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N-body problem: Difference between revisions
Add Swift
SqrtNegInf (talk | contribs) (Added Perl example) |
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Line 5,048:
Body 2 : 0.426346 -0.111425 -0.681150 | 0.234987 0.006241 -0.440245
Body 3 : -1.006089 -4.103186 -3.122591 | -0.359686 -1.177995 -0.875924</pre>
=={{header|Swift}}==
<lang swift>import Foundation
public struct Vector {
public var px = 0.0
public var py = 0.0
public var pz = 0.0
public init(px: Double, py: Double, pz: Double) {
(self.px, self.py, self.pz) = (px, py, pz)
}
public init?(array: [Double]) {
guard array.count == 3 else {
return nil
}
(self.px, self.py, self.pz) = (array[0], array[1], array[2])
}
public func mod() -> Double {
(px * px + py * py + pz * pz).squareRoot()
}
static func + (lhs: Vector, rhs: Vector) -> Vector {
return Vector(
px: lhs.px + rhs.px,
py: lhs.py + rhs.py,
pz: lhs.pz + rhs.pz
)
}
static func - (lhs: Vector, rhs: Vector) -> Vector {
return Vector(
px: lhs.px - rhs.px,
py: lhs.py - rhs.py,
pz: lhs.pz - rhs.pz
)
}
static func * (lhs: Vector, rhs: Double) -> Vector {
return Vector(
px: lhs.px * rhs,
py: lhs.py * rhs,
pz: lhs.pz * rhs
)
}
}
extension Vector {
public static let origin = Vector(px: 0, py: 0, pz: 0)
}
extension Vector: Equatable {
public static func == (lhs: Vector, rhs: Vector) -> Bool {
return lhs.px == rhs.px && lhs.py == rhs.py && lhs.pz == rhs.pz
}
}
extension Vector: CustomStringConvertible {
public var description: String {
return String(format: "%.6f\t%.6f\t%.6f", px, py, pz)
}
}
public class NBody {
public let gravitationalConstant: Double
public let numBodies: Int
public let timeSteps: Int
public private(set) var masses: [Double]
public private(set) var positions: [Vector]
public private(set) var velocities: [Vector]
public private(set) var accelerations: [Vector]
public init?(file: String) {
guard let data = try? String(contentsOfFile: file) else {
return nil
}
print("Input file:\n\(data)")
let lines = data.components(separatedBy: "\n").map({ $0.components(separatedBy: " ") })
let worldData = lines.first!
guard worldData.count == 3,
let gc = Double(worldData[0]),
let bodies = Int(worldData[1]),
let timeSteps = Int(worldData[2]) else {
return nil
}
let defaultState = Array(repeating: Vector.origin, count: bodies)
self.gravitationalConstant = gc
self.numBodies = bodies
self.timeSteps = timeSteps
self.masses = Array(repeating: 0, count: bodies)
self.positions = defaultState
self.accelerations = defaultState
self.velocities = defaultState
let bodyData = lines.dropFirst().map({ $0.compactMap(Double.init) })
guard bodyData.count == bodies * 3 else {
return nil
}
for n in 0..<bodies {
masses[n] = bodyData[0 + n * 3][0]
guard let position = Vector(array: bodyData[1 + n * 3]),
let velocity = Vector(array: bodyData[2 + n * 3]) else {
return nil
}
positions[n] = position
velocities[n] = velocity
}
}
private func computeAccelerations() {
for i in 0..<numBodies {
accelerations[i] = .origin
for j in 0..<numBodies where i != j {
let t = gravitationalConstant * masses[j] / pow((positions[i] - positions[j]).mod(), 3)
accelerations[i] = accelerations[i] + (positions[j] - positions[i]) * t
}
}
}
private func resolveCollisions() {
for i in 0..<numBodies {
for j in 0..<numBodies where positions[i] == positions[j] {
velocities.swapAt(i, j)
}
}
}
private func computeVelocities() {
for i in 0..<numBodies {
velocities[i] = velocities[i] + accelerations[i]
}
}
private func computePositions() {
for i in 0..<numBodies {
positions[i] = positions[i] + velocities[i] + accelerations[i] * 0.5
}
}
public func printState() {
for i in 0..<numBodies {
print("Body \(i + 1): \(positions[i]) | \(velocities[i])")
}
}
public func simulate() {
computeAccelerations()
computePositions()
computeVelocities()
resolveCollisions()
}
}
guard let sim = NBody(file: "input.txt") else {
fatalError()
}
print()
print("Body : x y z | vx vy vz")
for i in 0..<sim.timeSteps {
print("Step \(i + 1)")
sim.simulate()
sim.printState()
print()
}
</lang>
{{out}}
<pre style="height: 20em; overflow: auto;">Input file:
0.01 3 20
1
0.000000 0.000000 0.000000
0.010000 0.000000 0.000000
0.100000
1.000000 1.000000 0.000000
0.000000 0.000000 0.020000
0.001000
0.000000 1.000000 1.000000
0.010000 -0.010000 -0.010000
Body : x y z | vx vy vz
Step 1
Body 1: 0.010177 0.000179 0.000002 | 0.010354 0.000357 0.000004
Body 2: 0.998230 0.998232 0.020002 | -0.003539 -0.003536 0.020004
Body 3: 0.010177 0.988232 0.988055 | 0.010354 -0.013536 -0.013889
Step 2
Body 1: 0.020709 0.000718 0.000011 | 0.010710 0.000721 0.000014
Body 2: 0.992907 0.992896 0.039971 | -0.007109 -0.007138 0.019935
Body 3: 0.020717 0.972888 0.972173 | 0.010727 -0.017153 -0.017876
Step 3
Body 1: 0.031600 0.001625 0.000034 | 0.011072 0.001094 0.000033
Body 2: 0.983985 0.983910 0.059834 | -0.010735 -0.010835 0.019790
Body 3: 0.031643 0.953868 0.952235 | 0.011125 -0.020886 -0.021999
Step 4
Body 1: 0.042858 0.002913 0.000081 | 0.011443 0.001481 0.000060
Body 2: 0.971393 0.971163 0.079509 | -0.014448 -0.014659 0.019561
Body 3: 0.042981 0.931039 0.928087 | 0.011552 -0.024772 -0.026299
Step 5
Body 1: 0.054492 0.004595 0.000160 | 0.011826 0.001884 0.000097
Body 2: 0.955030 0.954509 0.098909 | -0.018278 -0.018649 0.019238
Body 3: 0.054766 0.904225 0.899522 | 0.012018 -0.028857 -0.030829
Step 6
Body 1: 0.066517 0.006691 0.000281 | 0.012224 0.002308 0.000145
Body 2: 0.934759 0.933760 0.117931 | -0.022265 -0.022849 0.018806
Body 3: 0.067040 0.873197 0.866280 | 0.012530 -0.033199 -0.035655
Step 7
Body 1: 0.078950 0.009225 0.000456 | 0.012642 0.002759 0.000206
Body 2: 0.910400 0.908677 0.136456 | -0.026454 -0.027316 0.018244
Body 3: 0.079856 0.837662 0.828023 | 0.013101 -0.037871 -0.040861
Step 8
Body 1: 0.091815 0.012227 0.000702 | 0.013086 0.003245 0.000284
Body 2: 0.881722 0.878958 0.154340 | -0.030902 -0.032122 0.017523
Body 3: 0.093281 0.797239 0.784313 | 0.013749 -0.042975 -0.046559
Step 9
Body 1: 0.105140 0.015737 0.001035 | 0.013564 0.003775 0.000383
Body 2: 0.848429 0.844216 0.171401 | -0.035684 -0.037362 0.016600
Body 3: 0.107405 0.751427 0.734579 | 0.014498 -0.048649 -0.052908
Step 10
Body 1: 0.118964 0.019805 0.001481 | 0.014085 0.004362 0.000509
Body 2: 0.810137 0.803953 0.187408 | -0.040900 -0.043166 0.015414
Body 3: 0.122346 0.699554 0.678056 | 0.015384 -0.055097 -0.060138
Step 11
Body 1: 0.133337 0.024498 0.002071 | 0.014662 0.005025 0.000672
Body 2: 0.766343 0.757509 0.202050 | -0.046687 -0.049720 0.013868
Body 3: 0.138268 0.640690 0.613685 | 0.016460 -0.062633 -0.068603
Step 12
Body 1: 0.148327 0.029907 0.002851 | 0.015317 0.005792 0.000888
Body 2: 0.716377 0.703998 0.214889 | -0.053246 -0.057302 0.011810
Body 3: 0.155406 0.573482 0.539941 | 0.017816 -0.071782 -0.078886
Step 13
Body 1: 0.164025 0.036157 0.003887 | 0.016079 0.006709 0.001184
Body 2: 0.659310 0.642172 0.225282 | -0.060887 -0.066351 0.008976
Body 3: 0.174112 0.495836 0.454475 | 0.019596 -0.083511 -0.092045
Step 14
Body 1: 0.180564 0.043437 0.005286 | 0.017000 0.007852 0.001613
Body 2: 0.593807 0.570186 0.232208 | -0.070119 -0.077621 0.004875
Body 3: 0.194929 0.404136 0.353320 | 0.022038 -0.099890 -0.110265
Step 15
Body 1: 0.198150 0.052049 0.007234 | 0.018171 0.009372 0.002283
Body 2: 0.517817 0.485100 0.233878 | -0.081861 -0.092550 -0.001535
Body 3: 0.218605 0.290860 0.228583 | 0.025314 -0.126661 -0.139210
Step 16
Body 1: 0.217126 0.062542 0.010117 | 0.019781 0.011614 0.003484
Body 2: 0.427899 0.381659 0.226654 | -0.097974 -0.114332 -0.012913
Body 3: 0.244268 0.131956 0.057562 | 0.026013 -0.191148 -0.202831
Step 17
Body 1: 0.238346 0.076539 0.015221 | 0.022658 0.016380 0.006723
Body 2: 0.317489 0.248502 0.200967 | -0.122846 -0.151982 -0.038461
Body 3: 0.075592 -0.559591 -0.487315 | -0.363366 -1.191945 -0.886924
Step 18
Body 1: 0.263123 0.097523 0.026918 | 0.026898 0.025587 0.016672
Body 2: 0.173428 0.050424 0.112716 | -0.165275 -0.244174 -0.138041
Body 3: -0.286241 -1.745597 -1.369528 | -0.360299 -1.180066 -0.877501
Step 19
Body 1: 0.270854 0.113045 0.061923 | -0.011436 0.005457 0.053339
Body 2: 0.199821 -0.093105 -0.208666 | 0.218061 -0.042882 -0.504723
Body 3: -0.646318 -2.924909 -2.246453 | -0.359856 -1.178559 -0.876350
Step 20
Body 1: 0.258572 0.116046 0.112038 | -0.013129 0.000544 0.046890
Body 2: 0.426346 -0.111425 -0.681150 | 0.234987 0.006241 -0.440245
Body 3: -1.006089 -4.103186 -3.122591 | -0.359686 -1.177995 -0.875924
Process finished with exit code 0
</pre>
=={{header|Tcl}}==
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