Calling a Matlab function in Fortran using mex tool

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Hi!
Using the MATLAB Engine API for Fortran, I am trying to call a simple Matlab function from a Fortran code.
I followed the fengdemo example found here : https://fr.mathworks.com/help/matlab/matlab_external/build-and-run-fortran-engine-applications-on-linux.html . It worked, so I want to adapt my Fortran code to call a specific Matlab script I wrote.
My Matlab script call_fortran.m is very simple: it takes x as an entry and multiplies it by 2:
function multiply = call_fortran(x)
multiply = 2*x;
end
I want my Fortran code to generate a variable my_x, open a Matlab session, send the variable to the workspace, apply the function call_fortran and display the result. Using the fengdemo.f code, I wrote
program main
C Declarations
implicit none
mwPointer engOpen, engGetVariable, mxCreateDoubleMatrix
mwPointer mxGetPr
mwPointer ep, my_x ! ep: variable linked to engOpen, starting a Matlab session, my_x: variable que je veux donner a Matlab
double precision my_x
integer engPutVariable, engEvalString, engClose
integer temp, status
mwSize i
my_x = 6
ep = engOpen('matlab ')
if (ep .eq. 0) then
write(6,*) 'Can''t start MATLAB engine'
stop
endif
C Place the variable my_x into the MATLAB workspace
status = engPutVariable(ep, 'my_x', my_x)
C
if (status .ne. 0) then
write(6,*) 'engPutVariable failed'
stop
endif
! My issue now is to call the correct Matlab script
C nlhs = 1
C plhs = 1
C nrhs = 1
C prhs = 1
C integer*4 mexCallMATLAB(nlhs, plhs, nrhs, prhs, functionName)
So I have my my_x, I send it to Matlab, but how do I apply the call_fortran.m function and get the new value of my_x ?
Thank you in advance for your help!

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