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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 mat_test
import (
"fmt"
"log"
"math"
"gonum.org/v1/gonum/mat"
)
func ExampleGSVD() {
// Perform a GSVD factorization on food production/consumption data for the
// three years 1990, 2000 and 2014, for Africa and Latin America/Caribbean.
//
// See Lee et al. doi:10.1371/journal.pone.0030098 and
// Alter at al. doi:10.1073/pnas.0530258100 for more details.
var gsvd mat.GSVD
ok := gsvd.Factorize(FAO.Africa, FAO.LatinAmericaCaribbean, mat.GSVDU|mat.GSVDV|mat.GSVDQ)
if !ok {
log.Fatal("GSVD factorization failed")
}
var u, v mat.Dense
gsvd.UTo(&u)
gsvd.VTo(&v)
s1 := gsvd.ValuesA(nil)
s2 := gsvd.ValuesB(nil)
fmt.Printf("Africa\n\ts1 = %.4f\n\n\tU = %.4f\n\n",
s1, mat.Formatted(&u, mat.Prefix("\t "), mat.Excerpt(2)))
fmt.Printf("Latin America/Caribbean\n\ts2 = %.4f\n\n\tV = %.4f\n",
s2, mat.Formatted(&v, mat.Prefix("\t "), mat.Excerpt(2)))
var q, zR mat.Dense
gsvd.QTo(&q)
gsvd.ZeroRTo(&zR)
q.Mul(&zR, &q)
fmt.Printf("\nCommon basis vectors\n\n\tQᵀ = %.4f\n",
mat.Formatted(q.T(), mat.Prefix("\t ")))
// Calculate the antisymmetric angular distances for each eigenvariable.
fmt.Println("\nSignificance:")
for i := 0; i < 3; i++ {
fmt.Printf("\teigenvar_%d: %+.4f\n", i, math.Atan(s1[i]/s2[i])-math.Pi/4)
}
// Output:
//
// Africa
// s1 = [1.0000 0.9344 0.5118]
//
// U = Dims(21, 21)
// ⎡-0.0005 0.0142 ... ... -0.0060 -0.0055⎤
// ⎢-0.0010 0.0019 0.0071 0.0075⎥
// .
// .
// .
// ⎢-0.0007 -0.0024 0.9999 -0.0001⎥
// ⎣-0.0010 -0.0016 ... ... -0.0001 0.9999⎦
//
// Latin America/Caribbean
// s2 = [0.0047 0.3563 0.8591]
//
// V = Dims(14, 14)
// ⎡ 0.1362 0.0008 ... ... 0.0700 0.2636⎤
// ⎢ 0.1830 -0.0040 0.2908 0.7834⎥
// .
// .
// .
// ⎢-0.2598 -0.0324 0.9339 -0.2170⎥
// ⎣-0.8386 0.1494 ... ... -0.1639 0.4121⎦
//
// Common basis vectors
//
// Qᵀ = ⎡ 14508.5881 4524.2933 -4813.9616⎤
// ⎢ 15562.9323 12397.1070 -16364.8933⎥
// ⎣-14262.7217 -10902.1488 15762.8719⎦
//
// Significance:
// eigenvar_0: +0.7807
// eigenvar_1: +0.4211
// eigenvar_2: -0.2482
}
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