mirror of
https://github.com/gonum/gonum.git
synced 2025-10-12 02:20:23 +08:00
142f1a8c6b
This is a change in design for the graph.NodesOf family of functions. The alternative was to provide an equivalent set of non-panicking routines in graph for internal use. The protection that was intended with the panic was to panic early rather than late when an indeterminate iterator exhausts slice index space. I think in hindsight this was an error and we should let things blow up in that (likely rare) situation. The majority of changes are in test code. Outside the iterator package, which is intimately tied to the determined iterator implementations, only one test now fails if an indeterminate iterator is used, product's Modular extended sub-graph isomorphism example, which is an algorithm that would have time complexity issues with large iterators anyway.
134 lines
3.4 KiB
Go
134 lines
3.4 KiB
Go
// Copyright ©2017 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 spectral
|
|
|
|
import (
|
|
"math"
|
|
|
|
"gonum.org/v1/gonum/graph"
|
|
"gonum.org/v1/gonum/mat"
|
|
)
|
|
|
|
// Laplacian is a graph Laplacian matrix.
|
|
type Laplacian struct {
|
|
// Matrix holds the Laplacian matrix.
|
|
mat.Matrix
|
|
|
|
// Nodes holds the input graph nodes.
|
|
Nodes []graph.Node
|
|
|
|
// Index is a mapping from the graph
|
|
// node IDs to row and column indices.
|
|
Index map[int64]int
|
|
}
|
|
|
|
// NewLaplacian returns a Laplacian matrix for the simple undirected graph g.
|
|
// The Laplacian is defined as D-A where D is a diagonal matrix holding the
|
|
// degree of each node and A is the graph adjacency matrix of the input graph.
|
|
// If g contains self edges, NewLaplacian will panic.
|
|
func NewLaplacian(g graph.Undirected) Laplacian {
|
|
nodes := graph.NodesOf(g.Nodes())
|
|
indexOf := make(map[int64]int, len(nodes))
|
|
for i, n := range nodes {
|
|
id := n.ID()
|
|
indexOf[id] = i
|
|
}
|
|
|
|
l := mat.NewSymDense(len(nodes), nil)
|
|
for j, u := range nodes {
|
|
uid := u.ID()
|
|
to := graph.NodesOf(g.From(uid))
|
|
l.SetSym(j, j, float64(len(to)))
|
|
for _, v := range to {
|
|
vid := v.ID()
|
|
if uid == vid {
|
|
panic("network: self edge in graph")
|
|
}
|
|
if uid < vid {
|
|
l.SetSym(indexOf[vid], j, -1)
|
|
}
|
|
}
|
|
}
|
|
|
|
return Laplacian{Matrix: l, Nodes: nodes, Index: indexOf}
|
|
}
|
|
|
|
// NewSymNormLaplacian returns a symmetric normalized Laplacian matrix for the
|
|
// simple undirected graph g.
|
|
// The normalized Laplacian is defined as I-D^(-1/2)AD^(-1/2) where D is a
|
|
// diagonal matrix holding the degree of each node and A is the graph adjacency
|
|
// matrix of the input graph.
|
|
// If g contains self edges, NewSymNormLaplacian will panic.
|
|
func NewSymNormLaplacian(g graph.Undirected) Laplacian {
|
|
nodes := graph.NodesOf(g.Nodes())
|
|
indexOf := make(map[int64]int, len(nodes))
|
|
for i, n := range nodes {
|
|
id := n.ID()
|
|
indexOf[id] = i
|
|
}
|
|
|
|
l := mat.NewSymDense(len(nodes), nil)
|
|
for j, u := range nodes {
|
|
uid := u.ID()
|
|
to := graph.NodesOf(g.From(uid))
|
|
if len(to) == 0 {
|
|
continue
|
|
}
|
|
l.SetSym(j, j, 1)
|
|
squdeg := math.Sqrt(float64(len(to)))
|
|
for _, v := range to {
|
|
vid := v.ID()
|
|
if uid == vid {
|
|
panic("network: self edge in graph")
|
|
}
|
|
if uid < vid {
|
|
to := g.From(vid)
|
|
k := to.Len()
|
|
if k < 0 {
|
|
k = len(graph.NodesOf(to))
|
|
}
|
|
l.SetSym(indexOf[vid], j, -1/(squdeg*math.Sqrt(float64(k))))
|
|
}
|
|
}
|
|
}
|
|
|
|
return Laplacian{Matrix: l, Nodes: nodes, Index: indexOf}
|
|
}
|
|
|
|
// NewRandomWalkLaplacian returns a damp-scaled random walk Laplacian matrix for
|
|
// the simple graph g.
|
|
// The random walk Laplacian is defined as I-D^(-1)A where D is a diagonal matrix
|
|
// holding the degree of each node and A is the graph adjacency matrix of the input
|
|
// graph.
|
|
// If g contains self edges, NewRandomWalkLaplacian will panic.
|
|
func NewRandomWalkLaplacian(g graph.Graph, damp float64) Laplacian {
|
|
nodes := graph.NodesOf(g.Nodes())
|
|
indexOf := make(map[int64]int, len(nodes))
|
|
for i, n := range nodes {
|
|
id := n.ID()
|
|
indexOf[id] = i
|
|
}
|
|
|
|
l := mat.NewDense(len(nodes), len(nodes), nil)
|
|
for j, u := range nodes {
|
|
uid := u.ID()
|
|
to := graph.NodesOf(g.From(uid))
|
|
if len(to) == 0 {
|
|
continue
|
|
}
|
|
l.Set(j, j, 1-damp)
|
|
rudeg := (damp - 1) / float64(len(to))
|
|
for _, v := range to {
|
|
vid := v.ID()
|
|
if uid == vid {
|
|
panic("network: self edge in graph")
|
|
}
|
|
l.Set(indexOf[vid], j, rudeg)
|
|
}
|
|
}
|
|
|
|
return Laplacian{Matrix: l, Nodes: nodes, Index: indexOf}
|
|
}
|