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# -*- coding: utf-8 -*-
# ######### COPYRIGHT #########
# Credits
# #######
#
# Copyright(c) 2015-2025
# ----------------------
#
# * `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) 2005-2025 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 = 1.1.2
# * 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 sampling of all Hermite function computation
Ported from ltfat_2.1.0/comp/comp_hermite_all.m
.. moduleauthor:: Denis Arrivault
"""
from __future__ import print_function, division
import numpy as np
def comp_hermite_all(n, x):
""" Compute all Hermite functions up to an order
- Usage:
| ``y = comp_hermite_all(n, x)``
This function evaluates the Hermite functions
of degree 0 through n-1 at the vector x.
The functions are normalized to have the :math:`L^2` norm
on :math:`]-\\infty,\\infty[` equal to one. No effort is made to
avoid unerflow during recursion.
- Input parameters:
:param int n: the number of Hermite functions
:param numpy.ndarray x: the vector of arguments
- Output parameters:
:return numpy.ndarray y: the values of the first n Hermite functions at
the nodes x
"""
if not isinstance(x, np.ndarray) or len(x.shape) > 1:
raise TypeError("x should be a numpy array of dimension 1")
rt = 1 / np.sqrt(np.sqrt(np.pi))
# conducting the recursion.
y = np.zeros((len(x), n))
if n == 0:
y = rt * np.exp(-0.5 * x**2)
else:
y[:, 0] = rt * np.exp(-0.5 * x**2)
if n > 1:
y[:, 1] = rt * np.sqrt(2) * x * np.exp(-0.5 * x**2)
for k in range(2, n):
y[:, k] = np.sqrt(2)*x*y[:, k-1] - np.sqrt(k-1)*y[:, k-2]
y[:, k] = y[:, k] / np.sqrt(k)
return y
|
