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// Copyright ©2015 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 gen
import (
"fmt"
"math"
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/graph"
"gonum.org/v1/gonum/internal/order"
)
// UndirectedMutator is an undirected graph builder that can remove edges.
type UndirectedMutator interface {
graph.UndirectedBuilder
graph.EdgeRemover
}
// Duplication constructs a graph in the destination, dst, of order n. New nodes
// are created by duplicating an existing node and all its edges. Each new edge is
// deleted with probability delta. Additional edges are added between the new node
// and existing nodes with probability alpha/|V|. An exception to this addition
// rule is made for the parent node when sigma is not NaN; in this case an edge is
// created with probability sigma. With the exception of the sigma parameter, this
// corresponds to the completely correlated case in doi:10.1016/S0022-5193(03)00028-6.
// If src is not nil it is used as the random source, otherwise rand.Float64 is used.
func Duplication(dst UndirectedMutator, n int, delta, alpha, sigma float64, src rand.Source) error {
// As described in doi:10.1016/S0022-5193(03)00028-6 but
// also clarified in doi:10.1186/gb-2007-8-4-r51.
if delta < 0 || delta > 1 {
return fmt.Errorf("gen: bad delta: delta=%v", delta)
}
if alpha <= 0 || alpha > 1 {
return fmt.Errorf("gen: bad alpha: alpha=%v", alpha)
}
if sigma < 0 || sigma > 1 {
return fmt.Errorf("gen: bad sigma: sigma=%v", sigma)
}
var (
rnd func() float64
rndN func(int) int
)
if src == nil {
rnd = rand.Float64
rndN = rand.Intn
} else {
r := rand.New(src)
rnd = r.Float64
rndN = r.Intn
}
nodes := graph.NodesOf(dst.Nodes())
order.ByID(nodes)
if len(nodes) == 0 {
n--
u := dst.NewNode()
dst.AddNode(u)
nodes = append(nodes, u)
}
for i := 0; i < n; i++ {
u := nodes[rndN(len(nodes))]
d := dst.NewNode()
did := d.ID()
// Add the duplicate node.
dst.AddNode(d)
// Loop until we have connectivity
// into the rest of the graph.
for {
// Add edges to parent's neighbours.
to := graph.NodesOf(dst.From(u.ID()))
order.ByID(to)
for _, v := range to {
vid := v.ID()
if rnd() < delta || dst.HasEdgeBetween(vid, did) {
continue
}
if vid < did {
dst.SetEdge(dst.NewEdge(v, d))
} else {
dst.SetEdge(dst.NewEdge(d, v))
}
}
// Add edges to old nodes.
scaledAlpha := alpha / float64(len(nodes))
for _, v := range nodes {
uid := u.ID()
vid := v.ID()
switch vid {
case uid:
if !math.IsNaN(sigma) {
if i == 0 || rnd() < sigma {
if vid < did {
dst.SetEdge(dst.NewEdge(v, d))
} else {
dst.SetEdge(dst.NewEdge(d, v))
}
}
continue
}
fallthrough
default:
if rnd() < scaledAlpha && !dst.HasEdgeBetween(vid, did) {
if vid < did {
dst.SetEdge(dst.NewEdge(v, d))
} else {
dst.SetEdge(dst.NewEdge(d, v))
}
}
}
}
if dst.From(did).Len() != 0 {
break
}
}
nodes = append(nodes, d)
}
return nil
}
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