def swhtImageCoeffs(vis, uvw, freqs, lmax, lmin=0):
"""Generate brightness coefficients by transforming visibilities with the SWHT
vis: complex array [Q, F], Q observed visibilities at F frequencies, can be size [Q] if only using 1 frequency
uvw: float array [Q, 3, F], meters, has a F frequency axis because of the time steps in LOFAR station obsevrations changes uvw with respect to the frequency
freqs: float array [F, 1] or [F], observing frequencies in Hz
lmax: positive int, maximum spherical harmonic l number
lmin: positive int, minimum spherical harmonic l number, usually 0
"""
start_time = time.time()
#single subband cases
if vis.ndim==1: vis = vis[np.newaxis].T
if uvw.ndim==2: uvw = uvw.reshape(uvw.shape[0], uvw.shape[1], 1)
if freqs.ndim==1: freqs = freqs[np.newaxis].T
k = 2. * np.pi * freqs/cc #obs freq/c
#convert u,v,w to r,phi,theta
r, phi, theta = util.cart2sph(uvw[:,0], uvw[:,1], uvw[:,2])
if r.ndim==1: #make arrays 2D
r = r[np.newaxis].T
phi = phi[np.newaxis].T
theta = theta[np.newaxis].T
phi = phi - np.pi #make range -pi to pi
theta = np.pi - theta #flip theta values
#from matplotlib import pyplot as plt
#from mpl_toolkits.mplot3d import Axes3D
#fig = plt.figure()
#ax = fig.add_subplot(111, projection='3d')
#ax.scatter(uvw[:,0], uvw[:,1], uvw[:,2], c=r, alpha=0.5, edgecolors='none')
#plt.show()
#exit()
#r = np.sqrt(uvw[:,0]**2. + uvw[:,1]**2. + uvw[:,2]**2.)[np.newaxis].T
#phi = np.arctan2(uvw[:,1], uvw[:,0])[np.newaxis].T
#theta = (np.pi/2.) - np.arctan2(uvw[:,2], np.sqrt(uvw[:,0]**2. + uvw[:,1]**2.))[np.newaxis].T #make range -pi/2 to pi/2
#compute the SWHT visibility coefficients
vislm = computeVislm(lmax, k, r, theta, phi, vis, lmin=lmin)
#compute the SWHT brightness coefficients
blm = computeblm(vislm)
print 'Run time: %f s'%(time.time() - start_time)
return blm
def swhtImageCoeffs(vis, uvw, freqs, lmax, lmin=0):
"""Generate brightness coefficients by transforming visibilities with the SWHT
vis: complex array [Q, F], Q observed visibilities at F frequencies, can be size [Q] if only using 1 frequency
uvw: float array [Q, 3, F], meters, has a F frequency axis because of the time steps in LOFAR station obsevrations changes uvw with respect to the frequency
freqs: float array [F, 1] or [F], observing frequencies in Hz
lmax: positive int, maximum spherical harmonic l number
lmin: positive int, minimum spherical harmonic l number, usually 0
"""
start_time = time.time()
#single subband cases
if vis.ndim == 1: vis = vis[np.newaxis].T
if uvw.ndim == 2: uvw = uvw.reshape(uvw.shape[0], uvw.shape[1], 1)
if freqs.ndim == 1: freqs = freqs[np.newaxis].T
k = 2. * np.pi * freqs / cc #obs freq/c
#convert u,v,w to r,phi,theta
r, phi, theta = util.cart2sph(uvw[:, 0], uvw[:, 1], uvw[:, 2])
if r.ndim == 1: #make arrays 2D
r = r[np.newaxis].T
phi = phi[np.newaxis].T
theta = theta[np.newaxis].T
phi = phi - np.pi #make range -pi to pi
theta = np.pi - theta #flip theta values
#from matplotlib import pyplot as plt
#from mpl_toolkits.mplot3d import Axes3D
#fig = plt.figure()
#ax = fig.add_subplot(111, projection='3d')
#ax.scatter(uvw[:,0], uvw[:,1], uvw[:,2], c=r, alpha=0.5, edgecolors='none')
#plt.show()
#exit()
#r = np.sqrt(uvw[:,0]**2. + uvw[:,1]**2. + uvw[:,2]**2.)[np.newaxis].T
#phi = np.arctan2(uvw[:,1], uvw[:,0])[np.newaxis].T
#theta = (np.pi/2.) - np.arctan2(uvw[:,2], np.sqrt(uvw[:,0]**2. + uvw[:,1]**2.))[np.newaxis].T #make range -pi/2 to pi/2
#compute the SWHT visibility coefficients
vislm = computeVislm(lmax, k, r, theta, phi, vis, lmin=lmin)
#compute the SWHT brightness coefficients
blm = computeblm(vislm)
print 'Run time: %f s' % (time.time() - start_time)
return blm
def iswhtVisibilities(blm, uvw, freqs):
"""Generate visibilities by inverse transforming brightness coefficients with the iSWHT
blm: [LMAX+1, 2*LMAX + 1] array, brightness coefficients
uvw: float array [Q, 3, F], meters, has a F frequency axis because of the time steps in LOFAR station obsevrations changes uvw with respect to the frequency
freqs: float array [F, 1] or [F], observing frequencies in Hz
"""
start_time = time.time()
#Convert brightness coefficients into visibility coefficients
vislm = computeblm(blm, reverse=True)
#single subband cases
if uvw.ndim==2: uvw = uvw.reshape(uvw.shape[0], uvw.shape[1], 1)
if freqs.ndim==1: freqs = freqs[np.newaxis].T
k = 2. * np.pi * freqs/cc #obs freq/c
#from matplotlib import pyplot as plt
#from mpl_toolkits.mplot3d import Axes3D
#fig = plt.figure()
#ax = fig.add_subplot(111, projection='3d')
#ax.scatter(uvw[:,0], uvw[:,1], uvw[:,2])
#plt.show()
#exit()
#convert u,v,w to r,phi,theta
r, phi, theta = util.cart2sph(uvw[:,0], uvw[:,1], uvw[:,2])
if r.ndim==1: #make arrays 2D
r = r[np.newaxis].T
phi = phi[np.newaxis].T
theta = theta[np.newaxis].T
phi = phi - np.pi #make range -pi to pi
theta = np.pi - theta #flip theta values
#compute visibilities
vis = computeVisSamples(vislm, k, r, theta, phi)
print 'Run time: %f s'%(time.time() - start_time)
return vis
def iswhtVisibilities(blm, uvw, freqs):
"""Generate visibilities by inverse transforming brightness coefficients with the iSWHT
blm: [LMAX+1, 2*LMAX + 1] array, brightness coefficients
uvw: float array [Q, 3, F], meters, has a F frequency axis because of the time steps in LOFAR station obsevrations changes uvw with respect to the frequency
freqs: float array [F, 1] or [F], observing frequencies in Hz
"""
start_time = time.time()
#Convert brightness coefficients into visibility coefficients
vislm = computeblm(blm, reverse=True)
#single subband cases
if uvw.ndim == 2: uvw = uvw.reshape(uvw.shape[0], uvw.shape[1], 1)
if freqs.ndim == 1: freqs = freqs[np.newaxis].T
k = 2. * np.pi * freqs / cc #obs freq/c
#from matplotlib import pyplot as plt
#from mpl_toolkits.mplot3d import Axes3D
#fig = plt.figure()
#ax = fig.add_subplot(111, projection='3d')
#ax.scatter(uvw[:,0], uvw[:,1], uvw[:,2])
#plt.show()
#exit()
#convert u,v,w to r,phi,theta
r, phi, theta = util.cart2sph(uvw[:, 0], uvw[:, 1], uvw[:, 2])
if r.ndim == 1: #make arrays 2D
r = r[np.newaxis].T
phi = phi[np.newaxis].T
theta = theta[np.newaxis].T
phi = phi - np.pi #make range -pi to pi
theta = np.pi - theta #flip theta values
#compute visibilities
vis = computeVisSamples(vislm, k, r, theta, phi)
print 'Run time: %f s' % (time.time() - start_time)
return vis
def make2Dimage(coeffs, res, px=[64, 64], phs=[0., 0.]):
"""Make a flat image of a single hemisphere from SWHT image coefficients
coeffs: SWHT brightness coefficients
px: [int, int], number of pixels, note these are equivalent to the l,m coordinates in FT imaging
res: float, resolution of the central pixel in radians
phs: [float, float], RA and Dec (radians) position at the center of the image
"""
start_time = time.time()
#start from a regular Cartesian grid
lrange = np.linspace(-1.*px[0]*res/2., px[0]*res/2., num=px[0], endpoint=True)/(np.pi/2.) #m range (-1,1)
mrange = np.linspace(-1.*px[1]*res/2., px[1]*res/2., num=px[1], endpoint=True)/(np.pi/2.) #l range (-1,1)
xx,yy = np.meshgrid(lrange, mrange)
#xx,yy = np.meshgrid(np.linspace(-1., 1., num=px[0]), np.linspace(-1., 1., num=px[1])) #Full hemisphere, no FoV control
img = np.zeros(xx.shape, dtype='complex')
#convert to polar positions
r = np.sqrt(xx**2. + yy**2.)
phi = np.arctan2(yy, xx)
# zero out undefined regions of the image where r>0
# overly tedious steps for something that should be much easier to do
rflat = r.flatten()
phiflat = phi.flatten()
maxRcond = r.flatten() > 1
idx = np.argwhere(maxRcond)
rflat[idx] = 0.
phiflat[idx] = 0.
r = np.reshape(rflat, r.shape)
phi = np.reshape(phiflat, phi.shape)
#convert to unit sphere coordinates
thetap = np.arccos(r) - np.pi/2. #north pole is at 0 in spherical coordinates
phip = np.pi - phi #azimuth range [-pi, pi] -> [2pi, 0]
#Determine the theta, phi coordinates for a hemisphere at the snapshot zenith
X, Y, Z = util.sph2cart(thetap, phip)
ra = phs[0]
raRotation = np.array([[np.cos(ra), -1.*np.sin(ra), 0.],
[np.sin(ra), np.cos(ra), 0.],
[ 0., 0., 1.]]) #rotate about the z-axis
dec = np.pi - phs[1] #adjust relative to the north pole at -pi/2
print 'dec', dec, 'phs', phs[1]
# TODO: might need to do a transpose to apply the inverse rotation
decRotation = np.array([[1.,0.,0.],
[0., np.cos(dec), -1.*np.sin(dec)],
[0., np.sin(dec), np.cos(dec)]]) #rotate about the x-axis
XYZ = np.vstack((X.flatten(), Y.flatten(), Z.flatten()))
rotMatrix = np.dot(decRotation, raRotation)
XYZ0 = np.dot(rotMatrix, XYZ) #order of rotation is important
#XYZ0 = np.dot(np.dot(raRotation, decRotation), XYZ) #order of rotation is important
r0, phi0, theta0 = util.cart2sph(XYZ0[0,:], XYZ0[1,:], XYZ0[2,:])
r0 = r0.reshape(thetap.shape) #not used, should all be nearly 1
phi0 = phi0.reshape(thetap.shape) #rotated phi values
theta0 = theta0.reshape(thetap.shape) #rotated theta values
lmax = coeffs.shape[0]
print 'L:',
for l in np.arange(lmax):
print l,
sys.stdout.flush()
for m in np.arange(-1*l, l+1):
img += coeffs[l, l+m] * Ylm.Ylm(l, m, phi0, theta0) #TODO: a slow call
print 'done'
print 'Run time: %f s'%(time.time() - start_time)
return np.ma.array(img, mask=maxRcond)
def make2Dimage(coeffs, res, px=[64, 64], phs=[0., 0.]):
"""Make a flat image of a single hemisphere from SWHT image coefficients
coeffs: SWHT brightness coefficients
px: [int, int], number of pixels, note these are equivalent to the l,m coordinates in FT imaging
res: float, resolution of the central pixel in radians
phs: [float, float], RA and Dec (radians) position at the center of the image
"""
start_time = time.time()
#start from a regular Cartesian grid
lrange = np.linspace(
-1. * px[0] * res / 2., px[0] * res / 2., num=px[0], endpoint=True) / (
np.pi / 2.) #m range (-1,1)
mrange = np.linspace(
-1. * px[1] * res / 2., px[1] * res / 2., num=px[1], endpoint=True) / (
np.pi / 2.) #l range (-1,1)
xx, yy = np.meshgrid(lrange, mrange)
#xx,yy = np.meshgrid(np.linspace(-1., 1., num=px[0]), np.linspace(-1., 1., num=px[1])) #Full hemisphere, no FoV control
img = np.zeros(xx.shape, dtype='complex')
#convert to polar positions
r = np.sqrt(xx**2. + yy**2.)
phi = np.arctan2(yy, xx)
# zero out undefined regions of the image where r>0
# overly tedious steps for something that should be much easier to do
rflat = r.flatten()
phiflat = phi.flatten()
maxRcond = r.flatten() > 1
idx = np.argwhere(maxRcond)
rflat[idx] = 0.
phiflat[idx] = 0.
r = np.reshape(rflat, r.shape)
phi = np.reshape(phiflat, phi.shape)
#convert to unit sphere coordinates
thetap = np.arccos(
r) - np.pi / 2. #north pole is at 0 in spherical coordinates
phip = np.pi - phi #azimuth range [-pi, pi] -> [2pi, 0]
#Determine the theta, phi coordinates for a hemisphere at the snapshot zenith
X, Y, Z = util.sph2cart(thetap, phip)
ra = phs[0]
raRotation = np.array([[np.cos(ra), -1. * np.sin(ra), 0.],
[np.sin(ra), np.cos(ra), 0.],
[0., 0., 1.]]) #rotate about the z-axis
dec = np.pi - phs[1] #adjust relative to the north pole at -pi/2
print 'dec', dec, 'phs', phs[1]
# TODO: might need to do a transpose to apply the inverse rotation
decRotation = np.array([[1., 0., 0.], [0.,
np.cos(dec), -1. * np.sin(dec)],
[0., np.sin(dec),
np.cos(dec)]]) #rotate about the x-axis
XYZ = np.vstack((X.flatten(), Y.flatten(), Z.flatten()))
rotMatrix = np.dot(decRotation, raRotation)
XYZ0 = np.dot(rotMatrix, XYZ) #order of rotation is important
#XYZ0 = np.dot(np.dot(raRotation, decRotation), XYZ) #order of rotation is important
r0, phi0, theta0 = util.cart2sph(XYZ0[0, :], XYZ0[1, :], XYZ0[2, :])
r0 = r0.reshape(thetap.shape) #not used, should all be nearly 1
phi0 = phi0.reshape(thetap.shape) #rotated phi values
theta0 = theta0.reshape(thetap.shape) #rotated theta values
lmax = coeffs.shape[0]
print 'L:',
for l in np.arange(lmax):
print l,
sys.stdout.flush()
for m in np.arange(-1 * l, l + 1):
img += coeffs[l, l + m] * Ylm.Ylm(l, m, phi0,
theta0) #TODO: a slow call
print 'done'
print 'Run time: %f s' % (time.time() - start_time)
return np.ma.array(img, mask=maxRcond)
