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// 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 layout
import (
"math"
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/graph"
"gonum.org/v1/gonum/spatial/barneshut"
"gonum.org/v1/gonum/spatial/r2"
)
// EadesR2 implements the graph layout algorithm essentially as
// described in "A heuristic for graph drawing", Congressus
// numerantium 42:149-160.
// The implementation here uses the Barnes-Hut approximation for
// global repulsion calculation, and edge weights are considered
// when calculating adjacent node attraction.
type EadesR2 struct {
// Updates is the number of updates to perform.
Updates int
// Repulsion is the strength of the global
// repulsive force between nodes in the
// layout. It corresponds to C3 in the paper.
Repulsion float64
// Rate is the gradient descent rate. It
// corresponds to C4 in the paper.
Rate float64
// Theta is the Barnes-Hut theta constant.
Theta float64
// Src is the source of randomness used
// to initialize the nodes' locations. If
// Src is nil, the global random number
// generator is used.
Src rand.Source
nodes graph.Nodes
indexOf map[int64]int
particles []barneshut.Particle2
forces []r2.Vec
}
// Update is the EadesR2 spatial graph update function.
func (u *EadesR2) Update(g graph.Graph, layout LayoutR2) bool {
if u.Updates <= 0 {
return false
}
u.Updates--
if !layout.IsInitialized() {
var rnd func() float64
if u.Src == nil {
rnd = rand.Float64
} else {
rnd = rand.New(u.Src).Float64
}
u.nodes = g.Nodes()
u.indexOf = make(map[int64]int, u.nodes.Len())
if u.nodes.Len() >= 0 {
u.particles = make([]barneshut.Particle2, 0, u.nodes.Len())
}
for u.nodes.Next() {
id := u.nodes.Node().ID()
u.indexOf[id] = len(u.particles)
u.particles = append(u.particles, eadesR2Node{id: id, pos: r2.Vec{X: rnd(), Y: rnd()}})
}
u.forces = make([]r2.Vec, len(u.particles))
}
u.nodes.Reset()
// Apply global repulsion.
plane, err := barneshut.NewPlane(u.particles)
if err != nil {
return false
}
var updated bool
for i, p := range u.particles {
f := r2.Scale(-u.Repulsion, plane.ForceOn(p, u.Theta, barneshut.Gravity2))
// Prevent marginal updates that can be caused by
// floating point error when nodes are very far apart.
if math.Hypot(f.X, f.Y) > 1e-12 {
updated = true
}
u.forces[i] = f
}
// Handle edge weighting for attraction.
var weight func(uid, vid int64) float64
if wg, ok := g.(graph.Weighted); ok {
if _, ok := g.(graph.Directed); ok {
weight = func(xid, yid int64) float64 {
var w float64
f, ok := wg.Weight(xid, yid)
if ok {
w += f
}
r, ok := wg.Weight(yid, xid)
if ok {
w += r
}
return w
}
} else {
weight = func(xid, yid int64) float64 {
w, ok := wg.Weight(xid, yid)
if ok {
return w
}
return 0
}
}
} else {
// This is only called when the adjacency is known so just return unit.
weight = func(_, _ int64) float64 { return 1 }
}
seen := make(map[[2]int64]bool)
for u.nodes.Next() {
xid := u.nodes.Node().ID()
xidx := u.indexOf[xid]
to := g.From(xid)
for to.Next() {
yid := to.Node().ID()
if seen[[2]int64{xid, yid}] {
continue
}
seen[[2]int64{yid, xid}] = true
yidx := u.indexOf[yid]
// Apply adjacent node attraction.
v := r2.Sub(u.particles[yidx].Coord2(), u.particles[xidx].Coord2())
f := r2.Scale(weight(xid, yid)*math.Log(math.Hypot(v.X, v.Y)), v)
if math.IsInf(f.X, 0) || math.IsInf(f.Y, 0) {
return false
}
if math.Hypot(f.X, f.Y) > 1e-12 {
updated = true
}
u.forces[xidx] = r2.Add(u.forces[xidx], f)
u.forces[yidx] = r2.Sub(u.forces[yidx], f)
}
}
if !updated {
return false
}
rate := u.Rate
if rate == 0 {
rate = 0.1
}
for i, f := range u.forces {
n := u.particles[i].(eadesR2Node)
n.pos = r2.Add(n.pos, r2.Scale(rate, f))
u.particles[i] = n
layout.SetCoord2(n.id, n.pos)
}
return true
}
type eadesR2Node struct {
id int64
pos r2.Vec
}
func (p eadesR2Node) Coord2() r2.Vec { return p.pos }
func (p eadesR2Node) Mass() float64 { return 1 }
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