def singleBandSampleExample(
datafilename='../data/SDSSJ203817.37+003029.8.fits',
band='g',
nsamples=1000,
basefilename='SDSSJ203817.37+003029.8'):
"""
NAME:
singleBandSampleExample
PURPOSE:
Sample an example of a power-law structure function GP covariance
function to an SDSS quasar
INPUT:
datafilename
band - band to fit
nsamples - number of samples to use
basefilename
OUTPUT:
HISTORY:
2010-08-08 - Written - Bovy (NYU)
"""
nu.random.seed(1)
#Get data
file = fu.table_fields(datafilename)
if band == 'u':
mjd_g = nu.array(file.mjd_u) / 365.25
g = nu.array(file.u)
err_g = nu.array(file.err_u)
elif band == 'g':
mjd_g = nu.array(file.mjd_g) / 365.25
g = nu.array(file.g)
err_g = nu.array(file.err_g)
elif band == 'r':
mjd_g = nu.array(file.mjd_r) / 365.25
g = nu.array(file.r)
err_g = nu.array(file.err_r)
elif band == 'i':
mjd_g = nu.array(file.mjd_i) / 365.25
g = nu.array(file.i)
err_g = nu.array(file.err_i)
elif band == 'z':
mjd_g = nu.array(file.mjd_z) / 365.25
g = nu.array(file.z)
err_g = nu.array(file.err_z)
mjd_r = nu.array(file.mjd_r) / 365.25
r = nu.array(file.r)
err_r = nu.array(file.err_r)
mjd_i = nu.array(file.mjd_i) / 365.25
i = nu.array(file.i)
err_i = nu.array(file.err_i)
mask = (mjd_g != 0) * (g < 20.6) * (g > 19.7)
g = g[mask]
g -= nu.mean(g)
err_g = err_g[mask]
mjd_g = mjd_g[mask]
mjd_g -= nu.amin(mjd_g)
meanErr_g = nu.mean(err_g)
r = r[mask]
r -= nu.mean(r)
err_r = err_r[mask]
mjd_r = mjd_r[mask]
mjd_r -= nu.amin(mjd_r)
meanErr_r = nu.mean(err_r)
i = i[mask]
i -= nu.mean(i)
err_i = err_i[mask]
mjd_i = mjd_i[mask]
mjd_i -= nu.amin(mjd_i)
meanErr_i = nu.mean(err_i)
savefilename = basefilename + '.sav'
if os.path.exists(savefilename):
savefile = open(savefilename, 'rb')
gammas = pickle.load(savefile)
if 'gr' in basefilename:
logGammas = pickle.load(savefile)
gammagrs = pickle.load(savefile)
logGammagrs = pickle.load(savefile)
else:
logAs = pickle.load(savefile)
out = pickle.load(savefile)
savefile.close()
else:
if 'gri' in basefilename:
raise NotImplementedError
from powerlawSFgr import covarFunc
params = {
'logGamma': array([-7.79009776]),
'logGammagr': array([-28.0487848]),
'gamma': array([0.45918053]),
'gammagr': array([0.21333858])
}
SF = covarFunc(**params)
listx = [(t, 'g') for t in mjd_g]
listx.extend([(t, 'r') for t in mjd_r])
listx.extend([(t, 'i') for t in mjd_i])
listy = [m for m in g]
listy.extend([m for m in r])
listy.extend([m for m in i])
listy = nu.array(listy)
noise = [m for m in err_g]
noise.extend([m for m in err_r])
noise.extend([m for m in err_i])
noise = nu.array(noise)
trainSet = trainingSet(listx=listx, listy=listy, noise=noise)
elif 'gr' in basefilename:
raise NotImplementedError
from powerlawSFgr import covarFunc
params = {
'logGamma': array([-7.79009776]),
'logGammagr': array([-28.0487848]),
'gamma': array([0.45918053]),
'gammagr': array([0.21333858])
}
SF = covarFunc(**params)
listx = [(t, 'g') for t in mjd_g]
listx.extend([(t, 'r') for t in mjd_r])
listy = [m for m in g]
listy.extend([m for m in r])
listy = nu.array(listy)
noise = [m for m in err_g]
noise.extend([m for m in err_r])
noise = nu.array(noise)
trainSet = trainingSet(listx=listx, listy=listy, noise=noise)
else:
from gp.powerlawSF import covarFunc
trainSet = trainingSet(listx=mjd_g, listy=g, noise=err_g)
params = [0., 0.]
SF = covarFunc(gamma=.2, A=0.000524) #Power
#SF= covarFunc(a=.0001,l=.001) #OU
#Train
print "Training ..."
outcovarFunc = trainGP(trainSet, SF, useDerivs=False)
print "Best-fit:"
print outcovarFunc._dict
print "Sampling ..."
out = sampleGP(trainSet,
outcovarFunc,
nsamples=nsamples,
step=[0.2 for ii in range(len(params))])
gammas = nu.array([o._dict['gamma'] for o in out]).reshape(len(out))
if 'gr' in basefilename:
gammagrs = nu.array([o._dict['gammagr']
for o in out]).reshape(len(out))
logGammas = nu.array([o._dict['logGamma']
for o in out]).reshape(len(out))
logGammagrs = nu.array([o._dict['logGammagr']
for o in out]).reshape(len(out))
else:
logAs = nu.array([o._dict['logA'] for o in out]).reshape(len(out))
print nu.mean(logAs), nu.sqrt(nu.var(logAs))
print nu.mean(gammas), nu.sqrt(nu.var(gammas))
#Save
savefile = open(savefilename, 'wb')
pickle.dump(gammas, savefile)
if 'gr' in basefilename:
pickle.dump(logGammas, savefile)
pickle.dump(gammagrs, savefile)
pickle.dump(logGammagrs, savefile)
else:
pickle.dump(logAs, savefile)
pickle.dump(out, savefile)
savefile.close()
#if not 'gr' in basefilename:
# logGammas= logAs/gammas
#Plot
bovy_plot.bovy_print()
bovy_plot.scatterplot(logAs / 2.,
gammas,
'k,',
ylabel=r'$\gamma$',
xlabel=r'\log A',
xrange=[-9.21 / 2., 0.],
yrange=[0., 1.25],
bins=50,
onedhists=True)
bovy_plot.bovy_end_print(basefilename + '_sample_2d.png')
def showExamplegr(filename='../data/SDSSJ203817.37+003029.8.fits',
constraints=None,basefilename='SDSSJ203817.37+003029.8'):
"""
NAME:
showExamplegr
PURPOSE:
show an example of a power-law structure function GP covariance function
fit to an SDSS quasar for g and r
INPUT:
filename - filename with the data
constraints - if None, use all constraints, if [] use no constraints!
basefilename - basefilename for plots
OUTPUT:
writes several plots
HISTORY:
2010-08-11 - Written - Bovy (NYU)
"""
file= fu.table_fields(filename)
mjd_g= nu.array(file.mjd_g)/365.25
g= nu.array(file.g)
err_g= nu.array(file.err_g)
mjd_r= nu.array(file.mjd_r)/365.25
r= nu.array(file.r)
err_r= nu.array(file.err_r)
mask= (mjd_g != 0)*(g < 20.6)*(g > 19.7)#Adjust for non-g
g= g[mask]
g-= nu.mean(g)
err_g= err_g[mask]
mjd_g= mjd_g[mask]
mjd_g-= nu.amin(mjd_g)
meanErr_g= nu.mean(err_g)
r= r[mask]
r-= nu.mean(r)
err_r= err_r[mask]
mjd_r= mjd_r[mask]
mjd_r-= nu.amin(mjd_r)
meanErr_r= nu.mean(err_r)
meanErr_gr= nu.mean(nu.sqrt(err_r**2.+err_g**2.))
nu.random.seed(4)
nGP=5
nx=201
params_mean= ()
from powerlawSFgr import covarFunc
params= {'logGamma': array([-9.27821954]), 'logGammagr': array([-19.85172122]), 'gamma': array([ 0.45932629]), 'gammagr': array([ 0.29784021])}
cf= covarFunc(**params)
params_covar= (cf)
ndata= len(g)
if constraints is None:
listx= [(t,'g') for t in mjd_g]
listx.extend([(t,'r') for t in mjd_r])
listy= [m for m in g]
listy.extend([m for m in r])
listy= nu.array(listy)
noise= [m for m in err_g]
noise.extend([m for m in err_r])
noise= nu.array(noise)
trainSet= trainingSet(listx=listx,listy=listy,noise=noise)
constraints= trainSet
else:
constraints= nu.array([])
useconstraints= constraints
txs= nu.linspace(-0.1,6.5,nx)
xs= [(txs[ii],'g') for ii in range(nx)]
xs.extend([(txs[ii],'r') for ii in range(nx)])
GPsamples= eval_gp(xs,mean,covar,(),params_covar,nGP=nGP,constraints=useconstraints,tiny_cholesky=.000001)
thismean= calc_constrained_mean(xs,mean,params_mean,covar,params_covar,useconstraints)
thiscovar= calc_constrained_covar(xs,covar,params_covar,useconstraints)
plot.bovy_print()
pyplot.plot(txs,GPsamples[0,:nx],'-',color='0.25')
if isinstance(constraints,trainingSet):
pyplot.plot(mjd_g,g,'k.',zorder=5,ms=10)
plot.bovy_text(r'$\mathrm{'+basefilename+r'}$',title=True)
#pyplot.fill_between(xs,thismean-sc.sqrt(sc.diagonal(thiscovar)),thismean+sc.sqrt(sc.diagonal(thiscovar)),color='.75')
for ii in range(1,nGP):
pyplot.plot(txs,GPsamples[ii,:nx],'-',color=str(0.25+ii*.5/(nGP-1)))
pyplot.plot(txs,thismean[:nx],'k-',linewidth=2)
if isinstance(constraints,trainingSet):
pyplot.errorbar(6.15,-0.25,yerr=meanErr_g,color='k')
pyplot.xlabel(r'$\mathrm{MJD-constant}\ [\mathrm{yr}]$')
pyplot.ylabel(r'$g-\langle g\rangle\ [\mathrm{mag}]$')
pyplot.xlim(-0.1,6.5)
plot._add_ticks()
plot.bovy_end_print(basefilename+'_full.ps')
plot.bovy_print()
pyplot.figure()
pyplot.plot(txs,GPsamples[0,nx-1:-1],'-',color='0.25')
if isinstance(constraints,trainingSet):
pyplot.plot(mjd_r,r,'k.',zorder=5,ms=10)
plot.bovy_text(r'$\mathrm{'+basefilename+r'}$',title=True)
#pyplot.fill_between(xs,thismean-sc.sqrt(sc.diagonal(thiscovar)),thismean+sc.sqrt(sc.diagonal(thiscovar)),color='.75')
for ii in range(1,nGP):
pyplot.plot(txs,GPsamples[ii,nx-1:-1],'-',color=str(0.25+ii*.5/(nGP-1)))
pyplot.plot(txs,thismean[nx-1:-1],'k-',linewidth=2)
if isinstance(constraints,trainingSet):
pyplot.errorbar(6.15,-0.25,yerr=meanErr_r,color='k')
pyplot.xlabel(r'$\mathrm{MJD-constant}\ [\mathrm{yr}]$')
pyplot.ylabel(r'$r-\langle r\rangle\ [\mathrm{mag}]$')
pyplot.xlim(-0.1,6.5)
plot._add_ticks()
plot.bovy_end_print(basefilename+'_fullr.ps')
plot.bovy_print()
pyplot.figure()
ii= 0
colors= nu.array([GPsamples[ii,jj]-GPsamples[ii,jj+nx] for jj in range(nx)])
colors= colors-nu.mean(colors)
pyplot.plot(txs,colors,'-',color='0.25')
if isinstance(constraints,trainingSet):
plot.bovy_plot(mjd_g,g-r,'k.',zorder=5,ms=10,overplot=True)
plot.bovy_text(r'$\mathrm{'+basefilename+r'}$',title=True)
#pyplot.fill_between(xs,thismean-sc.sqrt(sc.diagonal(thiscovar)),thismean+sc.sqrt(sc.diagonal(thiscovar)),color='.75')
for ii in range(1,nGP):
colors= nu.array([GPsamples[ii,jj]-GPsamples[ii,jj+nx] for jj in range(nx)])
colors= colors-nu.mean(colors)
pyplot.plot(txs,colors,'-',color=str(0.25+ii*.5/(nGP-1)))
plotthismean= nu.zeros(nx)
for ii in range(nx):
plotthismean[ii]= thismean[ii]-thismean[ii+nx]
pyplot.plot(txs,plotthismean,'k-',linewidth=2)
if isinstance(constraints,trainingSet):
pyplot.errorbar(6.15,-0.18,yerr=meanErr_gr,color='k')
pyplot.xlabel(r'$\mathrm{MJD-constant}\ [\mathrm{yr}]$')
pyplot.ylabel(r'$g-r- \langle g - r \rangle\ [\mathrm{mag}]$')
pyplot.xlim(-0.1,6.5)
if isinstance(constraints,trainingSet):
pyplot.ylim(-0.25,.25)
else:
pass #pyplot.ylim(-10.,10.)
plot._add_ticks()
plot.bovy_end_print(basefilename+'_color.ps')
plot.bovy_print()
pyplot.figure()
ii= 2
colors= nu.array([GPsamples[ii,jj]-GPsamples[ii,jj+nx] for jj in range(nx)])
pyplot.plot(colors,GPsamples[ii,:nx],'-',color='0.25')
if isinstance(constraints,trainingSet):
pyplot.plot(g-r,g,'k.',zorder=5,ms=10)
plot.bovy_text(r'$\mathrm{'+basefilename+r'}$',title=True)
#pyplot.fill_between(xs,thismean-sc.sqrt(sc.diagonal(thiscovar)),thismean+sc.sqrt(sc.diagonal(thiscovar)),color='.75')
for ii in range(1,nGP):
colors= nu.array([GPsamples[ii,jj]-GPsamples[ii,jj+nx] for jj in range(nx)])
pyplot.plot(colors,GPsamples[ii,0:nx],'-',color=str(0.25+ii*.5/(nGP-1)))
colors= nu.array([thismean[jj]-thismean[jj+nx] for jj in range(nx)])
pyplot.plot(colors,thismean[:nx],'k-',linewidth=2)
if isinstance(constraints,trainingSet):
pyplot.errorbar(.13,-0.3,yerr=meanErr_g,xerr=meanErr_gr,color='k')
pyplot.xlabel(r'$g-r-\langle g-r\rangle\ [\mathrm{mag}]$')
pyplot.ylabel(r'$g-\langle g\rangle\ [\mathrm{mag}]$')
pyplot.xlim(-.2,.2)
plot._add_ticks()
plot.bovy_end_print(basefilename+'_ggr.ps')
return
plot.bovy_print()
pyplot.plot(xs,GPsamples[0,:],'-',color='0.25')
if not constraints == []:
plot.bovy_plot(mjd_g,g,'k.',zorder=5,ms=10,overplot=True)
#plot.bovy_text(r'$\mathrm{SDSSJ203817.37+003029.8}$',title=True)
#pyplot.fill_between(xs,thismean-sc.sqrt(sc.diagonal(thiscovar)),thismean+sc.sqrt(sc.diagonal(thiscovar)),color='.75')
for ii in range(1,nGP):
pyplot.plot(xs,GPsamples[ii,:],'-',color=str(0.25+ii*.5/(nGP-1)))
#pyplot.plot(xs,thismean,'k-',linewidth=2)
if not constraints == []:
pyplot.errorbar(6.15,-0.1,yerr=meanErr_g,color='k')
pyplot.xlabel(r'$\mathrm{MJD-constant}\ [\mathrm{yr}]$')
pyplot.ylabel(r'$m-\langle m\rangle\ [\mathrm{mag}]$')
pyplot.xlim(3,6.5)
plot._add_ticks()
plot.bovy_end_print(basefilename+'_zoom.ps')
plot.bovy_print()
pyplot.figure()
for ii in range(nGP):
pyplot.loglog(sc.arange(1.,len(GPsamples[ii,:])/2)*(xs[1]-xs[0]),
2.*sc.var(GPsamples[ii,:])-2.*sc.correlate(GPsamples[ii,:]-sc.mean(GPsamples[ii,:]),GPsamples[ii,:]-sc.mean(GPsamples[ii,:]),"same")[1:len(GPsamples[ii,:])/2][::-1]/len(GPsamples[ii,:]),
color=str(0.25+ii*.5/(nGP-1)))
xline= [(xs[1]-xs[0]),xs[len(xs)/2]]
pyplot.loglog(xline,nu.exp(-3.02045715)*nu.array(xline)**(0.5868293),'k--')
pyplot.xlabel(r'$\Delta t\ [\mathrm{yr}]$')
pyplot.ylabel(r'$\mathrm{structure\ function}$')
#plot.bovy_text(r'$\mathrm{SDSSJ203817.37+003029.8}$',title=True)
plot.bovy_end_print(basefilename+'_structfunc.ps')
def singleBandSampleExample(
datafilename="SDSSJ000051.56+001202.5.fit", band="g", nsamples=1000, basefilename="SDSSJ203817.37+003029.8"
):
"""
NAME:
singleBandSampleExample
PURPOSE:
Sample an example of a power-law structure function GP covariance
function to an SDSS quasar
INPUT:
datafilename
band - band to fit
nsamples - number of samples to use
basefilename
OUTPUT:
HISTORY:
2010-08-08 - Written - Bovy (NYU)
"""
nu.random.seed(1)
# Get data
file = fu.table_fields(datafilename)
if band == "u":
mjd_g = nu.array(file.mjd_u) / 365.25
g = nu.array(file.u)
err_g = nu.array(file.err_u)
elif band == "g":
mjd_g = nu.array(file.mjd_g) / 365.25
g = nu.array(file.g)
err_g = nu.array(file.err_g)
elif band == "r":
mjd_g = nu.array(file.mjd_r) / 365.25
g = nu.array(file.r)
err_g = nu.array(file.err_r)
elif band == "i":
mjd_g = nu.array(file.mjd_i) / 365.25
g = nu.array(file.i)
err_g = nu.array(file.err_i)
elif band == "z":
mjd_g = nu.array(file.mjd_z) / 365.25
g = nu.array(file.z)
err_g = nu.array(file.err_z)
mjd_r = nu.array(file.mjd_r) / 365.25
r = nu.array(file.r)
err_r = nu.array(file.err_r)
mjd_i = nu.array(file.mjd_i) / 365.25
i = nu.array(file.i)
err_i = nu.array(file.err_i)
mask = (mjd_g != 0) * (g < 20.6) * (g > 19.7)
g = g[mask]
g -= nu.mean(g)
err_g = err_g[mask]
mjd_g = mjd_g[mask]
mjd_g -= nu.amin(mjd_g)
meanErr_g = nu.mean(err_g)
r = r[mask]
r -= nu.mean(r)
err_r = err_r[mask]
mjd_r = mjd_r[mask]
mjd_r -= nu.amin(mjd_r)
meanErr_r = nu.mean(err_r)
i = i[mask]
i -= nu.mean(i)
err_i = err_i[mask]
mjd_i = mjd_i[mask]
mjd_i -= nu.amin(mjd_i)
meanErr_i = nu.mean(err_i)
savefilename = basefilename + ".sav"
if os.path.exists(savefilename):
savefile = open(savefilename, "rb")
gammas = pickle.load(savefile)
if "gr" in basefilename:
logGammas = pickle.load(savefile)
gammagrs = pickle.load(savefile)
logGammagrs = pickle.load(savefile)
else:
logAs = pickle.load(savefile)
out = pickle.load(savefile)
savefile.close()
else:
if "gri" in basefilename:
raise NotImplementedError
from powerlawSFgr import covarFunc
params = {
"logGamma": array([-7.79009776]),
"logGammagr": array([-28.0487848]),
"gamma": array([0.45918053]),
"gammagr": array([0.21333858]),
}
SF = covarFunc(**params)
listx = [(t, "g") for t in mjd_g]
listx.extend([(t, "r") for t in mjd_r])
listx.extend([(t, "i") for t in mjd_i])
listy = [m for m in g]
listy.extend([m for m in r])
listy.extend([m for m in i])
listy = nu.array(listy)
noise = [m for m in err_g]
noise.extend([m for m in err_r])
noise.extend([m for m in err_i])
noise = nu.array(noise)
trainSet = trainingSet(listx=listx, listy=listy, noise=noise)
elif "gr" in basefilename:
raise NotImplementedError
from powerlawSFgr import covarFunc
params = {
"logGamma": array([-7.79009776]),
"logGammagr": array([-28.0487848]),
"gamma": array([0.45918053]),
"gammagr": array([0.21333858]),
}
SF = covarFunc(**params)
listx = [(t, "g") for t in mjd_g]
listx.extend([(t, "r") for t in mjd_r])
listy = [m for m in g]
listy.extend([m for m in r])
listy = nu.array(listy)
noise = [m for m in err_g]
noise.extend([m for m in err_r])
noise = nu.array(noise)
trainSet = trainingSet(listx=listx, listy=listy, noise=noise)
else:
from gp.powerlawSF import covarFunc
trainSet = trainingSet(listx=mjd_g, listy=g, noise=err_g)
params = [0.0, 0.0]
SF = covarFunc(gamma=0.2, A=0.000524) # Power
# SF= covarFunc(a=.0001,l=.001) #OU
# Train
print "Training ..."
outcovarFunc = trainGP(trainSet, SF, useDerivs=False)
print "Best-fit:"
print outcovarFunc._dict
print "Sampling ..."
out = sampleGP(trainSet, outcovarFunc, nsamples=nsamples, step=[0.2 for ii in range(len(params))])
gammas = nu.array([o._dict["gamma"] for o in out]).reshape(len(out))
if "gr" in basefilename:
gammagrs = nu.array([o._dict["gammagr"] for o in out]).reshape(len(out))
logGammas = nu.array([o._dict["logGamma"] for o in out]).reshape(len(out))
logGammagrs = nu.array([o._dict["logGammagr"] for o in out]).reshape(len(out))
else:
logAs = nu.array([o._dict["logA"] for o in out]).reshape(len(out))
print nu.mean(logAs), nu.sqrt(nu.var(logAs))
print nu.mean(gammas), nu.sqrt(nu.var(gammas))
# Save
savefile = open(savefilename, "wb")
pickle.dump(gammas, savefile)
if "gr" in basefilename:
pickle.dump(logGammas, savefile)
pickle.dump(gammagrs, savefile)
pickle.dump(logGammagrs, savefile)
else:
pickle.dump(logAs, savefile)
pickle.dump(out, savefile)
savefile.close()
# if not 'gr' in basefilename:
# logGammas= logAs/gammas
# Plot
bovy_plot.bovy_print()
bovy_plot.scatterplot(
logAs / 2.0,
gammas,
"k,",
ylabel=r"$\gamma$",
xlabel=r"\log A",
xrange=[-9.21 / 2.0, 0.0],
yrange=[0.0, 1.25],
bins=50,
onedhists=True,
)
bovy_plot.bovy_end_print(basefilename + "_sample_2d.png")
def dualBandExample(filename='../data/SDSSJ203817.37+003029.8.fits',
constraints=None,basefilename='SDSSJ203817.37+003029.8',
covarType='SF'):
"""
NAME:
dualBandExample
PURPOSE:
show an example of a power-law structure function GP covariance function
fit to an SDSS quasar for g and r
INPUT:
filename - filename with the data
constraints - if None, use all constraints, if [] use no constraints!
basefilename - basefilename for plots
covarType - 'SF' or 'DRW'
OUTPUT:
writes several plots
HISTORY:
2010-08-11 - Written - Bovy (NYU)
"""
file= fu.table_fields(filename)
mjd_g= nu.array(file.mjd_g)/365.25
g= nu.array(file.g)
err_g= nu.array(file.err_g)
mjd_r= nu.array(file.mjd_r)/365.25
r= nu.array(file.r)
err_r= nu.array(file.err_r)
mask= (mjd_g != 0)*(g < 20.6)*(g > 19.7)#Adjust for non-g
g= g[mask]
g-= nu.mean(g)
err_g= err_g[mask]
mjd_g= mjd_g[mask]
mjd_g-= nu.amin(mjd_g)
meanErr_g= nu.mean(err_g)
r= r[mask]
r-= nu.mean(r)
err_r= err_r[mask]
mjd_r= mjd_r[mask]
mjd_r-= nu.amin(mjd_r)
meanErr_r= nu.mean(err_r)
meanErr_gr= nu.mean(nu.sqrt(err_r**2.+err_g**2.))
nu.random.seed(4)
nGP=5
nx=201
params_mean= ()
if covarType == 'SF':
from powerlawSFgr import covarFunc
params= {'logGamma': array([-7.33271548]), 'logGammagr': array([-10.5]), 'gamma': array([ 0.4821092]), 'gammagr': array([ 0.5])}
params= {'logGamma': array([-7.79009776]), 'logGammagr': array([-28.0487848]), 'gamma': array([ 0.45918053]), 'gammagr': array([ 0.21333858])}
else:
from OUgr import covarFunc
params= {'logl': array([ 1.94844503]), 'loglgr': array([ 7.36282174]), 'logagr2': array([ 1.0196474]), 'loga2': array([-0.00588868])}
params= {'logl':-1.37742591,'loga':-3.47341754,
'loglgr': -2.3777,'logagr': -4.}
params= {'logl': array([-1.38968195]), 'loglgr': array([-2.46684501]), 'logagr2': array([-6.62320832]), 'loga2': array([-3.52099305])}
paramsSF= params
cf= covarFunc(**params)
params_covar= (cf)
ndata= len(g)
if constraints is None:
listx= [(t,'g') for t in mjd_g]
listx.extend([(t,'r') for t in mjd_r])
listy= [m for m in g]
listy.extend([m for m in r])
listy= nu.array(listy)
noise= [m for m in err_g]
noise.extend([m for m in err_r])
noise= nu.array(noise)
trainSet= trainingSet(listx=listx,listy=listy,noise=noise)
constraints= trainSet
else:
constraints= nu.array([])
useconstraints= constraints
txs= nu.linspace(-0.1,6.5,nx)
xs= [(txs[ii],'g') for ii in range(nx)]
xs.extend([(txs[ii],'r') for ii in range(nx)])
GPsamples= eval_gp(xs,mean,covar,(),params_covar,nGP=nGP,constraints=useconstraints,tiny_cholesky=.00000001)
thismean= calc_constrained_mean(xs,mean,params_mean,covar,params_covar,useconstraints)
thiscovar= calc_constrained_covar(xs,covar,params_covar,useconstraints)
#Calculate loglike
if isinstance(constraints,trainingSet):
(params,packing)= pack_params(cf)
covarFuncName= inspect.getmodule(cf).__name__
thisCovarClass= __import__(covarFuncName)
loglike= marginalLikelihood(params,constraints,packing,
thisCovarClass)
plot.bovy_print()
pyplot.plot(txs,GPsamples[0,:nx],'-',color='0.25')
if isinstance(constraints,trainingSet):
pyplot.plot(mjd_g,g,'k.',zorder=5,ms=10)
title= re.split(r'_',basefilename)[0]
if covarType == 'SF':
method= '\mathrm{power-law\ structure\ functions}'
else:
method= '\mathrm{damped\ random\ walk}'
plot.bovy_text(r'$\mathrm{'+title+'\ / \ '+method+r'}$',title=True)
if isinstance(constraints,trainingSet):
plot.bovy_text(r'$\log P({\bf x}|\mathrm{parameters}) = %5.2f$' %(-loglike),
top_left=True)
#pyplot.fill_between(xs,thismean-sc.sqrt(sc.diagonal(thiscovar)),thismean+sc.sqrt(sc.diagonal(thiscovar)),color='.75')
for ii in range(1,nGP):
pyplot.plot(txs,GPsamples[ii,:nx],'-',color=str(0.25+ii*.5/(nGP-1)))
#pyplot.plot(txs,thismean[:nx],'k-',linewidth=2)
if isinstance(constraints,trainingSet):
pyplot.errorbar(6.15,-0.25,yerr=meanErr_g,color='k')
pyplot.xlabel(r'$\mathrm{MJD-constant}\ [\mathrm{yr}]$')
pyplot.ylabel(r'$g-\langle g\rangle\ [\mathrm{mag}]$')
pyplot.xlim(-0.1,6.5)
pyplot.ylim(-0.6,0.6)
plot._add_ticks()
plot.bovy_end_print(basefilename+'_fullg.ps')
plot.bovy_print()
pyplot.figure()
pyplot.plot(txs,GPsamples[0,nx-1:-1],'-',color='0.25')
if isinstance(constraints,trainingSet):
pyplot.plot(mjd_r,r,'k.',zorder=5,ms=10)
#plot.bovy_text(r'$\mathrm{'+title+'\ / \ '+method+r'}$',title=True)
#pyplot.fill_between(xs,thismean-sc.sqrt(sc.diagonal(thiscovar)),thismean+sc.sqrt(sc.diagonal(thiscovar)),color='.75')
for ii in range(1,nGP):
pyplot.plot(txs,GPsamples[ii,nx-1:-1],'-',color=str(0.25+ii*.5/(nGP-1)))
#pyplot.plot(txs,thismean[nx-1:-1],'k-',linewidth=2)
if isinstance(constraints,trainingSet):
pyplot.errorbar(6.15,-0.25,yerr=meanErr_r,color='k')
pyplot.xlabel(r'$\mathrm{MJD-constant}\ [\mathrm{yr}]$')
pyplot.ylabel(r'$r-\langle r\rangle\ [\mathrm{mag}]$')
pyplot.xlim(-0.1,6.5)
pyplot.ylim(-0.6,0.6)
plot._add_ticks()
plot.bovy_end_print(basefilename+'_fullr.ps')
plot.bovy_print()
pyplot.figure()
ii= 0
colors= nu.array([GPsamples[ii,jj]-GPsamples[ii,jj+nx] for jj in range(nx)])
if not isinstance(constraints,trainingSet):
colors= colors-nu.mean(colors)
pyplot.plot(txs,colors,'-',color='0.25')
if isinstance(constraints,trainingSet):
plot.bovy_plot(mjd_g,g-r,'k.',zorder=5,ms=10,overplot=True)
#plot.bovy_text(r'$\mathrm{'+basefilename+r'}$',title=True)
#pyplot.fill_between(xs,thismean-sc.sqrt(sc.diagonal(thiscovar)),thismean+sc.sqrt(sc.diagonal(thiscovar)),color='.75')
for ii in range(1,nGP):
colors= nu.array([GPsamples[ii,jj]-GPsamples[ii,jj+nx] for jj in range(nx)])
if not isinstance(constraints,trainingSet):
colors= colors-nu.mean(colors)
pyplot.plot(txs,colors,'-',color=str(0.25+ii*.5/(nGP-1)))
plotthismean= nu.zeros(nx)
for ii in range(nx):
plotthismean[ii]= thismean[ii]-thismean[ii+nx]
#pyplot.plot(txs,plotthismean,'k-',linewidth=2)
if isinstance(constraints,trainingSet):
pyplot.errorbar(6.15,-0.18,yerr=meanErr_gr,color='k')
pyplot.xlabel(r'$\mathrm{MJD-constant}\ [\mathrm{yr}]$')
pyplot.ylabel(r'$g-r- \langle g - r \rangle\ [\mathrm{mag}]$')
pyplot.xlim(-0.1,6.5)
if isinstance(constraints,trainingSet):
pyplot.ylim(-0.25,.25)
else:
pass #pyplot.ylim(-10.,10.)
plot._add_ticks()
plot.bovy_end_print(basefilename+'_color.ps')
if covarType == 'DRW':
return
#Plot structure functions
#g
plot.bovy_print()
pyplot.figure()
for ii in range(nGP):
thisSample= GPsamples[ii,:nx]
pyplot.loglog(sc.arange(1.,len(thisSample)/2)*(txs[1]-txs[0]),
2.*sc.var(thisSample)\
-2.*sc.correlate(thisSample-sc.mean(thisSample),thisSample-sc.mean(thisSample),"same")[1:len(thisSample)/2][::-1]/len(thisSample),
color=str(0.25+ii*.5/(nGP-1)))
xline= [(txs[1]-txs[0]),txs[len(txs)/2]]
pyplot.loglog(xline,(nu.exp(paramsSF['logGamma'])*nu.array(xline))**(paramsSF['gamma']),'k--')
pyplot.xlabel(r'$\Delta t\ [\mathrm{yr}]$')
pyplot.ylabel(r'$\mathrm{structure\ function\ in}\ g$')
#plot.bovy_text(r'$\mathrm{SDSSJ203817.37+003029.8}$',title=True)
plot.bovy_end_print(basefilename+'_structfuncg.ps')
#r
plot.bovy_print()
pyplot.figure()
for ii in range(nGP):
thisSample= GPsamples[ii,nx-1:-1]
pyplot.loglog(sc.arange(1.,len(thisSample)/2)*(txs[1]-txs[0]),
2.*sc.var(thisSample)\
-2.*sc.correlate(thisSample-sc.mean(thisSample),thisSample-sc.mean(thisSample),"same")[1:len(thisSample)/2][::-1]/len(thisSample),
color=str(0.25+ii*.5/(nGP-1)))
xline= [(txs[1]-txs[0]),txs[len(txs)/2]]
pyplot.loglog(xline,(nu.exp(paramsSF['logGamma'])*nu.array(xline))**(paramsSF['gamma']),'k--')
pyplot.xlabel(r'$\Delta t\ [\mathrm{yr}]$')
pyplot.ylabel(r'$\mathrm{structure\ function\ in}\ r$')
#plot.bovy_text(r'$\mathrm{SDSSJ203817.37+003029.8}$',title=True)
plot.bovy_end_print(basefilename+'_structfuncr.ps')
#g-r
plot.bovy_print()
pyplot.figure()
for ii in range(nGP):
thisSample= nu.array([GPsamples[ii,jj]-GPsamples[ii,jj+nx] for jj in range(nx)])
pyplot.loglog(sc.arange(1.,len(thisSample)/2)*(txs[1]-txs[0]),
2.*sc.var(thisSample)\
-2.*sc.correlate(thisSample-sc.mean(thisSample),thisSample-sc.mean(thisSample),"same")[1:len(thisSample)/2][::-1]/len(thisSample),
color=str(0.25+ii*.5/(nGP-1)))
xline= [(txs[1]-txs[0]),txs[len(txs)/2]]
pyplot.loglog(xline,(nu.exp(paramsSF['logGammagr'])*nu.array(xline))**(paramsSF['gammagr']),'k--')
pyplot.xlabel(r'$\Delta t\ [\mathrm{yr}]$')
pyplot.ylabel(r'$\mathrm{color\ structure\ function}$')
#plot.bovy_text(r'$\mathrm{SDSSJ203817.37+003029.8}$',title=True)
plot.bovy_end_print(basefilename+'_structfuncgr.ps')
def showExample(filename='../data/SDSSJ203817.37+003029.8.fits',band='g',
constraints=None,basefilename='SDSSJ203817.37+003029.8'):
"""
NAME:
showExample
PURPOSE:
show an example of a power-law structure function GP covariance function
fit to an SDSS quasar
INPUT:
filename - filename with the data
band - band to consider
constraints - if None, use all constraints, if [] use no constraints!
basefilename - basefilename for plots
OUTPUT:
writes several plots
HISTORY:
2010-06-20 - Written - Bovy (NYU)
"""
file= fu.table_fields(filename)
if band == 'u':
mjd_g= nu.array(file.mjd_u)/365.25
g= nu.array(file.u)
err_g= nu.array(file.err_u)
elif band == 'g':
mjd_g= nu.array(file.mjd_g)/365.25
g= nu.array(file.g)
err_g= nu.array(file.err_g)
elif band == 'r':
mjd_g= nu.array(file.mjd_r)/365.25
g= nu.array(file.r)
err_g= nu.array(file.err_r)
elif band == 'i':
mjd_g= nu.array(file.mjd_i)/365.25
g= nu.array(file.i)
err_g= nu.array(file.err_i)
elif band == 'z':
mjd_g= nu.array(file.mjd_z)/365.25
g= nu.array(file.z)
err_g= nu.array(file.err_z)
mask= (mjd_g != 0)*(g < 20.6)*(g > 19.7)#Adjust for non-g
g= g[mask]
g-= nu.mean(g)
err_g= err_g[mask]
mjd_g= mjd_g[mask]
mjd_g-= nu.amin(mjd_g)
meanErr_g= nu.mean(err_g)
nu.random.seed(4)
nGP=5
nx=201
params_mean= ()
from powerlawSFgr import covarFunc
params= {'logA': array([ 1.63714183]), 'gamma': array([ 0.60216581])}
params= {'gamma': array([ 0.49500723]), 'logA': array([-3.36044037])}
cf= covarFunc(**params)
params_covar= (cf)
ndata= len(g)
if constraints is None:
listx= mjd_g
listy= g
noise= err_g
trainSet= trainingSet(listx=listx,listy=listy,noise=noise)
constraints= trainSet
else:
constraints= None
useconstraints= constraints
xs= nu.linspace(-0.1,6.5,nx)
GPsamples= eval_gp(xs,mean,covar,(),params_covar,nGP=nGP,constraints=useconstraints)
thismean= calc_constrained_mean(xs,mean,params_mean,covar,params_covar,useconstraints)
thiscovar= calc_constrained_covar(xs,covar,params_covar,useconstraints)
plot.bovy_print()
pyplot.plot(xs,GPsamples[0,:],'-',color='0.25')
if not constraints is None:
plot.bovy_plot(mjd_g,g,'k.',zorder=5,ms=10,overplot=True)
plot.bovy_text(r'$\mathrm{'+basefilename+r'}$',title=True)
#pyplot.fill_between(xs,thismean-sc.sqrt(sc.diagonal(thiscovar)),thismean+sc.sqrt(sc.diagonal(thiscovar)),color='.75')
for ii in range(nGP):
pyplot.plot(xs,GPsamples[ii,:],'-',color=str(0.25+ii*.5/(nGP-1)))
#pyplot.plot(xs,thismean,'k-',linewidth=2)
if not constraints == []:
pyplot.errorbar(6.15,-0.25,yerr=meanErr_g,color='k')
pyplot.xlabel(r'$\mathrm{MJD-constant}\ [\mathrm{yr}]$')
pyplot.ylabel(r'$m-\langle m\rangle\ [\mathrm{mag}]$')
pyplot.xlim(-0.1,6.5)
pyplot.ylim(-1.,1.)
plot._add_ticks()
plot.bovy_end_print(basefilename+'_full.ps')
plot.bovy_print()
pyplot.plot(xs,GPsamples[0,:],'-',color='0.25')
if not constraints is None:
plot.bovy_plot(mjd_g,g,'k.',zorder=5,ms=10,overplot=True)
#plot.bovy_text(r'$\mathrm{SDSSJ203817.37+003029.8}$',title=True)
#pyplot.fill_between(xs,thismean-sc.sqrt(sc.diagonal(thiscovar)),thismean+sc.sqrt(sc.diagonal(thiscovar)),color='.75')
for ii in range(1,nGP):
pyplot.plot(xs,GPsamples[ii,:],'-',color=str(0.25+ii*.5/(nGP-1)))
#pyplot.plot(xs,thismean,'k-',linewidth=2)
if not constraints == []:
pyplot.errorbar(6.15,-0.25,yerr=meanErr_g,color='k')
pyplot.xlabel(r'$\mathrm{MJD-constant}\ [\mathrm{yr}]$')
pyplot.ylabel(r'$m-\langle m\rangle\ [\mathrm{mag}]$')
pyplot.xlim(3,6.5)
plot._add_ticks()
plot.bovy_end_print(basefilename+'_zoom.ps')
plot.bovy_print()
pyplot.figure()
for ii in range(nGP):
pyplot.loglog(sc.arange(1.,len(GPsamples[ii,:])/2)*(xs[1]-xs[0]),
2.*sc.var(GPsamples[ii,:])-2.*sc.correlate(GPsamples[ii,:]-sc.mean(GPsamples[ii,:]),GPsamples[ii,:]-sc.mean(GPsamples[ii,:]),"same")[1:len(GPsamples[ii,:])/2][::-1]/len(GPsamples[ii,:]),
color=str(0.25+ii*.5/(nGP-1)))
xline= [(xs[1]-xs[0]),xs[len(xs)/2]]
pyplot.loglog(xline,nu.exp(-3.02045715)*nu.array(xline)**(0.5868293),'k--')
pyplot.xlabel(r'$\Delta t\ [\mathrm{yr}]$')
pyplot.ylabel(r'$\mathrm{structure\ function}$')
#plot.bovy_text(r'$\mathrm{SDSSJ203817.37+003029.8}$',title=True)
plot.bovy_end_print(basefilename+'_structfunc.ps')
def dualBandExample(filename='../data/SDSSJ203817.37+003029.8.fits',
constraints=None,
basefilename='SDSSJ203817.37+003029.8',
covarType='SF'):
"""
NAME:
dualBandExample
PURPOSE:
show an example of a power-law structure function GP covariance function
fit to an SDSS quasar for g and r
INPUT:
filename - filename with the data
constraints - if None, use all constraints, if [] use no constraints!
basefilename - basefilename for plots
covarType - 'SF' or 'DRW'
OUTPUT:
writes several plots
HISTORY:
2010-08-11 - Written - Bovy (NYU)
"""
file = fu.table_fields(filename)
mjd_g = nu.array(file.mjd_g) / 365.25
g = nu.array(file.g)
err_g = nu.array(file.err_g)
mjd_r = nu.array(file.mjd_r) / 365.25
r = nu.array(file.r)
err_r = nu.array(file.err_r)
mask = (mjd_g != 0) * (g < 20.6) * (g > 19.7) #Adjust for non-g
g = g[mask]
g -= nu.mean(g)
err_g = err_g[mask]
mjd_g = mjd_g[mask]
mjd_g -= nu.amin(mjd_g)
meanErr_g = nu.mean(err_g)
r = r[mask]
r -= nu.mean(r)
err_r = err_r[mask]
mjd_r = mjd_r[mask]
mjd_r -= nu.amin(mjd_r)
meanErr_r = nu.mean(err_r)
meanErr_gr = nu.mean(nu.sqrt(err_r**2. + err_g**2.))
nu.random.seed(4)
nGP = 5
nx = 201
params_mean = ()
if covarType == 'SF':
from powerlawSFgr import covarFunc
params = {
'logGamma': array([-7.33271548]),
'logGammagr': array([-10.5]),
'gamma': array([0.4821092]),
'gammagr': array([0.5])
}
params = {
'logGamma': array([-7.79009776]),
'logGammagr': array([-28.0487848]),
'gamma': array([0.45918053]),
'gammagr': array([0.21333858])
}
else:
from OUgr import covarFunc
params = {
'logl': array([1.94844503]),
'loglgr': array([7.36282174]),
'logagr2': array([1.0196474]),
'loga2': array([-0.00588868])
}
params = {
'logl': -1.37742591,
'loga': -3.47341754,
'loglgr': -2.3777,
'logagr': -4.
}
params = {
'logl': array([-1.38968195]),
'loglgr': array([-2.46684501]),
'logagr2': array([-6.62320832]),
'loga2': array([-3.52099305])
}
paramsSF = params
cf = covarFunc(**params)
params_covar = (cf)
ndata = len(g)
if constraints is None:
listx = [(t, 'g') for t in mjd_g]
listx.extend([(t, 'r') for t in mjd_r])
listy = [m for m in g]
listy.extend([m for m in r])
listy = nu.array(listy)
noise = [m for m in err_g]
noise.extend([m for m in err_r])
noise = nu.array(noise)
trainSet = trainingSet(listx=listx, listy=listy, noise=noise)
constraints = trainSet
else:
constraints = nu.array([])
useconstraints = constraints
txs = nu.linspace(-0.1, 6.5, nx)
xs = [(txs[ii], 'g') for ii in range(nx)]
xs.extend([(txs[ii], 'r') for ii in range(nx)])
GPsamples = eval_gp(xs,
mean,
covar, (),
params_covar,
nGP=nGP,
constraints=useconstraints,
tiny_cholesky=.00000001)
thismean = calc_constrained_mean(xs, mean, params_mean, covar,
params_covar, useconstraints)
thiscovar = calc_constrained_covar(xs, covar, params_covar, useconstraints)
#Calculate loglike
if isinstance(constraints, trainingSet):
(params, packing) = pack_params(cf)
covarFuncName = inspect.getmodule(cf).__name__
thisCovarClass = __import__(covarFuncName)
loglike = marginalLikelihood(params, constraints, packing,
thisCovarClass)
plot.bovy_print()
pyplot.plot(txs, GPsamples[0, :nx], '-', color='0.25')
if isinstance(constraints, trainingSet):
pyplot.plot(mjd_g, g, 'k.', zorder=5, ms=10)
title = re.split(r'_', basefilename)[0]
if covarType == 'SF':
method = '\mathrm{power-law\ structure\ functions}'
else:
method = '\mathrm{damped\ random\ walk}'
plot.bovy_text(r'$\mathrm{' + title + '\ / \ ' + method + r'}$',
title=True)
if isinstance(constraints, trainingSet):
plot.bovy_text(r'$\log P({\bf x}|\mathrm{parameters}) = %5.2f$' %
(-loglike),
top_left=True)
#pyplot.fill_between(xs,thismean-sc.sqrt(sc.diagonal(thiscovar)),thismean+sc.sqrt(sc.diagonal(thiscovar)),color='.75')
for ii in range(1, nGP):
pyplot.plot(txs,
GPsamples[ii, :nx],
'-',
color=str(0.25 + ii * .5 / (nGP - 1)))
#pyplot.plot(txs,thismean[:nx],'k-',linewidth=2)
if isinstance(constraints, trainingSet):
pyplot.errorbar(6.15, -0.25, yerr=meanErr_g, color='k')
pyplot.xlabel(r'$\mathrm{MJD-constant}\ [\mathrm{yr}]$')
pyplot.ylabel(r'$g-\langle g\rangle\ [\mathrm{mag}]$')
pyplot.xlim(-0.1, 6.5)
pyplot.ylim(-0.6, 0.6)
plot._add_ticks()
plot.bovy_end_print(basefilename + '_fullg.ps')
plot.bovy_print()
pyplot.figure()
pyplot.plot(txs, GPsamples[0, nx - 1:-1], '-', color='0.25')
if isinstance(constraints, trainingSet):
pyplot.plot(mjd_r, r, 'k.', zorder=5, ms=10)
#plot.bovy_text(r'$\mathrm{'+title+'\ / \ '+method+r'}$',title=True)
#pyplot.fill_between(xs,thismean-sc.sqrt(sc.diagonal(thiscovar)),thismean+sc.sqrt(sc.diagonal(thiscovar)),color='.75')
for ii in range(1, nGP):
pyplot.plot(txs,
GPsamples[ii, nx - 1:-1],
'-',
color=str(0.25 + ii * .5 / (nGP - 1)))
#pyplot.plot(txs,thismean[nx-1:-1],'k-',linewidth=2)
if isinstance(constraints, trainingSet):
pyplot.errorbar(6.15, -0.25, yerr=meanErr_r, color='k')
pyplot.xlabel(r'$\mathrm{MJD-constant}\ [\mathrm{yr}]$')
pyplot.ylabel(r'$r-\langle r\rangle\ [\mathrm{mag}]$')
pyplot.xlim(-0.1, 6.5)
pyplot.ylim(-0.6, 0.6)
plot._add_ticks()
plot.bovy_end_print(basefilename + '_fullr.ps')
plot.bovy_print()
pyplot.figure()
ii = 0
colors = nu.array(
[GPsamples[ii, jj] - GPsamples[ii, jj + nx] for jj in range(nx)])
if not isinstance(constraints, trainingSet):
colors = colors - nu.mean(colors)
pyplot.plot(txs, colors, '-', color='0.25')
if isinstance(constraints, trainingSet):
plot.bovy_plot(mjd_g, g - r, 'k.', zorder=5, ms=10, overplot=True)
#plot.bovy_text(r'$\mathrm{'+basefilename+r'}$',title=True)
#pyplot.fill_between(xs,thismean-sc.sqrt(sc.diagonal(thiscovar)),thismean+sc.sqrt(sc.diagonal(thiscovar)),color='.75')
for ii in range(1, nGP):
colors = nu.array(
[GPsamples[ii, jj] - GPsamples[ii, jj + nx] for jj in range(nx)])
if not isinstance(constraints, trainingSet):
colors = colors - nu.mean(colors)
pyplot.plot(txs, colors, '-', color=str(0.25 + ii * .5 / (nGP - 1)))
plotthismean = nu.zeros(nx)
for ii in range(nx):
plotthismean[ii] = thismean[ii] - thismean[ii + nx]
#pyplot.plot(txs,plotthismean,'k-',linewidth=2)
if isinstance(constraints, trainingSet):
pyplot.errorbar(6.15, -0.18, yerr=meanErr_gr, color='k')
pyplot.xlabel(r'$\mathrm{MJD-constant}\ [\mathrm{yr}]$')
pyplot.ylabel(r'$g-r- \langle g - r \rangle\ [\mathrm{mag}]$')
pyplot.xlim(-0.1, 6.5)
if isinstance(constraints, trainingSet):
pyplot.ylim(-0.25, .25)
else:
pass #pyplot.ylim(-10.,10.)
plot._add_ticks()
plot.bovy_end_print(basefilename + '_color.ps')
if covarType == 'DRW':
return
#Plot structure functions
#g
plot.bovy_print()
pyplot.figure()
for ii in range(nGP):
thisSample = GPsamples[ii, :nx]
pyplot.loglog(sc.arange(1.,len(thisSample)/2)*(txs[1]-txs[0]),
2.*sc.var(thisSample)\
-2.*sc.correlate(thisSample-sc.mean(thisSample),thisSample-sc.mean(thisSample),"same")[1:len(thisSample)/2][::-1]/len(thisSample),
color=str(0.25+ii*.5/(nGP-1)))
xline = [(txs[1] - txs[0]), txs[len(txs) / 2]]
pyplot.loglog(xline, (nu.exp(paramsSF['logGamma']) *
nu.array(xline))**(paramsSF['gamma']), 'k--')
pyplot.xlabel(r'$\Delta t\ [\mathrm{yr}]$')
pyplot.ylabel(r'$\mathrm{structure\ function\ in}\ g$')
#plot.bovy_text(r'$\mathrm{SDSSJ203817.37+003029.8}$',title=True)
plot.bovy_end_print(basefilename + '_structfuncg.ps')
#r
plot.bovy_print()
pyplot.figure()
for ii in range(nGP):
thisSample = GPsamples[ii, nx - 1:-1]
pyplot.loglog(sc.arange(1.,len(thisSample)/2)*(txs[1]-txs[0]),
2.*sc.var(thisSample)\
-2.*sc.correlate(thisSample-sc.mean(thisSample),thisSample-sc.mean(thisSample),"same")[1:len(thisSample)/2][::-1]/len(thisSample),
color=str(0.25+ii*.5/(nGP-1)))
xline = [(txs[1] - txs[0]), txs[len(txs) / 2]]
pyplot.loglog(xline, (nu.exp(paramsSF['logGamma']) *
nu.array(xline))**(paramsSF['gamma']), 'k--')
pyplot.xlabel(r'$\Delta t\ [\mathrm{yr}]$')
pyplot.ylabel(r'$\mathrm{structure\ function\ in}\ r$')
#plot.bovy_text(r'$\mathrm{SDSSJ203817.37+003029.8}$',title=True)
plot.bovy_end_print(basefilename + '_structfuncr.ps')
#g-r
plot.bovy_print()
pyplot.figure()
for ii in range(nGP):
thisSample = nu.array(
[GPsamples[ii, jj] - GPsamples[ii, jj + nx] for jj in range(nx)])
pyplot.loglog(sc.arange(1.,len(thisSample)/2)*(txs[1]-txs[0]),
2.*sc.var(thisSample)\
-2.*sc.correlate(thisSample-sc.mean(thisSample),thisSample-sc.mean(thisSample),"same")[1:len(thisSample)/2][::-1]/len(thisSample),
color=str(0.25+ii*.5/(nGP-1)))
xline = [(txs[1] - txs[0]), txs[len(txs) / 2]]
pyplot.loglog(xline, (nu.exp(paramsSF['logGammagr']) *
nu.array(xline))**(paramsSF['gammagr']), 'k--')
pyplot.xlabel(r'$\Delta t\ [\mathrm{yr}]$')
pyplot.ylabel(r'$\mathrm{color\ structure\ function}$')
#plot.bovy_text(r'$\mathrm{SDSSJ203817.37+003029.8}$',title=True)
plot.bovy_end_print(basefilename + '_structfuncgr.ps')