CODEWITHSUNDEEP
juliasymbolic-mathcalculusdifferentiation
Frank Seidl
Frank Seidl

Reputation: 170

Julia symbolic differentiation

Though I've looked through several pages documenting various differentiation tools in Julia, I have yet to find the following simple functionality. I want to define a function which is differentiable by hand, e.g, f(x) = 2x.^3, then call a symbolic computation function to obtain fprime = derivative(f). This code should produce the same results as fprime(x) = 6x.^2. Is there a library function which acts like the made-up function derivative above?

Upvotes: 2

Views: 1795

Answers (3)

SGJ
SGJ

Reputation: 1058

There are various packages for automatic differentiation (AD) in Julia. For a single-variable function like the one you describe, the simplest and fastest is probably the ForwardDiff package, which lets you do:

using ForwardDiff
fprime(x) = ForwardDiff.derivative(f, x)

ForwardDiff and other AD packages indeed compute the exact analytical derivative, equivalent to the 6x^2 you might write by hand. (However, the algorithms are a bit different from the "form a big symbolic expression then differentiate" that you might imagine.)

Upvotes: 1

Przemyslaw Szufel
Przemyslaw Szufel

Reputation: 42244

If you work numerically with symbolic derivatives you can also use code-to-code symbolic differentiation by using Zygote

Assume you have f(x) = 2x^3 than having Zygote loaded you can do

julia> f'(5)
150.0

to understand what just happened peek into the compilation process to see that the function f has been actually symbolically differentiated.

julia> @code_llvm f'(5)
define double @"julia_#79_991"(i64 signext %0) #0 {
  top:
       %1 = mul i64 %0, 3
       %2 = mul i64 %1, %0
       %3 = sitofp i64 %2 to double
       %4 = fmul double %3, 2.000000e+00
  ret double %4
}

Upvotes: 1

QtizedQ
QtizedQ

Reputation: 310

The Symbolics.jl package is capable of what you're looking for, although you need to explicitly declare what your variables are

In [2]: using Symbolics

In [3]: @variables x
Out[3]: 1-element Vector{Num}:
 x

In [4]: D = Differential(x)
Out[4]: (::Differential) (generic function with 2 methods)

In [5]: f(t) = 2*t^3
Out[5]: f (generic function with 1 method)

In [6]: expand_derivatives(D(f(x)))
Out[6]: 6(x^2)

You can read more about it here: https://symbolics.juliasymbolics.org/dev/manual/derivatives/

Upvotes: 2

Related Questions