Cross Section for Many Lines using PreMODIT
===========================================

Update: October 30/2022, Hajime Kawahara

We demonstarte the Precomputation of opacity version of Modified
Discrete Integral Transform (PreMODIT), which is the modified version of
MODIT for exojax. PreMODIT uses the evenly-spaced logarithm grid (ESLOG)
as a wavenumber dimension. PreMODIT takes advantage especially for the
case that the number of the molecular line is large (typically >
100,000). We here compare the results by PreMODIT with the direct
computation (LPF).

Here, we use FP64, but if you want you can use FP32 (but slightly large
errors):

.. code:: ipython3

    from jax.config import config
    config.update("jax_enable_x64", True)

.. code:: ipython3

    import matplotlib.pyplot as plt
    from exojax.spec.hitran import SijT, doppler_sigma, gamma_hitran, gamma_natural
    from exojax.spec import api
    from exojax.utils.grids import wavenumber_grid
    
    # Setting wavenumber bins and loading HITRAN database
    nus, wav, R = wavenumber_grid(1900.0,
                                  2300.0,
                                  350000,
                                  unit="cm-1",
                                  xsmode="premodit")
    isotope=1
    mdbCO = api.MdbHitran('CO', nus, isotope=isotope)
    
    # set T, P and partition function
    Mmol = 28.01  # molecular weight
    Tfix = 1000.0  # we assume T=1000K
    Pfix = 1.e-3  # we compute P=1.e-3 bar
    Ppart = Pfix  #partial pressure of CO. here we assume a 100% CO atmosphere.



.. parsed-literal::

    xsmode assumes ESLOG in wavenumber space: mode=premodit


We need to precompute some quantities. These can be computed using
initspec.init_premodit.

.. code:: ipython3

    from exojax.spec import initspec
    Ttyp=1000.0
    interval_contrast = 0.1
    dit_grid_resolution=0.1
    lbd, multi_index_uniqgrid, elower_grid, ngamma_ref_grid, n_Texp_grid, R, pmarray = initspec.init_premodit(
            mdbCO.nu_lines,
            nus,
            mdbCO.elower,
            mdbCO.gamma_air,
            mdbCO.n_air,
            mdbCO.Sij0,
            Ttyp,
            interval_contrast=interval_contrast,
            dit_grid_resolution=dit_grid_resolution,
            warning=False)



.. parsed-literal::

    uniqidx: 100%|██████████| 11/11 [00:00<00:00, 43732.08it/s]


Precompute the normalized Dopper width and the partition function ratio:

.. code:: ipython3

    from exojax.spec.molinfo import molmass
    from exojax.spec import normalized_doppler_sigma
    
    Mmol = molmass("CO")
    nsigmaD = normalized_doppler_sigma(Tfix, Mmol, R)
    qt = mdbCO.qr_interp(isotope, Tfix)
        

Let’s compute the cross section!

.. code:: ipython3

    from exojax.spec.premodit import xsvector
    
    xs = xsvector(Tfix, Pfix, nsigmaD, lbd, R, pmarray, nus,
                       elower_grid, multi_index_uniqgrid, ngamma_ref_grid,
                       n_Texp_grid, qt)
        


Also, we here try the direct computation using LPF for the comparison
purpose

.. code:: ipython3

    from exojax.spec.lpf import auto_xsection
    
    #computes logsij0 etc in device
    mdbCO.generate_jnp_arrays()
    # compute Sij, gamma_L, sigmaD
    Sij=SijT(Tfix,mdbCO.logsij0,mdbCO.nu_lines,mdbCO.elower,qt)
    gammaL = gamma_hitran(Pfix,Tfix, Ppart, mdbCO.n_air, \
                          mdbCO.gamma_air, mdbCO.gamma_self) \
    + gamma_natural(mdbCO.A)
    
    sigmaD=doppler_sigma(mdbCO.nu_lines,Tfix,Mmol)
    xsv=auto_xsection(nus,mdbCO.nu_lines,sigmaD,gammaL,Sij,memory_size=30)


.. parsed-literal::

    100%|██████████| 13/13 [00:01<00:00,  8.07it/s]


.. code:: ipython3

    fig=plt.figure(figsize=(10,5))
    ax=fig.add_subplot(211)
    plt.plot(nus,xs,lw=1,alpha=0.5,label="PreMODIT")
    plt.plot(nus,xsv,lw=1,alpha=0.5,label="Direct LPF")
    plt.legend(loc="upper right")
    plt.ylabel("Cross Section (cm2)")
    ax=fig.add_subplot(212)
    plt.plot(nus,xsv-xs,lw=2,alpha=0.5,label="PreMODIT")
    plt.ylabel("LPF - DIT (cm2)")
    plt.legend(loc="upper left")
    plt.show()



.. image:: Cross_Section_using_Precomputation_Modified_Discrete_Integral_Transform_files/Cross_Section_using_Precomputation_Modified_Discrete_Integral_Transform_12_0.png


There is about 1 % deviation between LPF and PreMODIT.

.. code:: ipython3

    fig=plt.figure(figsize=(10,5))
    ax=fig.add_subplot(211)
    plt.plot(nus,xs,lw=2,alpha=0.5,label="PreMODIT")
    plt.plot(nus,xsv,lw=1,alpha=0.5,label="Direct")
    plt.legend(loc="upper right")
    plt.xlim(2050.8,2050.9)
    plt.ylabel("Cross Section (cm2)")
    ax=fig.add_subplot(212)
    plt.plot(nus,xsv-xs,lw=2,alpha=0.6,label="MODIT")
    plt.legend(loc="upper left")
    plt.ylabel("Difference (cm2)")
    plt.xlim(2050.8,2050.9)
    #plt.yscale("log")
    plt.savefig("fine_grid.png")



.. image:: Cross_Section_using_Precomputation_Modified_Discrete_Integral_Transform_files/Cross_Section_using_Precomputation_Modified_Discrete_Integral_Transform_14_0.png