Forward Mode Automatic Differentiation in Go

advance.go

package main

import (
    "fmt"
    "math"
)

// Dual represents a dual number: a + bε.
type Dual struct {
    Real float64
    Dual float64
}

// Add adds two dual numbers.
func (d Dual) Add(other Dual) Dual {
    return Dual{Real: d.Real + other.Real, Dual: d.Dual + other.Dual}
}

// Mul multiplies two dual numbers.
func (d Dual) Mul(other Dual) Dual {
    return Dual{
        Real: d.Real * other.Real,
        Dual: d.Real*other.Dual + d.Dual*other.Real,
    }
}

// Sin computes the sine of a dual number.
func (d Dual) Sin() Dual {
    return Dual{
        Real: math.Sin(d.Real),
        Dual: d.Dual * math.Cos(d.Real),
    }
}

// Exp computes the exponential of a dual number.
func (d Dual) Exp() Dual {
    val := math.Exp(d.Real)
    return Dual{
        Real: val,
        Dual: d.Dual * val,
    }
}

// g defines the function: g(x) = sin(x) * exp(x).
func g(x Dual) Dual {
    return x.Sin().Mul(x.Exp())
}

// differentiate computes the derivative of function f at x0.
func differentiate(f func(Dual) Dual, x0 float64) float64 {
    x := Dual{Real: x0, Dual: 1}
    return f(x).Dual
}

func main() {
    x0 := 1.0
    value := g(Dual{Real: x0, Dual: 0}).Real
    deriv := differentiate(g, x0)
    fmt.Printf("Advanced Example: At x = %v, g(x) = %v and g'(x) = %v\n", x0, value, deriv)

    // Expected derivative: e^x (sin(x) + cos(x)) at x = 1
    expected := math.Exp(1) * (math.Sin(1) + math.Cos(1))
    fmt.Printf("Expected derivative: %v\n", expected)
}

simple.go

package main

import (
    "fmt"
)

// Dual represents a dual number: a + bε, where ε² = 0.
type Dual struct {
    Real float64
    Dual float64
}

// Add returns the sum of two dual numbers.
func (d Dual) Add(other Dual) Dual {
    return Dual{Real: d.Real + other.Real, Dual: d.Dual + other.Dual}
}

// Mul returns the product of two dual numbers.
func (d Dual) Mul(other Dual) Dual {
    return Dual{
        Real: d.Real * other.Real,
        Dual: d.Real*other.Dual + d.Dual*other.Real,
    }
}

// Pow returns the dual number raised to an integer power.
func (d Dual) Pow(n int) Dual {
    result := Dual{Real: 1, Dual: 0}
    for i := 0; i < n; i++ {
        result = result.Mul(d)
    }
    return result
}

// f defines the function: f(x) = x² + 3x + 5.
func f(x Dual) Dual {
    return x.Pow(2).Add(Dual{Real: 3, Dual: 0}.Mul(x)).Add(Dual{Real: 5, Dual: 0})
}

// differentiate computes the derivative of f at x0.
func differentiate(f func(Dual) Dual, x0 float64) float64 {
    x := Dual{Real: x0, Dual: 1}
    return f(x).Dual
}

func main() {
    x0 := 2.0
    value := f(Dual{Real: x0, Dual: 0}).Real
    deriv := differentiate(f, x0)
    fmt.Printf("Simple Example: At x = %v, f(x) = %v and f'(x) = %v\n", x0, value, deriv)
}