I'm building a homecooked-function to return the symbolic derivative expression and a callable derivative function.
Pkg.add("Symbolics")
using Symbolics
function derivative(exp,x)
@variables x
Dx=Differential(x)
ϕe = exp
return (expand_derivatives(Dx(ϕe))), first(substitute.(expand_derivatives(Dx(ϕe)), (Dict(x => ξ),)))
end
# RESULTS: : derivative
derivative(-x^2 0.1*sin(x) 2*sin(x)^2,x)
# RESULTS: (error)
ERROR: MethodError: no method matching ^(::StepRangeLen{Float64, Base.TwicePrecis
ion{Float64}, Base.TwicePrecision{Float64}}, ::Int64)
Closest candidates are:
^(::Union{AbstractChar, AbstractString}, ::Integer) at strings/basic.jl:718
^(::LinearAlgebra.Symmetric{var"#s814", S} where {var"#s814"<:Real, S<:(Abstrac
tMatrix{var"#s814"} where var"#s814"<:var"#s814")}, ::Integer) at /build/julia/sr
c/julia-1.6.3/usr/share/julia/stdlib/v1.6/LinearAlgebra/src/symmetric.jl:868
^(::LinearAlgebra.Symmetric{var"#s814", S} where {var"#s814"<:Complex, S<:(Abst
ractMatrix{var"#s814"} where var"#s814"<:var"#s814")}, ::Integer) at /build/julia
/src/julia-1.6.3/usr/share/julia/stdlib/v1.6/LinearAlgebra/src/symmetric.jl:869
...
Stacktrace:
[1] macro expansion
@ ./none:0 [inlined]
[2] literal_pow(f::typeof(^), x::StepRangeLen{Float64, Base.TwicePrecision{Float
64}, Base.TwicePrecision{Float64}}, #unused#::Val{2})
@ Base ./none:0
[3] top-level scope
@ REPL[191]:1
Calling interactively what I would like that the function does (expected behavior):
@variables x
Dx=Differential(x)
ϕe = -x^2 0.1*sin(x) 2*sin(x)^2
(expand_derivatives(Dx(ϕe)))
# RESULTS: : 0.1cos(x) 4cos(x)*sin(x) - 2x
dϕ(ξ) = first(substitute.(expand_derivatives(Dx(ϕe)), (Dict(x => ξ),)))
# RESULTS: : dϕ
dϕ(1)
# RESULTS: : -0.12737491576182247
CodePudding user response:
You may turn the exp
into a anonymous function that receives x
as a variable, like the following:
julia> function derivative(exp, ξ)
@variables x
Dx=Differential(x)
ϕe = exp(x) # <-- change here
return (expand_derivatives(Dx(ϕe))), first(substitute.(expand_derivatives(Dx(ϕe)), (Dict(x => ξ),)))
end
julia> derivative(x->-x^2 0.1*sin(x) 2*sin(x)^2, 1)
(0.1cos(x) 4cos(x)*sin(x) - (2x), -0.12737491576182247)
You can also use the do syntax if you like, which is equivalent to passing x -> ...
.
julia> derivative(1) do x
-x^2 0.1*sin(x) 2*sin(x)^2
end
(0.1cos(x) 4cos(x)*sin(x) - (2x), -0.12737491576182247)