# -*- coding: utf-8 -*-
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from collections import namedtuple
import numba
import numpy as np
from africanus.constants import minus_two_pi_over_c
from africanus.util.docs import doc_tuple_to_str
from africanus.util.numba import is_numba_type_none, generated_jit
[docs]@generated_jit(nopython=True, nogil=True, cache=True)
def im_to_vis(image, uvw, lm, frequency, dtype=None):
# Infer complex output dtype if none provided
if is_numba_type_none(dtype):
out_dtype = np.result_type(np.complex64,
*(np.dtype(a.dtype.name) for a in
(image, uvw, lm, frequency)))
else:
out_dtype = dtype.dtype
def _im_to_vis_impl(image, uvw, lm, frequency, dtype=None):
vis_of_im = np.zeros((uvw.shape[0], frequency.shape[0]),
dtype=out_dtype)
# For each uvw coordinate
for row in range(uvw.shape[0]):
u, v, w = uvw[row]
# For each source
for source in range(lm.shape[0]):
l, m = lm[source]
n = np.sqrt(1.0 - l**2 - m**2) - 1.0
# e^(-2*pi*(l*u + m*v + n*w)/c)
real_phase = minus_two_pi_over_c * (l * u + m * v + n * w)
# Multiple in frequency for each channel
for chan in range(frequency.shape[0]):
p = real_phase * frequency[chan] * 1.0j
# Our phase input is purely imaginary
# so we can can elide a call to exp
# and just compute the cos and sin
# @simon does this really make a difference?
# I thought a complex exponential is evaluated
# as a sum of sin and cos anyway
vis_of_im[row, chan] += np.exp(p)*image[source, chan]
return vis_of_im
return _im_to_vis_impl
[docs]@generated_jit(nopython=True, nogil=True, cache=True)
def vis_to_im(vis, uvw, lm, frequency, dtype=None):
# Infer output dtype if none provided
if is_numba_type_none(dtype):
# Support both real and complex visibilities...
if isinstance(vis.dtype, numba.types.scalars.Complex):
vis_comp_dtype = np.dtype(vis.dtype.underlying_float.name)
else:
vis_comp_dtype = np.dtype(vis.dtype.name)
out_dtype = np.result_type(vis_comp_dtype,
*(np.dtype(a.dtype.name) for a in
(uvw, lm, frequency)))
else:
if isinstance(dtype, numba.types.scalars.Complex):
raise TypeError("dtype must be complex")
out_dtype = dtype.dtype
def _vis_to_im_impl(vis, uvw, lm, frequency, dtype=None):
im_of_vis = np.zeros((lm.shape[0], frequency.shape[0]),
dtype=out_dtype)
# For each source
for source in range(lm.shape[0]):
l, m = lm[source]
n = np.sqrt(1.0 - l ** 2 - m ** 2) - 1.0
# For each uvw coordinate
for row in range(uvw.shape[0]):
u, v, w = uvw[row]
# e^(-2*pi*(l*u + m*v + n*w)/c)
real_phase = -minus_two_pi_over_c * (l * u + m * v + n * w)
# Multiple in frequency for each channel
for chan in range(frequency.shape[0]):
p = real_phase * frequency[chan]
im_of_vis[source,
chan] += (np.cos(p) * vis[row, chan].real -
np.sin(p) * vis[row, chan].imag)
# Note for the adjoint we don't need the imaginary part
# and we can elide the call to exp
return im_of_vis
return _vis_to_im_impl
_DFT_DOCSTRING = namedtuple(
"_DFTDOCSTRING", ["preamble", "parameters", "returns"])
im_to_vis_docs = _DFT_DOCSTRING(
preamble="""
Computes the discrete image to visibility mapping of an ideal
unpolarised interferometer :
.. math::
{\\Large \\sum_s e^{-2 \\pi i (u l_s + v m_s + w (n_s - 1))} \\cdot I_s }
""", # noqa
parameters="""
Parameters
----------
image : :class:`numpy.ndarray`
image of shape :code:`(source, chan)`
The Stokes I intensity in each pixel (flatten 2D array per channel).
uvw : :class:`numpy.ndarray`
UVW coordinates of shape :code:`(row, 3)` with
U, V and W components in the last dimension.
lm : :class:`numpy.ndarray`
LM coordinates of shape :code:`(source, 2)` with
L and M components in the last dimension.
frequency : :class:`numpy.ndarray`
frequencies of shape :code:`(chan,)`
dtype : np.dtype, optional
Datatype of result. Should be either np.complex64 or np.complex128.
If ``None``, :func:`numpy.result_type` is used to infer the data type
from the inputs.
""",
returns="""
Returns
-------
visibilties : :class:`numpy.ndarray`
complex of shape :code:`(row, chan)`
"""
)
im_to_vis.__doc__ = doc_tuple_to_str(im_to_vis_docs)
vis_to_im_docs = _DFT_DOCSTRING(
preamble="""
Computes visibility to image mapping of an ideal
unpolarised interferometer:
.. math::
{\\Large \\sum_k e^{ 2 \\pi i (u_k l + v_k m + w_k (n - 1))} \\cdot V_k}
""", # noqa
parameters="""
Parameters
----------
vis : :class:`numpy.ndarray`
visibilities of shape :code:`(row, chan)`
The Stokes I visibilities of which to compute a dirty image
uvw : :class:`numpy.ndarray`
UVW coordinates of shape :code:`(row, 3)` with
U, V and W components in the last dimension.
lm : :class:`numpy.ndarray`
LM coordinates of shape :code:`(source, 2)` with
L and M components in the last dimension.
frequency : :class:`numpy.ndarray`
frequencies of shape :code:`(chan,)`
dtype : np.dtype, optional
Datatype of result. Should be either np.float32 or np.float64.
If ``None``, :func:`numpy.result_type` is used to infer the data type
from the inputs.
""",
returns="""
Returns
-------
image : :class:`numpy.ndarray`
float of shape :code:`(source, chan)`
"""
)
vis_to_im.__doc__ = doc_tuple_to_str(vis_to_im_docs)