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

     1  // Copyright ©2016 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  	"math"
    10  	"math/rand"
    11  	"testing"
    12  
    13  	"github.com/gonum/blas"
    14  	"github.com/gonum/blas/blas64"
    15  )
    16  
    17  type Dorghrer interface {
    18  	Dorghr(n, ilo, ihi int, a []float64, lda int, tau, work []float64, lwork int)
    19  
    20  	Dgehrder
    21  }
    22  
    23  func DorghrTest(t *testing.T, impl Dorghrer) {
    24  	rnd := rand.New(rand.NewSource(1))
    25  
    26  	for _, n := range []int{1, 2, 3, 4, 5, 6, 7, 8, 23, 34} {
    27  		for _, extra := range []int{0, 1, 13} {
    28  			for _, optwork := range []bool{true, false} {
    29  				for cas := 0; cas < 100; cas++ {
    30  					ilo := rnd.Intn(n)
    31  					ihi := rnd.Intn(n)
    32  					if ilo > ihi {
    33  						ilo, ihi = ihi, ilo
    34  					}
    35  					testDorghr(t, impl, n, ilo, ihi, extra, optwork, rnd)
    36  				}
    37  			}
    38  		}
    39  	}
    40  	testDorghr(t, impl, 0, 0, -1, 0, false, rnd)
    41  	testDorghr(t, impl, 0, 0, -1, 0, true, rnd)
    42  }
    43  
    44  func testDorghr(t *testing.T, impl Dorghrer, n, ilo, ihi, extra int, optwork bool, rnd *rand.Rand) {
    45  	const tol = 1e-14
    46  
    47  	// Construct the matrix A with elementary reflectors and scalar factors tau.
    48  	a := randomGeneral(n, n, n+extra, rnd)
    49  	var tau []float64
    50  	if n > 1 {
    51  		tau = nanSlice(n - 1)
    52  	}
    53  	work := nanSlice(max(1, n)) // Minimum work for Dgehrd.
    54  	impl.Dgehrd(n, ilo, ihi, a.Data, a.Stride, tau, work, len(work))
    55  
    56  	// Extract Q for later comparison.
    57  	q := eye(n, n)
    58  	qCopy := cloneGeneral(q)
    59  	for j := ilo; j < ihi; j++ {
    60  		h := eye(n, n)
    61  		v := blas64.Vector{
    62  			Inc:  1,
    63  			Data: make([]float64, n),
    64  		}
    65  		v.Data[j+1] = 1
    66  		for i := j + 2; i < ihi+1; i++ {
    67  			v.Data[i] = a.Data[i*a.Stride+j]
    68  		}
    69  		blas64.Ger(-tau[j], v, v, h)
    70  		copy(qCopy.Data, q.Data)
    71  		blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, qCopy, h, 0, q)
    72  	}
    73  
    74  	if optwork {
    75  		work = nanSlice(1)
    76  		impl.Dorghr(n, ilo, ihi, a.Data, a.Stride, tau, work, -1)
    77  		work = nanSlice(int(work[0]))
    78  	} else {
    79  		work = nanSlice(max(1, ihi-ilo))
    80  	}
    81  	impl.Dorghr(n, ilo, ihi, a.Data, a.Stride, tau, work, len(work))
    82  
    83  	prefix := fmt.Sprintf("Case n=%v, ilo=%v, ihi=%v, extra=%v, optwork=%v", n, ilo, ihi, extra, optwork)
    84  	if !generalOutsideAllNaN(a) {
    85  		t.Errorf("%v: out-of-range write to A\n%v", prefix, a.Data)
    86  	}
    87  	if !isOrthonormal(a) {
    88  		t.Errorf("%v: A is not orthogonal\n%v", prefix, a.Data)
    89  	}
    90  	for i := 0; i < n; i++ {
    91  		for j := 0; j < n; j++ {
    92  			aij := a.Data[i*a.Stride+j]
    93  			qij := q.Data[i*q.Stride+j]
    94  			if math.Abs(aij-qij) > tol {
    95  				t.Errorf("%v: unexpected value of A[%v,%v]. want %v, got %v", prefix, i, j, qij, aij)
    96  			}
    97  		}
    98  	}
    99  }