dual R6 class for forward-mode automatic differentiation

dual R6 class for forward-mode automatic differentiation

dual R6 class for forward-mode automatic differentiation

Details

Represents a dual number (primal, tangent) for computing directional derivatives via forward-mode AD. When combined with reverse-mode (value), enables Hessian computation via forward-over-reverse.

Forward-mode AD propagates derivatives alongside values during the forward pass. For a function f(x), setting tangent(x) = 1 gives f'(x) in the tangent of the output.

For Hessian computation (forward-over-reverse):

• primal is a value object (for reverse-mode gradient)

• tangent is also a value object (tracks d/dx of the gradient)

• After backward() on primal, tangent of grad gives Hessian entries

Public fields

primal

The function value (can be numeric or value object)

tangent

The directional derivative (can be numeric or value object)

Methods

Public methods

• dual$new()

• dual$clone()

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Method new()

Create a new dual number

Usage

dual$new(primal, tangent = 0)

Arguments

primal

The primal value (numeric or value object)

tangent

The tangent (derivative direction), default 0

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Method clone()

The objects of this class are cloneable with this method.

Usage

dual$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.