graph/spectral: add some examples
diff --git a/graph/spectral/spectral_example_test.go b/graph/spectral/spectral_example_test.go
new file mode 100644
index 0000000..64ee078
--- /dev/null
+++ b/graph/spectral/spectral_example_test.go
@@ -0,0 +1,147 @@
+// Copyright ©2019 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_test
+
+import (
+ "fmt"
+ "math"
+
+ "gonum.org/v1/gonum/graph"
+ "gonum.org/v1/gonum/graph/simple"
+ "gonum.org/v1/gonum/graph/spectral"
+ "gonum.org/v1/gonum/mat"
+)
+
+func Example_cospectral() {
+ // Output the spectra of two isospectral enneahedra.
+ // https://commons.wikimedia.org/wiki/File:Isospectral_enneahedra.svg
+
+ enneahedron1 := simple.NewUndirectedMatrix(8, 0, 0, 0)
+ for _, e := range []simple.Edge{
+ {F: simple.Node(0), T: simple.Node(1)},
+ {F: simple.Node(0), T: simple.Node(2)},
+ {F: simple.Node(0), T: simple.Node(6)},
+ {F: simple.Node(1), T: simple.Node(2)},
+ {F: simple.Node(1), T: simple.Node(3)},
+ {F: simple.Node(1), T: simple.Node(5)},
+ {F: simple.Node(1), T: simple.Node(7)},
+ {F: simple.Node(2), T: simple.Node(3)},
+ {F: simple.Node(2), T: simple.Node(6)},
+ {F: simple.Node(3), T: simple.Node(4)},
+ {F: simple.Node(4), T: simple.Node(5)},
+ {F: simple.Node(4), T: simple.Node(6)},
+ {F: simple.Node(5), T: simple.Node(6)},
+ {F: simple.Node(5), T: simple.Node(7)},
+ {F: simple.Node(6), T: simple.Node(7)},
+ } {
+ enneahedron1.SetEdge(e)
+ }
+
+ enneahedron2 := simple.NewUndirectedMatrix(8, 0, 0, 0)
+ for _, e := range []simple.Edge{
+ {F: simple.Node(0), T: simple.Node(1)},
+ {F: simple.Node(0), T: simple.Node(2)},
+ {F: simple.Node(0), T: simple.Node(6)},
+ {F: simple.Node(1), T: simple.Node(2)},
+ {F: simple.Node(1), T: simple.Node(3)},
+ {F: simple.Node(1), T: simple.Node(7)},
+ {F: simple.Node(2), T: simple.Node(3)},
+ {F: simple.Node(2), T: simple.Node(4)},
+ {F: simple.Node(2), T: simple.Node(5)},
+ {F: simple.Node(3), T: simple.Node(5)},
+ {F: simple.Node(4), T: simple.Node(5)},
+ {F: simple.Node(4), T: simple.Node(6)},
+ {F: simple.Node(5), T: simple.Node(6)},
+ {F: simple.Node(5), T: simple.Node(7)},
+ {F: simple.Node(6), T: simple.Node(7)},
+ } {
+ enneahedron2.SetEdge(e)
+ }
+
+ for _, en := range []*simple.UndirectedMatrix{
+ enneahedron1,
+ enneahedron2,
+ } {
+ var ed mat.EigenSym
+ ed.Factorize(en.Matrix().(mat.Symmetric), false)
+ fmt.Printf("%.2f\n", ed.Values(nil))
+ }
+
+ // Output:
+ // [-2.41 -2.10 -1.25 -0.74 0.48 0.77 1.36 3.88]
+ // [-2.41 -2.10 -1.25 -0.74 0.48 0.77 1.36 3.88]
+}
+
+func Example_connecting() {
+ g := simple.NewUndirectedMatrix(8, 0, 0, 0)
+ edges := []graph.Edge{
+ nil,
+
+ // Left lobe.
+ simple.Edge{F: simple.Node(0), T: simple.Node(1)},
+ simple.Edge{F: simple.Node(0), T: simple.Node(2)},
+ simple.Edge{F: simple.Node(0), T: simple.Node(3)},
+ simple.Edge{F: simple.Node(1), T: simple.Node(2)},
+ simple.Edge{F: simple.Node(1), T: simple.Node(3)},
+ simple.Edge{F: simple.Node(2), T: simple.Node(3)},
+
+ // Right lobe.
+ simple.Edge{F: simple.Node(4), T: simple.Node(5)},
+ simple.Edge{F: simple.Node(4), T: simple.Node(6)},
+ simple.Edge{F: simple.Node(4), T: simple.Node(7)},
+ simple.Edge{F: simple.Node(5), T: simple.Node(6)},
+ simple.Edge{F: simple.Node(5), T: simple.Node(7)},
+ simple.Edge{F: simple.Node(6), T: simple.Node(7)},
+
+ // Bridge.
+ simple.Edge{F: simple.Node(0), T: simple.Node(4)},
+ }
+ fmt.Println("eigenvalues as edges are added:")
+ for i, e := range edges {
+ if e != nil {
+ g.SetEdge(e)
+ }
+
+ l := spectral.NewLaplacian(g)
+ var ed mat.EigenSym
+ ed.Factorize(l.Matrix.(mat.Symmetric), i == len(edges)-1)
+ vals := ed.Values(nil)
+ for i, v := range vals {
+ // Zero-out near zero values.
+ if math.Abs(v) < 1e-15 {
+ vals[i] = 0
+ }
+ }
+ fmt.Printf(" %2.1f\n", vals)
+
+ if i == len(edges)-1 {
+ var vecs mat.Dense
+ ed.VectorsTo(&vecs)
+ fiedler := vecs.ColView(1)
+ fmt.Println("Fiedler vector after joining lobes:")
+ fmt.Printf(" %2.2f\n", mat.Formatted(fiedler.T()))
+ }
+
+ }
+
+ // Output:
+ // eigenvalues as edges are added:
+ // [0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0]
+ // [0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.0]
+ // [0.0 0.0 0.0 0.0 0.0 0.0 1.0 3.0]
+ // [0.0 0.0 0.0 0.0 0.0 1.0 1.0 4.0]
+ // [0.0 0.0 0.0 0.0 0.0 1.0 3.0 4.0]
+ // [0.0 0.0 0.0 0.0 0.0 2.0 4.0 4.0]
+ // [0.0 0.0 0.0 0.0 0.0 4.0 4.0 4.0]
+ // [0.0 0.0 0.0 0.0 2.0 4.0 4.0 4.0]
+ // [0.0 0.0 0.0 1.0 3.0 4.0 4.0 4.0]
+ // [0.0 0.0 1.0 1.0 4.0 4.0 4.0 4.0]
+ // [0.0 0.0 1.0 3.0 4.0 4.0 4.0 4.0]
+ // [0.0 0.0 2.0 4.0 4.0 4.0 4.0 4.0]
+ // [0.0 0.0 4.0 4.0 4.0 4.0 4.0 4.0]
+ // [0.0 0.4 4.0 4.0 4.0 4.0 4.0 5.6]
+ // Fiedler vector after joining lobes:
+ // [ 0.25 0.38 0.38 0.38 -0.25 -0.38 -0.38 -0.38]
+}
