def disp3D(img, phi, theta, dmode='abs', cmap='jet'):
"""Display 3D, equal in phi and theta (Driscoll and Healy mapping) image
img: 2D array of complex flux values
phi: 2D array of phi values
theta: 2D array of theta values
img, phi, theta are of the same shape, they are the output of swht.make3Dimage()
dmode: string, data mode (abs, real, imaginary, phase)
cmap: string, matplotlib colormap name
"""
if dmode.startswith('abs'): img = np.abs(img)
elif dmode.startswith('real'): img = img.real
elif dmode.startswith('imag'): img = img.imag
elif dmode.startswith('phase'): img = np.angle(img)
else:
print 'WARNING: Unknown data mode, defaulting to absolute value'
img = np.abs(img)
#X = np.cos(theta-(np.pi/2.)) * np.cos(phi)
#Y = np.cos(theta-(np.pi/2.)) * np.sin(phi)
#Z = np.sin(theta-(np.pi/2.))
X, Y, Z = util.sph2cart(theta, phi)
# North-South Flip
#Z *= -1.
#http://stackoverflow.com/questions/22175533/what-is-the-equivalent-of-matlabs-surfx-y-z-c-in-matplotlib
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.colors import Normalize
fig = plt.figure(figsize=(10, 8))
ax = fig.gca(projection='3d')
imin = img.min()
imax = img.max()
scalarMap = cm.ScalarMappable(norm=Normalize(vmin=imin, vmax=imax),
cmap=plt.get_cmap(cmap))
#scalarMap = cm.ScalarMappable(norm=Normalize(vmin=imin, vmax=imax), cmap=cm.jet)
#scalarMap = cm.ScalarMappable(norm=Normalize(vmin=imin, vmax=imax), cmap=cm.gist_earth_r)
scalarMap.set_array(img)
C = scalarMap.to_rgba(img)
surf = ax.plot_surface(X,
Y,
Z,
rstride=1,
cstride=1,
facecolors=C,
antialiased=True,
linewidth=1)
#wire = ax.plot_wireframe(1.01*X, 1.01*Y, 1.01*Z, rstride=5, cstride=5, color='black') # RA/Dec grid
fig.colorbar(scalarMap, shrink=0.7)
ax.set_axis_off()
ax.set_xlim(-0.75, 0.75)
ax.set_ylim(-0.75, 0.75)
ax.set_zlim(-0.75, 0.75)
ax.set_aspect('auto')
return fig, ax
def disp3D(img, phi, theta, dmode='abs', cmap='jet'):
"""Display 3D, equal in phi and theta (Driscoll and Healy mapping) image
img: 2D array of complex flux values
phi: 2D array of phi values
theta: 2D array of theta values
img, phi, theta are of the same shape, they are the output of swht.make3Dimage()
dmode: string, data mode (abs, real, imaginary, phase)
cmap: string, matplotlib colormap name
"""
if dmode.startswith('abs'): img = np.abs(img)
elif dmode.startswith('real'): img = img.real
elif dmode.startswith('imag'): img = img.imag
elif dmode.startswith('phase'): img = np.angle(img)
else:
print 'WARNING: Unknown data mode, defaulting to absolute value'
img = np.abs(img)
#X = np.cos(theta-(np.pi/2.)) * np.cos(phi)
#Y = np.cos(theta-(np.pi/2.)) * np.sin(phi)
#Z = np.sin(theta-(np.pi/2.))
X, Y, Z = util.sph2cart(theta, phi)
# North-South Flip
#Z *= -1.
#http://stackoverflow.com/questions/22175533/what-is-the-equivalent-of-matlabs-surfx-y-z-c-in-matplotlib
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.colors import Normalize
fig = plt.figure()
ax = fig.gca(projection='3d')
imin = img.min()
imax = img.max()
scalarMap = cm.ScalarMappable(norm=Normalize(vmin=imin, vmax=imax), cmap=plt.get_cmap(cmap))
#scalarMap = cm.ScalarMappable(norm=Normalize(vmin=imin, vmax=imax), cmap=cm.jet)
#scalarMap = cm.ScalarMappable(norm=Normalize(vmin=imin, vmax=imax), cmap=cm.gist_earth_r)
scalarMap.set_array(img)
C = scalarMap.to_rgba(img)
surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, facecolors=C, antialiased=True)
#wire = ax.plot_wireframe(1.05*X, 1.05*Y, 1.05*Z, rstride=10, cstride=10, color='black') # RA/Dec grid
fig.colorbar(scalarMap)
return fig, ax
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)
