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// Copyright ©2019 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"
"testing"
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/floats"
)
type Dlassqer interface {
Dlassq(n int, x []float64, incx int, scale, ssq float64) (float64, float64)
}
func DlassqTest(t *testing.T, impl Dlassqer) {
values := []float64{
0,
0.5 * safmin,
smlnum,
ulp,
1,
1 / ulp,
bignum,
safmax,
math.Inf(1),
math.NaN(),
}
rnd := rand.New(rand.NewSource(1))
for _, n := range []int{0, 1, 2, 3, 4, 5, 10, 20, 30, 40} {
for _, incx := range []int{1, 3} {
for cas := 0; cas < 3; cas++ {
for _, v0 := range values {
if v0 > 1 {
v0 *= 0.5
}
for _, v1 := range values {
if v1 > 1 {
v1 = 0.5 * v1 / math.Sqrt(float64(n+1))
}
dlassqTest(t, impl, rnd, n, incx, cas, v0, v1)
}
}
}
}
}
}
func dlassqTest(t *testing.T, impl Dlassqer, rnd *rand.Rand, n, incx, cas int, v0, v1 float64) {
const (
rogue = 1234.5678
tol = 1e-15
)
name := fmt.Sprintf("n=%v,incx=%v,cas=%v,v0=%v,v1=%v", n, incx, cas, v0, v1)
// Generate n random values in (-1,1].
work := make([]float64, n)
for i := range work {
work[i] = 1 - 2*rnd.Float64()
}
// Compute the sum of squares by an unscaled algorithm.
var workssq float64
for _, wi := range work {
workssq += wi * wi
}
// Set initial scale and ssq corresponding to sqrt(v0).
var scale, ssq float64
switch cas {
case 0:
scale = 1
ssq = v0
case 1:
scale = math.Sqrt(v0)
ssq = 1
case 2:
if v0 < 1 {
scale = 1.0 / 3
ssq = 9 * v0
} else {
scale = 3
ssq = v0 / 9
}
default:
panic("bad cas")
}
// Allocate input slice for Dlassq and fill it with
// x[:] = scaling factor * work[:].
x := make([]float64, max(0, 1+(n-1)*incx))
for i := range x {
x[i] = rogue
}
for i, wi := range work {
x[i*incx] = v1 * wi
}
xCopy := make([]float64, len(x))
copy(xCopy, x)
scaleGot, ssqGot := impl.Dlassq(n, x, incx, scale, ssq)
nrmGot := scaleGot * math.Sqrt(ssqGot)
if !floats.Same(x, xCopy) {
t.Fatalf("%v: unexpected modification of x", name)
}
// Compute the expected value of the sum of squares.
z0 := math.Sqrt(v0)
var z1n float64
if n >= 1 {
z1n = v1 * math.Sqrt(workssq)
}
zmin := math.Min(z0, z1n)
zmax := math.Max(z0, z1n)
var nrmWant float64
switch {
case math.IsNaN(z0) || math.IsNaN(z1n):
nrmWant = math.NaN()
case zmin == zmax:
nrmWant = math.Sqrt2 * zmax
case zmax == 0:
nrmWant = 0
default:
nrmWant = zmax * math.Sqrt(1+(zmin/zmax)*(zmin/zmax))
}
// Check the result.
switch {
case math.IsNaN(nrmGot) || math.IsNaN(nrmWant):
if !math.IsNaN(nrmGot) {
t.Errorf("%v: expected NaN; got %v", name, nrmGot)
}
if !math.IsNaN(nrmWant) {
t.Errorf("%v: unexpected NaN; want %v", name, nrmWant)
}
case nrmGot == nrmWant:
case nrmWant == 0:
if nrmGot > tol {
t.Errorf("%v: unexpected result; got %v, want 0", name, nrmGot)
}
default:
diff := math.Abs(nrmGot-nrmWant) / nrmWant / math.Max(1, float64(n))
if math.IsNaN(diff) || diff > tol {
t.Errorf("%v: unexpected result; got %v, want %v", name, nrmGot, nrmWant)
}
}
}
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