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Allow a dual to be raised to a complex power. #102

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Allow a dual to be raised to a complex power. #102

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1 change: 1 addition & 0 deletions src/dual.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -283,6 +283,7 @@ for T1 ∈ (:Integer, :Rational, :Number)
@eval Base.:^(z::Dual{T}, n::$T1) where T = pow(z, n)
end

Base.:^(x::Dual, p::Complex) = exp((log(abs2(x))/2 + im * angle(x)) * p)

NaNMath.pow(z::Dual{T}, n::Number) where T = Dual(NaNMath.pow(value(z),n), epsilon(z)*n*NaNMath.pow(value(z),n-1))
NaNMath.pow(z::Number, w::Dual{T}) where T = Dual(NaNMath.pow(z,value(w)), epsilon(w)*NaNMath.pow(z,value(w))*log(z))
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8 changes: 8 additions & 0 deletions test/automatic_differentiation_test.jl
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Expand Up @@ -62,6 +62,14 @@ y = Dual(2.0, 1)^UInt64(0)
@test !isnan(epsilon(y))
@test epsilon(y) == 0

# test dual^complex
a, b = rand(), rand(ComplexF64)
@test realpart(Dual(a, 1)^b) ≈ a^b
@test dualpart(Dual(a, 1)^b) ≈ b * a^(b - 1)
a, b = rand(ComplexF64), rand(ComplexF64)
@test realpart(Dual(a, 1)^b) ≈ a^b
@test dualpart(Dual(a, 1)^b) ≈ b * a^(b - 1)

y = sin(x)+exp(x)
@test value(y) ≈ sin(2)+exp(2)
@test epsilon(y) ≈ cos(2)+exp(2)
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