manyi/apps/web/core/mathematics.py

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

# Francisco Mota, 2011-11-09
# http://fmota.eu/blog/monoids-in-python.html
# see also: http://arxiv.org/abs/1304.7544

import math

class Monoid(object):
    def __init__(self, null, lift, op):
        self.null = null
        self.lift = lift
        self.op = op

    def fold(self, xs):
        if hasattr(xs, "__fold__"):
            return xs.__fold__(self)
        else:
            return reduce(self.op, (self.lift(x) for x in xs), self.null)

    def __call__(self, *args):
        return self.fold(args)

    def star(self):
        return Monoid(self.null, self.fold, self.op)


summ = Monoid(0, lambda x: x, lambda a, b: a + b)
joinm = Monoid('', lambda x: str(x), lambda a, b: a + b)
listm = Monoid([], lambda x: [x], lambda a, b: a + b)
tuplem = Monoid((), lambda x: (x,), lambda a, b: a + b)
lenm = Monoid(0, lambda x: 1, lambda a, b: a + b)
prodm = Monoid(1, lambda x: x, lambda a, b: a * b)


## extended to define a monoid for folding Python `dict`

def dict_op(a, b):
    for key, val in b.items():
        if not key in a:
            a[key] = val
        else:
            if isinstance(val, dict):
                a[key] = dict_op(a[key], val)
            else:
                a[key] += val

    return a


dictm = Monoid({}, lambda x: x, lambda a, b: dict_op(a, b))


class Haversine(object):
    """
    half of the versed sine
    use the haversine class to calculate the distance between
    two lon/lat coordinate pairs.
    output distance available in kilometers, meters, miles, and feet.
    example usage: Haversine([lon1,lat1],[lon2,lat2]).feet
    """

    def __init__(self, coord1, coord2):
        lon1, lat1 = coord1
        lon2, lat2 = coord2

        R = 6371000  # radius of Earth in meters
        phi_1 = math.radians(lat1)
        phi_2 = math.radians(lat2)

        delta_phi = math.radians(lat2 - lat1)
        delta_lambda = math.radians(lon2 - lon1)

        a = math.sin(delta_phi / 2.0) ** 2 + \
            math.cos(phi_1) * math.cos(phi_2) * \
            math.sin(delta_lambda / 2.0) ** 2
        c = 2 * math.atan2(math.sqrt(a), math.sqrt(1 - a))

        self.meters = R * c  # output distance in meters
        self.km = self.meters / 1000.0  # output distance in kilometers
        self.miles = self.meters * 0.000621371  # output distance in miles
        self.feet = self.miles * 5280  # output distance in feet

def get_haversine_by_km(point1, point2):
    """

    :param point1:
    :param point2:
    :return:
    """
    return Haversine(point1, point2).km

if __name__=='__main__':
    xs  = [{ "a": i, "b": i + 1 } for i in range(0, 1000)]
    ys  = [{ "a": i, "b": i } for i in range(0, 1000)]

    x1 = { "a": 2, "b": 3 }
    x2 = { "b": 2, "c": 7 }

    print x1, x2
    print dictm.fold(xs + ys)