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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 continuous Hermite function computation
Ported from ltfat_2.1.0/comp/comp_hermite.m
.. moduleauthor:: Denis Arrivault
"""
from __future__ import print_function, division
import numpy as np
import math
def comp_hermite(n, x):
""" Compute sampling of continuous Hermite function.
- Usage:
| ``y = comp_hermite(n, x)``
`comp_hermite(n, x)` evaluates the n-th Hermite function at the vector
**x**. The function is normalized to have the :math:`L^2` norm
on :math:`]-\\infty,\\infty[` equal to one.
A minimal effort is made to avoid underflow in recursion.
If used to evaluate the Hermite quadratures, it works for n <= 2400
"""
rt = 1 / math.sqrt(math.sqrt(math.pi))
if n == 0:
y = rt * np.exp(-0.5 * x**2)
if n == 1:
y = rt * math.sqrt(2) * x * np.exp(-0.5 * x**2)
# if n > 2, conducting the recursion.
if n >= 2:
ef = np.exp(-0.5 * (x**2) / (n+1))
tmp1 = rt * ef
tmp2 = rt * math.sqrt(2) * x * (ef**2)
for k in range(2, n+1):
y = math.sqrt(2)*x*tmp2 - math.sqrt(k-1)*tmp1*ef
y = ef * y / math.sqrt(k)
tmp1 = tmp2
tmp2 = y
return y
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