###############################################################################
#   GaussianAmplitudeWrapperPotential.py: Wrapper to modulate the amplitude
#                                         of a potential with a Gaussian
###############################################################################
import numpy
from .WrapperPotential import parentWrapperPotential
from ..util import conversion
class GaussianAmplitudeWrapperPotential(parentWrapperPotential):
    """Potential wrapper class that allows the amplitude of a Potential object to be modulated as a Gaussian. The amplitude A applied to a potential wrapped by an instance of this class is changed as

    .. math::

        A(t) = amp\\,\\exp\\left(-\\frac{[t-t_0]^2}{2\\,\\sigma^2}\\right)
    """
    def __init__(self,amp=1.,pot=None,to=0.,sigma=1.,ro=None,vo=None):
        """
        NAME:

           __init__

        PURPOSE:

           initialize a GaussianAmplitudeWrapper Potential

        INPUT:

           amp - amplitude to be applied to the potential (default: 1.)

           pot - Potential instance or list thereof; this potential is made to rotate around the z axis by the wrapper

           to= (0.) time at which the Gaussian peaks

           sigma= (1.) standard deviation of the Gaussian (can be a Quantity)

        OUTPUT:

           (none)

        HISTORY:

           2018-02-21 - Started - Bovy (UofT)

        """
        to= conversion.parse_time(to,ro=self._ro,vo=self._vo)
        sigma= conversion.parse_time(sigma,ro=self._ro,vo=self._vo)
        self._to= to
        self._sigma2= sigma**2.
        self.hasC= True
        self.hasC_dxdv= True

    def _smooth(self,t):
        return numpy.exp(-0.5*(t-self._to)**2./self._sigma2)

    def _wrap(self,attribute,*args,**kwargs):
        return self._smooth(kwargs.get('t',0.))\
                *self._wrap_pot_func(attribute)(self._pot,*args,**kwargs)
