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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 (
"math"
"testing"
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/blas/blas64"
"gonum.org/v1/gonum/floats"
)
type Dlarfger interface {
Dlarfg(n int, alpha float64, x []float64, incX int) (beta, tau float64)
}
func DlarfgTest(t *testing.T, impl Dlarfger) {
const tol = 1e-14
rnd := rand.New(rand.NewSource(1))
for i, test := range []struct {
alpha float64
n int
x []float64
}{
{
alpha: 4,
n: 3,
},
{
alpha: -2,
n: 3,
},
{
alpha: 0,
n: 3,
},
{
alpha: 1,
n: 1,
},
{
alpha: 1,
n: 4,
x: []float64{4, 5, 6},
},
{
alpha: 1,
n: 4,
x: []float64{0, 0, 0},
},
{
alpha: dlamchS,
n: 4,
x: []float64{dlamchS, dlamchS, dlamchS},
},
} {
n := test.n
incX := 1
var x []float64
if test.x == nil {
x = make([]float64, n-1)
for i := range x {
x[i] = rnd.Float64()
}
} else {
if len(test.x) != n-1 {
panic("bad test")
}
x = make([]float64, n-1)
copy(x, test.x)
}
xcopy := make([]float64, n-1)
copy(xcopy, x)
alpha := test.alpha
beta, tau := impl.Dlarfg(n, alpha, x, incX)
// Verify the returns and the values in v. Construct h and perform
// the explicit multiplication.
h := make([]float64, n*n)
for i := 0; i < n; i++ {
h[i*n+i] = 1
}
hmat := blas64.General{
Rows: n,
Cols: n,
Stride: n,
Data: h,
}
v := make([]float64, n)
copy(v[1:], x)
v[0] = 1
vVec := blas64.Vector{
Inc: 1,
Data: v,
}
blas64.Ger(-tau, vVec, vVec, hmat)
eye := blas64.General{
Rows: n,
Cols: n,
Stride: n,
Data: make([]float64, n*n),
}
blas64.Gemm(blas.Trans, blas.NoTrans, 1, hmat, hmat, 0, eye)
dist := distFromIdentity(n, eye.Data, n)
if dist > tol {
t.Errorf("Hᵀ * H is not close to I, dist=%v", dist)
}
xVec := blas64.Vector{
Inc: 1,
Data: make([]float64, n),
}
xVec.Data[0] = test.alpha
copy(xVec.Data[1:], xcopy)
ans := make([]float64, n)
ansVec := blas64.Vector{
Inc: 1,
Data: ans,
}
blas64.Gemv(blas.NoTrans, 1, hmat, xVec, 0, ansVec)
if math.Abs(ans[0]-beta) > tol {
t.Errorf("Case %v, beta mismatch. Want %v, got %v", i, ans[0], beta)
}
if floats.Norm(ans[1:n], math.Inf(1)) > tol {
t.Errorf("Case %v, nonzero answer %v", i, ans[1:n])
}
}
}
|
