Python lazy evaluation numpy ndarray

Question

I have a large 2D array that I would like to declare once, and change occasionnaly only some values depending on a parameter, without traversing the whole array.

To build this array, I have subclassed the numpy ndarray class with dtype=object and assign to the elements I want to change a function e.g. :

def f(parameter):
     return parameter**2

for i in range(np.shape(A)[0]):
    A[i,i]=f
    for j in range(np.shape(A)[0]):
        A[i,j]=1.

I have then overridden the __getitem__ method so that it returns the evaluation of the function with given parameter if it is callable, otherwise return the value itself.

    def __getitem__(self, key):
        value = super(numpy.ndarray, self).__getitem__(key)
        if callable(value):
            return value(*self.args)
        else:
            return value

where self.args were previously given to the instance of myclass.

However, I need to work with float arrays at the end, and I can't simply convert this array into a dtype=float array with this technique. I also tried to use numpy views, which does not work either for dtype=object.

Do you have any better alternative ? Should I override the view method rather than getitem ?

Edit I will maybe have to use Cython in the future, so if you have a solution involving e.g. C pointers, I am interested.

Answer 1

In this case, it does not make sens to bind a transformation function, to every index of your array.

Instead, a more efficient approach would be to define a transformation, as a function, together with a subset of the array it applies to. Here is a basic implementation,

import numpy as np

class LazyEvaluation(object):
    def __init__(self):
        self.transforms = []

    def add_transform(self, function, selection=slice(None), args={}):
        self.transforms.append( (function, selection, args))

    def __call__(self, x):
        y = x.copy() 
        for function, selection, args in self.transforms:
            y[selection] = function(y[selection], **args)
        return y

that can be used as follows:

x = np.ones((6, 6))*2

le = LazyEvaluation()
le.add_transform(lambda x: 0, [[3], [0]]) # equivalent to x[3,0]
le.add_transform(lambda x: x**2, (slice(4), slice(4,6)))  # equivalent to x[4,4:6]
le.add_transform(lambda x: -1,  np.diag_indices(x.shape[0], x.ndim), ) # setting the diagonal 
result =  le(x)
print(result)

which prints,

array([[-1.,  2.,  2.,  2.,  4.,  4.],
       [ 2., -1.,  2.,  2.,  4.,  4.],
       [ 2.,  2., -1.,  2.,  4.,  4.],
       [ 0.,  2.,  2., -1.,  4.,  4.],
       [ 2.,  2.,  2.,  2., -1.,  2.],
       [ 2.,  2.,  2.,  2.,  2., -1.]])

This way you can easily support all advanced Numpy indexing (element by element access, slicing, fancy indexing etc.), while at the same time keeping your data in an array with a native data type (float, int, etc) which is much more efficient than using dtype='object'.