# -*- coding: utf-8 -*-
import numpy as np
from africanus.util.docs import DocstringTemplate
from africanus.util.numba import generated_jit, njit
from africanus.calibration.utils import check_type
from africanus.calibration.utils.utils import DIAG_DIAG, DIAG, FULL
def jones_inverse_mul_factory(mode):
if mode == DIAG_DIAG:
def jones_inverse_mul(a1j, blj, a2j, out):
for c in range(out.shape[-1]):
out[c] = blj[c]/(a1j[c]*np.conj(a2j[c]))
elif mode == DIAG:
def jones_inverse_mul(a1j, blj, a2j, out):
out[0, 0] = blj[0, 0]/(a1j[0]*np.conj(a2j[0]))
out[0, 1] = blj[0, 1]/(a1j[0]*np.conj(a2j[1]))
out[1, 0] = blj[1, 0]/(a1j[1]*np.conj(a2j[0]))
out[1, 1] = blj[1, 1]/(a1j[1]*np.conj(a2j[1]))
elif mode == FULL:
def jones_inverse_mul(a1j, blj, a2j, out):
# get determinant
deta1j = a1j[0, 0]*a1j[1, 1]-a1j[0, 1]*a1j[1, 0]
# compute inverse
a00 = a1j[1, 1]/deta1j
a01 = -a1j[0, 1]/deta1j
a10 = -a1j[1, 0]/deta1j
a11 = a1j[0, 0]/deta1j
# get determinant
a2j = np.conj(a2j)
deta2j = a2j[0, 0]*a2j[1, 1]-a2j[0, 1]*a2j[1, 0]
# get conjugate transpose inverse
b00 = a2j[1, 1]/deta2j
b01 = -a2j[1, 0]/deta2j
b10 = -a2j[0, 1]/deta2j
b11 = a2j[0, 0]/deta2j
# precompute resuable terms
t1 = a00*blj[0, 0]
t2 = a01*blj[1, 0]
t3 = a00*blj[0, 1]
t4 = a01*blj[1, 1]
# overwrite with result
out[0, 0] = t1*b00 +\
t2*b00 +\
t3*b10 +\
t4*b10
out[0, 1] = t1*b01 +\
t2*b01 +\
t3*b11 +\
t4*b11
t1 = a10*blj[0, 0]
t2 = a11*blj[1, 0]
t3 = a10*blj[0, 1]
t4 = a11*blj[1, 1]
out[1, 0] = t1*b00 +\
t2*b00 +\
t3*b10 +\
t4*b10
out[1, 1] = t1*b01 +\
t2*b01 +\
t3*b11 +\
t4*b11
return njit(nogil=True, inline='always')(jones_inverse_mul)
[docs]@generated_jit(nopython=True, nogil=True, cache=True)
def correct_vis(time_bin_indices, time_bin_counts,
antenna1, antenna2, jones, vis, flag):
mode = check_type(jones, vis)
jones_inverse_mul = jones_inverse_mul_factory(mode)
def _correct_vis_fn(time_bin_indices, time_bin_counts,
antenna1, antenna2, jones, vis, flag):
# for dask arrays we need to adjust the chunks to
# start counting from zero
time_bin_indices -= time_bin_indices.min()
jones_shape = np.shape(jones)
n_tim = jones_shape[0]
n_dir = jones_shape[3]
if n_dir > 1:
raise ValueError("Jones has n_dir > 1. Cannot correct "
"for direction dependent gains")
n_chan = jones_shape[2]
corrected_vis = np.zeros_like(vis, dtype=vis.dtype)
for t in range(n_tim):
for row in range(time_bin_indices[t],
time_bin_indices[t] + time_bin_counts[t]):
p = int(antenna1[row])
q = int(antenna2[row])
gp = jones[t, p]
gq = jones[t, q]
for nu in range(n_chan):
if not np.any(flag[row, nu]):
jones_inverse_mul(gp[nu, 0], vis[row, nu], gq[nu, 0],
corrected_vis[row, nu])
return corrected_vis
return _correct_vis_fn
CORRECT_VIS_DOCS = DocstringTemplate("""
Apply inverse of direction independent gains to
visibilities to generate corrected visibilities.
For a measurement model of the form
.. math::
V_{pq} = G_{p} X_{pq} G_{q}^H + n_{pq}
the corrected visibilities are defined as
.. math::
C_{pq} = G_{p}^{-1} V_{pq} G_{q}^{-H}
The corrected visibilities therefore have
a non-trivial noise contribution. Note
it is only possible to form corrected
data from direction independent gains
solutions so the :code:`dir` axis on
the jones terms should always be one.
Parameters
----------
time_bin_indices : $(array_type)
The start indices of the time bins
of shape :code:`(utime)`.
time_bin_counts : $(array_type)
The counts of unique time in each
time bin of shape :code:`(utime)`.
antenna1 : $(array_type)
Antenna 1 index used to look up the antenna Jones
for a particular baseline with shape :code:`(row,)`.
antenna2 : $(array_type)
Antenna 2 index used to look up the antenna Jones
for a particular baseline with shape :code:`(row,)`.
jones : $(array_type)
Gain solutions of shape :code:`(time, ant, chan, dir, corr)`
or :code:`(time, ant, chan, dir, corr, corr)`.
vis : $(array_type)
Data values of shape :code:`(row, chan, corr)`
or :code:`(row, chan, corr, corr)`.
flag : $(array_type)
Flag data of shape :code:`(row, chan, corr)`
or :code:`(row, chan, corr, corr)`.
Returns
-------
corrected_vis : $(array_type)
True visibilities of shape :code:`(row,chan,corr_1,corr_2)`
""")
try:
correct_vis.__doc__ = CORRECT_VIS_DOCS.substitute(
array_type=":class:`numpy.ndarray`")
except AttributeError:
pass