Shortest isotonic transform function in the world. Generates increasing formula.

IsotonicRegression.py

def isotonic_transform(x, y, alpha=0.001):
    target = y + 0.
    output = numpy.zeros(len(x))
    steps = 2 ** numpy.arange(int(numpy.log2(len(x)) - 1))[::-1]
    print steps
    for i in range(100):
        for step in steps:
            penalty = 2 * (target - output)
            diffs = - (output[step:] - output[:-step])
            diffs = diffs.clip(0) 
            misorder_penalty = numpy.zeros(len(x))
            misorder_penalty[step:] += diffs / 2.
            misorder_penalty[:-step] -= diffs / 2.

            output += alpha * penalty + misorder_penalty
    return output