| // 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/rand" |
| "testing" |
| |
| "gonum.org/v1/gonum/blas" |
| "gonum.org/v1/gonum/blas/blas64" |
| ) |
| |
| type Dsytrder interface { |
| Dsytrd(uplo blas.Uplo, n int, a []float64, lda int, d, e, tau, work []float64, lwork int) |
| |
| Dorgqr(m, n, k int, a []float64, lda int, tau, work []float64, lwork int) |
| Dorgql(m, n, k int, a []float64, lda int, tau, work []float64, lwork int) |
| } |
| |
| func DsytrdTest(t *testing.T, impl Dsytrder) { |
| const tol = 1e-13 |
| rnd := rand.New(rand.NewSource(1)) |
| for tc, test := range []struct { |
| n, lda int |
| }{ |
| {1, 0}, |
| {2, 0}, |
| {3, 0}, |
| {4, 0}, |
| {10, 0}, |
| {50, 0}, |
| {100, 0}, |
| {150, 0}, |
| {300, 0}, |
| |
| {1, 3}, |
| {2, 3}, |
| {3, 7}, |
| {4, 9}, |
| {10, 20}, |
| {50, 70}, |
| {100, 120}, |
| {150, 170}, |
| {300, 320}, |
| } { |
| for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} { |
| for _, wl := range []worklen{minimumWork, mediumWork, optimumWork} { |
| n := test.n |
| lda := test.lda |
| if lda == 0 { |
| lda = n |
| } |
| a := randomGeneral(n, n, lda, rnd) |
| for i := 1; i < n; i++ { |
| for j := 0; j < i; j++ { |
| a.Data[i*a.Stride+j] = a.Data[j*a.Stride+i] |
| } |
| } |
| aCopy := cloneGeneral(a) |
| |
| d := nanSlice(n) |
| e := nanSlice(n - 1) |
| tau := nanSlice(n - 1) |
| |
| var lwork int |
| switch wl { |
| case minimumWork: |
| lwork = 1 |
| case mediumWork: |
| work := make([]float64, 1) |
| impl.Dsytrd(uplo, n, a.Data, a.Stride, d, e, tau, work, -1) |
| lwork = (int(work[0]) + 1) / 2 |
| lwork = max(1, lwork) |
| case optimumWork: |
| work := make([]float64, 1) |
| impl.Dsytrd(uplo, n, a.Data, a.Stride, d, e, tau, work, -1) |
| lwork = int(work[0]) |
| } |
| work := make([]float64, lwork) |
| |
| impl.Dsytrd(uplo, n, a.Data, a.Stride, d, e, tau, work, lwork) |
| |
| prefix := fmt.Sprintf("Case #%v: uplo=%v,n=%v,lda=%v,work=%v", |
| tc, uplo, n, lda, wl) |
| |
| if !generalOutsideAllNaN(a) { |
| t.Errorf("%v: out-of-range write to A", prefix) |
| } |
| |
| // Extract Q by doing what Dorgtr does. |
| q := cloneGeneral(a) |
| if uplo == blas.Upper { |
| for j := 0; j < n-1; j++ { |
| for i := 0; i < j; i++ { |
| q.Data[i*q.Stride+j] = q.Data[i*q.Stride+j+1] |
| } |
| q.Data[(n-1)*q.Stride+j] = 0 |
| } |
| for i := 0; i < n-1; i++ { |
| q.Data[i*q.Stride+n-1] = 0 |
| } |
| q.Data[(n-1)*q.Stride+n-1] = 1 |
| if n > 1 { |
| work = make([]float64, n-1) |
| impl.Dorgql(n-1, n-1, n-1, q.Data, q.Stride, tau, work, len(work)) |
| } |
| } else { |
| for j := n - 1; j > 0; j-- { |
| q.Data[j] = 0 |
| for i := j + 1; i < n; i++ { |
| q.Data[i*q.Stride+j] = q.Data[i*q.Stride+j-1] |
| } |
| } |
| q.Data[0] = 1 |
| for i := 1; i < n; i++ { |
| q.Data[i*q.Stride] = 0 |
| } |
| if n > 1 { |
| work = make([]float64, n-1) |
| impl.Dorgqr(n-1, n-1, n-1, q.Data[q.Stride+1:], q.Stride, tau, work, len(work)) |
| } |
| } |
| if !isOrthonormal(q) { |
| t.Errorf("%v: Q not orthogonal", prefix) |
| } |
| |
| // Contruct symmetric tridiagonal T from d and e. |
| tMat := zeros(n, n, n) |
| for i := 0; i < n; i++ { |
| tMat.Data[i*tMat.Stride+i] = d[i] |
| } |
| if uplo == blas.Upper { |
| for j := 1; j < n; j++ { |
| tMat.Data[(j-1)*tMat.Stride+j] = e[j-1] |
| tMat.Data[j*tMat.Stride+j-1] = e[j-1] |
| } |
| } else { |
| for j := 0; j < n-1; j++ { |
| tMat.Data[(j+1)*tMat.Stride+j] = e[j] |
| tMat.Data[j*tMat.Stride+j+1] = e[j] |
| } |
| } |
| |
| // Compute Q^T * A * Q. |
| tmp := zeros(n, n, n) |
| blas64.Gemm(blas.Trans, blas.NoTrans, 1, q, aCopy, 0, tmp) |
| got := zeros(n, n, n) |
| blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, tmp, q, 0, got) |
| |
| // Compare with T. |
| if !equalApproxGeneral(got, tMat, tol) { |
| t.Errorf("%v: Q^T*A*Q != T", prefix) |
| } |
| } |
| } |
| } |
| } |