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 // Copyright ©2016 The Gonum Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. package testlapack import ( "fmt" "math" "testing" "golang.org/x/exp/rand" "gonum.org/v1/gonum/blas" "gonum.org/v1/gonum/blas/blas64" ) type Dorghrer interface { Dorghr(n, ilo, ihi int, a []float64, lda int, tau, work []float64, lwork int) Dgehrder } func DorghrTest(t *testing.T, impl Dorghrer) { rnd := rand.New(rand.NewSource(1)) for _, n := range []int{1, 2, 3, 4, 5, 6, 7, 8, 23, 34} { for _, extra := range []int{0, 1, 13} { for _, optwork := range []bool{true, false} { for cas := 0; cas < 100; cas++ { ilo := rnd.Intn(n) ihi := rnd.Intn(n) if ilo > ihi { ilo, ihi = ihi, ilo } testDorghr(t, impl, n, ilo, ihi, extra, optwork, rnd) } } } } testDorghr(t, impl, 0, 0, -1, 0, false, rnd) testDorghr(t, impl, 0, 0, -1, 0, true, rnd) } func testDorghr(t *testing.T, impl Dorghrer, n, ilo, ihi, extra int, optwork bool, rnd *rand.Rand) { const tol = 1e-14 // Construct the matrix A with elementary reflectors and scalar factors tau. a := randomGeneral(n, n, n+extra, rnd) var tau []float64 if n > 1 { tau = nanSlice(n - 1) } work := nanSlice(max(1, n)) // Minimum work for Dgehrd. impl.Dgehrd(n, ilo, ihi, a.Data, a.Stride, tau, work, len(work)) // Extract Q for later comparison. q := eye(n, n) qCopy := cloneGeneral(q) for j := ilo; j < ihi; j++ { h := eye(n, n) v := blas64.Vector{ Inc: 1, Data: make([]float64, n), } v.Data[j+1] = 1 for i := j + 2; i < ihi+1; i++ { v.Data[i] = a.Data[i*a.Stride+j] } blas64.Ger(-tau[j], v, v, h) copy(qCopy.Data, q.Data) blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, qCopy, h, 0, q) } if optwork { work = nanSlice(1) impl.Dorghr(n, ilo, ihi, a.Data, a.Stride, tau, work, -1) work = nanSlice(int(work[0])) } else { work = nanSlice(max(1, ihi-ilo)) } impl.Dorghr(n, ilo, ihi, a.Data, a.Stride, tau, work, len(work)) prefix := fmt.Sprintf("Case n=%v, ilo=%v, ihi=%v, extra=%v, optwork=%v", n, ilo, ihi, extra, optwork) if !generalOutsideAllNaN(a) { t.Errorf("%v: out-of-range write to A\n%v", prefix, a.Data) } if resid := residualOrthogonal(a, false); resid > tol { t.Errorf("%v: A is not orthogonal; resid=%v, want<=%v", prefix, resid, tol) } for i := 0; i < n; i++ { for j := 0; j < n; j++ { aij := a.Data[i*a.Stride+j] qij := q.Data[i*q.Stride+j] if math.Abs(aij-qij) > tol { t.Errorf("%v: unexpected value of A[%v,%v]. want %v, got %v", prefix, i, j, qij, aij) } } } }