Stacked 2D plots with interconnections in Matplotlib - python

I need to visualize some complex multivariate datasets and the preferrable choice is to use a modification of parallel axis visualization, using stacked 2D plots, where each plot maps a degree of freedom/model parameter and data points belonging to the same data sets should be interconnected across different plots. I am attaching a conceptual sketch. How could I implement it in matplotlib?

To have a rough idea, this could be a possible solution in matplotlib using Axes3D
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import Rectangle, PathPatch
import mpl_toolkits.mplot3d.art3d as art3d
x = np.array([1,2,3])
y = np.array([2,3,1])
z = np.array([1,1,1])
fig = plt.figure(figsize=(6,6))
ax = fig.add_axes([0,0,1,1], projection='3d')
#plot the points
ax.scatter(x,y,z*0.4, c="r", facecolor="r", s=60)
ax.scatter(y,x,z*0.9, c="b", facecolor="b", s=60)
ax.scatter(x,y,z*1.6, c="g", facecolor="g", s=60)
#plot connection lines
ax.plot([x[0],y[0],x[0]],[y[0],x[0],y[0]],[0.4,0.9,1.6], color="k")
ax.plot([x[2],y[2],x[2]],[y[2],x[2],y[2]],[0.4,0.9,1.6], color="k")
#plot planes
p = Rectangle((0,0), 4,4, color="r", alpha=0.2)
ax.add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=0.4, zdir="z")
p = Rectangle((0,0), 4,4, color="b", alpha=0.2)
ax.add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=0.9, zdir="z")
p = Rectangle((0,0), 4,4, color="g", alpha=0.2)
ax.add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=1.6, zdir="z")
ax.set_aspect('equal')
ax.view_init(13,-63)
ax.set_xlim3d([0,4])
ax.set_ylim3d([0,4])
ax.set_zlim3d([0,2])
plt.savefig(__file__+".png")
plt.show()
Update
Creating three different axes is possible. One has to add the axes and make the upper ones transparent (ax2.patch.set_alpha(0.)). Then the grid has to be turned off (ax.grid(False)) and the panes and lines that we don't need set invisible.
However, I have no clue how to draw a connection with between the axes. The 2D approach of matplotlib.patches.ConnectionPatch does not work for 3D axes.
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import Rectangle
import mpl_toolkits.mplot3d.art3d as art3d
x = np.array([1,2,3])
y = np.array([2,3,1])
z = np.array([0,0,0])
fig = plt.figure(figsize=(6,6))
ax = fig.add_axes([0,0,1,1], projection='3d')
ax2 = fig.add_axes([0.0,0.24,1,1], projection='3d')
ax2.patch.set_alpha(0.)
ax3 = fig.add_axes([0.0,0.48,1,1], projection='3d')
ax3.patch.set_alpha(0.)
#plot the points
ax.scatter(x,y,z, c="r", facecolor="r", s=60)
ax2.scatter(y*4,x*4,z, c="b", facecolor="b", s=60)
ax3.scatter(x*100,y*100,z, c="g", facecolor="g", s=60)
#plot connection lines
#ax.plot([x[0],y[0],x[0]],[y[0],x[0],y[0]],[0.4,0.9,1.6], color="k")
#ax.plot([x[2],y[2],x[2]],[y[2],x[2],y[2]],[0.4,0.9,1.6], color="k")
#plot planes
p = Rectangle((0,0), 4,4, color="r", alpha=0.2)
ax.add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=0, zdir="z")
p = Rectangle((0,0), 16,16, color="b", alpha=0.2)
ax2.add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=0, zdir="z")
p = Rectangle((0,0), 400,400, color="g", alpha=0.2)
ax3.add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=0, zdir="z")
ax.set_aspect('equal')
ax2.set_aspect('equal')
ax3.set_aspect('equal')
ax.view_init(13,-63)
ax2.view_init(10,-63)
ax3.view_init(8,-63)
ax.set_xlim3d([0,4])
ax.set_ylim3d([0,4])
ax.set_zlim3d([0,2])
ax2.set_xlim3d([0,16])
ax2.set_ylim3d([0,16])
ax2.set_zlim3d([0,2])
ax3.set_xlim3d([0,400])
ax3.set_ylim3d([0,400])
ax3.set_zlim3d([0,2])
ax.grid(False)
ax2.grid(False)
ax3.grid(False)
def axinvisible(ax):
for zax in (ax.w_zaxis, ax.w_xaxis, ax.w_yaxis):
zax.pane.set_visible(False)
if zax == ax.w_zaxis:
zax.line.set_visible(False)
for ll in zax.get_ticklines()+zax.get_ticklabels():
ll.set_visible(False)
axinvisible(ax)
axinvisible(ax2)
axinvisible(ax3)
# setting a ConnectionPatch does NOT work
from matplotlib.patches import ConnectionPatch
con = ConnectionPatch(xyA=(2,2), xyB=(2,2),
coordsA='data', coordsB='data',
axesA=ax, axesB=ax2,
arrowstyle='->', clip_on=True)
ax2.add_artist(con) # artist is not shown :-(
plt.show()

A solution could be based on matplotlib's 3D capabilities. You can use Axes3D.plot_surface to plot the axes, and user scatter and line plots for the rest.

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My code looks something like this:
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the result:
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Two approaches here, one with a Delaunay triangulation, the other using the Radial Basis Function. Snippet and figure below.
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import matplotlib.pyplot as plt
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plotting single 3D point on top of plot_surface in python matplotlib

I have some code to plot 3D surfaces in Python using matplotlib:
import math
import numpy as np
import matplotlib.pyplot as plt
from pylab import meshgrid,cm,imshow,contour,clabel,colorbar,axis
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import seaborn as sns
sns.set(style="white")
def surface_map(func, xmin=0, xmax=1, ymin=0, ymax=1, step_size=0.05, maxz=25000):
X, Y = meshgrid(
np.arange(xmin, xmax, step_size),
np.arange(ymin, ymax, step_size))
Z = np.zeros(X.shape)
for i in range(X.shape[0]):
for j in range(X.shape[1]):
Z[i, j] = min(func(X[i, j], Y[i, j]), maxz)
return X, Y, Z
def plot_surface(X, Y, Z, xlabel, ylabel, zlabel, title, point=None, size=25):
fig = plt.figure()
ax = fig.gca(projection='3d')
surf = ax.plot_surface(X, Y, Z,
rstride=1, cstride=1, vmin=0, vmax=20*1000,
cmap=cm.RdBu, linewidth=0, antialiased=True)
ax.zaxis.set_major_locator(LinearLocator(10))
ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))
ax.set_xlabel(xlabel)
ax.set_ylabel(ylabel)
ax.set_zlabel(zlabel)
ax.set_title(title)
fig.colorbar(surf, shrink=0.5, aspect=5)
if point:
ax.hold(True)
func, fpr, recall = point
ax.scatter([fpr], [recall], [
func(fpr, recall)
], s=size, c='b', marker='.', zorder=10)
plt.show()
And then I call it like so:
# create mesh
R, FPR, FuncValue = surface_map(my_function, xmin=0, xmax=1, ymin=0, ymax=1, step_size=0.05, maxz=20*1000)
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plot_surface(R, FPR, FuncValue,
xlabel="Recall",
ylabel="FPR",
zlabel="Function Value",
title="Recall Settings Payout Function",
point=(my_function, 0.5, 0.5))
I'm setting ax.scatter to use large marker sizes and a high zorder, but no point gets drawn on the surface when the plot gets rendered.
What am I missing?
The point you are looking for is there, but hidden "inside" the surface. This is a common problem in matplotlib.
I see two options here:
Make the surface plot semitransparent, i.e. use alpha=.8 or similar.
Use plot instead of scatter.

matplotlib 3D surface - gaps / holes in surface

A grid is interpolated with scipy's griddata() and contains values and NaNs. However, when the grid is plotted with mplot3d's plot_surface() there are gaps in the surface (see upper plot). The lower the view height, the more of such gaps are rendered. When the grid is plotted in 2D with imshow() there are no gaps (see lower plot).
Comparison plot_surface and imshow
Here is a close-up:
I couldn't find an answer to this problem and I am wondering whether this is a known issue.
This small example reproduces the problem: (data.txt)
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
Z = np.loadtxt('data.txt')
X = np.linspace(0,3,301)
Y = np.linspace(0,3,301)
X = np.array([X,]*(301)).transpose()
Y = np.array([Y,]*(301))
fig = plt.figure(figsize=(15,15), dpi=100)
ax = fig.add_subplot(2, 1, 1, projection='3d')
plt.hold(True)
ax.view_init(40,300)
surf = ax.plot_surface(X, Y, Z, cmap='jet', rstride=1, cstride=1, antialiased=False, shade=False, alpha=1.0, linewidth=0, vmin=0.25, vmax=0.35);
ax.invert_yaxis()
ax.dist = 11
ax = fig.add_subplot(2, 1, 2)
plt.hold(True)
plt.imshow(Z, cmap='jet', vmin=0.25, vmax=0.35, origin='lower');
plt.show()

With MatPlotLib, how do I apply autoscaled axes from one graph to a separate graph?

So I have a dataset I want to plot. In this case, I want to plot all the data on the same graph, and then graph each point in the set on its own graph, but keep the axis scale/limits the same for each graph.
So what I need to do is find the values of the autoscaled axis limits that were set for the full set of data, and apply those limits to the graph for each individual points.
I am and have been reading the mpl docs to see if theres any kind of function I can use that will return the axis limits values, but I haven't found anything so far.
Im using Python 3.4 with matplotlib
Thanks,
evamvid
Although it is possible to find the limits with
xmin, xmax = ax.get_xlim()
ymin, ymax = ax.get_ylim()
and set them on another axes with
ax2.set_xlim(xmin, xmax)
ax2.set_ylim(ymin, ymax)
it might be easier to use plt.subplots with sharex=True and sharey=True:
import numpy as np
import matplotlib.pyplot as plt
np.random.seed(2015)
N = 5
x, y = np.random.randint(100, size=(2,N))
fig, axs = plt.subplots(nrows=2, ncols=3, sharex=True, sharey=True)
colors = np.linspace(0, 1, N)
axs[0,0].scatter(x,y, s=200, c=colors)
for i, ax in enumerate(axs.ravel()[1:]):
ax.scatter(x[i], y[i], s=200, c=colors[i], vmin=0, vmax=1)
plt.show()
Another option is to pass an axes to sharex and sharey:
ax3 = subplot(313, sharex=ax1, sharey=ax1)
For example,
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
import itertools as IT
np.random.seed(2015)
N = 6
x, y = np.random.randint(100, size=(2,N))
colors = np.linspace(0, 1, N)
gs = gridspec.GridSpec(4, 2)
ax = plt.subplot(gs[0, :])
ax.scatter(x, y, s=200, c=colors)
for k, coord in enumerate(IT.product(range(1,4), range(2))):
i, j = coord
ax = plt.subplot(gs[i, j], sharex=ax, sharey=ax)
ax.scatter(x[k], y[k], s=200, c=colors[k], vmin=0, vmax=1)
plt.tight_layout()
plt.show()

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