In a long list of plots that Martin wants me to add to the paper draft I sent out last week, the following:
Is it possible to show the histograms projected along each axis in addition to the 2D density? I know people do this in IDL frequently, I'm not sure how to do this in matplotlib. If it's possible we could play a similar game with the L-z figure. The 1D histograms contain lots of useful information, including how significant our clustering detection is in each bin.
Ask and you shall receive Martin. Below is the "money plot" (the temperature 2D histogram which shows amplitudes the bright versus dim correlation function) with histograms on the side of either axis.
I based this plot on code from here.
There are some cool features that I'll describe in the comments below. I think this plot rocks.
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.ticker import NullFormatter
def makeTempHistogramPlot(xdata,ydata,rexp,filename=None,xlims=-99, ylims =-99 , \
nxbins = 50,nybins=50, bw=0, nbins=100,contours=1,sigma=1,line=1):
#bw = 0 for color, = 1 for black and white
#line = 0 for no line, =1 for line
#sigma = 1 for display % below line, =0 for not
#contours = 1 for display 1,2,3 sigma contours, = 0 for not.
# Define the x and y data
x = xdata
y = ydata
# Set up default x and y limits
if (xlims == -99): xlims = [0,max(x)]
if (ylims == -99): ylims = [0,max(y)]
# Set up your x and y labels
xlabel = '$\mathrm{Your\\ X\\ Label}$'
ylabel = '$\mathrm{Your\\ X\\ Label}$'
mtitle = ''
# Define the locations for the axes
left, width = 0.12, 0.55
bottom, height = 0.12, 0.55
bottom_h = left_h = left+width+0.02
# Set up the geometry of the three plots
rect_temperature = [left, bottom, width, height] # dimensions of temp plot
rect_histx = [left, bottom_h, width, 0.25] # dimensions of x-histogram
rect_histy = [left_h, bottom, 0.25, height] # dimensions of y-histogram
# Set up the size of the figure
fig = plt.figure(1, figsize=(9.5,9))
# Make the three plots
axTemperature = plt.axes(rect_temperature) # temperature plot
axHistx = plt.axes(rect_histx) # x histogram
axHisty = plt.axes(rect_histy) # y histogram
# Remove the inner axes numbers of the histograms
nullfmt = NullFormatter()
axHistx.xaxis.set_major_formatter(nullfmt)
axHisty.yaxis.set_major_formatter(nullfmt)
# Find the min/max of the data
xmin = min(xlims)
xmax = max(xlims)
ymin = min(ylims)
ymax = max(y)
# Make the 'main' temperature plot
xbins = linspace(start = 0, stop = xmax, num = nxbins)
ybins = linspace(start = 0, stop = ymax, num = nybins)
xcenter = (xbins[0:-1]+xbins[1:])/2.0
ycenter = (ybins[0:-1]+ybins[1:])/2.0
aspectratio = 1.0*(xmax - 0)/(1.0*ymax - 0)
H, xedges,yedges = N.histogram2d(y,x,bins=(ybins,xbins))
X = xcenter
Y = ycenter
Z = H
# Plot the temperature data
if(bw): cax = axTemperature.imshow(H, extent=[xmin,xmax,ymin,ymax], \
interpolation='nearest', origin='lower',aspect=aspectratio, cmap=cm.gist_yarg)
else : cax = axTemperature.imshow(H, extent=[xmin,xmax,ymin,ymax], \
interpolation='nearest', origin='lower',aspect=aspectratio)
# Plot the temperature plot contours
if(bw): contourcolor = 'black'
else: contourcolor = 'white'
if (contours==0):
print ''
elif (contours==1):
xcenter = N.mean(x)
ycenter = N.mean(y)
ra = N.std(x)
rb = N.std(y)
ang = 0
X,Y=ellipse(ra,rb,ang,xcenter,ycenter)
axTemperature.plot(X,Y,"k:",ms=1,linewidth=2.0)
axTemperature.annotate('$1\\sigma$', xy=(X[15], Y[15]), xycoords='data',xytext=(10, 10), textcoords='offset points',horizontalalignment='right', verticalalignment='bottom',fontsize=25)
X,Y=ellipse(2*ra,2*rb,ang,xcenter,ycenter)
axTemperature.plot(X,Y,"k:",color = contourcolor,ms=1,linewidth=2.0)
axTemperature.annotate('$2\\sigma$', xy=(X[15], Y[15]), xycoords='data',xytext=(10, 10), textcoords='offset points',horizontalalignment='right', verticalalignment='bottom',fontsize=25, color = contourcolor)
X,Y=ellipse(3*ra,3*rb,ang,xcenter,ycenter)
axTemperature.plot(X,Y,"k:",color = contourcolor, ms=1,linewidth=2.0)
axTemperature.annotate('$3\\sigma$', xy=(X[15], Y[15]), xycoords='data',xytext=(10, 10), textcoords='offset points',horizontalalignment='right', verticalalignment='bottom',fontsize=25, color = contourcolor)
else:
xcenter = N.mean(x)
ycenter = N.mean(y)
ra = N.std(x)
rb = N.std(y)
ang = contours*N.pi/180.0
X,Y=ellipse(ra,rb,ang,xcenter,ycenter)
axTemperature.plot(X,Y,"k:",ms=1,linewidth=2.0)
axTemperature.annotate('$1\\sigma$', xy=(X[15], Y[15]), xycoords='data', xytext=(10, 10), textcoords='offset points',horizontalalignment='right', verticalalignment='bottom',fontsize=25)
X,Y=ellipse(2*ra,2*rb,ang,xcenter,ycenter)
axTemperature.plot(X,Y,"k:",ms=1,linewidth=2.0, color = contourcolor)
axTemperature.annotate('$2\\sigma$', xy=(X[15], Y[15]), xycoords='data', xytext=(10, 10), textcoords='offset points',horizontalalignment='right', verticalalignment='bottom',fontsize=25, color = contourcolor)
X,Y=ellipse(3*ra,3*rb,ang,xcenter,ycenter)
axTemperature.plot(X,Y,"k:",ms=1,linewidth=2.0, color = contourcolor)
axTemperature.annotate('$3\\sigma$', xy=(X[15], Y[15]), xycoords='data', xytext=(10, 10), textcoords='offset points',horizontalalignment='right', verticalalignment='bottom',fontsize=25, color = contourcolor)
#Plot the % below line
belowline = 1.0*size(where((x - y) > 0.0))/size(x)*1.0*100
if(sigma): axTemperature.annotate('$%.2f\%%\mathrm{\\ Below\\ Line}$'%(belowline), xy=(xmax-100, ymin+3),fontsize=20, color = contourcolor)
#Plot the axes labels
axTemperature.set_xlabel(xlabel,fontsize=25)
axTemperature.set_ylabel(ylabel,fontsize=25)
#Make the tickmarks pretty
ticklabels = axTemperature.get_xticklabels()
for label in ticklabels:
label.set_fontsize(18)
label.set_family('serif')
ticklabels = axTemperature.get_yticklabels()
for label in ticklabels:
label.set_fontsize(18)
label.set_family('serif')
#Plot the line on the temperature plot
if(line): axTemperature.plot([-1000,1000], [-1000,1000], 'k-', linewidth=2.0, color = contourcolor)
#Set up the plot limits
axTemperature.set_xlim(xlims)
axTemperature.set_ylim(ylims)
#Set up the histogram bins
xbins = N.arange(xmin, xmax, (xmax-xmin)/nbins)
ybins = N.arange(ymin, ymax, (ymax-ymin)/nbins)
#Plot the histograms
if (bw):
axHistx.hist(x, bins=xbins, color = 'silver')
axHisty.hist(y, bins=ybins, orientation='horizontal', color = 'dimgray')
else:
axHistx.hist(x, bins=xbins, color = 'blue')
axHisty.hist(y, bins=ybins, orientation='horizontal', color = 'red')
#Set up the histogram limits
axHistx.set_xlim( 0, max(x) )
axHisty.set_ylim( 0, max(y))
#Make the tickmarks pretty
ticklabels = axHistx.get_yticklabels()
for label in ticklabels:
label.set_fontsize(12)
label.set_family('serif')
#Make the tickmarks pretty
ticklabels = axHisty.get_xticklabels()
for label in ticklabels:
label.set_fontsize(12)
label.set_family('serif')
#Cool trick that changes the number of tickmarks for the histogram axes
axHisty.xaxis.set_major_locator(MaxNLocator(4))
axHistx.yaxis.set_major_locator(MaxNLocator(4))
if(filename):
savefig(filename + '.eps',format = 'eps', transparent=True)
savefig(filename + '.pdf',format = 'pdf', transparent=True)
savefig(filename + '.png',format = 'png', transparent=True)
return 0
There are some cool features that I'll describe in the comments below. I think this plot rocks.
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.ticker import NullFormatter
def makeTempHistogramPlot(xdata,ydata,rexp,filename=None,xlims=-99, ylims =-99 , \
nxbins = 50,nybins=50, bw=0, nbins=100,contours=1,sigma=1,line=1):
#bw = 0 for color, = 1 for black and white
#line = 0 for no line, =1 for line
#sigma = 1 for display % below line, =0 for not
#contours = 1 for display 1,2,3 sigma contours, = 0 for not.
# Define the x and y data
x = xdata
y = ydata
# Set up default x and y limits
if (xlims == -99): xlims = [0,max(x)]
if (ylims == -99): ylims = [0,max(y)]
# Set up your x and y labels
xlabel = '$\mathrm{Your\\ X\\ Label}$'
ylabel = '$\mathrm{Your\\ X\\ Label}$'
mtitle = ''
# Define the locations for the axes
left, width = 0.12, 0.55
bottom, height = 0.12, 0.55
bottom_h = left_h = left+width+0.02
# Set up the geometry of the three plots
rect_temperature = [left, bottom, width, height] # dimensions of temp plot
rect_histx = [left, bottom_h, width, 0.25] # dimensions of x-histogram
rect_histy = [left_h, bottom, 0.25, height] # dimensions of y-histogram
# Set up the size of the figure
fig = plt.figure(1, figsize=(9.5,9))
# Make the three plots
axTemperature = plt.axes(rect_temperature) # temperature plot
axHistx = plt.axes(rect_histx) # x histogram
axHisty = plt.axes(rect_histy) # y histogram
# Remove the inner axes numbers of the histograms
nullfmt = NullFormatter()
axHistx.xaxis.set_major_formatter(nullfmt)
axHisty.yaxis.set_major_formatter(nullfmt)
# Find the min/max of the data
xmin = min(xlims)
xmax = max(xlims)
ymin = min(ylims)
ymax = max(y)
# Make the 'main' temperature plot
xbins = linspace(start = 0, stop = xmax, num = nxbins)
ybins = linspace(start = 0, stop = ymax, num = nybins)
xcenter = (xbins[0:-1]+xbins[1:])/2.0
ycenter = (ybins[0:-1]+ybins[1:])/2.0
aspectratio = 1.0*(xmax - 0)/(1.0*ymax - 0)
H, xedges,yedges = N.histogram2d(y,x,bins=(ybins,xbins))
X = xcenter
Y = ycenter
Z = H
# Plot the temperature data
if(bw): cax = axTemperature.imshow(H, extent=[xmin,xmax,ymin,ymax], \
interpolation='nearest', origin='lower',aspect=aspectratio, cmap=cm.gist_yarg)
else : cax = axTemperature.imshow(H, extent=[xmin,xmax,ymin,ymax], \
interpolation='nearest', origin='lower',aspect=aspectratio)
# Plot the temperature plot contours
if(bw): contourcolor = 'black'
else: contourcolor = 'white'
if (contours==0):
print ''
elif (contours==1):
xcenter = N.mean(x)
ycenter = N.mean(y)
ra = N.std(x)
rb = N.std(y)
ang = 0
X,Y=ellipse(ra,rb,ang,xcenter,ycenter)
axTemperature.plot(X,Y,"k:",ms=1,linewidth=2.0)
axTemperature.annotate('$1\\sigma$', xy=(X[15], Y[15]), xycoords='data',xytext=(10, 10), textcoords='offset points',horizontalalignment='right', verticalalignment='bottom',fontsize=25)
X,Y=ellipse(2*ra,2*rb,ang,xcenter,ycenter)
axTemperature.plot(X,Y,"k:",color = contourcolor,ms=1,linewidth=2.0)
axTemperature.annotate('$2\\sigma$', xy=(X[15], Y[15]), xycoords='data',xytext=(10, 10), textcoords='offset points',horizontalalignment='right', verticalalignment='bottom',fontsize=25, color = contourcolor)
X,Y=ellipse(3*ra,3*rb,ang,xcenter,ycenter)
axTemperature.plot(X,Y,"k:",color = contourcolor, ms=1,linewidth=2.0)
axTemperature.annotate('$3\\sigma$', xy=(X[15], Y[15]), xycoords='data',xytext=(10, 10), textcoords='offset points',horizontalalignment='right', verticalalignment='bottom',fontsize=25, color = contourcolor)
else:
xcenter = N.mean(x)
ycenter = N.mean(y)
ra = N.std(x)
rb = N.std(y)
ang = contours*N.pi/180.0
X,Y=ellipse(ra,rb,ang,xcenter,ycenter)
axTemperature.plot(X,Y,"k:",ms=1,linewidth=2.0)
axTemperature.annotate('$1\\sigma$', xy=(X[15], Y[15]), xycoords='data', xytext=(10, 10), textcoords='offset points',horizontalalignment='right', verticalalignment='bottom',fontsize=25)
X,Y=ellipse(2*ra,2*rb,ang,xcenter,ycenter)
axTemperature.plot(X,Y,"k:",ms=1,linewidth=2.0, color = contourcolor)
axTemperature.annotate('$2\\sigma$', xy=(X[15], Y[15]), xycoords='data', xytext=(10, 10), textcoords='offset points',horizontalalignment='right', verticalalignment='bottom',fontsize=25, color = contourcolor)
X,Y=ellipse(3*ra,3*rb,ang,xcenter,ycenter)
axTemperature.plot(X,Y,"k:",ms=1,linewidth=2.0, color = contourcolor)
axTemperature.annotate('$3\\sigma$', xy=(X[15], Y[15]), xycoords='data', xytext=(10, 10), textcoords='offset points',horizontalalignment='right', verticalalignment='bottom',fontsize=25, color = contourcolor)
#Plot the % below line
belowline = 1.0*size(where((x - y) > 0.0))/size(x)*1.0*100
if(sigma): axTemperature.annotate('$%.2f\%%\mathrm{\\ Below\\ Line}$'%(belowline), xy=(xmax-100, ymin+3),fontsize=20, color = contourcolor)
#Plot the axes labels
axTemperature.set_xlabel(xlabel,fontsize=25)
axTemperature.set_ylabel(ylabel,fontsize=25)
#Make the tickmarks pretty
ticklabels = axTemperature.get_xticklabels()
for label in ticklabels:
label.set_fontsize(18)
label.set_family('serif')
ticklabels = axTemperature.get_yticklabels()
for label in ticklabels:
label.set_fontsize(18)
label.set_family('serif')
#Plot the line on the temperature plot
if(line): axTemperature.plot([-1000,1000], [-1000,1000], 'k-', linewidth=2.0, color = contourcolor)
#Set up the plot limits
axTemperature.set_xlim(xlims)
axTemperature.set_ylim(ylims)
#Set up the histogram bins
xbins = N.arange(xmin, xmax, (xmax-xmin)/nbins)
ybins = N.arange(ymin, ymax, (ymax-ymin)/nbins)
#Plot the histograms
if (bw):
axHistx.hist(x, bins=xbins, color = 'silver')
axHisty.hist(y, bins=ybins, orientation='horizontal', color = 'dimgray')
else:
axHistx.hist(x, bins=xbins, color = 'blue')
axHisty.hist(y, bins=ybins, orientation='horizontal', color = 'red')
#Set up the histogram limits
axHistx.set_xlim( 0, max(x) )
axHisty.set_ylim( 0, max(y))
#Make the tickmarks pretty
ticklabels = axHistx.get_yticklabels()
for label in ticklabels:
label.set_fontsize(12)
label.set_family('serif')
#Make the tickmarks pretty
ticklabels = axHisty.get_xticklabels()
for label in ticklabels:
label.set_fontsize(12)
label.set_family('serif')
#Cool trick that changes the number of tickmarks for the histogram axes
axHisty.xaxis.set_major_locator(MaxNLocator(4))
axHistx.yaxis.set_major_locator(MaxNLocator(4))
if(filename):
savefig(filename + '.eps',format = 'eps', transparent=True)
savefig(filename + '.pdf',format = 'pdf', transparent=True)
savefig(filename + '.png',format = 'png', transparent=True)
return 0
