github.com/gonum/lapack@v0.0.0-20181123203213-e4cdc5a0bff9/testlapack/dgeqr2.go (about)

     1  // Copyright ©2015 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 testlapack
     6  
     7  import (
     8  	"math"
     9  	"math/rand"
    10  	"testing"
    11  
    12  	"github.com/gonum/blas"
    13  	"github.com/gonum/blas/blas64"
    14  	"github.com/gonum/floats"
    15  )
    16  
    17  type Dgeqr2er interface {
    18  	Dgeqr2(m, n int, a []float64, lda int, tau []float64, work []float64)
    19  }
    20  
    21  func Dgeqr2Test(t *testing.T, impl Dgeqr2er) {
    22  	rnd := rand.New(rand.NewSource(1))
    23  	for c, test := range []struct {
    24  		m, n, lda int
    25  	}{
    26  		{1, 1, 0},
    27  		{2, 2, 0},
    28  		{3, 2, 0},
    29  		{2, 3, 0},
    30  		{1, 12, 0},
    31  		{2, 6, 0},
    32  		{3, 4, 0},
    33  		{4, 3, 0},
    34  		{6, 2, 0},
    35  		{12, 1, 0},
    36  		{1, 1, 20},
    37  		{2, 2, 20},
    38  		{3, 2, 20},
    39  		{2, 3, 20},
    40  		{1, 12, 20},
    41  		{2, 6, 20},
    42  		{3, 4, 20},
    43  		{4, 3, 20},
    44  		{6, 2, 20},
    45  		{12, 1, 20},
    46  	} {
    47  		n := test.n
    48  		m := test.m
    49  		lda := test.lda
    50  		if lda == 0 {
    51  			lda = test.n
    52  		}
    53  		a := make([]float64, m*lda)
    54  		for i := range a {
    55  			a[i] = rnd.Float64()
    56  		}
    57  		aCopy := make([]float64, len(a))
    58  		k := min(m, n)
    59  		tau := make([]float64, k)
    60  		for i := range tau {
    61  			tau[i] = rnd.Float64()
    62  		}
    63  		work := make([]float64, n)
    64  		for i := range work {
    65  			work[i] = rnd.Float64()
    66  		}
    67  		copy(aCopy, a)
    68  		impl.Dgeqr2(m, n, a, lda, tau, work)
    69  
    70  		// Test that the QR factorization has completed successfully. Compute
    71  		// Q based on the vectors.
    72  		q := constructQ("QR", m, n, a, lda, tau)
    73  
    74  		// Check that q is orthonormal
    75  		for i := 0; i < m; i++ {
    76  			nrm := blas64.Nrm2(m, blas64.Vector{Inc: 1, Data: q.Data[i*m:]})
    77  			if math.Abs(nrm-1) > 1e-14 {
    78  				t.Errorf("Case %v, q not normal", c)
    79  			}
    80  			for j := 0; j < i; j++ {
    81  				dot := blas64.Dot(m, blas64.Vector{Inc: 1, Data: q.Data[i*m:]}, blas64.Vector{Inc: 1, Data: q.Data[j*m:]})
    82  				if math.Abs(dot) > 1e-14 {
    83  					t.Errorf("Case %v, q not orthogonal", c)
    84  				}
    85  			}
    86  		}
    87  		// Check that A = Q * R
    88  		r := blas64.General{
    89  			Rows:   m,
    90  			Cols:   n,
    91  			Stride: n,
    92  			Data:   make([]float64, m*n),
    93  		}
    94  		for i := 0; i < m; i++ {
    95  			for j := i; j < n; j++ {
    96  				r.Data[i*n+j] = a[i*lda+j]
    97  			}
    98  		}
    99  		atmp := blas64.General{
   100  			Rows:   m,
   101  			Cols:   n,
   102  			Stride: lda,
   103  			Data:   make([]float64, m*lda),
   104  		}
   105  		copy(atmp.Data, a)
   106  		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, q, r, 0, atmp)
   107  		if !floats.EqualApprox(atmp.Data, aCopy, 1e-14) {
   108  			t.Errorf("Q*R != a")
   109  		}
   110  	}
   111  }