github.com/jingcheng-WU/gonum@v0.9.1-0.20210323123734-f1a2a11a8f7b/mat/gsvd_example_test.go (about)

     1  // Copyright ©2017 The Gonum Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package mat_test
     6  
     7  import (
     8  	"fmt"
     9  	"log"
    10  	"math"
    11  
    12  	"github.com/jingcheng-WU/gonum/mat"
    13  )
    14  
    15  func ExampleGSVD() {
    16  	// Perform a GSVD factorization on food production/consumption data for the
    17  	// three years 1990, 2000 and 2014, for Africa and Latin America/Caribbean.
    18  	//
    19  	// See Lee et al. doi:10.1371/journal.pone.0030098 and
    20  	// Alter at al. doi:10.1073/pnas.0530258100 for more details.
    21  	var gsvd mat.GSVD
    22  	ok := gsvd.Factorize(FAO.Africa, FAO.LatinAmericaCaribbean, mat.GSVDU|mat.GSVDV|mat.GSVDQ)
    23  	if !ok {
    24  		log.Fatal("GSVD factorization failed")
    25  	}
    26  	var u, v mat.Dense
    27  	gsvd.UTo(&u)
    28  	gsvd.VTo(&v)
    29  
    30  	s1 := gsvd.ValuesA(nil)
    31  	s2 := gsvd.ValuesB(nil)
    32  
    33  	fmt.Printf("Africa\n\ts1 = %.4f\n\n\tU = %.4f\n\n",
    34  		s1, mat.Formatted(&u, mat.Prefix("\t    "), mat.Excerpt(2)))
    35  	fmt.Printf("Latin America/Caribbean\n\ts2 = %.4f\n\n\tV = %.4f\n",
    36  		s2, mat.Formatted(&v, mat.Prefix("\t    "), mat.Excerpt(2)))
    37  
    38  	var q, zR mat.Dense
    39  	gsvd.QTo(&q)
    40  	gsvd.ZeroRTo(&zR)
    41  	q.Mul(&zR, &q)
    42  	fmt.Printf("\nCommon basis vectors\n\n\tQᵀ = %.4f\n",
    43  		mat.Formatted(q.T(), mat.Prefix("\t     ")))
    44  
    45  	// Calculate the antisymmetric angular distances for each eigenvariable.
    46  	fmt.Println("\nSignificance:")
    47  	for i := 0; i < 3; i++ {
    48  		fmt.Printf("\teigenvar_%d: %+.4f\n", i, math.Atan(s1[i]/s2[i])-math.Pi/4)
    49  	}
    50  
    51  	// Output:
    52  	//
    53  	// Africa
    54  	// 	s1 = [1.0000 0.9344 0.5118]
    55  	//
    56  	// 	U = Dims(21, 21)
    57  	// 	    ⎡-0.0005   0.0142  ...  ...  -0.0060  -0.0055⎤
    58  	// 	    ⎢-0.0010   0.0019             0.0071   0.0075⎥
    59  	// 	     .
    60  	// 	     .
    61  	// 	     .
    62  	// 	    ⎢-0.0007  -0.0024             0.9999  -0.0001⎥
    63  	// 	    ⎣-0.0010  -0.0016  ...  ...  -0.0001   0.9999⎦
    64  	//
    65  	// Latin America/Caribbean
    66  	// 	s2 = [0.0047 0.3563 0.8591]
    67  	//
    68  	// 	V = Dims(14, 14)
    69  	// 	    ⎡ 0.1362   0.0008  ...  ...   0.0700   0.2636⎤
    70  	// 	    ⎢ 0.1830  -0.0040             0.2908   0.7834⎥
    71  	// 	     .
    72  	// 	     .
    73  	// 	     .
    74  	// 	    ⎢-0.2598  -0.0324             0.9339  -0.2170⎥
    75  	// 	    ⎣-0.8386   0.1494  ...  ...  -0.1639   0.4121⎦
    76  	//
    77  	// Common basis vectors
    78  	//
    79  	// 	Qᵀ = ⎡ 14508.5881    4524.2933   -4813.9616⎤
    80  	// 	     ⎢ 15562.9323   12397.1070  -16364.8933⎥
    81  	// 	     ⎣-14262.7217  -10902.1488   15762.8719⎦
    82  	//
    83  	// Significance:
    84  	// 	eigenvar_0: +0.7807
    85  	// 	eigenvar_1: +0.4211
    86  	// 	eigenvar_2: -0.2482
    87  }