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74 lines
2.0 KiB
Go
74 lines
2.0 KiB
Go
// Copyright ©2016 The Gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package integrate
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import (
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"math"
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"testing"
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"golang.org/x/exp/rand"
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"gonum.org/v1/gonum/integrate/testquad"
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)
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func TestTrapezoidal(t *testing.T) {
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rnd := rand.New(rand.NewSource(1))
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for i, test := range []struct {
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integral testquad.Integral
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n int
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tol float64
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}{
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{integral: testquad.Constant(0), n: 2, tol: 0},
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{integral: testquad.Constant(0), n: 10, tol: 0},
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{integral: testquad.Poly(0), n: 2, tol: 1e-14},
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{integral: testquad.Poly(0), n: 10, tol: 1e-14},
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{integral: testquad.Poly(1), n: 2, tol: 1e-14},
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{integral: testquad.Poly(1), n: 10, tol: 1e-14},
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{integral: testquad.Poly(2), n: 1e5, tol: 1e-8},
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{integral: testquad.Poly(3), n: 1e5, tol: 1e-8},
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{integral: testquad.Poly(4), n: 1e5, tol: 1e-7},
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{integral: testquad.Poly(5), n: 1e5, tol: 1e-7},
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{integral: testquad.Sin(), n: 1e5, tol: 1e-11},
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{integral: testquad.XExpMinusX(), n: 1e5, tol: 1e-10},
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{integral: testquad.Sqrt(), n: 1e5, tol: 1e-8},
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{integral: testquad.ExpOverX2Plus1(), n: 1e5, tol: 1e-10},
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} {
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n := test.n
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a := test.integral.A
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b := test.integral.B
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x := jitterSpan(n, a, b, rnd)
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y := make([]float64, n)
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for i, xi := range x {
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y[i] = test.integral.F(xi)
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}
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got := Trapezoidal(x, y)
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want := test.integral.Value
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diff := math.Abs(got - want)
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if diff > test.tol {
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t.Errorf("Test #%d: %v, n=%v: unexpected result; got=%v want=%v diff=%v",
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i, test.integral.Name, n, got, want, diff)
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}
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}
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}
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func jitterSpan(n int, a, b float64, rnd *rand.Rand) []float64 {
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dx := (b - a) / float64(n-1)
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x := make([]float64, n)
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x[0] = a
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for i := 1; i < n-1; i++ {
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// Set x[i] to its regular location.
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x[i] = a + float64(i)*dx
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// Generate a random number in [-1,1).
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jitter := 2*rnd.Float64() - 1
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// Jitter x[i] without crossing over its neighbors.
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x[i] += 0.4 * jitter * dx
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}
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x[n-1] = b
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return x
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}
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