def generic_gradient_magnitude(
input, derivative, output=None, mode="reflect", cval=0.0, extra_arguments=(), extra_keywords={}
):
"""Calculate a gradient magnitude using the provdide function for
the gradient.
The derivative parameter must be a callable with the following
signature:
derivative(input, axis, output, mode, cval,
*extra_arguments, **extra_keywords)
The extra_arguments and extra_keywords arguments can be used to pass
extra arguments and keywords that are passed to derivative2 at each
call.
"""
input = numarray.asarray(input)
output, return_value = _ni_support._get_output(output, input)
axes = range(input.rank)
if len(axes) > 0:
derivative(input, axes[0], output, mode, cval, *extra_arguments, **extra_keywords)
numarray.multiply(output, output, output)
for ii in range(1, len(axes)):
tmp = derivative(input, axes[ii], output.type(), mode, cval, *extra_arguments, **extra_keywords)
numarray.multiply(tmp, tmp, tmp)
output += tmp
numarray.sqrt(output, output)
else:
output[...] = input[...]
return return_value
def getpositions(ximage, yimage, xmax, ymax):
dmin = 5. #minimum distance to object + sqrt(isoarea)
xpos = []
ypos = []
d = N.zeros(len(ximage), 'f')
#print len(d)
i = 0
while i < npoints:
xtemp = int(round(random.uniform(
5., 125.))) #random.uniform(5.,125.)#*xmax
ytemp = int(round(random.uniform(
5., 140.))) #random.uniform(5.,140.)#*ymax
if (xtemp > 10.) & (ytemp < (ymax - 10)):
d = N.sqrt((ximage - xtemp)**2 + (yimage - ytemp)**2)
if (min(d) > dmin):
if i > 2:
xap = N.array(xpos, 'f')
yap = N.array(ypos, 'f')
d2 = N.sqrt((xtemp - xap)**2 + (ytemp - yap)**2)
if (min(d2) > dmin):
xpos.append(xtemp)
ypos.append(ytemp)
i = i + 1
else:
xpos.append(xtemp)
ypos.append(ytemp)
i = i + 1
xpos = N.array(xpos, 'f')
ypos = N.array(ypos, 'f')
return xpos, ypos
def plot_source_info(self,event):
ra = event.xdata
dec = event.ydata
#print (event.key,ra,dec)
if event.key == 's':
#print self.constructed_pos[:,0]
#print self.constructed_pos[:,1]
dist = numarray.sqrt( (self.constructed_pos[:,0] - ra)**2 + (self.constructed_pos[:,1] - dec)**2)
#print dist
#print "min distance = %f " % min(dist)
the_source_ind = numarray.compress(dist == min(dist), numarray.fromlist(range(len(self.constructed_source_list))))
#print the_source_ind
#the_source_ind = numarray.compress(dist == min(dist),numarray.arange(len(self.constructed_source_list)))
the_source = self.constructed_source_list[the_source_ind[0]]
print the_source
dist = numarray.sqrt( (the_source.current_pos[0] - self.real_pos[:,0])**2 + (the_source.current_pos[1] - self.real_pos[:,1])**2)
print "min distances to nearest real source = %f arcsec" % min(dist)
the_source_ind = numarray.compress(dist == min(dist), numarray.fromlist(range(len(self.real_list))))
the_source = self.real_list[the_source_ind[0]]
print "That real source is at ra=%f dec=%f" % (the_source.start_pos[0],the_source.start_pos[1])
if event.key == 'r':
dist = numarray.sqrt( (self.real_pos[:,0] - ra)**2 + (self.real_pos[:,1] - dec)**2)
#print dist
#print "min distance = %f " % min(dist)
the_source_ind = numarray.compress(dist == min(dist), numarray.fromlist(range(len(self.real_list))))
#print the_source_ind
#the_source_ind = numarray.compress(dist == min(dist),numarray.arange(len(self.constructed_source_list)))
the_source = self.real_list[the_source_ind[0]]
print the_source
def getnearest(self,j):
self.sig5=N.zeros(len(self.ra),'f')
self.sig10=N.zeros(len(self.ra),'f')
self.sig5phot=N.zeros(len(self.ra),'f')
self.sig10phot=N.zeros(len(self.ra),'f')
self.nearest=N.zeros(len(self.ra),'f')#distance to nearest neighbor
self.dmagnearest=N.zeros(len(self.ra),'f')#mag diff b/w spec obj and nearest
for i in range(len(self.ra)):
angdist=my.DA(c.z[j],h100)#kpc/arcsec
if self.memb[i] > 0:
dspec=N.sqrt((self.ra[i]-self.ra)**2+(self.dec[i]-self.dec)**2)#sorted array of distances in degrees
dphot=N.sqrt((self.ra[i]-self.photra)**2+(self.dec[i]-self.photdec)**2)#sorted array of distances in degrees
Mvsort=N.take(self.V,N.argsort(dspec))
phMvsort=N.take(self.phMv,N.argsort(dphot))
dspecsort=N.take(dspec,N.argsort(dspec))
self.sig5[i]=5./(N.pi)/(dspecsort[5]*3600.*angdist/1000.)**2#convert from deg to arcsec, multiply by DA (kpc/arcsec), divide by 1000 to convert to Mpc, index 5 element b/c 0 is itself
if (len(dspecsort) > 10):
self.sig10[i]=10./(N.pi)/(dspecsort[10]*3600.*angdist/1000.)**2
else:
self.sig10[i]=0.
dphotsort=N.take(dphot,N.argsort(dphot))
self.nearest[i]=dphotsort[0]
self.dmagnearest[i]=phMvsort[0]-Mvsort[0]
self.sig5phot[i]=5./(N.pi)/(dphotsort[5]*3600.*angdist/1000.)**2
self.sig10phot[i]=10./(N.pi)/(dphotsort[10]*3600.*angdist/1000.)**2
def plotFitRms(root, polyroot, gcfitdir):
s = starset.StarSet(root)
s.loadPolyfit(polyroot, arcsec=1, accel=0)
years = s.stars[0].years
fitPx = s.getArray('fitXv.p')
fitVx = s.getArray('fitXv.v')
fitPy = s.getArray('fitYv.p')
fitVy = s.getArray('fitYv.v')
t0x = s.getArray('fitXv.t0')
t0y = s.getArray('fitYv.t0')
rmsX = na.zeros(len(s.stars), type=na.Float)
rmsY = na.zeros(len(s.stars), type=na.Float)
rms = na.zeros(len(s.stars), type=na.Float)
cnt = na.zeros(len(s.stars), type=na.Int)
for ee in range(len(years)):
dtX = years[ee] - t0x
dtY = years[ee] - t0y
xfit = fitPx + (dtX * fitVx)
yfit = fitPy + (dtY * fitVy)
x = s.getArrayFromEpoch(ee, 'x')
y = s.getArrayFromEpoch(ee, 'y')
xpix = s.getArrayFromEpoch(ee, 'xpix')
ypix = s.getArrayFromEpoch(ee, 'ypix')
diffx = xfit - x
diffy = yfit - y
diff = na.sqrt(diffx**2 + diffy**2)
idx = (na.where(xpix > -999))[0]
rmsX[idx] += diffx**2
rmsY[idx] += diffy**2
rms[idx] += diff**2
cnt[idx] += 1
rmsX = na.sqrt(rmsX / cnt) * 1000.0
rmsY = na.sqrt(rmsY / cnt) * 1000.0
rms = na.sqrt(rms / cnt) * 1000.0
mag = s.getArray('mag')
x = s.getArray('x')
y = s.getArray('y')
r = na.sqrt(x**2 + y**2)
idx = (na.where(mag < 15))[0]
p.clf()
p.semilogy(r[idx], rms[idx], 'k.')
def plotFitRms(root, polyroot, gcfitdir):
s = starset.StarSet(root)
s.loadPolyfit(polyroot, arcsec=1, accel=0)
years = s.stars[0].years
fitPx = s.getArray('fitXv.p')
fitVx = s.getArray('fitXv.v')
fitPy = s.getArray('fitYv.p')
fitVy = s.getArray('fitYv.v')
t0x = s.getArray('fitXv.t0')
t0y = s.getArray('fitYv.t0')
rmsX = na.zeros(len(s.stars), type=na.Float)
rmsY = na.zeros(len(s.stars), type=na.Float)
rms = na.zeros(len(s.stars), type=na.Float)
cnt = na.zeros(len(s.stars), type=na.Int)
for ee in range(len(years)):
dtX = years[ee] - t0x
dtY = years[ee] - t0y
xfit = fitPx + (dtX * fitVx)
yfit = fitPy + (dtY * fitVy)
x = s.getArrayFromEpoch(ee, 'x')
y = s.getArrayFromEpoch(ee, 'y')
xpix = s.getArrayFromEpoch(ee, 'xpix')
ypix = s.getArrayFromEpoch(ee, 'ypix')
diffx = xfit - x
diffy = yfit - y
diff = na.sqrt(diffx**2 + diffy**2)
idx = (na.where(xpix > -999))[0]
rmsX[idx] += diffx**2
rmsY[idx] += diffy**2
rms[idx] += diff**2
cnt[idx] += 1
rmsX = na.sqrt(rmsX / cnt) * 1000.0
rmsY = na.sqrt(rmsY / cnt) * 1000.0
rms = na.sqrt(rms / cnt) * 1000.0
mag = s.getArray('mag')
x = s.getArray('x')
y = s.getArray('y')
r = na.sqrt(x**2 + y**2)
idx = (na.where(mag < 15))[0]
p.clf()
p.semilogy(r[idx], rms[idx], 'k.')
def phaselag(spectrum, coherence, numinbin):
"""Compute phase lags from a cross spectrum.
lag, error = phaselag(spectrum, coherence, numinbin)
Inputs:
spectrum: The cross spectrum. A complex array.
coherence: The uncorrected coherence.
numinbin: The number of raw estimates that went into each frequency bin.
Outputs:
lag: The phase of the input spectrum. In radians.
error: The standard deviation of the lag. Also in radians.
Calculated from eq. (9.52) in Bendat & Piersol 2000."""
lag = num.arctan2(spectrum.imag, spectrum.real)
# eq. (9.52) in Bendat & Piersol 2000
error = num.sqrt((1 - coherence) / (2 * numinbin * coherence))
return lag, error
def binitbins(xmin, xmax, nbin, x, y): #use equally spaced bins
dx = float((xmax - xmin) / (nbin))
xbin = N.arange(xmin, (xmax), dx) + dx / 2.
#print "within binitbins"
#print "xbin = ",xbin
#print "dx = ",dx
#print "xmax = ",xmax
#print "xmin = ",xmin
ybin = N.zeros(len(xbin), 'd')
ybinerr = N.zeros(len(xbin), 'd')
xbinnumb = N.array(len(x), 'd')
x1 = N.compress((x >= xmin) & (x <= xmax), x)
y1 = N.compress((x >= xmin) & (x <= xmax), y)
x = x1
y = y1
xbinnumb = ((x - xmin) * nbin / (xmax - xmin)
) #calculate x bin number for each point
j = -1
for i in range(len(xbin)):
ydata = N.compress(abs(xbinnumb - float(i)) < .5, y)
try:
ybin[i] = N.average(ydata)
#ybin[i]=pylab.median(ydata)
ybinerr[i] = pylab.std(ydata) / N.sqrt(float(len(ydata)))
except ZeroDivisionError:
ybin[i] = 0.
ybinerr[i] = 0.
return xbin, ybin, ybinerr
def binitbinsfix(binsleft, binsright, x, y): #give bins for binning
nbin = len(binsleft)
xbin = N.zeros(len(binsleft), 'f')
ybin = N.zeros(len(binsleft), 'f')
ybinerr = N.zeros(len(binsleft), 'f')
y = N.take(y, N.argsort(x)) #sort y according to x rankings
x = N.take(x, N.argsort(x))
j = -1
for i in range(len(xbin)):
xmin = binsleft[i]
xmax = binsright[i]
yb = []
for j in range(len(x)):
if x[j] > xmin:
yb.append(y[j])
if x[j] > xmax:
yb = N.array(yb, 'f')
xbin[i] = 0.5 * (xmin + xmax)
try:
ybin[i] = pylab.median(yb)
ybinerr[i] = pylab.std(yb) / N.sqrt(1. * len(yb))
except ZeroDivisionError:
print "warning: ZeroDivision error in binitbinsfix"
ybin[i] = 0.
ybinerr[i] = 0.
break
return xbin, ybin, ybinerr
def horizontalhist(x, xmin, xmax, nbin): #give bins for binning
#nbin=len(bins)
xbin = N.zeros(nbin, 'f')
ybin = N.zeros(nbin, 'f')
ybinerr = N.zeros(nbin, 'f')
dbin = (xmax - xmin) / (1. * nbin)
bins = N.arange(xmin, (xmax + dbin), dbin)
x = N.take(x, N.argsort(x))
xmin = min(bins)
xmax = max(bins)
xbinnumb = ((x - xmin) * nbin / (xmax - xmin)
) #calculate x bin number for each point
#print "from within horizontal hist"
#print "bins = ",bins
for i in range(len(xbin) - 1):
xmin = bins[i]
xmax = bins[i + 1]
xbin[i] = xmin
yb = 0.
for j in range(len(x)):
if (x[j] > xmin) & (x[j] <= xmax):
yb = yb + 1.
ybin[i] = yb
ybinerr[i] = N.sqrt(yb)
#print i,len(xbin),xbin[i],xmin,xmax,ybin[i],bins[i]
xbin[(len(xbin) - 1)] = xbin[(len(xbin) - 2)] + dbin
#xbin=bins
#print "from w/in horizontal hist, ybin = ",ybin
return xbin, ybin, ybinerr
def points(self,npoints):
"""
compute arrays of npoints equally spaced
intermediate points along the great circle.
input parameter npoints is the number of points
to compute.
Returns lons, lats (lists with longitudes and latitudes
of intermediate points in degrees).
For example npoints=10 will return arrays lons,lats of 10
equally spaced points along the great circle.
"""
# can't do it if endpoints of great circle are antipodal, since
# route is undefined.
if self.antipodal:
raise ValueError,'cannot compute intermediate points on a great circle whose endpoints are antipodal'
d = self.distance
delta = 1.0/(npoints-1)
f = delta*N.arange(npoints)
lat1 = self.lat1
lat2 = self.lat2
lon1 = self.lon1
lon2 = self.lon2
A = N.sin((1-f)*d)/math.sin(d)
B = N.sin(f*d)/math.sin(d)
x = A*math.cos(lat1)*math.cos(lon1)+B*math.cos(lat2)*math.cos(lon2)
y = A*math.cos(lat1)*math.sin(lon1)+B*math.cos(lat2)*math.sin(lon2)
z = A*math.sin(lat1) +B*math.sin(lat2)
lats=N.arctan2(z,N.sqrt(x**2+y**2))
lons=N.arctan2(y,x)
lons = map(math.degrees,lons.tolist())
lats = map(math.degrees,lats.tolist())
return lons,lats
def abs_fft(self, points=None, zoom=None,write = 'off'): """ Fourier transforms the timesignal; points is the number of points to transform, if more points given than data points the rest is zero padded absfft(points=4096) """ realdata = numarray.array(self.the_result.y[0]) imdata = numarray.array(self.the_result.y[1]) data = realdata + 1j*imdata fftdata = self.rearrange(numarray.fft.fft(data, points)) absfft = numarray.sqrt(fftdata.real**2 + fftdata.imag**2) # create our x axis n = fftdata.size() self.the_result.x = numarray.arange(n)*(self.sampling_rate/n)-(self.sampling_rate/2.0) self.the_result.y[0] = absfft self.the_result.y[1] = numarray.zeros(n) if write == 'on': return self else: if zoom is None: return self.the_result else: center, width = zoom return self.zoom(self.the_result, center, width)
def phaselag(spectrum, coherence, numinbin):
"""Compute phase lags from a cross spectrum.
lag, error = phaselag(spectrum, coherence, numinbin)
Inputs:
spectrum: The cross spectrum. A complex array.
coherence: The uncorrected coherence.
numinbin: The number of raw estimates that went into each frequency bin.
Outputs:
lag: The phase of the input spectrum. In radians.
error: The standard deviation of the lag. Also in radians.
Calculated from eq. (9.52) in Bendat & Piersol 2000."""
lag = num.arctan2(spectrum.imag, spectrum.real)
# eq. (9.52) in Bendat & Piersol 2000
error = num.sqrt((1 - coherence) / (2 * numinbin * coherence))
return lag, error
def scipyhist2(bins, y): #give bins for binning
nbin = len(bins)
xbin = N.zeros(len(bins), 'f')
ybin = N.zeros(len(bins), 'f')
ybinerr = N.zeros(len(bins), 'f')
y = N.take(y, N.argsort(y))
xmin = min(bins)
xmax = max(bins)
xbinnumb = ((y - xmin) * nbin / (xmax - xmin)
) #calculate x bin number for each point
for i in range(len(xbin) - 1):
xmin = bins[i]
xmax = bins[i + 1]
yb = 0.
for j in range(len(y)):
if y[j] > xmin:
yb = yb + 1.
if y[j] > xmax:
ybin[i] = yb
ybinerr[i] = N.sqrt(yb)
xbin[i] = 0.5 * (xmin + xmax)
break
return xbin, ybin, ybinerr
def readpsoutput(self,file,z): input=open(file,'r') mass=[] frac=[] for line in input: t=line.split() mass.append(float(t[2])) frac.append(float(t[3])) #try: #frac.append(float(t[3])) #except: # frac.append(1.e-10) input.close() mass=N.array(mass,'d') sigma=((mass/(1.2e15/h)*N.sqrt(.7+.3*(1+z)**3))**(1./3.))*1000. frac=N.array(frac,'d') sigma=N.log10(sigma) #maccret=(frac*mass) maccret=N.zeros(len(mass),'d') for i in range(len(mass)): maccret[i]=mass[i]*frac[i] print i,mass[i],frac[i],maccret[i] frac=N.log10(frac) self.sigma=sigma self.mass=mass self.frac=frac self.maccret=maccret
def verticalhist(y, ymin, ymax, nbin): #give bins for binning
#nbin=len(bins)
xbin = N.zeros(nbin, 'f')
ybin = N.zeros(nbin, 'f')
ybinerr = N.zeros(nbin, 'f')
dbin = (ymax - ymin) / (1. * nbin)
bins = N.arange(ymin, (ymax + dbin), dbin)
y = N.take(y, N.argsort(y))
xmin = min(bins)
xmax = max(bins)
xbinnumb = ((y - xmin) * nbin / (xmax - xmin)
) #calculate x bin number for each point
for i in range(len(xbin) - 1):
xmin = bins[i]
xmax = bins[i + 1]
yb = 0.
for j in range(len(y)):
if y[j] > xmin:
yb = yb + 1.
if y[j] > xmax:
ybin[i] = yb
ybinerr[i] = N.sqrt(yb)
#xbin[i]=0.5*(xmin+xmax)
xbin[i] = xmax
break
drawhist(ybin, xbin)
def points(self,npoints):
"""
compute arrays of npoints equally spaced
intermediate points along the great circle.
input parameter npoints is the number of points
to compute.
Returns lons, lats (lists with longitudes and latitudes
of intermediate points in degrees).
For example npoints=10 will return arrays lons,lats of 10
equally spaced points along the great circle.
"""
# must ask for at least 2 points.
if npoints <= 1:
raise ValueError,'npoints must be greater than 1'
elif npoints == 2:
return [math.degrees(self.lon1),math.degrees(self.lon2)],[math.degrees(self.lat1),math.degrees(self.lat2)]
# can't do it if endpoints are antipodal, since
# route is undefined.
if self.antipodal:
raise ValueError,'cannot compute intermediate points on a great circle whose endpoints are antipodal'
d = self.gcarclen
delta = 1.0/(npoints-1)
f = delta*N.arange(npoints) # f=0 is point 1, f=1 is point 2.
incdist = self.distance/(npoints-1)
lat1 = self.lat1
lat2 = self.lat2
lon1 = self.lon1
lon2 = self.lon2
# perfect sphere, use great circle formula
if self.f == 0.:
A = N.sin((1-f)*d)/math.sin(d)
B = N.sin(f*d)/math.sin(d)
x = A*math.cos(lat1)*math.cos(lon1)+B*math.cos(lat2)*math.cos(lon2)
y = A*math.cos(lat1)*math.sin(lon1)+B*math.cos(lat2)*math.sin(lon2)
z = A*math.sin(lat1) +B*math.sin(lat2)
lats=N.arctan2(z,N.sqrt(x**2+y**2))
lons=N.arctan2(y,x)
lons = map(math.degrees,lons.tolist())
lats = map(math.degrees,lats.tolist())
# use ellipsoid formulas
else:
latpt = self.lat1
lonpt = self.lon1
azimuth = self.azimuth12
lons = [math.degrees(lonpt)]
lats = [math.degrees(latpt)]
for n in range(npoints-2):
latptnew,lonptnew,alpha21=vinc_pt(self.f,self.a,latpt,lonpt,azimuth,incdist)
d,azimuth,a21=vinc_dist(self.f,self.a,latptnew,lonptnew,lat2,lon2)
lats.append(math.degrees(latptnew))
lons.append(math.degrees(lonptnew))
latpt = latptnew; lonpt = lonptnew
lons.append(math.degrees(self.lon2))
lats.append(math.degrees(self.lat2))
return lons,lats
def mask(clus_id, line_s):
imagefile = c.imagefile
sex_cata = c.sex_cata
threshold = c.threshold
thresh_area = c.thresh_area
size = c.size
mask_reg = c.mask_reg
x = n.reshape(n.arange(size*size),(size,size)) % size
x = x.astype(n.Float32)
y = n.reshape(n.arange(size*size),(size,size)) / size
y = y.astype(n.Float32)
values = line_s.split()
mask_file = 'mask_' + str(imagefile)[:6] + '_' + str(clus_id) + '.fits'
xcntr_o = float(values[1]) #x center of the object
ycntr_o = float(values[2]) #y center of the object
xcntr = size / 2.0 + 1.0 + xcntr_o - int(xcntr_o)
ycntr = size / 2.0 + 1.0 + ycntr_o - int(ycntr_o)
mag = float(values[7]) #Magnitude
radius = float(values[9]) #Half light radius
mag_zero = c.mag_zero #magnitude zero point
sky = float(values[10]) #sky
pos_ang = float(values[11]) - 90.0 #position angle
axis_rat = 1.0 / float(values[12]) #axis ration b/a
major_axis = float(values[14]) #major axis of the object
z = n.zeros((size,size))
for line_j in open(sex_cata,'r'):
try:
values = line_j.split()
xcntr_n = float(values[1]) #x center of the neighbour
ycntr_n = float(values[2]) #y center of the neighbour
mag = float(values[7]) #Magnitude
radius = float(values[9]) #Half light radius
sky = float(values[10]) #sky
pos_ang = float(values[11]) - 90.0 #position angle
axis_rat = 1.0/float(values[12]) #axis ration b/a
area = float(values[13])
maj_axis = float(values[14])#major axis of neighbour
if(abs(xcntr_n - xcntr_o) < size/2.0 and abs(ycntr_n - ycntr_o) \
< size/2.0 and area < thresh_area):
if(abs(xcntr_n - xcntr_o) >= major_axis * threshold or \
abs(ycntr_n - ycntr_o) >= major_axis * threshold):
if((xcntr_o - xcntr_n) < 0):
xn = xcntr + abs(xcntr_n - xcntr_o)
if((ycntr_o - ycntr_n) < 0):
yn = ycntr + abs(ycntr_n - ycntr_o)
if((xcntr_o - xcntr_n) > 0):
xn = xcntr - (xcntr_o - xcntr_n)
if((ycntr_o - ycntr_n) > 0):
yn = ycntr - (ycntr_o - ycntr_n)
tx = x - xn + 0.5
ty = y - yn + 0.5
R = n.sqrt(tx**2.0 + ty**2.0)
z[n.where(R<=mask_reg*maj_axis)] = 1
except:
pass
hdu = pyfits.PrimaryHDU(z.astype(n.Float32))
hdu.writeto(mask_file)
def drawmeridians(self,ax,meridians,color='k',linewidth=1., \
linestyle='--',dashes=[1,1]):
"""
draw meridians (longitude lines).
ax - current axis instance.
meridians - list containing longitude values to draw (in degrees).
color - color to draw meridians (default black).
linewidth - line width for meridians (default 1.)
linestyle - line style for meridians (default '--', i.e. dashed).
dashes - dash pattern for meridians (default [1,1], i.e. 1 pixel on,
1 pixel off).
"""
if self.projection not in ['merc','cyl']:
lats = N.arange(-80,81).astype('f')
else:
lats = N.arange(-90,91).astype('f')
xdelta = 0.1*(self.xmax-self.xmin)
ydelta = 0.1*(self.ymax-self.ymin)
for merid in meridians:
lons = merid*N.ones(len(lats),'f')
x,y = self(lons,lats)
# remove points outside domain.
testx = N.logical_and(x>=self.xmin-xdelta,x<=self.xmax+xdelta)
x = N.compress(testx, x)
y = N.compress(testx, y)
testy = N.logical_and(y>=self.ymin-ydelta,y<=self.ymax+ydelta)
x = N.compress(testy, x)
y = N.compress(testy, y)
if len(x) > 1 and len(y) > 1:
# split into separate line segments if necessary.
# (not necessary for mercator or cylindrical).
xd = (x[1:]-x[0:-1])**2
yd = (y[1:]-y[0:-1])**2
dist = N.sqrt(xd+yd)
split = dist > 500000.
if N.sum(split) and self.projection not in ['merc','cyl']:
ind = (N.compress(split,MLab.squeeze(split*N.indices(xd.shape)))+1).tolist()
xl = []
yl = []
iprev = 0
ind.append(len(xd))
for i in ind:
xl.append(x[iprev:i])
yl.append(y[iprev:i])
iprev = i
else:
xl = [x]
yl = [y]
# draw each line segment.
for x,y in zip(xl,yl):
# skip if only a point.
if len(x) > 1 and len(y) > 1:
l = Line2D(x,y,linewidth=linewidth,linestyle=linestyle)
l.set_color(color)
l.set_dashes(dashes)
ax.add_line(l)
def plot_source_info(self, event):
ra = event.xdata
dec = event.ydata
#print (event.key,ra,dec)
if event.key == 's':
#print self.constructed_pos[:,0]
#print self.constructed_pos[:,1]
dist = numarray.sqrt((self.constructed_pos[:, 0] - ra)**2 +
(self.constructed_pos[:, 1] - dec)**2)
#print dist
#print "min distance = %f " % min(dist)
the_source_ind = numarray.compress(
dist == min(dist),
numarray.fromlist(range(len(self.constructed_source_list))))
#print the_source_ind
#the_source_ind = numarray.compress(dist == min(dist),numarray.arange(len(self.constructed_source_list)))
the_source = self.constructed_source_list[the_source_ind[0]]
print the_source
dist = numarray.sqrt(
(the_source.current_pos[0] - self.real_pos[:, 0])**2 +
(the_source.current_pos[1] - self.real_pos[:, 1])**2)
print "min distances to nearest real source = %f arcsec" % min(
dist)
the_source_ind = numarray.compress(
dist == min(dist),
numarray.fromlist(range(len(self.real_list))))
the_source = self.real_list[the_source_ind[0]]
print "That real source is at ra=%f dec=%f" % (
the_source.start_pos[0], the_source.start_pos[1])
if event.key == 'r':
dist = numarray.sqrt((self.real_pos[:, 0] - ra)**2 +
(self.real_pos[:, 1] - dec)**2)
#print dist
#print "min distance = %f " % min(dist)
the_source_ind = numarray.compress(
dist == min(dist),
numarray.fromlist(range(len(self.real_list))))
#print the_source_ind
#the_source_ind = numarray.compress(dist == min(dist),numarray.arange(len(self.constructed_source_list)))
the_source = self.real_list[the_source_ind[0]]
print the_source
def getnearestgen(self,ra1,dec1,ra2,dec2,j):#measure distances from ra1, dec1 to members in catalog ra2, dec2
sig5=N.zeros(len(ra1),'f')
sig10=N.zeros(len(ra1),'f')
for i in range(len(ra1)):
angdist=my.DA(c.z[j],h100)#kpc/arcsec
dspec=N.sqrt((ra1[i]-ra2)**2+(dec1[i]-dec2)**2)#sorted array of distances in degrees
dspecsort=N.take(dspec,N.argsort(dspec))
sig5[i]=5./(N.pi)/(dspecsort[5]*3600.*angdist/1000.)**2#convert from deg to arcsec, multiply by DA (kpc/arcsec), divide by 1000 to convert to Mpc, index 5 element b/c 0 is itself
sig10[i]=10./(N.pi)/(dspecsort[10]*3600.*angdist/1000.)**2#convert from deg to arcsec, multiply by DA (kpc/arcsec), divide by 1000 to convert to Mpc, index 5 element b/c 0 is itself
return sig5, sig10
def line_search_BFGS(f, xk, pk, gfk, args=(), c1=1e-4, alpha0=1):
"""alpha, fc, gc = line_search(f, xk, pk, gfk,
args=(), c1=1e-4, alpha0=1)
minimize over alpha, the function f(xk+alpha pk) using the interpolation
algorithm (Armiijo backtracking) as suggested by
Wright and Nocedal in 'Numerical Optimization', 1999, pg. 56-57
"""
fc = 0
phi0 = apply(f, (xk, ) + args) # compute f(xk)
phi_a0 = apply(f, (xk + alpha0 * pk, ) + args) # compute f
fc = fc + 2
derphi0 = Num.dot(gfk, pk)
if (phi_a0 <= phi0 + c1 * alpha0 * derphi0):
return alpha0, fc, 0
# Otherwise compute the minimizer of a quadratic interpolant:
alpha1 = -(derphi0) * alpha0**2 / 2.0 / (phi_a0 - phi0 - derphi0 * alpha0)
phi_a1 = apply(f, (xk + alpha1 * pk, ) + args)
fc = fc + 1
if (phi_a1 <= phi0 + c1 * alpha1 * derphi0):
return alpha1, fc, 0
# Otherwise loop with cubic interpolation until we find an alpha which satifies
# the first Wolfe condition (since we are backtracking, we will assume that
# the value of alpha is not too small and satisfies the second condition.
while 1: # we are assuming pk is a descent direction
factor = alpha0**2 * alpha1**2 * (alpha1 - alpha0)
a = alpha0**2 * (phi_a1 - phi0 - derphi0*alpha1) - \
alpha1**2 * (phi_a0 - phi0 - derphi0*alpha0)
a = a / factor
b = -alpha0**3 * (phi_a1 - phi0 - derphi0*alpha1) + \
alpha1**3 * (phi_a0 - phi0 - derphi0*alpha0)
b = b / factor
alpha2 = (-b + Num.sqrt(abs(b**2 - 3 * a * derphi0))) / (3.0 * a)
phi_a2 = apply(f, (xk + alpha2 * pk, ) + args)
fc = fc + 1
if (phi_a2 <= phi0 + c1 * alpha2 * derphi0):
return alpha2, fc, 0
if (alpha1 - alpha2) > alpha1 / 2.0 or (1 - alpha2 / alpha1) < 0.96:
alpha2 = alpha1 / 2.0
alpha0 = alpha1
alpha1 = alpha2
phi_a0 = phi_a1
phi_a1 = phi_a2
def __call__(self, x):
if (type(x) == type(1) or type(x) == type(1.)):
return self.value(x)
elif (type(x) == type([])):
my_list = []
for xx in x:
my_list.append(self.value(xx))
return my_list
elif (type(x) == numarray.NumArray):
return (numarray.exp(-numarray.power((x-self.mean)/self.sigma, 2)/2.)
/numarray.sqrt(2.*numarray.pi)/self.sigma)
def fit_i(x, y, sig, int_scat=0.0):
#Given a set of data points x, y,
#with individual measurement error standard deviations sig,
#fit them to a straight line relation y = a + bx
#with intrinsic scatter int_scat by minimizing chi-sq.
#Returned are a, b and their respective probable uncertainties siga and sigb,
#the chi-square chi2, and the scatter sigdat.
#If mwt=0 on input, then the standard deviations are assumed to be unavailable:
#the normalization of chi2 is to unit standard deviation on all points.
sigtot = N.sqrt(sig**2 + int_scat**2)
return fit(x, y, sigtot)
def fit_intercept_i(x, y, sig, int_scat, b=0.0, sigb=0.0):
#Given a set of data points x, y,
#with individual standard deviations sig,
#fit them to a straight line y = a + bx by minimizing chi-sq,
#where the intercept of the line is fixed.
#Returned are a and its probable uncertainty siga,
#the chi-square chi2, and the scatter sigdat.
#If mwt=0 on input, then the standard deviations are assumed to be unavailable:
#the normalization of chi2 is to unit standard deviation on all points.
sigtot = N.sqrt(sig**2 + int_scat**2)
return fit_intercept(x, y, sigtot, 1, b, sigb)
def __call__(self, x):
if (type(x) == type(1) or type(x) == type(1.)):
return self.value(x)
elif (type(x) == type([])):
my_list = []
for xx in x:
my_list.append(self.value(xx))
return my_list
elif (type(x) == numarray.NumArray):
return (numarray.exp(-numarray.power(
(x - self.mean) / self.sigma, 2) / 2.) /
numarray.sqrt(2. * numarray.pi) / self.sigma)
def gauss(x,m,sigma):
""" Return a Gaussian with mean, sigma for a numarray x """
sigma2 = sigma*sigma
exponent = -(x-m)**2/(2.*sigma2)
exponent = numarray.choose(exponent<-700.,(exponent,-700.))
try:
result = numarray.exp(exponent)/numarray.sqrt(2.*numarray.pi*sigma2)
except OverflowError:
print "gauss: overflow error"
print "sigma = ", sigma
print "m = ", m
print "x = ", x
sys.exit()
return result
def generic_gradient_magnitude(input,
derivative,
output=None,
mode="reflect",
cval=0.0,
extra_arguments=(),
extra_keywords={}):
"""Calculate a gradient magnitude using the provdide function for
the gradient.
The derivative parameter must be a callable with the following
signature:
derivative(input, axis, output, mode, cval,
*extra_arguments, **extra_keywords)
The extra_arguments and extra_keywords arguments can be used to pass
extra arguments and keywords that are passed to derivative2 at each
call.
"""
input = numarray.asarray(input)
output, return_value = _ni_support._get_output(output, input)
axes = range(input.rank)
if len(axes) > 0:
derivative(input, axes[0], output, mode, cval, *extra_arguments,
**extra_keywords)
numarray.multiply(output, output, output)
for ii in range(1, len(axes)):
tmp = derivative(input, axes[ii], output.type(), mode, cval,
*extra_arguments, **extra_keywords)
numarray.multiply(tmp, tmp, tmp)
output += tmp
numarray.sqrt(output, output)
else:
output[...] = input[...]
return return_value
def _SampleDist(self, sep, ntrials=20, nsamp=100):
srcDir = SkyDir(180., sep)
nobs = []
for j in range(ntrials):
naccept = 0
for i in range(nsamp):
appDir = self.psf.appDir(self.energy, srcDir, self.scZAxis,
self.scXAxis)
if self.cones[0].inside(appDir):
naccept += 1
nobs.append(naccept)
nobs = num.array(nobs)
navg = sum(nobs)/float(ntrials)
return (navg/float(nsamp),
num.sqrt(sum(nobs**2)/float(ntrials) - navg**2)/float(nsamp))
def solveforab(aveaperr, avearea): #(a,b)=solveforab(aveap,avearea)
amin = .0
amax = 1
bmin = .0
bmax = 1
step = .005
a = N.arange(amin, amax, step, 'f')
b = N.arange(bmin, bmax, step, 'f')
y = N.zeros(len(aveaperr), 'f')
diff = N.zeros(len(aveaperr), 'f')
mini = 1000000000.
for ai in a:
for bi in b:
y = N.zeros(len(avearea), 'f')
y = N.sqrt(avearea) * ai * (1. + bi * N.sqrt(avearea))
#diff = N.sqrt((y - aveap)**2)
diff = (y - aveaperr)
sumdiff = N.sum(abs(diff))
#print "%5.3f %5.3f %8.2f %8.2f" %(ai,bi,sumdiff,mini)
if sumdiff < mini:
afinal = ai
bfinal = bi
mini = sumdiff
return afinal, bfinal
def gauss(x, m, sigma):
""" Return a Gaussian with mean, sigma for a numarray x """
sigma2 = sigma * sigma
exponent = -(x - m)**2 / (2. * sigma2)
exponent = numarray.choose(exponent < -700., (exponent, -700.))
try:
result = numarray.exp(exponent) / numarray.sqrt(
2. * numarray.pi * sigma2)
except OverflowError:
print "gauss: overflow error"
print "sigma = ", sigma
print "m = ", m
print "x = ", x
sys.exit()
return result
def ratioerrorold(a, b):
a = 1. * a #make sure it's a real number, not integer
b = 1. * b
try:
len(a) #continue of a in an array
ratio = []
err = []
for i in range(len(a)):
try:
ratio.append(a[i] / b[i])
if a[i] > 0.:
err.append(a[i] / b[i] * N.sqrt(1. / a[i] + 1. / b[i]))
else:
err.append(0.)
except ZeroDivisionError:
ratio.append(-1)
err.append(0.)
except TypeError: #a is a number rather than an array
ratio = a / b
try:
err = a / b * N.sqrt(1. / a + 1. / b)
except:
err = 0.
return ratio, err
def findnearest(x1, y1, x2, y2, delta):
dmin = 100000000000000000000000000000000000.
matchflag = 1
nmatch = 0
for i in range(len(x2)):
d = N.sqrt((x1 - x2[i])**2 + (y1 - y2[i])**2)
if d < delta:
nmatch = nmatch + 1
if d < dmin:
dmin = d
imatch = i
if dmin > delta:
imatch = 0
matchflag = 0
return imatch, matchflag, nmatch
def makeplot():
psplotinit("noise.ps")
DATAMIN = 0.
DATAMAX = 15.
ppgplot.pgbox("", 0.0, 0, "L", 0.0, 0)
#print "making graph, ncl = ",ncl
path = os.getcwd()
f = path.split('/')
#print path
#print f
prefix = f[4]
title = prefix
ymin = -.05
ymax = max(aveaperr) + .1
#ymax=10.
ppgplot.pgenv(DATAMIN, DATAMAX, ymin, ymax, 0)
ppgplot.pglab("linear size N of aperture (pixel)", "rms in Sky (ADU/s)",
title)
ppgplot.pgsci(2) #red
ppgplot.pgslw(4) #line width
x = N.sqrt(avearea)
y = aveaperr
ppgplot.pgpt(x, y, 7)
#errory(x,y,erry)
ppgplot.pgsci(1) #black
#ppgplot.pgpt(isoarea,fluxerriso,3)
#x1=N.sqrt(contsubisoarea)
#y1=contsuberr
#x1=N.sqrt(isoarea)
#y1=fluxerriso
#y=n*y1
#ppgplot.pgpt(x1,y1,1)
#ppgplot.pgsci(4)#blue
#ppgplot.pgpt(x1,y,1)
#ppgplot.pgsci(1)#black
x = N.arange(0, 50, 1)
y = x * (a + b * a * x)
#y=N.sqrt(x)*.02
ppgplot.pgline(x, y)
#errory(x,y,erry)
ppgplot.pgend()
def findnearestalt(x1, y1, x2, y2, delta): #use where command
dmin = 100000000000000000000000000000000000.
matchflag = 1
nmatch = 0
d = N.sqrt((x1 - x2)**2 + (y1 - y2)**2) #x2 and y2 are arrays
t = pylab.where(d < delta)
matches = t[0]
if len(matches) > 0:
nmatch = len(matches)
z = d[matches]
imatch = matches[pylab.where(z == z.min())]
else:
imatch = 0
matchflag = 0
return imatch, matchflag, nmatch
def _stdev(data):
n = len(data[:,0,0])
s = num.zeros(data[0,:,:].shape, num.Float32)
# First pass to get the mean.
for j in range(n): s += data[j,:,:]
ave = s/n
var = num.zeros(s.shape, num.Float32)
ep = num.zeros(s.shape, num.Float32)
for j in range(n):
s = data[j,:,:]-ave
num.add(ep, s, ep)
p = s**2
num.add(var, p, var)
# Corrected two-pass formula.
num.subtract(var, ep*ep/n, var)
num.divide(var, (n-1), var)
return num.sqrt(var)
def xy2rd(self, pos):
"""
This method would apply the WCS keywords to a position to
generate a new sky position.
The algorithm comes directly from 'imgtools.xy2rd'
translate (x,y) to (ra, dec)
"""
if self.ctype1.find('TAN') < 0 or self.ctype2.find('TAN') < 0:
print 'XY2RD only supported for TAN projections.'
raise TypeError
if isinstance(pos, N.NumArray):
# If we are working with an array of positions,
# point to just X and Y values
posx = pos[:, 0]
posy = pos[:, 1]
else:
# Otherwise, we are working with a single X,Y tuple
posx = pos[0]
posy = pos[1]
xi = self.cd11 * (posx - self.crpix1) + self.cd12 * (posy -
self.crpix2)
eta = self.cd21 * (posx - self.crpix1) + self.cd22 * (posy -
self.crpix2)
xi = DEGTORAD(xi)
eta = DEGTORAD(eta)
ra0 = DEGTORAD(self.crval1)
dec0 = DEGTORAD(self.crval2)
ra = N.arctan((xi / (N.cos(dec0) - eta * N.sin(dec0)))) + ra0
dec = N.arctan(
((eta * N.cos(dec0) + N.sin(dec0)) /
(N.sqrt((N.cos(dec0) - eta * N.sin(dec0))**2 + xi**2))))
ra = RADTODEG(ra)
dec = RADTODEG(dec)
ra = DIVMOD(ra, 360.)
# Otherwise, just return the RA,Dec tuple.
return ra, dec
def xy2rd(filename, x,y,hdu = -1, hms = 0, verbose = 0):
from numarray import sin,cos,arctan2,sqrt
def degtorad(num):
return num/180.0*numarray.pi
def radtodeg(num):
return num/numarray.pi * 180.0
def degtoHMS(num):
mmm = int((num-int(num))*60.0)
sss = ((num-int(num))*60.0-mmm)*60.0
num = `int(num)`+":"+ `mmm`+":"+`sss`
return num
keys = ["CRPIX1","CRPIX2","CRVAL1","CRVAL2","CD1_1","CD1_2","CD2_1","CD2_2"]
CD = read_keys(filename,keys,hdu)
crpix = numarray.zeros((2),numarray.Float)
cd = numarray.zeros((2,2),numarray.Float)
crpix[0] = CD['CRPIX1'][0]
crpix[1] = CD['CRPIX2'][0]
ra0 = CD['CRVAL1'][0]
dec0 = CD['CRVAL2'][0]
cd[0,0] = CD['CD1_1'][0]
cd[0,1] = CD['CD1_2'][0]
cd[1,0] = CD['CD2_1'][0]
cd[1,1] = CD['CD2_2'][0]
xi = cd[0, 0] * (x - crpix[0]) + cd[0, 1] * (y - crpix[1])
eta = cd[1, 0] * (x - crpix[0]) + cd[1, 1] * (y - crpix[1])
xi = degtorad(xi)
eta = degtorad(eta)
ra0 = degtorad(ra0)
dec0 = degtorad(dec0)
ra = arctan2(xi,cos(dec0)-eta*sin(dec0)) + ra0
dec = arctan2(eta*cos(dec0)+sin(dec0),sqrt((cos(dec0)-eta*sin(dec0))**2 + xi**2))
ra = radtodeg(ra)# % 360.0
# if ra < 0: ra = ra + 360.0
dec = radtodeg(dec)
if (hms):
return degtoHMS(ra/15.0),degtoHMS(dec)
else:
return ra,dec
def plotPosError(starlist, outsuffix, imgtype='png'):
"""
Load up a starlist output by align_rms.
"""
tab = asciidata.open(starlist)
mag = tab[1].tonumarray()
x = tab[3].tonumarray()
y = tab[4].tonumarray()
xerr = tab[5].tonumarray()
yerr = tab[6].tonumarray()
xdiff = x - 512.0
ydiff = y - 512.0
r = na.sqrt(xdiff**2 + ydiff**2)
err = (xerr + yerr) / 2.0
# Plot magnitude dependance
p.clf()
p.semilogy(mag, err*9.94, 'k.')
idx = (na.where(mag < 14))[0]
medianPix = na.linear_algebra.mlab.median(err[idx])
medianArc = medianPix * 9.94
p.text(9, 60, 'For (8 < K < 14)')
p.text(9, 40, 'Median Error = %5.3f pix (%5.3f mas)' %
(medianPix, medianArc))
p.xlabel('Magnitude')
p.ylabel('Positional Uncertainty (mas)''Positional Uncertainty (mas)')
p.savefig('pos_error_mag_%s.%s' % (outsuffix, imgtype))
# Plot radial dependance
p.clf()
p.semilogy(r[idx] * 0.00994, err[idx] * 9.94, 'k.')
p.xlabel('Radius from Field Center (arcsec)')
p.ylabel('Positional Uncertainty (mas)')
p.savefig('pos_error_r_%s.%s' % (outsuffix, imgtype))
def xy2rd(self,pos):
"""
This method would apply the WCS keywords to a position to
generate a new sky position.
The algorithm comes directly from 'imgtools.xy2rd'
translate (x,y) to (ra, dec)
"""
if self.ctype1.find('TAN') < 0 or self.ctype2.find('TAN') < 0:
print 'XY2RD only supported for TAN projections.'
raise TypeError
if isinstance(pos,N.NumArray):
# If we are working with an array of positions,
# point to just X and Y values
posx = pos[:,0]
posy = pos[:,1]
else:
# Otherwise, we are working with a single X,Y tuple
posx = pos[0]
posy = pos[1]
xi = self.cd11 * (posx - self.crpix1) + self.cd12 * (posy - self.crpix2)
eta = self.cd21 * (posx - self.crpix1) + self.cd22 * (posy - self.crpix2)
xi = DEGTORAD(xi)
eta = DEGTORAD(eta)
ra0 = DEGTORAD(self.crval1)
dec0 = DEGTORAD(self.crval2)
ra = N.arctan((xi / (N.cos(dec0)-eta*N.sin(dec0)))) + ra0
dec = N.arctan( ((eta*N.cos(dec0)+N.sin(dec0)) /
(N.sqrt((N.cos(dec0)-eta*N.sin(dec0))**2 + xi**2))) )
ra = RADTODEG(ra)
dec = RADTODEG(dec)
ra = DIVMOD(ra, 360.)
# Otherwise, just return the RA,Dec tuple.
return ra,dec
def plotPosError(starlist, outsuffix, imgtype='png'):
"""
Load up a starlist output by align_rms.
"""
tab = asciidata.open(starlist)
mag = tab[1].tonumarray()
x = tab[3].tonumarray()
y = tab[4].tonumarray()
xerr = tab[5].tonumarray()
yerr = tab[6].tonumarray()
xdiff = x - 512.0
ydiff = y - 512.0
r = na.sqrt(xdiff**2 + ydiff**2)
err = (xerr + yerr) / 2.0
# Plot magnitude dependance
p.clf()
p.semilogy(mag, err * 9.94, 'k.')
idx = (na.where(mag < 14))[0]
medianPix = na.linear_algebra.mlab.median(err[idx])
medianArc = medianPix * 9.94
p.text(9, 60, 'For (8 < K < 14)')
p.text(9, 40,
'Median Error = %5.3f pix (%5.3f mas)' % (medianPix, medianArc))
p.xlabel('Magnitude')
p.ylabel('Positional Uncertainty (mas)' 'Positional Uncertainty (mas)')
p.savefig('pos_error_mag_%s.%s' % (outsuffix, imgtype))
# Plot radial dependance
p.clf()
p.semilogy(r[idx] * 0.00994, err[idx] * 9.94, 'k.')
p.xlabel('Radius from Field Center (arcsec)')
p.ylabel('Positional Uncertainty (mas)')
p.savefig('pos_error_r_%s.%s' % (outsuffix, imgtype))
def biniterr(
x, y, n
): #bin arrays x, y into n equally-populated bins, returning xbin,ybin
nx = len(x)
#x=N.array(x,'f')
#y=N.array(y,'f')
y = N.take(y, N.argsort(x))
x = N.take(x, N.argsort(x))
xbin = N.zeros(n, 'f')
xbin = N.zeros(n, 'f')
ybin = N.zeros(n, 'f')
ybinerr = N.zeros(n, 'f')
for i in range(n):
nmin = i * int(float(nx) / float(n))
nmax = (i + 1) * int(float(nx) / float(n))
#xbin[i]=scipy.stats.stats.median(x[nmin:nmax])
#ybin[i]=scipy.stats.stats.median(y[nmin:nmax])
xbin[i] = N.average(x[nmin:nmax])
ybin[i] = N.average(y[nmin:nmax])
ybinerr[i] = pylab.std(y[nmin:nmax]) / N.sqrt(1. * (nmax - nmin))
return xbin, ybin, ybinerr
def points(self, npoints):
"""
compute arrays of npoints equally spaced
intermediate points along the great circle.
input parameter npoints is the number of points
to compute.
Returns lons, lats (lists with longitudes and latitudes
of intermediate points in degrees).
For example npoints=10 will return arrays lons,lats of 10
equally spaced points along the great circle.
"""
# can't do it if endpoints of great circle are antipodal, since
# route is undefined.
if self.antipodal:
raise ValueError, 'cannot compute intermediate points on a great circle whose endpoints are antipodal'
d = self.distance
delta = 1.0 / (npoints - 1)
f = delta * N.arange(npoints)
lat1 = self.lat1
lat2 = self.lat2
lon1 = self.lon1
lon2 = self.lon2
A = N.sin((1 - f) * d) / math.sin(d)
B = N.sin(f * d) / math.sin(d)
x = A * math.cos(lat1) * math.cos(lon1) + B * math.cos(
lat2) * math.cos(lon2)
y = A * math.cos(lat1) * math.sin(lon1) + B * math.cos(
lat2) * math.sin(lon2)
z = A * math.sin(lat1) + B * math.sin(lat2)
lats = N.arctan2(z, N.sqrt(x**2 + y**2))
lons = N.arctan2(y, x)
lons = map(math.degrees, lons.tolist())
lats = map(math.degrees, lats.tolist())
return lons, lats
def kaiser_window(self, beta=4, show=0, use_scipy=None): if use_scipy == None: # modified Bessel function of zero kind order def I_0(x): i0=0 fac = lambda n:reduce(lambda a,b:a*(b+1),range(n),1) for n in range(20): i0 += ((x/2.0)**n/(fac(n)))**2 return i0 t = numarray.arange(self.data_points, type=numarray.Float) - self.data_points/2.0 T = self.data_points # this is the window function array apod = I_0(beta*numarray.sqrt(1-(2*t/T)**2))/I_0(beta) else: # alternative method using scipy import scipy apod=scipy.kaiser(self.data_points, beta) for i in range(2): self.the_result.y[i] = self.the_result.y[i]*apod if show == 1: return self.the_result return self
def calcCorrelationHelper(s1p, s2p):
# if the traits share less than six strains, then we don't
# bother with the correlations
if len(s1p) < 6:
return 0.0
# subtract by x-bar and y-bar elementwise
#oldS1P = s1p.copy()
#oldS2P = s2p.copy()
s1p = (s1p - numarray.average(s1p)).astype(numarray.Float64)
s2p = (s2p - numarray.average(s2p)).astype(numarray.Float64)
# square for the variances
s1p_2 = numarray.sum(s1p**2)
s2p_2 = numarray.sum(s2p**2)
try:
corr = (numarray.sum(s1p*s2p)/
numarray.sqrt(s1p_2 * s2p_2))
except ZeroDivisionError:
corr = 0.0
return corr
def coherence(cross_spectrum, power_spectra, noise=None, numinbin=1,
subbed=1):
"""Compute coherence from cross and power spectra.
uncoh, uncoh_err, corcoh = coherence(cross_spectrum, power_spectra,
noise=None, numinbin=1, subbed=1)
Inputs:
cross_spectrum, power_spectra: Complex and real arrays, respectively.
power_spectra has one row for each signal band.
cross_spectrum has one fewer, and it is assumed that the cross spectra
of all bands but the first have been taken with respect to the first.
Will correct[1] for noise if it is supplied.
numinbin: The number of independent estimates that have gone into
each frequency bin.
If subbed is true, noise has already been subtracted from
the power spectra, and will not be during the calculations.
Outputs:
uncoh: The raw coherence. Eq. (6.51) in Bendat & Piersol 2000.
uncoh_err: Standard deviation in the raw coherence.
Eq. (9.81) in Bendat & Piersol 2000.
corcoh: The corrected coherence. Eq. (8) in Vaughan & Nowak 1997.
[1] Vaughan & Nowak 1997, ApJ 474:L43"""
cross_spectrum = num.asarray(cross_spectrum)
power_spectra = num.asarray(power_spectra)
if noise is not None:
correct = 1
noise = num.asarray(noise)
if subbed:
unsubtracted = power_spectra + noise
if correct:
subtracted = power_spectra
else:
unsubtracted = power_spectra
if correct:
subtracted = power_spectra - noise
s_one = unsubtracted[..., :1, :]
s_two = unsubtracted[..., 1:, :]
numerator = num.absolute(cross_spectrum) ** 2
uncorrected = numerator / (s_one * s_two)
# Sometimes floating-point issues cause these limits to be violated.
uncorrected = num.minimum(uncorrected, 1.0)
uncorrected = num.maximum(uncorrected, 0.0)
# error in uncorrected coherence
# eq. (9.81) in Bendat & Piersol 2000
varcoh = 2 * uncorrected * (1 - uncorrected) ** 2 / numinbin
uncoh_error = num.sqrt(varcoh)
if correct:
s_one = subtracted[..., :1, :]
s_two = subtracted[..., 1:, :]
n_one = noise[..., :1, :]
n_two = noise[..., 1:, :]
n_square = (s_one * n_two + n_one * s_two + n_one * n_two) / numinbin
numerator -= n_square
corrected = numerator / (s_one * s_two)
if correct:
return uncorrected, uncoh_error, corrected
else:
return uncorrected, uncoh_error
def mad_combine(infileglob, outfilebase):
# get list of files to operate on
files = glob.glob(infileglob)
# check more than one image exists
if files < 2:
print 'Less than two input files found!'
return
print 'Operating on images',infileglob
# get images
images = _get_images(files)
lenimages = len(images)
print 'Found', lenimages, 'images'
# get header of first image
hdr = images[0][0].header
# get ascard of first image
hdrascard = hdr.ascard
# get data from images into num (untidy tuple concatenation)
data = num.zeros((lenimages,) + images[0][0].data.shape, num.Float32)
for i in range(lenimages):
data[i,:,:] = images[i][0].data
# delete array
del images
# sort data
print 'Sorting... (this may take a while, i.e an hour or so!)'
#data_sorted = num.sort(data, axis=0)
data_sorted = data # for debugging
# find standard deviation of lowest n - n_discard pixels
print 'Calculating mad_low...'
mad_low = _mad3(data_sorted[:-n_discard,:,:])
# correct for bias to stddev
num.multiply(mad_low, corr[`lenimages - n_discard` + ',' + `lenimages`], mad_low)
# make median image
print 'Calculating median...'
if lenimages%2 != 0: # then odd number of images
m = (lenimages - 1) / 2
median = data_sorted[m,:,:]
else: # even number of images
m = lenimages / 2
median = (data_sorted[m,:,:] + data_sorted[m-1,:,:]) / 2
# delete array
del data_sorted
# get ccd properties from header
# these keywords are for FORS2
# - they may need altering for other instruments
gain = hdr['OUT1GAIN'] # N_{ADU} = gain * N_{e-}
invgain = 1.0 / gain # N_{e-} = invgain * N_{ADU}
ron = hdr['OUT1RON'] # read out noise in e-
# take only +ve values in median
median_pos = num.choose(median < 0.0, (median, 0.0))
# calculate sigma due to ccd noise for each pixel
print 'Calculating noise_med...'
noise_med = num.sqrt(median_pos * invgain + ron*ron) * gain
# delete array
del median_pos
# find maximum of noise and mad_low
# -> sigma to test pixels against to identify cosmics
print 'Calculating sigma_test...'
sigma_test = num.choose(noise_med < mad_low, (noise_med, mad_low))
# delete arrays
del mad_low, noise_med
# calculate 'relative residual' for each pixel
print 'Calculating rel_res...'
rel_res = num.zeros(data.shape, num.Float32)
res = num.zeros(data[0].shape, num.Float32)
for i in range(lenimages):
num.subtract(data[i,:,:], median, res)
num.divide(res, sigma_test, rel_res[i,:,:])
# delete arrays
del sigma_test, res
# now average over all pixels for which rel_res < sigma_limit
# first count number included for each pixel
# by testing to produce a boolean array, then summing over.
print 'Calculating included...'
included = num.zeros(rel_res[0].shape, num.Int16)
included[:,:] = num.sum(rel_res <= sigma_limit)
# put all discarded pixels to zero
print 'Calculating combined...'
pre_combine = num.choose(rel_res <= sigma_limit, (0.0,data))
# delete array
del rel_res
# sum all pixels and divide by included to give mean
combined = num.sum(pre_combine)
# delete array
del pre_combine
num.divide(combined, included, combined)
# Work out errors on this combined image
# take only +ve values in combined
mean_pos = num.choose(combined < 0.0, (combined, 0.0))
# calculate sigma due to ccd noise for each pixel
print 'Calculating noise_mean...'
noise_mean = num.sqrt(mean_pos * invgain + ron*ron) * gain
# delete array
del mean_pos
# create standard error image
print 'Calculating error...'
error = noise_mean / num.sqrt(included)
# delete array
del noise_mean
# write all images to disk
print 'Writing images to disk...'
_write_images(combined, error, included,
hdrascard, outfilebase)
def vc_v200_nfw(x, c):
top = N.log(1.0 + c*x) - c*x / (1.0 + c*x)
bottom = N.log(1.0 + c) - c / (1.0 + c)
vc2 = top / (x * bottom)
vc = N.sqrt(vc2)
return vc
def points(self, npoints):
"""
compute arrays of npoints equally spaced
intermediate points along the great circle.
input parameter npoints is the number of points
to compute.
Returns lons, lats (lists with longitudes and latitudes
of intermediate points in degrees).
For example npoints=10 will return arrays lons,lats of 10
equally spaced points along the great circle.
"""
# must ask for at least 2 points.
if npoints <= 1:
raise ValueError, 'npoints must be greater than 1'
elif npoints == 2:
return [math.degrees(self.lon1),
math.degrees(self.lon2)
], [math.degrees(self.lat1),
math.degrees(self.lat2)]
# can't do it if endpoints are antipodal, since
# route is undefined.
if self.antipodal:
raise ValueError, 'cannot compute intermediate points on a great circle whose endpoints are antipodal'
d = self.gcarclen
delta = 1.0 / (npoints - 1)
f = delta * N.arange(npoints) # f=0 is point 1, f=1 is point 2.
incdist = self.distance / (npoints - 1)
lat1 = self.lat1
lat2 = self.lat2
lon1 = self.lon1
lon2 = self.lon2
# perfect sphere, use great circle formula
if self.f == 0.:
A = N.sin((1 - f) * d) / math.sin(d)
B = N.sin(f * d) / math.sin(d)
x = A * math.cos(lat1) * math.cos(lon1) + B * math.cos(
lat2) * math.cos(lon2)
y = A * math.cos(lat1) * math.sin(lon1) + B * math.cos(
lat2) * math.sin(lon2)
z = A * math.sin(lat1) + B * math.sin(lat2)
lats = N.arctan2(z, N.sqrt(x**2 + y**2))
lons = N.arctan2(y, x)
lons = map(math.degrees, lons.tolist())
lats = map(math.degrees, lats.tolist())
# use ellipsoid formulas
else:
latpt = self.lat1
lonpt = self.lon1
azimuth = self.azimuth12
lons = [math.degrees(lonpt)]
lats = [math.degrees(latpt)]
for n in range(npoints - 2):
latptnew, lonptnew, alpha21 = vinc_pt(self.f, self.a, latpt,
lonpt, azimuth, incdist)
d, azimuth, a21 = vinc_dist(self.f, self.a, latptnew, lonptnew,
lat2, lon2)
lats.append(math.degrees(latptnew))
lons.append(math.degrees(lonptnew))
latpt = latptnew
lonpt = lonptnew
lons.append(math.degrees(self.lon2))
lats.append(math.degrees(self.lat2))
return lons, lats
NA.array([0, 0, 0]),
NA.array([[1, r12, r13], [r12, 1, r23], [r13, r23, 1]]), nsamps)
print 'correlations (r12,r13,r23) = ', r12, r13, r23
print 'number of realizations = ', nsamps
# training data.
obs = x[:, 0]
climprob = NA.sum((obs > 0).astype('f')) / nsamps
fcst = NA.transpose(x[:, 1:]) # 2 predictors.
obs_binary = obs > 0.
# independent data for verification.
obs2 = x2[:, 0]
fcst2 = NA.transpose(x2[:, 1:])
# compute logistic regression.
beta, Jbar, llik = logistic_regression(fcst, obs_binary, verbose=True)
covmat = LA.inverse(Jbar)
stderr = NA.sqrt(mlab.diag(covmat))
print 'beta =', beta
print 'standard error =', stderr
# forecasts from independent data.
prob = calcprob(beta, fcst2)
# compute Brier Skill Score
verif = (obs2 > 0.).astype('f')
bs = mlab.mean((0.01 * prob - verif)**2)
bsclim = mlab.mean((climprob - verif)**2)
bss = 1. - (bs / bsclim)
print 'Brier Skill Score (should be within +/- 0.1 of 0.18) = ', bss
# calculate reliability.
# see http://www.bom.gov.au/bmrc/wefor/staff/eee/verif/verif_web_page.html
# for information on the Brier Skill Score and reliability diagrams.
totfreq = NA.zeros(10, 'f')
obfreq = NA.zeros(10, 'f')
def drawmeridians(self,ax,meridians,color='k',linewidth=1., \
linestyle='--',dashes=[1,1],labels=[0,0,0,0],\
font='rm',fontsize=12):
"""
draw meridians (longitude lines).
ax - current axis instance.
meridians - list containing longitude values to draw (in degrees).
color - color to draw meridians (default black).
linewidth - line width for meridians (default 1.)
linestyle - line style for meridians (default '--', i.e. dashed).
dashes - dash pattern for meridians (default [1,1], i.e. 1 pixel on,
1 pixel off).
labels - list of 4 values (default [0,0,0,0]) that control whether
meridians are labelled where they intersect the left, right, top or
bottom of the plot. For example labels=[1,0,0,1] will cause meridians
to be labelled where they intersect the left and bottom of the plot,
but not the right and top. Labels are located with a precision of 0.1
degrees and are drawn using mathtext.
font - mathtext font used for labels ('rm','tt','it' or 'cal', default 'rm'.
fontsize - font size in points for labels (default 12).
"""
# don't draw meridians past latmax, always draw parallel at latmax.
latmax = 80. # not used for cyl, merc projections.
# offset for labels.
yoffset = (self.urcrnry-self.llcrnry)/100./self.aspect
xoffset = (self.urcrnrx-self.llcrnrx)/100.
if self.projection not in ['merc','cyl']:
lats = N.arange(-latmax,latmax+1).astype('f')
else:
lats = N.arange(-90,91).astype('f')
xdelta = 0.1*(self.xmax-self.xmin)
ydelta = 0.1*(self.ymax-self.ymin)
for merid in meridians:
lons = merid*N.ones(len(lats),'f')
x,y = self(lons,lats)
# remove points outside domain.
testx = N.logical_and(x>=self.xmin-xdelta,x<=self.xmax+xdelta)
x = N.compress(testx, x)
y = N.compress(testx, y)
testy = N.logical_and(y>=self.ymin-ydelta,y<=self.ymax+ydelta)
x = N.compress(testy, x)
y = N.compress(testy, y)
if len(x) > 1 and len(y) > 1:
# split into separate line segments if necessary.
# (not necessary for mercator or cylindrical).
xd = (x[1:]-x[0:-1])**2
yd = (y[1:]-y[0:-1])**2
dist = N.sqrt(xd+yd)
split = dist > 500000.
if N.sum(split) and self.projection not in ['merc','cyl']:
ind = (N.compress(split,pylab.squeeze(split*N.indices(xd.shape)))+1).tolist()
xl = []
yl = []
iprev = 0
ind.append(len(xd))
for i in ind:
xl.append(x[iprev:i])
yl.append(y[iprev:i])
iprev = i
else:
xl = [x]
yl = [y]
# draw each line segment.
for x,y in zip(xl,yl):
# skip if only a point.
if len(x) > 1 and len(y) > 1:
l = Line2D(x,y,linewidth=linewidth,linestyle=linestyle)
l.set_color(color)
l.set_dashes(dashes)
ax.add_line(l)
# draw labels for meridians.
# search along edges of map to see if parallels intersect.
# if so, find x,y location of intersection and draw a label there.
if self.projection == 'cyl':
dx = 0.01; dy = 0.01
elif self.projection == 'merc':
dx = 0.01; dy = 1000
else:
dx = 1000; dy = 1000
for dolab,side in zip(labels,['l','r','t','b']):
if not dolab: continue
# for cyl or merc, don't draw meridians on left or right.
if self.projection in ['cyl','merc'] and side in ['l','r']: continue
if side in ['l','r']:
nmax = int((self.ymax-self.ymin)/dy+1)
if self.urcrnry < self.llcrnry:
yy = self.llcrnry-dy*N.arange(nmax)
else:
yy = self.llcrnry+dy*N.arange(nmax)
if side == 'l':
lons,lats = self(self.llcrnrx*N.ones(yy.shape,'f'),yy,inverse=True)
else:
lons,lats = self(self.urcrnrx*N.ones(yy.shape,'f'),yy,inverse=True)
lons = N.where(lons < 0, lons+360, lons)
lons = [int(lon*10) for lon in lons.tolist()]
lats = [int(lat*10) for lat in lats.tolist()]
else:
nmax = int((self.xmax-self.xmin)/dx+1)
if self.urcrnrx < self.llcrnrx:
xx = self.llcrnrx-dx*N.arange(nmax)
else:
xx = self.llcrnrx+dx*N.arange(nmax)
if side == 'b':
lons,lats = self(xx,self.llcrnry*N.ones(xx.shape,'f'),inverse=True)
else:
lons,lats = self(xx,self.urcrnry*N.ones(xx.shape,'f'),inverse=True)
lons = N.where(lons < 0, lons+360, lons)
lons = [int(lon*10) for lon in lons.tolist()]
lats = [int(lat*10) for lat in lats.tolist()]
for lon in meridians:
if lon<0: lon=lon+360.
# find index of meridian (there may be two, so
# search from left and right).
try:
nl = lons.index(int(lon*10))
except:
nl = -1
try:
nr = len(lons)-lons[::-1].index(int(lon*10))-1
except:
nr = -1
if lon>180:
lonlab = r'$\%s{%g\/^{\circ}\/W}$'%(font,N.fabs(lon-360))
elif lon<180 and lon != 0:
lonlab = r'$\%s{%g\/^{\circ}\/E}$'%(font,lon)
else:
lonlab = r'$\%s{%g\/^{\circ}}$'%(font,lon)
# meridians can intersect each map edge twice.
for i,n in enumerate([nl,nr]):
lat = lats[n]/10.
# no meridians > latmax for projections other than merc,cyl.
if self.projection not in ['merc','cyl'] and lat > latmax: continue
# don't bother if close to the first label.
if i and abs(nr-nl) < 100: continue
if n > 0:
if side == 'l':
pylab.text(self.llcrnrx-xoffset,yy[n],lonlab,horizontalalignment='right',verticalalignment='center',fontsize=fontsize)
elif side == 'r':
pylab.text(self.urcrnrx+xoffset,yy[n],lonlab,horizontalalignment='left',verticalalignment='center',fontsize=fontsize)
elif side == 'b':
pylab.text(xx[n],self.llcrnry-yoffset,lonlab,horizontalalignment='center',verticalalignment='top',fontsize=fontsize)
else:
pylab.text(xx[n],self.urcrnry+yoffset,lonlab,horizontalalignment='center',verticalalignment='bottom',fontsize=fontsize)
# make sure axis ticks are turned off
ax.set_xticks([])
ax.set_yticks([])
def distance_transform_edt(input, sampling = None,
return_distances = True, return_indices = False,
distances = None, indices = None):
"""Exact euclidean distance transform.
In addition to the distance transform, the feature transform can
be calculated. In this case the index of the closest background
element is returned along the first axis of the result.
The return_distances, and return_indices flags can be used to
indicate if the distance transform, the feature transform, or both
must be returned.
Optionally the sampling along each axis can be given by the
sampling parameter which should be a sequence of length equal to
the input rank, or a single number in which the sampling is assumed
to be equal along all axes.
the distances and indices arguments can be used to give optional
output arrays that must be of the correct size and type (Float64
and Int32).
"""
if (not return_distances) and (not return_indices):
msg = 'at least one of distances/indices must be specified'
raise RuntimeError, msg
ft_inplace = isinstance(indices, numarray.NumArray)
dt_inplace = isinstance(distances, numarray.NumArray)
# calculate the feature transform
input = numarray.where(input, 1, 0).astype(numarray.Int8)
if sampling is not None:
sampling = _ni_support._normalize_sequence(sampling, input.rank)
sampling = numarray.asarray(sampling, type = numarray.Float64)
if not sampling.iscontiguous():
sampling = sampling.copy()
if ft_inplace:
ft = indices
if ft.shape != (input.rank,) + input.shape:
raise RuntimeError, 'indices has wrong shape'
if ft.type() != numarray.Int32:
raise RuntimeError, 'indices must be of Int32 type'
else:
ft = numarray.zeros((input.rank,) + input.shape,
type = numarray.Int32)
_nd_image.euclidean_feature_transform(input, sampling, ft)
# if requested, calculate the distance transform
if return_distances:
dt = ft - numarray.indices(input.shape, type = ft.type())
dt = dt.astype(numarray.Float64)
if sampling is not None:
for ii in range(len(sampling)):
dt[ii, ...] *= sampling[ii]
numarray.multiply(dt, dt, dt)
if dt_inplace:
dt = numarray.add.reduce(dt, axis = 0)
if distances.shape != dt.shape:
raise RuntimeError, 'indices has wrong shape'
if distances.type() != numarray.Float64:
raise RuntimeError, 'indices must be of Float64 type'
numarray.sqrt(dt, distances)
del dt
else:
dt = numarray.add.reduce(dt, axis = 0)
dt = numarray.sqrt(dt)
# construct and return the result
result = []
if return_distances and not dt_inplace:
result.append(dt)
if return_indices and not ft_inplace:
result.append(ft)
if len(result) == 2:
return tuple(result)
elif len(result) == 1:
return result[0]
else:
return None
def abs_fft(self, points=None, zoom=None,write = 'off'): """ Fourier transforms the timesignal; points is the number of points to transform, if more points given than data points the rest is zero padded absfft(points=4096) """ realdata = numarray.array(self.the_result.y[0]) imdata = numarray.array(self.the_result.y[1]) data = realdata + 1j*imdata fftdata = self.rearrange(numarray.fft.fft(data, points)) absfft = numarray.sqrt(fftdata.real**2 + fftdata.imag**2) # create our x axis n = fftdata.size() self.the_result.x = (numarray.arange(n)*(self.sampling_rate/n)- (self.sampling_rate/2.0)) self.the_result.y[0] = absfft self.the_result.y[1] = numarray.zeros(n) if write == 'on': return self else: if zoom is None: return self.the_result else: center, width = zoom return self.zoom(self.the_result, center, width) def fft(self, points=None, zoom=None, write='off'): realdata = numarray.array(self.the_result.y[0]) imdata = numarray.array(self.the_result.y[1]) data = realdata + 1j*imdata fftdata = self.rearrange(numarray.fft.fft(data, points)) #phase = numarray.arctan(fftdata.real.sum() / fftdata.imag.sum()) #print "PHASE:", phase*180/numarray.pi # create our x axis n = fftdata.size() self.the_result.x = numarray.arange(n)*(self.sampling_rate/n)-(self.sampling_rate/2.0) # create new result self.the_result.y[0] = fftdata.real self.the_result.y[1] = fftdata.imag if write == 'on': return self else: if zoom is None: return self.the_result else: center, width = zoom return self.zoom(self.the_result, center, width) def realfft(self, points=None, zoom=None, write = 'off'): realdata = numarray.array(self.the_result.y[0]) imdata = numarray.array(self.the_result.y[1]) data = realdata + 1j*imdata fftdata = self.rearrange(numarray.fft.fft(data, points)) realfft = fftdata.real # create our x axis n = fftdata.size() self.the_result.x = numarray.arange(n)*(self.sampling_rate/n)-(self.sampling_rate/2.0) self.the_result.y[0] = realfft self.the_result.y[1] = numarray.zeros(n) if write == 'on': return self else: if zoom is None: return self.the_result else: center, width = zoom return self.zoom(self.the_result, center, width) def zoom(self,some_result, center="auto", width=1000): if center == "auto": i_center = int(self.the_result.y[0].argmax()) maximum = self.the_result.y[0][i_center] print "Maximum at Frequency:", self.the_result.x[i_center] else: i_center = int(self.data_points/2.0+self.data_points*center/self.sampling_rate) #print "TODO: set width automagically" #if width == "auto": # i_width = int(self.data_points*width) i_width = int(self.data_points*width/self.sampling_rate) some_result.x=some_result.x[i_center-i_width/2:i_center+i_width/2] some_result.y[0]=some_result.y[0][i_center-i_width/2:i_center+i_width/2] some_result.y[1]=some_result.y[1][i_center-i_width/2:i_center+i_width/2] return some_result """ Apodization functions: * exp_window and gauss_window are S/N enhancing, * dexp_window and traf_window are resolution enhancing * standard windows [hamming, hanning, bartlett, blackman, kaiser-bessel] are also available self.timepoints = time points self.aquisition_time = aquisition time (no. samples / sampling_rate) line_broadening = line broadening factor (standard = 10 Hz) gaussian_multiplicator = Gaussian Multiplication Factor for the double exponential apodization function (standard = 0.3) """ def exp_window(self, line_broadening=10, show=0): apod = numarray.exp(-self.timepoints*line_broadening) for i in range(2): self.the_result.y[i] = self.the_result.y[i]*apod if show == 1 : return self.the_result return self def gauss_window(self, line_broadening=10, show=0): apod = numarray.exp(-(self.timepoints*line_broadening)**2) for i in range(2): self.the_result.y[i] = self.the_result.y[i]*apod if show == 1 : return self.the_result return self def dexp_window(self, line_broadening=10, gaussian_multiplicator=0.3, show=0): apod = numarray.exp(-(self.timepoints*line_broadening - gaussian_multiplicator*self.aquisition_time)**2) for i in range(2): self.the_result.y[i] = self.the_result.y[i]*apod if show == 1: return self.the_result return self def traf_window(self, line_broadening=10, show=0): apod = (numarray.exp(-self.timepoints*line_broadening))**2 / ( (numarray.exp(-self.timepoints*line_broadening))**3 + (numarray.exp(-self.aquisition_time*line_broadening))**3 ) for i in range(2): self.the_result.y[i] = self.the_result.y[i]*apod if show == 1: return self.the_result return self def hanning_window(self, show=0): apod = numarray.mlab.hanning(self.data_points) for i in range(2): self.the_result.y[i] = self.the_result.y[i]*apod if show == 1: return self.the_result return self def hamming_window(self, show=0): apod = numarray.mlab.hamming(self.data_points) for i in range(2): self.the_result.y[i] = self.the_result.y[i]*apod if show == 1: return self.the_result return self def blackman_window(self, show=0): apod = numarray.mlab.blackman(self.data_points) for i in range(2): self.the_result.y[i] = self.the_result.y[i]*apod if show == 1: return self.the_result return self def bartlett_window(self, show=0): apod = numarray.mlab.bartlett(self.data_points) for i in range(2): self.the_result.y[i] = self.the_result.y[i]*apod if show == 1: return self.the_result return self def kaiser_window(self, beta=4, show=0, use_scipy=None): if use_scipy == None: # modified Bessel function of zero kind order def I_0(x): i0=0 fac = lambda n:reduce(lambda a,b:a*(b+1),range(n),1) for n in range(20): i0 += ((x/2.0)**n/(fac(n)))**2 return i0 t = numarray.arange(self.data_points, type=numarray.Float) - self.data_points/2.0 T = self.data_points # this is the window function array apod = I_0(beta*numarray.sqrt(1-(2*t/T)**2))/I_0(beta) else: # alternative method using scipy import scipy apod=scipy.kaiser(self.data_points, beta) for i in range(2): self.the_result.y[i] = self.the_result.y[i]*apod if show == 1: return self.the_result return self
def getNorm(self):
return sqrt(dot(self.array, self.array))
def plotRadial():
# Constants take from Bender et al. (2005)
cc = objects.Constants()
m31mass = 1.4e8
m31dist = 760000.0
# Construct an array of radii out to 5 arcsec in steps of 0.05''
r = (na.arange(12 * 5) * 0.05) + 0.05
r_au = r * m31dist
r_pc = r_au / cc.au_in_pc
r_cm = r_au * cc.cm_in_au
# Determine the theoretical amount for a vs. r
a_cm_s2 = cc.G * m31mass * cc.msun / r_cm**2
a_km_s_yr = a_cm_s2 * cc.sec_in_yr / 1.0e5
a_mas_yr2 = a_cm_s2 * pow(cc.sec_in_yr, 2) * 1000.0
a_mas_yr2 /= (cc.cm_in_au * m31dist)
# Plot circular velocity in both mas/yr and km/s
v_cm_s = na.sqrt(cc.G * m31mass * cc.msun / r_cm)
v_km_s = v_cm_s / 1.0e5
v_mas_yr = v_cm_s * cc.sec_in_yr * 1000.0/ (cc.cm_in_au * m31dist)
masyr_kms = (1.0/1000.0) * m31dist * cc.cm_in_au / (1.0e5 * cc.sec_in_yr)
masyr2_kmsyr = (1.0/1000.0) * m31dist * cc.cm_in_au
masyr2_kmsyr /= 1.0e5 * pow(cc.sec_in_yr, 2)
##########
#
# Calculate some useful quantities for Keck/TMT
#
##########
dKeck = 10.0
dTMT = 10.0
resKeckK = 1.0e3 * 0.25 * 2.2 / dKeck # K (GC) on Keck has similar Strehl
resTMTZ = 1.0e3 * 0.25 * 1.035 / dTMT # to obs with Z on TMT (mas).
posErrKeck = 0.15 # mas
ratioKeck = resKeckK / posErrKeck
posErrTMT = resTMTZ / ratioKeck
print('Estimated positional error for TMT at Z-band: %5.3f' % (posErrTMT))
# 1 years, 3 sigma
velLo1 = 3.0 * posErrTMT
velLoKms1 = velLo1 * masyr_kms
# 3 years, 3 sigma
velLo3 = posErrTMT
velLoKms3 = velLo3 * masyr_kms
print('Lowest detectable velocities in:')
print('\t 1 year, 3 sigma -- low vel = %4.2f mas/yr = %4d km/s' % \
(velLo1, velLoKms1))
print('\t 3 year, 3 sigma -- low vel = %4.2f mas/yr = %4d km/s' % \
(velLo3, velLoKms3))
##########
#
# Velocity vs. Radius
#
##########
pylab.figure(2, figsize=(7, 7))
pylab.clf()
# pylab.plot(r, v_mas_yr, linewidth=2)
# pylab.xlabel('Distance from Mbh (arcsec)')
# pylab.ylabel('Circular Velocity (mas/yr)')
pylab.plot(r, v_km_s, linewidth=2)
pylab.xlabel('Distance from Mbh (arcsec)')
pylab.ylabel('Circular Velocity (km/s)')
# Detection limit
# pylab.plot([0, 10], [velLo1, velLo1], 'k--')
# pylab.plot([0, 10], [velLo3, velLo3], 'k--')
# pylab.text(2.5, velLo1, '1 year')
# pylab.text(2.5, velLo3, '3 years')
pylab.plot([0, 10], [velLoKms1, velLoKms1], 'k--')
pylab.plot([0, 10], [velLoKms3, velLoKms3], 'k--')
pylab.plot([0, 10], [30.0, 30.0], 'k--')
pylab.text(2.5, velLoKms1, '1 year')
pylab.text(2.5, velLoKms3, '3 years')
pylab.text(0.3, 35.0, 'Radial Vel.')
arr1 = pylab.Arrow(2.4, velLoKms1, 0, 0.04*masyr_kms, width=0.09)
arr3 = pylab.Arrow(2.4, velLoKms3, 0, 0.04*masyr_kms, width=0.09)
arrRv = pylab.Arrow(0.2, 30.0, 0, 0.04*masyr_kms, width=0.09)
fig = pylab.gca()
fig.add_patch(arr1)
fig.add_patch(arr3)
fig.add_patch(arrRv)
str = '0.1 mas/yr = %4d km/s' % (0.1 * masyr_kms)
pylab.axis([0.0, 3, 0.0, 0.5*masyr_kms])
pylab.text(1.3, 0.45*masyr_kms, str)
pylab.savefig('m31theory_vel.png')
pylab.savefig('m31theory_vel.eps')
pylab.clf()
pylab.plot(r, a_mas_yr2)
pylab.xlabel('Distance from Mbh (arcsec)')
pylab.ylabel('Acceleration (mas/yr^2)')
str = '1 mas/yr^2 = %5.2f km/s/yr' % (1.0 * masyr2_kmsyr)
pylab.text(1.0e-3, 1.5, str)
pylab.savefig('m31theory_acc.eps')
pylab.savefig('m31theory_acc.png')
def plotRadial():
# Constants take from Bender et al. (2005)
cc = objects.Constants()
m31mass = 1.4e8
m31dist = 760000.0
# Construct an array of radii out to 5 arcsec in steps of 0.05''
r = (na.arange(12 * 5) * 0.05) + 0.05
r_au = r * m31dist
r_pc = r_au / cc.au_in_pc
r_cm = r_au * cc.cm_in_au
# Determine the theoretical amount for a vs. r
a_cm_s2 = cc.G * m31mass * cc.msun / r_cm**2
a_km_s_yr = a_cm_s2 * cc.sec_in_yr / 1.0e5
a_mas_yr2 = a_cm_s2 * pow(cc.sec_in_yr, 2) * 1000.0
a_mas_yr2 /= (cc.cm_in_au * m31dist)
# Plot circular velocity in both mas/yr and km/s
v_cm_s = na.sqrt(cc.G * m31mass * cc.msun / r_cm)
v_km_s = v_cm_s / 1.0e5
v_mas_yr = v_cm_s * cc.sec_in_yr * 1000.0 / (cc.cm_in_au * m31dist)
masyr_kms = (1.0 / 1000.0) * m31dist * cc.cm_in_au / (1.0e5 * cc.sec_in_yr)
masyr2_kmsyr = (1.0 / 1000.0) * m31dist * cc.cm_in_au
masyr2_kmsyr /= 1.0e5 * pow(cc.sec_in_yr, 2)
##########
#
# Calculate some useful quantities for Keck/TMT
#
##########
dKeck = 10.0
dTMT = 10.0
resKeckK = 1.0e3 * 0.25 * 2.2 / dKeck # K (GC) on Keck has similar Strehl
resTMTZ = 1.0e3 * 0.25 * 1.035 / dTMT # to obs with Z on TMT (mas).
posErrKeck = 0.15 # mas
ratioKeck = resKeckK / posErrKeck
posErrTMT = resTMTZ / ratioKeck
print('Estimated positional error for TMT at Z-band: %5.3f' % (posErrTMT))
# 1 years, 3 sigma
velLo1 = 3.0 * posErrTMT
velLoKms1 = velLo1 * masyr_kms
# 3 years, 3 sigma
velLo3 = posErrTMT
velLoKms3 = velLo3 * masyr_kms
print('Lowest detectable velocities in:')
print('\t 1 year, 3 sigma -- low vel = %4.2f mas/yr = %4d km/s' % \
(velLo1, velLoKms1))
print('\t 3 year, 3 sigma -- low vel = %4.2f mas/yr = %4d km/s' % \
(velLo3, velLoKms3))
##########
#
# Velocity vs. Radius
#
##########
pylab.figure(2, figsize=(7, 7))
pylab.clf()
# pylab.plot(r, v_mas_yr, linewidth=2)
# pylab.xlabel('Distance from Mbh (arcsec)')
# pylab.ylabel('Circular Velocity (mas/yr)')
pylab.plot(r, v_km_s, linewidth=2)
pylab.xlabel('Distance from Mbh (arcsec)')
pylab.ylabel('Circular Velocity (km/s)')
# Detection limit
# pylab.plot([0, 10], [velLo1, velLo1], 'k--')
# pylab.plot([0, 10], [velLo3, velLo3], 'k--')
# pylab.text(2.5, velLo1, '1 year')
# pylab.text(2.5, velLo3, '3 years')
pylab.plot([0, 10], [velLoKms1, velLoKms1], 'k--')
pylab.plot([0, 10], [velLoKms3, velLoKms3], 'k--')
pylab.plot([0, 10], [30.0, 30.0], 'k--')
pylab.text(2.5, velLoKms1, '1 year')
pylab.text(2.5, velLoKms3, '3 years')
pylab.text(0.3, 35.0, 'Radial Vel.')
arr1 = pylab.Arrow(2.4, velLoKms1, 0, 0.04 * masyr_kms, width=0.09)
arr3 = pylab.Arrow(2.4, velLoKms3, 0, 0.04 * masyr_kms, width=0.09)
arrRv = pylab.Arrow(0.2, 30.0, 0, 0.04 * masyr_kms, width=0.09)
fig = pylab.gca()
fig.add_patch(arr1)
fig.add_patch(arr3)
fig.add_patch(arrRv)
str = '0.1 mas/yr = %4d km/s' % (0.1 * masyr_kms)
pylab.axis([0.0, 3, 0.0, 0.5 * masyr_kms])
pylab.text(1.3, 0.45 * masyr_kms, str)
pylab.savefig('m31theory_vel.png')
pylab.savefig('m31theory_vel.eps')
pylab.clf()
pylab.plot(r, a_mas_yr2)
pylab.xlabel('Distance from Mbh (arcsec)')
pylab.ylabel('Acceleration (mas/yr^2)')
str = '1 mas/yr^2 = %5.2f km/s/yr' % (1.0 * masyr2_kmsyr)
pylab.text(1.0e-3, 1.5, str)
pylab.savefig('m31theory_acc.eps')
pylab.savefig('m31theory_acc.png')
def recenter(self):
"""
Reset the reference position values to correspond to the center
of the reference frame.
Algorithm used here developed by Colin Cox - 27-Jan-2004.
"""
if self.ctype1.find('TAN') < 0 or self.ctype2.find('TAN') < 0:
print 'WCS.recenter() only supported for TAN projections.'
raise TypeError
# Check to see if WCS is already centered...
if self.crpix1 == self.naxis1/2. and self.crpix2 == self.naxis2/2.:
# No recentering necessary... return without changing WCS.
return
# This offset aligns the WCS to the center of the pixel, in accordance
# with the 'align=center' option used by 'drizzle'.
#_drz_off = -0.5
_drz_off = 0.
_cen = (self.naxis1/2.+ _drz_off,self.naxis2/2. + _drz_off)
# Compute the RA and Dec for center pixel
_cenrd = self.xy2rd(_cen)
_cd = N.array([[self.cd11,self.cd12],[self.cd21,self.cd22]],type=N.Float64)
_ra0 = DEGTORAD(self.crval1)
_dec0 = DEGTORAD(self.crval2)
_ra = DEGTORAD(_cenrd[0])
_dec = DEGTORAD(_cenrd[1])
# Set up some terms for use in the final result
_dx = self.naxis1/2. - self.crpix1
_dy = self.naxis2/2. - self.crpix2
_dE,_dN = DEGTORAD(N.dot(_cd,(_dx,_dy)))
_dE_dN = 1 + N.power(_dE,2) + N.power(_dN,2)
_cosdec = N.cos(_dec)
_sindec = N.sin(_dec)
_cosdec0 = N.cos(_dec0)
_sindec0 = N.sin(_dec0)
_n1 = N.power(_cosdec,2) + _dE*_dE + _dN*_dN*N.power(_sindec,2)
_dra_dE = (_cosdec0 - _dN*_sindec0)/_n1
_dra_dN = _dE*_sindec0 /_n1
_ddec_dE = -_dE*N.tan(_dec) / _dE_dN
_ddec_dN = (1/_cosdec) * ((_cosdec0 / N.sqrt(_dE_dN)) - (_dN*N.sin(_dec) / _dE_dN))
# Compute new CD matrix values now...
_cd11n = _cosdec * (self.cd11*_dra_dE + self.cd21 * _dra_dN)
_cd12n = _cosdec * (self.cd12*_dra_dE + self.cd22 * _dra_dN)
_cd21n = self.cd11 * _ddec_dE + self.cd21 * _ddec_dN
_cd22n = self.cd12 * _ddec_dE + self.cd22 * _ddec_dN
_new_orient = RADTODEG(N.arctan2(_cd12n,_cd22n))
# Update the values now...
self.crpix1 = _cen[0]
self.crpix2 = _cen[1]
self.crval1 = RADTODEG(_ra)
self.crval2 = RADTODEG(_dec)
# Keep the same plate scale, only change the orientation
self.rotateCD(_new_orient)
# These would update the CD matrix with the new rotation
# ALONG with the new plate scale which we do not want.
self.cd11 = _cd11n
self.cd12 = _cd12n
self.cd21 = _cd21n
self.cd22 = _cd22n
def mask(clus_id, line_s):
imagefile = c.imagefile
sex_cata = c.sex_cata
clus_cata = c.out_cata
threshold = c.threshold
thresh_area = c.thresh_area
size = c.size
mask_reg = c.mask_reg
x = n.reshape(n.arange(size*size),(size,size)) % size
x = x.astype(n.Float32)
y = n.reshape(n.arange(size*size),(size,size)) / size
y = y.astype(n.Float32)
values = line_s.split()
mask_file = 'ell_mask_' + str(imagefile)[:6] + '_' + str(clus_id) + '.fits'
xcntr_o = float(values[1]) #x center of the object
ycntr_o = float(values[2]) #y center of the object
xcntr = size / 2.0 + 1.0 + xcntr_o - int(xcntr_o)
ycntr = size / 2.0 + 1.0 + ycntr_o - int(ycntr_o)
mag = float(values[7]) #Magnitude
radius = float(values[9]) #Half light radius
mag_zero = c.mag_zero #magnitude zero point
sky = float(values[10]) #sky
pos_ang = float(values[11]) - 90.0 #position angle
axis_rat = 1.0 / float(values[12]) #axis ration b/a
major_axis = float(values[14]) #major axis of the object
z = n.zeros((size,size))
for line_j in open(sex_cata,'r'):
try:
values = line_j.split()
xcntr_n = float(values[1]) #x center of the neighbour
ycntr_n = float(values[2]) #y center of the neighbour
mag = float(values[7]) #Magnitude
radius = float(values[9]) #Half light radius
sky = float(values[10]) #sky
pos_ang = float(values[11]) #position angle
axis_rat = 1.0/float(values[12]) #axis ration b/a
si = n.sin(pos_ang * n.pi / 180.0)
co = n.cos(pos_ang * n.pi / 180.0)
area = float(values[13])
maj_axis = float(values[14])#major axis of neighbour
eg = 1.0 - axis_rat
one_minus_eg_sq = (1.0-eg)**2.0
if(abs(xcntr_n - xcntr_o) < size/2.0 and \
abs(ycntr_n - ycntr_o) < size/2.0 and \
xcntr_n != xcntr_o and ycntr_n != ycntr_o):
if((xcntr_o - xcntr_n) < 0):
xn = xcntr + abs(xcntr_n - xcntr_o)
if((ycntr_o - ycntr_n) < 0):
yn = ycntr + abs(ycntr_n - ycntr_o)
if((xcntr_o - xcntr_n) > 0):
xn = xcntr - (xcntr_o -xcntr_n)
if((ycntr_o - ycntr_n) > 0):
yn = ycntr - (ycntr_o -ycntr_n)
tx = (x - xn + 0.5) * co + (y - yn + 0.5) * si
ty = (xn - 0.5 -x) * si + (y - yn + 0.5) * co
R = n.sqrt(tx**2.0 + ty**2.0 / one_minus_eg_sq)
z[n.where(R<=mask_reg*maj_axis)] = 1
except:
i=1
hdu = pyfits.PrimaryHDU(z.astype(n.Float32))
hdu.writeto(mask_file)
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'))