def LUdecomp(a, tol=1.0e-9):
n = len(a)
seq = array(range(n))
# Set up scale factors
s = zeros((n), type=Float64)
for i in range(n):
s[i] = max(abs(a[i, :]))
for k in range(0, n - 1):
# Row interchange, if needed
p = int(argmax(abs(a[k:n, k]) / s[k:n])) + k
if abs(a[p, k]) < tol:
error.err("Matrix is singular")
if p != k:
swap.swapRows(s, k, p)
swap.swapRows(a, k, p)
swap.swapRows(seq, k, p)
# Elimination
for i in range(k + 1, n):
if a[i, k] != 0.0:
lam = a[i, k] / a[k, k]
a[i, k + 1 : n] = a[i, k + 1 : n] - lam * a[k, k + 1 : n]
a[i, k] = lam
return a, seq
def gaussJordanPivot(a, tol=1.0e-9):
n = len(a)
seq = array(range(n))
# Set up scale factors
s = zeros((n), type=Float64)
for i in range(n):
s[i] = max(abs(a[i, :]))
for i in range(n):
# Row interchange, if needed
p = int(argmax(abs(a[i:n, i]) / s[i:n])) + i
if abs(a[p, i]) < tol: error.err('Matrix is singular')
if p != i:
swap.swapRows(s, i, p)
swap.swapRows(a, i, p)
swap.swapRows(seq, i, p)
# Elimination phase
temp = a[i, i]
a[i, i] = 1.0
a[i, 0:n] = a[i, 0:n] / temp
for k in range(n):
if k != i:
temp = a[k, i]
a[k, i] = 0.0
a[k, 0:n] = a[k, 0:n] - a[i, 0:n] * temp
# Rearrange columns in the right sequence
for i in range(n):
swap.swapCols(a, i, seq[i])
swap.swapRows(seq, i, seq[i])
return a
def ddtohms(xsky, ysky, verbose=no):
""" Convert sky position(s) from decimal degrees to HMS format."""
xskyh = xsky / 15.
xskym = (xskyh - N.floor(xskyh)) * 60.
xskys = (xskym - N.floor(xskym)) * 60.
yskym = (N.abs(ysky) - N.floor(N.abs(ysky))) * 60.
yskys = (yskym - N.floor(yskym)) * 60.
if isinstance(xskyh, N.NumArray):
rah, dech = [], []
for i in xrange(len(xskyh)):
rastr = repr(int(xskyh[i])) + ':' + repr(int(
xskym[i])) + ':' + repr(xskys[i])
decstr = repr(int(ysky[i])) + ':' + repr(int(
yskym[i])) + ':' + repr(yskys[i])
rah.append(rastr)
dech.append(decstr)
if verbose:
print 'RA = ', rastr, ', Dec = ', decstr
else:
rastr = repr(int(xskyh)) + ':' + repr(int(xskym)) + ':' + repr(xskys)
decstr = repr(int(ysky)) + ':' + repr(int(yskym)) + ':' + repr(yskys)
rah = rastr
dech = decstr
if verbose:
print 'RA = ', rastr, ', Dec = ', decstr
return rah, dech
def gaussJordanPivot(a,tol=1.0e-9):
n = len(a)
seq = array(range(n))
# Set up scale factors
s = zeros((n),type=Float64)
for i in range(n):
s[i] = max(abs(a[i,:]))
for i in range(n):
# Row interchange, if needed
p = int(argmax(abs(a[i:n,i])/s[i:n])) + i
if abs(a[p,i]) < tol: error.err('Matrix is singular')
if p != i:
swap.swapRows(s,i,p)
swap.swapRows(a,i,p)
swap.swapRows(seq,i,p)
# Elimination phase
temp = a[i,i]
a[i,i] = 1.0
a[i,0:n] = a[i,0:n]/temp
for k in range(n):
if k != i:
temp = a[k,i]
a[k,i] = 0.0
a[k,0:n] = a[k,0:n] - a[i,0:n]*temp
# Rearrange columns in the right sequence
for i in range(n):
swap.swapCols(a,i,seq[i])
swap.swapRows(seq,i,seq[i])
return a
def ddtohms(xsky,ysky,verbose=no):
""" Convert sky position(s) from decimal degrees to HMS format."""
xskyh = xsky /15.
xskym = (xskyh - N.floor(xskyh)) * 60.
xskys = (xskym - N.floor(xskym)) * 60.
yskym = (N.abs(ysky) - N.floor(N.abs(ysky))) * 60.
yskys = (yskym - N.floor(yskym)) * 60.
if isinstance(xskyh,N.NumArray):
rah,dech = [],[]
for i in xrange(len(xskyh)):
rastr = repr(int(xskyh[i]))+':'+repr(int(xskym[i]))+':'+repr(xskys[i])
decstr = repr(int(ysky[i]))+':'+repr(int(yskym[i]))+':'+repr(yskys[i])
rah.append(rastr)
dech.append(decstr)
if verbose:
print 'RA = ',rastr,', Dec = ',decstr
else:
rastr = repr(int(xskyh))+':'+repr(int(xskym))+':'+repr(xskys)
decstr = repr(int(ysky))+':'+repr(int(yskym))+':'+repr(yskys)
rah = rastr
dech = decstr
if verbose:
print 'RA = ',rastr,', Dec = ',decstr
return rah,dech
def LUdecomp(a,tol=1.0e-9):
n = len(a)
seq = array(range(n))
# Set up scale factors
s = zeros((n),type=Float64)
for i in range(n):
s[i] = max(abs(a[i,:]))
for k in range(0,n-1):
# Row interchange, if needed
p = int(argmax(abs(a[k:n,k])/s[k:n])) + k
if abs(a[p,k]) < tol: error.err('Matrix is singular')
if p != k:
swap.swapRows(s,k,p)
swap.swapRows(a,k,p)
swap.swapRows(seq,k,p)
# Elimination
for i in range(k+1,n):
if a[i,k] != 0.0:
lam = a[i,k]/a[k,k]
a[i,k+1:n] = a[i,k+1:n] - lam*a[k,k+1:n]
a[i,k] = lam
return a,seq
def sharpenImage(self, image, alpha):
# FIXME: support RGB images
rep = image.representations()[0]
height = rep.pixelsHigh()
width = rep.pixelsWide()
samplesPerPixel = rep.samplesPerPixel()
bytesPerRow = rep.bytesPerRow()
bitmapData = rep.bitmapData()
# Convert the image to a numarray array
size = (width, height)
imgData = numarray.fromstring(datastring=bitmapData,
type=numarray.UInt8,
shape=size)
# Convert to double and do a FFT2D
G = numarray.fft.fft2d(imgData.astype(numarray.Float64))
# Compute the power spectrum
SG = (numarray.abs(G)**2.) / (width * height)
# KD = 0.14711
D1 = (numarray.abs(SG)**(alpha / 2.))
# Find the normalization constant KD by requiring ||D1|| <= 1
firstPass = numarray.add.reduce(D1**2)
norm = math.sqrt(numarray.add.reduce(firstPass))
KD = 1. / norm
D1 *= KD
# Divide the fft by its power spectrum and go back to real space.
F1 = G / D1
f2 = numarray.fft.inverse_fft2d(F1).real
# Bring f2 into the [0, 255] range
min = f2.min()
if (min != 0):
f2 -= min
max = f2.max()
if (max != 0):
f2 /= max
f2 *= 255.
return(f2.astype(numarray.UInt8))
def find(P, p):
''' In the 2D neighbourhood P, find the point closest to p.
The approach is based on the selection of a trial value Pt, from
P, and
discarding all values further than Pt from p.
To avoid repeated sqrt calculations the discard is based on an
enclosing square.
'''
global lengthRemaining, trial
lengthRemaining+= [[P.shape[0]]]
Pz= P - p # zero based neighbourhood
while len(Pz):
Pt= Pz[0] # trial value
Pta= N.abs(Pt)
Pz= Pz[1:]
pd= math.sqrt(N.dot(Pta, Pta)) # distance of p from the trial
def plot_rspgenIntegral(self, energy, inclination, phi=0, nsamp=2000):
rmin = 1e-2
rmax = 30.
npts = 20
rstep = num.log(rmax / rmin) / (npts - 1)
radii = rmin * num.exp(rstep * num.arange(npts))
self._setPsf(energy, inclination, phi)
seps = []
srcDir = SkyDir(180, 0)
for i in range(nsamp):
appDir = self.psf.appDir(energy, srcDir, self.scZAxis,
self.scXAxis)
seps.append(appDir.difference(srcDir) * 180. / num.pi)
seps.sort()
fraction = num.arange(nsamp, type=num.Float) / nsamp
disp = plot.scatter(seps,
fraction,
xlog=1,
xname='ROI radius',
yname='enclosed Psf fraction',
pointRep='Line',
color='red')
disp.setTitle("%s: %i MeV, %.1f deg" %
(self.irfs, energy, inclination))
npred = []
resids = []
for radius in radii:
npred.append(
self.psf.angularIntegral(energy, inclination, phi, radius))
resids.append(
num.abs(
(self._interpolate(seps, fraction, radius) - npred[-1]) /
npred[-1]))
plot.scatter(radii, npred, pointRep='Line', oplot=1)
residplot = plot.scatter(radii,
resids,
'ROI radius',
yname='abs(sim - npred)/npred',
xlog=1,
ylog=1)
# Npred = Interpolator(radii, npred)
ks_prob = ks2(npred, seps)
plot.hline(0)
residplot.setTitle("%s: %i MeV, %.1f deg\n ks prob=%.2e" %
(self.irfs, energy, inclination, ks_prob[1]))
return energy, inclination, ks_prob[1]
def generate_binary_structure(rank, connectivity):
"""Generate a binary structure for binary morphological operations.
The inputs are the rank of the array to which the structure will
be applied and the square of the connectivity of the structure.
"""
if connectivity < 1:
connectivity = 1
if rank < 1:
if connectivity < 1:
return numarray.array(0, type = numarray.Bool)
else:
return numarray.array(1, type = numarray.Bool)
output = numarray.zeros([3] * rank, numarray.Bool)
output = numarray.abs(numarray.indices([3] * rank) - 1)
output = numarray.add.reduce(output, 0)
return numarray.asarray(output <= connectivity, type = numarray.Bool)
def generate_binary_structure(rank, connectivity):
"""Generate a binary structure for binary morphological operations.
The inputs are the rank of the array to which the structure will
be applied and the square of the connectivity of the structure.
"""
if connectivity < 1:
connectivity = 1
if rank < 1:
if connectivity < 1:
return numarray.array(0, type=numarray.Bool)
else:
return numarray.array(1, type=numarray.Bool)
output = numarray.zeros([3] * rank, numarray.Bool)
output = numarray.abs(numarray.indices([3] * rank) - 1)
output = numarray.add.reduce(output, 0)
return numarray.asarray(output <= connectivity, type=numarray.Bool)
def matchum(file1,
file2,
tol=10,
perr=4,
aerr=1.0,
nmax=40,
im_masks1=[],
im_masks2=[],
debug=0,
domags=0,
xrange=None,
yrange=None,
sigma=4,
aoffset=0):
'''Take the output of two sextractor runs and match up the objects with
each other (find out which objects in the first file match up with
objects in the second file. The routine considers a 'match' to be any
two objects that are closer than tol pixels (after applying the shift).
Returns a 6-tuple: (x1,y1,x2,y2,o1,o2). o1 and o2 are the ojbects
numbers such that o1[i] in file 1 corresponds to o2[i] in file 2.'''
NA = num.NewAxis
sexdata1 = readsex(file1)
sexdata2 = readsex(file2)
# Use the readsex data to get arrays of the (x,y) positions
x1 = num.asarray(sexdata1[0]['X_IMAGE'])
y1 = num.asarray(sexdata1[0]['Y_IMAGE'])
x2 = num.asarray(sexdata2[0]['X_IMAGE'])
y2 = num.asarray(sexdata2[0]['Y_IMAGE'])
m1 = num.asarray(sexdata1[0]['MAG_BEST'])
m2 = num.asarray(sexdata2[0]['MAG_BEST'])
o1 = num.asarray(sexdata1[0]['NUMBER'])
o2 = num.asarray(sexdata2[0]['NUMBER'])
f1 = num.asarray(sexdata1[0]['FLAGS'])
f2 = num.asarray(sexdata2[0]['FLAGS'])
# First, make a cut on the flags:
gids = num.where(f1 < 4)
x1 = x1[gids]
y1 = y1[gids]
m1 = m1[gids]
o1 = o1[gids]
gids = num.where(f2 < 4)
x2 = x2[gids]
y2 = y2[gids]
m2 = m2[gids]
o2 = o2[gids]
# next, if there is a range to use:
if xrange is not None and yrange is not None:
cond = num.greater(x1, xrange[0])*num.less(x1,xrange[1])*\
num.greater(y1, yrange[0])*num.less(y1,yrange[1])
gids = num.where(cond)
x1 = x1[gids]
y1 = y1[gids]
m1 = m1[gids]
o1 = o1[gids]
cond = num.greater(x2, xrange[0])*num.less(x2,xrange[1])*\
num.greater(y2, yrange[0])*num.less(y2,yrange[1])
gids = num.where(cond)
x2 = x2[gids]
y2 = y2[gids]
m2 = m2[gids]
o2 = o2[gids]
# Use the user masks
for m in im_masks1:
print "applying mask (%d,%d,%d,%d)" % tuple(m)
condx = num.less(x1, m[0]) + num.greater(x1, m[1])
condy = num.less(y1, m[2]) + num.greater(y1, m[3])
gids = num.where(condx + condy)
x1 = x1[gids]
y1 = y1[gids]
m1 = m1[gids]
o1 = o1[gids]
for m in im_masks2:
print "applying mask (%d,%d,%d,%d)" % tuple(m)
condx = num.less(x2, m[0]) + num.greater(x2, m[1])
condy = num.less(y2, m[2]) + num.greater(y2, m[3])
gids = num.where(condx + condy)
x2 = x2[gids]
y2 = y2[gids]
m2 = m2[gids]
o2 = o2[gids]
if nmax:
if len(x1) > nmax:
ids = num.argsort(m1)[0:nmax]
x1 = x1[ids]
y1 = y1[ids]
m1 = m1[ids]
o1 = o1[ids]
if len(x2) > nmax:
ids = num.argsort(m2)[0:nmax]
x2 = x2[ids]
y2 = y2[ids]
m2 = m2[ids]
o2 = o2[ids]
if debug:
print "objects in frame 1:"
print o1
print "objects in frame 2:"
print o2
mp = pygplot.MPlot(2, 1, device='/XWIN')
p = pygplot.Plot()
p.point(x1, y1)
[p.label(x1[i], y1[i], "%d" % o1[i]) for i in range(len(x1))]
mp.add(p)
p = pygplot.Plot()
p.point(x2, y2)
[p.label(x2[i], y2[i], "%d" % o2[i]) for i in range(len(x2))]
mp.add(p)
mp.plot()
mp.close()
# Now, we make 2-D arrays of all the differences in x and y between each pair
# of objects. e.g., dx1[n,m] is the delta-x between object n and m in file 1 and
# dy2[n,m] is the y-distance between object n and m in file 2.
dx1 = x1[NA, :] - x1[:, NA]
dx2 = x2[NA, :] - x2[:, NA]
dy1 = y1[NA, :] - y1[:, NA]
dy2 = y2[NA, :] - y2[:, NA]
# Same, but with angles
da1 = num.arctan2(dy1, dx1) * 180 / num.pi
da2 = num.arctan2(dy2, dx2) * 180 / num.pi
# Same, but with absolute distances
ds1 = num.sqrt(num.power(dx1, 2) + num.power(dy1, 2))
ds2 = num.sqrt(num.power(dx2, 2) + num.power(dy2, 2))
# Here's the real magic: this is a matrix of matrices (4-D). Consider 4 objects:
# objects i and j in file 1 and objects m and n in file 2. dx[i,j,m,n] is the
# difference between delta-xs for objects i,j in file 1 and m,n in file 2. If object
# i corresponds to object m and object j corresponds to object n, this should be a small
# number, irregardless of an overall shift in coordinate systems between file 1 and 2.
dx = dx1[::, ::, NA, NA] - dx2[NA, NA, ::, ::]
dy = dy1[::, ::, NA, NA] - dy2[NA, NA, ::, ::]
da = da1[::, ::, NA, NA] - da2[NA, NA, ::, ::] + aoffset
ds = ds1[::, ::, NA, NA] - ds2[NA, NA, ::, ::]
# pick out close pairs.
#use = num.less(dy,perr)*num.less(dx,perr)*num.less(num.abs(da),aerr)
use = num.less(ds, perr) * num.less(num.abs(da), aerr)
use = use.astype(num.Int32)
#use = num.less(num.abs(da),perr)
suse = num.add.reduce(num.add.reduce(use, 3), 1)
print suse[0]
guse = num.greater(suse, suse.flat.max() / 2)
i = [j for j in range(x1.shape[0]) if num.sum(guse[j])]
m = [num.argmax(guse[j]) for j in range(x1.shape[0]) if num.sum(guse[j])]
xx0, yy0, oo0, mm0 = num.take([x1, y1, o1, m1], i, 1)
xx1, yy1, oo1, mm1 = num.take([x2, y2, o2, m2], m, 1)
if debug:
mp = pygplot.MPlot(2, 1, device='/XWIN')
p = pygplot.Plot()
p.point(xx0, yy0)
[p.label(xx0[i], yy0[i], "%d" % oo0[i]) for i in range(len(xx0))]
mp.add(p)
p = pygplot.Plot()
p.point(xx1, yy1)
[p.label(xx1[i], yy1[i], "%d" % oo1[i]) for i in range(len(xx1))]
mp.add(p)
mp.plot()
mp.close()
xshift, xscat = stats.bwt(xx0 - xx1)
xscat = max([1.0, xscat])
yshift, yscat = stats.bwt(yy0 - yy1)
yscat = max([1.0, yscat])
mshift, mscat = stats.bwt(mm0 - mm1)
print "xscat = ", xscat
print "yscat = ", yscat
print "xshift = ", xshift
print "yshift = ", yshift
print "mshift = ", mshift
print "mscat = ", mscat
keep = num.less(num.abs(xx0-xx1-xshift),sigma*xscat)*\
num.less(num.abs(yy0-yy1-yshift),sigma*yscat)
# This is a list of x,y,object# in each file.
xx0, yy0, oo0, xx1, yy1, oo1 = num.compress(keep,
[xx0, yy0, oo0, xx1, yy1, oo1],
1)
if debug:
print file1, oo0
print file2, oo1
mp = pygplot.MPlot(2, 1, device='temp.ps/CPS')
p1 = pygplot.Plot()
p1.point(xx0, yy0, symbol=25, color='red')
for i in range(len(xx0)):
p1.label(xx0[i], yy0[i], " %d" % oo0[i], color='red')
mp.add(p1)
p2 = pygplot.Plot()
p2.point(xx1, yy1, symbol=25, color='green')
for i in range(len(xx1)):
p2.label(xx1[i], yy1[i], " %d" % oo1[i], color='green')
mp.add(p2)
mp.plot()
mp.close()
if domags:
return (xx0, yy0, mm0, xx1, yy1, mm1, mshift, mscat, oo0, oo1)
else:
return (xx0, yy0, xx1, yy1, oo0, oo1)
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'))
