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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 Dgehd2er interface { Dgehd2(n, ilo, ihi int, a []float64, lda int, tau, work []float64) } func Dgehd2Test(t *testing.T, impl Dgehd2er) { rnd := rand.New(rand.NewSource(1)) for _, n := range []int{1, 2, 3, 4, 5, 7, 10, 30} { for _, extra := range []int{0, 1, 13} { for cas := 0; cas < 100; cas++ { testDgehd2(t, impl, n, extra, rnd) } } } } func testDgehd2(t *testing.T, impl Dgehd2er, n, extra int, rnd *rand.Rand) { const tol = 1e-14 ilo := rnd.Intn(n) ihi := rnd.Intn(n) if ilo > ihi { ilo, ihi = ihi, ilo } tau := nanSlice(n - 1) work := nanSlice(n) a := randomGeneral(n, n, n+extra, rnd) // NaN out elements under the diagonal except // for the [ilo:ihi,ilo:ihi] block. for i := 1; i <= ihi; i++ { for j := 0; j < min(ilo, i); j++ { a.Data[i*a.Stride+j] = math.NaN() } } for i := ihi + 1; i < n; i++ { for j := 0; j < i; j++ { a.Data[i*a.Stride+j] = math.NaN() } } aCopy := a aCopy.Data = make([]float64, len(a.Data)) copy(aCopy.Data, a.Data) impl.Dgehd2(n, ilo, ihi, a.Data, a.Stride, tau, work) prefix := fmt.Sprintf("Case n=%v, ilo=%v, ihi=%v, extra=%v", n, ilo, ihi, extra) // Check any invalid modifications of a. if !generalOutsideAllNaN(a) { t.Errorf("%v: out-of-range write to A\n%v", prefix, a.Data) } for i := ilo; i <= ihi; i++ { for j := 0; j < min(ilo, i); j++ { if !math.IsNaN(a.Data[i*a.Stride+j]) { t.Errorf("%v: expected NaN at A[%v,%v]", prefix, i, j) } } } for i := ihi + 1; i < n; i++ { for j := 0; j < i; j++ { if !math.IsNaN(a.Data[i*a.Stride+j]) { t.Errorf("%v: expected NaN at A[%v,%v]", prefix, i, j) } } } for i := 0; i <= ilo; i++ { for j := i; j < ilo+1; j++ { if a.Data[i*a.Stride+j] != aCopy.Data[i*aCopy.Stride+j] { t.Errorf("%v: unexpected modification at A[%v,%v]", prefix, i, j) } } for j := ihi + 1; j < n; j++ { if a.Data[i*a.Stride+j] != aCopy.Data[i*aCopy.Stride+j] { t.Errorf("%v: unexpected modification at A[%v,%v]", prefix, i, j) } } } for i := ihi + 1; i < n; i++ { for j := i; j < n; j++ { if a.Data[i*a.Stride+j] != aCopy.Data[i*aCopy.Stride+j] { t.Errorf("%v: unexpected modification at A[%v,%v]", prefix, i, j) } } } // Check that tau has been assigned properly. for i, v := range tau { if i < ilo || i >= ihi { if !math.IsNaN(v) { t.Errorf("%v: expected NaN at tau[%v]", prefix, i) } } else { if math.IsNaN(v) { t.Errorf("%v: unexpected NaN at tau[%v]", prefix, i) } } } // Extract Q and check that it is orthogonal. q := blas64.General{ Rows: n, Cols: n, Stride: n, Data: make([]float64, n*n), } for i := 0; i < q.Rows; i++ { q.Data[i*q.Stride+i] = 1 } qCopy := q qCopy.Data = make([]float64, len(q.Data)) for j := ilo; j < ihi; j++ { h := blas64.General{ Rows: n, Cols: n, Stride: n, Data: make([]float64, n*n), } for i := 0; i < h.Rows; i++ { h.Data[i*h.Stride+i] = 1 } 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 resid := residualOrthogonal(q, false); resid > tol { t.Errorf("%v: Q is not orthogonal; resid=%v, want<=%v", prefix, resid, tol) } // Overwrite NaN elements of aCopy with zeros // (we will multiply with it below). for i := 1; i <= ihi; i++ { for j := 0; j < min(ilo, i); j++ { aCopy.Data[i*aCopy.Stride+j] = 0 } } for i := ihi + 1; i < n; i++ { for j := 0; j < i; j++ { aCopy.Data[i*aCopy.Stride+j] = 0 } } // Construct Qᵀ * AOrig * Q and check that it is // equal to A from Dgehd2. aq := blas64.General{ Rows: n, Cols: n, Stride: n, Data: make([]float64, n*n), } blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, aCopy, q, 0, aq) qaq := blas64.General{ Rows: n, Cols: n, Stride: n, Data: make([]float64, n*n), } blas64.Gemm(blas.Trans, blas.NoTrans, 1, q, aq, 0, qaq) for i := ilo; i <= ihi; i++ { for j := ilo; j <= ihi; j++ { qaqij := qaq.Data[i*qaq.Stride+j] if j < i-1 { if math.Abs(qaqij) > tol { t.Errorf("%v: Qᵀ*A*Q is not upper Hessenberg, [%v,%v]=%v", prefix, i, j, qaqij) } continue } diff := qaqij - a.Data[i*a.Stride+j] if math.Abs(diff) > tol { t.Errorf("%v: Qᵀ*AOrig*Q and A are not equal, diff at [%v,%v]=%v", prefix, i, j, diff) } } } }