CODEWITHSUNDEEP
pythonnumpyvectorization
fabriz-io
fabriz-io

Reputation: 33

(Surprisingly challenging?) Numpy Vectorization

I want to find a way to avoid the loop in my code. I need to implement the following formula, which is at first straightforward:

formula

In words: A list of indices is parsed called I. For every index specified in I, the values of all following indices in the array x need to be subtracted. Do some calculations on the subtracted value. Sum everything up. Done.

My current code:

def loss(x, indices):
    """ 
    Args:
        x: array_like, dtype=float
        indices: array_like, dtype=int

    Example:
        >>> x = np.array([0.3, 0.5, 0.2, 0.1, 1.2, 2.4, 2.8, 1.5, 3.2])
        >>> indices = np.array([0, 2, 3, 6])
        >>> print(loss(x, indices))
        21.81621815885847
    """

    total = 0.0
    for index in indices:
        # Broadcasting here, as all values from all following indices have
        # to be subtracted from the value at the given i index.
        difference = x[index] - x[index + 1:]

        # Sum all up
        log_addition = 1.0 + np.log(np.abs(difference))
        total += np.sum(log_addition)

    return total

The challenging part is that the 'i' indices are spread randomly over the range of the output. Any ideas?

Upvotes: 3

Views: 101

Answers (1)

Divakar
Divakar

Reputation: 221544

Here's one with NumPy-based vectorization -

mask = indices[:,None] < np.arange(len(x))
v = x[indices,None] - x
vmasked = v[mask]
log_addition = np.log(np.abs(vmasked))
out = log_addition.sum() + mask.sum()

Alternatively, using the laws of log, we can replace the final two steps with -

out = np.log(np.prod(np.abs(vmasked))).sum() + mask.sum()

Pushing the abs out, so that it operates on a scalar instead, it would be -

out = np.log(np.abs(np.prod(vmasked))).sum() + mask.sum()

Again, we can leverage multi-cores with numexpr -

import numexpr as ne
out = np.log(np.abs(ne.evaluate('prod(vmasked)'))) + mask.sum()

If you find that even v has too many unwanted elements, we can directly go to vmasked with -

xi = x[indices]
x2D = np.broadcast_to(x, (len(indices),len(x)))
vmasked = np.repeat(xi,mask.sum(1))-x2D[mask]

Upvotes: 4

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