gonum.org/v1/gonum@v0.14.0/graph/graphs/gen/duplication.go (about)

     1  // Copyright ©2015 The Gonum Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package gen
     6  
     7  import (
     8  	"fmt"
     9  	"math"
    10  
    11  	"golang.org/x/exp/rand"
    12  
    13  	"gonum.org/v1/gonum/graph"
    14  	"gonum.org/v1/gonum/graph/internal/ordered"
    15  )
    16  
    17  // UndirectedMutator is an undirected graph builder that can remove edges.
    18  type UndirectedMutator interface {
    19  	graph.UndirectedBuilder
    20  	graph.EdgeRemover
    21  }
    22  
    23  // Duplication constructs a graph in the destination, dst, of order n. New nodes
    24  // are created by duplicating an existing node and all its edges. Each new edge is
    25  // deleted with probability delta. Additional edges are added between the new node
    26  // and existing nodes with probability alpha/|V|. An exception to this addition
    27  // rule is made for the parent node when sigma is not NaN; in this case an edge is
    28  // created with probability sigma. With the exception of the sigma parameter, this
    29  // corresponds to the completely correlated case in doi:10.1016/S0022-5193(03)00028-6.
    30  // If src is not nil it is used as the random source, otherwise rand.Float64 is used.
    31  func Duplication(dst UndirectedMutator, n int, delta, alpha, sigma float64, src rand.Source) error {
    32  	// As described in doi:10.1016/S0022-5193(03)00028-6 but
    33  	// also clarified in doi:10.1186/gb-2007-8-4-r51.
    34  
    35  	if delta < 0 || delta > 1 {
    36  		return fmt.Errorf("gen: bad delta: delta=%v", delta)
    37  	}
    38  	if alpha <= 0 || alpha > 1 {
    39  		return fmt.Errorf("gen: bad alpha: alpha=%v", alpha)
    40  	}
    41  	if sigma < 0 || sigma > 1 {
    42  		return fmt.Errorf("gen: bad sigma: sigma=%v", sigma)
    43  	}
    44  
    45  	var (
    46  		rnd  func() float64
    47  		rndN func(int) int
    48  	)
    49  	if src == nil {
    50  		rnd = rand.Float64
    51  		rndN = rand.Intn
    52  	} else {
    53  		r := rand.New(src)
    54  		rnd = r.Float64
    55  		rndN = r.Intn
    56  	}
    57  
    58  	nodes := graph.NodesOf(dst.Nodes())
    59  	ordered.ByID(nodes)
    60  	if len(nodes) == 0 {
    61  		n--
    62  		u := dst.NewNode()
    63  		dst.AddNode(u)
    64  		nodes = append(nodes, u)
    65  	}
    66  	for i := 0; i < n; i++ {
    67  		u := nodes[rndN(len(nodes))]
    68  		d := dst.NewNode()
    69  		did := d.ID()
    70  
    71  		// Add the duplicate node.
    72  		dst.AddNode(d)
    73  
    74  		// Loop until we have connectivity
    75  		// into the rest of the graph.
    76  		for {
    77  			// Add edges to parent's neighbours.
    78  			to := graph.NodesOf(dst.From(u.ID()))
    79  			ordered.ByID(to)
    80  			for _, v := range to {
    81  				vid := v.ID()
    82  				if rnd() < delta || dst.HasEdgeBetween(vid, did) {
    83  					continue
    84  				}
    85  				if vid < did {
    86  					dst.SetEdge(dst.NewEdge(v, d))
    87  				} else {
    88  					dst.SetEdge(dst.NewEdge(d, v))
    89  				}
    90  			}
    91  
    92  			// Add edges to old nodes.
    93  			scaledAlpha := alpha / float64(len(nodes))
    94  			for _, v := range nodes {
    95  				uid := u.ID()
    96  				vid := v.ID()
    97  				switch vid {
    98  				case uid:
    99  					if !math.IsNaN(sigma) {
   100  						if i == 0 || rnd() < sigma {
   101  							if vid < did {
   102  								dst.SetEdge(dst.NewEdge(v, d))
   103  							} else {
   104  								dst.SetEdge(dst.NewEdge(d, v))
   105  							}
   106  						}
   107  						continue
   108  					}
   109  					fallthrough
   110  				default:
   111  					if rnd() < scaledAlpha && !dst.HasEdgeBetween(vid, did) {
   112  						if vid < did {
   113  							dst.SetEdge(dst.NewEdge(v, d))
   114  						} else {
   115  							dst.SetEdge(dst.NewEdge(d, v))
   116  						}
   117  					}
   118  				}
   119  			}
   120  
   121  			if dst.From(did).Len() != 0 {
   122  				break
   123  			}
   124  		}
   125  
   126  		nodes = append(nodes, d)
   127  	}
   128  
   129  	return nil
   130  }