nbody_iter.py

"""
    N-body simulation.
    Final optimal version
    Runtime: 36.697s
    R = L_orig / L_opt = 4.28
"""
# use itertools combinations to reduce loop overhead
from itertools import combinations
import timeit
    
PI = 3.14159265358979323
SOLAR_MASS = 4 * PI * PI
DAYS_PER_YEAR = 365.24

planet = {'sun', 'jupiter', 'saturn', 'uranus', 'neptune'}
bodies = BODIES.copy()
pairs = set(combinations(bodies.keys(), 2))

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)}

def advance(iterations, bodies, dt = 0.01):
    '''
        advance the system one timestep
    '''

    for _ in range(iterations):

        for (body1, body2) in pairs:
            ([x1, y1, z1], v1, m1) = bodies[body1]
            ([x2, y2, z2], v2, m2) = bodies[body2]
            (dx, dy, dz) = (x1-x2, y1-y2, z1-z2)
            mag = dt * ((dx * dx + dy * dy + dz * dz) ** (-1.5))
            v1[0] -= dx * m2 * mag
            v1[1] -= dy * m2 * mag
            v1[2] -= dz * m2 * mag
            v2[0] += dx * m1 * mag
            v2[1] += dy * m1 * mag

        for body in planet:
            (r, [vx, vy, vz], m) = BODIES[body]
            r[0] += dt * vx
            r[1] += dt * vy
            r[2] += dt * vz
    
def report_energy(bodies, e=0.0):
    '''
        compute the energy and return it so that it can be printed
    '''
    for (body1, body2) in pairs:
        ([x1, y1, z1], v1, m1) = bodies[body1]
        ([x2, y2, z2], v2, m2) = bodies[body2]
        (dx, dy, dz) = (x1-x2, y1-y2, z1-z2)
        (dx, dy, dz) = (x1-x2, y1-y2, z1-z2)
        e -= (m1 * m2) / ((dx * dx + dy * dy + dz * dz) ** 0.5)
                
        
    for body in planet:
        (r, [vx, vy, vz], m) = BODIES[body]
        e += m * (vx * vx + vy * vy + vz * vz) / 2.
        
    return e


def nbody(loops, reference, iterations):
    
    '''
        nbody simulation
        loops - number of loops to run
        reference - body at center of system
        iterations - number of timesteps to advance
    '''

    # Set up global state
    # reference is the body in the center of the system
    # offset values from this reference

    px=0.0
    py=0.0
    pz=0.0
    for body in planet:
        (r, [vx, vy, vz], m) = BODIES[body]
        px -= vx * m
        py -= vy * m
        pz -= vz * m

    (r, v, m) = BODIES[reference]
    v[0] = px / m
    v[1] = py / m
    v[2] = pz / m

    for _ in range(loops):
        report_energy(bodies = BODIES)
        advance(iterations, bodies = BODIES)
        print(report_energy(bodies = BODIES))

if __name__ == '__main__':

    print (timeit.timeit("nbody(100, 'sun', 20000)", setup = "from __main__ import nbody", number = 1))