def test_phase_rotate(self):
uvw = numpy.array([(1, 0, 0), (0, 1, 0), (0, 0, 1)])
pos = [
SkyCoord(17, 35, unit=u.deg),
SkyCoord(17, 30, unit=u.deg),
SkyCoord(12, 30, unit=u.deg),
SkyCoord(11, 35, unit=u.deg),
SkyCoord(51, 35, unit=u.deg),
SkyCoord(15, 70, unit=u.deg)
]
# Sky coordinates to reproject to
for phasecentre in pos:
for newphasecentre in pos:
# Rotate UVW
xyz = uvw_to_xyz(uvw, -phasecentre.ra.rad, phasecentre.dec.rad)
uvw_rotated = xyz_to_uvw(xyz, -newphasecentre.ra.rad,
newphasecentre.dec.rad)
# Determine phasor
l_p, m_p, n_p = skycoord_to_lmn(phasecentre, newphasecentre)
phasor = simulate_point(uvw_rotated, l_p, m_p)
for sourcepos in pos:
# Simulate visibility at old and new phase centre
l, m, _ = skycoord_to_lmn(sourcepos, phasecentre)
vis = simulate_point(uvw, l, m)
l_r, m_r, _ = skycoord_to_lmn(sourcepos, newphasecentre)
vis_rotated = simulate_point(uvw_rotated, l_r, m_r)
# Difference should be given by phasor
assert_allclose(vis * phasor, vis_rotated, atol=1e-10)
def predict_skycomponent_visibility(
vis: Union[Visibility, BlockVisibility],
sc: Union[Skycomponent, List[Skycomponent]]) -> Visibility:
"""Predict the visibility from a Skycomponent, add to existing visibility, for Visibility or BlockVisibility
:param vis: Visibility or BlockVisibility
:param sc: Skycomponent or list of SkyComponents
:return: Visibility or BlockVisibility
"""
if not isinstance(sc, collections.Iterable):
sc = [sc]
if isinstance(vis, Visibility):
_, im_nchan = list(get_frequency_map(vis, None))
npol = vis.polarisation_frame.npol
for comp in sc:
assert_same_chan_pol(vis, comp)
l, m, n = skycoord_to_lmn(comp.direction, vis.phasecentre)
phasor = simulate_point(vis.uvw, l, m)
for ivis in range(vis.nvis):
for pol in range(npol):
vis.data['vis'][ivis, pol] += comp.flux[im_nchan[ivis],
pol] * phasor[ivis]
elif isinstance(vis, BlockVisibility):
nchan = vis.nchan
npol = vis.npol
k = numpy.array(vis.frequency) / constants.c.to('m/s').value
for comp in sc:
assert_same_chan_pol(vis, comp)
flux = comp.flux
if comp.polarisation_frame != vis.polarisation_frame:
flux = convert_pol_frame(flux, comp.polarisation_frame,
vis.polarisation_frame)
l, m, n = skycoord_to_lmn(comp.direction, vis.phasecentre)
for chan in range(nchan):
phasor = simulate_point(vis.uvw * k[chan], l, m)
for pol in range(npol):
vis.data['vis'][..., chan,
pol] += flux[chan, pol] * phasor[...]
return vis
def predict_skycomponent_visibility(
vis: Visibility, sc: Union[Skycomponent,
List[Skycomponent]]) -> Visibility:
"""Predict the visibility from a Skycomponent, add to existing visibility, for Visibility
:param vis: Visibility
:param sc: Skycomponent or list of SkyComponents
:return: Visibility
"""
assert type(vis) is Visibility, "vis is not a Visibility: %r" % vis
if not isinstance(sc, collections.Iterable):
sc = [sc]
_, ichan = list(get_frequency_map(vis, None))
npol = vis.polarisation_frame.npol
for comp in sc:
l, m, n = skycoord_to_lmn(comp.direction, vis.phasecentre)
phasor = simulate_point(vis.uvw, l, m)
for ivis in range(vis.nvis):
for pol in range(npol):
vis.data['vis'][ivis, pol] += comp.flux[ichan[ivis],
pol] * phasor[ivis]
# coords = phasor, ichan
# for pol in range(npol):
# vis.data['vis'][:,pol] += [comp.flux[ic, pol] * p for p, ic in zip(*coords)]
return vis
def sum_visibility(vis: Visibility, direction: SkyCoord) -> numpy.array:
""" Direct Fourier summation in a given direction
:param vis: Visibility to be summed
:param direction: Direction of summation
:return: flux[nch,npol], weight[nch,pol]
"""
# TODO: Convert to Visibility or remove?
svis = copy_visibility(vis)
l, m, n = skycoord_to_lmn(direction, svis.phasecentre)
phasor = numpy.conjugate(simulate_point(svis.uvw, l, m))
# Need to put correct mapping here
_, frequency = get_frequency_map(svis, None)
frequency = list(frequency)
nchan = max(frequency) + 1
npol = svis.polarisation_frame.npol
flux = numpy.zeros([nchan, npol])
weight = numpy.zeros([nchan, npol])
coords = svis.vis, svis.weight, phasor, list(frequency)
for v, wt, p, ic in zip(*coords):
for pol in range(npol):
flux[ic, pol] += numpy.real(wt[pol] * v[pol] * p)
weight[ic, pol] += wt[pol]
flux[weight > 0.0] = flux[weight > 0.0] / weight[weight > 0.0]
flux[weight <= 0.0] = 0.0
return flux, weight
def phaserotate_visibility(vis: Visibility, newphasecentre: SkyCoord, tangent=True, inverse=False) -> Visibility:
"""
Phase rotate from the current phase centre to a new phase centre
If tangent is False the uvw are recomputed and the visibility phasecentre is updated.
Otherwise only the visibility phases are adjusted
:param vis: Visibility to be rotated
:param newphasecentre:
:param tangent: Stay on the same tangent plane? (True)
:param inverse: Actually do the opposite
:return: Visibility
"""
assert isinstance(vis, Visibility), "vis is not a Visibility: %r" % vis
l, m, n = skycoord_to_lmn(newphasecentre, vis.phasecentre)
# No significant change?
if numpy.abs(n) > 1e-15:
# Make a new copy
newvis = copy_visibility(vis)
phasor = simulate_point(newvis.uvw, l, m)
nvis, npol = vis.vis.shape
# TODO: Speed up (broadcast rules not obvious to me)
if inverse:
for i in range(nvis):
for pol in range(npol):
newvis.data['vis'][i, pol] *= phasor[i]
else:
for i in range(nvis):
for pol in range(npol):
newvis.data['vis'][i, pol] *= numpy.conj(phasor[i])
# To rotate UVW, rotate into the global XYZ coordinate system and back. We have the option of
# staying on the tangent plane or not. If we stay on the tangent then the raster will
# join smoothly at the edges. If we change the tangent then we will have to reproject to get
# the results on the same image, in which case overlaps or gaps are difficult to deal with.
if not tangent:
if inverse:
xyz = uvw_to_xyz(vis.data['uvw'], ha=-newvis.phasecentre.ra.rad, dec=newvis.phasecentre.dec.rad)
newvis.data['uvw'][...] = \
xyz_to_uvw(xyz, ha=-newphasecentre.ra.rad, dec=newphasecentre.dec.rad)[...]
else:
# This is the original (non-inverse) code
xyz = uvw_to_xyz(newvis.data['uvw'], ha=-newvis.phasecentre.ra.rad, dec=newvis.phasecentre.dec.rad)
newvis.data['uvw'][...] = xyz_to_uvw(xyz, ha=-newphasecentre.ra.rad, dec=newphasecentre.dec.rad)[
...]
newvis.phasecentre = newphasecentre
return newvis
else:
return vis
def predict_skycomponent_blockvisibility(vis: BlockVisibility,
sc: Union[Skycomponent,
List[Skycomponent]],
**kwargs) -> BlockVisibility:
"""Predict the visibility from a Skycomponent, add to existing visibility, for BlockVisibility
:param vis: BlockVisibility
:param sc: Skycomponent or list of SkyComponents
:param spectral_mode: {mfs|channel} (channel)
:return: BlockVisibility
"""
assert type(
vis) is BlockVisibility, "vis is not a BlockVisibility: %r" % vis
if not isinstance(sc, collections.Iterable):
sc = [sc]
nchan = vis.nchan
npol = vis.npol
if not isinstance(sc, collections.Iterable):
sc = [sc]
k = vis.frequency / constants.c.to('m/s').value
for comp in sc:
assert_same_chan_pol(vis, comp)
flux = comp.flux
if comp.polarisation_frame != vis.polarisation_frame:
flux = convert_pol_frame(flux, comp.polarisation_frame,
vis.polarisation_frame)
l, m, n = skycoord_to_lmn(comp.direction, vis.phasecentre)
for chan in range(nchan):
phasor = simulate_point(vis.uvw * k[chan], l, m)
for pol in range(npol):
vis.data['vis'][..., chan,
pol] += flux[chan, pol] * phasor[...]
return vis
def fit_visibility(vis,
sc,
tol=1e-6,
niter=20,
verbose=False,
method='trust-exact',
**kwargs):
"""Fit a single component to a visibility
Uses the scipy.optimize.minimize function.
:param vis:
:param sc: Initial component
:param tol: Tolerance of fit
:param niter: Number of iterations
:param verbose:
:param method: 'CG', 'BFGS', 'Powell', 'trust-ncg', 'trust-exact', 'trust-krylov': default 'trust-exact'
:param kwargs:
:return: component, convergence info as a dictionary
"""
assert vis.polarisation_frame.type == 'stokesI', "Currently restricted to stokesI"
# These derivative have been calculated using sympy. See visibility_fitting_sympy.py
def J(params):
# Params are flux, l, m
S = params[0]
l = params[1]
m = params[2]
u = vis.u[:, numpy.newaxis]
v = vis.v[:, numpy.newaxis]
vobs = vis.vis
p = numpy.exp(-2j * numpy.pi * (u * l + v * m))
vres = vobs - S * p
J = numpy.sum(vis.weight * (vres * numpy.conjugate(vres)).real)
return J
def Jboth(params):
# Params are flux, l, m
S = params[0]
l = params[1]
m = params[2]
u = vis.u[:, numpy.newaxis]
v = vis.v[:, numpy.newaxis]
vobs = vis.vis
p = numpy.exp(-2j * numpy.pi * (u * l + v * m))
vres = vobs - S * p
Vrp = vres * numpy.conjugate(p) * vis.weight
J = numpy.sum(vis.weight * (vres * numpy.conjugate(vres)).real)
gradJ = numpy.array([
-2.0 * numpy.sum(Vrp.real),
+4.0 * numpy.pi * S * numpy.sum(u * Vrp.imag),
+4.0 * numpy.pi * S * numpy.sum(v * Vrp.imag)
])
return J, gradJ
def hessian(params):
S = params[0]
l = params[1]
m = params[2]
u = vis.u[:, numpy.newaxis]
v = vis.v[:, numpy.newaxis]
w = vis.w[:, numpy.newaxis]
wt = vis.weight
vobs = vis.vis
p = numpy.exp(-2j * numpy.pi * (u * l + v * m))
vres = vobs - S * p
Vrp = vres * numpy.conjugate(p)
hess = numpy.zeros([3, 3])
hess[0, 0] = 2.0 * numpy.sum(wt)
hess[0, 1] = 4.0 * numpy.pi * numpy.sum(wt * u * Vrp.imag)
hess[0, 2] = 4.0 * numpy.pi * numpy.sum(wt * v * Vrp.imag)
hess[1,
1] = 8.0 * numpy.pi**2 * S * numpy.sum(wt * u**2 * (S + Vrp.real))
hess[1, 2] = 8.0 * numpy.pi**2 * S * numpy.sum(wt * u * v *
(S + Vrp.real))
hess[2,
2] = 8.0 * numpy.pi**2 * S * numpy.sum(wt * v**2 * (S + Vrp.real))
hess[1, 0] = hess[0, 1]
hess[2, 0] = hess[0, 2]
hess[2, 1] = hess[1, 2]
return hess
# Initialize l,m,n to be in the direction of the component as defined in the frame of
# visibility phasecentre
l, m, n = skycoord_to_lmn(sc.direction, vis.phasecentre)
x0 = numpy.array([sc.flux[0, 0], l, m])
bounds = ((None, None), (-0.1, -0.1), (-0.1, 0.1))
options = {'maxiter': niter, 'disp': verbose}
res = {}
import time
start = time.time()
if method == 'BFGS' or method == 'CG' or method == 'Powell':
res = minimize(J, x0, method=method, options=options, tol=tol)
elif method == 'Nelder-Mead':
res = minimize(Jboth, x0, method=method, options=options, tol=tol)
elif method == 'L-BFGS-B':
res = minimize(Jboth,
x0,
method=method,
jac=True,
bounds=bounds,
options=options,
tol=tol)
else:
res = minimize(Jboth,
x0,
method=method,
jac=True,
hess=hessian,
options=options,
tol=tol)
if verbose:
print("Solution for %s took %.6f seconds" %
(method, time.time() - start))
print("Solution = %s" % str(res.x))
print(res)
sc.flux[...] = res.x[0]
lmn = (res.x[1], res.x[2], 0.0)
sc.direction = lmn_to_skycoord(lmn, vis.phasecentre)
return sc, res
def test_skycoord_to_lmn(self):
center = SkyCoord(ra=0, dec=0, unit=u.deg)
north = SkyCoord(ra=0, dec=90, unit=u.deg)
south = SkyCoord(ra=0, dec=-90, unit=u.deg)
east = SkyCoord(ra=90, dec=0, unit=u.deg)
west = SkyCoord(ra=-90, dec=0, unit=u.deg)
assert_allclose(skycoord_to_lmn(center, center), (0, 0, 0))
assert_allclose(skycoord_to_lmn(north, center), (0, 1, -1))
assert_allclose(skycoord_to_lmn(south, center), (0, -1, -1))
assert_allclose(skycoord_to_lmn(south, north), (0, 0, -2), atol=1e-14)
assert_allclose(skycoord_to_lmn(east, center), (1, 0, -1))
assert_allclose(skycoord_to_lmn(west, center), (-1, 0, -1))
assert_allclose(skycoord_to_lmn(center, west), (1, 0, -1))
assert_allclose(skycoord_to_lmn(north, west), (0, 1, -1), atol=1e-14)
assert_allclose(skycoord_to_lmn(south, west), (0, -1, -1), atol=1e-14)
assert_allclose(skycoord_to_lmn(north, east), (0, 1, -1), atol=1e-14)
assert_allclose(skycoord_to_lmn(south, east), (0, -1, -1), atol=1e-14)
