Source code for africanus.rime.phase

# -*- coding: utf-8 -*-

import numpy as np

from africanus.constants import minus_two_pi_over_c
from import DocstringTemplate
from africanus.util.numba import generated_jit
from africanus.util.type_inference import infer_complex_dtype

[docs]@generated_jit(nopython=True, nogil=True, cache=True) def phase_delay(lm, uvw, frequency, convention='fourier'): # Bake constants in with the correct type one = lm.dtype(1.0) zero = lm.dtype(0.0) neg_two_pi_over_c = lm.dtype(minus_two_pi_over_c) out_dtype = infer_complex_dtype(lm, uvw, frequency) def _phase_delay_impl(lm, uvw, frequency, convention='fourier'): if convention == 'fourier': constant = neg_two_pi_over_c elif convention == 'casa': constant = -neg_two_pi_over_c else: raise ValueError("convention not in ('fourier', 'casa')") shape = (lm.shape[0], uvw.shape[0], frequency.shape[0]) complex_phase = np.zeros(shape, dtype=out_dtype) # For each source for source in range(lm.shape[0]): l, m = lm[source] n = one - l**2 - m**2 n = np.sqrt(zero if n < zero else n) - one # 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 = constant * (l * u + m * v + n * w) # Multiple in frequency for each channel for chan in range(frequency.shape[0]): p = real_phase * frequency[chan] # Our phase input is purely imaginary # so we can can elide a call to exp # and just compute the cos and sin complex_phase.real[source, row, chan] = np.cos(p) complex_phase.imag[source, row, chan] = np.sin(p) return complex_phase return _phase_delay_impl
PHASE_DELAY_DOCS = DocstringTemplate( r""" Computes the phase delay (K) term: .. math:: & {\Large e^{-2 \pi i (u l + v m + w (n - 1))} } & \textrm{where } n = \sqrt{1 - l^2 - m^2} Notes ----- Corresponds to the complex exponential of the `Van Cittert-Zernike Theorem <>`_. `MeqTrees < 6a7e873d4d1fe538981dec5851418cbd371b8388/MeqNodes/src/>`_ uses the CASA sign convention. Parameters ---------- lm : $(array_type) LM coordinates of shape :code:`(source, 2)` with L and M components in the last dimension. uvw : $(array_type) UVW coordinates of shape :code:`(row, 3)` with U, V and W components in the last dimension. frequency : $(array_type) frequencies of shape :code:`(chan,)` convention : {'fourier', 'casa'} Uses the :math:`e^{-2 \pi \mathit{i}}` sign convention if ``fourier`` and :math:`e^{2 \pi \mathit{i}}` if ``casa``. Returns ------- complex_phase : $(array_type) complex of shape :code:`(source, row, chan)` """) try: phase_delay.__doc__ = PHASE_DELAY_DOCS.substitute( array_type=":class:`numpy.ndarray`") except AttributeError: pass