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// 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 (
"testing"
"gonum.org/v1/gonum/floats/scalar"
"gonum.org/v1/gonum/graph"
"gonum.org/v1/gonum/graph/iterator"
"gonum.org/v1/gonum/graph/simple"
"gonum.org/v1/gonum/internal/order"
"gonum.org/v1/gonum/mat"
)
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)); !scalar.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())
order.ByID(n)
return iterator.NewOrderedNodes(n)
}
const (
A = iota
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
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W
X
Y
Z
)
// set is an integer set.
type set map[int64]struct{}
func linksTo(i ...int64) set {
if len(i) == 0 {
return nil
}
s := make(set)
for _, v := range i {
s[v] = struct{}{}
}
return s
}
|
