Python surface plotting - python
I have following table data(Please see the image)
for which I want to have a surface plot in python. Using surface plotting from matplotlib,
import matplotlib.pyplot as plt
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import numpy as np
fig = plt.figure()
ax = fig.gca(projection='3d')
X=[2,3,5,8,20,30,50,80,100,150,175,200,250,300]
Y=[2,3,4,5,10,15,20,30,40,50,80,100,125,150,175,200]
Y,X=np.meshgrid(Y,X)
Z=np.array([
[0.2885307,0.269452,0.259193,0.2548041,0.2731868,0.4801551,0.7992361,1.7577641,3.2611327,5.428839,19.647976,37.59729,78.0871,152.21466,268.14572,0],
[0.2677955,0.2538363,0.2380033,0.2306999,0.4779794,0.9251045,1.5448972,3.508644,6.4968576,11.252151,0,0,0,0,0,0],
[0.2432982,0.2283371,0.2514196,0.3392502,0,0,0,0,0,0,0,0,0,0,0,0],
[0.2342575,0.3158406,0.4770729, 0.6795485,2.353042, 5.260077,9.78172,25.87004,59.52568, 0,0,0,0,0,0,0],
[0.6735384, 1.3873291,2.346506, 3.5654,0,0,0,0,0,0,0,0,0,0,0,0],
[1.3584715, 2.9405127,5.096819,8.155857,0,0,0,0,0,0,0,0,0,0,0,0],
[3.558062,8.216592,15.768077,27.386694,0,0,0,0,0,0,0,0,0,0,0,0],
[9.537899,25.202589,58.20041,0,0,0,0,0,0,0,0,0,0,0,0,0],
[16.083374,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[54.936775,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[89.185974,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]])
my_col = cm.jet(Z/np.amax(Z))
surf = ax.plot_surface(X, Y, Z,cmap=cm.coolwarm,linewidth=0, antialiased=False)
ax.set_zlim(0, 300)
ax.zaxis.set_major_locator(LinearLocator(10))
ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))
fig.colorbar(surf, shrink=0.5, aspect=5)
plt.show()
I get a plot like this
which is correct but not very attractive or intuitive. How can I make the visualizations more smooth and clear? Please note that I have many blanks in my data. Should I use 'zero' for the blanks or 'nan'(not a number)? For the same data, excel shows a much better graph.
I appreciate your inputs in order to make python plot more visually attractive.
The difference between the matplotlib and excel plots is that matplotlib is plotting on a linear scale and excel is logarithmic (or something that looks deceptively like a log axis but actually isn't -- see below). Therefore, in the matplotlib the slopes look extremely steep, but in excel the slopes are dramatically stretched out by the log.
Unfortunately, matplotlib doesn't yet have log axes working well in 3D. I'm not sure why this is, but it is a serious shortcoming. You can see a plot similar to Excel though if you take the log10 of your X and Y data before you do the plots. You can also go further to DIY your own log axes, but I've just done a shorthand for that using a tick formatter.
import matplotlib.pyplot as plt
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter, FuncFormatter
from mpl_toolkits.mplot3d import axes3d
import numpy as np
def format_log(x, pos=None):
x1 = 10**x
s = "%.3f" % x1
return s[:-4] if s[-3:]=="000" else " "
fig = plt.figure()
ax = fig.gca(projection='3d')
X=[2,3,5,8,20,30,50,80,100,150,175,200,250,300]
Y=[2,3,4,5,10,15,20,30,40,50,80,100,125,150,175,200]
X = np.log10(np.array(X))
Y = np.log10(np.array(Y))
Y,X=np.meshgrid(Y,X)
Z=np.array([
[0.2885307,0.269452,0.259193,0.2548041,0.2731868,0.4801551,0.7992361,1.7577641,3.2611327,5.428839,19.647976,37.59729,78.0871,152.21466,268.14572,0],
[0.2677955,0.2538363,0.2380033,0.2306999,0.4779794,0.9251045,1.5448972,3.508644,6.4968576,11.252151,0,0,0,0,0,0],
[0.2432982,0.2283371,0.2514196,0.3392502,0,0,0,0,0,0,0,0,0,0,0,0],
[0.2342575,0.3158406,0.4770729, 0.6795485,2.353042, 5.260077,9.78172,25.87004,59.52568, 0,0,0,0,0,0,0],
[0.6735384, 1.3873291,2.346506, 3.5654,0,0,0,0,0,0,0,0,0,0,0,0],
[1.3584715, 2.9405127,5.096819,8.155857,0,0,0,0,0,0,0,0,0,0,0,0],
[3.558062,8.216592,15.768077,27.386694,0,0,0,0,0,0,0,0,0,0,0,0],
[9.537899,25.202589,58.20041,0,0,0,0,0,0,0,0,0,0,0,0,0],
[16.083374,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[54.936775,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[89.185974,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]])
my_col = cm.jet(Z/np.amax(Z))
surf = ax.plot_surface(X, Y, Z,cmap=cm.coolwarm)
ax.set_zlim(0, 300)
ax.zaxis.set_major_locator(LinearLocator(10))
ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))
ax.xaxis.set_major_formatter(FuncFormatter(format_log))
ax.yaxis.set_major_formatter(FuncFormatter(format_log))
fig.colorbar(surf, shrink=0.5, aspect=5)
plt.show()
Edit:
After coming back to this question, I realize that the Excel plot isn't actually showing a logarithmic axis, but is instead just plotting the X and Y values given with equal spacing along the axis even those values have no clear mathematical progression.
It's critical to note that this isn't a good representation of the data, since it gives the obvious impression that it's logarithmic (for the specific data presented), but it's actually not, although it requires unusually close inspection to see that. Here the gaps between adjacent numbers aren't even monotonic.
So I discourage this representation, but to reproduce that Excel plot, I'd suggest making equally spaced data, but labeling it with different numbers (and just this sentence alone should be enough to discourage this approach). But here's the code and approach:
fig = plt.figure()
ax = fig.gca(projection='3d')
x=[2,3,5,8,20,30,50,80,100,150,175,200,250,300]
y=[2,3,4,5,10,15,20,30,40,50,80,100,125,150,175,200]
Y,X=np.meshgrid(range(len(y)),range(len(x)))
Z=np.array([
[0.2885307,0.269452,0.259193,0.2548041,0.2731868,0.4801551,0.7992361,1.7577641,3.2611327,5.428839,19.647976,37.59729,78.0871,152.21466,268.14572,0],
[0.2677955,0.2538363,0.2380033,0.2306999,0.4779794,0.9251045,1.5448972,3.508644,6.4968576,11.252151,0,0,0,0,0,0],
[0.2432982,0.2283371,0.2514196,0.3392502,0,0,0,0,0,0,0,0,0,0,0,0],
[0.2342575,0.3158406,0.4770729, 0.6795485,2.353042, 5.260077,9.78172,25.87004,59.52568, 0,0,0,0,0,0,0],
[0.6735384, 1.3873291,2.346506, 3.5654,0,0,0,0,0,0,0,0,0,0,0,0],
[1.3584715, 2.9405127,5.096819,8.155857,0,0,0,0,0,0,0,0,0,0,0,0],
[3.558062,8.216592,15.768077,27.386694,0,0,0,0,0,0,0,0,0,0,0,0],
[9.537899,25.202589,58.20041,0,0,0,0,0,0,0,0,0,0,0,0,0],
[16.083374,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[54.936775,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[89.185974,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]])
my_col = cm.jet(Z/np.amax(Z))
surf = ax.plot_surface(X, Y, Z,cmap=cm.coolwarm)
ax.tick_params(axis='both', which='major', labelsize=6)
ax.set_zlim(0, 300)
ax.xaxis.set_major_locator(IndexLocator(1, 0))
ax.xaxis.set_major_formatter(FixedFormatter([repr(v) for v in x]))
ax.yaxis.set_major_locator(IndexLocator(1, 0))
ax.yaxis.set_major_formatter(FixedFormatter([repr(v) for v in y]))
fig.colorbar(surf, shrink=0.5, aspect=5)
If one wanted to show the specific numbers given for X and Y, one solution would be to plot with a logarithmic axis (since the numbers are spaced very approximately in a log way), and then plot the numbers specifically by lines on the axes, or alternatively, don't use these numbers instead of the usual regularly spaced numbers. (But to plot these as axes values, and space them visually at regular intervals, that is a problem.)
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I've been looking high and low for a solution to this simple problem but I can't find it anywhere! There are a loads of posts detailing semilog / loglog plotting of data in 2D e.g. plt.setxscale('log') however I'm interested in using log scales on a 3d plot(mplot3d). I don't have the exact code to hand and so can't post it here, however the simple example below should be enough to explain the situation. I'm currently using Matplotlib 0.99.1 but should shortly be updating to 1.0.0 - I know I'll have to update my code for the mplot3d implementation. from mpl_toolkits.mplot3d import Axes3D from matplotlib import cm from matplotlib.ticker import LinearLocator, FixedLocator, FormatStrFormatter import matplotlib.pyplot as plt import numpy as np fig = plt.figure() ax = Axes3D(fig) X = np.arange(-5, 5, 0.025) Y = np.arange(-5, 5, 0.025) X, Y = np.meshgrid(X, Y) R = np.sqrt(X**2 + Y**2) Z = np.sin(R) surf = ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.jet, extend3d=True) ax.set_zlim3d(-1.01, 1.01) ax.w_zaxis.set_major_locator(LinearLocator(10)) ax.w_zaxis.set_major_formatter(FormatStrFormatter('%.03f')) fig.colorbar(surf) plt.show() The above code will plot fine in 3D, however the three scales (X, Y, Z) are all linear. My 'Y' data spans several orders of magnitude (like 9!), so it would be very useful to plot it on a log scale. I can work around this by taking the log of the 'Y', recreating the numpy array and plotting the log(Y) on a linear scale, but in true python style I'm looking for smarter solution which will plot the data on a log scale. Is it possible to produce a 3D surface plot of my XYZ data using log scales, ideally I'd like X & Z on linear scales and Y on a log scale? Any help would be greatly appreciated. Please forgive any obvious mistakes in the above example, as mentioned I don't have my exact code to have and so have altered a matplotlib gallery example from my memory. Thanks
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I came up with a nice and easy solution taking inspiration from Issue 209. You define a small formatter function in which you set your own notation. import matplotlib.ticker as mticker # My axis should display 10⁻¹ but you can switch to e-notation 1.00e+01 def log_tick_formatter(val, pos=None): return f"$10^{{{int(val)}}}$" # remove int() if you don't use MaxNLocator # return f"{10**val:.2e}" # e-Notation ax.zaxis.set_major_formatter(mticker.FuncFormatter(log_tick_formatter)) ax.zaxis.set_major_locator(mticker.MaxNLocator(integer=True)) set_major_locator sets the exponential to only use integers 10⁻¹, 10⁻² without 10^-1.5 etc. Source Important! remove the cast int() in the return statement if you don't use set_major_locator and you want to display 10^-1.5 otherwise it will still print 10⁻¹ instead of 10^-1.5. Example: Try it yourself! from mpl_toolkits.mplot3d import axes3d import numpy as np import matplotlib.pyplot as plt import matplotlib.ticker as mticker fig = plt.figure(figsize=(11,8)) ax1 = fig.add_subplot(121,projection="3d") # Grab some test data. X, Y, Z = axes3d.get_test_data(0.05) # Now Z has a range from 10⁻³ until 10³, so 6 magnitudes Z = (np.full((120, 120), 10)) ** (Z / 20) ax1.plot_wireframe(X, Y, Z, rstride=10, cstride=10) ax1.set(title="Linear z-axis (small values not visible)") def log_tick_formatter(val, pos=None): return f"$10^{{{int(val)}}}$" ax2 = fig.add_subplot(122,projection="3d") # You still have to take log10(Z) but thats just one operation ax2.plot_wireframe(X, Y, np.log10(Z), rstride=10, cstride=10) ax2.zaxis.set_major_formatter(mticker.FuncFormatter(log_tick_formatter)) ax2.zaxis.set_major_locator(mticker.MaxNLocator(integer=True)) ax2.set(title="Logarithmic z-axis (much better)") plt.savefig("LinearLog.png", bbox_inches='tight') plt.show()
in osx: ran ax.zaxis._set_scale('log') (notice the underscore)
There is no solution because of the issue 209. However, you can try doing this: ax.plot_surface(X, np.log10(Y), Z, cmap='jet', linewidth=0.5) If in "Y" there is a 0, it is going to appear a warning but still works. Because of this warning color maps don´t work, so try to avoid 0 and negative numbers. For example: Y[Y != 0] = np.log10(Y[Y != 0]) ax.plot_surface(X, Y, Z, cmap='jet', linewidth=0.5)
I wanted a symlog plot and, since I fill the data array by hand, I just made a custom function to calculate the log to avoid having negative bars in the bar3d if the data is < 1: import math as math def manual_log(data): if data < 10: # Linear scaling up to 1 return data/10 else: # Log scale above 1 return math.log10(data) Since I have no negative values, I did not implement handling this values in this function, but it should not be hard to change it.