Generating data from meshgrid data (Numpy)

Question

I'd like to ask how to generate corresponding values from a meshgrid. I have a function "foo" that takes one 1D array with the length of 2, and returns some real number.

import numpy as np

def foo(X):  
    #this function takes a vector, e.g., np.array([2,3]), and returns a real number.
    return sum(X)**np.sin( sum(X) );

x = np.arange(-2, 1, 1)          # points in the x axis
y = np.arange( 3, 8, 1)          # points in the y axis
X, Y = np.meshgrid(x, y)         # X, Y : grid

I generate X and Y grids using meshgrid.

Then, how can I generate corresponding Z values using "foo" function, in order to plot them in 3D, e.g., plotting using plot_surface function with X,Y,Z values?

Here the question is how to generate Z values, which has the same shape to X and Y, using "foo" function. Since my "foo" function only takes an 1D array, I do not know how I can uses this function with X and Y to generate corresponding Z values.

Do you want z = foo([x, y]) for each point (x, y) in the meshgrid? — Praveen
– Praveen, Commented Sep 27, 2016 at 0:30

Praveen · Accepted Answer · 2016-09-27 04:09:00Z

3

Stack your two numpy arrays in "depth" using np.dstack, and then modify your foo function, so that it operates on only the last axis of your stacked array. This is easily done using np.sum with parameter axis=-1, instead of using the builtin sum:

import numpy as np

def foo(xy):
    return np.sum(xy, axis=-1) ** np.sin(np.sum(xy, axis=-1))

x = np.arange(-2, 1, 1)          # points in the x axis
y = np.arange( 3, 8, 1)          # points in the y axis
X, Y = np.meshgrid(x, y)         # X, Y : grid
XY = np.dstack((X, Y))

And now, you should get:

>>> XY.shape
(5, 3, 2)
>>> foo(XY)
array([[ 1.        ,  1.87813065,  1.1677002 ],
       [ 1.87813065,  1.1677002 ,  0.35023496],
       [ 1.1677002 ,  0.35023496,  0.2136686 ],
       [ 0.35023496,  0.2136686 ,  0.60613935],
       [ 0.2136686 ,  0.60613935,  3.59102217]])

If you want to achieve the same effect, but without modifying foo, then you can use np.apply_along_axis, which should do exactly what you need:

>>> np.apply_along_axis(foo, -1, XY)
array([[ 1.        ,  1.87813065,  1.1677002 ],
       [ 1.87813065,  1.1677002 ,  0.35023496],
       [ 1.1677002 ,  0.35023496,  0.2136686 ],
       [ 0.35023496,  0.2136686 ,  0.60613935],
       [ 0.2136686 ,  0.60613935,  3.59102217]])

edited Sep 27, 2016 at 4:09

answered Sep 27, 2016 at 0:59

Praveen

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7 Comments

Ann Descomp Over a year ago

Thanks for the wonderful solution. This is exactly what I wanted to do. However, I have some problems to apply this approach to my code bock. I actually posted another question regarding this matter link. My actual foo function is actually something like return X[0] + X[1];, so it cannot perform an iterative operation on a nested array, and can only take the shape of (2,). Thus, if I put XY into my actual foo function, it spits our error. In this case, how can generate Z as you did?

Ann Descomp Over a year ago

Oops, sorry, I forgot it!

Ann Descomp Over a year ago

By the way, can you let me know how I should change your ode if I just want to use my current foo function, which can only take (2,) shape?

Praveen Over a year ago

@AnnDescomp I've posted an answer on your other question. See if that works for you...

Ann Descomp Over a year ago

I am now looking at "..." indexing. In addition, I'd want to know if there is a way to generate Z with my current foo function, which can explicitly take only one (2,) shape Numpy array as an argument.

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