MethodError: no method matching adjoint(::typeof(f))

I’m trying to optimize quadratic function to learn julia as below, but dind’t work.
Can anyone tell me what is wrong?

input

using PyPlot
using ForwardDiff

x_opt = 0.50
f(x) = -2(x - x_opt)^2
xs = range(-3, 3, length = 100)

fig, ax = subplots()
ax.plot(xs, f.(xs))
ax = grid()

function gradient_method_dim1(f, x_init, eta, maxiter)
    x_seq = Array{typeof(x_init), 1}(undef, maxiter)

    Dxf(x) = ForwardDiff.derivative(f, x)
    x_seq[1] = x_init
    
    for i in 2:maxiter
        x_seq[i] = x_seq[i-1] + eta*f'(x_seq[i-1])
    end

    x_seq
end

x_init = -2.5
maxiter = 100
eta = 0.1
x_seq = gradient_method_dim1(f, x_init, eta, maxiter)
f_seq = f.(x_seq)
println(f_seq)

output

ERROR: LoadError: MethodError: no method matching adjoint(::typeof(f))
Closest candidates are:
  adjoint(::Union{LinearAlgebra.QR, LinearAlgebra.QRCompactWY, LinearAlgebra.QRPivoted}) at /opt/julia-1.7.2/share/julia/stdlib/v1.7/LinearAlgebra/src/qr.jl:509
  adjoint(::Union{LinearAlgebra.Cholesky, LinearAlgebra.CholeskyPivoted}) at /opt/julia-1.7.2/share/julia/stdlib/v1.7/LinearAlgebra/src/cholesky.jl:538
  adjoint(::LinearAlgebra.SVD) at /opt/julia-1.7.2/share/julia/stdlib/v1.7/LinearAlgebra/src/svd.jl:262
  ...
Stacktrace:
 [1] gradient_method_dim1(f::Function, x_init::Float64, eta::Float64, maxiter::Int64)
   @ Main ~/path/to/optimization:22
 [2] top-level scope
   @ ~/path/to/optimization.jl:32
 [3] include(fname::String)
   @ Base.MainInclude ./client.jl:451
 [4] top-level scope
   @ REPL[49]:1
in expression starting at /path/to/optimization.jl:32

Welcome to Julia Discourse, and thanks for providing your code and stacktrace!

This means you tried to call adjoint on the function f (whose type is typeof(f)), but that method isn’t defined. Even though you didn’t explicitly write adjoint(f) anywhere, you do have

Specifically, f' is parsed as adjoint(f), so an equivalent statement to the above is

x_seq[i] = x_seq[i-1] + eta * adjoint(f)(x_seq[i-1])

It looks like you meant to take the derivative of f, so you should instead write

x_seq[i] = x_seq[i-1] + eta * Dxf(x_seq[i-1])

Thank you for your kind instruction.
I’ve noticed my super easy mistake :frowning: