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 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):
"""
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 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 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