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actionAngleAdiabaticGrid.py
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actionAngleAdiabaticGrid.py
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###############################################################################
# actionAngle: a Python module to calculate actions, angles, and frequencies
#
# class: actionAngleAdiabaticGrid
#
# build grid in integrals of motion to quickly evaluate
# actionAngleAdiabatic
#
# methods:
# __call__: returns (jr,lz,jz)
#
###############################################################################
import numpy
from scipy import interpolate
from .. import potential
from ..potential.Potential import _evaluatePotentials
from ..potential.Potential import flatten as flatten_potential
from ..util import multi
from .actionAngle import UnboundError, actionAngle
from .actionAngleAdiabatic import actionAngleAdiabatic
_PRINTOUTSIDEGRID = False
class actionAngleAdiabaticGrid(actionAngle):
"""Action-angle formalism for axisymmetric potentials using the adiabatic approximation, grid-based interpolation"""
def __init__(
self,
pot=None,
zmax=1.0,
gamma=1.0,
Rmax=5.0,
nR=16,
nEz=16,
nEr=31,
nLz=31,
numcores=1,
**kwargs
):
"""
Initialize an actionAngleAdiabaticGrid object
Parameters
----------
pot : Potential or list of Potential instances
The potential (instance) or list of potentials (instances) that make up the potential
zmax : float
Maximum height to which to calculate Ez
gamma : float
Replace Lz by Lz+gamma Jz in effective potential
Rmax : float
Maximum radius to which to calculate Er
nR : int
Number of radii to use in the grid
nEz : int
Number of Ez values to use in the grid
nEr : int
Number of Er values to use in the grid
nLz : int
Number of Lz values to use in the grid
numcores : int
Number of cores to use for multi-processing
ro : float or Quantity, optional
Distance scale for translation into internal units (default from configuration file).
vo : float or Quantity, optional
Velocity scale for translation into internal units (default from configuration file).
Notes
-----
- 2012-07-27 - Written - Bovy (IAS@MPIA)
"""
actionAngle.__init__(self, ro=kwargs.get("ro", None), vo=kwargs.get("vo", None))
if pot is None: # pragma: no cover
raise OSError("Must specify pot= for actionAngleAdiabaticGrid")
self._c = kwargs.pop("c", False)
self._gamma = gamma
self._pot = flatten_potential(pot)
self._zmax = zmax
self._Rmax = Rmax
self._Rmin = 0.01
# Set up the actionAngleAdiabatic object that we will use to interpolate
self._aA = actionAngleAdiabatic(pot=self._pot, gamma=self._gamma, c=self._c)
# Build grid for Ez, first calculate Ez(zmax;R) function
self._Rs = numpy.linspace(self._Rmin, self._Rmax, nR)
self._EzZmaxs = _evaluatePotentials(
self._pot, self._Rs, self._zmax * numpy.ones(nR)
) - _evaluatePotentials(self._pot, self._Rs, numpy.zeros(nR))
self._EzZmaxsInterp = interpolate.InterpolatedUnivariateSpline(
self._Rs, numpy.log(self._EzZmaxs), k=3
)
y = numpy.linspace(0.0, 1.0, nEz)
jz = numpy.zeros((nR, nEz))
jzEzzmax = numpy.zeros(nR)
thisRs = (numpy.tile(self._Rs, (nEz, 1)).T).flatten()
thisEzZmaxs = (numpy.tile(self._EzZmaxs, (nEz, 1)).T).flatten()
this = (numpy.tile(y, (nR, 1))).flatten()
if self._c:
jz = self._aA(
thisRs,
numpy.zeros(len(thisRs)),
numpy.ones(len(thisRs)), # these two r dummies
numpy.zeros(len(thisRs)),
numpy.sqrt(2.0 * this * thisEzZmaxs),
**kwargs
)[2]
jz = numpy.reshape(jz, (nR, nEz))
jzEzzmax[0:nR] = jz[:, nEz - 1]
else:
if numcores > 1:
jz = multi.parallel_map(
(
lambda x: self._aA(
thisRs[x],
0.0,
1.0, # these two r dummies
0.0,
numpy.sqrt(2.0 * this[x] * thisEzZmaxs[x]),
_justjz=True,
**kwargs
)[2]
),
range(nR * nEz),
numcores=numcores,
)
jz = numpy.reshape(jz, (nR, nEz))
jzEzzmax[0:nR] = jz[:, nEz - 1]
else:
for ii in range(nR):
for jj in range(nEz):
# Calculate Jz
jz[ii, jj] = self._aA(
self._Rs[ii],
0.0,
1.0, # these two r dummies
0.0,
numpy.sqrt(2.0 * y[jj] * self._EzZmaxs[ii]),
_justjz=True,
**kwargs
)[2][0]
if jj == nEz - 1:
jzEzzmax[ii] = jz[ii, jj]
for ii in range(nR):
jz[ii, :] /= jzEzzmax[ii]
# First interpolate Ez=Ezmax
self._jzEzmaxInterp = interpolate.InterpolatedUnivariateSpline(
self._Rs, numpy.log(jzEzzmax + 10.0**-5.0), k=3
)
self._jz = jz
self._jzInterp = interpolate.RectBivariateSpline(
self._Rs, y, jz, kx=3, ky=3, s=0.0
)
# JR grid
self._Lzmin = 0.01
self._Lzs = numpy.linspace(
self._Lzmin, self._Rmax * potential.vcirc(self._pot, self._Rmax), nLz
)
self._Lzmax = self._Lzs[-1]
# Calculate ER(vr=0,R=RL)
self._RL = numpy.array([potential.rl(self._pot, l) for l in self._Lzs])
self._RLInterp = interpolate.InterpolatedUnivariateSpline(
self._Lzs, self._RL, k=3
)
self._ERRL = (
_evaluatePotentials(self._pot, self._RL, numpy.zeros(nLz))
+ self._Lzs**2.0 / 2.0 / self._RL**2.0
)
self._ERRLmax = numpy.amax(self._ERRL) + 1.0
self._ERRLInterp = interpolate.InterpolatedUnivariateSpline(
self._Lzs, numpy.log(-(self._ERRL - self._ERRLmax)), k=3
)
self._Ramax = 99.0
self._ERRa = (
_evaluatePotentials(self._pot, self._Ramax, 0.0)
+ self._Lzs**2.0 / 2.0 / self._Ramax**2.0
)
self._ERRamax = numpy.amax(self._ERRa) + 1.0
self._ERRaInterp = interpolate.InterpolatedUnivariateSpline(
self._Lzs, numpy.log(-(self._ERRa - self._ERRamax)), k=3
)
y = numpy.linspace(0.0, 1.0, nEr)
jr = numpy.zeros((nLz, nEr))
jrERRa = numpy.zeros(nLz)
thisRL = (numpy.tile(self._RL, (nEr - 1, 1)).T).flatten()
thisLzs = (numpy.tile(self._Lzs, (nEr - 1, 1)).T).flatten()
thisERRL = (numpy.tile(self._ERRL, (nEr - 1, 1)).T).flatten()
thisERRa = (numpy.tile(self._ERRa, (nEr - 1, 1)).T).flatten()
this = (numpy.tile(y[0:-1], (nLz, 1))).flatten()
if self._c:
mjr = self._aA(
thisRL,
numpy.sqrt(
2.0
* (
thisERRa
+ this * (thisERRL - thisERRa)
- _evaluatePotentials(
self._pot, thisRL, numpy.zeros((nEr - 1) * nLz)
)
)
- thisLzs**2.0 / thisRL**2.0
),
thisLzs / thisRL,
numpy.zeros(len(thisRL)),
numpy.zeros(len(thisRL)),
**kwargs
)[0]
jr[:, 0:-1] = numpy.reshape(mjr, (nLz, nEr - 1))
jrERRa[0:nLz] = jr[:, 0]
else:
if numcores > 1:
mjr = multi.parallel_map(
(
lambda x: self._aA(
thisRL[x],
numpy.sqrt(
2.0
* (
thisERRa[x]
+ this[x] * (thisERRL[x] - thisERRa[x])
- _evaluatePotentials(self._pot, thisRL[x], 0.0)
)
- thisLzs[x] ** 2.0 / thisRL[x] ** 2.0
),
thisLzs[x] / thisRL[x],
0.0,
0.0,
_justjr=True,
**kwargs
)[0]
),
range((nEr - 1) * nLz),
numcores=numcores,
)
jr[:, 0:-1] = numpy.reshape(mjr, (nLz, nEr - 1))
jrERRa[0:nLz] = jr[:, 0]
else:
for ii in range(nLz):
for jj in range(nEr - 1): # Last one is zero by construction
try:
jr[ii, jj] = self._aA(
self._RL[ii],
numpy.sqrt(
2.0
* (
self._ERRa[ii]
+ y[jj] * (self._ERRL[ii] - self._ERRa[ii])
- _evaluatePotentials(
self._pot, self._RL[ii], 0.0
)
)
- self._Lzs[ii] ** 2.0 / self._RL[ii] ** 2.0
),
self._Lzs[ii] / self._RL[ii],
0.0,
0.0,
_justjr=True,
**kwargs
)[0][0]
except UnboundError: # pragma: no cover
raise
if jj == 0:
jrERRa[ii] = jr[ii, jj]
for ii in range(nLz):
jr[ii, :] /= jrERRa[ii]
# First interpolate Ez=Ezmax
self._jr = jr
self._jrERRaInterp = interpolate.InterpolatedUnivariateSpline(
self._Lzs, numpy.log(jrERRa + 10.0**-5.0), k=3
)
self._jrInterp = interpolate.RectBivariateSpline(
self._Lzs, y, jr, kx=3, ky=3, s=0.0
)
# Check the units
self._check_consistent_units()
return None
def _evaluate(self, *args, **kwargs):
"""
Evaluate the actions (jr,lz,jz).
Parameters
----------
*args : tuple
Either:
a) R,vR,vT,z,vz[,phi]:
1) floats: phase-space value for single object (phi is optional) (each can be a Quantity)
2) numpy.ndarray: [N] phase-space values for N objects (each can be a Quantity)
b) Orbit instance: initial condition used if that's it, orbit(t) if there is a time given as well as the second argument
**kwargs: dict, optional
scipy.integrate.quadrature keywords (used when directly evaluating a point off the grid)
Returns
-------
tuple
(jr,lz,jz)
Notes
-----
- 2012-07-27 - Written - Bovy (IAS@MPIA)
"""
if len(args) == 5: # R,vR.vT, z, vz
R, vR, vT, z, vz = args
elif len(args) == 6: # R,vR.vT, z, vz, phi
R, vR, vT, z, vz, phi = args
else:
self._parse_eval_args(*args)
R = self._eval_R
vR = self._eval_vR
vT = self._eval_vT
z = self._eval_z
vz = self._eval_vz
# First work on the vertical action
Phi = _evaluatePotentials(self._pot, R, z)
try:
Phio = _evaluatePotentials(self._pot, R, numpy.zeros(len(R)))
except TypeError:
Phio = _evaluatePotentials(self._pot, R, 0.0)
Ez = Phi - Phio + vz**2.0 / 2.0
# Bigger than Ezzmax?
thisEzZmax = numpy.exp(self._EzZmaxsInterp(R))
if isinstance(R, numpy.ndarray):
indx = R > self._Rmax
indx += R < self._Rmin
indx += (Ez != 0.0) * (numpy.log(Ez) > thisEzZmax)
indxc = True ^ indx
jz = numpy.empty(R.shape)
if numpy.sum(indxc) > 0:
jz[indxc] = self._jzInterp.ev(
R[indxc], Ez[indxc] / thisEzZmax[indxc]
) * (numpy.exp(self._jzEzmaxInterp(R[indxc])) - 10.0**-5.0)
if numpy.sum(indx) > 0:
jz[indx] = self._aA(
R[indx],
numpy.zeros(numpy.sum(indx)),
numpy.ones(numpy.sum(indx)), # these two r dummies
numpy.zeros(numpy.sum(indx)),
numpy.sqrt(2.0 * Ez[indx]),
_justjz=True,
**kwargs
)[2]
else:
if (
R > self._Rmax
or R < self._Rmin
or (Ez != 0 and numpy.log(Ez) > thisEzZmax)
): # Outside of the grid
if _PRINTOUTSIDEGRID: # pragma: no cover
print(
"Outside of grid in Ez",
R > self._Rmax,
R < self._Rmin,
(Ez != 0 and numpy.log(Ez) > thisEzZmax),
)
jz = self._aA(
R,
0.0,
1.0, # these two r dummies
0.0,
numpy.sqrt(2.0 * Ez),
_justjz=True,
**kwargs
)[2]
else:
jz = (
self._jzInterp(R, Ez / thisEzZmax)
* (numpy.exp(self._jzEzmaxInterp(R)) - 10.0**-5.0)
)[0][0]
# Radial action
ERLz = numpy.fabs(R * vT) + self._gamma * jz
ER = Phio + vR**2.0 / 2.0 + ERLz**2.0 / 2.0 / R**2.0
thisRL = self._RLInterp(ERLz)
thisERRL = -numpy.exp(self._ERRLInterp(ERLz)) + self._ERRLmax
thisERRa = -numpy.exp(self._ERRaInterp(ERLz)) + self._ERRamax
if isinstance(R, numpy.ndarray):
indx = ((ER - thisERRa) / (thisERRL - thisERRa) > 1.0) * (
((ER - thisERRa) / (thisERRL - thisERRa) - 1.0) < 10.0**-2.0
)
ER[indx] = thisERRL[indx]
indx = ((ER - thisERRa) / (thisERRL - thisERRa) < 0.0) * (
(ER - thisERRa) / (thisERRL - thisERRa) > -(10.0**-2.0)
)
ER[indx] = thisERRa[indx]
indx = ERLz < self._Lzmin
indx += ERLz > self._Lzmax
indx += (ER - thisERRa) / (thisERRL - thisERRa) > 1.0
indx += (ER - thisERRa) / (thisERRL - thisERRa) < 0.0
indxc = True ^ indx
jr = numpy.empty(R.shape)
if numpy.sum(indxc) > 0:
jr[indxc] = self._jrInterp.ev(
ERLz[indxc],
(ER[indxc] - thisERRa[indxc]) / (thisERRL[indxc] - thisERRa[indxc]),
) * (numpy.exp(self._jrERRaInterp(ERLz[indxc])) - 10.0**-5.0)
if numpy.sum(indx) > 0:
jr[indx] = self._aA(
thisRL[indx],
numpy.sqrt(
2.0
* (ER[indx] - _evaluatePotentials(self._pot, thisRL[indx], 0.0))
- ERLz[indx] ** 2.0 / thisRL[indx] ** 2.0
),
ERLz[indx] / thisRL[indx],
numpy.zeros(len(thisRL)),
numpy.zeros(len(thisRL)),
_justjr=True,
**kwargs
)[0]
else:
if (ER - thisERRa) / (thisERRL - thisERRa) > 1.0 and (
(ER - thisERRa) / (thisERRL - thisERRa) - 1.0
) < 10.0**-2.0:
ER = thisERRL
elif (ER - thisERRa) / (thisERRL - thisERRa) < 0.0 and (ER - thisERRa) / (
thisERRL - thisERRa
) > -(10.0**-2.0):
ER = thisERRa
# Outside of grid?
if (
ERLz < self._Lzmin
or ERLz > self._Lzmax
or (ER - thisERRa) / (thisERRL - thisERRa) > 1.0
or (ER - thisERRa) / (thisERRL - thisERRa) < 0.0
):
if _PRINTOUTSIDEGRID: # pragma: no cover
print(
"Outside of grid in ER/Lz",
ERLz < self._Lzmin,
ERLz > self._Lzmax,
(ER - thisERRa) / (thisERRL - thisERRa) > 1.0,
(ER - thisERRa) / (thisERRL - thisERRa) < 0.0,
ER,
thisERRL,
thisERRa,
(ER - thisERRa) / (thisERRL - thisERRa),
)
jr = self._aA(
thisRL[0],
numpy.sqrt(
2.0 * (ER - _evaluatePotentials(self._pot, thisRL, 0.0))
- ERLz**2.0 / thisRL**2.0
)[0],
(ERLz / thisRL)[0],
0.0,
0.0,
_justjr=True,
**kwargs
)[0]
else:
jr = (
self._jrInterp(ERLz, (ER - thisERRa) / (thisERRL - thisERRa))
* (numpy.exp(self._jrERRaInterp(ERLz)) - 10.0**-5.0)
)[0][0]
return (jr, R * vT, jz)
def Jz(self, *args, **kwargs):
"""
Evaluate the action jz.
Parameters
----------
*args : tuple
Either:
a) R,vR,vT,z,vz
b) Orbit instance: initial condition used if that's it, orbit(t)
if there is a time given as well
**kwargs: dict
scipy.integrate.quadrature keywords
Returns
-------
float
The action jz.
Notes
-----
- 2012-07-30 - Written - Bovy (IAS@MPIA)
"""
self._parse_eval_args(*args)
Phi = _evaluatePotentials(self._pot, self._eval_R, self._eval_z)
Phio = _evaluatePotentials(self._pot, self._eval_R, 0.0)
Ez = Phi - Phio + self._eval_vz**2.0 / 2.0
# Bigger than Ezzmax?
thisEzZmax = numpy.exp(self._EzZmaxsInterp(self._eval_R))
if (
self._eval_R > self._Rmax
or self._eval_R < self._Rmin
or (Ez != 0.0 and numpy.log(Ez) > thisEzZmax)
): # Outside of the grid
if _PRINTOUTSIDEGRID: # pragma: no cover
print("Outside of grid in Ez")
jz = self._aA(
self._eval_R,
0.0,
1.0, # these two r dummies
0.0,
numpy.sqrt(2.0 * Ez),
_justjz=True,
**kwargs
)[2]
else:
jz = (
self._jzInterp(self._eval_R, Ez / thisEzZmax)
* (numpy.exp(self._jzEzmaxInterp(self._eval_R)) - 10.0**-5.0)
)[0][0]
return jz