.. note::
    :class: sphx-glr-download-link-note

    Click :ref:`here <sphx_glr_download_auto_examples_wasserstein_loss_plot_wasserstein.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_wasserstein_loss_plot_wasserstein.py:


==================================================================
Wasserstein loss and its derivative used in jl_spectra_2_structure
==================================================================

This example shows how to deconvolute spectra using the model

The parity plot for the mixtures where concentrations are known is shown in
figure 1 and the plot of concentration with time for the experimental spectra
from reacting systems are shown in figure 2 and 3 for different starting
concentrations


.. code-block:: default


    import numpy as np
    from scipy.special import kl_div
    import matplotlib.pyplot as plt
    from matplotlib import gridspec
    from jl_spectra_2_structure.plotting_tools import set_figure_settings







set figure settings
-------------------

First we'll set up vectors to store the wasserstein loss of A1, A2, and A3, with respect to B.
The kl-divergence loss does not change with these threee vectors.
Second we'll set up the vectors to store the derivative of the loss with respect to the non-zero indices.


.. code-block:: default


    set_figure_settings('presentation')
    a = np.linspace(0,1,num=100,endpoint=True)
    B = [0,0,0,1]
    Wl = np.zeros_like(a)
    Wl2 = np.zeros_like(a)
    Wl3 = np.zeros_like(a)
    KL = np.zeros_like(a)
    dEdO1 = np.zeros_like(a)
    dEdO2 = np.zeros_like(a)
    dEdO3 = np.zeros_like(a)
    dEdO14 = np.zeros_like(a)
    dEdO24 = np.zeros_like(a)
    dEdO34 = np.zeros_like(a)
    dKLdOi = np.zeros_like(a)
    for i in range(len(a)):
        A = np.array([a[i],0,0,1-a[i]])
        Akl = [a[i]+10**-12,+10**-12,+10**-12,1-a[i]+10**-12]
        Bkl = [10**-12,10**-12,10**-12,1+10**-12]
        KL[i] = np.sum(kl_div(Bkl,Akl))
        dKLdOi[i] = a[i]
        W = (1/len(A)*np.sum((np.cumsum(A)-np.cumsum(B))**2))**0.5
        dEdO = 2*A*(np.cumsum((np.cumsum(A)-np.cumsum(B))[::-1])[::-1]-np.sum(np.cumsum(A)*(np.cumsum(A)-np.cumsum(B))))
        dEdO1[i] = dEdO[0]
        dEdO14[i] = dEdO[3]
        Wl[i]= W
        A = np.array([0,a[i],0,1-a[i]])
        W = (1/len(A)*np.sum((np.cumsum(A)-np.cumsum(B))**2))**0.5
        dEdO = 2*A*(np.cumsum((np.cumsum(A)-np.cumsum(B))[::-1])[::-1]-np.sum(np.cumsum(A)*(np.cumsum(A)-np.cumsum(B))))
        dEdO2[i] = dEdO[1]
        dEdO24[i] = dEdO[3]
        Wl2[i]= W
        A = np.array([0,0,a[i],1-a[i]])
        W = (1/len(A)*np.sum((np.cumsum(A)-np.cumsum(B))**2))**0.5
        dEdO = 2*A*(np.cumsum((np.cumsum(A)-np.cumsum(B))[::-1])[::-1]-np.sum(np.cumsum(A)*(np.cumsum(A)-np.cumsum(B))))
        dEdO3[i] = dEdO[2]
        dEdO34[i] = dEdO[3]
        Wl3[i]= W
   
    KL/= np.max(KL)
    G = gridspec.GridSpec(2, 1)
    plt.figure(0,figsize=(7,7.6))
    ax1 = plt.subplot(G[0,0])
    ax1.plot(a,Wl,'g',a,Wl2,'b',a,Wl3,'darkorange',a,KL,'k')
    plt.xticks([])
    plt.ylabel('Loss')
    plt.legend(['[a,0,0,1-a]','[0,a,0,1-a]','[0,0,a,1-a]','kl-div'])
    ax2 = plt.subplot(G[1,0])
    ax2.plot(a,dEdO1,'g--')
    ax2.plot(a,dEdO2,'b--')
    ax2.plot(a,dEdO3,'darkorange',linestyle='--')
    ax2.plot(a,dKLdOi,'k--')
    ax2.plot(a,dEdO14,'g:')
    ax2.plot(a,dEdO24,'b:')
    ax2.plot(a,dEdO34,'darkorange',linestyle=':')
    ax2.plot(a,-dKLdOi,'k:')
    plt.xlabel('a')
    plt.ylabel('Derivative wrt\n nonzero elements')
    plt.legend(['[a,0,0,1-a]','[0,a,0,1-a]','[0,0,a,1-a]','kl-div'])
    plt.show()




.. image:: /auto_examples/wasserstein_loss/images/sphx_glr_plot_wasserstein_001.png
    :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    C:\Users\lansf\Box Sync\Synced_Files\Coding\Python\Github\jl_spectra_2_structure\examples\wasserstein_loss\plot_wasserstein.py:86: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
      plt.show()




.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  0.219 seconds)


.. _sphx_glr_download_auto_examples_wasserstein_loss_plot_wasserstein.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: sphx-glr-footer-example



  .. container:: sphx-glr-download

     :download:`Download Python source code: plot_wasserstein.py <plot_wasserstein.py>`



  .. container:: sphx-glr-download

     :download:`Download Jupyter notebook: plot_wasserstein.ipynb <plot_wasserstein.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_