Parameters to numpy's fromfunction

Question

I haven't grokked the key concepts in numpy yet.

I would like to create a 3-dimensional array and populate each cell with the result of a function call - i.e. the function would be called many times with different indices and return different values.

Note: Since writing this question, the documentation has been updated to be clearer.

I could create it with zeros (or empty), and then overwrite every value with a for loop, but it seems cleaner to populate it directly from the function.

fromfunction sounds perfect. Reading the documentation it sounds like the function gets called once per cell.

But when I actually try it...

from numpy import *  def sum_of_indices(x, y, z):     # What type are X, Y and Z ? Expect int or duck-type equivalent.     # Getting 3 individual arrays     print "Value of X is:"     print x      print "Type of X is:", type(x)     return x + y + z  a = fromfunction(sum_of_indices, (2, 2, 2)) 

I expect to get something like:

Value of X is: 0 Type of X is: int Value of X is: 1 Type of X is: int 

repeated 4 times.

I get:

Value of X is: [[[ 0.  0.]   [ 0.  0.]]   [[ 1.  1.]   [ 1.  1.]]] [[[ 0.  0.]   [ 1.  1.]]   [[ 0.  0.]   [ 1.  1.]]] [[[ 0.  1.]   [ 0.  1.]]   [[ 0.  1.]   [ 0.  1.]]] Type of X is: <type 'numpy.ndarray'> 

The function is only called once, and seems to return the entire array as result.

What is the correct way to populate an array based on multiple calls to a function of the indices?

Answer 1

The documentation is very misleading in that respect. It's just as you note: instead of performing f(0,0), f(0,1), f(1,0), f(1,1), numpy performs

f([[0., 0.], [0., 1.]], [[1., 0.], [1., 1.]]) 

Using ndarrays rather than the promised integer coordinates is quite frustrating when you try and use something likelambda i: l[i], where l is another array or list (though really, there are probably better ways to do this in numpy).

The numpy vectorize function fixes this. Where you have

m = fromfunction(f, shape) 

Try using

g = vectorize(f) m = fromfunction(g, shape)