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| 1 | + |
| 2 | +# The Computer Language Benchmarks Game |
| 3 | +# https://salsa.debian.org/benchmarksgame-team/benchmarksgame/ |
| 4 | +# |
| 5 | +# originally by Kevin Carson |
| 6 | +# modified by Tupteq, Fredrik Johansson, and Daniel Nanz |
| 7 | +# modified by Maciej Fijalkowski |
| 8 | +# 2to3 |
| 9 | +# modified by Andriy Misyura |
| 10 | + |
| 11 | +from math import sqrt |
| 12 | + |
| 13 | +def combinations(l): |
| 14 | + result = [] |
| 15 | + for x in range(len(l) - 1): |
| 16 | + ls = l[x+1:] |
| 17 | + for y in ls: |
| 18 | + result.append((l[x][0],l[x][1],l[x][2],y[0],y[1],y[2])) |
| 19 | + return result |
| 20 | + |
| 21 | +PI = 3.14159265358979323 |
| 22 | +SOLAR_MASS = 4 * PI * PI |
| 23 | +DAYS_PER_YEAR = 365.24 |
| 24 | + |
| 25 | +BODIES = { |
| 26 | + 'sun': ([0.0, 0.0, 0.0], [0.0, 0.0, 0.0], SOLAR_MASS), |
| 27 | + |
| 28 | + 'jupiter': ([4.84143144246472090e+00, |
| 29 | + -1.16032004402742839e+00, |
| 30 | + -1.03622044471123109e-01], |
| 31 | + [1.66007664274403694e-03 * DAYS_PER_YEAR, |
| 32 | + 7.69901118419740425e-03 * DAYS_PER_YEAR, |
| 33 | + -6.90460016972063023e-05 * DAYS_PER_YEAR], |
| 34 | + 9.54791938424326609e-04 * SOLAR_MASS), |
| 35 | + |
| 36 | + 'saturn': ([8.34336671824457987e+00, |
| 37 | + 4.12479856412430479e+00, |
| 38 | + -4.03523417114321381e-01], |
| 39 | + [-2.76742510726862411e-03 * DAYS_PER_YEAR, |
| 40 | + 4.99852801234917238e-03 * DAYS_PER_YEAR, |
| 41 | + 2.30417297573763929e-05 * DAYS_PER_YEAR], |
| 42 | + 2.85885980666130812e-04 * SOLAR_MASS), |
| 43 | + |
| 44 | + 'uranus': ([1.28943695621391310e+01, |
| 45 | + -1.51111514016986312e+01, |
| 46 | + -2.23307578892655734e-01], |
| 47 | + [2.96460137564761618e-03 * DAYS_PER_YEAR, |
| 48 | + 2.37847173959480950e-03 * DAYS_PER_YEAR, |
| 49 | + -2.96589568540237556e-05 * DAYS_PER_YEAR], |
| 50 | + 4.36624404335156298e-05 * SOLAR_MASS), |
| 51 | + |
| 52 | + 'neptune': ([1.53796971148509165e+01, |
| 53 | + -2.59193146099879641e+01, |
| 54 | + 1.79258772950371181e-01], |
| 55 | + [2.68067772490389322e-03 * DAYS_PER_YEAR, |
| 56 | + 1.62824170038242295e-03 * DAYS_PER_YEAR, |
| 57 | + -9.51592254519715870e-05 * DAYS_PER_YEAR], |
| 58 | + 5.15138902046611451e-05 * SOLAR_MASS) } |
| 59 | + |
| 60 | +SYSTEM = tuple(BODIES.values()) |
| 61 | +PAIRS = tuple(combinations(SYSTEM)) |
| 62 | + |
| 63 | +def advance(dt, n, bodies=SYSTEM, pairs=PAIRS): |
| 64 | + for i in range(n): |
| 65 | + for ([x1, y1, z1], v1, m1, [x2, y2, z2], v2, m2) in pairs: |
| 66 | + dx = x1 - x2 |
| 67 | + dy = y1 - y2 |
| 68 | + dz = z1 - z2 |
| 69 | + dist = sqrt(dx * dx + dy * dy + dz * dz); |
| 70 | + mag = dt / (dist*dist*dist) |
| 71 | + b1m = m1 * mag |
| 72 | + b2m = m2 * mag |
| 73 | + v1[0] -= dx * b2m |
| 74 | + v1[1] -= dy * b2m |
| 75 | + v1[2] -= dz * b2m |
| 76 | + v2[2] += dz * b1m |
| 77 | + v2[1] += dy * b1m |
| 78 | + v2[0] += dx * b1m |
| 79 | + for (r, [vx, vy, vz], m) in bodies: |
| 80 | + r[0] += dt * vx |
| 81 | + r[1] += dt * vy |
| 82 | + r[2] += dt * vz |
| 83 | + |
| 84 | +def report_energy(bodies=SYSTEM, pairs=PAIRS, e=0.0): |
| 85 | + for ((x1, y1, z1), v1, m1, (x2, y2, z2), v2, m2) in pairs: |
| 86 | + dx = x1 - x2 |
| 87 | + dy = y1 - y2 |
| 88 | + dz = z1 - z2 |
| 89 | + e -= (m1 * m2) / ((dx * dx + dy * dy + dz * dz) ** 0.5) |
| 90 | + for (r, [vx, vy, vz], m) in bodies: |
| 91 | + e += m * (vx * vx + vy * vy + vz * vz) / 2. |
| 92 | + print(f"{e}") |
| 93 | + |
| 94 | +def offset_momentum(ref, bodies=SYSTEM, px=0.0, py=0.0, pz=0.0): |
| 95 | + for (r, [vx, vy, vz], m) in bodies: |
| 96 | + px -= vx * m |
| 97 | + py -= vy * m |
| 98 | + pz -= vz * m |
| 99 | + (r, v, m) = ref |
| 100 | + v[0] = px / m |
| 101 | + v[1] = py / m |
| 102 | + v[2] = pz / m |
| 103 | + |
| 104 | +def main(n, ref='sun'): |
| 105 | + offset_momentum(BODIES[ref]) |
| 106 | + report_energy() |
| 107 | + advance(0.01, n) |
| 108 | + report_energy() |
| 109 | + |
| 110 | +main(500) |
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