mirror of
https://github.com/gonum/gonum.git
synced 2025-10-06 15:47:01 +08:00
5f0141ca4c
Changes made in dsp/fourier/internal/fftpack break the formatting used there, so these are reverted. There will be complaints in CI. [git-generate] gofmt -w . go generate gonum.org/v1/gonum/blas go generate gonum.org/v1/gonum/blas/gonum go generate gonum.org/v1/gonum/unit go generate gonum.org/v1/gonum/unit/constant go generate gonum.org/v1/gonum/graph/formats/dot go generate gonum.org/v1/gonum/graph/formats/rdf go generate gonum.org/v1/gonum/stat/card git checkout -- dsp/fourier/internal/fftpack
115 lines
2.1 KiB
Go
115 lines
2.1 KiB
Go
// 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,
|
|
}
|
|
}
|