def __init__(self,amp=1.,ro=1.,hr=1./3.,hz=1./16.,
maxiter=_MAXITER,tol=0.001,normalize=False,
new=True,kmaxFac=2.,glorder=10):
"""
NAME:
__init__
PURPOSE:
initialize a double-exponential disk potential
INPUT:
amp - amplitude to be applied to the potential (default: 1)
hr - disk scale-length in terms of ro
hz - scale-height
tol - relative accuracy of potential-evaluations
maxiter - scipy.integrate keyword
normalize - if True, normalize such that vc(1.,0.)=1., or, if given as a number, such that the force is this fraction of the force necessary to make vc(1.,0.)=1.
OUTPUT:
DoubleExponentialDiskPotential object
HISTORY:
2010-04-16 - Written - Bovy (NYU)
2013-01-01 - Re-implemented using faster integration techniques - Bovy (IAS)
"""
Potential.__init__(self,amp=amp)
self.hasC= True
self._new= new
self._kmaxFac= kmaxFac
self._glorder= glorder
self._ro= ro
self._hr= hr
self._scale= self._hr
self._hz= hz
self._alpha= 1./self._hr
self._beta= 1./self._hz
self._gamma= self._alpha/self._beta
self._maxiter= maxiter
self._tol= tol
self._zforceNotSetUp= True #We have not calculated a typical Kz yet
#Setup j0 zeros etc.
self._glx, self._glw= nu.polynomial.legendre.leggauss(self._glorder)
self._nzeros=100
#j0 for potential and z
self._j0zeros= nu.zeros(self._nzeros+1)
self._j0zeros[1:self._nzeros+1]= special.jn_zeros(0,self._nzeros)
self._dj0zeros= self._j0zeros-nu.roll(self._j0zeros,1)
self._dj0zeros[0]= self._j0zeros[0]
#j1 for R
self._j1zeros= nu.zeros(self._nzeros+1)
self._j1zeros[1:self._nzeros+1]= special.jn_zeros(1,self._nzeros)
self._dj1zeros= self._j1zeros-nu.roll(self._j1zeros,1)
self._dj1zeros[0]= self._j1zeros[0]
#j2 for R2deriv
self._j2zeros= nu.zeros(self._nzeros+1)
self._j2zeros[1:self._nzeros+1]= special.jn_zeros(2,self._nzeros)
self._dj2zeros= self._j2zeros-nu.roll(self._j2zeros,1)
self._dj2zeros[0]= self._j2zeros[0]
if normalize or \
(isinstance(normalize,(int,float)) \
and not isinstance(normalize,bool)):
self.normalize(normalize)
#Load Kepler potential for large R
self._kp= KeplerPotential(normalize=4.*nu.pi/self._alpha**2./self._beta)
class DoubleExponentialDiskPotential(Potential):
"""Class that implements the double exponential disk potential
rho(R,z) = rho_0 e^-R/h_R e^-|z|/h_z"""
def __init__(self,amp=1.,ro=1.,hr=1./3.,hz=1./16.,
maxiter=_MAXITER,tol=0.001,normalize=False,
new=True,kmaxFac=2.,glorder=10):
"""
NAME:
__init__
PURPOSE:
initialize a double-exponential disk potential
INPUT:
amp - amplitude to be applied to the potential (default: 1)
hr - disk scale-length in terms of ro
hz - scale-height
tol - relative accuracy of potential-evaluations
maxiter - scipy.integrate keyword
normalize - if True, normalize such that vc(1.,0.)=1., or, if given as a number, such that the force is this fraction of the force necessary to make vc(1.,0.)=1.
OUTPUT:
DoubleExponentialDiskPotential object
HISTORY:
2010-04-16 - Written - Bovy (NYU)
2013-01-01 - Re-implemented using faster integration techniques - Bovy (IAS)
"""
Potential.__init__(self,amp=amp)
self.hasC= True
self._new= new
self._kmaxFac= kmaxFac
self._glorder= glorder
self._ro= ro
self._hr= hr
self._scale= self._hr
self._hz= hz
self._alpha= 1./self._hr
self._beta= 1./self._hz
self._gamma= self._alpha/self._beta
self._maxiter= maxiter
self._tol= tol
self._zforceNotSetUp= True #We have not calculated a typical Kz yet
#Setup j0 zeros etc.
self._glx, self._glw= nu.polynomial.legendre.leggauss(self._glorder)
self._nzeros=100
#j0 for potential and z
self._j0zeros= nu.zeros(self._nzeros+1)
self._j0zeros[1:self._nzeros+1]= special.jn_zeros(0,self._nzeros)
self._dj0zeros= self._j0zeros-nu.roll(self._j0zeros,1)
self._dj0zeros[0]= self._j0zeros[0]
#j1 for R
self._j1zeros= nu.zeros(self._nzeros+1)
self._j1zeros[1:self._nzeros+1]= special.jn_zeros(1,self._nzeros)
self._dj1zeros= self._j1zeros-nu.roll(self._j1zeros,1)
self._dj1zeros[0]= self._j1zeros[0]
#j2 for R2deriv
self._j2zeros= nu.zeros(self._nzeros+1)
self._j2zeros[1:self._nzeros+1]= special.jn_zeros(2,self._nzeros)
self._dj2zeros= self._j2zeros-nu.roll(self._j2zeros,1)
self._dj2zeros[0]= self._j2zeros[0]
if normalize or \
(isinstance(normalize,(int,float)) \
and not isinstance(normalize,bool)):
self.normalize(normalize)
#Load Kepler potential for large R
self._kp= KeplerPotential(normalize=4.*nu.pi/self._alpha**2./self._beta)
def _evaluate(self,R,z,phi=0.,t=0.,dR=0,dphi=0):
"""
NAME:
_evaluate
PURPOSE:
evaluate the potential at (R,z)
INPUT:
R - Cylindrical Galactocentric radius
z - vertical height
phi - azimuth
t - time
OUTPUT:
potential at (R,z)
HISTORY:
2010-04-16 - Written - Bovy (NYU)
2012-12-26 - New method using Gaussian quadrature between zeros - Bovy (IAS)
DOCTEST:
>>> doubleExpPot= DoubleExponentialDiskPotential()
>>> r= doubleExpPot(1.,0) #doctest: +ELLIPSIS
...
>>> assert( r+1.89595350484)**2.< 10.**-6.
"""
if dR == 1 and dphi == 0:
return -self._Rforce(R,z,phi=phi,t=t)
elif dR == 0 and dphi == 1:
return -self._phiforce(R,z,phi=phi,t=t)
elif dR == 2 and dphi == 0:
return self._R2deriv(R,z,phi=phi,t=t)
elif dR != 0 and dphi != 0:
warnings.warn("High-order derivatives for DoubleExponentialDiskPotential not implemented",galpyWarning)
return None
if self._new:
if isinstance(R,float):
floatIn= True
R= nu.array([R])
z= nu.array([z])
else:
floatIn= False
out= nu.empty(len(R))
indx= (R <= 6.)
out[True-indx]= self._kp(R[True-indx],z[True-indx])
R4max= nu.copy(R)
R4max[(R < 1.)]= 1.
kmax= self._kmaxFac*self._beta
for jj in range(len(R)):
if not indx[jj]: continue
maxj0zeroIndx= nu.argmin((self._j0zeros-kmax*R4max[jj])**2.) #close enough
ks= nu.array([0.5*(self._glx+1.)*self._dj0zeros[ii+1] + self._j0zeros[ii] for ii in range(maxj0zeroIndx)]).flatten()
weights= nu.array([self._glw*self._dj0zeros[ii+1] for ii in range(maxj0zeroIndx)]).flatten()
evalInt= special.jn(0,ks*R[jj])*(self._alpha**2.+ks**2.)**-1.5*(self._beta*nu.exp(-ks*nu.fabs(z[jj]))-ks*nu.exp(-self._beta*nu.fabs(z[jj])))/(self._beta**2.-ks**2.)
out[jj]= -2.*nu.pi*self._alpha*nu.sum(weights*evalInt)
if floatIn: return out[0]
else: return out
#Old code, uses scipy's quadrature to do the relevant integrals, split into two
notConvergedSmall= True
notConvergedLarge= True
smallkIntegral= integrate.quadrature(_doubleExponentialDiskPotentialPotentialIntegrandSmallk,
0.,1./self._gamma,
args=(self._alpha*R,
self._beta*nu.fabs(z),
self._gamma),tol=_TOL,
maxiter=self._maxiter,
vec_func=False)
largekIntegral= integrate.quadrature(_doubleExponentialDiskPotentialPotentialIntegrandLargek,
0.,self._gamma,
args=(self._alpha*R,
self._beta*nu.fabs(z),
self._gamma),tol=_TOL,
maxiter=self._maxiter,
vec_func=False)
maxiterFactorSmall= 2
maxiterFactorLarge= 2
if nu.fabs(smallkIntegral[1]/(smallkIntegral[0]+largekIntegral[0])) <= self._tol:
notConvergedSmall= False
if nu.fabs(largekIntegral[1]/(largekIntegral[0]+smallkIntegral[0])) <= self._tol:
notConvergedLarge= False
while notConvergedSmall or notConvergedLarge:
if notConvergedSmall:
smallkIntegral= integrate.quadrature(_doubleExponentialDiskPotentialPotentialIntegrandSmallk,
0.,1./self._gamma,
args=(self._alpha*R,
self._beta*nu.fabs(z),
self._gamma),tol=_TOL,
maxiter= maxiterFactorSmall*self._maxiter,
vec_func=False)
if nu.fabs(smallkIntegral[1]/(smallkIntegral[0]+largekIntegral[0])) > self._tol:
maxiterFactorSmall*= 2
else:
notConvergedSmall= False
if notConvergedLarge:
largekIntegral= integrate.quadrature(_doubleExponentialDiskPotentialPotentialIntegrandLargek,
0.,self._gamma,
args=(self._alpha*R,
self._beta*nu.fabs(z),
self._gamma),tol=_TOL,
maxiter=maxiterFactorLarge*self._maxiter,
vec_func=False)
if nu.fabs(largekIntegral[1]/(largekIntegral[0]+smallkIntegral[0])) > self._tol:
maxiterFactorLarge*= 2
else:
notConvergedLarge= False
return -4.*nu.pi/self._alpha/self._beta*(smallkIntegral[0]+largekIntegral[0])
def _Rforce(self,R,z,phi=0.,t=0.):
"""
NAME:
Rforce
PURPOSE:
evaluate radial force K_R (R,z)
INPUT:
R - Cylindrical Galactocentric radius
z - vertical height
phi - azimuth
t - time
OUTPUT:
K_R (R,z)
HISTORY:
2010-04-16 - Written - Bovy (NYU)
DOCTEST:
"""
if self._new:
if isinstance(R,nu.ndarray):
if not isinstance(z,nu.ndarray): z= nu.ones_like(R)*z
out= nu.array([self._Rforce(rr,zz) for rr,zz in zip(R,z)])
return out
if R > 6.: return self._kp.Rforce(R,z)
if R < 1.: R4max= 1.
else: R4max= R
kmax= self._kmaxFac*self._beta
kmax= 2.*self._kmaxFac*self._beta
maxj1zeroIndx= nu.argmin((self._j1zeros-kmax*R4max)**2.) #close enough
ks= nu.array([0.5*(self._glx+1.)*self._dj1zeros[ii+1] + self._j1zeros[ii] for ii in range(maxj1zeroIndx)]).flatten()
weights= nu.array([self._glw*self._dj1zeros[ii+1] for ii in range(maxj1zeroIndx)]).flatten()
evalInt= ks*special.jn(1,ks*R)*(self._alpha**2.+ks**2.)**-1.5*(self._beta*nu.exp(-ks*nu.fabs(z))-ks*nu.exp(-self._beta*nu.fabs(z)))/(self._beta**2.-ks**2.)
return -2.*nu.pi*self._alpha*nu.sum(weights*evalInt)
#Old code, uses scipy's quadrature to do the relevant integrals, split into two
notConvergedSmall= True
notConvergedLarge= True
smallkIntegral= integrate.quadrature(_doubleExponentialDiskPotentialRForceIntegrandSmallk,
0.,1./self._gamma,
args=(self._alpha*R,
self._beta*nu.fabs(z),
self._gamma),tol=_TOL,
maxiter= 2*self._maxiter,
vec_func=False)
largekIntegral= integrate.quadrature(_doubleExponentialDiskPotentialRForceIntegrandLargek,
0.,self._gamma,
args=(self._alpha*R,
self._beta*nu.fabs(z),
self._gamma),tol=_TOL,
maxiter= 2*self._maxiter,
vec_func=False)
maxiterFactorSmall= 4
maxiterFactorLarge= 4
if nu.fabs(smallkIntegral[1]/(smallkIntegral[0]+largekIntegral[0])) <= self._tol:
notConvergedSmall= False
if nu.fabs(largekIntegral[1]/(largekIntegral[0]+smallkIntegral[0])) <= self._tol:
notConvergedLarge= False
while notConvergedSmall or notConvergedLarge:
if notConvergedSmall:
smallkIntegral= integrate.quadrature(_doubleExponentialDiskPotentialRForceIntegrandSmallk,
0.,1./self._gamma,
args=(self._alpha*R,
self._beta*nu.fabs(z),
self._gamma),
tol=_TOL,
maxiter= maxiterFactorSmall*self._maxiter,
vec_func=False)
if nu.fabs(smallkIntegral[1]/(smallkIntegral[0]+largekIntegral[0])) > self._tol:
maxiterFactorSmall*= 2
else:
notConvergedSmall= False
if notConvergedLarge:
largekIntegral= integrate.quadrature(_doubleExponentialDiskPotentialRForceIntegrandLargek,
0.,self._gamma,
args=(self._alpha*R,
self._beta*nu.fabs(z),
self._gamma),
tol=_TOL,
maxiter=maxiterFactorLarge*self._maxiter,
vec_func=False)
if nu.fabs(largekIntegral[1]/(largekIntegral[0]+smallkIntegral[0])) > self._tol:
maxiterFactorLarge*= 2
else:
notConvergedLarge= False
return -4.*nu.pi/self._beta*(smallkIntegral[0]+largekIntegral[0])
def _zforce(self,R,z,phi=0.,t=0.):
"""
NAME:
zforce
PURPOSE:
evaluate vertical force K_z (R,z)
INPUT:
R - Cylindrical Galactocentric radius
z - vertical height
phi - azimuth
t - time
OUTPUT:
K_z (R,z)
HISTORY:
2010-04-16 - Written - Bovy (NYU)
DOCTEST:
"""
if self._new:
if isinstance(R,nu.ndarray):
if not isinstance(z,nu.ndarray): z= nu.ones_like(R)*z
out= nu.array([self._zforce(rr,zz) for rr,zz in zip(R,z)])
return out
if R > 6.: return self._kp.zforce(R,z)
if R < 1.: R4max= 1.
else: R4max= R
kmax= self._kmaxFac*self._beta
maxj0zeroIndx= nu.argmin((self._j0zeros-kmax*R4max)**2.) #close enough
ks= nu.array([0.5*(self._glx+1.)*self._dj0zeros[ii+1] + self._j0zeros[ii] for ii in range(maxj0zeroIndx)]).flatten()
weights= nu.array([self._glw*self._dj0zeros[ii+1] for ii in range(maxj0zeroIndx)]).flatten()
evalInt= ks*special.jn(0,ks*R)*(self._alpha**2.+ks**2.)**-1.5*(nu.exp(-ks*nu.fabs(z))-nu.exp(-self._beta*nu.fabs(z)))/(self._beta**2.-ks**2.)
if z > 0.:
return -2.*nu.pi*self._alpha*self._beta*nu.sum(weights*evalInt)
else:
return 2.*nu.pi*self._alpha*self._beta*nu.sum(weights*evalInt)
#Old code, uses scipy's quadrature to do the relevant integrals, split into two
if self._zforceNotSetUp:
self._zforceNotSetUp= False
self._typicalKz= self._zforce(self._ro,self._hz)
notConvergedSmall= True
notConvergedLarge= True
smallkIntegral= integrate.quadrature(_doubleExponentialDiskPotentialzForceIntegrandSmallk,
0.,1./self._gamma,
args=(self._alpha*R,
self._beta*nu.fabs(z),
self._gamma),tol=_TOL,
maxiter= 2*self._maxiter,
vec_func=False)
largekIntegral= integrate.quadrature(_doubleExponentialDiskPotentialzForceIntegrandLargek,
0.,self._gamma,
args=(self._alpha*R,
self._beta*nu.fabs(z),
self._gamma),tol=_TOL,
maxiter=2*self._maxiter,
vec_func=False)
maxiterFactorSmall= 4
maxiterFactorLarge= 4
try:
if smallkIntegral[1]/self._typicalKz <= self._tol:
notConvergedSmall= False
except AttributeError:
if nu.fabs(smallkIntegral[1]/(smallkIntegral[0]+largekIntegral[0])) <= self._tol:
notConvergedSmall= False
try:
if largekIntegral[1]/self._typicalKz <= self._tol:
notConvergedLarge= False
except AttributeError:
if nu.fabs(largekIntegral[1]/(largekIntegral[0]+smallkIntegral[0])) <= self._tol:
notConvergedLarge= False
while notConvergedSmall or notConvergedLarge:
if notConvergedSmall:
smallkIntegral= integrate.quadrature(_doubleExponentialDiskPotentialzForceIntegrandSmallk,
0.,1./self._gamma,
args=(self._alpha*R,
self._beta*nu.fabs(z),
self._gamma),tol=_TOL,
maxiter= maxiterFactorSmall*self._maxiter,
vec_func=False)
try:
if smallkIntegral[1]/self._typicalKz > self._tol:
maxiterFactorSmall*= 2
else:
notConvergedSmall= False
except AttributeError:
if nu.fabs(smallkIntegral[1]/(smallkIntegral[0]+largekIntegral[0])) > self._tol:
maxiterFactorSmall*= 2
else:
notConvergedSmall= False
if notConvergedLarge:
largekIntegral= integrate.quadrature(_doubleExponentialDiskPotentialzForceIntegrandLargek,
0.,self._gamma,
args=(self._alpha*R,
self._beta*nu.fabs(z),
self._gamma),tol=_TOL,
maxiter=maxiterFactorLarge*self._maxiter,
vec_func=False)
try:
if largekIntegral[1]/self._typicalKz > self._tol:
maxiterFactorLarge*= 2
else:
notConvergedLarge= False
except AttributeError:
if largekIntegral[1]/(largekIntegral[0]+smallkIntegral[0]) > self._tol:
maxiterFactorLarge*= 2
else:
notConvergedLarge= False
if z < 0.:
return 4.*nu.pi/self._beta*(smallkIntegral[0]+largekIntegral[0])
else:
return -4.*nu.pi/self._beta*(smallkIntegral[0]+largekIntegral[0])
def _R2deriv(self,R,z,phi=0.,t=0.):
"""
NAME:
R2deriv
PURPOSE:
evaluate R2 derivative
INPUT:
R - Cylindrical Galactocentric radius
z - vertical height
phi - azimuth
t - time
OUTPUT:
-d K_R (R,z) d R
HISTORY:
2012-12-27 - Written - Bovy (IAS)
"""
if self._new:
if isinstance(R,nu.ndarray):
if not isinstance(z,nu.ndarray): z= nu.ones_like(R)*z
out= nu.array([self._R2deriv(rr,zz) for rr,zz in zip(R,z)])
return out
if R > 16.*self._hr or R > 6.: return self._kp.R2deriv(R,z)
if R < 1.: R4max= 1.
else: R4max= R
kmax= 2.*self._kmaxFac*self._beta
maxj0zeroIndx= nu.argmin((self._j0zeros-kmax*R4max)**2.) #close enough
maxj2zeroIndx= nu.argmin((self._j2zeros-kmax*R4max)**2.) #close enough
ks0= nu.array([0.5*(self._glx+1.)*self._dj0zeros[ii+1] + self._j0zeros[ii] for ii in range(maxj0zeroIndx)]).flatten()
weights0= nu.array([self._glw*self._dj0zeros[ii+1] for ii in range(maxj0zeroIndx)]).flatten()
ks2= nu.array([0.5*(self._glx+1.)*self._dj2zeros[ii+1] + self._j2zeros[ii] for ii in range(maxj2zeroIndx)]).flatten()
weights2= nu.array([self._glw*self._dj2zeros[ii+1] for ii in range(maxj2zeroIndx)]).flatten()
evalInt0= ks0**2.*special.jn(0,ks0*R)*(self._alpha**2.+ks0**2.)**-1.5*(self._beta*nu.exp(-ks0*nu.fabs(z))-ks0*nu.exp(-self._beta*nu.fabs(z)))/(self._beta**2.-ks0**2.)
evalInt2= ks2**2.*special.jn(2,ks2*R)*(self._alpha**2.+ks2**2.)**-1.5*(self._beta*nu.exp(-ks2*nu.fabs(z))-ks2*nu.exp(-self._beta*nu.fabs(z)))/(self._beta**2.-ks2**2.)
return nu.pi*self._alpha*(nu.sum(weights0*evalInt0)
-nu.sum(weights2*evalInt2))
#Old code, uses scipy's quadrature to do the relevant integrals, split into two
notConvergedSmall= True
notConvergedLarge= True
smallkIntegral= integrate.quadrature(_doubleExponentialDiskPotentialR2derivIntegrandSmallk,
0.,1./self._gamma,
args=(self._alpha*R,
self._beta*nu.fabs(z),
self._gamma),tol=_TOL,
maxiter= 2*self._maxiter,
vec_func=True)
largekIntegral= integrate.quadrature(_doubleExponentialDiskPotentialR2derivIntegrandLargek,
0.,self._gamma,
args=(self._alpha*R,
self._beta*nu.fabs(z),
self._gamma),tol=_TOL,
maxiter= 2*self._maxiter,
vec_func=True)
maxiterFactorSmall= 4
maxiterFactorLarge= 4
if nu.fabs(smallkIntegral[1]/(smallkIntegral[0]+largekIntegral[0])) <= self._tol:
notConvergedSmall= False
if nu.fabs(largekIntegral[1]/(largekIntegral[0]+smallkIntegral[0])) <= self._tol:
notConvergedLarge= False
while notConvergedSmall or notConvergedLarge:
if notConvergedSmall:
smallkIntegral= integrate.quadrature(_doubleExponentialDiskPotentialR2derivIntegrandSmallk,
0.,1./self._gamma,
args=(self._alpha*R,
self._beta*nu.fabs(z),
self._gamma),
tol=_TOL,
maxiter= maxiterFactorSmall*self._maxiter,
vec_func=True)
if nu.fabs(smallkIntegral[1]/(smallkIntegral[0]+largekIntegral[0])) > self._tol:
maxiterFactorSmall*= 2
else:
notConvergedSmall= False
if notConvergedLarge:
largekIntegral= integrate.quadrature(_doubleExponentialDiskPotentialR2derivIntegrandLargek,
0.,self._gamma,
args=(self._alpha*R,
self._beta*nu.fabs(z),
self._gamma),
tol=_TOL,
maxiter=maxiterFactorLarge*self._maxiter,
vec_func=True)
if nu.fabs(largekIntegral[1]/(largekIntegral[0]+smallkIntegral[0])) > self._tol:
maxiterFactorLarge*= 2
else:
notConvergedLarge= False
return 4.*nu.pi*self._alpha/self._beta*(smallkIntegral[0]+largekIntegral[0])
def _z2deriv(self,R,z,phi=0.,t=0.):
"""
NAME:
z2deriv
PURPOSE:
evaluate z2 derivative
INPUT:
R - Cylindrical Galactocentric radius
z - vertical height
phi - azimuth
t - time
OUTPUT:
-d K_Z (R,z) d Z
HISTORY:
2012-12-26 - Written - Bovy (IAS)
"""
if self._new:
if isinstance(R,nu.ndarray):
if not isinstance(z,nu.ndarray): z= nu.ones_like(R)*z
out= nu.array([self._z2deriv(rr,zz) for rr,zz in zip(R,z)])
return out
if R > 6.: return self._kp.z2deriv(R,z)
if R < 1.: R4max= 1.
else: R4max= R
kmax= self._kmaxFac*self._beta
maxj0zeroIndx= nu.argmin((self._j0zeros-kmax*R4max)**2.) #close enough
ks= nu.array([0.5*(self._glx+1.)*self._dj0zeros[ii+1] + self._j0zeros[ii] for ii in range(maxj0zeroIndx)]).flatten()
weights= nu.array([self._glw*self._dj0zeros[ii+1] for ii in range(maxj0zeroIndx)]).flatten()
evalInt= ks*special.jn(0,ks*R)*(self._alpha**2.+ks**2.)**-1.5*(ks*nu.exp(-ks*nu.fabs(z))-self._beta*nu.exp(-self._beta*nu.fabs(z)))/(self._beta**2.-ks**2.)
return -2.*nu.pi*self._alpha*self._beta*nu.sum(weights*evalInt)
raise NotImplementedError("none 'new' z2deriv not implemented for DoubleExponentialDiskPotential")
def _Rzderiv(self,R,z,phi=0.,t=0.):
"""
NAME:
Rzderiv
PURPOSE:
evaluate the mixed R,z derivative
INPUT:
R - Cylindrical Galactocentric radius
z - vertical height
phi - azimuth
t - time
OUTPUT:
d2phi/dR/dz
HISTORY:
2013-08-28 - Written - Bovy (IAS)
"""
if self._new:
if isinstance(R,nu.ndarray):
if not isinstance(z,nu.ndarray): z= nu.ones_like(R)*z
out= nu.array([self._Rzderiv(rr,zz) for rr,zz in zip(R,z)])
return out
if R > 6.: return self._kp.Rzderiv(R,z)
if R < 1.: R4max= 1.
else: R4max= R
kmax= 2.*self._kmaxFac*self._beta
maxj1zeroIndx= nu.argmin((self._j1zeros-kmax*R4max)**2.) #close enough
ks= nu.array([0.5*(self._glx+1.)*self._dj1zeros[ii+1] + self._j1zeros[ii] for ii in range(maxj1zeroIndx)]).flatten()
weights= nu.array([self._glw*self._dj1zeros[ii+1] for ii in range(maxj1zeroIndx)]).flatten()
evalInt= ks**2.*special.jn(1,ks*R)*(self._alpha**2.+ks**2.)**-1.5*(nu.exp(-ks*nu.fabs(z))-nu.exp(-self._beta*nu.fabs(z)))/(self._beta**2.-ks**2.)
if z >= 0.:
return -2.*nu.pi*self._alpha*self._beta*nu.sum(weights*evalInt)
else:
return 2.*nu.pi*self._alpha*self._beta*nu.sum(weights*evalInt)
raise NotImplementedError("none 'new' Rzderiv not implemented for DoubleExponentialDiskPotential")
def _dens(self,R,z,phi=0.,t=0.):
"""
NAME:
dens
PURPOSE:
evaluate the density
INPUT:
R - Cylindrical Galactocentric radius
z - vertical height
phi - azimuth
t - time
OUTPUT:
rho (R,z)
HISTORY:
2010-08-08 - Written - Bovy (NYU)
"""
return nu.exp(-self._alpha*R-self._beta*nu.fabs(z))