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Cartesian zoom with polar plot in python

I am trying to plot some data in polar coordinates (I am currently using the polar projection):
The code I am using is the following:
import matplotlib.pyplot as plt
import numpy as np
# Create radial and angular array
r = np.linspace(1.0,10,11)
t = np.linspace(0.0,0.5*np.pi,101)
# Define the quantity that I want to plot
z = np.zeros((len(t),len(r)))
for yval in range(len(r)):
z[:,yval] = np.cos(16.0*t)/r[yval]
#Create the figure
f = plt.figure(figsize=(13,8))
ax = plt.subplot(111, projection='polar')
ax.set_rorigin(-1)
#Plot the data
pcm = ax.pcolormesh(t,r,z.T,cmap = 'hot',shading='gouraud')
ax.set_xlim([0.0,0.5*np.pi])
ax.set_ylim([1.0,10.0])
#Add colorbar and show
bar = f.colorbar(pcm)
plt.show()
So far I have no problem, but I would like to zoom on a particular region of this plot.
However, when I set the axes range the axes is still polar, therefore I cannot zoom on a "cartesian" region of the domain (i.e. a square box).
A possible option would be to transform the data into cartesian coordinates, but when I do it I lose a lot of resolution in the inner part of the domain, which is something that I should absolutely avoid.
How can I select a rectangular zone of a plot in polar coordinates without transforming by hand the data? And in case I have to switch to cartesian coordinates, is there any matplotlib or python function that does it while taking care of the resolution in the inner regions of the domain?
Thanks in advance

You can create an X, Y mesh yourself that is has a higher resolution on the inner part of the domain and use that with ax.pcolormesh()
# Create radial and angular array
r = np.linspace(1.0,10,11)
t = np.linspace(0.0,0.5*np.pi,101)
# Define the quantity that I want to plot
z = np.zeros((len(t),len(r)))
for yval in range(len(r)):
z[:,yval] = np.cos(16.0*t)/r[yval]
#Create the figure, bigger figsize to make the resulting plot square
f = plt.figure(figsize=(13,10))
ax = plt.subplot(111) # Drop back to XY coordinates
# Generate the XY corners of the colormesh
X = np.array([[ri*np.cos(j) for j in t] for ri in r])
Y = np.array([[ri*np.sin(j) for j in t] for ri in r])
#Plot the data
pcm = ax.pcolormesh(X,Y,z.T,cmap = 'hot',shading='gouraud')
#Add colorbar and show
bar = f.colorbar(pcm)
plt.show()
The figure from the question
The figure generated by code above

A way to do this is to create an expanded polar plot and then clip a rectangle of it. A picture is worth a thousand words:
Here is a function that allows you to do so. The arguments are the original axes, the xlims and ylims of the region to be zoomed and the inset axes bounds (x0, y0, width, height) in the original axes coordinates. The function outputs a cartesian ax with the specified limits, a polar axes where you can plot and the rmax value you need to set AFTER plotting (if you do it before, it will change after plotting).
def create_polar_zoom_inset(ax, xlims, ylims, inset_bounds):
# Create cartesian axes for inset
ax_inset_cart = ax.inset_axes(inset_bounds)
ax_inset_cart.set_xlim(xlims)
ax_inset_cart.set_ylim(ylims)
# Calculate location of expanded polar inset
# Scale factor from data to axes coordinates
xscalefactor = inset_bounds[2]/(xlims[1] - xlims[0])
yscalefactor = inset_bounds[3]/(ylims[1] - ylims[0])
# Center of expanded polar inset
center_inset_polar = [
inset_bounds[0] - xlims[0]*xscalefactor,
inset_bounds[1] - ylims[0]*yscalefactor
]
# Max value of r in the inset
rmax_inset = 2*np.sqrt(np.power(xlims, 2).max() + np.power(ylims, 2).max())
# Size of the expanded polar inset
size_inset_polar = [2*rmax_inset*xscalefactor, 2*rmax_inset*yscalefactor]
# Create expanded polar inset
polar_inset_bounds = [
center_inset_polar[0] - 0.5*size_inset_polar[0],
center_inset_polar[1] - 0.5*size_inset_polar[1],
size_inset_polar[0],
size_inset_polar[1]
]
ax_inset_polar = ax.inset_axes(polar_inset_bounds, projection="polar")
ax_inset_polar.set_facecolor("None")
# Remove tick labels from expanded polar inset
ax_inset_polar.xaxis.set_ticklabels([])
ax_inset_polar.yaxis.set_ticklabels([])
# Clip elements of the expanded inset outside the cartesian inset
ax_inset_polar.patch = ax_inset_cart.patch
for axis in [ax_inset_polar.xaxis, ax_inset_polar.yaxis]:
axis.set_clip_path(ax_inset_cart.patch)
ax_inset_polar.spines['polar'].set_clip_path(ax_inset_cart.patch)
return ax_inset_cart, ax_inset_polar, rmax_inset
The code in your example is especially hard since the origin of the axes is not (0,0) but (-1,-1). That would need additional tinkering. But if we set rorigin to 0 (as it will be usually the case), the code would look as follows
# Create radial and angular array
r = np.linspace(1.0,10,11)
t = np.linspace(0.0,0.5*np.pi,101)
# Define the quantity that I want to plot
z = np.zeros((len(t),len(r)))
for yval in range(len(r)):
z[:,yval] = np.cos(16.0*t)/r[yval]
#Create the figure
f = plt.figure(figsize=(13,8))
ax = plt.subplot(111, projection='polar')
ax.set_rorigin(0)
#Plot the data
pcm = ax.pcolormesh(t,r,z.T,cmap = 'hot',shading='gouraud')
ax.set_xlim([0.0,0.5*np.pi])
ax.set_ylim([1.0,10.0])
#Add colorbar and show
bar = f.colorbar(pcm)
#Create inset
ax_c, ax_p, rmax_inset = create_polar_zoom_inset(
ax, xlims=[0., 2.], ylims=[1, 2], inset_bounds=[0.4, 0.3, 0.6, 0.3])
#Plot on inset
ax_p.pcolormesh(t,r,z.T,cmap = 'hot',shading='gouraud')
#Make rorigin and rmin coincide with the original plot
ax_p.set_rorigin(0)
ax_p.set_rmin(1)
#Set rmax
ax_p.set_rmax(rmax_inset)
plt.show()

Reducing axis length while maintaining equal aspect ratio in 3D plot

I am trying to create a 3-D plot and a 2-D plot side-by-side in python. I need equal aspect ratios for both plots, which I managed using code provided by this answer: https://stackoverflow.com/a/31364297/125507. The problem I'm having now is how to effectively "crop" the 3-D plot so it doesn't take up so much white space. That is to say, I want to reduce the length of the X and Y axes while maintaining equal scale to the (longer) Z-axis. Here is a sample code and plot:
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
import matplotlib.pyplot as plt
import numpy as np
def set_axes_equal(ax):
'''Make axes of 3D plot have equal scale so that spheres appear as spheres,
cubes as cubes, etc.. This is one possible solution to Matplotlib's
ax.set_aspect('equal') and ax.axis('equal') not working for 3D.
Input
ax: a matplotlib axis, e.g., as output from plt.gca().
'''
x_limits = ax.get_xlim3d()
y_limits = ax.get_ylim3d()
z_limits = ax.get_zlim3d()
x_range = abs(x_limits[1] - x_limits[0])
x_middle = np.mean(x_limits)
y_range = abs(y_limits[1] - y_limits[0])
y_middle = np.mean(y_limits)
z_range = abs(z_limits[1] - z_limits[0])
z_middle = np.mean(z_limits)
# The plot bounding box is a sphere in the sense of the infinity
# norm, hence I call half the max range the plot radius.
plot_radius = 0.5*max([x_range, y_range, z_range])
ax.set_xlim3d([x_middle - plot_radius, x_middle + plot_radius])
ax.set_ylim3d([y_middle - plot_radius, y_middle + plot_radius])
ax.set_zlim3d([z_middle - plot_radius, z_middle + plot_radius])
ax = [None]*2
fig = plt.figure()
ax[0] = fig.add_subplot(121, projection='3d', aspect='equal')
ax[1] = fig.add_subplot(122, aspect='equal')
nn = 30
phis = np.linspace(0,np.pi, nn).reshape(1,nn)
psis = np.linspace(0,np.pi*2,nn).reshape(nn,1)
ones = np.ones((nn,1))
el_h = np.linspace(-5, 5, nn).reshape(1,nn)
x_sph = np.sin(phis)*np.cos(psis)
y_sph = np.sin(phis)*np.sin(psis)
z_sph = np.cos(phis)*ones
x_elp = np.sin(phis)*np.cos(psis)*.25
y_elp = np.sin(phis)*np.sin(psis)*.25
z_elp = el_h*ones
ax[0].scatter(x_sph, y_sph, z_sph)
ax[0].scatter(x_elp, y_elp, z_elp)
ax[1].scatter(y_sph, z_sph)
ax[1].scatter(y_elp, z_elp)
for ii in range(2):
ax[ii].set_xlabel('X')
ax[ii].set_ylabel('Y')
ax[0].set_zlabel('Z')
set_axes_equal(ax[0])
plt.savefig('SphereElipse.png', dpi=300)
And here is its image output:
3-D and 2-D sphere and ellipse side-by-side
Clearly the 2D plot automatically modifies the length of the axes while maintaining the scale, but the 3D plot doesn't, leading to a tiny representation which does not well use the space allotted to its subplot. Is there any way to do this? This question is similar to an earlier unanswered question How do I crop an Axes3D plot with square aspect ratio?, except it adds the stipulation of multiple subplots, which means the answers provided there do not work.

How to rotate tick labels in floating cylindrical axes?

http://matplotlib.org/mpl_toolkits/axes_grid/users/overview.html
Check out the VERY bottom of this link. I'm interested in that axes in the middle, where the axis objects are curved into the shape of a quarter-washer. If you check the sourcecode, this axes object is made by setup_axes2:
def setup_axes2(fig, rect):
"""
With custom locator and formatter.
Note that the extreme values are swapped.
"""
tr = PolarAxes.PolarTransform()
pi = np.pi
angle_ticks = [(0, r"$0$"),
(.25*pi, r"$\frac{1}{4}\pi$"),
(.5*pi, r"$\frac{1}{2}\pi$")]
grid_locator1 = FixedLocator([v for v, s in angle_ticks])
tick_formatter1 = DictFormatter(dict(angle_ticks))
grid_locator2 = MaxNLocator(2)
grid_helper = floating_axes.GridHelperCurveLinear(
tr, extremes=(.5*pi, 0, 2, 1),
grid_locator1=grid_locator1,
grid_locator2=grid_locator2,
tick_formatter1=tick_formatter1,
tick_formatter2=None)
ax1 = floating_axes.FloatingSubplot(fig, rect, grid_helper=grid_helper)
fig.add_subplot(ax1)
# create a parasite axes whose transData in RA, cz
aux_ax = ax1.get_aux_axes(tr)
aux_ax.patch = ax1.patch # for aux_ax to have a clip path as in ax
ax1.patch.zorder = 0.9 # but this has a side effect that the patch is
# drawn twice, and possibly over some other
# artists. So, we decrease the zorder a bit to
# prevent this.
return ax1, aux_ax
When I label the ticks in the theta axis, the labels are always upside down. I don't know how to flip them. I also don't know how to flip the axis labels upside down. Does anyone know about these confusing floating axes?

The hint was in setup_axes3() from the example you linked. The individual axes in the FloatingSubplot are referred to like ax.axis[side] where side is one of ["top","bottom","left","right"]. From there you get the usual.
ax = ax2.axis["bottom"]
ax.major_ticklabels.set_rotation(180)
ax.set_label("foo")
ax.label.set_rotation(180)
ax.LABELPAD += 10
Just do dir(ax) to see what you have access to.

2D histogram of events is misaligned with 1D bar charts of event probability x and y axes using python and matplotlib

I would like to plot a 2d histogram using matplotlib in order to visualize the influence of two variables on the occurrence of an event.
In my test case, the event is “wish coming true” and the variable x is the number of falling stars and y is the involvement of a fairy godmother. What I would like to do is to plot a 2d histogram of wishes coming true for bins of falling stars and fairy godmothers. Then next to each axis, I would like to show the probability of a wish coming true, event/(event+nonevent), for each bin of falling stars and fairy godmothers (1D bar chart containing probabilities for each histogram bin). The bar chart bins should correspond to and be aligned with the 2d histogram bins. However, there seems to be a slight misalignment between the bar charts and the histogram bins.
For aligning the bar chart correctly, will the settings of the limits of the axis corresponding to the first and last bin edges do the trick ? Once these limits are set, can I feed bin centers into plt.bar() as locations on the axis as opposed to indices ?
My code and the resulting images are as follows :
import numpy as np
import matplotlib.pyplot as plt
from numpy import linspace
import cubehelix
# Create random events and non-events
x_noneve = 3.*np.random.randn(10000) +22.
np.random.seed(seed=41)
y_noneve = np.random.randn(10000)
np.random.seed(seed=45)
x_eve = 3.*np.random.randn(1000) +22.
np.random.seed(seed=33)
y_eve = np.random.randn(1000)
x_all = np.concatenate((x_eve,x_noneve),axis=0)
y_all = np.concatenate((y_eve,y_noneve),axis=0)
# Set up default x and y limits
xlims = [min(x_all),max(x_all)]
ylims = [min(y_all),max(y_all)]
# Set up your x and y labels
xlabel = 'Falling Star'
ylabel = 'Fairy Godmother'
# Define the locations for the axes
left, width = 0.12, 0.55
bottom, height = 0.12, 0.55
bottom_h = left_h = left+width+0.03
# Set up the geometry of the three plots
rect_wishes = [left, bottom, width, height] # dimensions of wish 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))
fig.suptitle('Wishes coming true', fontsize=18, fontweight='bold')
cx1 = cubehelix.cmap(startHue=240,endHue=-300,minSat=1,maxSat=2.5,minLight=.3,maxLight=.8,gamma=.9)
# Make the three plots
axWishes = plt.axes(rect_wishes) # wishes plot
axStarx = plt.axes(rect_histx) # x bar chart
axFairy = plt.axes(rect_histy) # y bar chart
# Define the number of bins
nxbins = 50
nybins = 50
nbins = 100
xbins = linspace(start = xlims[0], stop = xlims[1], num = nxbins)
ybins = linspace(start = ylims[0], stop = ylims[1], num = nybins)
xcenter = (xbins[0:-1]+xbins[1:])/2.0
ycenter = (ybins[0:-1]+ybins[1:])/2.0
delx = np.around(xbins[1]-xbins[0], decimals=2,out=None)
dely = np.around(ybins[1]-ybins[0], decimals=2,out=None)
H, xedges,yedges = np.histogram2d(y_eve,x_eve,bins=(ybins,xbins))
X = xcenter
Y = ycenter
H = np.where(H==0,np.nan,H) # Remove 0's from plot
# Plot the 2D histogram
cax = (axWishes.imshow(H, extent=[xlims[0],xlims[1],ylims[0],ylims[1]],
interpolation='nearest', origin='lower',aspect="auto",cmap=cx1))
#Plot the axes labels
axWishes.set_xlabel(xlabel,fontsize=14)
axWishes.set_ylabel(ylabel,fontsize=14)
#Set up the plot limits
axWishes.set_xlim(xlims)
axWishes.set_ylim(ylims)
#Set up the probability bins
x_eve_hist, xoutbins = np.histogram(x_eve, bins=xbins)
y_eve_hist, youtbins = np.histogram(y_eve, bins=ybins)
x_noneve_hist, xoutbins = np.histogram(x_noneve, bins=xbins)
y_noneve_hist, youtbins = np.histogram(y_noneve, bins=ybins)
probax = [eve/(eve+noneve+0.0) if eve+noneve>0 else 0 for eve,noneve in zip(x_eve_hist,x_noneve_hist)]
probay = [eve/(eve+noneve+0.0) if eve+noneve>0 else 0 for eve,noneve in zip(y_eve_hist,y_noneve_hist)]
probax = probax/np.sum(probax)
probay = probay/np.sum(probay)
probax = np.round(probax*100., decimals=0, out=None)
probay = np.round(probay*100., decimals=0, out=None)
#Plot the bar charts
#Set up the limits
axStarx.set_xlim( xlims[0], xlims[1])
axFairy.set_ylim( ylims[0], ylims[1])
axStarx.bar(xcenter, probax, align='center', width =delx, color = 'royalblue')
axFairy.barh(ycenter,probay,align='center', height=dely, color = 'mediumorchid')
#Show the plot
plt.show()
resulting image
hex version

While my original code was functional, the limits of the 2D histo and bar chart were not defined using the histogram bins. Thus any changes to the bins resulted in a poorly-aligned graph. To ensure that the limits of the graph always correspond to the limits of the histogram bins, I changed
cax = (axWishes.imshow(H, extent=[xmin,xmax,ymin,ymax],
interpolation='nearest', origin='lower',aspect="auto",cmap=cx1))
to
cax = (axWishes.imshow(H, extent=[xbins[0],xbins[-1],ybins[0],ybins[-1]],
interpolation='nearest', origin='lower',aspect="auto",cmap=cx1))
and
axStarx.set_xlim( xlims[0], xlims[1])
axFairy.set_ylim( ylims[0], ylims[1])
to
axStarx.set_xlim(axWishes.get_xlim())
axFairy.set_ylim(axWishes.get_ylim())
For information, bar chart can accept either indices or values along the axis as bar locations. When the bars correspond to bins and not categorical variables, it is important to set axis limits and correctly define bar width. These are done automatically with histo. However, if you wish to explore a variable other than the number of members by bin, you must use a bar chart and define the limits by hand.

Understanding matplotlib verts

I'm trying to create custom markers in matplotlib for a scatter plot, where the markers are rectangles with fix height and varying width. The width of each marker is a function of the y-value. I tried it like this using this code as a template and assuming that if verts is given a list of N 2-D tuples it plots rectangles with the width of the corresponing first value and the height of the second (maybe this is already wrong, but then how else do I accomplish that?).
I have a list of x and y values, each containing angles in degrees. Then, I compute the width and height of each marker by
field_size = 2.
symb_vec_x = [(field_size / np.cos(i * np.pi / 180.)) for i in y]
symb_vec_y = [field_size for i in range(len(y))]
and build the verts list and plot everything with
symb_vec = list(zip(symb_vec_x, symb_vec_y))
fig = plt.figure(1, figsize=(14.40, 9.00))
ax = fig.add_subplot(1,1,1)
sc = ax.scatter(ra_i, dec_i, marker='None', verts=symb_vec)
But the resulting plot is empty, no error message however. Can anyone tell me what I did wrong with defining the verts and how to do it right?
Thanks!

As mentioned 'marker='None' need to be removed then the appropriate way to specify a rectangle with verts is something like
verts = list(zip([-10.,10.,10.,-10],[-5.,-5.,5.,5]))
ax.scatter([0.5,1.0],[1.0,2.0], marker=(verts,0))
The vertices are defined as ([x1,x2,x3,x4],[y1,y2,y3,y4]) so attention must be paid to which get minus signs etc.
This (verts,0) is mentioned in the docs as
For backward compatibility, the form (verts, 0) is also accepted,
but it is equivalent to just verts for giving a raw set of vertices
that define the shape.
However I find using just verts does not give the correct shape.
To automate the process you need to do something like
v_val=1.0
h_val=2.0
verts = list(zip([-h_val,h_val,h_val,-h_val],[-v_val,-v_val,v_val,v_val]))
Basic example:
import pylab as py
ax = py.subplot(111)
v_val=1.0
h_val=2.0
verts = list(zip([-h_val,h_val,h_val,-h_val],[-v_val,-v_val,v_val,v_val]))
ax.scatter([0.5,1.0],[1.0,2.0], marker=(verts,0))
*
edit
Individual markers
So you need to manually create a vert for each case. This will obviously depend on how you want your rectangles to change point to point. Here is an example
import pylab as py
ax = py.subplot(111)
def verts_function(x,y,r):
# Define the vertex's multiplying the x value by a ratio
x = x*r
y = y
return [(-x,-y),(x,-y),(x,y),(-x,y)]
n=5
for i in range(1,4):
ax.scatter(i,i, marker=(verts_function(i,i,0.3),0))
py.show()
so in my simple case I plot the points i,i and draw rectangles around them. The way the vert markers are specified is non intuitive. In the documentation it's described as follows:
verts: A list of (x, y) pairs used for Path vertices. The center of
the marker is located at (0,0) and the size is normalized, such that
the created path is encapsulated inside the unit cell.
Hence, the following are equivalent:
vert = [(-300.0, -1000), (300.0, -1000), (300.0, 1000), (-300.0, 1000)]
vert = [(-0.3, -1), (0.3, -1), (0.3, 1), (-0.3, 1)]
e.g they will produce the same marker. As such I have used a ratio, this is where you need to do put in the work. The value of r (the ratio) will change which axis remains constant.
This is all getting very complicated, I'm sure there must be a better way to do this.

I got the solution from Ryan of the matplotlib users mailing list. It's quite elegant, so I will share his example here:
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import Rectangle
from matplotlib.collections import PatchCollection
n = 100
# Get your xy data points, which are the centers of the rectangles.
xy = np.random.rand(n,2)
# Set a fixed height
height = 0.02
# The variable widths of the rectangles
widths = np.random.rand(n)*0.1
# Get a color map and make some colors
cmap = plt.cm.hsv
colors = np.random.rand(n)*10.
# Make a normalized array of colors
colors_norm = colors/colors.max()
# Here's where you have to make a ScalarMappable with the colormap
mappable = plt.cm.ScalarMappable(cmap=cmap)
# Give it your non-normalized color data
mappable.set_array(colors)
rects = []
for p, w in zip(xy, widths):
xpos = p[0] - w/2 # The x position will be half the width from the center
ypos = p[1] - height/2 # same for the y position, but with height
rect = Rectangle( (xpos, ypos), w, height ) # Create a rectangle
rects.append(rect) # Add the rectangle patch to our list
# Create a collection from the rectangles
col = PatchCollection(rects)
# set the alpha for all rectangles
col.set_alpha(0.3)
# Set the colors using the colormap
col.set_facecolor( cmap(colors_norm) )
# No lines
col.set_linewidth( 0 )
#col.set_edgecolor( 'none' )
# Make a figure and add the collection to the axis.
fig = plt.figure()
ax = fig.add_subplot(111)
ax.add_collection(col)
# Add your ScalarMappable to a figure colorbar
fig.colorbar(mappable)
plt.show()
Thank you, Ryan, and everyone who contributed their ideas!