How to use numpy.meshgrid to plot a function

Question

I use numpy.meshgrid method to draw a 3D plot in Python. the drawing is over variables d1, d2 but I have a function consist of array with 7 elements which is 3 elements are independent from d1, d2. When I try to draw my graph I face this error:

operands could not be broadcast together with shapes (7,) (120,120)

When I debug my code I see the array elements which are independent from d1, d2 has shape of 1 but the other ones have shape of 120. How I can draw such a function using numpy.meshgrid method ?

Thanks. The whole code is like as follows:

import numpy
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter

def function(a, b, c, d1, d2):
    Q = numpy.ones(7)

    EV = []
    EV.append(1 / (a + b))
    EV.append(1 / (a + b + c))
    EV.append(1 / (a + b + c))
    EV.append((1 - numpy.exp(-c * d1)) / c)
    EV.append((1 - numpy.exp(-c * d2)) / (c + a))
    EV.append((1 - numpy.exp(-c * d1)) / c)
    EV.append((1 - numpy.exp(-c * d2)) / (c + a))

    return numpy.sum(numpy.multiply(Q, EV) / numpy.sum(numpy.multiply(Q, EV)))


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

# Make data.
d1 = numpy.arange(0, 6, 0.05)
d2 = numpy.arange(0, 6, 0.05)
X, Y = numpy.meshgrid(d1, d2)

# Plot the surface.
ax.set_zlim(2.00, 8.00)
surf = ax.plot_surface(X, Y, function(1, 1, 1, X, Y), cmap='viridis', linewidth=0, antialiased=False)

# Customize the z axis.
ax.zaxis.set_major_locator(LinearLocator(10))
ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))

# Add a color bar which maps values to colors.
fig.colorbar(surf, shrink=0.5, aspect=5)

plt.show()

Your function produces an array of 7 numbers for each input; e.g. function(1, 1, 1, 0, 0) is array([0.42857143, 0.28571429, 0.28571429, 0. , 0. , 0. , 0. ]). How would you want this to be plotted? — fuglede
– fuglede, Commented Oct 11, 2019 at 9:37
sorry, you are right! this is a part of a bigger code. I edit the code recheck it, Imagine I plot the element wise sum of the output array. the error is not because of what you said but I change the code to have a 1D output — A.A. H.
– A.A. H., Commented Oct 11, 2019 at 9:43
what's the relation to np.meshgrid? the error occurs in numpy.sum(numpy.multiply(Q, EV) / numpy.sum(numpy.multiply(Q, EV))). not knowing what it is you want to calculate, anyhow, the result should be of shape (120,120) so you can call it in plot_surface(X, Y, Z) as Z. — FObersteiner
– FObersteiner, Commented Oct 11, 2019 at 10:14
The point is that my function accept originally single variables not arrays, but when I use numpy.meshgrid it produces a 2D array of all possible occurrence for d1, d2 and pass it to the function. If you watch my function precisely you could see it produce 7 numbers which is 3 is independent of d1, d2 and the other ones has d1, d2 so the dimension of result is strange. The out is a list of 3 single number and 4 array of 120 x 120. — A.A. H.
– A.A. H., Commented Oct 11, 2019 at 14:35

fuglede · Accepted Answer · 2019-10-11 12:49:26Z

1

You could do something like

Z = np.array([[function(1, 1, 1, x, y) for x in d1] for y in d2])
surf = ax.plot_surface(X, Y, Z, cmap='viridis', linewidth=0, antialiased=False)

The plot will not be particularly interesting though: First of all, element-wise multiplication by an array of ones is the identity operation, so np.multiply(Q, EV) is the same as turning EV into an array. For any array a, np.sum(a / np.sum(a)) is equal to 1 (since you can take the constant factor np.sum(a) outside of the outer sum). Therefore, function is constantly equal to one.

answered Oct 11, 2019 at 12:49

fuglede

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5 Comments

A.A. H. Over a year ago

Thank you very much for your answer which is completely right. But because matrix calculation has good performance in view of speed I don't want to use for loop. Do you know where is the point, I know it always has the value of 1 but it is not the point. The point is that my function accept originally single variables not arrays, but when I use numpy.meshgrid it produces a 2D array of all possible occurrence for d1, d2 and pass it to the function.

A.A. H. Over a year ago

If you watch my function precisely you could see it produce 7 numbers which is 3 is independent of d1, d2 and the other ones has d1, d2 so the dimension of result is strange. The output is a list of 3 single number and 4 array of 120 x 120.

fuglede Over a year ago

After your edit, the output is a single number, which is, modulo rounding issues, always 1.

A.A. H. Over a year ago

Dear @fuglede this is not a math problem, The error is because the output is always 1 ?? No I want to know how to use meshgrid with unbalanced functions.

fuglede Over a year ago

I never said that; only that in this particualr case, it causes the plot to be what it ends up being. The method applies in complete generality.

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