def transform_basis(nside, jones, z0_cza, R_z0):
"""
At zenith in the local frame the 'x' feed is aligned with 'theta' and
the 'y' feed is aligned with 'phi'
"""
npix = hp.nside2npix(nside)
hpxidx = np.arange(npix)
cza, ra = hp.pix2ang(nside, hpxidx)
# Rb is the rotation relating the E-field basis coordinate frame to the local horizontal zenith.
# (specific to this instrument response simulation data)
Rb = np.array([[0, 0, -1], [0, -1, 0], [-1, 0, 0]])
fR = np.einsum('ab,bc->ac', Rb, R_z0) # matrix product of two rotations
tb, pb = irf.rotate_sphr_coords(fR, cza, ra)
cza_v = irf.t_hat_cart(cza, ra)
ra_v = irf.p_hat_cart(cza, ra)
tb_v = irf.t_hat_cart(tb, pb)
fRcza_v = np.einsum('ab...,b...->a...', fR, cza_v)
fRra_v = np.einsum('ab...,b...->a...', fR, ra_v)
cosX = np.einsum('a...,a...', fRcza_v, tb_v)
sinX = np.einsum('a...,a...', fRra_v, tb_v)
basis_rot = np.array([[cosX, sinX], [-sinX, cosX]])
basis_rot = np.transpose(basis_rot, (2, 0, 1))
return irnf.M(jones, basis_rot)
def transform_basis(nside, jones, z0_cza, R_z0):
npix = hp.nside2npix(nside)
hpxidx = np.arange(npix)
cza, ra = hp.pix2ang(nside, hpxidx)
fR = R_z0
tb, pb = irf.rotate_sphr_coords(fR, cza, ra)
cza_v = irf.t_hat_cart(cza, ra)
ra_v = irf.p_hat_cart(cza, ra)
tb_v = irf.t_hat_cart(tb, pb)
fRcza_v = np.einsum('ab...,b...->a...', fR, cza_v)
fRra_v = np.einsum('ab...,b...->a...', fR, ra_v)
cosX = np.einsum('a...,a...', fRcza_v, tb_v)
sinX = np.einsum('a...,a...', fRra_v, tb_v)
basis_rot = np.array([[cosX, -sinX],[sinX, cosX]])
basis_rot = np.transpose(basis_rot,(2,0,1))
# return np.einsum('...ab,...bc->...ac', jones, basis_rot)
return irnf.M(jones, basis_rot)
def transform_basis(nside, jones, z0_cza, R_z0):
npix = hp.nside2npix(nside)
hpxidx = np.arange(npix)
cza, ra = hp.pix2ang(nside, hpxidx)
fR = R_z0
tb, pb = irf.rotate_sphr_coords(fR, cza, ra)
cza_v = irf.t_hat_cart(cza, ra)
ra_v = irf.p_hat_cart(cza, ra)
tb_v = irf.t_hat_cart(tb, pb)
fRcza_v = np.einsum('ab...,b...->a...', fR, cza_v)
fRra_v = np.einsum('ab...,b...->a...', fR, ra_v)
cosX = np.einsum('a...,a...', fRcza_v, tb_v)
sinX = np.einsum('a...,a...', fRra_v, tb_v)
basis_rot = np.array([[cosX, -sinX], [sinX, cosX]])
basis_rot = np.transpose(basis_rot, (2, 0, 1))
# return np.einsum('...ab,...bc->...ac', jones, basis_rot)
return irnf.M(jones, basis_rot)
def horizon_mask(jones, z0_cza):
npix = jones.shape[0]
nside = hp.npix2nside(npix)
hpxidx = np.arange(npix)
cza, ra = hp.pix2ang(nside, hpxidx)
if z0_cza == 0.:
tb, pb = cza, ra
else:
z0 = irf.r_hat_cart(z0_cza, 0.)
RotAxis = np.cross(z0, np.array([0,0,1.]))
RotAxis /= np.sqrt(np.dot(RotAxis,RotAxis))
RotAngle = np.arccos(np.dot(z0, [0,0,1.]))
R_z0 = irf.rotation_matrix(RotAxis, RotAngle)
tb, pb = irf.rotate_sphr_coords(R_z0, cza, ra)
hm = np.zeros((npix,2,2))
hm[np.where(tb < np.pi/2.)] = 1.
return hm
def horizon_mask(jones, z0_cza):
npix = jones.shape[0]
nside = hp.npix2nside(npix)
hpxidx = np.arange(npix)
cza, ra = hp.pix2ang(nside, hpxidx)
if z0_cza == 0.:
tb, pb = cza, ra
else:
z0 = irf.r_hat_cart(z0_cza, 0.)
RotAxis = np.cross(z0, np.array([0, 0, 1.]))
RotAxis /= np.sqrt(np.dot(RotAxis, RotAxis))
RotAngle = np.arccos(np.dot(z0, [0, 0, 1.]))
R_z0 = irf.rotation_matrix(RotAxis, RotAngle)
tb, pb = irf.rotate_sphr_coords(R_z0, cza, ra)
hm = np.zeros((npix, 2, 2))
hm[np.where(tb < np.pi / 2.)] = 1.
return hm
def transform_basis(nside, jones, z0_cza, R_z0):
"""
At zenith in the local frame the 'x' feed is aligned with 'theta' and
the 'y' feed is aligned with 'phi'
"""
npix = hp.nside2npix(nside)
hpxidx = np.arange(npix)
cza, ra = hp.pix2ang(nside, hpxidx)
# Rb is the rotation relating the E-field basis coordinate frame to the local horizontal zenith.
# (specific to this instrument response simulation data)
Rb = np.array([
[0,0,-1],
[0,-1,0],
[-1,0,0]
])
fR = np.einsum('ab,bc->ac', Rb, R_z0) # matrix product of two rotations
tb, pb = irf.rotate_sphr_coords(fR, cza, ra)
cza_v = irf.t_hat_cart(cza, ra)
ra_v = irf.p_hat_cart(cza, ra)
tb_v = irf.t_hat_cart(tb, pb)
fRcza_v = np.einsum('ab...,b...->a...', fR, cza_v)
fRra_v = np.einsum('ab...,b...->a...', fR, ra_v)
cosX = np.einsum('a...,a...', fRcza_v, tb_v)
sinX = np.einsum('a...,a...', fRra_v, tb_v)
basis_rot = np.array([[cosX, sinX],[-sinX, cosX]])
basis_rot = np.transpose(basis_rot,(2,0,1))
return irnf.M(jones, basis_rot)
def instrument_setup(z0_cza, freqs):
"""
This is the CST simulation using the efield basis of z' = -x, y' = -y, x' = -z
frequencies are every 10MHz, from 100-200
Each file contains 8 columns which are ordered as:
(Re(xt),Re(xp),Re(yt),Re(yp),Im(xt),Im(xp),Im(yt),Im(yp)).
Each column is a healpix map with resolution nside = 2**8
"""
nu0 = str(int(p.nu_axis[0] / 1e6))
nuf = str(int(p.nu_axis[-1] / 1e6))
band_str = nu0 + "-" + nuf
# restore_name = p.interp_type + "_" + "band_" + band_str + "mhz_nfreq" + str(p.nfreq)+ "_nside" + str(p.nside) + ".npy"
#
# if os.path.exists('jones_save/' + restore_name) == True:
# return np.load('jones_save/' + restore_name)
#
local_jones0_file = 'local_jones0/nside' + str(
p.nside) + '_band' + band_str + '_Jdata.npy'
if os.path.exists(local_jones0_file) == True:
return np.load(local_jones0_file)
fbase = '/data4/paper/zionos/HERA_jones_data/HERA_Jones_healpix_'
# fbase = '/home/zmart/radcos/polskysim/IonRIME/HERA_jones_data/HERA_Jones_healpix_'
nside_in = 2**8
fnames = [fbase + str(int(f / 1e6)) + 'MHz.txt' for f in freqs]
nfreq_nodes = len(freqs)
npix = hp.nside2npix(nside_in)
hpxidx = np.arange(npix)
cza, ra = hp.pix2ang(nside_in, hpxidx)
z0 = irf.r_hat_cart(z0_cza, 0.)
RotAxis = np.cross(z0, np.array([0, 0, 1.]))
RotAxis /= np.sqrt(np.dot(RotAxis, RotAxis))
RotAngle = np.arccos(np.dot(z0, [0, 0, 1.]))
R_z0 = irf.rotation_matrix(RotAxis, RotAngle)
t0, p0 = irf.rotate_sphr_coords(R_z0, cza, ra)
hm = np.zeros(npix)
hm[np.where(cza < (np.pi / 2. + np.pi / 20.)
)] = 1 # Horizon mask; is 0 below the local horizon.
# added some padding. Idea being to allow for some interpolation near the horizon. Questionable.
npix_out = hp.nside2npix(p.nside)
Jdata = np.zeros((nfreq_nodes, npix_out, 2, 2), dtype='complex128')
for i, f in enumerate(fnames):
J_f = np.loadtxt(f) # J_f.shape = (npix_in, 8)
J_f = J_f * np.tile(hm, 8).reshape(8, npix).transpose(
1, 0) # Apply horizon mask
# Could future "rotation" of these zeroed-maps have small errors at the
# edges of the horizon? due to the way healpy interpolates.
# Unlikely to be important.
# Comment update: Yep, it turns out this happens, BUT it is approximately
# power-preserving. The pixels at the edges of the rotated mask are not
# identically 1, but the sum over the mask is maintained to about a part
# in 1e-5
# Perform a scalar rotation of each component so that the instrument's boresight
# is pointed toward (z0_cza, 0), the location of the instrument on the
# earth in the Current-Epoch-RA/Dec coordinate frame.
J_f = irf.rotate_jones(J_f, R_z0, multiway=False)
if p.nside != nside_in:
# Change the map resolution as needed.
#d = lambda m: hp.ud_grade(m, nside=p.nside, power=-2.)
# I think these two ended up being (roughly) the same?
# The apparent normalization problem was really becuase of an freq. interpolation problem.
# irf.harmonic_ud_grade is probably better for increasing resolution, but hp.ud_grade is
# faster because it's just averaging/tiling instead of doing SHT's
d = lambda m: irf.harmonic_ud_grade(m, nside_in, p.nside)
J_f = (np.asarray(map(d, J_f.T))).T
# The inner transpose is so that correct dimension is map()'ed over,
# and then the outer transpose returns the array to its original shape.
J_f = irf.inverse_flatten_jones(
J_f) # Change shape to (nfreq,npix,2,2), complex-valued
J_f = transform_basis(
p.nside, J_f, z0_cza, R_z0
) # right-multiply by the basis transformation matrix from RA/CZA to the Local CST basis.
# Note that CZA = pi/2 - Dec! So this is not quite the RA/Dec basis. But the difference
# in the Stoke parameters between the two is only U -> -U
Jdata[i, :, :, :] = J_f
print i
# If the model at the current nside hasn't been generated before, save it for future reuse.
if os.path.exists(local_jones0_file) == False:
np.save(local_jones0_file, Jdata)
return Jdata
def make_jones(freq):
if freq in range(90, 221):
pass
else:
raise ValueError('Frequency is not available.')
nside = 512 # make this as large as possible to minimize singularity effects at zenith
## nside 512 seems to work well enough using the "neighbours of neighbours" patch
## of the zenith singularity in the ra/cza basis.
npix = hp.nside2npix(nside)
hpxidx = np.arange(npix)
t, p = hp.pix2ang(nside, hpxidx)
g1 = ecomp(csvname(freq, 'G', 'X'), csvname(freq, 'P', 'X'))
g2 = ecomp(csvname(freq, 'G', 'Y'), csvname(freq, 'P', 'Y'))
I = (abs(g1)**2. + abs(g2)**2.)
norm = np.sqrt(np.amax(I, axis=0))
# g1 /= norm
# g2 /= norm
rhm = irf.rotate_healpix_map
Rb = np.array([[0, 0, -1], [0, -1, 0], [-1, 0, 0]])
Et_b = udgrade(g1.real, nside) + 1j * udgrade(g1.imag, nside)
Ep_b = udgrade(g2.real, nside) + 1j * udgrade(g2.imag, nside)
tb, pb = irf.rotate_sphr_coords(Rb, t, p)
tb_v = irf.t_hat_cart(tb, pb)
pb_v = irf.p_hat_cart(tb, pb)
t_v = irf.t_hat_cart(t, p)
p_v = irf.p_hat_cart(t, p)
Rb_tb_v = np.einsum('ab...,b...->a...', Rb, tb_v)
Rb_pb_v = np.einsum('ab...,b...->a...', Rb, pb_v)
cosX = np.einsum('a...,a...', Rb_tb_v, t_v)
sinX = np.einsum('a...,a...', Rb_pb_v, t_v)
Et = Et_b * cosX + Ep_b * sinX
Ep = -Et_b * sinX + Ep_b * cosX
Ext = Et
Exp = Ep
## This assumes that Et and Ep are the components of a dipole oriented
## along the X axis, and we want to obtain the components of the same
## dipole if it was oriented along Y.
## In the current basis, this is done by a scalar rotation of the theta and phi
## components by 90 degrees about the Z axis.
Eyt = arm(Et.real) + 1j * arm(Et.imag)
Eyp = arm(Ep.real) + 1j * arm(Ep.imag)
jones_c = np.array([[Ext, Exp], [Eyt, Eyp]]).transpose(2, 0, 1)
# jones_a = np.array([[rhm(Ext,Rb), rhm(Exp,Rb)],[rhm(Eyt,Rb),rhm(Eyp,Rb)]]).transpose(2,0,1)
#
# basis_rot = np.array([[cosX,-sinX],[sinX,cosX]]).transpose(2,0,1)
#
# jones_b = np.einsum('...ab,...bc->...ac', jones_a, basis_rot)
#
# Ext_b, Exp_b, Eyt_b, Eyp_b = [rhm(jones_b[:,i,j],Rb) for i in range(2) for j in range(2)]
#
# jones_c = np.array([[Ext_b,Exp_b],[Eyt_b,Eyp_b]]).transpose(2,0,1)
return jones_c
def instrument_setup(z0_cza, freqs):
"""
This is the CST simulation using the efield basis of z' = -x, y' = -y, x' = -z
frequencies are every 10MHz, from 100-200
Each file contains 8 columns which are ordered as:
(Re(xt),Re(xp),Re(yt),Re(yp),Im(xt),Im(xp),Im(yt),Im(yp)).
Each column is a healpix map with resolution nside = 2**8
"""
nu0 = str(int(p.nu_axis[0] / 1e6))
nuf = str(int(p.nu_axis[-1] / 1e6))
band_str = nu0 + "-" + nuf
# restore_name = p.interp_type + "_" + "band_" + band_str + "mhz_nfreq" + str(p.nfreq)+ "_nside" + str(p.nside) + ".npy"
#
# if os.path.exists('jones_save/' + restore_name) == True:
# return np.load('jones_save/' + restore_name)
#
local_jones0_file = 'local_jones0/nside' + str(p.nside) + '_band' + band_str + '_Jdata.npy'
if os.path.exists(local_jones0_file) == True:
return np.load(local_jones0_file)
fbase = '/data4/paper/zionos/HERA_jones_data/HERA_Jones_healpix_'
# fbase = '/home/zmart/radcos/polskysim/IonRIME/HERA_jones_data/HERA_Jones_healpix_'
nside_in = 2**8
fnames = [fbase + str(int(f / 1e6)) + 'MHz.txt' for f in freqs]
nfreq_nodes = len(freqs)
npix = hp.nside2npix(nside_in)
hpxidx = np.arange(npix)
cza, ra = hp.pix2ang(nside_in, hpxidx)
z0 = irf.r_hat_cart(z0_cza, 0.)
RotAxis = np.cross(z0, np.array([0,0,1.]))
RotAxis /= np.sqrt(np.dot(RotAxis,RotAxis))
RotAngle = np.arccos(np.dot(z0, [0,0,1.]))
R_z0 = irf.rotation_matrix(RotAxis, RotAngle)
t0, p0 = irf.rotate_sphr_coords(R_z0, cza, ra)
hm = np.zeros(npix)
hm[np.where(cza < (np.pi / 2. + np.pi / 20.))] = 1 # Horizon mask; is 0 below the local horizon.
# added some padding. Idea being to allow for some interpolation near the horizon. Questionable.
npix_out = hp.nside2npix(p.nside)
Jdata = np.zeros((nfreq_nodes,npix_out,2,2),dtype='complex128')
for i,f in enumerate(fnames):
J_f = np.loadtxt(f) # J_f.shape = (npix_in, 8)
J_f = J_f * np.tile(hm, 8).reshape(8, npix).transpose(1,0) # Apply horizon mask
# Could future "rotation" of these zeroed-maps have small errors at the
# edges of the horizon? due to the way healpy interpolates.
# Unlikely to be important.
# Comment update: Yep, it turns out this happens, BUT it is approximately
# power-preserving. The pixels at the edges of the rotated mask are not
# identically 1, but the sum over the mask is maintained to about a part
# in 1e-5
# Perform a scalar rotation of each component so that the instrument's boresight
# is pointed toward (z0_cza, 0), the location of the instrument on the
# earth in the Current-Epoch-RA/Dec coordinate frame.
J_f = irf.rotate_jones(J_f, R_z0, multiway=False)
if p.nside != nside_in:
# Change the map resolution as needed.
#d = lambda m: hp.ud_grade(m, nside=p.nside, power=-2.)
# I think these two ended up being (roughly) the same?
# The apparent normalization problem was really becuase of an freq. interpolation problem.
# irf.harmonic_ud_grade is probably better for increasing resolution, but hp.ud_grade is
# faster because it's just averaging/tiling instead of doing SHT's
d = lambda m: irf.harmonic_ud_grade(m, nside_in, p.nside)
J_f = (np.asarray(map(d, J_f.T))).T
# The inner transpose is so that correct dimension is map()'ed over,
# and then the outer transpose returns the array to its original shape.
J_f = irf.inverse_flatten_jones(J_f) # Change shape to (nfreq,npix,2,2), complex-valued
J_f = transform_basis(p.nside, J_f, z0_cza, R_z0) # right-multiply by the basis transformation matrix from RA/CZA to the Local CST basis.
# Note that CZA = pi/2 - Dec! So this is not quite the RA/Dec basis. But the difference
# in the Stoke parameters between the two is only U -> -U
Jdata[i,:,:,:] = J_f
print i
# If the model at the current nside hasn't been generated before, save it for future reuse.
if os.path.exists(local_jones0_file) == False:
np.save(local_jones0_file, Jdata)
return Jdata
def make_jones(freq):
if freq in range(90,221):
pass
else:
raise ValueError('Frequency is not available.')
nside = 512 # make this as large as possible to minimize singularity effects at zenith
## nside 512 seems to work well enough using the "neighbours of neighbours" patch
## of the zenith singularity in the ra/cza basis.
npix = hp.nside2npix(nside)
hpxidx = np.arange(npix)
t,p = hp.pix2ang(nside,hpxidx)
g1 = ecomp(csvname(freq,'G','X'),csvname(freq,'P','X'))
g2 = ecomp(csvname(freq,'G','Y'),csvname(freq,'P','Y'))
I = (abs(g1)**2. + abs(g2)**2.)
norm = np.sqrt(np.amax(I, axis=0))
g1 /= norm
g2 /= norm
rhm = irf.rotate_healpix_map
Rb = np.array([
[0,0,-1],
[0,-1,0],
[-1,0,0]
])
Et_b = udgrade(g1.real, nside) + 1j * udgrade(g1.imag, nside)
Ep_b = udgrade(g2.real, nside) + 1j * udgrade(g2.imag, nside)
tb,pb = irf.rotate_sphr_coords(Rb, t, p)
tb_v = irf.t_hat_cart(tb,pb)
pb_v = irf.p_hat_cart(tb,pb)
t_v = irf.t_hat_cart(t,p)
p_v = irf.p_hat_cart(t,p)
Rb_tb_v = np.einsum('ab...,b...->a...', Rb, tb_v)
Rb_pb_v = np.einsum('ab...,b...->a...', Rb, pb_v)
cosX = np.einsum('a...,a...', Rb_tb_v,t_v)
sinX = np.einsum('a...,a...', Rb_pb_v,t_v)
Et = Et_b * cosX + Ep_b * sinX
Ep = -Et_b * sinX + Ep_b * cosX
Ext = Et
Exp = Ep
## This assumes that Et and Ep are the components of a dipole oriented
## along the X axis, and we want to obtain the components of the same
## dipole if it was oriented along Y.
## In the current basis, this is done by a scalar rotation of the theta and phi
## components by 90 degrees about the Z axis.
Eyt = arm(Et.real) + 1j*arm(Et.imag)
Eyp = arm(Ep.real) + 1j*arm(Ep.imag)
jones_c = np.array([[Ext,Exp],[Eyt,Eyp]]).transpose(2,0,1)
# jones_a = np.array([[rhm(Ext,Rb), rhm(Exp,Rb)],[rhm(Eyt,Rb),rhm(Eyp,Rb)]]).transpose(2,0,1)
#
# basis_rot = np.array([[cosX,-sinX],[sinX,cosX]]).transpose(2,0,1)
#
# jones_b = np.einsum('...ab,...bc->...ac', jones_a, basis_rot)
#
# Ext_b, Exp_b, Eyt_b, Eyp_b = [rhm(jones_b[:,i,j],Rb) for i in range(2) for j in range(2)]
#
# jones_c = np.array([[Ext_b,Exp_b],[Eyt_b,Eyp_b]]).transpose(2,0,1)
return jones_c