github.com/jingcheng-WU/gonum@v0.9.1-0.20210323123734-f1a2a11a8f7b/lapack/testlapack/dgerqf.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  	"fmt"
     9  	"testing"
    10  
    11  	"golang.org/x/exp/rand"
    12  
    13  	"github.com/jingcheng-WU/gonum/blas"
    14  	"github.com/jingcheng-WU/gonum/blas/blas64"
    15  	"github.com/jingcheng-WU/gonum/lapack"
    16  )
    17  
    18  type Dgerqfer interface {
    19  	Dgerqf(m, n int, a []float64, lda int, tau, work []float64, lwork int)
    20  }
    21  
    22  func DgerqfTest(t *testing.T, impl Dgerqfer) {
    23  	rnd := rand.New(rand.NewSource(1))
    24  	for _, m := range []int{0, 1, 2, 3, 4, 5, 6, 12, 129, 160} {
    25  		for _, n := range []int{0, 1, 2, 3, 4, 5, 6, 12, 129, 160} {
    26  			for _, lda := range []int{max(1, n), n + 4} {
    27  				dgerqfTest(t, impl, rnd, m, n, lda)
    28  			}
    29  		}
    30  	}
    31  }
    32  
    33  func dgerqfTest(t *testing.T, impl Dgerqfer, rnd *rand.Rand, m, n, lda int) {
    34  	const tol = 1e-14
    35  
    36  	a := randomGeneral(m, n, lda, rnd)
    37  	aCopy := cloneGeneral(a)
    38  
    39  	k := min(m, n)
    40  	tau := make([]float64, k)
    41  	for i := range tau {
    42  		tau[i] = rnd.Float64()
    43  	}
    44  
    45  	work := []float64{0}
    46  	impl.Dgerqf(m, n, a.Data, a.Stride, tau, work, -1)
    47  	lwkopt := int(work[0])
    48  	for _, wk := range []struct {
    49  		name   string
    50  		length int
    51  	}{
    52  		{name: "short", length: m},
    53  		{name: "medium", length: lwkopt - 1},
    54  		{name: "long", length: lwkopt},
    55  	} {
    56  		name := fmt.Sprintf("m=%d,n=%d,lda=%d,work=%v", m, n, lda, wk.name)
    57  
    58  		lwork := max(max(1, m), wk.length)
    59  		work = make([]float64, lwork)
    60  		for i := range work {
    61  			work[i] = rnd.Float64()
    62  		}
    63  
    64  		copyGeneral(a, aCopy)
    65  		impl.Dgerqf(m, n, a.Data, a.Stride, tau, work, lwork)
    66  
    67  		// Test that the RQ factorization has completed successfully. Compute
    68  		// Q based on the vectors.
    69  		q := constructQ("RQ", m, n, a.Data, a.Stride, tau)
    70  
    71  		// Check that Q is orthogonal.
    72  		if resid := residualOrthogonal(q, false); resid > tol*float64(m) {
    73  			t.Errorf("Case %v: Q not orthogonal; resid=%v, want<=%v", name, resid, tol*float64(m))
    74  		}
    75  
    76  		// Check that A = R * Q
    77  		r := zeros(m, n, n)
    78  		for i := 0; i < m; i++ {
    79  			off := m - n
    80  			for j := max(0, i-off); j < n; j++ {
    81  				r.Data[i*r.Stride+j] = a.Data[i*a.Stride+j]
    82  			}
    83  		}
    84  		qra := cloneGeneral(aCopy)
    85  		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, r, q, -1, qra)
    86  		resid := dlange(lapack.MaxColumnSum, qra.Rows, qra.Cols, qra.Data, qra.Stride)
    87  		if resid > tol*float64(m) {
    88  			t.Errorf("Case %v: |R*Q - A|=%v, want<=%v", name, resid, tol*float64(m))
    89  		}
    90  	}
    91  }