def plotRandomization():
#number of random points
points = 1000
# get the random values
rds = rand.randomUnitSphere(points)
# convert them to Cartesian coord
rd = conv.convertSphericalToCartesian(1,
rds['theta'],
rds['phi'])
#set figure limits
min = -1.3
max = 1.3
#make a figure
fig = plt.figure()
ax = Axes3D(fig)
#generate a sphere
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
x = np.outer(np.cos(u), np.sin(v))
y = np.outer(np.sin(u), np.sin(v))
z = np.outer(np.ones(np.size(u)), np.cos(v))
#plot it as a wire frame
ax.plot_wireframe(x, y, z,
rstride=4,
cstride=4,
color='k')
#plot the random points
ax.scatter(rd['x'], rd['y'], rd['z'],
color='red')
#project them on the bottom
ax.scatter(rd['x'], rd['y'],
zs=min, zdir='z')
#project them on the left
ax.scatter(rd['y'], rd['z'],
min, zdir='x')
ax.set_xlim3d(min, max)
ax.set_ylim3d(min, max)
ax.set_zlim3d(min, max)
plt.savefig('RandomTest1.pdf')
def plotRandomization():
#number of random points
points = 1000
# get the random values
rds = rand.randomUnitSphere(points)
# convert them to Cartesian coord
rd = conv.convertSphericalToCartesian(1, rds['theta'], rds['phi'])
#set figure limits
min = -1.3
max = 1.3
#make a figure
fig = plt.figure()
ax = Axes3D(fig)
#generate a sphere
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
x = np.outer(np.cos(u), np.sin(v))
y = np.outer(np.sin(u), np.sin(v))
z = np.outer(np.ones(np.size(u)), np.cos(v))
#plot it as a wire frame
ax.plot_wireframe(x, y, z, rstride=4, cstride=4, color='k')
#plot the random points
ax.scatter(rd['x'], rd['y'], rd['z'], color='red')
#project them on the bottom
ax.scatter(rd['x'], rd['y'], zs=min, zdir='z')
#project them on the left
ax.scatter(rd['y'], rd['z'], min, zdir='x')
ax.set_xlim3d(min, max)
ax.set_ylim3d(min, max)
ax.set_zlim3d(min, max)
plt.savefig('RandomTest1.pdf')
def quickPlot(galaxies=170, rvir=0.105):
"""
A single halo test
:param galaxies: number of subhalo galaxies
:param rvir: radius of the main halo [Mpc]
"""
conversion = 0.000277777778 # degree to arcsecond
#redshift
z = 4.477
#get the angular diameter distance to the galaxy
dd = cosmocalc(z, 71.0, 0.28)['PS_kpc'] #in kpc / arc seconds
#position of the main galaxy
RADeg1 = 189.41432
decDeg1 = 62.166702
# get the random values
rds = rand.randomUnitSphere(galaxies)
# convert them to Cartesian coord
rd = conv.convertSphericalToCartesian(rvir / dd / 2., rds['theta'],
rds['phi'])
data = {
'CD': np.matrix('-1 0; 0 1'),
'RA': RADeg1,
'DEC': decDeg1,
'X': rd['y'],
'Y': rd['z']
}
result = conv.RAandDECfromStandardCoordinates(data)
RADeg2 = result['RA']
decDeg2 = result['DEC']
#calculate the angular separation on the sky
sep = Coords.calcAngSepDeg(RADeg1, decDeg1, RADeg2, decDeg2) / 2.
physical_distance = sep * dd / conversion
text = r'Random Positions, z={0:.2f}, radius of the halo = {1:.0f} kpc'.format(
z, 1e3 * rvir)
#make a figure
fig = plt.figure(figsize=(12, 12))
ax1 = fig.add_subplot(221)
ax2 = fig.add_subplot(222)
ax3 = fig.add_subplot(223)
rect = fig.add_subplot(224, visible=False).get_position()
ax4 = Axes3D(fig, rect)
ax1.hist(sep * 1e4, bins=12)
ax2.hist(physical_distance, bins=12)
ax3.scatter(0, 0, c='k', s=120, marker='s')
ax3.scatter((RADeg2 - RADeg1) * 1e4, (decDeg2 - decDeg1) * 1e4,
c='b',
s=50,
marker='o',
alpha=0.45)
#generate a sphere
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
x = np.outer(np.cos(u), np.sin(v))
y = np.outer(np.sin(u), np.sin(v))
z = np.outer(np.ones(np.size(u)), np.cos(v))
#plot it as a wire frame
ax4.plot_wireframe(x * 1e4 * rvir / dd,
y * 1e4 * rvir / dd,
z * 1e4 * rvir / dd,
rstride=10,
cstride=10,
color='0.5',
alpha=0.7)
#plot the random points
ax4.scatter(rd['x'] * 2e4,
rd['y'] * 2e4,
rd['z'] * 2e4,
color='b',
s=30,
alpha=0.8)
ax1.set_xlabel(r'Projected Separation [$10^{-4}$ deg]')
ax2.set_xlabel(r'Projected Distance [kpc]')
ax3.set_xlabel(r'$\Delta$RA [$10^{-4}$ deg]')
#ax4.set_xlabel(r'$\Delta$RA [$10^{-4}$ deg]')
ax3.set_ylabel(r'$\Delta$DEC [$10^{-4}$ deg]')
#ax4.set_ylabel(r'$\Delta$DEC [$10^{-4}$ deg]')
ax3.set_xlim(-200, 200)
ax3.set_ylim(-100, 100)
ax4.set_xlim3d(-150, 150)
ax4.set_ylim3d(-150, 150)
ax4.set_zlim3d(-150, 150)
plt.annotate(text, (0.5, 0.95),
xycoords='figure fraction',
ha='center',
va='center',
fontsize=12)
plt.savefig('RandomHalo.pdf')
def testRandomizer():
#calculate a test case
conversion = 0.000277777778 # degree to arcsecond
#random distance between z = 0 and 5
z = np.random.rand() * 5.0
#random separation of the main galaxy and the subhalo
physical_distance = np.random.rand() * 1e3 #in kpc
#get the angular diameter distance to the galaxy
dd1 = cosmocalc(z, 71.0, 0.28)['PS_kpc'] #in kpc / arc seconds
dd = (physical_distance / dd1) * conversion # to degrees
# RA and DEC of the main galaxy, first one in GOODS south
ra_main = 52.904892 #in degrees
dec_main = -27.757082 #in degrees
# get the random position
rds = rand.randomUnitSphere(points=1)
# convert the position to Cartesian coord
# when dd is the radius of the sphere coordinates
# the dd is in units of degrees here so the results
# are also in degrees.
rd = conv.convertSphericalToCartesian(dd, rds['theta'], rds['phi'])
# Make the assumption that x is towards the observer
# z is north and y is west. Now if we assume that our z and y
# are Standard Coordinates, i.e., the projection of the RA and DEC
# of an object onto the tangent plane of the sky. We can now
# assume that the y coordinate is aligned with RA and the z coordinate
# is aligned with DEC. The origin of this system is at the tangent point
# in the dark matter halo.
# Poor man's solution to the problem would be:
new_ra = ra_main - (rd['y'][0] / np.cos(rd['z'][0]))
new_dec = dec_main + rd['z'][0]
# However, this only works if one is away from the pole.
# More general solution can be derived using spherical geometry:
data = {}
data['CD'] = np.matrix('-1 0; 0 1')
data['RA'] = ra_main
data['DEC'] = dec_main
data['X'] = rd['y'][0]
data['Y'] = rd['z'][0]
result = conv.RAandDECfromStandardCoordinates(data)
#print the output
print 'Redshift of the galaxy is %.3f while the subhaloes distance is %0.2f kpc' % (
z, physical_distance)
print '\nCoordinates of the main halo galaxy are (RA and DEC):'
print '%.7f %.7f' % (ra_main, dec_main)
print astCoords.decimal2hms(ra_main,
':'), astCoords.decimal2dms(dec_main, ':')
print '\nCoordinates for the subhalo galaxy are (RA and DEC):'
print '%.7f %.7f' % (new_ra, new_dec)
print astCoords.decimal2hms(new_ra,
':'), astCoords.decimal2dms(new_dec, ':')
print 'or when using more accurate technique'
print '%.7f %.7f' % (result['RA'], result['DEC'])
print astCoords.decimal2hms(result['RA'], ':'), astCoords.decimal2dms(
result['DEC'], ':')
#print 'Shift in RA and DEC [degrees]:'
#print rd['y'][0], (rd['z'][0]/np.cos(rd['z'][0]))
print '\nShift in RA and DEC [seconds]:'
print -rd['y'][0] / np.cos(
rd['z'][0]) / conversion, rd['z'][0] / conversion
print 'or again with the better method:'
print(result['RA'] - ra_main) / conversion, (result['DEC'] -
dec_main) / conversion
def quickPlot(galaxies=170, rvir=0.105):
"""
A single halo test
:param galaxies: number of subhalo galaxies
:param rvir: radius of the main halo [Mpc]
"""
conversion = 0.000277777778 # degree to arcsecond
#redshift
z = 4.477
#get the angular diameter distance to the galaxy
dd = cosmocalc(z, 71.0, 0.28)['PS_kpc'] #in kpc / arc seconds
#position of the main galaxy
RADeg1 = 189.41432
decDeg1 = 62.166702
# get the random values
rds = rand.randomUnitSphere(galaxies)
# convert them to Cartesian coord
rd = conv.convertSphericalToCartesian(rvir/dd/2., rds['theta'], rds['phi'])
data = {'CD': np.matrix('-1 0; 0 1'), 'RA': RADeg1, 'DEC': decDeg1, 'X': rd['y'], 'Y': rd['z']}
result = conv.RAandDECfromStandardCoordinates(data)
RADeg2 = result['RA']
decDeg2 = result['DEC']
#calculate the angular separation on the sky
sep = Coords.calcAngSepDeg(RADeg1, decDeg1, RADeg2, decDeg2) / 2.
physical_distance = sep * dd / conversion
text = r'Random Positions, z={0:.2f}, radius of the halo = {1:.0f} kpc'.format(z, 1e3 * rvir)
#make a figure
fig = plt.figure(figsize=(12,12))
ax1 = fig.add_subplot(221)
ax2 = fig.add_subplot(222)
ax3 = fig.add_subplot(223)
rect = fig.add_subplot(224, visible=False).get_position()
ax4 = Axes3D(fig, rect)
ax1.hist(sep * 1e4, bins=12)
ax2.hist(physical_distance, bins=12)
ax3.scatter(0, 0, c='k', s=120, marker='s')
ax3.scatter((RADeg2 - RADeg1) * 1e4, (decDeg2 - decDeg1) * 1e4, c='b', s=50, marker='o', alpha=0.45)
#generate a sphere
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
x = np.outer(np.cos(u), np.sin(v))
y = np.outer(np.sin(u), np.sin(v))
z = np.outer(np.ones(np.size(u)), np.cos(v))
#plot it as a wire frame
ax4.plot_wireframe(x*1e4*rvir/dd, y*1e4*rvir/dd, z*1e4*rvir/dd,
rstride=10, cstride=10, color='0.5', alpha=0.7)
#plot the random points
ax4.scatter(rd['x']*2e4, rd['y']*2e4, rd['z']*2e4, color='b', s=30, alpha=0.8)
ax1.set_xlabel(r'Projected Separation [$10^{-4}$ deg]')
ax2.set_xlabel(r'Projected Distance [kpc]')
ax3.set_xlabel(r'$\Delta$RA [$10^{-4}$ deg]')
#ax4.set_xlabel(r'$\Delta$RA [$10^{-4}$ deg]')
ax3.set_ylabel(r'$\Delta$DEC [$10^{-4}$ deg]')
#ax4.set_ylabel(r'$\Delta$DEC [$10^{-4}$ deg]')
ax3.set_xlim(-200, 200)
ax3.set_ylim(-100, 100)
ax4.set_xlim3d(-150, 150)
ax4.set_ylim3d(-150, 150)
ax4.set_zlim3d(-150, 150)
plt.annotate(text, (0.5, 0.95), xycoords='figure fraction', ha='center', va='center', fontsize=12)
plt.savefig('RandomHalo.pdf')
def testRandomizer():
#calculate a test case
conversion = 0.000277777778 # degree to arcsecond
#random distance between z = 0 and 5
z = np.random.rand() * 5.0
#random separation of the main galaxy and the subhalo
physical_distance = np.random.rand() * 1e3 #in kpc
#get the angular diameter distance to the galaxy
dd1 = cosmocalc(z, 71.0, 0.28)['PS_kpc'] #in kpc / arc seconds
dd = (physical_distance / dd1) * conversion # to degrees
# RA and DEC of the main galaxy, first one in GOODS south
ra_main = 52.904892 #in degrees
dec_main = -27.757082 #in degrees
# get the random position
rds = rand.randomUnitSphere(points=1)
# convert the position to Cartesian coord
# when dd is the radius of the sphere coordinates
# the dd is in units of degrees here so the results
# are also in degrees.
rd = conv.convertSphericalToCartesian(dd,
rds['theta'],
rds['phi'])
# Make the assumption that x is towards the observer
# z is north and y is west. Now if we assume that our z and y
# are Standard Coordinates, i.e., the projection of the RA and DEC
# of an object onto the tangent plane of the sky. We can now
# assume that the y coordinate is aligned with RA and the z coordinate
# is aligned with DEC. The origin of this system is at the tangent point
# in the dark matter halo.
# Poor man's solution to the problem would be:
new_ra = ra_main - (rd['y'][0] / np.cos(rd['z'][0]))
new_dec = dec_main + rd['z'][0]
# However, this only works if one is away from the pole.
# More general solution can be derived using spherical geometry:
data = {}
data['CD'] = np.matrix('-1 0; 0 1')
data['RA'] = ra_main
data['DEC'] = dec_main
data['X'] = rd['y'][0]
data['Y'] = rd['z'][0]
result = conv.RAandDECfromStandardCoordinates(data)
#print the output
print 'Redshift of the galaxy is %.3f while the subhaloes distance is %0.2f kpc' % (z, physical_distance)
print '\nCoordinates of the main halo galaxy are (RA and DEC):'
print '%.7f %.7f' % (ra_main, dec_main)
print astCoords.decimal2hms(ra_main, ':'), astCoords.decimal2dms(dec_main, ':')
print '\nCoordinates for the subhalo galaxy are (RA and DEC):'
print '%.7f %.7f' % (new_ra, new_dec)
print astCoords.decimal2hms(new_ra, ':'), astCoords.decimal2dms(new_dec, ':')
print 'or when using more accurate technique'
print '%.7f %.7f' % (result['RA'], result['DEC'])
print astCoords.decimal2hms(result['RA'], ':'), astCoords.decimal2dms(result['DEC'], ':')
#print 'Shift in RA and DEC [degrees]:'
#print rd['y'][0], (rd['z'][0]/np.cos(rd['z'][0]))
print '\nShift in RA and DEC [seconds]:'
print -rd['y'][0] / np.cos(rd['z'][0]) / conversion, rd['z'][0] / conversion
print 'or again with the better method:'
print (result['RA'] - ra_main) / conversion, (result['DEC'] - dec_main) / conversion