mat: add examples for Eigen and EigenSym

mat/eigen_example_test.go

@@ -0,0 +1,65 @@
+// Copyright ©2018 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 mat_test
+
+import (
+	"fmt"
+	"log"
+
+	"gonum.org/v1/gonum/mat"
+)
+
+func ExampleEigenSym() {
+	a := mat.NewSymDense(2, []float64{
+		7, 0.5,
+		0.5, 1,
+	})
+	fmt.Printf("A = %v\n\n", mat.Formatted(a, mat.Prefix("    ")))
+
+	var eigsym mat.EigenSym
+	ok := eigsym.Factorize(a, true)
+	if !ok {
+		log.Fatal("Symmetric eigendecomposition failed")
+	}
+	fmt.Printf("Eigenvalues of A:\n%1.3f\n\n", eigsym.Values(nil))
+
+	var ev mat.Dense
+	ev.EigenvectorsSym(&eigsym)
+	fmt.Printf("Eigenvectors of A:\n%1.3f\n\n", mat.Formatted(&ev))
+
+	// Output:
+	// A = ⎡  7  0.5⎤
+	//     ⎣0.5    1⎦
+	//
+	// Eigenvalues of A:
+	// [0.959 7.041]
+	//
+	// Eigenvectors of A:
+	// ⎡ 0.082  -0.997⎤
+	// ⎣-0.997  -0.082⎦
+	//
+}
+
+func ExampleEigen() {
+	a := mat.NewDense(2, 2, []float64{
+		1, -1,
+		1, 1,
+	})
+	fmt.Printf("A = %v\n\n", mat.Formatted(a, mat.Prefix("    ")))
+
+	var eig mat.Eigen
+	ok := eig.Factorize(a, true, false)
+	if !ok {
+		log.Fatal("Eigendecomposition failed")
+	}
+	fmt.Printf("Eigenvalues of A:\n%v\n", eig.Values(nil))
+
+	// Output:
+	// A = ⎡ 1  -1⎤
+	//     ⎣ 1   1⎦
+	//
+	// Eigenvalues of A:
+	// [(1+1i) (1-1i)]
+}