# Now pull out just the labels and limits we need:
limits = numpy.zeros([npars,2])
ii = 0
for i in index:
limits[ii,:] = alllimits[i,:]
ii = ii + 1
labels = alllabels[:]
# Set up dynamic axis limits, and smoothing scales:
dylimits = numpy.zeros([npars,2])
smooth = numpy.zeros(npars)
for i in range(npars):
col = index[i]
# Get data subarray, and measure its mean and stdev:
d = data[:,col].copy()
mean,stdev,Neff,N95 = pappy.meansd(d,wht=wht)
if vb: print "col = ",col," mean,stdev,nd = ",mean,stdev,Neff,N95
# Set smoothing scale for this parameter, in physical units.
smooth[i] = smoothscale*0.5*4.0*stdev/(N95**0.33)
# Cf Jullo et al 2007, who use a bin size given by
# w = 2*IQR/N^(1/3) for N samples, interquartile range IQR
# For a Gaussian, IQR is not too different from 2sigma. 4sigma/N^1/3?
# Also need N to be the effective number of parameters - return
# form meansd as sum of weights!
# Set 10 sigma limits:
dylimits[i,0] = mean - 10*stdev
dylimits[i,1] = mean + 10*stdev
def pdf2d(ax,ay,imp,xbins,ybins,smooth,color,style,conditional=False):
from scipy import ndimage
pylab.xlim([xbins[0],xbins[-1]])
pylab.ylim([ybins[0],ybins[-1]])
# npts = int((ax.size/4)**0.5)
H,x,y = pylab.histogram2d(ax,ay,weights=imp,bins=[xbins,ybins])
totalmass = sum(H.flatten())
# Smooth the histogram into a PDF:
if conditional:
ncolumns = len(H[0,:])
totalstdev = numpy.sqrt(numpy.var(ay))
for i in range(ncolumns):
p = H[i,:]
# Need to choose smoothing scale carefully here! Columns with fewer points need
# bigger smoothing scales:
norm = numpy.sum(p)
if (norm > 0.0):
yy = ybins[1:]
mean,stdev,Neff,N95 = pappy.meansd(yy,wht=p)
blur = (smooth + smooth*(stdev/totalstdev)**2)
# print "i,norm,totalmass, smooth,blur = ",i,norm,totalmass,smooth,blur
H[i,:] = ndimage.gaussian_filter1d(p.flatten(),blur)
else:
H = ndimage.gaussian_filter(H,smooth)
# For a conditional PDF Pr(y|x), normalise PDF in columns (constant x):
if conditional:
for i in range(len(H[0,:])):
p = H[i,:]
norm = numpy.sum(p.flatten())
# Can only estimate conditional where there are enough points! Rough
# estimate - focus on 99.9% of the mass:
norm = norm * (norm > 0.001*totalmass)
H[i,:] = p * (norm > 0.0) / (norm + (norm == 0.0))
else:
norm = numpy.sum(H.flatten())
H = H * (norm > 0.0) / (norm + (norm == 0.0))
sortH = numpy.sort(H.flatten())
cumH = sortH.cumsum()
# 1, 2, 3-sigma, for the old school:
lvl00 = 2*sortH.max()
lvl68 = sortH[cumH>cumH.max()*0.32].min()
lvl95 = sortH[cumH>cumH.max()*0.05].min()
lvl997 = sortH[cumH>cumH.max()*0.003].min()
# print "2D histogram: min,max = ",H.min(),H.max()
# print "Contour levels: ",[lvl00,lvl68,lvl95,lvl997]
if style == 'shaded':
# Plot shaded areas first:
pylab.contourf(H.T,[lvl997,lvl95],colors=color,alpha=0.1,\
extent=(xbins[0],xbins[-1],ybins[0],ybins[-1]))
pylab.contourf(H.T,[lvl95,lvl68],colors=color,alpha=0.4,\
extent=(xbins[0],xbins[-1],ybins[0],ybins[-1]))
pylab.contourf(H.T,[lvl68,lvl00],colors=color,alpha=0.7,\
extent=(xbins[0],xbins[-1],ybins[0],ybins[-1]))
# endif
# Always plot outlines:
pylab.contour(H.T,[lvl68,lvl95,lvl997],colors=color,\
extent=(xbins[0],xbins[-1],ybins[0],ybins[-1]))
# pylab.contour(H.T,[lvl68,lvl95],colors=color,\
# extent=(xbins[0],xbins[-1],ybins[0],ybins[-1]))
return
# Now pull out just the labels and limits we need:
limits = numpy.zeros([npars,2])
ii = 0
for i in index:
limits[ii,:] = alllimits[i,:]
ii = ii + 1
labels = alllabels[:]
# Set up dynamic axis limits, and smoothing scales:
dylimits = numpy.zeros([npars,2])
smooth = numpy.zeros(npars)
for i in range(npars):
col = index[i]
# Get data subarray, and measure its mean and stdev:
d = data[:,col].copy()
mean,stdev,Neff,N95 = pappy.meansd(d,wht=wht)
if vb: print "col = ",col," mean,stdev,nd = ",mean,stdev,Neff,N95
# Set smoothing scale for this parameter, in physical units.
smooth[i] = smoothscale*0.5*4.0*stdev/(N95**0.33)
# Cf Jullo et al 2007, who use a bin size given by
# w = 2*IQR/N^(1/3) for N samples, interquartile range IQR
# For a Gaussian, IQR is not too different from 2sigma. 4sigma/N^1/3?
# Also need N to be the effective number of parameters - return
# form meansd as sum of weights!
# Set 10 sigma limits:
dylimits[i,0] = mean - 10*stdev
dylimits[i,1] = mean + 10*stdev
def pdf2d(ax, ay, imp, xbins, ybins, smooth, color, style, conditional=False):
from scipy import ndimage
pylab.xlim([xbins[0], xbins[-1]])
pylab.ylim([ybins[0], ybins[-1]])
# npts = int((ax.size/4)**0.5)
H, x, y = pylab.histogram2d(ax, ay, weights=imp, bins=[xbins, ybins])
totalmass = sum(H.flatten())
# Smooth the histogram into a PDF:
if conditional:
ncolumns = len(H[0, :])
totalstdev = numpy.sqrt(numpy.var(ay))
for i in range(ncolumns):
p = H[i, :]
# Need to choose smoothing scale carefully here! Columns with fewer points need
# bigger smoothing scales:
norm = numpy.sum(p)
if (norm > 0.0):
yy = ybins[1:]
mean, stdev, Neff, N95 = pappy.meansd(yy, wht=p)
blur = (smooth + smooth * (stdev / totalstdev)**2)
# print "i,norm,totalmass, smooth,blur = ",i,norm,totalmass,smooth,blur
H[i, :] = ndimage.gaussian_filter1d(p.flatten(), blur)
else:
H = ndimage.gaussian_filter(H, smooth)
# For a conditional PDF Pr(y|x), normalise PDF in columns (constant x):
if conditional:
for i in range(len(H[0, :])):
p = H[i, :]
norm = numpy.sum(p.flatten())
# Can only estimate conditional where there are enough points! Rough
# estimate - focus on 99.9% of the mass:
norm = norm * (norm > 0.001 * totalmass)
H[i, :] = p * (norm > 0.0) / (norm + (norm == 0.0))
else:
norm = numpy.sum(H.flatten())
H = H * (norm > 0.0) / (norm + (norm == 0.0))
sortH = numpy.sort(H.flatten())
cumH = sortH.cumsum()
# 1, 2, 3-sigma, for the old school:
lvl00 = 2 * sortH.max()
lvl68 = sortH[cumH > cumH.max() * 0.32].min()
lvl95 = sortH[cumH > cumH.max() * 0.05].min()
lvl997 = sortH[cumH > cumH.max() * 0.003].min()
# print "2D histogram: min,max = ",H.min(),H.max()
# print "Contour levels: ",[lvl00,lvl68,lvl95,lvl997]
if style == 'shaded':
# Plot shaded areas first:
pylab.contourf(H.T,[lvl997,lvl95],colors=color,alpha=0.1,\
extent=(xbins[0],xbins[-1],ybins[0],ybins[-1]))
pylab.contourf(H.T,[lvl95,lvl68],colors=color,alpha=0.4,\
extent=(xbins[0],xbins[-1],ybins[0],ybins[-1]))
pylab.contourf(H.T,[lvl68,lvl00],colors=color,alpha=0.7,\
extent=(xbins[0],xbins[-1],ybins[0],ybins[-1]))
# endif
# Always plot outlines:
pylab.contour(H.T,[lvl68,lvl95,lvl997],colors=color,\
extent=(xbins[0],xbins[-1],ybins[0],ybins[-1]))
# pylab.contour(H.T,[lvl68,lvl95],colors=color,\
# extent=(xbins[0],xbins[-1],ybins[0],ybins[-1]))
return