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

     1  // Copyright ©2020 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  
    11  	"github.com/jingcheng-WU/gonum/mat"
    12  )
    13  
    14  func ExampleSVD_SolveTo() {
    15  	// The system described by A is rank deficient.
    16  	a := mat.NewDense(5, 3, []float64{
    17  		-1.7854591879711257, -0.42687285925779594, -0.12730256811265162,
    18  		-0.5728984211439724, -0.10093393134001777, -0.1181901192353067,
    19  		1.2484316018707418, 0.5646683943038734, -0.48229492403243485,
    20  		0.10174927665169475, -0.5805410929482445, 1.3054473231942054,
    21  		-1.134174808195733, -0.4732430202414438, 0.3528489486370508,
    22  	})
    23  
    24  	// Perform an SVD retaining all singular vectors.
    25  	var svd mat.SVD
    26  	ok := svd.Factorize(a, mat.SVDFull)
    27  	if !ok {
    28  		log.Fatal("failed to factorize A")
    29  	}
    30  
    31  	// Determine the rank of the A matrix with a near zero condition threshold.
    32  	const rcond = 1e-15
    33  	rank := svd.Rank(rcond)
    34  	if rank == 0 {
    35  		log.Fatal("zero rank system")
    36  	}
    37  
    38  	b := mat.NewDense(5, 2, []float64{
    39  		-2.318, -4.35,
    40  		-0.715, 1.451,
    41  		1.836, -0.119,
    42  		-0.357, 3.094,
    43  		-1.636, 0.021,
    44  	})
    45  
    46  	// Find a least-squares solution using the determined parts of the system.
    47  	var x mat.Dense
    48  	svd.SolveTo(&x, b, rank)
    49  
    50  	fmt.Printf("singular values = %v\nrank = %d\nx = %.15f",
    51  		format(svd.Values(nil), 4, rcond), rank, mat.Formatted(&x, mat.Prefix("    ")))
    52  
    53  	// Output:
    54  	// singular values = [2.685 1.526 <1e-15]
    55  	// rank = 2
    56  	// x = ⎡ 1.212064313552347   1.507467451093930⎤
    57  	//     ⎢ 0.415400738264774  -0.624498607705372⎥
    58  	//     ⎣-0.183184442255280   2.221334193689124⎦
    59  }
    60  
    61  func ExampleSVD_SolveVecTo() {
    62  	// The system described by A is rank deficient.
    63  	a := mat.NewDense(5, 3, []float64{
    64  		-1.7854591879711257, -0.42687285925779594, -0.12730256811265162,
    65  		-0.5728984211439724, -0.10093393134001777, -0.1181901192353067,
    66  		1.2484316018707418, 0.5646683943038734, -0.48229492403243485,
    67  		0.10174927665169475, -0.5805410929482445, 1.3054473231942054,
    68  		-1.134174808195733, -0.4732430202414438, 0.3528489486370508,
    69  	})
    70  
    71  	// Perform an SVD retaining all singular vectors.
    72  	var svd mat.SVD
    73  	ok := svd.Factorize(a, mat.SVDFull)
    74  	if !ok {
    75  		log.Fatal("failed to factorize A")
    76  	}
    77  
    78  	// Determine the rank of the A matrix with a near zero condition threshold.
    79  	const rcond = 1e-15
    80  	rank := svd.Rank(rcond)
    81  	if rank == 0 {
    82  		log.Fatal("zero rank system")
    83  	}
    84  
    85  	b := mat.NewVecDense(5, []float64{-2.318, -0.715, 1.836, -0.357, -1.636})
    86  
    87  	// Find a least-squares solution using the determined parts of the system.
    88  	var x mat.VecDense
    89  	svd.SolveVecTo(&x, b, rank)
    90  
    91  	fmt.Printf("singular values = %v\nrank = %d\nx = %.15f",
    92  		format(svd.Values(nil), 4, rcond), rank, mat.Formatted(&x, mat.Prefix("    ")))
    93  
    94  	// Output:
    95  	// singular values = [2.685 1.526 <1e-15]
    96  	// rank = 2
    97  	// x = ⎡ 1.212064313552347⎤
    98  	//     ⎢ 0.415400738264774⎥
    99  	//     ⎣-0.183184442255280⎦
   100  }
   101  
   102  func format(vals []float64, prec int, eps float64) []string {
   103  	s := make([]string, len(vals))
   104  	for i, v := range vals {
   105  		if v < eps {
   106  			s[i] = fmt.Sprintf("<%.*g", prec, eps)
   107  			continue
   108  		}
   109  		s[i] = fmt.Sprintf("%.*g", prec, v)
   110  	}
   111  	return s
   112  }