HW05: Wiener process

wiener.py

#!/usr/bin/env python3
# -*- coding: utf-8 -*-

import bisect
import numpy as np
from functools import total_ordering
from numpy.random import normal
from pylab import *


@total_ordering
class Elem:

    def __init__(self, key, value):
        self.key = key
        self.value = value

    def __eq__(self, other):
        return self.key == other.key

    def __lt__(self, other):
        return self.key < other.key

    def __str__(self):
        return '<%s, %s>' % (self.key, self.value)


def generator():
    values = [Elem(0, 0)]

    def inner(x):
        nonlocal values

        elem = Elem(x, None)
        ind = bisect.bisect_left(values, elem)

        l = values[ind - 1]
        if ind < len(values):
            if values[ind] == elem:
                return values

            r = values[ind]
            sigma12 = x - l.key
            sigma22 = r.key - x
            d = np.abs(l.value - r.value)

            a = d * sigma12 / (sigma12 + sigma22)
            sigma = np.sqrt(sigma12 * sigma22 / (sigma12 + sigma22))
        else:
            a = 0
            sigma = np.sqrt(x - values[ind - 1].key)

        elem.value = l.value + normal(a, sigma)
        bisect.insort_left(values, elem)

        return values

    return inner


def main():
    gen = generator()
    for i in range(10):
        vs = gen(i)

    vs = gen(7.3)
    vs = gen(0.1)

    print(';\n'.join(str(v) for v in vs))

    x = []
    y = []
    for elem in vs:
        x.append(elem.key)
        y.append(elem.value)
    plot(x, y)
    show()


if __name__ == '__main__':
    main()