nbody.py

# I had to modify this to work with pylang because
#    [a,[b,c]] = [1,[2,3]]
# is not implemented (correctly), and also tuples aren't
# implemented at all (so use lists).

# The Computer Language Benchmarks Game
# http://benchmarksgame.alioth.debian.org/
#
# originally by Kevin Carson
# modified by Tupteq, Fredrik Johansson, and Daniel Nanz
# modified by Maciej Fijalkowski
# 2to3

import sys


def combinations(l):
    result = []
    for x in range(len(l) - 1):
        ls = l[x + 1:]
        for y in ls:
            result.append((l[x], y))
    return result


PI = 3.14159265358979323
SOLAR_MASS = 4 * PI * PI
DAYS_PER_YEAR = 365.24

BODIES = {
    'sun': [[0.0, 0.0, 0.0], [0.0, 0.0, 0.0], SOLAR_MASS],
    'jupiter': [[
        4.84143144246472090e+00, -1.16032004402742839e+00,
        -1.03622044471123109e-01
    ],
                [
                    1.66007664274403694e-03 * DAYS_PER_YEAR,
                    7.69901118419740425e-03 * DAYS_PER_YEAR,
                    -6.90460016972063023e-05 * DAYS_PER_YEAR
                ], 9.54791938424326609e-04 * SOLAR_MASS],
    'saturn': [[
        8.34336671824457987e+00, 4.12479856412430479e+00,
        -4.03523417114321381e-01
    ],
               [
                   -2.76742510726862411e-03 * DAYS_PER_YEAR,
                   4.99852801234917238e-03 * DAYS_PER_YEAR,
                   2.30417297573763929e-05 * DAYS_PER_YEAR
               ], 2.85885980666130812e-04 * SOLAR_MASS],
    'uranus': [[
        1.28943695621391310e+01, -1.51111514016986312e+01,
        -2.23307578892655734e-01
    ],
               [
                   2.96460137564761618e-03 * DAYS_PER_YEAR,
                   2.37847173959480950e-03 * DAYS_PER_YEAR,
                   -2.96589568540237556e-05 * DAYS_PER_YEAR
               ], 4.36624404335156298e-05 * SOLAR_MASS],
    'neptune': [[
        1.53796971148509165e+01, -2.59193146099879641e+01,
        1.79258772950371181e-01
    ],
                [
                    2.68067772490389322e-03 * DAYS_PER_YEAR,
                    1.62824170038242295e-03 * DAYS_PER_YEAR,
                    -9.51592254519715870e-05 * DAYS_PER_YEAR
                ], 5.15138902046611451e-05 * SOLAR_MASS]
}

#SYSTEM = list(BODIES.values())
SYSTEM = [BODIES[x] for x in BODIES]
PAIRS = combinations(SYSTEM)


def advance(dt, n, bodies=SYSTEM, pairs=PAIRS):

    for i in range(n):
        #for [[[x1, y1, z1], v1, m1],
        #     [[x2, y2, z2], v2, m2]] in pairs:
        for pair in pairs:
            [x1, y1, z1] = pair[0][0]
            v1 = pair[0][1]
            m1 = pair[0][2]
            [x2, y2, z2] = pair[1][0]
            v2 = pair[1][1]
            m2 = pair[1][2]

            dx = x1 - x2
            dy = y1 - y2
            dz = z1 - z2
            mag = dt * ((dx * dx + dy * dy + dz * dz)**(-1.5))
            b1m = m1 * mag
            b2m = m2 * mag
            v1[0] -= dx * b2m
            v1[1] -= dy * b2m
            v1[2] -= dz * b2m
            v2[0] += dx * b1m
            v2[1] += dy * b1m
            v2[2] += dz * b1m
        #for (r, [vx, vy, vz], m) in bodies:
        for body in bodies:
            r = body[0]
            [vx, vy, vz] = body[1]
            m = body[2]
            r[0] += dt * vx
            r[1] += dt * vy
            r[2] += dt * vz


def report_energy(bodies=SYSTEM, pairs=PAIRS, e=0.0):

    #for (((x1, y1, z1), v1, m1),
    #     ((x2, y2, z2), v2, m2)) in pairs:
    for pair in pairs:
        [x1, y1, z1] = pair[0][0]
        v1 = pair[0][1]
        m1 = pair[0][2]
        [x2, y2, z2] = pair[1][0]
        v2 = pair[1][1]
        m2 = pair[1][2]

        dx = x1 - x2
        dy = y1 - y2
        dz = z1 - z2
        e -= (m1 * m2) / ((dx * dx + dy * dy + dz * dz)**0.5)
    #for (r, [vx, vy, vz], m) in bodies:
    for body in bodies:
        r = body[0]
        [vx, vy, vz] = body[1]
        m = body[2]

        e += m * (vx * vx + vy * vy + vz * vz) / 2.
    print(e)


def offset_momentum(ref, bodies=SYSTEM, px=0.0, py=0.0, pz=0.0):

    #for (r, [vx, vy, vz], m) in bodies:
    for body in bodies:
        r = body[0]
        [vx, vy, vz] = body[1]
        m = body[2]

        px -= vx * m
        py -= vy * m
        pz -= vz * m

    [r, v, m] = ref
    v[0] = px / m
    v[1] = py / m
    v[2] = pz / m


def main(n=20000, ref='sun'):
    offset_momentum(BODIES[ref])
    #report_energy()
    advance(0.01, n)
    #report_energy()


from bench import register, all

register("nbody", main)

if __name__ == '__main__':
    all()