integrate/testquad: add package with test integrals with known values

integrate/testquad/testquad.go

@@ -0,0 +1,106 @@
+// Copyright ©2019 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 testquad provides integrals for testing quadrature algorithms.
+package testquad
+
+import (
+	"fmt"
+	"math"
+)
+
+// Integral is a definite integral
+//  ∫_a^b f(x)dx
+// with a known value.
+type Integral struct {
+	Name  string
+	A, B  float64               // Integration limits
+	F     func(float64) float64 // Integrand
+	Value float64
+}
+
+// Constant returns the integral of a constant function
+//  ∫_{-1}^2 alpha dx
+func Constant(alpha float64) Integral {
+	return Integral{
+		Name: fmt.Sprintf("∫_{-1}^{2} %vdx", alpha),
+		A:    -1,
+		B:    2,
+		F: func(float64) float64 {
+			return alpha
+		},
+		Value: 3 * alpha,
+	}
+}
+
+// Poly returns the integral of a polynomial
+//  ∫_{-1}^2 x^degree dx
+func Poly(degree int) Integral {
+	d := float64(degree)
+	return Integral{
+		Name: fmt.Sprintf("∫_{-1}^{2} x^%vdx", degree),
+		A:    -1,
+		B:    2,
+		F: func(x float64) float64 {
+			return math.Pow(x, d)
+		},
+		Value: (math.Pow(2, d+1) - math.Pow(-1, d+1)) / (d + 1),
+	}
+}
+
+// Sin returns the integral
+//  ∫_0^1 sin(x)dx
+func Sin() Integral {
+	return Integral{
+		Name: "∫_0^1 sin(x)dx",
+		A:    0,
+		B:    1,
+		F: func(x float64) float64 {
+			return math.Sin(x)
+		},
+		Value: 1 - math.Cos(1),
+	}
+}
+
+// XExpMinusX returns the integral
+//  ∫_0^1 x*exp(-x)dx
+func XExpMinusX() Integral {
+	return Integral{
+		Name: "∫_0^1 x*exp(-x)dx",
+		A:    0,
+		B:    1,
+		F: func(x float64) float64 {
+			return x * math.Exp(-x)
+		},
+		Value: (math.E - 2) / math.E,
+	}
+}
+
+// Sqrt returns the integral
+//  ∫_0^1 sqrt(x)dx
+func Sqrt() Integral {
+	return Integral{
+		Name: "∫_0^1 sqrt(x)dx",
+		A:    0,
+		B:    1,
+		F: func(x float64) float64 {
+			return math.Sqrt(x)
+		},
+		Value: 2 / 3.0,
+	}
+}
+
+// ExpOverX2Plus1 returns the integral
+//  ∫_0^1 exp(x)/(x*x+1)dx
+func ExpOverX2Plus1() Integral {
+	return Integral{
+		Name: "∫_0^1 exp(x)/(x*x+1)dx",
+		A:    0,
+		B:    1,
+		F: func(x float64) float64 {
+			return math.Exp(x) / (x*x + 1)
+		},
+		Value: 1.270724139833620220138,
+	}
+}