import Stats
import Appearance as AP
import OneDim
# Open the chain with a GUI.
labels, data = PM.OpenData()
# Print information for the parameters.
print 'Param | Best-fit | Posterior Mean | 1 sigma Credible region'
for key, name in labels.iteritems():
if key == 0 or key == 1 or '\chi^2' in name:
continue
x = data[key]
pw = data[0]
chisq = data[1]
bestfit = Stats.BestFit(chisq, x)
postmean = Stats.PosteriorMean(pw, x)
pdf = OneDim.PosteriorPDF(
x,
pw,
nbins=AP.nbins,
bin_limits=AP.bin_limits).pdf
xc = OneDim.PosteriorPDF(
x,
pw,
nbins=AP.nbins,
bin_limits=AP.bin_limits).bins
lowercredibleregion = OneDim.CredibleRegions(
pdf,
xc,
epsilon=AP.epsilon).lowercredibleregion
def TwoDimPlotFilledPL(xdata,
ydata,
posterior,
chisq,
xlabel='',
ylabel='',
plottitle=AP.plottitle,
legtitle=AP.PLTitle,
plot_limits=AP.plot_limits,
number_bins=AP.nbins,
bin_limits=None):
""" Makes a two dimensional plot with filled confidence intervals only, showing
best-fit and posterior mean.
Arguments:
xdata -- x-axis data from chain.
ydata -- y-axis data from chain, same length as xdata.
posterior -- Posterior weight from chain, same length as xdata.
chisq -- Chi-squared from chain, same length as xdata.
xlabel -- Label for x-axis.
ylabel -- Label for y-axis.
plottitle --- Title for plot.
legtitle --- Title for legend.
plot_limits --- Limits for plotting.
number_bins -- Number of bins per dimension for histograms.
"""
# Find full extent of data.
extent = NP.zeros((4))
extent[0] = min(xdata)
extent[1] = max(xdata)
extent[2] = min(ydata)
extent[3] = max(ydata)
# If bin limits is None, make it the full extent of the data.
if bin_limits is None:
bin_limits = [[extent[0], extent[1]], [extent[2], extent[3]]]
# If plot limits is None, make it the full extent of the data.
if plot_limits is None:
plot_limits = extent
# Initialise plot.
fig, ax = PM.NewPlot()
PM.PlotTicks(AP.xticks, AP.yticks, ax)
PM.PlotLabels(xlabel, ylabel, plottitle)
PM.PlotLimits(ax, plot_limits)
PM.Appearance()
# Points of interest.
PM.PlotData(Stats.BestFit(chisq, xdata), Stats.BestFit(chisq, ydata),
AP.BestFit)
PM.PlotData(Stats.PosteriorMean(posterior, xdata),
Stats.PosteriorMean(posterior, ydata), AP.PosteriorMean)
proflike = TwoDim.ProfileLike(xdata,
ydata,
chisq,
nbins=number_bins,
bin_limits=bin_limits).proflike
levels = TwoDim.ConfidenceIntervals(epsilon=AP.epsilon).deltaPL
PM.PlotFilledContour(xdata,
ydata,
proflike,
levels,
AP.LevelNames,
AP.ProfLike,
bin_limits=bin_limits)
# Show the plot.
PM.Legend(legtitle)
return fig
def Scatter(xdata,
ydata,
zdata,
posterior,
chisq,
xlabel='',
ylabel='',
zlabel='',
plottitle=AP.plottitle,
legtitle=AP.PLTitle,
plot_limits=AP.plot_limits,
number_bins=AP.nbins,
bin_limits=None):
""" Makes a three dimensional scatter plot, showing
best-fit and posterior mean and credible regions and confidence intervals.
The scattered points are coloured by the zdata.
Arguments:
xdata -- x-axis data from chain, scattered on plot.
ydata -- y-axis data from chain, same length as xdata, scattered on plot.
zdata -- y-axis data from chain, same length as xdata, colours the scattered points.
posterior -- Posterior weight from chain, same length as xdata.
chisq -- Chi-squared from chain, same length as xdata.
xlabel -- Label for x-axis.
ylabel -- Label for y-axis.
zlabel -- Label for z-axis.
plottitle --- Title for plot.
legtitle --- Title for legend.
plot_limits --- Limits for plotting.
number_bins -- Number of bins per dimension for histograms.
"""
# Find full extent of data.
extent = NP.zeros((4))
extent[0] = min(xdata)
extent[1] = max(xdata)
extent[2] = min(ydata)
extent[3] = max(ydata)
# If bin limits is None, make it the full extent of the data.
if bin_limits is None:
bin_limits = [[extent[0], extent[1]], [extent[2], extent[3]]]
# If plot limits is None, make it the full extent of the data.
if plot_limits is None:
plot_limits = extent
# Initialise plot.
fig, ax = PM.NewPlot()
PM.PlotTicks(AP.xticks, AP.yticks, ax)
PM.PlotLabels(xlabel, ylabel, plottitle)
PM.PlotLimits(ax, plot_limits)
PM.Appearance()
# Points of interest.
PM.PlotData(Stats.BestFit(chisq, xdata), Stats.BestFit(chisq, ydata),
AP.BestFit)
PM.PlotData(Stats.PosteriorMean(posterior, xdata),
Stats.PosteriorMean(posterior, ydata), AP.PosteriorMean)
# Plot scatter of points.
sc = plt.scatter(xdata,
ydata,
s=AP.Scatter.Size,
c=zdata,
marker=AP.Scatter.Symbol,
cmap=AP.Scatter.ColourMap,
norm=None,
vmin=None,
vmax=None,
alpha=0.5,
linewidths=None,
verts=None)
# Plot a colour bar.
cb = plt.colorbar(sc, orientation='horizontal', shrink=0.5)
# Colour bar label.
cb.ax.set_xlabel(zlabel)
# Set reasonable number of ticks.
cb.locator = MaxNLocator(4)
cb.update_ticks()
# Confidence intervals and credible regions.
proflike = TwoDim.ProfileLike(xdata,
ydata,
chisq,
nbins=number_bins,
bin_limits=bin_limits).proflike
pdf = TwoDim.PosteriorPDF(xdata,
ydata,
posterior,
nbins=number_bins,
bin_limits=bin_limits).pdf
levels = TwoDim.ConfidenceIntervals(epsilon=AP.epsilon).deltaPL
PM.PlotContour(xdata,
ydata,
proflike,
levels,
AP.LevelNames,
AP.ProfLike,
bin_limits=bin_limits)
levels = TwoDim.CredibleRegions(pdf, epsilon=AP.epsilon).crediblelevel
# Make sure pdf is correctly normalised.
pdf = pdf / pdf.sum()
PM.PlotContour(xdata,
ydata,
pdf,
levels,
AP.LevelNames,
AP.Posterior,
bin_limits=bin_limits)
# Show the plot.
PM.Legend(legtitle)
return fig
def TwoDimPlotPDF(xdata,
ydata,
posterior,
chisq,
xlabel='',
ylabel='',
plottitle=AP.plottitle,
legtitle=AP.PDFTitle,
plot_limits=AP.plot_limits,
number_bins=AP.nbins,
bin_limits=None):
""" Makes a two dimensional marginalised posterior plot, showing
best-fit and posterior mean and credible regions.
Arguments:
xdata -- x-axis data from chain.
ydata -- y-axis data from chain, same length as xdata.
posterior -- Posterior weight from chain, same length as xdata.
chisq -- Chi-squared from chain, same length as xdata.
xlabel -- Label for x-axis.
ylabel -- Label for y-axis.
plottitle --- Title for plot.
legtitle --- Title for legend.
plot_limits --- Limits for plotting.
number_bins -- Number of bins per dimension for histograms.
"""
# Find full extent of data.
extent = NP.zeros((4))
extent[0] = min(xdata)
extent[1] = max(xdata)
extent[2] = min(ydata)
extent[3] = max(ydata)
# If bin limits is None, make it the full extent of the data.
if bin_limits is None:
bin_limits = [[extent[0], extent[1]], [extent[2], extent[3]]]
# If plot limits is None, make it the full extent of the data.
if plot_limits is None:
plot_limits = extent
# Initialise plot.
fig, ax = PM.NewPlot()
PM.PlotTicks(AP.xticks, AP.yticks, ax)
PM.PlotLabels(xlabel, ylabel, plottitle)
PM.PlotLimits(ax, plot_limits)
PM.Appearance()
# Points of interest.
PM.PlotData(Stats.BestFit(chisq, xdata), Stats.BestFit(chisq, ydata),
AP.BestFit)
PM.PlotData(Stats.PosteriorMean(posterior, xdata),
Stats.PosteriorMean(posterior, ydata), AP.PosteriorMean)
pdf = TwoDim.PosteriorPDF(xdata,
ydata,
posterior,
nbins=number_bins,
bin_limits=bin_limits).pdf
PM.PlotImage(xdata, ydata, pdf, bin_limits, plot_limits, AP.Posterior,
AP.PDFTitle)
levels = TwoDim.CredibleRegions(pdf, epsilon=AP.epsilon).crediblelevel
# Make sure pdf is correctly normalised.
pdf = pdf / pdf.sum()
PM.PlotContour(xdata,
ydata,
pdf,
levels,
AP.LevelNames,
AP.Posterior,
bin_limits=bin_limits)
# Show the plot.
PM.Legend(legtitle)
return fig
def OneDimPlot(xdata,
posterior,
chisq,
xlabel='x',
ylabel='',
plottitle=AP.plottitle,
legtitle=AP.PDFTitle,
plot_limits=AP.plot_limits,
number_bins=AP.nbins,
bin_limits=None):
""" Makes a one dimensional plot, showing profile likelihood,
marginalised posterior, and statistics.
Arguments:
xdata -- Data column from chain of variable to be plotted.
posterior -- Posterior weight from chain, same length as xdata.
chisq -- Chi-squared from chain, same length as xdata.
xlabel -- Label for x-axis.
ylabel -- Label for y-axis.
plottitle --- Title for plot.
legtitle --- Title for legend.
plot_limits --- Limits for plotting.
number_bins -- Number of bins per dimension for histograms.
"""
# Find the full extent of data.
extent = NP.zeros((4))
extent[0] = min(xdata)
extent[1] = max(xdata)
extent[2] = 0
extent[3] = 1.2
# If bin limits is None, make it the full extent of the data.
if bin_limits is None:
bin_limits = [extent[0], extent[1]]
# If plot limits is None, make it the full extent of the data.
if plot_limits is None:
plot_limits = extent
# Initialise plot.
fig, ax = PM.NewPlot()
PM.PlotTicks(AP.xticks, AP.yticks, ax)
PM.PlotLabels(xlabel, ylabel, plottitle)
PM.PlotLimits(ax, plot_limits)
PM.Appearance()
# Points of interest.
PM.PlotData(Stats.BestFit(chisq, xdata), 0.02, AP.BestFit)
PM.PlotData(Stats.PosteriorMean(posterior, xdata), 0.02, AP.PosteriorMean)
# Data itself.
pdf = OneDim.PosteriorPDF(xdata,
posterior,
nbins=number_bins,
bin_limits=bin_limits).pdf
x = OneDim.PosteriorPDF(xdata,
chisq,
nbins=number_bins,
bin_limits=bin_limits).bins
PM.PlotData(x, pdf, AP.Posterior)
proflike = OneDim.ProfileLike(xdata,
chisq,
nbins=number_bins,
bin_limits=bin_limits).proflike
profchisq = OneDim.ProfileLike(xdata,
chisq,
nbins=number_bins,
bin_limits=bin_limits).profchisq
x = OneDim.ProfileLike(xdata,
chisq,
nbins=number_bins,
bin_limits=bin_limits).bins
PM.PlotData(x, proflike, AP.ProfLike)
# Plot credible regions/confidence intervals above data.
lowercredibleregion = OneDim.CredibleRegions(
pdf, x, epsilon=AP.epsilon).lowercredibleregion
uppercredibleregion = OneDim.CredibleRegions(
pdf, x, epsilon=AP.epsilon).uppercredibleregion
confint = OneDim.ConfidenceIntervals(profchisq, x,
epsilon=AP.epsilon).confint
# Plot credible region at 1.1 - just above plotted data which has its maximum at 1.
# Plot confidence intervals at 1.
for i, value in enumerate(lowercredibleregion):
PM.PlotData([lowercredibleregion[i], uppercredibleregion[i]],
[1.1, 1.1], AP.CredibleRegion[i])
PM.PlotData(confint[i, :], [1] * int(number_bins), AP.ConfInterval[i])
# Show the plot.
PM.Legend(AP.OneDimTitle)
return fig
def OneDimChiSq(xdata,
chisq,
xlabel='x',
ylabel='$\Delta \chi^2$',
plottitle=AP.plottitle,
legtitle=AP.ChiSqTitle,
plot_limits=AP.plot_limits,
number_bins=AP.nbins,
bin_limits=None):
""" Makes a one dimensional plot, showing delta-chisq only,
and excluded regions.
Arguments:
xdata -- Data column from chain of variable to be plotted.
chisq -- Chi-squared from chain, same length as xdata.
xlabel -- Label for x-axis.
ylabel -- Label for y-axis.
plottitle --- Title for plot.
legtitle --- Title for legend.
plot_limits --- Limits for plotting.
number_bins -- Number of bins per dimension for histograms.
"""
# Find the full extent of data.
extent = NP.zeros((4))
extent[0] = min(xdata)
extent[1] = max(xdata)
extent[2] = 0
extent[3] = 1.2
# If bin limits is None, make it the full extent of the data.
if bin_limits is None:
bin_limits = [extent[0], extent[1]]
# If plot limits is None, make it the full extent of the data.
if plot_limits is None:
plot_limits = extent
# Initialise plot.
fig, ax = PM.NewPlot()
PM.PlotTicks(AP.xticks, AP.yticks, ax)
PM.PlotLabels(xlabel, ylabel, plottitle)
PM.Appearance()
# Data itself.
profchisq = OneDim.ProfileLike(xdata,
chisq,
nbins=number_bins,
bin_limits=bin_limits).profchisq
x = OneDim.ProfileLike(xdata,
chisq,
nbins=number_bins,
bin_limits=bin_limits).bins
PM.PlotData(x, profchisq, AP.ProfChiSq)
# Plot the delta chi-squared between default range, 0 - 10.
PM.PlotLimits(ax, plot_limits)
# Bestfit point.
PM.PlotData(Stats.BestFit(chisq, xdata), 0.08, AP.BestFit)
# Confidence intervals as filled.
deltachisq = OneDim.ConfidenceIntervals(profchisq, x,
epsilon=AP.epsilon).deltachisq
for i, dchi in enumerate(deltachisq):
ax.fill_between(x,
0,
10,
where=profchisq >= dchi,
facecolor=AP.ProfChiSq.Colours[i],
interpolate=False,
alpha=0.7)
# Plot a proxy for the legend - plot spurious data outside plot limits,
# with legend entry matching colours of filled regions.
plt.plot(-1,
-1,
's',
color=AP.ProfChiSq.Colours[i],
label=AP.ChiSqLevelNames[i],
alpha=0.7,
ms=15)
if AP.Tau is not None:
# Plot the theory error as a band around the usual line.
PM.PlotBand(x, profchisq, AP.Tau, ax)
# Show the plot.
PM.Legend(legtitle)
return fig