# -*- coding: utf-8 -*-
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import numpy as np
from africanus.util.docs import DocstringTemplate
from africanus.util.numba import generated_jit
from africanus.constants import c as lightspeed
[docs]@generated_jit(nopython=True, nogil=True, cache=True)
def gaussian(uvw, frequency, shape_params):
fwhmint = 1.0 / np.sqrt(np.log(256))
gauss_scale = fwhmint*np.sqrt(2.0)*np.pi/lightspeed
dtype = np.result_type(*(np.dtype(a.dtype.name) for
a in (uvw, frequency, shape_params)))
def impl(uvw, frequency, shape_params):
nsrc = shape_params.shape[0]
nrow = uvw.shape[0]
nchan = frequency.shape[0]
shape = np.empty((nsrc, nrow, nchan), dtype=dtype)
scaled_freq = np.empty_like(frequency)
for f in range(frequency.shape[0]):
scaled_freq[f] = frequency[f] * gauss_scale
for s in range(shape_params.shape[0]):
emaj, emin, angle = shape_params[s]
el = emaj * np.sin(angle)
em = emaj * np.cos(angle)
er = emaj / (1.0 if emin == 0.0 else emin)
for r in range(uvw.shape[0]):
u, v, w = uvw[r]
u1 = (u*em - v*el)*er
v1 = u*el + v*em
for f in range(scaled_freq.shape[0]):
fu1 = u1*scaled_freq[f]
fv1 = v1*scaled_freq[f]
shape[s, r, f] = np.exp(-(fu1*fu1 + fv1*fv1))
return shape
return impl
GAUSSIAN_DOCS = DocstringTemplate(r"""
Computes the Gaussian Shape Function.
.. math::
& \lambda^\prime = 2 \lambda \pi \\
& r = \frac{e_{maj}}{e_{min}} \\
& u_{1} = (u \, e_{maj} \, cos(\alpha) - v \, e_{maj} \, sin(\alpha))
r \lambda^\prime \\
& v_{1} = (u \, e_{maj} \, sin(\alpha) - v \, e_{maj} \, cos(\alpha))
\lambda^\prime \\
& \textrm{shape} = e^{(-u_{1}^2 - v_{1}^2)}
where:
- :math:`u` and :math:`v` are the UV coordinates and
:math:`\lambda` the frequency.
- :math:`e_{maj}` and :math:`e_{min}` are the major and minor axes
and :math:`\alpha` the position angle.
Parameters
----------
uvw : $(array_type)
UVW coordinates of shape :code:`(row, 3)`
frequency : $(array_type)
frequencies of shape :code:`(chan,)`
shape_param : $(array_type)
Gaussian Shape Parameters of shape :code:`(source, 3)`
where the second dimension contains the
`(emajor, eminor, angle)` parameters describing
the shape of the Gaussian
Returns
-------
gauss_shape : $(array_type)
Shape parameters of shape :code:`(source, row, chan)`
""")
try:
gaussian.__doc__ = GAUSSIAN_DOCS.substitute(
array_type=":class:`numpy.ndarray`")
except KeyError:
pass