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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 quad
import (
"math"
"testing"
"gonum.org/v1/gonum/floats"
"gonum.org/v1/gonum/floats/scalar"
)
func TestLegendre(t *testing.T) {
t.Parallel()
for i, test := range []struct {
f func(float64) float64
min, max float64
n []int
tol []float64
ans float64
}{
// Tolerances determined from intuition and a bit of post-hoc tweaking.
{
f: func(x float64) float64 { return math.Exp(x) },
min: -3,
max: 5,
n: []int{3, 4, 6, 7, 15, 16, 300, 301},
tol: []float64{5e-2, 5e-3, 5e-6, 1e-7, 1e-14, 1e-14, 1e-14, 1e-14},
ans: math.Exp(5) - math.Exp(-3),
},
} {
for j, n := range test.n {
ans := Fixed(test.f, test.min, test.max, n, Legendre{}, 0)
if !scalar.EqualWithinAbsOrRel(ans, test.ans, test.tol[j], test.tol[j]) {
t.Errorf("Mismatch. Case = %d, n = %d. Want %v, got %v", i, n, test.ans, ans)
}
ans2 := Fixed(test.f, test.min, test.max, n, Legendre{}, 3)
if !scalar.EqualWithinAbsOrRel(ans2, test.ans, test.tol[j], test.tol[j]) {
t.Errorf("Mismatch concurrent. Case = %d, n = %d. Want %v, got %v", i, n, test.ans, ans)
}
}
}
}
func TestLegendreSingle(t *testing.T) {
t.Parallel()
for c, test := range []struct {
n int
min, max float64
}{
{
n: 100,
min: -1,
max: 1,
},
{
n: 50,
min: -3,
max: -1,
},
{
n: 1000,
min: 2,
max: 7,
},
} {
l := Legendre{}
n := test.n
xs := make([]float64, n)
weights := make([]float64, n)
l.FixedLocations(xs, weights, test.min, test.max)
xsSingle := make([]float64, n)
weightsSingle := make([]float64, n)
for i := range xsSingle {
xsSingle[i], weightsSingle[i] = l.FixedLocationSingle(n, i, test.min, test.max)
}
if !floats.Equal(xs, xsSingle) {
t.Errorf("Case %d: xs mismatch batch and single", c)
}
if !floats.Equal(weights, weightsSingle) {
t.Errorf("Case %d: weights mismatch batch and single", c)
}
}
}
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