python - 3D discrete heatmap in matplotlib

Question

I have a list of tuples in python containing 3-dimenstional data, where each tuple is in the form: (x, y, z, data_value), i.e., I have data values at each (x, y, z) coordinate. I would like to make a 3D discrete heatmap plot where the colors represent the value of data_values in my list of tuples. Here, I give an example of such a heatmap for a 2D dataset where I have a list of (x, y, data_value) tuples:

import matplotlib.pyplot as plt
from matplotlib import colors
import numpy as np
from random import randint

# x and y coordinates
x = np.array(range(10))
y = np.array(range(10,15))
data = np.zeros((len(y),len(x)))

# Generate some discrete data (1, 2 or 3) for each (x, y) pair
for i,yy in enumerate(y):
    for j, xx in enumerate(x):
        data[i,j] = randint(1,3)

# Map 1, 2 and 3 to 'Red', 'Green' qnd 'Blue', respectively
colormap = colors.ListedColormap(['Red', 'Green', 'Blue'])
colorbar_ticklabels = ['1', '2', '3']

# Use matshow to create a heatmap
fig, ax = plt.subplots()
ms = ax.matshow(data, cmap = colormap, vmin=data.min() - 0.5, vmax=data.max() + 0.5, origin = 'lower')

# x and y axis ticks
ax.set_xticklabels([str(xx) for xx in x])
ax.set_yticklabels([str(yy) for yy in y])
ax.xaxis.tick_bottom()

# Put the x- qnd y-axis ticks at the middle of each cell 
ax.set_xticks(np.arange(data.shape[1]), minor = False)
ax.set_yticks(np.arange(data.shape[0]), minor = False)

# Set custom ticks and ticklabels for color bar
cbar = fig.colorbar(ms,ticks = np.arange(np.min(data),np.max(data)+1))
cbar.ax.set_yticklabels(colorbar_ticklabels)

plt.show()

This generates a plot like this:

How can I make a similar plot in 3D-space (i.e., having a z-axis), if my data have a third dimension. For example, if

# x and y and z coordinates
x = np.array(range(10))
y = np.array(range(10,15))
z = np.array(range(15,20))
data = np.zeros((len(y),len(x), len(y)))

# Generate some random discrete data (1, 2 or 3) for each (x, y, z) triplet. 
# Am I defining i, j and k correctly here?
for i,yy in enumerate(y):
    for j, xx in enumerate(x):
        for k, zz in enumerate(z):
            data[i,j, k] = randint(1,3)

I sounds like plot_surface in mplot3d should be able to do this, but z in the input of this function is essentially the value of data at (x, y) coordinate, i.e., (x, y, z = data_value), which is different from what I have, i.e., (x, y, z, data_value).

Answer 1

New answer:

It seems we really want to have a 3D Tetris game here ;-)

So here is a way to plot cubes of different color to fill the space given by the arrays (x,y,z).

from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.cm
import matplotlib.colorbar
import matplotlib.colors

def cuboid_data(center, size=(1,1,1)):
    # code taken from
    # http://stackoverflow.com/questions/30715083/python-plotting-a-wireframe-3d-cuboid?noredirect=1&lq=1
    # suppose axis direction: x: to left; y: to inside; z: to upper
    # get the (left, outside, bottom) point
    o = [a - b / 2 for a, b in zip(center, size)]
    # get the length, width, and height
    l, w, h = size
    x = [[o[0], o[0] + l, o[0] + l, o[0], o[0]],  # x coordinate of points in bottom surface
         [o[0], o[0] + l, o[0] + l, o[0], o[0]],  # x coordinate of points in upper surface
         [o[0], o[0] + l, o[0] + l, o[0], o[0]],  # x coordinate of points in outside surface
         [o[0], o[0] + l, o[0] + l, o[0], o[0]]]  # x coordinate of points in inside surface
    y = [[o[1], o[1], o[1] + w, o[1] + w, o[1]],  # y coordinate of points in bottom surface
         [o[1], o[1], o[1] + w, o[1] + w, o[1]],  # y coordinate of points in upper surface
         [o[1], o[1], o[1], o[1], o[1]],          # y coordinate of points in outside surface
         [o[1] + w, o[1] + w, o[1] + w, o[1] + w, o[1] + w]]    # y coordinate of points in inside surface
    z = [[o[2], o[2], o[2], o[2], o[2]],                        # z coordinate of points in bottom surface
         [o[2] + h, o[2] + h, o[2] + h, o[2] + h, o[2] + h],    # z coordinate of points in upper surface
         [o[2], o[2], o[2] + h, o[2] + h, o[2]],                # z coordinate of points in outside surface
         [o[2], o[2], o[2] + h, o[2] + h, o[2]]]                # z coordinate of points in inside surface
    return x, y, z

def plotCubeAt(pos=(0,0,0), c="b", alpha=0.1, ax=None):
    # Plotting N cube elements at position pos
    if ax !=None:
        X, Y, Z = cuboid_data( (pos[0],pos[1],pos[2]) )
        ax.plot_surface(X, Y, Z, color=c, rstride=1, cstride=1, alpha=0.1)

def plotMatrix(ax, x, y, z, data, cmap="jet", cax=None, alpha=0.1):
    # plot a Matrix 
    norm = matplotlib.colors.Normalize(vmin=data.min(), vmax=data.max())
    colors = lambda i,j,k : matplotlib.cm.ScalarMappable(norm=norm,cmap = cmap).to_rgba(data[i,j,k]) 
    for i, xi in enumerate(x):
            for j, yi in enumerate(y):
                for k, zi, in enumerate(z):
                    plotCubeAt(pos=(xi, yi, zi), c=colors(i,j,k), alpha=alpha,  ax=ax)



    if cax !=None:
        cbar = matplotlib.colorbar.ColorbarBase(cax, cmap=cmap,
                                norm=norm,
                                orientation='vertical')  
        cbar.set_ticks(np.unique(data))
        # set the colorbar transparent as well
        cbar.solids.set(alpha=alpha)              



if __name__ == '__main__':

    # x and y and z coordinates
    x = np.array(range(10))
    y = np.array(range(10,15))
    z = np.array(range(15,20))
    data_value = np.random.randint(1,4, size=(len(x), len(y), len(z)) )
    print data_value.shape

    fig = plt.figure(figsize=(10,4))
    ax = fig.add_axes([0.1, 0.1, 0.7, 0.8], projection='3d')
    ax_cb = fig.add_axes([0.8, 0.3, 0.05, 0.45])
    ax.set_aspect('equal')

    plotMatrix(ax, x, y, z, data_value, cmap="jet", cax = ax_cb)

    plt.savefig(__file__+".png")
    plt.show()

I find it really hard to see anything here, but that may be a question of taste and now hopefully also answers the question.

---

Original Answer:

It seems I misunderstood the question. Therefore the following does not answer the question. For the moment I leave it here, to keep the comments below available for others.

I think plot_surface is fine for the specified task.

Essentially you would plot a surface with the shape given by your points X,Y,Z in 3D and colorize it using the values from data_values as shown in the code below.

from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
import matplotlib.pyplot as plt
import numpy as np

fig = plt.figure()
ax = fig.gca(projection='3d')

# as plot_surface needs 2D arrays as input
x = np.arange(10)
y = np.array(range(10,15))
# we make a meshgrid from the x,y data
X, Y = np.meshgrid(x, y)
Z = np.sin(np.sqrt(X**2 + Y**2))

# data_value shall be represented by color
data_value = np.random.rand(len(y), len(x))
# map the data to rgba values from a colormap
colors = cm.ScalarMappable(cmap = "viridis").to_rgba(data_value)


# plot_surface with points X,Y,Z and data_value as colors
surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, facecolors=colors,
                       linewidth=0, antialiased=True)

plt.show()