gonum.org/v1/gonum@v0.14.0/integrate/simpsons_test.go (about)

     1  // Copyright ©2019 The Gonum Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package integrate
     6  
     7  import (
     8  	"math"
     9  	"testing"
    10  
    11  	"golang.org/x/exp/rand"
    12  
    13  	"gonum.org/v1/gonum/integrate/testquad"
    14  )
    15  
    16  func TestSimpsons(t *testing.T) {
    17  	t.Parallel()
    18  	rnd := rand.New(rand.NewSource(1))
    19  	for i, test := range []struct {
    20  		integral testquad.Integral
    21  		n        int
    22  		tol      float64
    23  	}{
    24  		{integral: testquad.Constant(0), n: 3, tol: 0},
    25  		{integral: testquad.Constant(0), n: 4, tol: 0},
    26  		{integral: testquad.Constant(0), n: 10, tol: 0},
    27  		{integral: testquad.Poly(0), n: 3, tol: 1e-14},
    28  		{integral: testquad.Poly(0), n: 4, tol: 1e-14},
    29  		{integral: testquad.Poly(0), n: 10, tol: 1e-14},
    30  		{integral: testquad.Poly(1), n: 3, tol: 1e-14},
    31  		{integral: testquad.Poly(1), n: 4, tol: 1e-14},
    32  		{integral: testquad.Poly(1), n: 10, tol: 1e-14},
    33  		{integral: testquad.Poly(2), n: 3, tol: 1e-14},
    34  		{integral: testquad.Poly(2), n: 4, tol: 1e-14},
    35  		{integral: testquad.Poly(2), n: 10, tol: 1e-14},
    36  		{integral: testquad.Poly(3), n: 1000, tol: 1e-8},
    37  		{integral: testquad.Poly(4), n: 1000, tol: 1e-8},
    38  		{integral: testquad.Poly(5), n: 1000, tol: 1e-7},
    39  		{integral: testquad.Sin(), n: 100, tol: 1e-8},
    40  		{integral: testquad.XExpMinusX(), n: 201, tol: 1e-8},
    41  		{integral: testquad.Sqrt(), n: 1e4, tol: 1e-6},
    42  		{integral: testquad.ExpOverX2Plus1(), n: 100, tol: 1e-7},
    43  	} {
    44  		n := test.n
    45  		a := test.integral.A
    46  		b := test.integral.B
    47  
    48  		x := jitterSpan(n, a, b, rnd)
    49  		y := make([]float64, n)
    50  		for i, xi := range x {
    51  			y[i] = test.integral.F(xi)
    52  		}
    53  
    54  		got := Simpsons(x, y)
    55  
    56  		want := test.integral.Value
    57  		diff := math.Abs(got - want)
    58  		if diff > test.tol {
    59  			t.Errorf("Test #%d: %v, n=%v: unexpected result; got=%v want=%v diff=%v",
    60  				i, test.integral.Name, n, got, want, diff)
    61  		}
    62  	}
    63  }