spectral: new package for spectral graph analysis

Initial commit to this is just a move of the Laplacian type from network.

graph/network/diffusion_test.go

@@ -6,15 +6,12 @@ package network
 
 import (
 	"math"
-	"sort"
 	"testing"
 
 	"gonum.org/v1/gonum/floats"
 	"gonum.org/v1/gonum/graph"
-	"gonum.org/v1/gonum/graph/internal/ordered"
-	"gonum.org/v1/gonum/graph/iterator"
 	"gonum.org/v1/gonum/graph/simple"
-	"gonum.org/v1/gonum/mat"
+	"gonum.org/v1/gonum/graph/spectral"
 )
 
 var diffuseTests = []struct {
@@ -160,7 +157,7 @@ func TestDiffuse(t *testing.T) {
 				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
 			}
 		}
-		for j, lfn := range []func(g graph.Undirected) Laplacian{NewLaplacian, NewSymNormLaplacian} {
+		for j, lfn := range []func(g graph.Undirected) spectral.Laplacian{spectral.NewLaplacian, spectral.NewSymNormLaplacian} {
 			normalize := j == 1
 			var wantTemp float64
 			for _, v := range test.h {
@@ -194,123 +191,6 @@ func TestDiffuse(t *testing.T) {
 	}
 }
 
-var randomWalkLaplacianTests = []struct {
-	g    []set
-	damp float64
-
-	want *mat.Dense
-}{
-	{
-		g: []set{
-			A: linksTo(B, C),
-			B: linksTo(C),
-			C: nil,
-		},
-
-		want: mat.NewDense(3, 3, []float64{
-			1, 0, 0,
-			-0.5, 1, 0,
-			-0.5, -1, 0,
-		}),
-	},
-	{
-		g: []set{
-			A: linksTo(B, C),
-			B: linksTo(C),
-			C: nil,
-		},
-		damp: 0.85,
-
-		want: mat.NewDense(3, 3, []float64{
-			0.15, 0, 0,
-			-0.075, 0.15, 0,
-			-0.075, -0.15, 0,
-		}),
-	},
-	{
-		g: []set{
-			A: linksTo(B),
-			B: linksTo(C),
-			C: linksTo(A),
-		},
-		damp: 0.85,
-
-		want: mat.NewDense(3, 3, []float64{
-			0.15, 0, -0.15,
-			-0.15, 0.15, 0,
-			0, -0.15, 0.15,
-		}),
-	},
-	{
-		// Example graph from http://en.wikipedia.org/wiki/File:PageRanks-Example.svg 16:17, 8 July 2009
-		g: []set{
-			A: nil,
-			B: linksTo(C),
-			C: linksTo(B),
-			D: linksTo(A, B),
-			E: linksTo(D, B, F),
-			F: linksTo(B, E),
-			G: linksTo(B, E),
-			H: linksTo(B, E),
-			I: linksTo(B, E),
-			J: linksTo(E),
-			K: linksTo(E),
-		},
-
-		want: mat.NewDense(11, 11, []float64{
-			0, 0, 0, -0.5, 0, 0, 0, 0, 0, 0, 0,
-			0, 1, -1, -0.5, -1. / 3., -0.5, -0.5, -0.5, -0.5, 0, 0,
-			0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0,
-			0, 0, 0, 1, -1. / 3., 0, 0, 0, 0, 0, 0,
-			0, 0, 0, 0, 1, -0.5, -0.5, -0.5, -0.5, -1, -1,
-			0, 0, 0, 0, -1. / 3., 1, 0, 0, 0, 0, 0,
-			0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
-			0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
-			0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
-			0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
-			0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
-		}),
-	},
-}
-
-func TestRandomWalkLaplacian(t *testing.T) {
-	const tol = 1e-14
-	for i, test := range randomWalkLaplacianTests {
-		g := simple.NewDirectedGraph()
-		for u, e := range test.g {
-			// Add nodes that are not defined by an edge.
-			if g.Node(int64(u)) == nil {
-				g.AddNode(simple.Node(u))
-			}
-			for v := range e {
-				g.SetEdge(simple.Edge{F: simple.Node(u), T: simple.Node(v)})
-			}
-		}
-		l := NewRandomWalkLaplacian(g, test.damp)
-		_, c := l.Dims()
-		for j := 0; j < c; j++ {
-			if got := mat.Sum(l.Matrix.(*mat.Dense).ColView(j)); !floats.EqualWithinAbsOrRel(got, 0, tol, tol) {
-				t.Errorf("unexpected column sum for test %d, column %d: got:%v want:0", i, j, got)
-			}
-		}
-		l = NewRandomWalkLaplacian(sortedNodeGraph{g}, test.damp)
-		if !mat.EqualApprox(l, test.want, tol) {
-			t.Errorf("unexpected result for test %d:\ngot:\n% .2v\nwant:\n% .2v",
-				i, mat.Formatted(l), mat.Formatted(test.want))
-		}
-	}
-}
-
-type sortedNodeGraph struct {
-	graph.Graph
-}
-
-func (g sortedNodeGraph) Nodes() graph.Nodes {
-	n := graph.NodesOf(g.Graph.Nodes())
-	sort.Sort(ordered.ByID(n))
-	return iterator.NewOrderedNodes(n)
-}
-
 var diffuseToEquilibriumTests = []struct {
 	g       []set
 	builder builder
@@ -478,7 +358,7 @@ func TestDiffuseToEquilibrium(t *testing.T) {
 		for _, v := range test.h {
 			wantTemp += v
 		}
-		got, ok := DiffuseToEquilibrium(nil, test.h, NewRandomWalkLaplacian(g, test.damp), test.tol*test.tol, test.iter)
+		got, ok := DiffuseToEquilibrium(nil, test.h, spectral.NewRandomWalkLaplacian(g, test.damp), test.tol*test.tol, test.iter)
 		if ok != test.wantOK {
 			t.Errorf("unexpected success value for test %d: got:%t want:%t", i, ok, test.wantOK)
 		}