How to implement numerical integration and differentiation in Go?

To implement numerical integration and differentiation in Go, you can use the popular scientific library called Gonum. Gonum provides various mathematical functions and algorithms for numerical computing tasks.

Here's how you can implement numerical integration using Gonum:

First, import the required packages:

import (
    "fmt"
    "math"

    "gonum.org/v1/gonum/integrate"
)

Define the function that you want to integrate. For example, let's integrate the function f(x) = x^2 within the interval [0, 1]:

func f(x float64) float64 {
    return math.Pow(x, 2)
}

Use the integrate.Romberg function to perform numerical integration:

result, err := integrate.Romberg(f, 0, 1, 10)
if err != nil {
    // Handle error
}
fmt.Printf("Integral result: %.6f\n", result)

Here, integrate.Romberg takes the function f, the lower and upper bounds of the integration interval (0 and 1 in this case), and the number of subdivisions (10). The result will be printed as Integral result: 0.333333.

To implement numerical differentiation using Gonum, you can use the finite difference method. Here's an example:

Import the required packages:

import (
    "fmt"
    "math"

    "gonum.org/v1/gonum/diff"
)

Define the function that you want to differentiate. Let's differentiate the function f(x) = x^2 at x=2:

func f(x float64) float64 {
    return math.Pow(x, 2)
}

Use the diff.FiniteDiff function to approximate the derivative:

fn := func(x float64) float64 {
    return f(x)
}
result := diff.FiniteDiff(fn, 2, 1e-6, 1)
fmt.Printf("Derivative result: %.6f\n", result)

Here, diff.FiniteDiff takes the function f, the point at which you want to calculate the derivative (in this case, x = 2), the step size (1e-6), and the order of the finite difference method (1 for first derivative). The result will be printed as Derivative result: 4.000000.

By using Gonum library's integrate and diff packages, you can efficiently implement numerical integration and differentiation in Go.