nbody2.py

# 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
# modified by Andriy Misyura

import sys
from math import sqrt

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 = tuple(BODIES.values())
PAIRS = tuple(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:
            dx = x1 - x2
            dy = y1 - y2
            dz = z1 - z2
            dist = sqrt(dx * dx + dy * dy + dz * dz);
            mag = dt / (dist*dist*dist)
            b1m = m1 * mag
            b2m = m2 * mag
            v1[0] -= dx * b2m
            v1[1] -= dy * b2m
            v1[2] -= dz * b2m
            v2[2] += dz * b1m
            v2[1] += dy * b1m
            v2[0] += dx * b1m
        for (r, [vx, vy, vz], m) in bodies:
            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:
        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:
        e += m * (vx * vx + vy * vy + vz * vz) / 2.
    print("%.9f" % e)

def offset_momentum(ref, bodies=SYSTEM, px=0.0, py=0.0, pz=0.0):
    for (r, [vx, vy, vz], m) in bodies:
        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, ref='sun'):
    offset_momentum(BODIES[ref])
    report_energy()
    advance(0.01, n)
    report_energy()

if __name__ == '__main__':
    if len(sys.argv) > 1: N = int(sys.argv[1])
    else: N = 5000000

    main(N)