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| abstract ForwardDiffNumber{N,T<:Number,C} <: Number | ||
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| # Subtypes F<:ForwardDiffNumber should define: | ||
| # npartials(::Type{F}) --> N from ForwardDiffNumber{N,T,C} | ||
| # eltype(::Type{F}) --> T from ForwardDiffNumber{N,T,C} | ||
| # value(n::F) --> the value of n | ||
| # grad(n::F) --> a container corresponding to all first order partials | ||
| # hess(n::F) --> a container corresponding to the lower | ||
| # triangular half of the symmetric | ||
| # Hessian (including the diagonal) | ||
| # tens(n::F) --> a container of corresponding to lower | ||
| # tetrahedral half of the symmetric | ||
| # Tensor (including the diagonal) | ||
| # isconstant(n::F) --> returns true if all partials stored by n are zero | ||
| # | ||
| #...as well as: | ||
| # ==(a::F, b::F) | ||
| # isequal(a::F, b::F) | ||
| # zero(::Type{F}) | ||
| # one(::Type{F}) | ||
| # rand(::Type{F}) | ||
| # hash(n::F) | ||
| # read(io::IO, ::Type{F}) | ||
| # write(io::IO, n::F) | ||
| # conversion/promotion rules | ||
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| ############################## | ||
| # Utility/Accessor Functions # | ||
| ############################## | ||
| halfhesslen(n) = div(n*(n+1),2) # correct length(hess(::ForwardDiffNumber)) | ||
| halftenslen(n) = div(n*(n+1)*(n+2),6) # correct length(tens(::ForwardDiffNumber)) | ||
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| switch_eltype{T,S}(::Type{Vector{T}}, ::Type{S}) = Vector{S} | ||
| switch_eltype{N,T,S}(::Type{NTuple{N,T}}, ::Type{S}) = NTuple{N,S} | ||
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| grad(n::ForwardDiffNumber, i) = grad(n)[i] | ||
| hess(n::ForwardDiffNumber, i) = hess(n)[i] | ||
| tens(n::ForwardDiffNumber, i) = tens(n)[i] | ||
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| npartials{N}(::ForwardDiffNumber{N}) = N | ||
| eltype{N,T}(::ForwardDiffNumber{N,T}) = T | ||
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| npartials{N,T,C}(::Type{ForwardDiffNumber{N,T,C}}) = N | ||
| eltype{N,T,C}(::Type{ForwardDiffNumber{N,T,C}}) = T | ||
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| zero(n::ForwardDiffNumber) = zero(typeof(n)) | ||
| one(n::ForwardDiffNumber) = one(typeof(n)) | ||
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| ==(n::ForwardDiffNumber, x::Real) = isconstant(n) && (value(n) == x) | ||
| ==(x::Real, n::ForwardDiffNumber) = ==(n, x) | ||
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| isequal(n::ForwardDiffNumber, x::Real) = isconstant(n) && isequal(value(n), x) | ||
| isequal(x::Real, n::ForwardDiffNumber) = isequal(n, x) | ||
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| isless(a::ForwardDiffNumber, b::ForwardDiffNumber) = value(a) < value(b) | ||
| isless(x::Real, n::ForwardDiffNumber) = x < value(n) | ||
| isless(n::ForwardDiffNumber, x::Real) = value(n) < x | ||
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| copy(n::ForwardDiffNumber) = n # assumes all types of ForwardDiffNumbers are immutable | ||
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| eps(n::ForwardDiffNumber) = eps(value(n)) | ||
| eps{F<:ForwardDiffNumber}(::Type{F}) = eps(eltype(F)) | ||
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| isnan(n::ForwardDiffNumber) = isnan(value(n)) | ||
| isfinite(n::ForwardDiffNumber) = isfinite(value(n)) | ||
| isreal(n::ForwardDiffNumber) = isconstant(n) | ||
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| ################## | ||
| # Math Functions # | ||
| ################## | ||
| conj(n::ForwardDiffNumber) = n | ||
| transpose(n::ForwardDiffNumber) = n | ||
| ctranspose(n::ForwardDiffNumber) = n |
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