L2 regularization using GradientDescent
-------------------------------------------

.. code:: python
    
    import numpy as np
    import jax.numpy as jnp
    from jaxsot.core.weight import comp_weight, comp_omega
    from jaxsot.core.lc import gen_lightcurve
    from jaxsot.io.earth import binarymap
    import jaxopt
    import healpy as hp
    import matplotlib.pyplot as plt


.. code:: python
    
    nside=8
    mmap=binarymap(nside=nside,show=False)
    inc=0.0
    Thetaeq=np.pi
    zeta=np.pi/3.0
    Pspin=23.9344699/24.0
    wspin=2*np.pi/Pspin
    Porb=40.0
    worb=2.*np.pi/Porb
    N=1024
    obst=np.linspace(0.0,Porb,N)
    Thetav=worb*obst
    Phiv=np.mod(wspin*obst,2*np.pi)
    omega=comp_omega(nside)
    WI,WV=comp_weight(nside,zeta,inc,Thetaeq,Thetav,Phiv,omega)
    W=jnp.array(WI*WV)
    lc=gen_lightcurve(W,mmap,0.1)

.. code:: python
    
    def objective(params,lam):
        residuals=lc - jnp.dot(W,params)
        return jnp.mean(residuals ** 2) + lam*lam * jnp.dot(params,params)
    
    gd = jaxopt.GradientDescent(fun=objective, maxiter=500)
    res = gd.run(init_params=np.random.normal(0.0,1.0,len(mmap)), lam=0.1)
    params, state = res
    hp.mollview(params)
    plt.show()