| // Copyright ©2015 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 ( |
| "math" |
| "math/rand" |
| "testing" |
| |
| "gonum.org/v1/gonum/blas" |
| "gonum.org/v1/gonum/blas/blas64" |
| "gonum.org/v1/gonum/floats" |
| ) |
| |
| type Dgeqr2er interface { |
| Dgeqr2(m, n int, a []float64, lda int, tau []float64, work []float64) |
| } |
| |
| func Dgeqr2Test(t *testing.T, impl Dgeqr2er) { |
| rnd := rand.New(rand.NewSource(1)) |
| for c, test := range []struct { |
| m, n, lda int |
| }{ |
| {1, 1, 0}, |
| {2, 2, 0}, |
| {3, 2, 0}, |
| {2, 3, 0}, |
| {1, 12, 0}, |
| {2, 6, 0}, |
| {3, 4, 0}, |
| {4, 3, 0}, |
| {6, 2, 0}, |
| {12, 1, 0}, |
| {1, 1, 20}, |
| {2, 2, 20}, |
| {3, 2, 20}, |
| {2, 3, 20}, |
| {1, 12, 20}, |
| {2, 6, 20}, |
| {3, 4, 20}, |
| {4, 3, 20}, |
| {6, 2, 20}, |
| {12, 1, 20}, |
| } { |
| n := test.n |
| m := test.m |
| lda := test.lda |
| if lda == 0 { |
| lda = test.n |
| } |
| a := make([]float64, m*lda) |
| for i := range a { |
| a[i] = rnd.Float64() |
| } |
| aCopy := make([]float64, len(a)) |
| k := min(m, n) |
| tau := make([]float64, k) |
| for i := range tau { |
| tau[i] = rnd.Float64() |
| } |
| work := make([]float64, n) |
| for i := range work { |
| work[i] = rnd.Float64() |
| } |
| copy(aCopy, a) |
| impl.Dgeqr2(m, n, a, lda, tau, work) |
| |
| // Test that the QR factorization has completed successfully. Compute |
| // Q based on the vectors. |
| q := constructQ("QR", m, n, a, lda, tau) |
| |
| // Check that q is orthonormal |
| for i := 0; i < m; i++ { |
| nrm := blas64.Nrm2(m, blas64.Vector{Inc: 1, Data: q.Data[i*m:]}) |
| if math.Abs(nrm-1) > 1e-14 { |
| t.Errorf("Case %v, q not normal", c) |
| } |
| for j := 0; j < i; j++ { |
| dot := blas64.Dot(m, blas64.Vector{Inc: 1, Data: q.Data[i*m:]}, blas64.Vector{Inc: 1, Data: q.Data[j*m:]}) |
| if math.Abs(dot) > 1e-14 { |
| t.Errorf("Case %v, q not orthogonal", c) |
| } |
| } |
| } |
| // Check that A = Q * R |
| r := blas64.General{ |
| Rows: m, |
| Cols: n, |
| Stride: n, |
| Data: make([]float64, m*n), |
| } |
| for i := 0; i < m; i++ { |
| for j := i; j < n; j++ { |
| r.Data[i*n+j] = a[i*lda+j] |
| } |
| } |
| atmp := blas64.General{ |
| Rows: m, |
| Cols: n, |
| Stride: lda, |
| Data: make([]float64, m*lda), |
| } |
| copy(atmp.Data, a) |
| blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, q, r, 0, atmp) |
| if !floats.EqualApprox(atmp.Data, aCopy, 1e-14) { |
| t.Errorf("Q*R != a") |
| } |
| } |
| } |