github.com/jingcheng-WU/gonum@v0.9.1-0.20210323123734-f1a2a11a8f7b/integrate/quad/legendre_test.go (about)

     1  // Copyright ©2015 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 quad
     6  
     7  import (
     8  	"math"
     9  	"testing"
    10  
    11  	"github.com/jingcheng-WU/gonum/floats"
    12  	"github.com/jingcheng-WU/gonum/floats/scalar"
    13  )
    14  
    15  func TestLegendre(t *testing.T) {
    16  	t.Parallel()
    17  	for i, test := range []struct {
    18  		f        func(float64) float64
    19  		min, max float64
    20  		n        []int
    21  		tol      []float64
    22  		ans      float64
    23  	}{
    24  		// Tolerances determined from intuition and a bit of post-hoc tweaking.
    25  		{
    26  			f:   func(x float64) float64 { return math.Exp(x) },
    27  			min: -3,
    28  			max: 5,
    29  			n:   []int{3, 4, 6, 7, 15, 16, 300, 301},
    30  			tol: []float64{5e-2, 5e-3, 5e-6, 1e-7, 1e-14, 1e-14, 1e-14, 1e-14},
    31  			ans: math.Exp(5) - math.Exp(-3),
    32  		},
    33  	} {
    34  		for j, n := range test.n {
    35  			ans := Fixed(test.f, test.min, test.max, n, Legendre{}, 0)
    36  			if !scalar.EqualWithinAbsOrRel(ans, test.ans, test.tol[j], test.tol[j]) {
    37  				t.Errorf("Mismatch. Case = %d, n = %d. Want %v, got %v", i, n, test.ans, ans)
    38  			}
    39  			ans2 := Fixed(test.f, test.min, test.max, n, Legendre{}, 3)
    40  			if !scalar.EqualWithinAbsOrRel(ans2, test.ans, test.tol[j], test.tol[j]) {
    41  				t.Errorf("Mismatch concurrent. Case = %d, n = %d. Want %v, got %v", i, n, test.ans, ans)
    42  			}
    43  		}
    44  	}
    45  }
    46  
    47  func TestLegendreSingle(t *testing.T) {
    48  	t.Parallel()
    49  	for c, test := range []struct {
    50  		n        int
    51  		min, max float64
    52  	}{
    53  		{
    54  			n:   100,
    55  			min: -1,
    56  			max: 1,
    57  		},
    58  		{
    59  			n:   50,
    60  			min: -3,
    61  			max: -1,
    62  		},
    63  		{
    64  			n:   1000,
    65  			min: 2,
    66  			max: 7,
    67  		},
    68  	} {
    69  		l := Legendre{}
    70  		n := test.n
    71  		xs := make([]float64, n)
    72  		weights := make([]float64, n)
    73  		l.FixedLocations(xs, weights, test.min, test.max)
    74  
    75  		xsSingle := make([]float64, n)
    76  		weightsSingle := make([]float64, n)
    77  		for i := range xsSingle {
    78  			xsSingle[i], weightsSingle[i] = l.FixedLocationSingle(n, i, test.min, test.max)
    79  		}
    80  		if !floats.Equal(xs, xsSingle) {
    81  			t.Errorf("Case %d: xs mismatch batch and single", c)
    82  		}
    83  		if !floats.Equal(weights, weightsSingle) {
    84  			t.Errorf("Case %d: weights mismatch batch and single", c)
    85  		}
    86  	}
    87  }