def psf_select(alpha_j, delta_j):
distance = 9999.0
psffile = 'test.fits'
psflist = c.psflist
r = 3.14159265 / 180.0
for element in psflist:
p=pyfits.open(element)
header = p[0].header
if (header.has_key('RA_TARG')):
ra = header['RA_TARG']
if (header.has_key('DEC_TARG')):
dec= header['DEC_TARG']
p.close()
# d = sqrt((ra - alpha_j) ** 2.0 + (dec - delta_j) ** 2.0)
d = n.arccos(n.cos((90.0 - delta_j) * r) * n.cos((90.0 - dec) *\
r) + n.sin((90.0 - delta_j) * r) * n.sin((90.0 - dec) * r) * \
n.cos((alpha_j - ra) * r))
if(d < distance):
psffile = element
distance = d
return psffile, distance
def getAngle(self, other):
distance = dot(self.array, other.array)
cosine = distance / (self.getNorm() * other.getNorm())
angle = arccos(cosine)
return angle
def run():
# Assume circular orbits with isotropic normal vectors on circular
# orbits with circular orbital velocity of 500 km/s.
ntrials = 10000
nstars = int((1.0 / 3.0) * 100)
gens = aorb.create_generators(7, ntrials*10)
velTot = 500.0 # km/s -- velocity amplitude
radTot = 2.04 # arcsec
def fitfunc(p, fjac=None, vx=None, vy=None, vz=None,
vxerr=None, vyerr=None, vzerr=None):
irad = math.radians(p[0])
orad = math.radians(p[1])
nx = math.sin(irad) * math.cos(orad)
ny = -math.sin(irad) * math.sin(orad)
nz = -math.cos(irad)
top = (nx*vx + ny*vy + nz*vz)**2
bot = (nx*vxerr + ny*vyerr + nz*vzerr)**2
devs = (1.0 / (len(vx) - 1.0)) * top / bot
status = 0
return [status, devs.flat]
# Keep track from every trial the incl, omeg, chi2, number of stars
incl = na.zeros(ntrials, type=na.Float)
omeg = na.zeros(ntrials, type=na.Float)
chi2 = na.zeros(ntrials, type=na.Float)
niter = na.zeros(ntrials)
stars = na.zeros(ntrials)
# Keep track of same stuff for spatial test
inclPos = na.zeros(ntrials, type=na.Float)
omegPos = na.zeros(ntrials, type=na.Float)
chi2Pos = na.zeros(ntrials, type=na.Float)
niterPos = na.zeros(ntrials)
angleAvg = na.zeros(ntrials, type=na.Float)
angleStd = na.zeros(ntrials, type=na.Float)
for trial in range(ntrials):
if ((trial % 100) == 0):
print 'Trial %d' % trial
x = na.zeros(nstars, type=na.Float)
y = na.zeros(nstars, type=na.Float)
z = na.zeros(nstars, type=na.Float)
vx = na.zeros(nstars, type=na.Float)
vy = na.zeros(nstars, type=na.Float)
vz = na.zeros(nstars, type=na.Float)
rmag = na.zeros(nstars, type=na.Float)
vmag = na.zeros(nstars, type=na.Float)
nx = na.zeros(nstars, type=na.Float)
ny = na.zeros(nstars, type=na.Float)
nz = na.zeros(nstars, type=na.Float)
for ss in range(nstars):
vx[ss] = gens[0].uniform(-velTot, velTot)
vyTot = math.sqrt(velTot**2 - vx[ss]**2)
vy[ss] = gens[1].uniform(-vyTot, vyTot)
vz[ss] = math.sqrt(velTot**2 - vx[ss]**2 - vy[ss]**2)
vz[ss] *= gens[2].choice([-1.0, 1.0])
x[ss] = gens[3].uniform(-radTot, radTot)
yTot = math.sqrt(radTot**2 - x[ss]**2)
y[ss] = gens[4].uniform(-yTot, yTot)
z[ss] = math.sqrt(radTot**2 - x[ss]**2 - y[ss]**2)
z[ss] *= gens[5].choice([-1.0, 1.0])
rmag[ss] = math.sqrt(x[ss]**2 + y[ss]**2 + z[ss]**2)
vmag[ss] = math.sqrt(vx[ss]**2 + vy[ss]**2 + vz[ss]**2)
rvec = [x[ss], y[ss], z[ss]]
vvec = [vx[ss], vy[ss], vz[ss]]
tmp = util.cross_product(rvec, vvec)
tmp /= rmag[ss] * vmag[ss]
nx[ss] = tmp[0]
ny[ss] = tmp[1]
nz[ss] = tmp[2]
r2d = na.hypot(x, y)
v2d = na.hypot(vx, vy)
top = (x * vy - y * vx)
jz = (x * vy - y * vx) / (r2d * v2d)
djzdx = (vy * r2d * v2d - (top * v2d * x / r2d)) / (r2d * v2d)**2
djzdy = (-vx * r2d * v2d - (top * v2d * y / r2d)) / (r2d * v2d)**2
djzdvx = (-y * r2d * v2d - (top * r2d * vx / v2d)) / (r2d * v2d)**2
djzdvy = (x * r2d * v2d - (top * r2d * vy / v2d)) / (r2d * v2d)**2
xerr = na.zeros(nstars, type=na.Float) + 0.001 # arcsec
yerr = na.zeros(nstars, type=na.Float) + 0.001
vxerr = na.zeros(nstars, type=na.Float) + 10.0 # km/s
vyerr = na.zeros(nstars, type=na.Float) + 10.0
vzerr = na.zeros(nstars, type=na.Float) + 30.0 # km/s
jzerr = na.sqrt((djzdx*xerr)**2 + (djzdy*yerr)**2 +
(djzdvx*vxerr)**2 + (djzdvy*vyerr)**2)
# Eliminate all stars with jz > 0 and jz/jzerr < 2
# I think these are they cuts they are doing
idx = (na.where((jz < 0) & (na.abs(jz/jzerr) > 2)))[0]
#idx = (na.where(jz < 0))[0]
#idx = range(len(jz))
cotTheta = vz / na.sqrt(vx**2 + vy**2)
phi = na.arctan2(vy, vx)
# Initial guess:
p0 = na.zeros(2, type=na.Float)
p0[0] = gens[5].uniform(0.1, 90) # deg -- inclination
p0[1] = gens[6].uniform(0.1, 360) # deg -- omega
# Setup properties of each free parameter.
parinfo = {'relStep':10.0, 'step':10.0, 'fixed':0,
'limits':[0.0,360.0],
'limited':[1,1], 'mpside':1}
pinfo = [parinfo.copy() for i in range(len(p0))]
pinfo[0]['limits'] = [0.0, 180.0]
pinfo[1]['limits'] = [0.0, 360.0]
# Stuff to pass into the fit function
functargs = {'vx': vx[idx], 'vy': vy[idx], 'vz': vz[idx],
'vxerr':vxerr[idx], 'vyerr':vyerr[idx], 'vzerr':vzerr[idx]}
m = mpfit.mpfit(fitfunc, p0, functkw=functargs, parinfo=pinfo,
quiet=1)
if (m.status <= 0):
print 'error message = ', m.errmsg
p = m.params
incl[trial] = p[0]
omeg[trial] = p[1]
stars[trial] = len(idx)
chi2[trial] = m.fnorm / (stars[trial] - len(p0))
niter[trial] = m.niter
n = [math.sin(p[0]) * math.cos(p[1]),
-math.sin(p[0]) * math.sin(p[1]),
-math.cos(p[0])]
# Now look at the angle between the best fit normal vector
# from the velocity data and the true r cross v normal vector.
# Take the dot product between n and nreal.
angle = na.arccos(n[0]*nx + n[1]*ny + n[2]*nz)
angle *= (180.0 / math.pi)
# What is the average angle and std angle
angleAvg[trial] = angle.mean()
angleStd[trial] = angle.stddev()
# print chi2[trial], chi2Pos[trial], incl[trial], inclPos[trial], \
# omeg[trial], omegPos[trial], niter[trial], niterPos[trial]
# print angleAvg[trial], angleStd[trial]
# Plot up chi2 for v-fit vs. chi2 for x-fit
pylab.clf()
pylab.semilogx(chi2, angleAvg, 'k.')
pylab.errorbar(chi2, angleAvg, fmt='k.', yerr=angleStd)
pylab.xlabel('Chi^2')
pylab.ylabel('Angle w.r.t. Best Fit')
foo = raw_input('Contine?')
# Probability of encountering solution with chi^2 < 2
idx = (na.where(chi2 < 2.0))[0]
print 'Prob(chi^2 < 2) = %5.3f ' % (len(idx) / float(ntrials))
# Probability of encountering solution with chi^2 < 2 AND
# inclination = 20 - 30 and Omega = 160 - 170
foo = (na.where((chi2 < 2.0) & (incl > 20) & (incl < 40)))[0]
print 'Prob of chi2 and incl = %5.3f' % (len(foo) / float(ntrials))
pylab.clf()
pylab.subplot(2, 2, 1)
pylab.hist(chi2, bins=na.arange(0, 10, 0.5))
pylab.xlabel('Log Chi^2')
pylab.subplot(2, 2, 2)
pylab.hist(incl[idx])
pylab.xlabel('Inclination for Chi^2 < 2')
rng = pylab.axis()
pylab.axis([0, 180, rng[2], rng[3]])
pylab.subplot(2, 2, 3)
pylab.hist(omeg[idx])
pylab.xlabel('Omega for Chi^2 < 2')
rng = pylab.axis()
pylab.axis([0, 360, rng[2], rng[3]])
pylab.subplot(2, 2, 4)
pylab.hist(stars[idx])
pylab.xlabel('Nstars for Chi^2 < 2')
rng = pylab.axis()
pylab.axis([0, 33, rng[2], rng[3]])
pylab.savefig('diskTest.png')
# Pickle everything
foo = {'incl': incl, 'omeg': omeg, 'star': stars,
'chi2': chi2, 'niter': niter}
pickle.dump(foo, open('diskTestSave.pick', 'w'))
def run():
# Assume circular orbits with isotropic normal vectors on circular
# orbits with circular orbital velocity of 500 km/s.
ntrials = 10000
nstars = int((1.0 / 3.0) * 100)
gens = aorb.create_generators(7, ntrials*10)
velTot = 500.0 # km/s -- velocity amplitude
radTot = 2.04 # arcsec
def fitfunc(p, fjac=None, vx=None, vy=None, vz=None,
vxerr=None, vyerr=None, vzerr=None):
irad = math.radians(p[0])
orad = math.radians(p[1])
nx = math.sin(irad) * math.cos(orad)
ny = -math.sin(irad) * math.sin(orad)
nz = -math.cos(irad)
top = (nx*vx + ny*vy + nz*vz)**2
bot = (nx*vxerr + ny*vyerr + nz*vzerr)**2
devs = (1.0 / (len(vx) - 1.0)) * top / bot
status = 0
return [status, devs.flat]
# Keep track from every trial the incl, omeg, chi2, number of stars
incl = na.zeros(ntrials, type=na.Float)
omeg = na.zeros(ntrials, type=na.Float)
chi2 = na.zeros(ntrials, type=na.Float)
niter = na.zeros(ntrials)
stars = na.zeros(ntrials)
# Keep track of same stuff for spatial test
inclPos = na.zeros(ntrials, type=na.Float)
omegPos = na.zeros(ntrials, type=na.Float)
chi2Pos = na.zeros(ntrials, type=na.Float)
niterPos = na.zeros(ntrials)
angleAvg = na.zeros(ntrials, type=na.Float)
angleStd = na.zeros(ntrials, type=na.Float)
for trial in range(ntrials):
if ((trial % 100) == 0):
print('Trial %d' % trial)
x = na.zeros(nstars, type=na.Float)
y = na.zeros(nstars, type=na.Float)
z = na.zeros(nstars, type=na.Float)
vx = na.zeros(nstars, type=na.Float)
vy = na.zeros(nstars, type=na.Float)
vz = na.zeros(nstars, type=na.Float)
rmag = na.zeros(nstars, type=na.Float)
vmag = na.zeros(nstars, type=na.Float)
nx = na.zeros(nstars, type=na.Float)
ny = na.zeros(nstars, type=na.Float)
nz = na.zeros(nstars, type=na.Float)
for ss in range(nstars):
vx[ss] = gens[0].uniform(-velTot, velTot)
vyTot = math.sqrt(velTot**2 - vx[ss]**2)
vy[ss] = gens[1].uniform(-vyTot, vyTot)
vz[ss] = math.sqrt(velTot**2 - vx[ss]**2 - vy[ss]**2)
vz[ss] *= gens[2].choice([-1.0, 1.0])
x[ss] = gens[3].uniform(-radTot, radTot)
yTot = math.sqrt(radTot**2 - x[ss]**2)
y[ss] = gens[4].uniform(-yTot, yTot)
z[ss] = math.sqrt(radTot**2 - x[ss]**2 - y[ss]**2)
z[ss] *= gens[5].choice([-1.0, 1.0])
rmag[ss] = math.sqrt(x[ss]**2 + y[ss]**2 + z[ss]**2)
vmag[ss] = math.sqrt(vx[ss]**2 + vy[ss]**2 + vz[ss]**2)
rvec = [x[ss], y[ss], z[ss]]
vvec = [vx[ss], vy[ss], vz[ss]]
tmp = util.cross_product(rvec, vvec)
tmp /= rmag[ss] * vmag[ss]
nx[ss] = tmp[0]
ny[ss] = tmp[1]
nz[ss] = tmp[2]
r2d = na.hypot(x, y)
v2d = na.hypot(vx, vy)
top = (x * vy - y * vx)
jz = (x * vy - y * vx) / (r2d * v2d)
djzdx = (vy * r2d * v2d - (top * v2d * x / r2d)) / (r2d * v2d)**2
djzdy = (-vx * r2d * v2d - (top * v2d * y / r2d)) / (r2d * v2d)**2
djzdvx = (-y * r2d * v2d - (top * r2d * vx / v2d)) / (r2d * v2d)**2
djzdvy = (x * r2d * v2d - (top * r2d * vy / v2d)) / (r2d * v2d)**2
xerr = na.zeros(nstars, type=na.Float) + 0.001 # arcsec
yerr = na.zeros(nstars, type=na.Float) + 0.001
vxerr = na.zeros(nstars, type=na.Float) + 10.0 # km/s
vyerr = na.zeros(nstars, type=na.Float) + 10.0
vzerr = na.zeros(nstars, type=na.Float) + 30.0 # km/s
jzerr = na.sqrt((djzdx*xerr)**2 + (djzdy*yerr)**2 +
(djzdvx*vxerr)**2 + (djzdvy*vyerr)**2)
# Eliminate all stars with jz > 0 and jz/jzerr < 2
# I think these are they cuts they are doing
idx = (na.where((jz < 0) & (na.abs(jz/jzerr) > 2)))[0]
#idx = (na.where(jz < 0))[0]
#idx = range(len(jz))
cotTheta = vz / na.sqrt(vx**2 + vy**2)
phi = na.arctan2(vy, vx)
# Initial guess:
p0 = na.zeros(2, type=na.Float)
p0[0] = gens[5].uniform(0.1, 90) # deg -- inclination
p0[1] = gens[6].uniform(0.1, 360) # deg -- omega
# Setup properties of each free parameter.
parinfo = {'relStep':10.0, 'step':10.0, 'fixed':0,
'limits':[0.0,360.0],
'limited':[1,1], 'mpside':1}
pinfo = [parinfo.copy() for i in range(len(p0))]
pinfo[0]['limits'] = [0.0, 180.0]
pinfo[1]['limits'] = [0.0, 360.0]
# Stuff to pass into the fit function
functargs = {'vx': vx[idx], 'vy': vy[idx], 'vz': vz[idx],
'vxerr':vxerr[idx], 'vyerr':vyerr[idx], 'vzerr':vzerr[idx]}
m = mpfit.mpfit(fitfunc, p0, functkw=functargs, parinfo=pinfo,
quiet=1)
if (m.status <= 0):
print('error message = ', m.errmsg)
p = m.params
incl[trial] = p[0]
omeg[trial] = p[1]
stars[trial] = len(idx)
chi2[trial] = m.fnorm / (stars[trial] - len(p0))
niter[trial] = m.niter
n = [math.sin(p[0]) * math.cos(p[1]),
-math.sin(p[0]) * math.sin(p[1]),
-math.cos(p[0])]
# Now look at the angle between the best fit normal vector
# from the velocity data and the true r cross v normal vector.
# Take the dot product between n and nreal.
angle = na.arccos(n[0]*nx + n[1]*ny + n[2]*nz)
angle *= (180.0 / math.pi)
# What is the average angle and std angle
angleAvg[trial] = angle.mean()
angleStd[trial] = angle.stddev()
# print chi2[trial], chi2Pos[trial], incl[trial], inclPos[trial], \
# omeg[trial], omegPos[trial], niter[trial], niterPos[trial]
# print angleAvg[trial], angleStd[trial]
# Plot up chi2 for v-fit vs. chi2 for x-fit
pylab.clf()
pylab.semilogx(chi2, angleAvg, 'k.')
pylab.errorbar(chi2, angleAvg, fmt='k.', yerr=angleStd)
pylab.xlabel('Chi^2')
pylab.ylabel('Angle w.r.t. Best Fit')
foo = input('Contine?')
# Probability of encountering solution with chi^2 < 2
idx = (na.where(chi2 < 2.0))[0]
print('Prob(chi^2 < 2) = %5.3f ' % (len(idx) / float(ntrials)))
# Probability of encountering solution with chi^2 < 2 AND
# inclination = 20 - 30 and Omega = 160 - 170
foo = (na.where((chi2 < 2.0) & (incl > 20) & (incl < 40)))[0]
print('Prob of chi2 and incl = %5.3f' % (len(foo) / float(ntrials)))
pylab.clf()
pylab.subplot(2, 2, 1)
pylab.hist(chi2, bins=na.arange(0, 10, 0.5))
pylab.xlabel('Log Chi^2')
pylab.subplot(2, 2, 2)
pylab.hist(incl[idx])
pylab.xlabel('Inclination for Chi^2 < 2')
rng = pylab.axis()
pylab.axis([0, 180, rng[2], rng[3]])
pylab.subplot(2, 2, 3)
pylab.hist(omeg[idx])
pylab.xlabel('Omega for Chi^2 < 2')
rng = pylab.axis()
pylab.axis([0, 360, rng[2], rng[3]])
pylab.subplot(2, 2, 4)
pylab.hist(stars[idx])
pylab.xlabel('Nstars for Chi^2 < 2')
rng = pylab.axis()
pylab.axis([0, 33, rng[2], rng[3]])
pylab.savefig('diskTest.png')
# Pickle everything
foo = {'incl': incl, 'omeg': omeg, 'star': stars,
'chi2': chi2, 'niter': niter}
pickle.dump(foo, open('diskTestSave.pick', 'w'))