def contours(M, contourKDEthin = 1):
'''
Plot likelihood contours for each pair of paramters
Parameters
----------
M : pymc.MCMC or pymc.database
The Markov chain to be plotted
contourKDEthin : int, optional
Thins the samples used for estimating the gaussian kernel density.
Defaults to 1 (no thinning).
See Also
--------
plot2Ddist (https://gist.github.com/665605)
'''
keys = ['R0', 'G0', 'Q', 'Beta', 'Delta', 'Tbase']
N = len(keys) - 1
pl.figure(figsize = (4 * N, 4 * N))
for i in range(N):
j = 0
while(j <= i):
ax = pl.subplot(N, N, i * N + j + 1)
p2d.plot2Ddist([M.trace(keys[i + 1])[:], M.trace(keys[j])[:]],
labels = [keys[i + 1], keys[j]],
contourKDEthin = contourKDEthin,
axeslist = [ax], plotscatter = False)
j += 1
pl.savefig('contours.png')
def compareto_normapprox(mcmodel, nmodel, varnames, truevalues=None,
markvalues=None,
axeslist=None, traceArgs = {}, **ellipseArgs):
"""Plot of confidence ellipses and samples from a NormApprox model
over points from another model trace.
logLStar versus alpha.
"""
nvars = names_to_obj(varnames, nmodel)
mu = nmodel.mu[nvars]
C = nmodel.C[nvars]
mcvars = names_to_obj(varnames, mcmodel)
mctraces = names_to_trace(varnames, mcmodel)
results = plot2Ddist.plot2Ddist(mcvars, axeslist=axeslist,
truevalues=truevalues,
markvalues=markvalues,
**traceArgs)
ells = plot_confidence_ellipse(mu, C, results['axeslist'][0], **ellipseArgs)
results['ells'] = ells
plot_normal(mu[0], C[0,0], ax=results['axeslist'][1]),
#normalization=mctraces[0].length())
plot_normal(mu[1], C[1,1], ax=results['axeslist'][2], rotate=True)
#test_confidence_ellipse(mcmodel, mu, C, varnames=varnames)
return results
for i in chain:
st = statistics_hist(i[int(burn_in*len(i)):],0.68,"stats")
print "Maximum Likelihood Value and 68% Confidence Interval: ", st[0],st[1]
#************************************************************************
"""
Parameter density estimation and pair correlations.
"""
from plot2Ddist import plot2Ddist, plot2DdistsPairs
plot_conts = False
if plot_conts:
for i in [12,13,14,15]:
for j in [12,13,14,15]:
if i !=j:
plot2Ddist([chain[i][int(burn_in*len(chain[i])):],chain[j][int(burn_in*len(chain[j])):]],plotcontours=True,plothists=True,contourFractions = [0.6827,0.9545,0.9973],labelcontours=False)
plt.show()
#************************************************************************
"""
Pair correlation between specific pair
"""
one_pair = False
param_1 = 0
param_2 = 12
if one_pair:
plot2Ddist([chain[param_1][int(burn_in*len(chain[param_1])):],chain[param_2][int(burn_in*len(chain[param_2])):]],plotcontours=True,plothists=True,contourFractions=[0.6827,0.9545,0.9973],labelcontours=False)
plt.show()
del fitsfile
del padding_cols
del prefix
del ext
for file in files:
scatterstyle={'color':'r', 'alpha':0.5}
styleargs = {'color':'k', 'scatterstyle':scatterstyle}
padding_cols = file['pad']
ncols = file['ncols']
for i in range (padding_cols, ncols):
for j in range (i + 1, ncols):
x = file['cols'][i]
y = file['cols'][j]
xlim = [col_name_att[file['col_names'][i]]['min'], col_name_att[file['col_names'][i]]['max']]
ylim = [col_name_att[file['col_names'][j]]['min'], col_name_att[file['col_names'][j]]['max']]
labelx = file['col_symbols'][i]
labely = file['col_symbols'][j]
plot2Ddist ([x, y], plothists = True, labels = [labelx, labely], xlim = xlim, ylim = ylim, **styleargs)
figfile = "%s_%s_%s.pdf" % (file['prefix'], file['col_names'][i], file['col_names'][j])
print ("# Saving figure: %s." % figfile)
pl.savefig (figfile)
pl.close ()
def test(nSims=100,
lmax=100,
lmin=2,
partialMax=4,
useCLASS=1,
useLensing=1,
cutSky=True,
myNSIDE=128,
newSC2=True,
saveFile='simpleSonehalfC2.npy',
nGrid=100):
"""
Purpose:
function for testing S_{1/2} calculations
Inputs:
nSims: the number of simulations to do
Overriden if newSC2 = False
Default: 100
lmax: the highest l to use in the calculation
Default: 100
lmin: the lowest l to use in the calculation
Default: 2
partialMax: the maximum l to use for partial Sonehalf plots
must be more than lmin
Overriden if newSC2 = False
Default: 4
useCLASS: set to 1 to use CLASS Cl, 0 for CAMB
Default: 1
useLensing: set to 1 to use lensed Cls
Default: 1
cutSky: set to True to do cut-sky sims
Default: True
myNSIDE: HEALPix parameter for simulated maps if cutSky=True
Default: 128
newSC2: set to True to simulate new ensemble and save S,C2 results
in file, False to skip simulation and load previous results
If false, values of nSims and partialMax will come from file
Default: True
saveFile: filename to save S,C2 result if newSC2 is true, to load if false
Default: 'simpleSonehalfC2.npy'
nGrid: to pass to plot2Ddist; controls grid for binning for contours
Default: 100
"""
# get power spectrum
# starts with ell[0]=2
ell, fullCl, primCl, lateCl, crossCl = gcp.loadCls(useCLASS=useCLASS,
useLensing=useLensing)
# fill beginning with zeros
startEll = int(ell[0])
ell = np.append(np.arange(startEll), ell)
Cl = np.append(np.zeros(startEll), fullCl)
#conv = ell*(ell+1)/(2*np.pi)
# Note: optimizeSx2 includes a multiplication of Cl by (beam*window)**2 at this point,
# but in this program I'm omitting it. Why? Effects are small, esp. at low ell
# get Jmn matrix for harmonic space S_{1/2} calc.
myJmn = getJmn(lmax=lmax) # do not include monopole, dipole
if cutSky:
# yeah.. disk access is annoying so...
RAMdisk = '/Volumes/ramdisk/'
ClTempFile = RAMdisk + 'tempCl.fits'
mapTempFile = RAMdisk + 'tempMap.fits'
mapDegFile = RAMdisk + 'smicaMapDeg.fits' #created by sim_stats.getSMICA
maskDegFile = RAMdisk + 'maskMapDeg.fits' #created by sim_stats.getSMICA
# create RAM Disk for SpICE and copy these files there using bash
RAMsize = 4 #Mb
ramDiskOutput = subprocess.check_output('./ramdisk.sh create ' +
str(RAMsize),
shell=True)
print ramDiskOutput
diskID = ramDiskOutput[
31:
41] # this might not grab the right part; works for '/dev/disk1'
subprocess.call('cp smicaMapDeg.fits ' + RAMdisk, shell=True)
subprocess.call('cp maskMapDeg.fits ' + RAMdisk, shell=True)
ispice(mapDegFile,
ClTempFile,
maskfile1=maskDegFile,
subav="YES",
subdipole="YES")
Clsmica = hp.read_cl(ClTempFile)
else:
ClTempFile = 'tempCl.fits'
mapTempFile = 'tempMap.fits'
mapDegFile = 'smicaMapDeg.fits' #created by sim_stats.getSMICA
maskDegFile = 'maskMapDeg.fits' #created by sim_stats.getSMICA
ispice(mapDegFile, ClTempFile, subav="YES", subdipole="YES")
Clsmica = hp.read_cl(ClTempFile)
# collect results
if newSC2:
sEnsemblePartial = np.zeros([nSims, partialMax + 1])
C2Ensemble = np.zeros(nSims)
for i in range(nSims):
print "starting sim ", i + 1, " of ", nSims, "... "
almSim = hp.synalm(Cl, lmax=lmax) # should start with ell[0] = 0
if cutSky:
mapSim = hp.alm2map(almSim, myNSIDE, lmax=lmax)
hp.write_map(mapTempFile, mapSim)
ispice(mapTempFile,
ClTempFile,
maskfile1=maskDegFile,
subav="YES",
subdipole="YES")
ClSim = hp.read_cl(ClTempFile)
else:
ClSim = hp.alm2cl(almSim)
for myLmin in range(lmin, partialMax + 1):
sEnsemblePartial[i, myLmin] = np.dot(
ClSim[myLmin:lmax + 1],
np.dot(myJmn[myLmin:, myLmin:], ClSim[myLmin:lmax + 1]))
C2Ensemble[i] = ClSim[2]
# save results
np.save(saveFile,
np.hstack((np.array([C2Ensemble]).T, sEnsemblePartial)))
else: # load from file
sEnsemblePartial = np.load(saveFile)
C2Ensemble = sEnsemblePartial[:, 0]
sEnsemblePartial = sEnsemblePartial[:, 1:]
nSims = sEnsemblePartial.shape[0]
partialMax = sEnsemblePartial.shape[1] - 1
if cutSky:
# free the RAM used by SpICE's RAM disk
ramDiskOutput = subprocess.check_output('./ramdisk.sh delete ' +
diskID,
shell=True)
print ramDiskOutput
# plot results
print 'plotting S_{1/2} distributions... '
#myBins = np.logspace(2,7,100)
myBins = np.logspace(2, 6, 100)
#plt.axvline(x=6763,color='b',linewidth=3,label='SMICA inpainted')
#plt.axvline(x=2145,color='g',linewidth=3,label='SMICA masked')
#plt.hist(sEnsembleFull,bins=myBins,color='b',histtype='step',label='full sky')
#plt.hist(sEnsembleCut, bins=myBins,color='g',histtype='step',label='cut sky')
myColors = ('g', 'b', 'r', 'c', 'm', 'k') #need more? prob. not.
myLines = ('-', '--', '-.') #need more?
for myEll in range(lmin, partialMax + 1):
plt.hist(sEnsemblePartial[:, myEll],
bins=myBins,
histtype='step',
label=r'sims: $\ell_{\rm min}$ = ' + str(myEll),
color=myColors[myEll - lmin],
linestyle=myLines[myEll - lmin],
linewidth=2)
Sonehalf = np.dot(
Clsmica[myEll:lmax + 1],
np.dot(myJmn[myEll:, myEll:], Clsmica[myEll:lmax + 1])) * 1e24
plt.axvline(x=Sonehalf,
linewidth=3,
label=r'SMICA: $\ell_{\rm min}$=' + str(myEll),
color=myColors[myEll - lmin],
linestyle=myLines[myEll - lmin])
# calculate and print p-value
pval = pValue(sEnsemblePartial[:, myEll], Sonehalf)
print 'l_min: ', myEll, ', Sonehalf: ', Sonehalf, ', p-value: ', pval
plt.gca().set_xscale("log")
plt.legend()
myfs = 16 # font size for labels
plt.xlabel(r'$S_{1/2} (\mu K^4)$', fontsize=myfs)
plt.ylabel('Counts', fontsize=myfs)
plt.xlim((500, 10**6))
if cutSky:
sName = ' cut-sky'
else:
sName = ' full-sky'
#plt.title(r'$S_{1/2}$ of '+str(nSims)+sName+' simulated CMBs')
plt.show()
print 'plotting C_2 vs. S_{1/2} histogram... '
SMICAvals = (np.log10(2145), 171.8
) # KLUDGE!!! #moved to earlier in program
SonehalfLabel = "$log_{10}(\ S_{1/2}\ /\ (\mu K)^4\ )$"
C2Label = "$C_2\ /\ (\mu K)^2$"
C2Label3 = "$C_2\ /\ (10^3 (\mu K)^2)$"
log10SonehalfEnsemble = np.log10(sEnsemblePartial[:, lmin])
myBinsLog10S = np.linspace(2, 6, 100)
myBinsC2 = np.linspace(0, 3000, 100)
cmap = cm.magma #Greens#Blues
plt.hist2d(log10SonehalfEnsemble,
C2Ensemble,
bins=[myBinsLog10S, myBinsC2],
cmap=cmap)
plt.plot(SMICAvals[0], SMICAvals[1], 'cD')
plt.colorbar()
#myfs = 16 # font size for labels
plt.xlabel(SonehalfLabel, fontsize=myfs)
plt.ylabel(C2Label, fontsize=myfs)
plt.show()
print 'plotting C_2 vs. S_{1/2} contours... '
H, xedges, yedges = np.histogram2d(log10SonehalfEnsemble,
C2Ensemble,
bins=(myBinsLog10S, myBinsC2))
H = H.T # Let each row list bins with common y range
myXedges = (xedges[1:] +
xedges[:-1]) / 2 #find midpoint of linspace for plotting
myYedges = (yedges[1:] + yedges[:-1]) / 2
hMax = np.max(H)
#levels = [hMax*0.0009,hMax*0.009,hMax*0.09,hMax*0.9,hMax]
#levels = [hMax*0.01,hMax*0.05,hMax*0.1,hMax*0.5,hMax*0.9,hMax]
levels = np.logspace(np.log10(0.01 * hMax), np.log10(0.9 * hMax), 5)
norm = cm.colors.Normalize(vmax=abs(H).max(), vmin=0)
#cmap = cm.PRGn
#plt.figure()
#plt.imshow(H,origin='lower',norm=norm,cmap=cmap)#,extent=extent) #extent is a coordinate zoom
#plt.imshow(H,norm=norm,cmap=cmap,extent=(2,6,0,3000)) #should match linspace above
#v = plt.axis()
CS = plt.contour(myXedges, myYedges, H, levels, colors='k', thickness=2)
plt.clabel(CS, inline=1, fontsize=10)
#plt.axis(v)
plt.colorbar()
#plt.title('do i want a title here?')
plt.xlim(2.8, 5.8)
#myfs = 16 # font size for labels
plt.xlabel(SonehalfLabel, fontsize=myfs)
plt.ylabel(C2Label, fontsize=myfs)
plt.plot(SMICAvals[0], SMICAvals[1], 'cD')
plt.show()
print 'plotting corner plot... '
toPlot = np.vstack((log10SonehalfEnsemble, C2Ensemble))
toPlot = toPlot.T
figure = corner.corner(toPlot,
labels=[SonehalfLabel, C2Label],
show_titles=False,
truths=SMICAvals,
range=((2.5, 6), (0, 3000)),
label_kwargs={'fontsize': myfs})
plt.show()
print 'plotting contours again but now using plot2Ddist (please wait)... '
doTime = True
startTime = time.time()
scatterstyle = {'color': 'r', 'alpha': 0.5}
styleargs = {'color': 'k', 'scatterstyle': scatterstyle}
bw_method = 0.05 #'scott'
axSize = "20%" #1.5
nstart = 600
# create separate figures to contain separate plots
"""plt.figure(1)
ax1=plt.gca()
plt.figure(2)
ax2=plt.gca()
plt.figure(3)
ax3=plt.gca()"""
#fig = plt.figure() #should be the same one used by plot2Ddist
# divide C2Ensemble by 1000 since that is approximate factor between ranges of C2,Sonehalf
# presumably useful for accuracy in contour plotting via kernel density estimation
fig1, axeslist = plot2Ddist.plot2Ddist(
[log10SonehalfEnsemble, C2Ensemble / 1000],
truevalues=[SMICAvals[0], SMICAvals[1] / 1000],
labels=[SonehalfLabel, C2Label3],
contourNGrid=nGrid,
bw_method=bw_method,
axSize=axSize,
nstart=nstart,
returnfigure=True,
**styleargs)
#bw_method=bw_method,axSize=axSize,axeslist=[ax1,ax2,ax3],**styleargs)
ax1, ax2, ax3 = axeslist
timeInterval1 = time.time() - startTime
if doTime:
print 'time elapsed: ', int(timeInterval1), ' seconds'
print 'starting second plot2Ddist call... '
ax1.set_xlim(left=2.9, right=6.1)
ax1.set_ylim(top=5.5)
ax1.plot(SMICAvals[0], SMICAvals[1] / 1000, 'cD')
#inset plot
left, bottom, width, height = [0.2, 0.4, 0.3, 0.3]
ax4 = fig1.add_axes([left, bottom, width, height])
#ax4.plot(range(10))
plt.figure(5)
ax5 = plt.gca()
plt.figure(6)
ax6 = plt.gca()
plot2Ddist.plot2Ddist([log10SonehalfEnsemble, C2Ensemble / 1000],
truevalues=[SMICAvals[0], SMICAvals[1] / 1000],
contourNGrid=nGrid,
bw_method=bw_method,
axSize=axSize,
nstart=nstart,
axeslist=[ax4, ax5, ax6],
contourFractions=[0.91, 0.93, 0.95, 0.97, 0.99],
labelcontours=False,
**styleargs)
timeInterval2 = time.time() - startTime
if doTime:
print 'time elapsed for both: ', int(timeInterval2), ' seconds'
ax4.set_xlim(left=3.15, right=3.45)
ax4.set_ylim(top=0.5)
ax4.plot(SMICAvals[0], SMICAvals[1] / 1000, 'cD')
ax4.xaxis.set_ticks((3.2, 3.3, 3.4))
#plt.figure(1)
#plt.xlim(2.9,6.1)
#plt.ylim(-0.03,5.5)
plt.show()
# calculate and print 1D p-values
pValueS12 = pValue(log10SonehalfEnsemble, SMICAvals[0])
pValueC2 = pValue(C2Ensemble, SMICAvals[1])
print 'S_{1/2} p-value = ', pValueS12
print 'C_2 p-value = ', pValueC2
print ''
def plot_fits(
filelist,
varname_pairs=None,
thin=1,
trim=0,
plotthin=None,
plot_spectra=True,
output_callback=None,
savename=None,
minlen=None,
):
"""Plot pairs of parameters from a set of fits.
returns value_pairs, which has shape:
(len(filelist), len(vpairs), 2, len(traces))
"""
if minlen is None:
minlen = trim
if varname_pairs is None:
m = PowerGaussMCMC.load(filelist[0])
if m.mcmodel.n_lines == 0:
varname_pairs = [("dw_alpha", "dw_lambda_e"), ("dw_alpha", "dw_tau0"), ("dw_lambda_e", "dw_tau0")]
if m.mcmodel.n_components == 2:
if m.mcmodel.vshifts[2] is m.mcmodel.vshifts[0]:
varname_pairs = [("vshift_1", "vshift_0")]
else:
varname_pairs = [("vshift_2", "vshift_0"), ("vshift_3", "vshift_1")]
elif m.mcmodel.n_components == 1:
if m.mcmodel.vshifts[1] is m.mcmodel.vshifts[0]:
varname_pairs = [
("peak_1", "peak_0"),
((numpy.divide, "peak_1", "contflux"), (numpy.divide, "peak_0", "contflux")),
("peak_1", "epeak_4"),
("peak_0", "epeak_4"),
("width_1", "width_0"),
("vshift_0", "evshift_4"),
("vshift_0", "peak_0"),
("vshift_0", "peak_1"),
("vshift_0", (numpy.divide, "peak_0", "peak_1")),
("vshift_0", (numpy.divide, "width_0", "width_1")),
("vshift_0", (numpy.divide, "ewidth_4", "width_1")),
("width_1", "ewidth_4"),
("width_0", "ewidth_4"),
("contflux", "vshift_1"),
("contindex", "vshift_1"),
]
else:
varname_pairs = [
("vshift_1", "vshift_0"),
("vshift_1", (numpy.subtract, "vshift_0", "vshift_1")),
((numpy.divide, "peak_1", "contflux"), (numpy.divide, "peak_0", "contflux")),
("vshift_1", (numpy.divide, "peak_0", "peak_1")),
("width_1", "width_0"),
("vshift_1", (numpy.divide, "width_0", "width_1")),
("evshift_4", (numpy.subtract, "vshift_0", "vshift_1")),
((numpy.subtract, "evshift_4", "vshift_1"), (numpy.subtract, "vshift_0", "vshift_1")),
("ewidth_4", (numpy.subtract, "vshift_0", "vshift_1")),
((numpy.divide, "ewidth_4", "width_1"), (numpy.subtract, "vshift_0", "vshift_1")),
((numpy.divide, "epeak_4", "peak_1"), (numpy.subtract, "vshift_0", "vshift_1")),
("evshift_3", "vshift_0"),
("ewidth_3", "width_0"),
("epeak_3", "peak_0"),
("contflux", "vshift_1"),
("contindex", "vshift_1"),
]
m.mcmodel.db.close()
del m
value_dict = defaultdict(list)
unique_varnames = set()
for vnames in varname_pairs:
unique_varnames.update(vnames)
final_filelist = []
for filename in filelist:
label = os.path.split(filename)[-1]
print filename
try:
m = PowerGaussMCMC.load(filename)
except Exception as e:
print "Couldn't load file. Got error:", e
continue
tracelen = len(m.mcmodel.db.deviance[:])
print "Found trace of len %i" % tracelen
if tracelen < minlen:
print "Not enough iterations in fit! Skipping", filename
continue
if plot_spectra:
pthin = plotthin
if pthin is None:
pthin = tracelen / 15
axeslist, total = m.plot_spectra(trim=trim, thin=pthin)
axes, resaxes, vaxes, vresaxes = axeslist
axes.set_title(label)
vaxes.set_title(label)
axes.figure.set_label(label + "_spectrum")
vaxes.figure.set_label(label + "_vspectrum")
xmin = 1150
xmax = 1275
axes.set_xlim(xmin, xmax)
vmin = max((xmin / 1215.67 - 1) * cc.c_light_cm_s / 1e5, -1.2e4)
vmax = min((xmax / 1215.67 - 1) * cc.c_light_cm_s / 1e5, 1.2e4)
vaxes.set_xlim(vmin, vmax)
scale = numpy.max(total)
axes.set_ylim(-0.1 * scale, 1.1 * scale)
vaxes.set_ylim(-0.1 * scale, 1.1 * scale)
resaxes.set_ylim(-0.1 * scale, 0.1 * scale)
vresaxes.set_ylim(-0.1 * scale, 0.1 * scale)
if output_callback is not None:
output_callback()
for vname in list(unique_varnames):
if type(vname) is tuple:
v1 = m.mcmodel.db.trace(vname[1])[trim::thin]
v2 = m.mcmodel.db.trace(vname[2])[trim::thin]
if not vname[1] in unique_varnames:
value_dict[vname[1]].append(v1)
unique_varnames.add(vname[1])
if not vname[2] in unique_varnames:
value_dict[vname[2]].append(v2)
unique_varnames.add(vname[2])
value_dict[vname].append(vname[0](v1, v2))
else:
value_dict[vname].append(m.mcmodel.db.trace(vname)[trim::thin])
print "mean", vname, numpy.mean(value_dict[vname][-1])
final_filelist.append(filename)
m.mcmodel.db.close()
del m
if savename is not None:
import hdf5_utils
hdf5_utils.save_hdf5(savename, dict((str(k), v) for k, v in value_dict.iteritems()))
colors = itertools.cycle(["r", "g", "b", "c", "m", "y", "k"])
alpha = 0.05
bins = 10
histbinslist = [bins] * 2
import plot2Ddist
for (ipair, vnames) in enumerate(varname_pairs):
results = dict(axeslist=None)
for ifile in xrange(len(final_filelist)):
results = plot2Ddist.plot2Ddist(
[value_dict[vnames[0]][ifile], value_dict[vnames[1]][ifile]],
labels=vnames,
axeslist=results["axeslist"],
color=colors.next(),
scatterstyle=dict(alpha=alpha),
histbinslist=histbinslist,
)
if output_callback is not None:
output_callback()
return value_dict
for i in range(padding_cols, ncols):
for j in range(i + 1, ncols):
x = file['cols'][i]
y = file['cols'][j]
xlim = [
col_name_att[file['col_names'][i]]['min'],
col_name_att[file['col_names'][i]]['max']
]
ylim = [
col_name_att[file['col_names'][j]]['min'],
col_name_att[file['col_names'][j]]['max']
]
labelx = file['col_symbols'][i]
labely = file['col_symbols'][j]
plot2Ddist([x, y],
plothists=True,
labels=[labelx, labely],
xlim=xlim,
ylim=ylim,
**styleargs)
figfile = "%s_%s_%s.pdf" % (file['prefix'], file['col_names'][i],
file['col_names'][j])
print("# Saving figure: %s." % figfile)
pl.savefig(figfile)
pl.close()