API

API for TaylorDiff.

TaylorDiff.TaylorArray — Type
TaylorArray{T, N, A, P}

Representation of Taylor polynomials in array mode.

Fields

  • value::A: zeroth order coefficient
  • partials::NTuple{P, A}: i-th element of this stores the i-th derivative
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TaylorDiff.TaylorScalar — Type
TaylorScalar{T, P}

Representation of Taylor polynomials.

Fields

  • value::T: zeroth order coefficient
  • partials::NTuple{P, T}: i-th element of this stores the i-th derivative
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TaylorDiff.TaylorScalar — Method
TaylorScalar{P}(value::T, seed::T)

Convenience function: construct a Taylor polynomial with zeroth and first order coefficient, acting as a seed.

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TaylorDiff.TaylorScalar — Method
TaylorScalar{P}(value::T) where {T, P}

Convenience function: construct a Taylor polynomial with zeroth order coefficient.

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TaylorDiff.can_taylorize — Method
TaylorDiff.can_taylorize(V::Type)

Determines whether the type V is allowed as the scalar type in a Dual. By default, only <:Number types are allowed.

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TaylorDiff.derivative — Function
derivative(f, x, ::Val{P})
derivative(f, x, l, ::Val{P})
derivative(f!, y, x, l, ::Val{P})

Computes P-th directional derivative of f w.r.t. vector x in direction l. If x is a Number, the direction l can be omitted.

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TaylorDiff.derivative! — Function
derivative!(result, f, x, l, ::Val{P})
derivative!(result, f!, y, x, l, ::Val{P})

In-place derivative calculation APIs. result is expected to be pre-allocated and have the same shape as y.

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TaylorDiff.derivatives — Function
derivatives(f, x, l, ::Val{P})
derivatives(f!, y, x, l, ::Val{P})

Computes all derivatives of f at x up to order P.

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TaylorDiff.get_term_raiser — Method
get_term_raiser(func)

Return the derivative of func as an expression in z, together with the strategy for raising it to higher orders: if the derivative is inv(term) or 1 / term (possibly negated), term (respectively -term) is raised with the division rule raiseinv; otherwise the derivative is raised with the multiplication rule raise.

The expression is evaluated on Taylor series, so it must equal the derivative as a function (not only numerically) and must not branch on values. Such expressions are taken from DiffRules, whose rules are value-free expressions by design (unlike ChainRules' rules, which are only meant to be evaluated on numbers).

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TaylorDiff.@immutable — Macro
immutable(def)

Transform a function definition to a @generated function.

  1. Allocations are removed by replacing the output with scalar variables;
  2. Loops are unrolled;
  3. Indices are modified to use 1-based indexing;
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