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NX01_bayesutils.py
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NX01_bayesutils.py
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"""
Created by stevertaylor
Copyright (c) 2014 Stephen R. Taylor
Code contributions by Rutger van Haasteren (piccard) and Justin Ellis (PAL/PAL2).
"""
from __future__ import division
import numpy as np
import matplotlib.pyplot as plt
import scipy.interpolate as interp
import scipy.ndimage.filters as filter
try:
import healpy as hp
except ImportError:
hp = None
try:
import plot
except ImportError:
plot = None
import matplotlib.mlab as ml
from matplotlib.ticker import FormatStrFormatter, \
LinearLocator, NullFormatter, NullLocator
import matplotlib.ticker
import matplotlib.colors
from scipy.stats import gaussian_kde
from optparse import OptionParser
import statsmodels.api as sm
from statsmodels.distributions.empirical_distribution import ECDF
import os
import matplotlib
import distutils.version
mpl_version = distutils.version.LooseVersion(matplotlib.__version__)
import NX01_utils as utils
"""
Plotting codes from Justin Ellis' PAL2 package, with additions by Steve Taylor
"""
"""
Given a 2D matrix of (marginalised) likelihood levels, this function returns
the 1, 2, 3- sigma levels. The 2D matrix is usually either a 2D histogram or a
likelihood scan
"""
def getsigmalevels(hist2d, sig_levels=[0.68, 0.95, 0.997]):
# We will draw contours with these levels
sigma1, sigma2, sigma3 = sig_levels
level1 = 0
level2 = 0
level3 = 0
#
lik = hist2d.reshape(hist2d.size)
sortlik = np.sort(lik)
# Figure out the 1sigma level
dTotal = np.sum(sortlik)
nIndex = sortlik.size
dSum = 0
while (dSum < dTotal * sigma1):
nIndex -= 1
dSum += sortlik[nIndex]
level1 = sortlik[nIndex]
# 2 sigma level
nIndex = sortlik.size
dSum = 0
while (dSum < dTotal * sigma2):
nIndex -= 1
dSum += sortlik[nIndex]
level2 = sortlik[nIndex]
# 3 sigma level
nIndex = sortlik.size
dSum = 0
while (dSum < dTotal * sigma3):
nIndex -= 1
dSum += sortlik[nIndex]
level3 = sortlik[nIndex]
return level1, level2, level3
def confinterval(samples, sigma=0.68, onesided=False, weights=None,
bins=40, type='equalArea'):
"""
Given a list of samples, return the desired cofidence intervals.
Returns the minimum and maximum confidence levels
@param samples: Samples that we wish to get confidence intervals
@param sigmalevel: Sigma level 1, 2, or 3 sigma, will return
corresponding confidence limits
@param onesided: Boolean to use onesided or twosided confidence
limits.
@param weights: Histogram Weights.
@param bins: Number of histogram bins
@param type: equalArea: Integrates from sides of posterior
minArea: Brute force search for confidence interval with smallest
paramter range
equalProb: Integrates from MAP downwards
"""
ecdf = ECDF(samples)
# Create the binning
x = np.linspace(min(samples), max(samples), 1000)
ecdf = ECDF(samples)
y = ecdf(x)
# Find the intervals
if type == 'equalArea' or onesided:
if onesided:
x2max = x[np.flatnonzero(y<=sigma)[-1]]
x2min = x2max
else:
x2min = x[np.flatnonzero(y<=0.5*(1-sigma))[-1]]
x2max = x[np.flatnonzero(y>=1-0.5*(1-sigma))[0]]
if type == 'minArea':
delta, xmin, xmax = np.zeros(len(y)), np.zeros(len(y)), np.zeros(len(y))
start = 0
for ii in range(len(y)):
ind = np.flatnonzero((y-y[ii])>=sigma)
if len(ind) == 0:
delta[ii] = np.inf
else:
delta[ii] = x[ind[0]] - x[ii]
xmin[ii] = x[ii]
xmax[ii] = x[ind[0]]
minind = np.argmin(delta)
x2min = xmin[minind]
x2max = xmax[minind]
if type == 'equalProb' and not(onesided):
hist, xedges = np.histogram(samples, bins=bins, weights=weights)
xedges = np.delete(xedges, -1) + 0.5*(xedges[1] - xedges[0])
x = np.linspace(xedges.min(), xedges.max(), 10000)
ifunc = interp.interp1d(xedges, hist, kind='linear')
sortlik = np.sort(ifunc(x))
sortlik /= sortlik.sum()
ind = np.argsort(ifunc(x))
idx = np.flatnonzero(np.cumsum(sortlik) > 1-sigma)
x2min = x[ind][idx].min()
x2max = x[ind][idx].max()
return x2min, x2max
def makesubplot2d(ax, samples1, samples2, cmap=None, color='k', weights=None,
smooth=True, bins=[40, 40], contours=True, x_range=None,
y_range=None, logx=False, logy=False, logz=False, lw=1.5,
conf_levels=[0.68, 0.95, 0.99]):
if x_range is None:
xmin = np.min(samples1)
xmax = np.max(samples1)
else:
xmin = x_range[0]
xmax = x_range[1]
if y_range is None:
ymin = np.min(samples2)
ymax = np.max(samples2)
else:
ymin = y_range[0]
ymax = y_range[1]
if logx:
bins[0] = np.logspace(np.log10(xmin), np.log10(xmax), bins[0])
if logy:
bins[1] = np.logspace(np.log10(ymin), np.log10(ymax), bins[1])
hist2d,xedges,yedges = np.histogram2d(samples1, samples2, weights=weights, \
bins=bins,range=[[xmin,xmax],[ymin,ymax]])
extent = [xedges[0], xedges[-1], yedges[0], yedges[-1] ]
if logz:
for ii in range(hist2d.shape[0]):
for jj in range(hist2d.shape[1]):
if hist2d[ii,jj] <= 0:
hist2d[ii,jj] = 1
xedges = np.delete(xedges, -1) + 0.5*(xedges[1] - xedges[0])
yedges = np.delete(yedges, -1) + 0.5*(yedges[1] - yedges[0])
# gaussian smoothing
if smooth:
hist2d = filter.gaussian_filter(hist2d, sigma=0.75)
if contours:
level1, level2, level3 = getsigmalevels(hist2d, conf_levels)
contourlevels = (level1, level2, level3)
contourcolors = (color, color, color)
contourlinestyles = ('dashed', 'dotted', 'dashdot')
contourlinewidths = (lw, lw, lw)
# patch to fix new level ordering in mpl v 1.5.1
if mpl_version >= '1.5.1':
contourlevels = contourlevels[::-1]
contourcolors = contourcolors[::-1]
contourlinestyles = contourlinestyles[::-1]
contourlinewidths = contourlinewidths[::-1]
c1 = ax.contour(xedges,yedges,hist2d.T,contourlevels[:3], \
colors=contourcolors[:3], linestyles=contourlinestyles[:3], \
linewidths=contourlinewidths[:3], zorder=2)
if cmap:
if logz:
c2 = ax.imshow(np.flipud(hist2d.T), extent=extent, aspect=ax.get_aspect(), \
interpolation='gaussian', norm=matplotlib.colors.LogNorm(), cmap=cmap)
else:
c2 = ax.imshow(np.flipud(hist2d.T), extent=extent, aspect=ax.get_aspect(), \
interpolation='gaussian', cmap=cmap)
if logx:
ax.set_xscale('log')
if logy:
ax.set_yscale('log')
def getMeanAndStd(samples, weights=None, bins=50):
"""
Get mean and standard deviation. Only really useful when weights != None
"""
hist, xedges = np.histogram(samples, bins, normed=True, weights=weights)
xedges = np.delete(xedges, -1) + 0.5*(xedges[1] - xedges[0])
# pdf
p = hist/np.sum(hist)
# mean
m = np.sum(xedges*p)
# variance
std = np.sqrt(np.sum(xedges**2*p) - m**2)
return m, std
def makesubplot1d(ax, samples, weights=None, interpolate=False, smooth=True,\
label=None, bins=30, range=None, color='k',
orientation='vertical', logbin=False, **kwargs):
"""
Make histogram of samples
"""
if range is None:
hist, xedges = np.histogram(samples, bins, normed=True, weights=weights)
else:
hist, xedges = np.histogram(samples, bins, normed=True, range=range, weights=weights)
xedges = np.delete(xedges, -1) + 0.5*(xedges[1] - xedges[0])
# gaussian smoothing
if smooth:
hist = filter.gaussian_filter(hist, sigma=0.75)
if interpolate:
f = interp.interp1d(xedges, hist, kind='cubic')
if logbin:
xedges = np.logspace(np.log10(xedges.min()),
np.log10(xedges.max()),
10000)
else:
xedges = np.linspace(xedges.min(), xedges.max(), 10000)
hist = f(xedges)
# make plot
if label is not None:
if orientation == 'horizontal':
ax.plot(hist, xedges, color=color, label=label, **kwargs)
else:
ax.plot(xedges, hist, color=color, label=label, **kwargs)
else:
if orientation == 'horizontal':
ax.plot(hist, xedges, color=color, **kwargs)
else:
ax.plot(xedges, hist, color=color, **kwargs)
def getMax(samples, weights=None, range=None, bins=50):
"""
Make histogram of samples
"""
if range is None:
hist, xedges = np.histogram(samples, bins, normed=True, weights=weights)
else:
hist, xedges = np.histogram(samples, bins, normed=True, range=range,\
weights=weights)
xedges = np.delete(xedges, -1) + 0.5*(xedges[1] - xedges[0])
# gaussian smoothing
hist = filter.gaussian_filter(hist, sigma=0.75)
# interpolation
f = interp.interp1d(xedges, hist, kind='cubic')
xedges = np.linspace(xedges.min(), xedges.max(), 10000)
hist = f(xedges)
return xedges[np.argmax(hist)]
# make triangle plot of marginalized posterior distribution
def triplot(chain, color='k', weights=None, interpolate=False, smooth=True, \
labels=None, figsize=(11,8.5), title=None, inj=None, tex=True, \
incMaxPost=True, cmap='YlOrBr', lw=1.5, ranges=False, axarr=None):
"""
Make Triangle plot
"""
# rcParams settings
if chain.shape[1] < 10:
ticksize = 10
#plt.rcParams['ytick.labelsize'] = 10.0
#plt.rcParams['xtick.labelsize'] = 10.0
else:
ticksize = 8
#plt.rcParams['ytick.labelsize'] = 8.0
#plt.rcParams['xtick.labelsize'] = 8.0
if tex:
plt.rcParams['text.usetex'] = True
# get number of parameters
ndim = chain.shape[1]
parameters = np.linspace(0,ndim-1,ndim)
if axarr is not None:
f = plt.gcf()
#fig, axarr = plt.subplots(nrows=len(parameters), ncols=len(parameters),figsize=figsize)
else:
f, axarr = plt.subplots(nrows=len(parameters), ncols=len(parameters),figsize=figsize)
for i in range(len(parameters)):
# for j in len(parameters[np.where(i <= parameters)]:
for j in range(len(parameters)):
ii = i
jj = len(parameters) - j - 1
# get ranges
if ranges:
xmin, xmax = confinterval(chain[:, parameters[ii]], sigma=0.95,
type='equalProb')
x_range = [xmin, xmax]
xmin, xmax = confinterval(chain[:, parameters[jj]], sigma=0.95,
type='equalProb')
y_range = [xmin, xmax]
else:
x_range = [chain[:, parameters[ii]].min(), chain[:, parameters[ii]].max()]
y_range = [chain[:, parameters[jj]].min(), chain[:, parameters[jj]].max()]
axarr[ii, jj].tick_params(axis='both', which='major', labelsize=10)
xmajorLocator = matplotlib.ticker.MaxNLocator(nbins=4,prune='both')
ymajorLocator = matplotlib.ticker.MaxNLocator(nbins=4,prune='both')
if j <= len(parameters)-i-1:
axarr[jj][ii].xaxis.set_minor_locator(NullLocator())
axarr[jj][ii].yaxis.set_minor_locator(NullLocator())
axarr[jj][ii].xaxis.set_major_locator(NullLocator())
axarr[jj][ii].yaxis.set_major_locator(NullLocator())
axarr[jj][ii].xaxis.set_minor_formatter(NullFormatter())
axarr[jj][ii].yaxis.set_minor_formatter(NullFormatter())
axarr[jj][ii].xaxis.set_major_formatter(NullFormatter())
axarr[jj][ii].yaxis.set_major_formatter(NullFormatter())
xmajorFormatter = FormatStrFormatter('%g')
ymajorFormatter = FormatStrFormatter('%g')
if ii == jj:
# Make a 1D plot
makesubplot1d(axarr[ii][ii], chain[:,parameters[ii]], \
weights=weights, interpolate=interpolate, \
smooth=smooth, color=color, lw=lw, range=x_range)
axarr[ii][jj].set_ylim(ymin=0)
if incMaxPost:
mx = getMax(chain[:,parameters[ii]], weights=weights)
axarr[ii][jj].set_title('%5.4g'%(mx), fontsize=10)
if inj is not None:
axarr[ii][ii].axvline(inj[ii], lw=2, color='k')
else:
# Make a 2D plot
makesubplot2d(axarr[jj][ii], chain[:,parameters[ii]],
chain[:,parameters[jj]], cmap=cmap,
color=color, weights=weights,
smooth=smooth, lw=lw, x_range=x_range,
y_range=y_range)
if inj is not None:
axarr[jj][ii].plot(inj[ii], inj[jj], 'x', color='k', markersize=12, \
mew=2, mec='k')
axarr[jj][ii].xaxis.set_major_locator(xmajorLocator)
axarr[jj][ii].yaxis.set_major_locator(ymajorLocator)
else:
axarr[jj][ii].set_visible(False)
#axarr[jj][ii].axis('off')
if jj == len(parameters)-1:
axarr[jj][ii].xaxis.set_major_formatter(xmajorFormatter)
if labels:
axarr[jj][ii].set_xlabel(labels[ii])
if ii == 0:
if jj == 0:
axarr[jj][ii].yaxis.set_major_locator(NullLocator())
#axarr[jj][ii].set_ylabel('Post.')
else:
axarr[jj][ii].yaxis.set_major_formatter(ymajorFormatter)
if labels:
axarr[jj][ii].set_ylabel(labels[jj])
# overall plot title
if title:
f.suptitle(title, fontsize=14, y=0.90)
# make plots closer together
f.subplots_adjust(hspace=0.1)
f.subplots_adjust(wspace=0.1)
return axarr
def pol2cart(lon, lat):
"""
Utility function to convert longitude,latitude on a unit sphere to
cartesian co-ordinates.
"""
x = np.cos(lat)*np.cos(lon)
y = np.cos(lat)*np.sin(lon)
z = np.sin(lat)
return np.array([x,y,z])
def greedy_bin_sky(skypos, skycarts):
"""
Greedy binning algorithm
"""
N = len(skycarts)
skycarts = np.array(skycarts)
bins = np.zeros(N)
for raSample, decSample in skypos:
sampcart = pol2cart(raSample, decSample)
dx = np.dot(skycarts, sampcart)
maxdx = np.argmax(dx)
bins[maxdx] += 1
# fill in skymap
histIndices = np.argsort(bins)[::-1] # in decreasing order
NSamples = len(skypos)
frac = 0.0
skymap = np.zeros(N)
for i in histIndices:
frac = float(bins[i])/float(NSamples)
skymap[i] = frac
return skymap
def plotSkyMap(raSample, decSample, nside=64, contours=None, colorbar=True, \
inj=None, psrs=None, cmap='YlOrBr', outfile='skymap.pdf'):
"""
Plot Skymap of chain samples on Mollwiede projection.
@param raSample: Array of right ascension samples
@param decSample: Array of declination samples
@param nside: Number of pixels across equator [default = 64]
@param contours: Confidence contours to draw eg. 68%, 95% etc
By default this is set to none and no contours
will be drawn.
@param colorbar: Boolean option to draw colorbar [default = True]
@param inj: list of injected values [ra, dec] in radians to plot
[default = None]
@param psrs: Stacked array of pulsar sky locations [ra, dec] in radians
[default=None] Will plot as white diamonds
"""
# clear figures
plt.clf()
# create stacked array of ra and dec
skypos = np.column_stack([raSample, decSample])
npix = hp.nside2npix(nside) # number of pixels total
# initialize theta and phi map coordinantes
skycarts=[]
for ii in range(npix):
skycarts.append(np.array(hp.pix2vec(nside,ii)))
# get skymap values from greedy binning algorithm
skymap = greedy_bin_sky(skypos, skycarts)
# smooth skymap
skymap = hp.smoothing(skymap, sigma=0.02)
# make plot
ax = plt.subplot(111, projection='astro mollweide')
# Add contours
if contours is not None:
for percent in contours:
indices = np.argsort(-skymap)
sky = skymap[indices]
region = np.zeros(skymap.shape)
ind = np.min(ml.find(np.cumsum(sky) >= 0.01*percent))
region[indices[0:ind]] = 1.0
cs = plot.contour(lambda lon, lat: region[hp.ang2pix(nside, 0.5*np.pi - lat, lon)], \
colors='k', linewidths=1.0, levels=[0.5])
#plt.clabel(cs, [0.5], fmt={0.5: '$\mathbf{%d\%%}$' % percent}, fontsize=8, inline=True)
# plot map
ax.grid()
plot.outline_text(ax)
plot.healpix_heatmap(skymap, cmap=cmap)
# add injection
if inj:
ax.plot(inj[0], inj[1], 'x', color='k', markersize=8, mew=2, mec='k')
# add pulsars
if np.all(psrs):
ax.plot(psrs[:,0], psrs[:,1], '*', color='lime', markersize=8, mew=1, mec='k')
# add colorbar and title
if colorbar:
plt.colorbar(orientation='horizontal')
plt.suptitle(r'$p(\alpha,\delta|d)$', y=0.1)
# save skymap
plt.savefig(outfile, bbox_inches='tight')
def upperlimitplot2d(x, y, sigma=0.95, ymin=None, ymax=None, bins=40, log=False, \
savename=None, labels=None, hold=False, **kwargs):
"""
Make upper limits of a parameter as a function of another.
@param x: Parameter we are making upper limits for
@param y: Parameter which we will bin
@param sigma: Sigma level of upper limit
@param ymin: Minimum value of binning parameter [default=None]
@param ymax: Maximum value of binning parameter [default=None]
@param bins: Number of bins
@param log: If True, plot on log-log scale
@param savename: Output filename for saved figure
@param labels: List of labels for axes [xlabel, ylabel]
@param hold: Hold current figure?
"""
# clear current figure
if hold == False:
plt.clf()
if ymin is None:
ymin = y.min()
if ymax is None:
ymax = y.max()
yedges = np.linspace(ymin, ymax, bins+1)
deltay = yedges[1] - yedges[0]
yvals = np.linspace(ymin+0.5*deltay, ymax-0.5*deltay, bins)
bin_index = []
upper = []
for i in range(bins):
# Obtain the indices in the range of the bin
indices = np.flatnonzero(np.logical_and(y>yedges[i], y<yedges[i+1]))
# Obtain the 1-sided x-sigma upper limit
if len(indices) > 0:
bin_index.append(i)
a, sigma1 = confinterval(x[indices], sigma=sigma, onesided=True)
upper.append(sigma1)
# make bin_indes and upper into arrays
bin_index = np.array(bin_index)
upper = np.array(upper)
# make plot
if log:
plt.plot(yvals[bin_index], 10**upper, **kwargs)
plt.grid(which='major')
plt.grid(which='minor')
plt.yscale('log')
else:
plt.plot(yvals[bin_index], upper, **kwargs)
plt.grid()
# labels
if labels:
plt.xlabel(labels[0])
plt.ylabel(labels[1])
if savename:
plt.savefig(savename, bbox_inches='tight')
else:
plt.savefig('2dUpperLimit.pdf', bbox_inches='tight')
"""
Given an mcmc chain, plot the log-spectrum
"""
def makespectrumplot(ax, chain, parstart=1, numfreqs=10, freqs=None, \
Apl=None, gpl=None, Asm=None, asm=None, fcsm=0.1, plotlog=False, \
lcolor='black', Tmax=None, Aref=None, title=None, \
values=False):
if freqs is None:
ufreqs = np.log10(np.arange(1, 1+numfreqs))
else:
ufreqs = np.log10(np.sort(np.array(list(set(freqs)))))
#ufreqs = np.array(list(set(freqs)))
yval = np.zeros(len(ufreqs))
yerr = np.zeros(len(ufreqs))
if len(ufreqs) != (numfreqs):
print "WARNING: parameter range does not correspond to #frequencies"
for ii in range(numfreqs):
fmin, fmax = confinterval(chain[:, parstart+ii], sigma=0.68)
yval[ii] = (fmax + fmin) * 0.5
yerr[ii] = (fmax - fmin) * 0.5
retvals = []
if values:
retvals.append(yval)
retvals.append(yerr)
# For plotting reference spectra
pfreqs = 10 ** ufreqs
ypl = None
ysm = None
if plotlog:
pic_spy = 3.16e7
ax.errorbar(ufreqs, yval, yerr=yerr, fmt='.', c=lcolor)
# outmatrix = np.array([ufreqs, yval, yerr]).T
# np.savetxt('spectrumplot.txt', outmatrix)
if Apl is not None and gpl is not None and Tmax is not None:
Apl = 10**Apl
ypl = (Apl**2 * pic_spy**3 / (12*np.pi*np.pi * (Tmax))) * ((pfreqs * pic_spy) ** (-gpl))
ax.plot(np.log10(pfreqs), np.log10(ypl), 'g--', linewidth=2.0)
if Asm is not None and asm is not None and Tmax is not None:
Asm = 10**Asm
fcsm = fcsm / pic_spy
ysm = (Asm * pic_spy**3 / Tmax) * ((1 + (pfreqs/fcsm)**2)**(-0.5*asm))
ax.plot(np.log10(pfreqs), np.log10(ysm), 'r--', linewidth=2.0)
#plt.axis([np.min(ufreqs)-0.1, np.max(ufreqs)+0.1, np.min(yval-yerr)-1, np.max(yval+yerr)+1])
ax.set_xlabel("Frequency [log(f/Hz)]")
#if True:
# #freqs = likobhy.ptapsrs[0].Ffreqs
# Tmax = 156038571.88061461
# Apl = 10**-13.3 ; Asm = 10**-24
# apl = 4.33 ; asm = 4.33
# fc = (10**-1.0)/pic_spy
# pcsm = (Asm * pic_spy**3 / Tmax) * ((1 + (freqs/fc)**2)**(-0.5*asm))
# pcpl = (Apl**2 * pic_spy**3 / (12*np.pi*np.pi * Tmax)) * \
# (freqs*pic_spy) ** (-apl)
# plt.plot(np.log10(freqs), np.log10(pcsm), 'r--', linewidth=2.0)
# plt.plot(np.log10(freqs), np.log10(pcpl), 'g--', linewidth=2.0)
else:
ax.errorbar(10**ufreqs, yval, yerr=yerr, fmt='.', c='black')
if Aref is not None:
ax.plot(10**ufreqs, np.log10(yinj), 'k--')
plt.axis([np.min(10**ufreqs)*0.9, np.max(10**ufreqs)*1.01,
np.min(yval-yerr)-1, np.max(yval+yerr)+1])
plt.xlabel("Frequency [Hz]")
#plt.title("Power spectrum")
if title is not None:
ax.set_title(title)
ax.set_ylabel("Power Spectrum [s^2]")
plt.grid(True)
return retvals
def makePostPlots(chain, labels, outDir='./postplots'):
import acor
if not os.path.exists(outDir):
try:
os.makedirs(outDir)
except OSError:
pass
ndim = chain.shape[1]
for ii in range(ndim):
xmajorLocator = matplotlib.ticker.MaxNLocator(nbins=6,prune='both')
ymajorLocator = matplotlib.ticker.MaxNLocator(nbins=6,prune='both')
fig = plt.figure(figsize=(10,4))
ax = fig.add_subplot(121)
acl = acor.acor(chain[:,ii])[0]
neff = len(chain[:,ii]) / acl * 10
ax.plot(chain[:,ii])
plt.title('Neff = {0}'.format(int(neff)))
plt.ylabel(labels[ii])
ax = fig.add_subplot(122)
if 'equad' in labels[ii] or 'jitter' in labels[ii] or \
'Amplitude' in labels[ii]:
ax.hist(10**chain[:,ii], 50, lw=2, color='b', \
weights=10**chain[:,ii], normed=True)
else:
ax.hist(chain[:,ii], 50, lw=2, color='b', normed=True)
plt.xlabel(labels[ii])
ax.xaxis.set_major_locator(xmajorLocator)
ax.yaxis.set_major_locator(ymajorLocator)
plt.savefig(outDir + '/' + labels[ii] + '_post.png', bbox_inches='tight', \
dpi=200)
def makePostPlots_show(chain, ndim, labels):
import acor
for ii in range(ndim):
xmajorLocator = matplotlib.ticker.MaxNLocator(nbins=6,prune='both')
ymajorLocator = matplotlib.ticker.MaxNLocator(nbins=6,prune='both')
fig = plt.figure(figsize=(10,4))
ax = fig.add_subplot(121)
try:
acl = acor.acor(chain[:,ii])[0]
neff = len(chain[:,ii]) / acl * 10
ax.plot(chain[:,ii])
plt.title('Neff = {0}'.format(int(neff)))
except:
ax.plot(chain[:,ii])
plt.ylabel(labels[ii])
majorFormatter = FormatStrFormatter('%d')
ax.xaxis.set_major_formatter(majorFormatter)
ax = fig.add_subplot(122)
ax.hist(chain[:,ii], 50, lw=2, color='b', normed=True)
plt.xlabel(labels[ii])
ax.xaxis.set_major_locator(xmajorLocator)
ax.yaxis.set_major_locator(ymajorLocator)
def makeCDF(sample, linestyle=None, linewidth=None, labels=None,
legendbox=False, title=None, tex=True):
if tex == True:
plt.rcParams['text.usetex'] = True
fig, ax = plt.subplots()
ecdf = sm.distributions.ECDF(sample)
x = np.linspace(min(sample), max(sample))
y = ecdf(x)
plt.step(x, y, linestyle, lw=linewidth)
up68 = confinterval(sample, sigma=0.68, onesided=True)[1]
up90 = confinterval(sample, sigma=0.90, onesided=True)[1]
up95 = confinterval(sample, sigma=0.95, onesided=True)[1]
lab68 = "%.2f" % up68
lab90 = "%.2f" % up90
lab95 = "%.2f" % up95
plt.hlines(y=0.68, xmin=0.0, xmax=up68, linewidth=3.0, linestyle='dashed',
color='green', label=r'$A_{h,68\%}=$'+str(lab68)+r'$\times 10^{-15}$')
plt.vlines(x=up68, ymin=0.0, ymax=0.68, linewidth=3.0, linestyle='dashed', color='green')
plt.hlines(y=0.90, xmin=0.0, xmax=up90, linewidth=3.0, linestyle='dashed',
color='blue', label=r'$A_{h,90\%}=$'+str(lab90)+r'$\times 10^{-15}$')
plt.vlines(x=up90, ymin=0.0, ymax=0.90, linewidth=3.0, linestyle='dashed', color='blue')
plt.hlines(y=0.95, xmin=0.0, xmax=up95, linewidth=3.0, linestyle='dashed',
color='red', label=r'$A_{h,95\%}=$'+str(lab95)+r'$\times 10^{-15}$')
plt.vlines(x=up95, ymin=0.0, ymax=0.95, linewidth=3.0, linestyle='dashed', color='red')
plt.legend(loc='lower right', shadow=True, frameon=True, prop={'size':15})
ax.xaxis.set_minor_locator(AutoMinorLocator(5))
ax.yaxis.set_minor_locator(AutoMinorLocator(5))
if labels:
plt.xlabel(labels[0])
plt.ylabel(labels[1])
plt.grid(which='both')
plt.title(title, fontsize=20)
def make_all_CDF(sample0, sample1, sample2, sample3, linestyle=None, linewidth=None,
labels=None, legendbox=False, title=None, tex=False):
if tex == True:
plt.rcParams['text.usetex'] = True
fig, ax = plt.subplots()
ecdf0 = ECDF(sample0)
ecdf1 = ECDF(sample1)
ecdf2 = ECDF(sample2)
ecdf3 = ECDF(sample3)
x0 = np.linspace(min(sample0), max(sample0))
y0 = ecdf0(x0)
x1 = np.linspace(min(sample1), max(sample1))
y1 = ecdf1(x1)
x2 = np.linspace(min(sample2), max(sample2))
y2 = ecdf2(x2)
x3 = np.linspace(min(sample3), max(sample3))
y3 = ecdf3(x3)
plt.step(x0, y0, linestyle, lw=linewidth, color='blue',label=r'$l_{max}=0$')
plt.step(x1, y1, linestyle, lw=linewidth, color='green',label=r'$l_{max}=1$')
plt.step(x2, y2, linestyle, lw=linewidth, color='black',label=r'$l_{max}=2$')
plt.step(x3, y3, linestyle, lw=linewidth, color='purple',label=r'$l_{max}=3$')
up68 = confinterval(sample3, sigma=0.68, onesided=True)[1]
up90 = confinterval(sample3, sigma=0.90, onesided=True)[1]
up95 = confinterval(sample3, sigma=0.95, onesided=True)[1]
lab68 = "%.2f" % up68
lab90 = "%.2f" % up90
lab95 = "%.2f" % up95
plt.hlines(y=0.68, xmin=0.0, xmax=up68, linewidth=3.0, linestyle='dashed',
color='green', label=r'$A_{h,68\%}=$'+str(lab68)+r'$\times 10^{-15}$, $l_{max}=3$')
plt.vlines(x=up68, ymin=0.0, ymax=0.68, linewidth=3.0, linestyle='dashed', color='green')
plt.hlines(y=0.90, xmin=0.0, xmax=up90, linewidth=3.0, linestyle='dashed',
color='blue', label=r'$A_{h,90\%}=$'+str(lab90)+r'$\times 10^{-15}$, $l_{max}=3$')
plt.vlines(x=up90, ymin=0.0, ymax=0.90, linewidth=3.0, linestyle='dashed', color='blue')
plt.hlines(y=0.95, xmin=0.0, xmax=up95, linewidth=3.0, linestyle='dashed',
color='red', label=r'$A_{h,95\%}=$'+str(lab95)+r'$\times 10^{-15}$, $l_{max}=3$')
plt.vlines(x=up95, ymin=0.0, ymax=0.95, linewidth=3.0, linestyle='dashed', color='red')
plt.legend(loc='lower right', shadow=True, frameon=True, prop={'size':15})
ax.xaxis.set_minor_locator(AutoMinorLocator(5))
ax.yaxis.set_minor_locator(AutoMinorLocator(5))
if labels:
plt.xlabel(labels[0])
plt.ylabel(labels[1])
plt.grid(which='both')
plt.title(title, fontsize=20)
def makeSkyMap(samples, lmax, nside=32, cmap=None, strain=None, tex=True,
psrs=None, axis=None):
if tex == True:
plt.rcParams['text.usetex'] = True
npix = hp.nside2npix(nside) # number of pixels total
# initialize theta and phi map coordinantes
skypos=[]
for ii in range(npix):
skypos.append(np.array(hp.pix2ang(nside,ii)))
skypos = np.array(skypos)
harmvals = utils.SetupSkymapPlottingGrid(lmax,skypos)
if np.atleast_2d(samples).shape[0]>1:
if strain is None:
samples = np.mean(samples, axis=0)
samples = np.append(2.*np.sqrt(np.pi), samples)
elif strain is not None:
samples = np.mean((samples.T * 10**(2.0*strain)).T, axis=0)
samples = np.append(np.mean(10**(2.0*strain) * (2.0*np.sqrt(np.pi))), samples)
else:
#### !!!!!
samples = np.append(2.*np.sqrt(np.pi), samples)
pwr = utils.GWpower(samples, harmvals)
print pwr, samples
if axis is None:
ax = plt.subplot(111, projection='astro mollweide')
ax.grid()
plot.outline_text(ax)
if cmap is not None:
if strain is None:
plot.healpix_heatmap(pwr,cmap=cmap)
elif strain is not None:
plot.healpix_heatmap(pwr,cmap=cmap)
else:
plot.healpix_heatmap(pwr)
plt.colorbar(orientation='horizontal')
if strain is None:
plt.suptitle(r'$\langle P_{\mathrm{GWB}}(\hat\Omega)\rangle$', y=0.1)
elif strain is not None:
plt.suptitle(r'$\langle A_h^2 P_{\mathrm{GWB}}(\hat\Omega)\rangle$', y=0.1)
# add pulsars locations
if psrs is not None:
ax.plot(psrs[:,0], np.pi/2. - psrs[:,1], '*', color='w',
markersize=15, mew=1, mec='k')
elif axis is not None:
axis.grid()
plot.outline_text(axis)
if cmap is not None:
plot.healpix_heatmap(pwr,cmap=cmap)
else:
plot.healpix_heatmap(pwr)
# add pulsars locations
if psrs is not None:
axis.plot(psrs[:,0], np.pi/2. - psrs[:,1], '*', color='w',
markersize=6, mew=1, mec='w')
def OSupperLimit(psr, GCGnoiseInv, ORF, OSsmbhb, ul_list=None,
far=None, drlist=None, tex=True, nlims=60):
if tex == True:
plt.rcParams['text.usetex'] = True
gam_bkgrd = np.linspace(1.01,6.99,nlims)
optStatList=[]
ct=0
for indx in gam_bkgrd:
optStatList.append( utils.optStat(psr, GCGnoiseInv, ORF, gam_gwb=indx)[:3] )
ct+=1
print "Finished {0}% of optimal-statistic upper-limit calculations...".format( 100.0*ct/(1.0*nlims) )
optStatList = np.array(optStatList)
fig, ax = plt.subplots()
stylelist = ['solid','dashed','dotted']
if ul_list is not None:
for ii in range(len(ul_list)):
ax.plot(gam_bkgrd, np.sqrt( optStatList[:,0] + optStatList[:,1]*np.sqrt(2.0)*( ss.erfcinv(2.0*(1.-ul_list[ii])) ) ),
linestyle=stylelist[ii], color='black', linewidth=3.0, label='$A_h$ {0}$\%$ upper-limit'.format(ul_list[ii]*100))
plt.hlines(y=np.sqrt( OSsmbhb[0] + OSsmbhb[1]*np.sqrt(2.0)*( ss.erfcinv(2.0*(1.-ul_list[ii])) ) ),
xmin=gam_bkgrd.min(), xmax=13./3., linewidth=3.0, linestyle='solid', color='red')
plt.vlines(x=13./3., ymin=0.0, ymax=np.sqrt( OSsmbhb[0] + OSsmbhb[1]*np.sqrt(2.0)*( ss.erfcinv(2.0*(1.-ul_list[ii])) ) ),
linewidth=3.0, linestyle='solid', color='red')
else:
for ii in range(len(drlist)):
ax.plot(gam_bkgrd, np.sqrt( optStatList[:,1]*np.sqrt(2.0)*( ss.erfcinv(2.0*far) - ss.erfcinv(2.0*drlist[ii]) ) ),
linestyle=stylelist[ii], color='black', linewidth=3.0, label='$A_h$ ({0}$\%$ FAR, {1}$\%$ DR)'.format(far*100,drlist[ii]*100))
plt.hlines(y=np.sqrt( OSsmbhb*np.sqrt(2.0)*( ss.erfcinv(2.0*far) - ss.erfcinv(2.0*drlist[ii]) ) ),
xmin=gam_bkgrd.min(), xmax=13./3., linewidth=3.0, linestyle='solid', color='red')
plt.vlines(x=13./3., ymin=0.0, ymax=np.sqrt( OSsmbhb*np.sqrt(2.0)*( ss.erfcinv(2.0*far) - ss.erfcinv(2.0*drlist[ii]) ) ),
linewidth=3.0, linestyle='solid', color='red')
ax.set_yscale('log')
ax.set_xlabel(r'$\gamma\equiv 3-2\alpha$', fontsize=20)
ax.set_ylabel(r'$A_h$', fontsize=20)
ax.minorticks_on()
plt.tick_params(labelsize=18)
plt.grid(which='major')
plt.grid(which='minor')