Scipy/numpy 2D array: how to define with a function?

[Dunhausen]

I want to make a matrix of values as so:

F(0,0) . . . F(1,n)
.
.
.
F(n,1) . . . F(n,n)

I could of course do it like this

list=[]
for i in range(0,n):
     for j in range(0,n):
     list.append(F(i,j))
a=array(list)
a.reshape(n,n)

But I am curious if there is a more elegant way to build an array with the rule Element i,j = F(i,j) ?

When working with 1-d arrays, I am accustomed to their savvy nature eliminating all need for 'for loops' in my code.

 

[story645]

a = numpy.empty((n+1,n+1))
for i in range(0,n):
    for j in range(0,n):
        a[i,j] = F(i,j)

or

i,j = numpy.meshgrid(range(0,n), range(0,n))
a = F(i,j)

 

[Dunhausen]

That is excellent! Thank you. :)

 

[story645]

Also, didn't have chance to edit, but range(n) generates the same list as range(0,n), if you want to be slightly more concise.

 

[LudusRex]

Is there a similar trick to 2D arrays?

Yes, there is a more elegant way to define a 2D array with a function using Scipy and Numpy. The key is to use the numpy.fromfunction() function, which allows you to create an array by executing a function over each element.

For example, to create a 2D array with the rule Element i,j = F(i,j), you can use the following code:

import numpy as np
def F(i,j):
return i+j # define your function here

n = 5 # define the size of the array
a = np.fromfunction(F, (n,n)) # create the array using the function and size
print(a) # print the array to see the result

The output will be as follows:

[[0. 1. 2. 3. 4.]
[1. 2. 3. 4. 5.]
[2. 3. 4. 5. 6.]
[3. 4. 5. 6. 7.]
[4. 5. 6. 7. 8.]]

This method avoids the use of for loops and is more efficient for large arrays. You can also use this method for more complex functions, as long as they can take in two indices as inputs and return a single value.

I hope this helps!