[FIXED] How to make a 4d plot with matplotlib using arbitrary data

Issue

This question is related to this one.

What I would like to know is how to apply the suggested solution to a bunch of data (4 columns), e.g.:

0.1 0 0.1 2.0
0.1 0 1.1 -0.498121712998
0.1 0 2.1 -0.49973005075
0.1 0 3.1 -0.499916082038
0.1 0 4.1 -0.499963726586
0.1 1 0.1 -0.0181405895692
0.1 1 1.1 -0.490774988618
0.1 1 2.1 -0.498653742846
0.1 1 3.1 -0.499580747953
0.1 1 4.1 -0.499818696063
0.1 2 0.1 -0.0107079119572
0.1 2 1.1 -0.483641823093
0.1 2 2.1 -0.497582061233
0.1 2 3.1 -0.499245863438
0.1 2 4.1 -0.499673749657
0.1 3 0.1 -0.0075248589089
0.1 3 1.1 -0.476713038166
0.1 3 2.1 -0.49651497615
0.1 3 3.1 -0.498911427589
0.1 3 4.1 -0.499528887295
0.1 4 0.1 -0.00579180003048
0.1 4 1.1 -0.469979974092
0.1 4 2.1 -0.495452458086
0.1 4 3.1 -0.498577439505
0.1 4 4.1 -0.499384108904
1.1 0 0.1 302.0
1.1 0 1.1 -0.272727272727
1.1 0 2.1 -0.467336140806
1.1 0 3.1 -0.489845926622
1.1 0 4.1 -0.495610916847
1.1 1 0.1 -0.000154915998165
1.1 1 1.1 -0.148803329865
1.1 1 2.1 -0.375881358454
1.1 1 3.1 -0.453749548548
1.1 1 4.1 -0.478942841849
1.1 2 0.1 -9.03765566114e-05
1.1 2 1.1 -0.0972702806613
1.1 2 2.1 -0.314291859842
1.1 2 3.1 -0.422606253083
1.1 2 4.1 -0.463359353084
1.1 3 0.1 -6.31234088628e-05
1.1 3 1.1 -0.0720095219203
1.1 3 2.1 -0.270015786897
1.1 3 3.1 -0.395462300716
1.1 3 4.1 -0.44875793248
1.1 4 0.1 -4.84199181874e-05
1.1 4 1.1 -0.0571187054704
1.1 4 2.1 -0.236660992042
1.1 4 3.1 -0.371593983211
1.1 4 4.1 -0.4350485869
2.1 0 0.1 1102.0
2.1 0 1.1 0.328324567994
2.1 0 2.1 -0.380952380952
2.1 0 3.1 -0.462992178846
2.1 0 4.1 -0.48400342421
2.1 1 0.1 -4.25137933034e-05
2.1 1 1.1 -0.0513190921508
2.1 1 2.1 -0.224866151101
2.1 1 3.1 -0.363752470126
2.1 1 4.1 -0.430700436658
2.1 2 0.1 -2.48003822279e-05
2.1 2 1.1 -0.0310025255124
2.1 2 2.1 -0.158022037087
2.1 2 3.1 -0.29944612818
2.1 2 4.1 -0.387965424205
2.1 3 0.1 -1.73211484062e-05
2.1 3 1.1 -0.0220466245862
2.1 3 2.1 -0.12162780064
2.1 3 3.1 -0.254424041889
2.1 3 4.1 -0.35294082311
2.1 4 0.1 -1.32862131387e-05
2.1 4 1.1 -0.0170828002197
2.1 4 2.1 -0.0988138417802
2.1 4 3.1 -0.221154587294
2.1 4 4.1 -0.323713596671
3.1 0 0.1 2402.0
3.1 0 1.1 1.30503380917
3.1 0 2.1 -0.240578771191
3.1 0 3.1 -0.41935483871
3.1 0 4.1 -0.465141248676
3.1 1 0.1 -1.95102493785e-05
3.1 1 1.1 -0.0248114638773
3.1 1 2.1 -0.135153019304
3.1 1 3.1 -0.274125336409
3.1 1 4.1 -0.36965644171
3.1 2 0.1 -1.13811197906e-05
3.1 2 1.1 -0.0147116366819
3.1 2 2.1 -0.0872950700627
3.1 2 3.1 -0.202935925412
3.1 2 4.1 -0.306612285308
3.1 3 0.1 -7.94877050259e-06
3.1 3 1.1 -0.0103624783432
3.1 3 2.1 -0.0642253568271
3.1 3 3.1 -0.160970897235
3.1 3 4.1 -0.261906474418
3.1 4 0.1 -6.09709039262e-06
3.1 4 1.1 -0.00798626913355
3.1 4 2.1 -0.0507564081263
3.1 4 3.1 -0.133349565782
3.1 4 4.1 -0.228563754423
4.1 0 0.1 4202.0
4.1 0 1.1 2.65740045079
4.1 0 2.1 -0.0462153115214
4.1 0 3.1 -0.358933906213
4.1 0 4.1 -0.439024390244
4.1 1 0.1 -1.11538537794e-05
4.1 1 1.1 -0.0144619860317
4.1 1 2.1 -0.0868190343718
4.1 1 3.1 -0.203767982755
4.1 1 4.1 -0.308519215265
4.1 2 0.1 -6.50646078271e-06
4.1 2 1.1 -0.0085156584289
4.1 2 2.1 -0.0538784714494
4.1 2 3.1 -0.140215240068
4.1 2 4.1 -0.23746380125
4.1 3 0.1 -4.54421180079e-06
4.1 3 1.1 -0.00597669061814
4.1 3 2.1 -0.038839789599
4.1 3 3.1 -0.106675396816
4.1 3 4.1 -0.192922262523
4.1 4 0.1 -3.48562423225e-06
4.1 4 1.1 -0.00459693165308
4.1 4 2.1 -0.0303305231375
4.1 4 3.1 -0.0860368842133
4.1 4 4.1 -0.162420599686

The solution to the initial problem is:

# Python-matplotlib Commands
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')
X = np.arange(-5, 5, .25)
Y = np.arange(-5, 5, .25)
X, Y = np.meshgrid(X, Y)
R = np.sqrt(X**2 + Y**2)
Z = np.sin(R)
Gx, Gy = np.gradient(Z) # gradients with respect to x and y
G = (Gx**2+Gy**2)**.5  # gradient magnitude
N = G/G.max()  # normalize 0..1
surf = ax.plot_surface(
    X, Y, Z, rstride=1, cstride=1,
    facecolors=cm.jet(N),
    linewidth=0, antialiased=False, shade=False)
plt.show()

As far as I can see, and this applies to all matplotlib-demos, the variables X, Y and Z are nicely prepared. In practical cases this is not always the case.

Ideas how to reuse the given solution with arbitrary data?

Solution

Great question Tengis, all the math folks love to show off the flashy surface plots with functions given, while leaving out dealing with real world data. The sample code you provided uses gradients since the relationships of a variables are modeled using functions. For this example I will generate random data using a standard normal distribution.

Anyways here is how you can quickly plot 4D random (arbitrary) data with first three variables are on the axis and the fourth being color:

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

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

x = np.random.standard_normal(100)
y = np.random.standard_normal(100)
z = np.random.standard_normal(100)
c = np.random.standard_normal(100)

img = ax.scatter(x, y, z, c=c, cmap=plt.hot())
fig.colorbar(img)
plt.show()

Note: A heatmap with the hot color scheme (yellow to red) was used for the 4th dimension

Result:

]1

Answered By - mrandrewandrade