# Licensed under a 3-clause BSD style license - see LICENSE.rst
# -*- coding: utf-8 -*-
"""
Implements a set of line profile parameterizations.
----
.. include license and copyright
.. include:: ../include/copy.rst
----
.. include common links, assuming primary doc root is up one directory
.. include:: ../include/links.rst
"""
import numpy
from scipy import special
[docs]class GaussianLSF:
r"""
Define a Gaussian line profile, *sampled* over the width of the
sampling step, parameterized by its integral (:math:`F`), center
(:math:`\mu`), and standard deviation (:math:`\sigma`). I.e:
.. math::
\mathcal{N}(x|f,\mu,\sigma) = \frac{f}{\sqrt{2\pi}\sigma}
\exp\left(\frac{-\Delta^2}{2\sigma^2}\right)
where :math:`\Delta = x-\mu`. The coordinate vector :math:`x` does
not need to be uniformly sampled.
Args:
p (array-like, optional):
Input parameters ordered as the total integral of the
profile, the profile center, and the profile standard
deviation. Assumed to be (1.0, 0.0, 1.0) by default.
Attributes:
p (numpy.ndarray):
Most recently used parameters
"""
def __init__(self, p=None):
self.set_par(p)
def __call__(self, x, p):
"""Calculate the profile.
Args:
x (array-like):
Independent variable.
p (array-like):
LSF parameters.
"""
self.set_par(p)
return self.sample(x)
[docs] @staticmethod
def npar():
return 3
[docs] def set_par(self, p):
"""
Set the internal parameters to the provided set.
Args:
p (array-like):
LSF parameters.
Raises:
ValueError:
Raised if the provided parameter vector is not 3
elements long.
"""
if p is None:
self.p = numpy.array([1.0, 0.0, 1.0])
return
if len(p) != GaussianLSF.npar():
raise ValueError('Must provide {0} parameters.'.format(GaussianLSF.npar()))
self.p = numpy.asarray(p)
[docs] def sample(self, x):
"""
Sample the profile.
Args:
x (array-like):
Independent variable.
"""
return self.p[0] * numpy.exp(-numpy.square((x-self.p[1])/self.p[2])/2.) \
/ numpy.sqrt(2.0*numpy.pi) / self.p[2]
[docs] def parameters_from_moments(self, mom0, mom1, mom2):
"""
Provided the 0th, 1st, and 2nd moments, produce a set of
parameters for the profile.
"""
return numpy.array([mom0, mom1, mom2])
[docs]class IntegratedGaussianLSF(GaussianLSF):
r"""
Define a Gaussian line profile, *integrated* over the width of the
sampling step, parameterized by its integral (:math:`F`), center
(:math:`\mu`), and standard deviation (:math:`\sigma`). I.e:
.. math::
\mathcal{N}(x|F,\mu,\sigma) = \frac{F}{2} \left[
{\rm erf}\left(\frac{\Delta+\delta_x/2}{\sqrt{2}\sigma}\right) -
{\rm erf}\left(\frac{\Delta-\delta_x/2}{\sqrt{2}\sigma}\right)\right]
where :math:`{\rm erf}(x)` is the error function, :math:`\Delta =
x-\mu`, and :math:`\delta_x` is the sampling step. The sampling
*must* be uniform in :math:`x`.
Args:
p (array-like, optional):
Input parameters ordered as the total integral of the
profile, the profile center, and the profile standard
deviation. Assumed to be (1.0, 0.0, 1.0) by default.
dx (:obj:`float`, optional):
Sampling width. Default is 1.
Attributes:
p (numpy.ndarray):
Most recently used parameters
dx (:obj:`float`):
Assumed sampling.
"""
def __init__(self, p=None, dx=None):
self.set_par(p)
self.dx = 1.0 if dx is None else dx
[docs] def sample(self, x):
"""
Sample the profile.
.. warning::
Does **not** check if the provided :math:`x` values are
sampled at :attr:`dx`.
Args:
x (array-like):
Independent variable.
"""
n = numpy.sqrt(2.)*self.p[2]
d = numpy.asarray(x)-self.p[1]
return self.p[0] * (special.erf((d+self.dx/2.)/n) - special.erf((d-self.dx/2.)/n))/2.
[docs]class FFTGaussianLSF(GaussianLSF):
r"""
Define a Gaussian line profile by first constructing the analytic
FFT of the profile and then returning the inverse real FFT. See
ppxf_util.emline by M. Cappellari. The sampling *must* be uniform
in :math:`x`.
Args:
p (array-like, optional):
Input parameters ordered as the total integral of the
profile, the profile center, and the profile standard
deviation. Assumed to be (1.0, 0.0, 1.0) by default.
dx (:obj:`float`, optional):
Sampling width. Default is 1.
pixel (:obj:`bool`, optional):
Flag to produce profile integrated over the sampling width.
Attributes:
p (numpy.ndarray):
Most recently used parameters
dx (:obj:`float`):
Assumed sampling.
pixel (:obj:`bool`):
Flag to produce profile integrated over the sampling width.
"""
def __init__(self, p=None, dx=None, pixel=True):
self.set_par(p)
self.dx = 1.0 if dx is None else dx
self.pixel = pixel
[docs] def sample(self, x):
"""
Sample the profile.
.. warning::
Does **not** check if the provided :math:`x` values are
sampled at :attr:`dx`.
Args:
x (array-like):
Independent variable.
"""
xsig = self.p[2]/self.dx
x0 = (self.p[1]-x[0])/self.dx
npad = 2**int(numpy.ceil(numpy.log2(x.size)))
w = numpy.linspace(0,numpy.pi,npad//2+1)
rfft = self.p[0]*numpy.exp(-0.5*numpy.square(w*xsig) - 1j*w*x0)
if self.pixel:
rfft *= numpy.sinc(w/(2*numpy.pi))
lsf = numpy.fft.irfft(rfft, n=npad)[:x.size]
return lsf if self.pixel else lsf/self.dx