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// 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 (
"testing"
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/blas/blas64"
"gonum.org/v1/gonum/floats"
"gonum.org/v1/gonum/lapack"
)
type Dlarfter interface {
Dgeqr2er
Dlarft(direct lapack.Direct, store lapack.StoreV, n, k int, v []float64, ldv int, tau []float64, t []float64, ldt int)
}
func DlarftTest(t *testing.T, impl Dlarfter) {
rnd := rand.New(rand.NewSource(1))
for _, store := range []lapack.StoreV{lapack.ColumnWise, lapack.RowWise} {
for _, direct := range []lapack.Direct{lapack.Forward, lapack.Backward} {
for _, test := range []struct {
m, n, ldv, ldt int
}{
{6, 6, 0, 0},
{8, 6, 0, 0},
{6, 8, 0, 0},
{6, 6, 10, 15},
{8, 6, 10, 15},
{6, 8, 10, 15},
{6, 6, 15, 10},
{8, 6, 15, 10},
{6, 8, 15, 10},
} {
// Generate a matrix
m := test.m
n := test.n
lda := n
if lda == 0 {
lda = n
}
a := make([]float64, m*lda)
for i := 0; i < m; i++ {
for j := 0; j < lda; j++ {
a[i*lda+j] = rnd.Float64()
}
}
// Use dgeqr2 to find the v vectors
k := min(m, n)
tau := make([]float64, k)
work := make([]float64, n)
impl.Dgeqr2(m, n, a, lda, tau, work)
// Construct H using these answers
vMatTmp := extractVMat(m, n, a, lda, lapack.Forward, lapack.ColumnWise)
vMat := constructVMat(vMatTmp, store, direct)
v := vMat.Data
ldv := vMat.Stride
h := constructH(tau, vMat, store, direct)
ldt := test.ldt
if ldt == 0 {
ldt = k
}
// Find T from the actual function
tm := make([]float64, k*ldt)
for i := range tm {
tm[i] = 100 + rnd.Float64()
}
// The v data has been put into a.
impl.Dlarft(direct, store, m, k, v, ldv, tau, tm, ldt)
tData := make([]float64, len(tm))
copy(tData, tm)
if direct == lapack.Forward {
// Zero out the lower triangular portion.
for i := 0; i < k; i++ {
for j := 0; j < i; j++ {
tData[i*ldt+j] = 0
}
}
} else {
// Zero out the upper triangular portion.
for i := 0; i < k; i++ {
for j := i + 1; j < k; j++ {
tData[i*ldt+j] = 0
}
}
}
T := blas64.General{
Rows: k,
Cols: k,
Stride: ldt,
Data: tData,
}
vMatT := blas64.General{
Rows: vMat.Cols,
Cols: vMat.Rows,
Stride: vMat.Rows,
Data: make([]float64, vMat.Cols*vMat.Rows),
}
for i := 0; i < vMat.Rows; i++ {
for j := 0; j < vMat.Cols; j++ {
vMatT.Data[j*vMatT.Stride+i] = vMat.Data[i*vMat.Stride+j]
}
}
var comp blas64.General
if store == lapack.ColumnWise {
// H = I - V * T * Vᵀ
tmp := blas64.General{
Rows: T.Rows,
Cols: vMatT.Cols,
Stride: vMatT.Cols,
Data: make([]float64, T.Rows*vMatT.Cols),
}
// T * Vᵀ
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, T, vMatT, 0, tmp)
comp = blas64.General{
Rows: vMat.Rows,
Cols: tmp.Cols,
Stride: tmp.Cols,
Data: make([]float64, vMat.Rows*tmp.Cols),
}
// V * (T * Vᵀ)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, vMat, tmp, 0, comp)
} else {
// H = I - Vᵀ * T * V
tmp := blas64.General{
Rows: T.Rows,
Cols: vMat.Cols,
Stride: vMat.Cols,
Data: make([]float64, T.Rows*vMat.Cols),
}
// T * V
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, T, vMat, 0, tmp)
comp = blas64.General{
Rows: vMatT.Rows,
Cols: tmp.Cols,
Stride: tmp.Cols,
Data: make([]float64, vMatT.Rows*tmp.Cols),
}
// Vᵀ * (T * V)
blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, vMatT, tmp, 0, comp)
}
// I - Vᵀ * T * V
for i := 0; i < comp.Rows; i++ {
for j := 0; j < comp.Cols; j++ {
comp.Data[i*m+j] *= -1
if i == j {
comp.Data[i*m+j] += 1
}
}
}
if !floats.EqualApprox(comp.Data, h.Data, 1e-14) {
t.Errorf("T does not construct proper H. Store = %v, Direct = %v.\nWant %v\ngot %v.", string(store), string(direct), h.Data, comp.Data)
}
}
}
}
}
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