"""
Routine to initialize weights.

@note: We assume that numpy.random.seed() has already been performed.
"""

from math import sqrt
import numpy.random
def random_weights(nin, nout, scale_by=sqrt(3)):
    """
    Generate an initial weight matrix with nin inputs (rows) and nout
    outputs (cols).
    Each weight is chosen uniformly at random to be in range:
        [-scale_by/sqrt(nin), +scale_by/sqrt(nin)]
    @note: Play with scale_by!
    Ronan derives scale_by=sqrt(3) because that gives variance of
    1 to something (I forget, ask Yoshua for the derivation). However,
    Ronan got better results by accidentally using scale_by=1. Yoshua
    hypothesizes this is because the variance will get telescopically
    smaller as we go up the layers [need more explanation of this
    argument].
    @note: Things may get even trickier if the same weights are being
    shared in multiple places.
    """
    return (numpy.random.rand(nin, nout) * 2.0 - 1) * scale_by / sqrt(nin)