| // 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" |
| "math/rand" |
| "testing" |
| |
| "gonum.org/v1/gonum/blas" |
| "gonum.org/v1/gonum/blas/blas64" |
| ) |
| |
| type Dlatrder interface { |
| Dlatrd(uplo blas.Uplo, n, nb int, a []float64, lda int, e, tau, w []float64, ldw int) |
| } |
| |
| func DlatrdTest(t *testing.T, impl Dlatrder) { |
| rnd := rand.New(rand.NewSource(1)) |
| for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} { |
| for _, test := range []struct { |
| n, nb, lda, ldw int |
| }{ |
| {5, 2, 0, 0}, |
| {5, 5, 0, 0}, |
| |
| {5, 3, 10, 11}, |
| {5, 5, 10, 11}, |
| } { |
| n := test.n |
| nb := test.nb |
| lda := test.lda |
| if lda == 0 { |
| lda = n |
| } |
| ldw := test.ldw |
| if ldw == 0 { |
| ldw = nb |
| } |
| |
| a := make([]float64, n*lda) |
| for i := range a { |
| a[i] = rnd.NormFloat64() |
| } |
| |
| e := make([]float64, n-1) |
| for i := range e { |
| e[i] = math.NaN() |
| } |
| tau := make([]float64, n-1) |
| for i := range tau { |
| tau[i] = math.NaN() |
| } |
| w := make([]float64, n*ldw) |
| for i := range w { |
| w[i] = math.NaN() |
| } |
| |
| aCopy := make([]float64, len(a)) |
| copy(aCopy, a) |
| |
| impl.Dlatrd(uplo, n, nb, a, lda, e, tau, w, ldw) |
| |
| // Construct Q. |
| ldq := n |
| q := blas64.General{ |
| Rows: n, |
| Cols: n, |
| Stride: ldq, |
| Data: make([]float64, n*ldq), |
| } |
| for i := 0; i < n; i++ { |
| q.Data[i*ldq+i] = 1 |
| } |
| if uplo == blas.Upper { |
| for i := n - 1; i >= n-nb; i-- { |
| if i == 0 { |
| continue |
| } |
| h := blas64.General{ |
| Rows: n, Cols: n, Stride: n, Data: make([]float64, n*n), |
| } |
| for j := 0; j < n; j++ { |
| h.Data[j*n+j] = 1 |
| } |
| v := blas64.Vector{ |
| Inc: 1, |
| Data: make([]float64, n), |
| } |
| for j := 0; j < i-1; j++ { |
| v.Data[j] = a[j*lda+i] |
| } |
| v.Data[i-1] = 1 |
| |
| blas64.Ger(-tau[i-1], v, v, h) |
| |
| qTmp := blas64.General{ |
| Rows: n, Cols: n, Stride: n, Data: make([]float64, n*n), |
| } |
| copy(qTmp.Data, q.Data) |
| blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, qTmp, h, 0, q) |
| } |
| } else { |
| for i := 0; i < nb; i++ { |
| if i == n-1 { |
| continue |
| } |
| h := blas64.General{ |
| Rows: n, Cols: n, Stride: n, Data: make([]float64, n*n), |
| } |
| for j := 0; j < n; j++ { |
| h.Data[j*n+j] = 1 |
| } |
| v := blas64.Vector{ |
| Inc: 1, |
| Data: make([]float64, n), |
| } |
| v.Data[i+1] = 1 |
| for j := i + 2; j < n; j++ { |
| v.Data[j] = a[j*lda+i] |
| } |
| blas64.Ger(-tau[i], v, v, h) |
| |
| qTmp := blas64.General{ |
| Rows: n, Cols: n, Stride: n, Data: make([]float64, n*n), |
| } |
| copy(qTmp.Data, q.Data) |
| blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, qTmp, h, 0, q) |
| } |
| } |
| errStr := fmt.Sprintf("isUpper = %v, n = %v, nb = %v", uplo == blas.Upper, n, nb) |
| if !isOrthonormal(q) { |
| t.Errorf("Q not orthonormal. %s", errStr) |
| } |
| aGen := genFromSym(blas64.Symmetric{N: n, Stride: lda, Uplo: uplo, Data: aCopy}) |
| if !dlatrdCheckDecomposition(t, uplo, n, nb, e, tau, a, lda, aGen, q) { |
| t.Errorf("Decomposition mismatch. %s", errStr) |
| } |
| } |
| } |
| } |
| |
| // dlatrdCheckDecomposition checks that the first nb rows have been successfully |
| // reduced. |
| func dlatrdCheckDecomposition(t *testing.T, uplo blas.Uplo, n, nb int, e, tau, a []float64, lda int, aGen, q blas64.General) bool { |
| // Compute Q^T * A * Q. |
| tmp := blas64.General{ |
| Rows: n, |
| Cols: n, |
| Stride: n, |
| Data: make([]float64, n*n), |
| } |
| |
| ans := blas64.General{ |
| Rows: n, |
| Cols: n, |
| Stride: n, |
| Data: make([]float64, n*n), |
| } |
| |
| blas64.Gemm(blas.Trans, blas.NoTrans, 1, q, aGen, 0, tmp) |
| blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, tmp, q, 0, ans) |
| |
| // Compare with T. |
| if uplo == blas.Upper { |
| for i := n - 1; i >= n-nb; i-- { |
| for j := 0; j < n; j++ { |
| v := ans.Data[i*ans.Stride+j] |
| switch { |
| case i == j: |
| if math.Abs(v-a[i*lda+j]) > 1e-10 { |
| return false |
| } |
| case i == j-1: |
| if math.Abs(a[i*lda+j]-1) > 1e-10 { |
| return false |
| } |
| if math.Abs(v-e[i]) > 1e-10 { |
| return false |
| } |
| case i == j+1: |
| default: |
| if math.Abs(v) > 1e-10 { |
| return false |
| } |
| } |
| } |
| } |
| } else { |
| for i := 0; i < nb; i++ { |
| for j := 0; j < n; j++ { |
| v := ans.Data[i*ans.Stride+j] |
| switch { |
| case i == j: |
| if math.Abs(v-a[i*lda+j]) > 1e-10 { |
| return false |
| } |
| case i == j-1: |
| case i == j+1: |
| if math.Abs(a[i*lda+j]-1) > 1e-10 { |
| return false |
| } |
| if math.Abs(v-e[i-1]) > 1e-10 { |
| return false |
| } |
| default: |
| if math.Abs(v) > 1e-10 { |
| return false |
| } |
| } |
| } |
| } |
| } |
| return true |
| } |
| |
| // genFromSym constructs a (symmetric) general matrix from the data in the |
| // symmetric. |
| // TODO(btracey): Replace other constructions of this with a call to this function. |
| func genFromSym(a blas64.Symmetric) blas64.General { |
| n := a.N |
| lda := a.Stride |
| uplo := a.Uplo |
| b := blas64.General{ |
| Rows: n, |
| Cols: n, |
| Stride: n, |
| Data: make([]float64, n*n), |
| } |
| |
| for i := 0; i < n; i++ { |
| for j := i; j < n; j++ { |
| v := a.Data[i*lda+j] |
| if uplo == blas.Lower { |
| v = a.Data[j*lda+i] |
| } |
| b.Data[i*n+j] = v |
| b.Data[j*n+i] = v |
| } |
| } |
| return b |
| } |