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// 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 integrate
import (
"math"
"testing"
"golang.org/x/exp/rand"
"gonum.org/v1/gonum/integrate/testquad"
)
func TestTrapezoidal(t *testing.T) {
t.Parallel()
rnd := rand.New(rand.NewSource(1))
for i, test := range []struct {
integral testquad.Integral
n int
tol float64
}{
{integral: testquad.Constant(0), n: 2, tol: 0},
{integral: testquad.Constant(0), n: 10, tol: 0},
{integral: testquad.Poly(0), n: 2, tol: 1e-14},
{integral: testquad.Poly(0), n: 10, tol: 1e-14},
{integral: testquad.Poly(1), n: 2, tol: 1e-14},
{integral: testquad.Poly(1), n: 10, tol: 1e-14},
{integral: testquad.Poly(2), n: 1e5, tol: 1e-8},
{integral: testquad.Poly(3), n: 1e5, tol: 1e-8},
{integral: testquad.Poly(4), n: 1e5, tol: 1e-7},
{integral: testquad.Poly(5), n: 1e5, tol: 1e-7},
{integral: testquad.Sin(), n: 1e5, tol: 1e-11},
{integral: testquad.XExpMinusX(), n: 1e5, tol: 1e-10},
{integral: testquad.Sqrt(), n: 1e5, tol: 1e-8},
{integral: testquad.ExpOverX2Plus1(), n: 1e5, tol: 1e-10},
} {
n := test.n
a := test.integral.A
b := test.integral.B
x := jitterSpan(n, a, b, rnd)
y := make([]float64, n)
for i, xi := range x {
y[i] = test.integral.F(xi)
}
got := Trapezoidal(x, y)
want := test.integral.Value
diff := math.Abs(got - want)
if diff > test.tol {
t.Errorf("Test #%d: %v, n=%v: unexpected result; got=%v want=%v diff=%v",
i, test.integral.Name, n, got, want, diff)
}
}
}
func jitterSpan(n int, a, b float64, rnd *rand.Rand) []float64 {
dx := (b - a) / float64(n-1)
x := make([]float64, n)
x[0] = a
for i := 1; i < n-1; i++ {
// Set x[i] to its regular location.
x[i] = a + float64(i)*dx
// Generate a random number in [-1,1).
jitter := 2*rnd.Float64() - 1
// Jitter x[i] without crossing over its neighbors.
x[i] += 0.4 * jitter * dx
}
x[n-1] = b
return x
}
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