# Source code for galpy.potential.PowerTriaxialPotential

###############################################################################
#   PowerTriaxialPotential: Potential of a triaxial power-law
#
#                                        amp
#                          rho(x,y,z)= ---------
#                                       m^\alpha
#
#                                 with m^2 = x^2+y^2/b^2+z^2/c^2
#
###############################################################################
import numpy
from ..util import conversion
from .EllipsoidalPotential import EllipsoidalPotential
[docs]class PowerTriaxialPotential(EllipsoidalPotential):
"""Class that implements triaxial potentials that are derived from power-law density models (including an elliptical power law)

.. math::

\\rho(r) = \\frac{\\mathrm{amp}}{r_1^3}\\,\\left(\\frac{r_1}{m}\\right)^{\\alpha}

where :math:m^2 = x^2+y^2/b^2+z^2/c^2.
"""
[docs]    def __init__(self,amp=1.,alpha=1.,r1=1.,b=1.,c=1.,
zvec=None,pa=None,glorder=50,
normalize=False,ro=None,vo=None):
"""
NAME:

__init__

PURPOSE:

initialize a triaxial power-law potential

INPUT:

amp - amplitude to be applied to the potential (default: 1); can be a Quantity with units of mass or Gxmass

alpha - power-law exponent

r1= (1.) reference radius for amplitude (can be Quantity)

b - y-to-x axis ratio of the density

c - z-to-x axis ratio of the density

zvec= (None) If set, a unit vector that corresponds to the z axis

pa= (None) If set, the position angle of the x axis (rad or Quantity)

glorder= (50) if set, compute the relevant force and potential integrals with Gaussian quadrature of this order

ro=, vo= distance and velocity scales for translation into internal units (default from configuration file)

OUTPUT:

(none)

HISTORY:

2021-05-07 - Started - Bovy (UofT)

"""
EllipsoidalPotential.__init__(self,amp=amp,b=b,c=c,
zvec=zvec,pa=pa,glorder=glorder,
ro=ro,vo=vo,amp_units='mass')
r1= conversion.parse_length(r1,ro=self._ro)
self.alpha= alpha
# Back to old definition
if self.alpha != 3.:
self._amp*= r1**(self.alpha-3.)*4.*numpy.pi/(3.-self.alpha)
# Multiply in constants
self._amp*= (3.-self.alpha)/4./numpy.pi
if normalize or \
(isinstance(normalize,(int,float)) \
and not isinstance(normalize,bool)): #pragma: no cover
self.normalize(normalize)
self.hasC= not self._glorder is None
self.hasC_dxdv= False
self.hasC_dens= self.hasC # works if mdens is defined, necessary for hasC
return None

def _psi(self,m):
"""\psi(m) = -\int_m^\infty d m^2 \rho(m^2)"""
return 2./(2.-self.alpha)*m**(2.-self.alpha)

def _mdens(self,m):
"""Density as a function of m"""
return m**-self.alpha

def _mdens_deriv(self,m):
"""Derivative of the density as a function of m"""
return -self.alpha*m**-(1.+self.alpha)