使用 python 中的最小化时 Julia 中的 Function 和 Lambda 表达式

Question

I have a code in Julia where I use the function minimize from python. Here I put a simplified example of it works the cose

using PyCall
@pyimport scipy.optimize as so

function fidelity1(x)
    f1 = x[1]*x[1]+3*x[2]*x[2]
    return f1
end

x0 = [1 1]
res = so.minimize(fidelity1,x0)

whose result is correctly

Dict{Any,Any} with 10 entries:
  "hess_inv" => [0.5 3.0102e-12; 3.0102e-12 0.166667]
  "fun"      => 2.22049e-16
  "nfev"     => 18
  "status"   => 0
  "message"  => "Optimization terminated successfully."
  "success"  => true
  "x"        => [-7.45039e-9, -7.45073e-9]
  "jac"      => [3.73556e-13, -9.08177e-13]
  "nit"      => 4
  "njev"     => 6

Now, it would be very useful to use a lambda expression, so I write the code in the following way

using PyCall
@pyimport scipy.optimize as so

fidelity2 = (x1,x2) ->  x1*x1+3*x2*x2

x0 = [1 1]
res = so.minimize(fidelity2,x0)

However, in this case I obtain

(in a Julia function called from Python)
JULIA: MethodError: no method matching (::var"#3#4")(::Array{Float64,1})
Closest candidates are:
  #3(::Any, !Matched::Any) at In[2]:4
Stacktrace:
 [1] #invokelatest#1 at ./essentials.jl:712 [inlined]
 [2] invokelatest(::Any, ::Any) at ./essentials.jl:711
 [3] _pyjlwrap_call(::Function, ::Ptr{PyCall.PyObject_struct}, ::Ptr{PyCall.PyObject_struct}) at /home/candeloro/.julia/packages/PyCall/tqyST/src/callback.jl:28
 [4] pyjlwrap_call(::Ptr{PyCall.PyObject_struct}, ::Ptr{PyCall.PyObject_struct}, ::Ptr{PyCall.PyObject_struct}) at /home/candeloro/.julia/packages/PyCall/tqyST/src/callback.jl:44
 [5] macro expansion at /home/candeloro/.julia/packages/PyCall/tqyST/src/exception.jl:95 [inlined]
 [6] #109 at /home/candeloro/.julia/packages/PyCall/tqyST/src/pyfncall.jl:43 [inlined]
 [7] disable_sigint at ./c.jl:446 [inlined]
 [8] __pycall! at /home/candeloro/.julia/packages/PyCall/tqyST/src/pyfncall.jl:42 [inlined]
 [9] _pycall!(::PyObject, ::PyObject, ::Tuple{var"#3#4",Array{Int64,2}}, ::Int64, ::Ptr{Nothing}) at /home/candeloro/.julia/packages/PyCall/tqyST/src/pyfncall.jl:29
 [10] _pycall!(::PyObject, ::PyObject, ::Tuple{var"#3#4",Array{Int64,2}}, ::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}) at /home/candeloro/.julia/packages/PyCall/tqyST/src/pyfncall.jl:11
 [11] (::PyObject)(::Function, ::Vararg{Any,N} where N; kwargs::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}) at /home/candeloro/.julia/packages/PyCall/tqyST/src/pyfncall.jl:86
 [12] (::PyObject)(::Function, ::Vararg{Any,N} where N) at /home/candeloro/.julia/packages/PyCall/tqyST/src/pyfncall.jl:86
 [13] top-level scope at In[2]:7
 [14] eval at ./boot.jl:331 [inlined]
 [15] softscope_include_string(::Module, ::String, ::String) at /home/candeloro/.julia/packages/SoftGlobalScope/u4UzH/src/SoftGlobalScope.jl:217
 [16] execute_request(::ZMQ.Socket, ::IJulia.Msg) at /home/candeloro/.julia/packages/IJulia/IDNmS/src/execute_request.jl:67
 [17] #invokelatest#1 at ./essentials.jl:712 [inlined]
 [18] invokelatest at ./essentials.jl:711 [inlined]
 [19] eventloop(::ZMQ.Socket) at /home/candeloro/.julia/packages/IJulia/IDNmS/src/eventloop.jl:8
 [20] (::IJulia.var"#15#18")() at ./task.jl:358

Stacktrace:
 [1] pyerr_check at /home/candeloro/.julia/packages/PyCall/tqyST/src/exception.jl:62 [inlined]
 [2] pyerr_check at /home/candeloro/.julia/packages/PyCall/tqyST/src/exception.jl:66 [inlined]
 [3] _handle_error(::String) at /home/candeloro/.julia/packages/PyCall/tqyST/src/exception.jl:83
 [4] macro expansion at /home/candeloro/.julia/packages/PyCall/tqyST/src/exception.jl:97 [inlined]
 [5] #109 at /home/candeloro/.julia/packages/PyCall/tqyST/src/pyfncall.jl:43 [inlined]
 [6] disable_sigint at ./c.jl:446 [inlined]
 [7] __pycall! at /home/candeloro/.julia/packages/PyCall/tqyST/src/pyfncall.jl:42 [inlined]
 [8] _pycall!(::PyObject, ::PyObject, ::Tuple{var"#3#4",Array{Int64,2}}, ::Int64, ::Ptr{Nothing}) at /home/candeloro/.julia/packages/PyCall/tqyST/src/pyfncall.jl:29
 [9] _pycall!(::PyObject, ::PyObject, ::Tuple{var"#3#4",Array{Int64,2}}, ::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}) at /home/candeloro/.julia/packages/PyCall/tqyST/src/pyfncall.jl:11
 [10] (::PyObject)(::Function, ::Vararg{Any,N} where N; kwargs::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}) at /home/candeloro/.julia/packages/PyCall/tqyST/src/pyfncall.jl:86
 [11] (::PyObject)(::Function, ::Vararg{Any,N} where N) at /home/candeloro/.julia/packages/PyCall/tqyST/src/pyfncall.jl:86
 [12] top-level scope at In[2]:7

I can't figure out why the second code doesn't work

Answer 1

scipy.optimize.minimize expects the objective function, in your case fidelity2 , to take an array of size (n,) as its first argument that holds the values for n independent variables. While migrating to the second format where you use a lambda expression, observe that you also change the signature: fidelity2 expects the independent variables in different function parameters rather than in an array, but that is not how scipy.optimize.minimize operates.

If all you want is to use lambda expressions, you may change fidelity2 to be more like in your first example

using PyCall
@pyimport scipy.optimize as so

fidelity2 = x -> x[1]*x[1]+3*x[2]*x[2]

x0 = [1 1]
res = so.minimize(fidelity2, x0)

Note that you do not have to name your lambda expression. You may use it as an anonymous function inside your call to minimize . That means the following also works:

using PyCall
@pyimport scipy.optimize as so

x0 = [1 1]
res = so.minimize(x -> x[1]*x[1]+3*x[2]*x[2], x0)