utils.pyx
# -*- mode: python; coding: utf-8 -*-
# Copyright (c) 2020 Radio Astronomy Software Group
# Licensed under the 2-clause BSD License
# distutils: language = c
# cython: linetrace=True
# distutils: define_macros=CYTHON_TRACE_NOGIL=1
# python imports
import numpy as np
import warnings
# cython imports
cimport numpy
cimport cython
from libc.math cimport sin, cos, sqrt, atan2
# in order to not have circular dependencies
# define transformation parameters here
# parameters for transforming between xyz & lat/lon/alt
gps_b = 6356752.31424518
gps_a = 6378137
e_squared = 6.69437999014e-3
e_prime_squared = 6.73949674228e-3
# make c-viewed versions of these variables
cdef numpy.float64_t _gps_a = gps_a
cdef numpy.float64_t _gps_b = gps_b
cdef numpy.float64_t _e2 = e_squared
cdef numpy.float64_t _ep2 = e_prime_squared
# this one is useful in the xyz from lla calculation
cdef numpy.float64_t b_div_a2 = (_gps_b / _gps_a)**2
@cython.boundscheck(False)
@cython.wraparound(False)
cpdef tuple baseline_to_antnums(numpy.ndarray[ndim=1, dtype=numpy.int64_t] baseline):
cdef unsigned long n = baseline.size
cdef numpy.ndarray[ndim=1, dtype=numpy.int64_t] ant1 = np.empty(n, dtype=np.int64)
cdef numpy.ndarray[ndim=1, dtype=numpy.int64_t] ant2 = np.empty(n, dtype=np.int64)
cdef long _min = baseline.min()
cdef Py_ssize_t i
# make views as c-contiguous arrays of a known dtype
# effectivly turns the numpy array into a c-array
cdef numpy.int64_t[::1] _a1 = ant1
cdef numpy.int64_t[::1] _a2 = ant2
cdef numpy.int64_t[::1] _bl = baseline
for i in range(n):
if _min > 2 ** 16:
_a2[i] = (_bl[i] - 2 ** 16) % 2048 - 1
_a1[i] = (_bl[i] - 2 ** 16 - (_a2[i] + 1)) // 2048 - 1
else:
_a2[i] = (_bl[i]) % 256 - 1
_a1[i] = (_bl[i] - (_a2[i] + 1)) // 256 - 1
return ant1, ant2
@cython.boundscheck(False)
@cython.wraparound(False)
cdef numpy.ndarray[dtype=numpy.int64_t] _antnum_to_bl_2048(
numpy.int64_t[::1] ant1,
numpy.int64_t[::1] ant2,
):
cdef unsigned long n = ant1.shape[0]
cdef Py_ssize_t i
cdef numpy.ndarray[ndim=1, dtype=numpy.int64_t] baselines = np.empty(n, dtype=np.int64)
# make views as c-contiguous arrays of a known dtype
# effectivly turns the numpy array into a c-array
cdef numpy.int64_t[::1] _bl = baselines
for i in range(n):
_bl[i] = 2048 * (ant1[i] + 1) + (ant2[i] + 1) + 2 ** 16
return baselines
@cython.boundscheck(False)
@cython.wraparound(False)
cdef numpy.ndarray[dtype=numpy.int64_t] _antnum_to_bl_256(
numpy.int64_t[::1] ant1,
numpy.int64_t[::1] ant2,
):
cdef unsigned long n = ant1.shape[0]
cdef Py_ssize_t i
cdef numpy.ndarray[dtype=numpy.int64_t, ndim=1] baselines = np.empty(n, dtype=np.int64)
# make views as c-contiguous arrays of a known dtype
# effectivly turns the numpy array into a c-array
cdef numpy.int64_t[::1] _bl = baselines
for i in range(n):
_bl[i] = 256 * (ant1[i] + 1) + (ant2[i] + 1)
return baselines
cpdef numpy.ndarray[dtype=numpy.int64_t] antnums_to_baseline(
numpy.ndarray[dtype=numpy.int64_t, ndim=1] ant1,
numpy.ndarray[dtype=numpy.int64_t, ndim=1] ant2,
bint attempt256=False
):
if attempt256 and np.max([ant1, ant2]) < 255:
baseline = _antnum_to_bl_256(ant1, ant2)
elif attempt256 and np.max([ant1, ant2]) >= 255:
message = (
"antnums_to_baseline: found > 256 antennas, using "
"2048 baseline indexing. Beware compatibility "
"with CASA etc"
)
warnings.warn(message)
baseline = _antnum_to_bl_2048(ant1, ant2)
else:
baseline = _antnum_to_bl_2048(ant1, ant2)
return baseline
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cpdef numpy.ndarray[dtype=numpy.float64_t, ndim=2] _lla_from_xyz(
numpy.float64_t[:, ::1] xyz,
):
cdef Py_ssize_t ind
cdef int n_pts = xyz.shape[1]
cdef numpy.float64_t gps_p, gps_theta
cdef numpy.ndarray[dtype=numpy.float64_t, ndim=2] lla = np.empty((3, n_pts), dtype=np.float64)
cdef numpy.float64_t[:, ::1] _lla = lla
# see wikipedia geodetic_datum and Datum transformations of
# GPS positions PDF in docs/references folder
for ind in range(n_pts):
gps_p = sqrt(xyz[0, ind] ** 2 + xyz[1, ind] ** 2)
gps_theta = atan2(xyz[2, ind] * _gps_a, gps_p * _gps_b)
_lla[0, ind] = atan2(
xyz[2, ind] + _ep2 * _gps_b * sin(gps_theta) ** 3,
gps_p - _e2 * _gps_a * cos(gps_theta) ** 3,
)
_lla[1, ind] = atan2(xyz[1, ind], xyz[0, ind])
_lla[2, ind] = (gps_p / cos(lla[0, ind])) - _gps_a / sqrt(1.0 - _e2 * sin(lla[0, ind]) ** 2)
return lla
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
cpdef numpy.ndarray[dtype=numpy.float64_t, ndim=2] _xyz_from_latlonalt(
numpy.float64_t[::1] _lat,
numpy.float64_t[::1] _lon,
numpy.float64_t[::1] _alt,
):
cdef Py_ssize_t i
cdef int n_pts = _lat.shape[0]
cdef numpy.ndarray[dtype=numpy.float64_t, ndim=2] xyz = np.empty((3, n_pts), dtype=np.float64)
cdef numpy.float64_t[:, ::1] _xyz = xyz
cdef numpy.float64_t sin_lat, cos_lat, sin_lon, cos_lon, gps_n
for ind in range(n_pts):
sin_lat = sin(_lat[ind])
sin_lon = sin(_lon[ind])
cos_lat = cos(_lat[ind])
cos_lon = cos(_lon[ind])
gps_n = _gps_a / sqrt(1.0 - _e2 * sin_lat ** 2)
_xyz[0, ind] = (gps_n + _alt[ind]) * cos_lat * cos_lon
_xyz[1, ind] = (gps_n + _alt[ind]) * cos_lat * sin_lon
_xyz[2, ind] = (b_div_a2 * gps_n + _alt[ind]) * sin_lat
return xyz
# this function takes memoryviews as inputs
# that is why _lat, _lon, and _alt are indexed below to get the 0th entry
@cython.boundscheck(False)
@cython.wraparound(False)
cpdef numpy.ndarray[numpy.float64_t, ndim=2] _ENU_from_ECEF(
numpy.float64_t[:, ::1] xyz,
numpy.float64_t[::1] _lat,
numpy.float64_t[::1] _lon,
numpy.float64_t[::1] _alt,
):
cdef Py_ssize_t i
cdef int nblts = xyz.shape[1]
cdef numpy.float64_t xyz_use[3]
cdef numpy.float64_t sin_lat, cos_lat, sin_lon, cos_lon
# we want a memoryview of the xyz of the center
# this looks a little silly but we don't have to define 2 different things
cdef numpy.float64_t[:] xyz_center = _xyz_from_latlonalt(_lat, _lon, _alt)[:, 0]
cdef numpy.ndarray[numpy.float64_t, ndim=2] _enu = np.empty((3, nblts), dtype=np.float64)
cdef numpy.float64_t[:, ::1] enu = _enu
sin_lat = sin(_lat[0])
cos_lat = cos(_lat[0])
sin_lon = sin(_lon[0])
cos_lon = cos(_lon[0])
for i in range(nblts):
xyz_use[0] = xyz[0, i] - xyz_center[0]
xyz_use[1] = xyz[1, i] - xyz_center[1]
xyz_use[2] = xyz[2, i] - xyz_center[2]
enu[0, i] = -sin_lon * xyz_use[0] + cos_lon * xyz_use[1]
enu[1, i] = (
- sin_lat * cos_lon * xyz_use[0]
- sin_lat * sin_lon * xyz_use[1]
+ cos_lat * xyz_use[2]
)
enu[2, i] = (
cos_lat * cos_lon * xyz_use[0]
+ cos_lat * sin_lon * xyz_use[1]
+ sin_lat * xyz_use[2]
)
return _enu
# this function takes memoryviews as inputs
# that is why _lat, _lon, and _alt are indexed below to get the 0th entry
@cython.boundscheck(False)
@cython.wraparound(False)
cpdef numpy.ndarray[dtype=numpy.float64_t] _ECEF_FROM_ENU(
numpy.float64_t[:, ::1] enu,
numpy.float64_t[::1] _lat,
numpy.float64_t[::1] _lon,
numpy.float64_t[::1] _alt,
):
cdef Py_ssize_t i
cdef int nblts = enu.shape[1]
cdef numpy.float64_t sin_lat, cos_lat, sin_lon, cos_lon
# allocate memory then make memory view for faster access
cdef numpy.ndarray[dtype=numpy.float64_t, ndim=2] _xyz = np.zeros((3, nblts), dtype=np.float64)
cdef numpy.float64_t[:, ::1] xyz = _xyz
# we want a memoryview of the xyz of the center
# this looks a little silly but we don't have to define 2 different things
cdef numpy.float64_t[:] xyz_center = _xyz_from_latlonalt(_lat, _lon, _alt)[:, 0]
sin_lat = sin(_lat[0])
cos_lat = cos(_lat[0])
sin_lon = sin(_lon[0])
cos_lon = cos(_lon[0])
for i in range(nblts):
xyz[0, i] = (
- sin_lat * cos_lon * enu[1, i]
- sin_lon * enu[0, i]
+ cos_lat * cos_lon * enu[2, i]
+ xyz_center[0]
)
xyz[1, i] = (
- sin_lat * sin_lon * enu[1, i]
+ cos_lon * enu[0, i]
+ cos_lat * sin_lon * enu[2, i]
+ xyz_center[1]
)
xyz[2, i] = cos_lat * enu[1, i] + sin_lat * enu[2, i] + xyz_center[2]
return _xyz
# inital_uvw is a memoryviewed array as an input
@cython.boundscheck(False)
@cython.wraparound(False)
cpdef numpy.ndarray[dtype=numpy.float64_t, ndim=2] _phase_uvw(
numpy.float64_t ra,
numpy.float64_t dec,
numpy.float64_t[:, ::1] initial_uvw
):
cdef int i
cdef int nuvw = initial_uvw.shape[1]
cdef numpy.ndarray[dtype=numpy.float64_t, ndim=2] uvw = np.empty((3, nuvw), dtype=np.float64)
# make a memoryview for the numpy array in c
cdef numpy.float64_t[:, ::1] _uvw = uvw
cdef numpy.float64_t sin_ra, cos_ra, sin_dec, cos_dec
sin_ra = sin(ra)
cos_ra = cos(ra)
sin_dec = sin(dec)
cos_dec = cos(dec)
for i in range(nuvw):
_uvw[0, i] = - sin_ra * initial_uvw[0, i] + cos_ra * initial_uvw[1, i]
_uvw[1, i] = (
- sin_dec * cos_ra * initial_uvw[0, i]
- sin_dec * sin_ra * initial_uvw[1, i]
+ cos_dec * initial_uvw[2, i]
)
_uvw[2, i] = (
cos_dec * cos_ra * initial_uvw[0, i]
+ cos_dec * sin_ra * initial_uvw[1, i]
+ sin_dec * initial_uvw[2, i]
)
return uvw
# uvw is a memoryviewed array as an input
@cython.boundscheck(False)
@cython.wraparound(False)
cpdef numpy.ndarray[dtype=numpy.float64_t, ndim=2] _unphase_uvw(
numpy.float64_t ra,
numpy.float64_t dec,
numpy.float64_t[:, ::1] uvw
):
cdef int i
cdef int nuvw = uvw.shape[1]
cdef numpy.ndarray[dtype=numpy.float64_t, ndim=2] unphased_uvw = np.empty((3, nuvw), dtype=np.float64)
# make a memoryview for the numpy array in c
cdef numpy.float64_t[:, ::1] _u_uvw = unphased_uvw
cdef numpy.float64_t sin_ra, cos_ra, sin_dec, cos_dec
sin_ra = sin(ra)
cos_ra = cos(ra)
sin_dec = sin(dec)
cos_dec = cos(dec)
for i in range(nuvw):
_u_uvw[0, i] = (
- sin_ra * uvw[0, i]
- sin_dec * cos_ra * uvw[1, i]
+ cos_dec * cos_ra * uvw[2, i]
)
_u_uvw[1, i] = (
cos_ra * uvw[0, i]
- sin_dec * sin_ra * uvw[1, i]
+ cos_dec * sin_ra * uvw[2, i]
)
_u_uvw[2, i] = cos_dec * uvw[1, i] + sin_dec * uvw[2, i]
return unphased_uvw
