########
# Credits
# #######
#
# Copyright(c) 2015-2018
# ----------------------
#
# * `LabEx Archimède <http://labex-archimede.univ-amu.fr/>`_
# * `Laboratoire d'Informatique Fondamentale <http://www.lif.univ-mrs.fr/>`_
# (now `Laboratoire d'Informatique et Systèmes <http://www.lis-lab.fr/>`_)
# * `Institut de Mathématiques de Marseille <http://www.i2m.univ-amu.fr/>`_
# * `Université d'Aix-Marseille <http://www.univ-amu.fr/>`_
#
# This software is a port from LTFAT 2.1.0 :
# Copyright (C) 2005-2018 Peter L. Soendergaard <peter@sonderport.dk>.
#
# Contributors
# ------------
#
# * Denis Arrivault <contact.dev_AT_lis-lab.fr>
# * Florent Jaillet <contact.dev_AT_lis-lab.fr>
#
# Description
# -----------
#
# ltfatpy is a partial Python port of the
# `Large Time/Frequency Analysis Toolbox <http://ltfat.sourceforge.net/>`_,
# a MATLAB®/Octave toolbox for working with time-frequency analysis and
# synthesis.
#
# Version
# -------
#
# * ltfatpy version = 1.0.16
# * LTFAT version = 2.1.0
#
# Licence
# -------
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
# ######### COPYRIGHT #########
""" Module of derivative of smooth periodic function computation
Ported from ltfat_2.1.0/fourier/pderiv.m
.. moduleauthor:: Florent Jaillet
"""
from __future__ import print_function, division
import numpy as np
from ltfatpy.fourier.fftindex import fftindex
from ltfatpy.comp.assert_sigreshape_pre import assert_sigreshape_pre
from ltfatpy.comp.assert_sigreshape_post import assert_sigreshape_post
[docs]def pderiv(f, dim=None, difforder=4):
""" Derivative of smooth periodic function
- Usage:
| ``fd = pderiv(f)``
| ``fd = pderiv(f, dim)``
| ``fd = pderiv(f, dim, difforder)``
- Input parameters:
:param numpy.ndarray f: Input array
:param int dim: Axis over which to compute the derivative
:param difforder: Order of the centered finite difference scheme used.
Possible values are: ``2``, ``4``, ``float('inf')``
:type difforder: int or float
- Output parameters:
:returns: Derivative of **f**
:rtype: numpy.ndarray
``pderiv(f)`` will compute the derivative of **f** using a using a 4th
order centered finite difference scheme. **f** must have been obtained by
a regular sampling. If **f** is a matrix, the derivative along the
columns will be found.
``pderiv(f, dim)`` will do the same along dimension **dim**.
``pderiv(f, dim, difforder)`` uses a centered finite difference scheme of
order difforder instead of the default.
``pderiv(f, dim, float('inf'))`` will compute the spectral derivative
using a DFT.
``pderiv`` assumes that **f** is a regular sampling of a function on the
torus ``[0, 1)``. The derivative of a function on a general torus
``[0, T)`` can be found by scaling the output by ``1/T``.
"""
f, L, Ls, W, dim, permutedsize, order = assert_sigreshape_pre(f, dim=dim)
if difforder == 2:
fd = L * (np.roll(f, -1, 0) - np.roll(f, 1, 0)) / 2
elif difforder == 4:
fd = L * (- np.roll(f, -2, 0) + 8*np.roll(f, -1, 0) -
8*np.roll(f, 1, 0) + np.roll(f, 2, 0)) / 12
elif difforder == float('inf'):
n = fftindex(L, 0)
n = np.tile(n, (W, 1)).transpose()
fd = 2*np.pi*np.fft.ifft(1j*n*np.fft.fft(f, axis=0), axis=0)
if np.isrealobj(f):
fd = np.real(fd)
else:
raise ValueError('The specified differentation order is not '
'implemented.')
fd = assert_sigreshape_post(fd, dim, permutedsize, order)
return fd