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 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 sortwindex(
x
): #sort array, return sorted array and array containing indices for unsorted array
nx = len(x)
y = N.arange(0, nx, 1) #index of array x
y = N.take(y, N.argsort(x)) #sort y according to x rankings
xs = N.take(x, N.argsort(x))
return xs, y #xs=sorted array, y=indices in unsorted array
def binit(x, y, n): #bin arrays x, y into n bins, returning xbin,ybin
nx = len(x)
y = N.take(y, N.argsort(x)) #sort y according to x rankings
x = N.take(x, N.argsort(x))
xbin = N.zeros(n, 'f')
ybin = 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] = pylab.median(x[nmin:nmax])
ybin[i] = pylab.median(y[nmin:nmax])
#xbin[i]=N.average(x[nmin:nmax])
#ybin[i]=N.average(y[nmin:nmax])
#ybinerr[i]=scipy.stats.std(y[nmin:nmax])
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 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 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 fig6b(m,w): # Cumulative Metallicity distribution
""" Plot differential metallicity distribution """
wnorm = w/sum(w)
i = numarray.argsort(m)
mm = m[i]
ww = wnorm[i]
pylab.plot(mm,numarray.cumsum(ww))
pylab.xlabel("[Fe/H]")
pylab.ylabel("N < [Fe/H]")
def fig6b(m, w): # Cumulative Metallicity distribution
""" Plot differential metallicity distribution """
wnorm = w / sum(w)
i = numarray.argsort(m)
mm = m[i]
ww = wnorm[i]
pylab.plot(mm, numarray.cumsum(ww))
pylab.xlabel("[Fe/H]")
pylab.ylabel("N < [Fe/H]")
def binitsumequal(x, y, n): #bin arrays x, y into n 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')
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] = N.average(x[nmin:nmax])
ybin[i] = N.sum(y[nmin:nmax])
#xbin[i]=N.average(x[nmin:nmax])
#ybin[i]=N.average(y[nmin:nmax])
#ybinerr[i]=scipy.stats.std(y[nmin:nmax])
return xbin, ybin #, ybinerr
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 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 getbins(x, y, n): #get left side of equally populated bins
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))
xbinright = N.zeros(n, 'f')
xbinleft = 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])
xbinleft[i] = (x[nmin])
xbinright[i] = (x[nmax])
#ybin[i]=N.average(y[nmin:nmax])
#ybinerr[i]=pylab.std(y[nmin:nmax])#/N.sqrt(1.*(nmax-nmin))
return xbinleft, xbinright
def process(self, X, V, C):
"""Do I need to compute the branch, or will it always be in the direction of freepar = constant?"""
BifPoint.process(self, X, V, C)
F = DiscreteMap(C.sysfunc, period=2*C.sysfunc.period)
FP = FixedPointMap(F)
J_coords = FP.jac(X, C.coords)
J_params = FP.jac(X, C.params)
# Locate branch of double period map
W, VL = linalg.eig(J_coords, left=1, right=0)
ind = argsort([abs(eig) for eig in W])[0]
psi = real(VL[:,ind])
A = r_[c_[J_coords, J_params], [V]]
W, VR = linalg.eig(A)
W0 = argsort([abs(eig) for eig in W])[0]
V1 = real(VR[:,W0])
H = FP.hess(X, C.coords+C.params, C.coords+C.params)
c11 = matrixmultiply(psi,[bilinearform(H[i,:,:], V, V) for i in range(H.shape[0])])
c12 = matrixmultiply(psi,[bilinearform(H[i,:,:], V, V1) for i in range(H.shape[0])])
c22 = matrixmultiply(psi,[bilinearform(H[i,:,:], V1, V1) for i in range(H.shape[0])])
beta = 1
alpha = -1*c22/(2*c12)
V1 = alpha*V + beta*V1
V1 /= linalg.norm(V1)
J_coords = C.sysfunc.jac(X, C.coords)
W = linalg.eig(J_coords, right=0)
self.found[-1].eigs = W
self.found[-1].branch_period = 2*C.sysfunc.period
self.found[-1].branch = todict(C, V1)
self.info(C, -1)
return True
def completeness(
bins, y, yflag
): #y is an array of input fluxes, yflag tells if sources was recovered
#for i in range(len(y)):
# print y[i],yflag[i]
nbin = len(bins)
xbin = N.zeros(len(bins), 'f')
ybin = N.zeros(len(bins), 'f')
ybin2 = N.zeros(len(bins), 'f')
yratio = N.zeros(len(bins), 'f')
ybinerr = N.zeros(len(bins), 'f')
yflag = N.take(yflag, N.argsort(y))
y = N.take(y, N.argsort(y))
#for i in range(20):
#print 'sorted',i,y[i],yflag[i]
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.
yf = 0.
for j in range(len(y)):
if y[j] > xmin:
yb = yb + 1.
if yflag[j] > 0.1:
yf = yf + 1.
if y[j] > xmax:
ybin[i] = yb
ybin2[i] = yf
(yratio[i], ybinerr[i]) = ratioerror(1. * yf, 1. * yb)
xbin[i] = 0.5 * (xmin + xmax)
#print 'completeness',xbin[i],yf,yb,yratio[i],ybinerr[i]
break
return xbin, yratio, ybinerr
def locate(self, P1, P2, C):
# Initiliaze p vector to eigenvector with smallest eigenvalue
X, V = P1
J_coords = C.CorrFunc.jac(X, C.coords)
W, VL = linalg.eig(J_coords, left=1, right=0)
ind = argsort([abs(eig) for eig in W])[0]
p = real(VL[:,ind])
initpoint = zeros(2*C.dim, Float)
initpoint[0:C.dim] = X
initpoint[C.dim+1:] = p
X = optimize.fsolve(self.__locate_newton, initpoint, C)
self.data.psi = X[C.dim+1:]
X = X[0:C.dim]
return X, V
def getMaps(pt, pttype, output=False, screen=False, cyclic=True):
jac0 = pt.labels['LC']['data'].jac0
jac1 = pt.labels['LC']['data'].jac1
flow = pt.labels[pttype]['flow']
n = jac0.shape[0]
# Compute jacobian times vec
J = linalg.solve(jac1, jac0)
if output:
print "Jacobian J*x"
print "------------\n"
print J
print "\n"
print "Check Jacobian"
print "--------------\n"
print " eigs = ", linalg.eig(J)[0]
print " eigs = ", pt.labels['LC']['data'].evals
# Compute composition of flow maps
print "Flow maps"
print "---------\n"
ntst = len(flow) / 2
maps = []
if not cyclic:
for i in range(ntst):
I = identity(n)
for j in mod(arange(i, i + ntst), ntst):
j = int(j)
I = linalg.solve(flow[2 * j + 1],
matrixmultiply(flow[2 * j], I))
maps.append(I)
# Check eigs of maps
evals = []
levecs = []
revecs = []
for m in maps:
w, vl, vr = linalg.eig(m, left=1, right=1)
evals.append(w)
levecs.append(vl)
revecs.append(vr)
if output:
for i in range(ntst):
print evals[i]
# Get left evecs along curve associated with 1 evalue
evec1 = []
good = []
for i in range(ntst):
ind = argsort(abs(evals[i] - 1.))[0]
if abs(evals[i][ind] - 1) > 0.05:
print "Bad floquet multipliers!"
else:
good.append(i)
evec1.append(levecs[i][:, ind])
else:
# CYCLIC METHOD
print "Similarity method!\n"
I = identity(n)
for i in range(ntst):
I = linalg.solve(flow[2 * i + 1], matrixmultiply(flow[2 * i], I))
evec1 = []
w, vl, vr = linalg.eig(I, left=1, right=1)
print w, vl
ind = argsort(abs(w - 1.))[0]
if abs(w[ind] - 1) > 0.05:
raise "Bad floquet multipliers!"
else:
v = vl[:, ind]
print v
for i in range(ntst):
v = matrixmultiply(transpose(flow[2 * i]),
linalg.solve(transpose(flow[2 * i + 1]), v))
evec1.append(v / linalg.norm(v))
# print "Cyclic method!\n"
# evals = []
# levecs = []
# revecs = []
# C0 = zeros((n*ntst, n*ntst), Float64)
# C1 = zeros((n*ntst, n*ntst), Float64)
# for i in range(ntst):
# C0[(n*i):(n*(i+1)), int(mod(n*(i+1), n*ntst)):int(mod(n*(i+2), n*ntst))] = flow[2*i]
# C1[(n*i):(n*(i+1)), (n*i):(n*(i+1))] = flow[2*i+1]
#
# w, vl, vr = linalg.eig(C0, C1, left=1, right=1)
# print w
# Same direction - if right eigenvector
cycle = pt.labels[pttype]['cycle']
coords = cycle.coordnames
#for i in range(ntst):
# if matrixmultiply(evec1[i], (cycle[4*i+1]-cycle[4*i]).toarray()) < 0:
# evec1[i] = -1*evec1[i]
if screen:
x = cycle[coords[0]]
y = cycle[coords[1]]
pylab.plot(x, y)
for i in good:
a = [x[4 * i], x[4 * i] + 10 * evec1[i][0]]
b = [y[4 * i], y[4 * i] + 10 * evec1[i][1]]
pylab.plot(a, b, 'r', linewidth=1)
pylab.plot([x[4 * i]], [y[4 * i]], 'gs')
#pylab.plot([x[4*i], x[4*i] + 0.5*vhd[0]], [y[4*i], y[4*i] + 0.5*vhd[1]], 'b')
#print evec1[i], vhd, "\n"
#print matrixmultiply(evec1[i], vhd)
if screen:
Je, JE = linalg.eig(jac0, jac1)
ind = argsort(abs(Je - 1.))[0]
#if abs(Je[ind]-1) > 0.05:
if 0:
print "Jacobian: Bad floquet multipliers!"
else:
u, s, vh = linalg.svd(jac0 - jac1, compute_uv=1)
evec2 = [transpose(vh)[:, -1]]
#evec2 = [JE[:,ind]]
for i in range(ntst):
evec2.append(
linalg.solve(flow[2 * i + 1],
matrixmultiply(flow[2 * i], evec2[i])))
# Same direction
for i in range(ntst):
if matrixmultiply(
evec2[i],
(cycle[4 * i + 1] - cycle[4 * i]).toarray()) < 0:
evec2[i] = -1 * evec2[i]
for i in range(ntst):
a = [x[4 * i], x[4 * i] + 0.5 * evec2[i][0]]
b = [y[4 * i], y[4 * i] + 0.5 * evec2[i][1]]
#pylab.plot(a, b, 'r', linewidth=1)
#pylab.plot([x[4*i]], [y[4*i]], 'gs')
return J, maps, evec1
def fmin(func,
x0,
args=(),
xtol=1e-4,
ftol=1e-4,
maxiter=None,
maxfun=None,
fulloutput=0,
printmessg=1):
"""xopt,{fval,warnflag} = fmin(function, x0, args=(), xtol=1e-4, ftol=1e-4,
maxiter=2000*len(x0), maxfun=2000*len(x0), fulloutput=0, printmessg=0)
Uses a Nelder-Mead Simplex algorithm to find the minimum of function
of one or more variables.
"""
x0 = Num.asarray(x0)
assert (len(x0.shape) == 1)
N = len(x0)
if maxiter is None:
maxiter = N * 200
if maxfun is None:
maxfun = N * 200
rho = 1
chi = 2
psi = 0.5
sigma = 0.5
one2np1 = range(1, N + 1)
sim = Num.zeros((N + 1, N), x0.typecode())
fsim = Num.zeros((N + 1, ), 'd')
sim[0] = x0
fsim[0] = apply(func, (x0, ) + args)
nonzdelt = 0.05
zdelt = 0.00025
for k in range(0, N):
y = Num.array(x0, copy=1)
if random.randint(0, 1):
y[k] += 10
else:
y[k] -= 10
## if y[k] != 0:
## y[k] = (1+nonzdelt)*y[k]
## else:
## y[k] = zdelt
sim[k + 1] = y
f = apply(func, (y, ) + args)
fsim[k + 1] = f
ind = Num.argsort(fsim)
fsim = Num.take(fsim,
ind) # sort so sim[0,:] has the lowest function value
sim = Num.take(sim, ind, 0)
iterations = 1
funcalls = N + 1
while (funcalls < maxfun and iterations < maxiter):
## if (max(Num.ravel(abs(sim[1:]-sim[0]))) <= xtol \
## and max(abs(fsim[0]-fsim[1:])) <= ftol):
## break
xbar = Num.add.reduce(sim[:-1], 0) / N
xr = (1 + rho) * xbar - rho * sim[-1]
fxr = apply(func, (xr, ) + args)
funcalls = funcalls + 1
doshrink = 0
if fxr < fsim[0]:
xe = (1 + rho * chi) * xbar - rho * chi * sim[-1]
fxe = apply(func, (xe, ) + args)
funcalls = funcalls + 1
if fxe < fxr:
sim[-1] = xe
fsim[-1] = fxe
else:
sim[-1] = xr
fsim[-1] = fxr
else: # fsim[0] <= fxr
if fxr < fsim[-2]:
sim[-1] = xr
fsim[-1] = fxr
else: # fxr >= fsim[-2]
# Perform contraction
if fxr < fsim[-1]:
xc = (1 + psi * rho) * xbar - psi * rho * sim[-1]
fxc = apply(func, (xc, ) + args)
funcalls = funcalls + 1
if fxc <= fxr:
sim[-1] = xc
fsim[-1] = fxc
else:
doshrink = 1
else:
# Perform an inside contraction
xcc = (1 - psi) * xbar + psi * sim[-1]
fxcc = apply(func, (xcc, ) + args)
funcalls = funcalls + 1
if fxcc < fsim[-1]:
sim[-1] = xcc
fsim[-1] = fxcc
else:
doshrink = 1
if doshrink:
for j in one2np1:
sim[j] = sim[0] + sigma * (sim[j] - sim[0])
fsim[j] = apply(func, (sim[j], ) + args)
funcalls = funcalls + N
ind = Num.argsort(fsim)
sim = Num.take(sim, ind, 0)
fsim = Num.take(fsim, ind)
iterations += 1
x = sim[0]
fval = min(fsim)
warnflag = 0
if funcalls >= maxfun:
warnflag = 1
if printmessg:
print "Warning: Maximum number of function evaluations has been exceeded:", funcalls
elif iterations >= maxiter:
warnflag = 2
if printmessg:
print "Warning: Maximum number of iterations has been exceeded:", iterations
else:
if printmessg:
print "Optimization terminated successfully."
print " Current function value: %f" % fval
print " Iterations: %d" % iterations
print " Function evaluations: %d" % funcalls
try:
apply(func, (None, )) #tell the function thread to stop
except TypeError:
print "Telling the function thread to stop"
if fulloutput:
return x, fval, warnflag
else:
return x
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 getMaps(pt, pttype, output=False, screen=False, cyclic=True):
jac0 = pt.labels['LC']['data'].jac0
jac1 = pt.labels['LC']['data'].jac1
flow = pt.labels[pttype]['flow']
n = jac0.shape[0]
# Compute jacobian times vec
J = linalg.solve(jac1, jac0)
if output:
print "Jacobian J*x"
print "------------\n"
print J
print "\n"
print "Check Jacobian"
print "--------------\n"
print " eigs = ", linalg.eig(J)[0]
print " eigs = ", pt.labels['LC']['data'].evals
# Compute composition of flow maps
print "Flow maps"
print "---------\n"
ntst = len(flow)/2
maps = []
if not cyclic:
for i in range(ntst):
I = identity(n)
for j in mod(arange(i, i + ntst), ntst):
j = int(j)
I = linalg.solve(flow[2*j+1], matrixmultiply(flow[2*j], I))
maps.append(I)
# Check eigs of maps
evals = []
levecs = []
revecs = []
for m in maps:
w, vl, vr = linalg.eig(m, left=1, right=1)
evals.append(w)
levecs.append(vl)
revecs.append(vr)
if output:
for i in range(ntst):
print evals[i]
# Get left evecs along curve associated with 1 evalue
evec1 = []
good = []
for i in range(ntst):
ind = argsort(abs(evals[i]-1.))[0]
if abs(evals[i][ind]-1) > 0.05:
print "Bad floquet multipliers!"
else:
good.append(i)
evec1.append(levecs[i][:,ind])
else:
# CYCLIC METHOD
print "Similarity method!\n"
I = identity(n)
for i in range(ntst):
I = linalg.solve(flow[2*i+1], matrixmultiply(flow[2*i], I))
evec1 = []
w, vl, vr = linalg.eig(I, left=1, right=1)
print w, vl
ind = argsort(abs(w-1.))[0]
if abs(w[ind]-1) > 0.05:
raise "Bad floquet multipliers!"
else:
v = vl[:,ind]
print v
for i in range(ntst):
v = matrixmultiply(transpose(flow[2*i]), linalg.solve(transpose(flow[2*i+1]), v))
evec1.append(v/linalg.norm(v))
# print "Cyclic method!\n"
# evals = []
# levecs = []
# revecs = []
# C0 = zeros((n*ntst, n*ntst), Float64)
# C1 = zeros((n*ntst, n*ntst), Float64)
# for i in range(ntst):
# C0[(n*i):(n*(i+1)), int(mod(n*(i+1), n*ntst)):int(mod(n*(i+2), n*ntst))] = flow[2*i]
# C1[(n*i):(n*(i+1)), (n*i):(n*(i+1))] = flow[2*i+1]
#
# w, vl, vr = linalg.eig(C0, C1, left=1, right=1)
# print w
# Same direction - if right eigenvector
cycle = pt.labels[pttype]['cycle']
coords = cycle.coordnames
#for i in range(ntst):
# if matrixmultiply(evec1[i], (cycle[4*i+1]-cycle[4*i]).toarray()) < 0:
# evec1[i] = -1*evec1[i]
if screen:
x = cycle[coords[0]]
y = cycle[coords[1]]
pylab.plot(x,y)
for i in good:
a = [x[4*i], x[4*i] + 10*evec1[i][0]]
b = [y[4*i], y[4*i] + 10*evec1[i][1]]
pylab.plot(a, b, 'r', linewidth=1)
pylab.plot([x[4*i]], [y[4*i]], 'gs')
#pylab.plot([x[4*i], x[4*i] + 0.5*vhd[0]], [y[4*i], y[4*i] + 0.5*vhd[1]], 'b')
#print evec1[i], vhd, "\n"
#print matrixmultiply(evec1[i], vhd)
if screen:
Je, JE = linalg.eig(jac0, jac1)
ind = argsort(abs(Je-1.))[0]
#if abs(Je[ind]-1) > 0.05:
if 0:
print "Jacobian: Bad floquet multipliers!"
else:
u, s, vh = linalg.svd(jac0-jac1, compute_uv=1)
evec2 = [transpose(vh)[:,-1]]
#evec2 = [JE[:,ind]]
for i in range(ntst):
evec2.append(linalg.solve(flow[2*i+1], matrixmultiply(flow[2*i], evec2[i])))
# Same direction
for i in range(ntst):
if matrixmultiply(evec2[i], (cycle[4*i+1]-cycle[4*i]).toarray()) < 0:
evec2[i] = -1*evec2[i]
for i in range(ntst):
a = [x[4*i], x[4*i] + 0.5*evec2[i][0]]
b = [y[4*i], y[4*i] + 0.5*evec2[i][1]]
#pylab.plot(a, b, 'r', linewidth=1)
#pylab.plot([x[4*i]], [y[4*i]], 'gs')
return J, maps, evec1