Created
June 25, 2022 21:29
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N-body problem in Python?
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# Just trying to cheat at the Benchmarks Game | |
# https://benchmarksgame-team.pages.debian.net/benchmarksgame/description/nbody.html | |
def wrapper(n): | |
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()) | |
PAIRS = combinations(SYSTEM) | |
def advance(dt, n, bodies=SYSTEM, pairs=PAIRS): | |
for i in range(n): | |
for j in pairs: | |
xyz1, v1, m1 = j[0] | |
xyz2, v2, m2 = j[1] | |
x1, y1, z1 = xyz1 | |
x2, y2, z2 = xyz2 | |
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 i in bodies: | |
r, vxyz, m = i | |
vx, vy, vz = vxyz | |
r[0] += dt * vx | |
r[1] += dt * vy | |
r[2] += dt * vz | |
def report_energy(bodies=SYSTEM, pairs=PAIRS, e=0.0): | |
for j in pairs: | |
xyz1, v1, m1 = j[0] | |
xyz2, v2, m2 = j[1] | |
x1, y1, z1 = xyz1 | |
x2, y2, z2 = xyz2 | |
dx = x1 - x2 | |
dy = y1 - y2 | |
dz = z1 - z2 | |
e -= (m1 * m2) / ((dx * dx + dy * dy + dz * dz) ** 0.5) | |
for i in bodies: | |
r, vxyz, m = i | |
vx, vy, vz = vxyz | |
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 i in bodies: | |
r, vxyz, m = i | |
vx, vy, vz = vxyz | |
px -= vx * m | |
py -= vy * m | |
pz -= vz * m | |
m = ref[2] | |
v = ref[1] | |
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() | |
print(main(int(n))) | |
from pscript import py2js, evaljs | |
print(evaljs(py2js(wrapper) + '; wrapper(50000000)').replace('null\n','').replace('null','')) |
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