+++ /dev/null
-// 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 (
- "math"
- "testing"
-
- "golang.org/x/exp/rand"
-
- "gonum.org/v1/gonum/blas"
- "gonum.org/v1/gonum/blas/blas64"
-)
-
-type Dsytd2er interface {
- Dsytd2(uplo blas.Uplo, n int, a []float64, lda int, d, e, tau []float64)
-}
-
-func Dsytd2Test(t *testing.T, impl Dsytd2er) {
- rnd := rand.New(rand.NewSource(1))
- for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
- for _, test := range []struct {
- n, lda int
- }{
- {3, 0},
- {4, 0},
- {5, 0},
-
- {3, 10},
- {4, 10},
- {5, 10},
- } {
- n := test.n
- lda := test.lda
- if lda == 0 {
- lda = n
- }
- a := make([]float64, n*lda)
- for i := range a {
- a[i] = rnd.NormFloat64()
- }
- aCopy := make([]float64, len(a))
- copy(aCopy, a)
-
- d := make([]float64, n)
- for i := range d {
- d[i] = math.NaN()
- }
- 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()
- }
-
- impl.Dsytd2(uplo, n, a, lda, d, e, tau)
-
- // Construct Q
- qMat := blas64.General{
- Rows: n,
- Cols: n,
- Stride: n,
- Data: make([]float64, n*n),
- }
- qCopy := blas64.General{
- Rows: n,
- Cols: n,
- Stride: n,
- Data: make([]float64, len(qMat.Data)),
- }
- // Set Q to I.
- for i := 0; i < n; i++ {
- qMat.Data[i*qMat.Stride+i] = 1
- }
- for i := 0; i < n-1; i++ {
- hMat := blas64.General{
- Rows: n,
- Cols: n,
- Stride: n,
- Data: make([]float64, n*n),
- }
- // Set H to I.
- for i := 0; i < n; i++ {
- hMat.Data[i*hMat.Stride+i] = 1
- }
- var vi blas64.Vector
- if uplo == blas.Upper {
- vi = blas64.Vector{
- Inc: 1,
- Data: make([]float64, n),
- }
- for j := 0; j < i; j++ {
- vi.Data[j] = a[j*lda+i+1]
- }
- vi.Data[i] = 1
- } else {
- vi = blas64.Vector{
- Inc: 1,
- Data: make([]float64, n),
- }
- vi.Data[i+1] = 1
- for j := i + 2; j < n; j++ {
- vi.Data[j] = a[j*lda+i]
- }
- }
- blas64.Ger(-tau[i], vi, vi, hMat)
- copy(qCopy.Data, qMat.Data)
-
- // Multiply q by the new h.
- if uplo == blas.Upper {
- blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, hMat, qCopy, 0, qMat)
- } else {
- blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, qCopy, hMat, 0, qMat)
- }
- }
- // Check that Q is orthonormal
- othonormal := true
- for i := 0; i < n; i++ {
- for j := i; j < n; j++ {
- dot := blas64.Dot(n,
- blas64.Vector{Inc: 1, Data: qMat.Data[i*qMat.Stride:]},
- blas64.Vector{Inc: 1, Data: qMat.Data[j*qMat.Stride:]},
- )
- if i == j {
- if math.Abs(dot-1) > 1e-10 {
- othonormal = false
- }
- } else {
- if math.Abs(dot) > 1e-10 {
- othonormal = false
- }
- }
- }
- }
- if !othonormal {
- t.Errorf("Q not orthonormal")
- }
-
- // Compute Q^T * A * Q.
- aMat := blas64.General{
- Rows: n,
- Cols: n,
- Stride: n,
- Data: make([]float64, len(a)),
- }
-
- for i := 0; i < n; i++ {
- for j := i; j < n; j++ {
- v := aCopy[i*lda+j]
- if uplo == blas.Lower {
- v = aCopy[j*lda+i]
- }
- aMat.Data[i*aMat.Stride+j] = v
- aMat.Data[j*aMat.Stride+i] = v
- }
- }
-
- 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, qMat, aMat, 0, tmp)
- blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, tmp, qMat, 0, ans)
-
- // Compare with T.
- tMat := blas64.General{
- Rows: n,
- Cols: n,
- Stride: n,
- Data: make([]float64, n*n),
- }
- for i := 0; i < n-1; i++ {
- tMat.Data[i*tMat.Stride+i] = d[i]
- tMat.Data[i*tMat.Stride+i+1] = e[i]
- tMat.Data[(i+1)*tMat.Stride+i] = e[i]
- }
- tMat.Data[(n-1)*tMat.Stride+n-1] = d[n-1]
-
- same := true
- for i := 0; i < n; i++ {
- for j := 0; j < n; j++ {
- if math.Abs(ans.Data[i*ans.Stride+j]-tMat.Data[i*tMat.Stride+j]) > 1e-10 {
- same = false
- }
- }
- }
- if !same {
- t.Errorf("Matrix answer mismatch")
- }
- }
- }
-}
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