| // Copyright ©2019 The Gonum Authors. All rights reserved. |
| // Use of this source code is governed by a BSD-style |
| // license that can be found in the LICENSE file. |
| |
| package barneshut |
| |
| import ( |
| "fmt" |
| "math" |
| "reflect" |
| "testing" |
| |
| "golang.org/x/exp/rand" |
| |
| "gonum.org/v1/gonum/floats/scalar" |
| "gonum.org/v1/gonum/spatial/r2" |
| ) |
| |
| type particle2 struct { |
| x, y, m float64 |
| name string |
| } |
| |
| func (p particle2) Coord2() r2.Vec { return r2.Vec{X: p.x, Y: p.y} } |
| func (p particle2) Mass() float64 { return p.m } |
| |
| var planeTests = []struct { |
| name string |
| particles []particle2 |
| want *Plane |
| }{ |
| { |
| name: "nil", |
| particles: nil, |
| want: &Plane{}, |
| }, |
| { |
| name: "empty", |
| particles: []particle2{}, |
| want: &Plane{Particles: []Particle2{}}, |
| }, |
| { |
| name: "one", |
| particles: []particle2{{m: 1}}, // Must have a mass to avoid vacuum decay. |
| want: &Plane{ |
| root: tile{ |
| particle: particle2{x: 0, y: 0, m: 1}, |
| bounds: r2.Box{Min: r2.Vec{X: 0, Y: 0}, Max: r2.Vec{X: 0, Y: 0}}, |
| center: r2.Vec{X: 0, Y: 0}, |
| mass: 1, |
| }, |
| |
| Particles: []Particle2{ |
| particle2{m: 1}, |
| }, |
| }, |
| }, |
| { |
| name: "3 corners", |
| particles: []particle2{ |
| {x: 1, y: 1, m: 1}, |
| {x: -1, y: 1, m: 1}, |
| {x: -1, y: -1, m: 1}, |
| }, |
| want: &Plane{ |
| root: tile{ |
| bounds: r2.Box{Min: r2.Vec{X: -1, Y: -1}, Max: r2.Vec{X: 1, Y: 1}}, |
| nodes: [4]*tile{ |
| se: { |
| particle: particle2{x: 1, y: 1, m: 1}, |
| bounds: r2.Box{Min: r2.Vec{X: 0, Y: 0}, Max: r2.Vec{X: 1, Y: 1}}, |
| center: r2.Vec{X: 1, Y: 1}, mass: 1, |
| }, |
| sw: { |
| particle: particle2{x: -1, y: 1, m: 1}, |
| bounds: r2.Box{Min: r2.Vec{X: -1, Y: 0}, Max: r2.Vec{X: 0, Y: 1}}, |
| center: r2.Vec{X: -1, Y: 1}, mass: 1, |
| }, |
| nw: { |
| particle: particle2{x: -1, y: -1, m: 1}, |
| bounds: r2.Box{Min: r2.Vec{X: -1, Y: -1}, Max: r2.Vec{X: 0, Y: 0}}, |
| center: r2.Vec{X: -1, Y: -1}, mass: 1, |
| }, |
| }, |
| center: r2.Vec{X: -0.3333333333333333, Y: 0.3333333333333333}, |
| mass: 3, |
| }, |
| |
| Particles: []Particle2{ |
| particle2{x: 1, y: 1, m: 1}, |
| particle2{x: -1, y: 1, m: 1}, |
| particle2{x: -1, y: -1, m: 1}, |
| }, |
| }, |
| }, |
| { |
| name: "4 corners", |
| particles: []particle2{ |
| {x: 1, y: 1, m: 1}, |
| {x: -1, y: 1, m: 1}, |
| {x: 1, y: -1, m: 1}, |
| {x: -1, y: -1, m: 1}, |
| }, |
| want: &Plane{ |
| root: tile{ |
| bounds: r2.Box{Min: r2.Vec{X: -1, Y: -1}, Max: r2.Vec{X: 1, Y: 1}}, |
| nodes: [4]*tile{ |
| { |
| particle: particle2{x: 1, y: -1, m: 1}, |
| bounds: r2.Box{Min: r2.Vec{X: 0, Y: -1}, Max: r2.Vec{X: 1, Y: 0}}, |
| center: r2.Vec{X: 1, Y: -1}, |
| mass: 1, |
| }, |
| { |
| particle: particle2{x: 1, y: 1, m: 1}, |
| bounds: r2.Box{Min: r2.Vec{X: 0, Y: 0}, Max: r2.Vec{X: 1, Y: 1}}, |
| center: r2.Vec{X: 1, Y: 1}, |
| mass: 1, |
| }, |
| { |
| particle: particle2{x: -1, y: 1, m: 1}, |
| bounds: r2.Box{Min: r2.Vec{X: -1, Y: 0}, Max: r2.Vec{X: 0, Y: 1}}, |
| center: r2.Vec{X: -1, Y: 1}, |
| mass: 1, |
| }, |
| { |
| particle: particle2{x: -1, y: -1, m: 1}, |
| bounds: r2.Box{Min: r2.Vec{X: -1, Y: -1}, Max: r2.Vec{X: 0, Y: 0}}, |
| center: r2.Vec{X: -1, Y: -1}, |
| mass: 1, |
| }, |
| }, |
| center: r2.Vec{X: 0, Y: 0}, |
| mass: 4, |
| }, |
| |
| Particles: []Particle2{ |
| particle2{x: 1, y: 1, m: 1}, |
| particle2{x: -1, y: 1, m: 1}, |
| particle2{x: 1, y: -1, m: 1}, |
| particle2{x: -1, y: -1, m: 1}, |
| }, |
| }, |
| }, |
| { |
| name: "5 corners", |
| particles: []particle2{ |
| {x: 1, y: 1, m: 1}, |
| {x: -1, y: 1, m: 1}, |
| {x: 1, y: -1, m: 1}, |
| {x: -1, y: -1, m: 1}, |
| {x: -1.1, y: -1, m: 1}, |
| }, |
| want: &Plane{ |
| root: tile{ |
| bounds: r2.Box{Min: r2.Vec{X: -1.1, Y: -1}, Max: r2.Vec{X: 1, Y: 1}}, |
| nodes: [4]*tile{ |
| { |
| particle: particle2{x: 1, y: -1, m: 1}, |
| bounds: r2.Box{Min: r2.Vec{X: -0.050000000000000044, Y: -1}, Max: r2.Vec{X: 1, Y: 0}}, |
| center: r2.Vec{X: 1, Y: -1}, |
| mass: 1, |
| }, |
| { |
| particle: particle2{x: 1, y: 1, m: 1}, |
| bounds: r2.Box{Min: r2.Vec{X: -0.050000000000000044, Y: 0}, Max: r2.Vec{X: 1, Y: 1}}, |
| center: r2.Vec{X: 1, Y: 1}, |
| mass: 1, |
| }, |
| { |
| particle: particle2{x: -1, y: 1, m: 1}, |
| bounds: r2.Box{Min: r2.Vec{X: -1.1, Y: 0}, Max: r2.Vec{X: -0.050000000000000044, Y: 1}}, |
| center: r2.Vec{X: -1, Y: 1}, |
| mass: 1, |
| }, |
| { |
| bounds: r2.Box{Min: r2.Vec{X: -1.1, Y: -1}, Max: r2.Vec{X: -0.050000000000000044, Y: 0}}, |
| nodes: [4]*tile{ |
| nw: { |
| bounds: r2.Box{Min: r2.Vec{X: -1.1, Y: -1}, Max: r2.Vec{X: -0.5750000000000001, Y: -0.5}}, |
| nodes: [4]*tile{ |
| nw: { |
| bounds: r2.Box{Min: r2.Vec{X: -1.1, Y: -1}, Max: r2.Vec{X: -0.8375000000000001, Y: -0.75}}, |
| nodes: [4]*tile{ |
| nw: { |
| bounds: r2.Box{Min: r2.Vec{X: -1.1, Y: -1}, Max: r2.Vec{X: -0.9687500000000001, Y: -0.875}}, |
| nodes: [4]*tile{ |
| ne: { |
| particle: particle2{x: -1, y: -1, m: 1}, |
| bounds: r2.Box{Min: r2.Vec{X: -1.034375, Y: -1}, Max: r2.Vec{X: -0.9687500000000001, Y: -0.9375}}, |
| center: r2.Vec{X: -1, Y: -1}, |
| mass: 1, |
| }, |
| nw: { |
| particle: particle2{x: -1.1, y: -1, m: 1}, |
| bounds: r2.Box{Min: r2.Vec{X: -1.1, Y: -1}, Max: r2.Vec{X: -1.034375, Y: -0.9375}}, |
| center: r2.Vec{X: -1.1, Y: -1}, |
| mass: 1, |
| }, |
| }, |
| center: r2.Vec{X: -1.05, Y: -1}, |
| mass: 2, |
| }, |
| }, |
| center: r2.Vec{X: -1.05, Y: -1}, |
| mass: 2, |
| }, |
| }, |
| center: r2.Vec{X: -1.05, Y: -1}, |
| mass: 2, |
| }, |
| }, |
| center: r2.Vec{X: -1.05, Y: -1}, |
| mass: 2, |
| }, |
| }, |
| center: r2.Vec{X: -0.22000000000000003, Y: -0.2}, |
| mass: 5, |
| }, |
| |
| Particles: []Particle2{ |
| particle2{x: 1, y: 1, m: 1}, |
| particle2{x: -1, y: 1, m: 1}, |
| particle2{x: 1, y: -1, m: 1}, |
| particle2{x: -1, y: -1, m: 1}, |
| particle2{x: -1.1, y: -1, m: 1}, |
| }, |
| }, |
| }, |
| { |
| // Note that the code here subdivides the space differently to |
| // how it is split in the example, since Plane makes a minimum |
| // bounding box based on the data, while the example does not. |
| name: "http://arborjs.org/docs/barnes-hut example", |
| particles: []particle2{ |
| {x: 64.5, y: 81.5, m: 1, name: "A"}, |
| {x: 242, y: 34, m: 1, name: "B"}, |
| {x: 199, y: 69, m: 1, name: "C"}, |
| {x: 285, y: 106.5, m: 1, name: "D"}, |
| {x: 170, y: 194.5, m: 1, name: "E"}, |
| {x: 42.5, y: 334.5, m: 1, name: "F"}, |
| {x: 147, y: 309, m: 1, name: "G"}, |
| {x: 236.5, y: 324, m: 1, name: "H"}, |
| }, |
| want: &Plane{ |
| root: tile{ |
| bounds: r2.Box{Min: r2.Vec{X: 42.5, Y: 34}, Max: r2.Vec{X: 285, Y: 334.5}}, |
| nodes: [4]*tile{ |
| { |
| bounds: r2.Box{Min: r2.Vec{X: 163.75, Y: 34}, Max: r2.Vec{X: 285, Y: 184.25}}, |
| nodes: [4]*tile{ |
| ne: { |
| bounds: r2.Box{Min: r2.Vec{X: 224.375, Y: 34}, Max: r2.Vec{X: 285, Y: 109.125}}, |
| nodes: [4]*tile{ |
| se: { |
| particle: particle2{x: 285, y: 106.5, m: 1, name: "D"}, |
| bounds: r2.Box{Min: r2.Vec{X: 254.6875, Y: 71.5625}, Max: r2.Vec{X: 285, Y: 109.125}}, |
| center: r2.Vec{X: 285, Y: 106.5}, |
| mass: 1, |
| }, |
| nw: { |
| particle: particle2{x: 242, y: 34, m: 1, name: "B"}, |
| bounds: r2.Box{Min: r2.Vec{X: 224.375, Y: 34}, Max: r2.Vec{X: 254.6875, Y: 71.5625}}, |
| center: r2.Vec{X: 242, Y: 34}, |
| mass: 1, |
| }, |
| }, |
| center: r2.Vec{X: 263.5, Y: 70.25}, |
| mass: 2, |
| }, |
| nw: { |
| particle: particle2{x: 199, y: 69, m: 1, name: "C"}, |
| bounds: r2.Box{Min: r2.Vec{X: 163.75, Y: 34}, Max: r2.Vec{X: 224.375, Y: 109.125}}, |
| center: r2.Vec{X: 199, Y: 69}, |
| mass: 1, |
| }, |
| }, |
| center: r2.Vec{X: 242, Y: 69.83333333333333}, |
| mass: 3, |
| }, |
| { |
| bounds: r2.Box{Min: r2.Vec{X: 163.75, Y: 184.25}, Max: r2.Vec{X: 285, Y: 334.5}}, |
| nodes: [4]*tile{ |
| se: { |
| particle: particle2{x: 236.5, y: 324, m: 1, name: "H"}, |
| bounds: r2.Box{Min: r2.Vec{X: 224.375, Y: 259.375}, Max: r2.Vec{X: 285, Y: 334.5}}, |
| center: r2.Vec{X: 236.5, Y: 324}, |
| mass: 1, |
| }, |
| nw: { |
| particle: particle2{x: 170, y: 194.5, m: 1, name: "E"}, |
| bounds: r2.Box{Min: r2.Vec{X: 163.75, Y: 184.25}, Max: r2.Vec{X: 224.375, Y: 259.375}}, |
| center: r2.Vec{X: 170, Y: 194.5}, |
| mass: 1, |
| }, |
| }, |
| center: r2.Vec{X: 203.25, Y: 259.25}, |
| mass: 2, |
| }, |
| { |
| bounds: r2.Box{Min: r2.Vec{X: 42.5, Y: 184.25}, Max: r2.Vec{X: 163.75, Y: 334.5}}, |
| nodes: [4]*tile{ |
| se: { |
| particle: particle2{x: 147, y: 309, m: 1, name: "G"}, |
| bounds: r2.Box{Min: r2.Vec{X: 103.125, Y: 259.375}, Max: r2.Vec{X: 163.75, Y: 334.5}}, |
| center: r2.Vec{X: 147, Y: 309}, |
| mass: 1, |
| }, |
| sw: { |
| particle: particle2{x: 42.5, y: 334.5, m: 1, name: "F"}, |
| bounds: r2.Box{Min: r2.Vec{X: 42.5, Y: 259.375}, Max: r2.Vec{X: 103.125, Y: 334.5}}, |
| center: r2.Vec{X: 42.5, Y: 334.5}, |
| mass: 1, |
| }, |
| }, |
| center: r2.Vec{X: 94.75, Y: 321.75}, |
| mass: 2, |
| }, |
| { |
| particle: particle2{x: 64.5, y: 81.5, m: 1, name: "A"}, |
| bounds: r2.Box{Min: r2.Vec{X: 42.5, Y: 34}, Max: r2.Vec{X: 163.75, Y: 184.25}}, |
| center: r2.Vec{X: 64.5, Y: 81.5}, |
| mass: 1, |
| }, |
| }, |
| center: r2.Vec{X: 173.3125, Y: 181.625}, |
| mass: 8, |
| }, |
| |
| Particles: []Particle2{ |
| particle2{x: 64.5, y: 81.5, m: 1, name: "A"}, |
| particle2{x: 242, y: 34, m: 1, name: "B"}, |
| particle2{x: 199, y: 69, m: 1, name: "C"}, |
| particle2{x: 285, y: 106.5, m: 1, name: "D"}, |
| particle2{x: 170, y: 194.5, m: 1, name: "E"}, |
| particle2{x: 42.5, y: 334.5, m: 1, name: "F"}, |
| particle2{x: 147, y: 309, m: 1, name: "G"}, |
| particle2{x: 236.5, y: 324, m: 1, name: "H"}, |
| }, |
| }, |
| }, |
| } |
| |
| func TestPlane(t *testing.T) { |
| t.Parallel() |
| const tol = 1e-15 |
| |
| for _, test := range planeTests { |
| var particles []Particle2 |
| if test.particles != nil { |
| particles = make([]Particle2, len(test.particles)) |
| } |
| for i, p := range test.particles { |
| particles[i] = p |
| } |
| |
| got, err := NewPlane(particles) |
| if err != nil { |
| t.Errorf("unexpected error: %v", err) |
| continue |
| } |
| |
| if test.want != nil && !reflect.DeepEqual(got, test.want) { |
| t.Errorf("unexpected result for %q: got:%v want:%v", test.name, got, test.want) |
| } |
| |
| // Recursively check all internal centers of mass. |
| walkPlane(&got.root, func(tl *tile) { |
| var sub []Particle2 |
| walkPlane(tl, func(tl *tile) { |
| if tl.particle != nil { |
| sub = append(sub, tl.particle) |
| } |
| }) |
| center, mass := centerOfMass2(sub) |
| if !scalar.EqualWithinAbsOrRel(center.X, tl.center.X, tol, tol) || !scalar.EqualWithinAbsOrRel(center.Y, tl.center.Y, tol, tol) { |
| t.Errorf("unexpected result for %q for center of mass: got:%f want:%f", test.name, tl.center, center) |
| } |
| if !scalar.EqualWithinAbsOrRel(mass, tl.mass, tol, tol) { |
| t.Errorf("unexpected result for %q for total mass: got:%f want:%f", test.name, tl.mass, mass) |
| } |
| }) |
| } |
| } |
| |
| func centerOfMass2(particles []Particle2) (center r2.Vec, mass float64) { |
| for _, p := range particles { |
| m := p.Mass() |
| mass += m |
| c := p.Coord2() |
| center.X += c.X * m |
| center.Y += c.Y * m |
| } |
| if mass != 0 { |
| center.X /= mass |
| center.Y /= mass |
| } |
| return center, mass |
| } |
| |
| func walkPlane(t *tile, fn func(*tile)) { |
| if t == nil { |
| return |
| } |
| fn(t) |
| for _, q := range t.nodes { |
| walkPlane(q, fn) |
| } |
| } |
| |
| func TestPlaneForceOn(t *testing.T) { |
| t.Parallel() |
| const ( |
| size = 1000 |
| tol = 0.07 |
| ) |
| for _, n := range []int{3e3, 1e4, 3e4} { |
| rnd := rand.New(rand.NewSource(1)) |
| particles := make([]Particle2, n) |
| for i := range particles { |
| particles[i] = particle2{x: size * rnd.Float64(), y: size * rnd.Float64(), m: 1} |
| } |
| |
| moved := make([]r2.Vec, n) |
| for i, p := range particles { |
| var v r2.Vec |
| m := p.Mass() |
| pv := p.Coord2() |
| for _, e := range particles { |
| v = r2.Add(v, Gravity2(p, e, m, e.Mass(), r2.Sub(e.Coord2(), pv))) |
| } |
| moved[i] = r2.Add(p.Coord2(), v) |
| } |
| |
| plane, err := NewPlane(particles) |
| if err != nil { |
| t.Errorf("unexpected error: %v", err) |
| continue |
| } |
| for _, theta := range []float64{0, 0.3, 0.6, 0.9} { |
| theta := theta |
| t.Run(fmt.Sprintf("%d-body/theta=%v", len(particles), theta), func(t *testing.T) { |
| t.Parallel() |
| var ssd, sd float64 |
| var calls int |
| for i, p := range particles { |
| v := plane.ForceOn(p, theta, func(p1, p2 Particle2, m1, m2 float64, v r2.Vec) r2.Vec { |
| calls++ |
| return Gravity2(p1, p2, m1, m2, v) |
| }) |
| pos := r2.Add(p.Coord2(), v) |
| d := r2.Sub(moved[i], pos) |
| ssd += d.X*d.X + d.Y*d.Y |
| sd += math.Hypot(d.X, d.Y) |
| } |
| rmsd := math.Sqrt(ssd / float64(len(particles))) |
| if rmsd > tol { |
| t.Error("RMSD for approximation too high") |
| } |
| t.Logf("rmsd=%.4v md=%.4v calls/particle=%.5v", |
| rmsd, sd/float64(len(particles)), float64(calls)/float64(len(particles))) |
| }) |
| } |
| } |
| } |
| |
| var ( |
| fv2sink r2.Vec |
| planeSink *Plane |
| ) |
| |
| func BenchmarkNewPlane(b *testing.B) { |
| for _, n := range []int{1e3, 1e4, 1e5, 1e6} { |
| rnd := rand.New(rand.NewSource(1)) |
| particles := make([]Particle2, n) |
| for i := range particles { |
| particles[i] = particle2{x: rnd.Float64(), y: rnd.Float64(), m: 1} |
| } |
| b.ResetTimer() |
| var err error |
| b.Run(fmt.Sprintf("%d-body", len(particles)), func(b *testing.B) { |
| for i := 0; i < b.N; i++ { |
| planeSink, err = NewPlane(particles) |
| if err != nil { |
| b.Fatalf("unexpected error: %v", err) |
| } |
| } |
| }) |
| } |
| } |
| |
| func BenchmarkPlaneForceOn(b *testing.B) { |
| for _, n := range []int{1e3, 1e4, 1e5} { |
| for _, theta := range []float64{0, 0.1, 0.5, 1, 1.5} { |
| if n > 1e4 && theta < 0.5 { |
| // Don't run unreasonably long benchmarks. |
| continue |
| } |
| rnd := rand.New(rand.NewSource(1)) |
| particles := make([]Particle2, n) |
| for i := range particles { |
| particles[i] = particle2{x: rnd.Float64(), y: rnd.Float64(), m: 1} |
| } |
| plane, err := NewPlane(particles) |
| if err != nil { |
| b.Fatalf("unexpected error: %v", err) |
| } |
| b.ResetTimer() |
| b.Run(fmt.Sprintf("%d-body/theta=%v", len(particles), theta), func(b *testing.B) { |
| for i := 0; i < b.N; i++ { |
| for _, p := range particles { |
| fv2sink = plane.ForceOn(p, theta, Gravity2) |
| } |
| } |
| }) |
| } |
| } |
| } |
| |
| func BenchmarkPlaneFull(b *testing.B) { |
| for _, n := range []int{1e3, 1e4, 1e5} { |
| for _, theta := range []float64{0, 0.1, 0.5, 1, 1.5} { |
| if n > 1e4 && theta < 0.5 { |
| // Don't run unreasonably long benchmarks. |
| continue |
| } |
| rnd := rand.New(rand.NewSource(1)) |
| particles := make([]Particle2, n) |
| for i := range particles { |
| particles[i] = particle2{x: rnd.Float64(), y: rnd.Float64(), m: 1} |
| } |
| b.ResetTimer() |
| b.Run(fmt.Sprintf("%d-body/theta=%v", len(particles), theta), func(b *testing.B) { |
| for i := 0; i < b.N; i++ { |
| plane, err := NewPlane(particles) |
| if err != nil { |
| b.Fatalf("unexpected error: %v", err) |
| } |
| for _, p := range particles { |
| fv2sink = plane.ForceOn(p, theta, Gravity2) |
| } |
| } |
| }) |
| } |
| } |
| } |
