.. _nnevo_scipy_infinite_well:

Optimizing well width for specific target transition energy in an infinite quantum well
======================================================================================== 

.. attention::
   |The_nextnanoevo_package| is under development. 

.. contents::
   :local:
   :backlinks: none


Header
---------

    Relevant files
      - :guilabel:`1D_IntersubbandAbsorption_InfiniteWell_GaAs_Chuang_sg_nnp.in` 
      - :guilabel:`InfiniteWell_example.py` (not public yet, provided on request)

    Relevant output files:
      - :guilabel:`bias_00000/Quantum/energy_spectrum_quantum_region_Gamma_00000.dat`
    
    Scope
      - design optimization
      - quantum well
      - transition energies

    Important variables
      - ``$QuantumWellWidth`` = thickness of the GaAs quantum well


Introduction
------------

This tutorial demonstrates the use of nextnanoevo for optimization of a simple quantum well structure to achieve desired transition energy.
The tutorial is based on the :ref:`Intersubband absorption of an infinite quantum well <tutorial_intersubband_InfiniteQW>` tutorial.


Objective
^^^^^^^^^

The goal of this optimization is to determine the quantum well thickness that aligns the transition between the first and second electron states with a specified target energy.

Variables under optimization: 

.. table::

    ================ ======== ================= ========
    Name              Units      Initial value   Bounds  
    ================ ======== ================= ========
    QuantumWellWidth    nm          10.0           --      
    ================ ======== ================= ========


Target output:

.. table::

    ================= ======== ================= ========
    Name              Units      Initial value   Target  
    ================= ======== ================= ========
    Transition energy   eV          0.1668         0.1      
    ================= ======== ================= ========



Scipy.optimize.root
^^^^^^^^^^^^^^^^^^^

In this example scipy.optimize.root root-solver is used. The algorithm searches for the root of the equation

.. math::
   f(x) - target = 0


where :math:`x` represents the vector of input variables and :math:`f` is the user-defined metric.


Optimization script
-------------------

Initially, create a nextnanoevo.IO instance specifying the input file, optimization variables, and output files relevant for the metric.


.. code:: Python

    from nextnanoevo.IO import IO
    nn_io = NextnanoIO(input_file_path,
                     variable_names=['QuantumWellWidth'],
                     target_output_paths=[('bias_00000', 'Quantum', 'energy_spectrum_quantum_region_Gamma_00000.dat')])


Next, define the metric function to extract the transition energy from the energy_spectrum datafile.

.. code:: Python

    def first_transition_extraction_function(df_list):
        df_energy_spectrum = df_list[0]  # df_list will be a list containing one datafile
        energy_spectrum = df_energy_spectrum.variables['Energy'].value
        transition_energy = energy_spectrum[1] - energy_spectrum[0]  # transition energy between the ground state and second state
        return np.array([transition_energy])


A nextnanoevo.Metric is created with the custom metric function. 
Extraction function takes single output file and converts it to single value, so both input length and output length equal 1.

.. code:: Python

    from nextnanoevo.MetricExtractor import Metric
    metric = Metric(input_length=1, output_length=1, extraction_function=first_transition_extraction_function)


Create the Optimizer, and set the initial value for quantum well thickness and target transition energy.


.. code:: Python

    from nextnanoevo.OptimizerClass import Optimizer
    optimizer = Optimizer(nextnanoio=nn_io, metric=metric, optimization_method='root')
    # arguments of the optimization_method. For scipy optimize.root x0 is mandatory
    optimizer.set_optimization_parameters(x0=np.array([10]))
    # set target 
    optimizer.set_target(np.array([0.1]))


Run the optimization. The details are recorded in the Simulation*.log file, which tracks each input file execution.

.. code:: Python

    
    result = optimizer.run_optimization()
    print(f"The optimal quantum well thickness is {result.x} nm")
    
Output:

.. code:: shell

    The optimal quantum well thickness is [12.80762256] nm


Conclusion
----------

In summary, this tutorial has demonstrated an approach to optimize a quantum well structure to match a specific transition energy using nextnanoevo.
The process involved setting up the NextnanoIO instance, defining a custom metric function, utilizing the NextnanoMetricExtractor, and finally employing the NextnanoOptimizer for the actual optimization task.