def _phiforce(self, R, z, phi=0, t=0):
"""
NAME:
_phiforce
PURPOSE:
evaluate the azimuth force at (R,z, phi)
INPUT:
R - Cylindrical Galactocentric radius
z - vertical height
phi - azimuth
t - time
OUTPUT:
azimuth force at (R,z, phi)
HISTORY:
2016-06-06 - Written - Aladdin
"""
if not self.isNonAxi and phi is None:
phi = 0.
r, theta, phi = bovy_coords.cyl_to_spher(R, z, phi)
#x = phi
dr_dphi = 0
dtheta_dphi = 0
dphi_dphi = 1
return self._computeforceArray(dr_dphi, dtheta_dphi, dphi_dphi, R, z,
phi)
def _compute(self, funcTilde, R, z, phi):
"""
NAME:
_compute
PURPOSE:
evaluate the NxLxM density or potential
INPUT:
funcTidle - must be _rhoTilde or _phiTilde
R - Cylindrical Galactocentric radius
z - vertical height
phi - azimuth
OUTPUT:
An NxLxM density or potential at (R,z, phi)
HISTORY:
2016-05-18 - Written - Aladdin
"""
Acos, Asin = self._Acos, self._Asin
N, L, M = Acos.shape
r, theta, phi = bovy_coords.cyl_to_spher(R,z,phi)
PP = lpmn(M-1,L-1,nu.cos(theta))[0].T ##Get the Legendre polynomials
func_tilde = funcTilde(r, N, L) ## Tilde of the function of interest
func = nu.zeros((N,L,M), float) ## The function of interest (density or potential)
m = nu.arange(0, M)[nu.newaxis, nu.newaxis, :]
mcos = nu.cos(m*phi)
msin = nu.sin(m*phi)
func = func_tilde[:,:,None]*(Acos[:,:,:]*mcos + Asin[:,:,:]*msin)*PP[None,:,:]
return func
def _compute(self, funcTilde, R, z, phi):
"""
NAME:
_compute
PURPOSE:
evaluate the NxLxM density or potential
INPUT:
funcTidle - must be _rhoTilde or _phiTilde
R - Cylindrical Galactocentric radius
z - vertical height
phi - azimuth
OUTPUT:
An NxLxM density or potential at (R,z, phi)
HISTORY:
2016-05-18 - Written - Aladdin
"""
Acos, Asin = self._Acos, self._Asin
N, L, M = Acos.shape
r, theta, phi = bovy_coords.cyl_to_spher(R, z, phi)
PP = lpmn(M - 1, L - 1,
nu.cos(theta))[0].T ##Get the Legendre polynomials
func_tilde = funcTilde(r, N, L) ## Tilde of the function of interest
func = nu.zeros(
(N, L, M),
float) ## The function of interest (density or potential)
m = nu.arange(0, M)[nu.newaxis, nu.newaxis, :]
mcos = nu.cos(m * phi)
msin = nu.sin(m * phi)
func = func_tilde[:, :, None] * (Acos[:, :, :] * mcos +
Asin[:, :, :] * msin) * PP[None, :, :]
return func
def _computeforce(self, R, z, phi=0, t=0):
"""
NAME:
_computeforce
PURPOSE:
Evaluate the first derivative of Phi with respect to R, z and phi
INPUT:
R - Cylindrical Galactocentric radius
z - vertical height
phi - azimuth
t - time
OUTPUT:
dPhi/dr, dPhi/dtheta, dPhi/dphi
HISTORY:
2016-06-07 - Written - Aladdin
"""
Acos, Asin = self._Acos, self._Asin
N, L, M = Acos.shape
r, theta, phi = bovy_coords.cyl_to_spher(R, z, phi)
new_hash = hashlib.md5(nu.array([R, z, phi])).hexdigest()
if new_hash == self._force_hash:
dPhi_dr = self._cached_dPhi_dr
dPhi_dtheta = self._cached_dPhi_dtheta
dPhi_dphi = self._cached_dPhi_dphi
else:
PP, dPP = lpmn(M - 1, L - 1,
nu.cos(theta)) ##Get the Legendre polynomials
PP = PP.T[None, :, :]
dPP = dPP.T[None, :, :]
phi_tilde = self._phiTilde(r, N, L)[:, :, nu.newaxis]
dphi_tilde = self._dphiTilde(r, N, L)[:, :, nu.newaxis]
m = nu.arange(0, M)[nu.newaxis, nu.newaxis, :]
mcos = nu.cos(m * phi)
msin = nu.sin(m * phi)
dPhi_dr = -nu.sum((Acos * mcos + Asin * msin) * PP * dphi_tilde)
dPhi_dtheta = -nu.sum(
(Acos * mcos + Asin * msin) * phi_tilde * dPP *
(-nu.sin(theta)))
dPhi_dphi = -nu.sum(m *
(Asin * mcos - Acos * msin) * phi_tilde * PP)
self._force_hash = new_hash
self._cached_dPhi_dr = dPhi_dr
self._cached_dPhi_dtheta = dPhi_dtheta
self._cached_dPhi_dphi = dPhi_dphi
return dPhi_dr, dPhi_dtheta, dPhi_dphi
def _computeforce(self,R,z,phi=0,t=0):
"""
NAME:
_computeforce
PURPOSE:
Evaluate the first derivative of Phi with respect to R, z and phi
INPUT:
R - Cylindrical Galactocentric radius
z - vertical height
phi - azimuth
t - time
OUTPUT:
dPhi/dr, dPhi/dtheta, dPhi/dphi
HISTORY:
2016-06-07 - Written - Aladdin
"""
Acos, Asin = self._Acos, self._Asin
N, L, M = Acos.shape
r, theta, phi = bovy_coords.cyl_to_spher(R,z,phi)
new_hash= hashlib.md5(nu.array([R, z,phi])).hexdigest()
if new_hash == self._force_hash:
dPhi_dr = self._cached_dPhi_dr
dPhi_dtheta = self._cached_dPhi_dtheta
dPhi_dphi = self._cached_dPhi_dphi
else:
PP, dPP = lpmn(M-1,L-1,nu.cos(theta)) ##Get the Legendre polynomials
PP = PP.T[None,:,:]
dPP = dPP.T[None,:,:]
phi_tilde = self._phiTilde(r, N, L)[:,:,nu.newaxis]
dphi_tilde = self._dphiTilde(r,N,L)[:,:,nu.newaxis]
m = nu.arange(0, M)[nu.newaxis, nu.newaxis, :]
mcos = nu.cos(m*phi)
msin = nu.sin(m*phi)
dPhi_dr = -nu.sum((Acos*mcos + Asin*msin)*PP*dphi_tilde)
dPhi_dtheta = -nu.sum((Acos*mcos + Asin*msin)*phi_tilde*dPP*(-nu.sin(theta)))
dPhi_dphi =-nu.sum(m*(Asin*mcos - Acos*msin)*phi_tilde*PP)
self._force_hash = new_hash
self._cached_dPhi_dr = dPhi_dr
self._cached_dPhi_dtheta = dPhi_dtheta
self._cached_dPhi_dphi = dPhi_dphi
return dPhi_dr,dPhi_dtheta,dPhi_dphi
def _phiforce(self, R,z,phi=0,t=0):
"""
NAME:
_phiforce
PURPOSE:
evaluate the azimuth force at (R,z, phi)
INPUT:
R - Cylindrical Galactocentric radius
z - vertical height
phi - azimuth
t - time
OUTPUT:
azimuth force at (R,z, phi)
HISTORY:
2016-06-06 - Written - Aladdin
"""
if not self.isNonAxi and phi is None:
phi= 0.
r, theta, phi = bovy_coords.cyl_to_spher(R,z,phi)
#x = phi
dr_dphi = 0; dtheta_dphi = 0; dphi_dphi = 1
return self._computeforceArray(dr_dphi, dtheta_dphi, dphi_dphi, R,z,phi)
def _zforce(self, R, z, phi=0., t=0.):
"""
NAME:
_zforce
PURPOSE:
evaluate the vertical force at (R,z, phi)
INPUT:
R - Cylindrical Galactocentric radius
z - vertical height
phi - azimuth
t - time
OUTPUT:
vertical force at (R,z, phi)
HISTORY:
2016-06-06 - Written - Aladdin
"""
if not self.isNonAxi and phi is None:
phi= 0.
r, theta, phi = bovy_coords.cyl_to_spher(R,z,phi)
#x = z
dr_dz = nu.divide(z,r); dtheta_dz = nu.divide(-R,r**2); dphi_dz = 0
return self._computeforceArray(dr_dz, dtheta_dz, dphi_dz, R,z,phi)
def _zforce(self, R, z, phi=0., t=0.):
"""
NAME:
_zforce
PURPOSE:
evaluate the vertical force at (R,z, phi)
INPUT:
R - Cylindrical Galactocentric radius
z - vertical height
phi - azimuth
t - time
OUTPUT:
vertical force at (R,z, phi)
HISTORY:
2016-06-06 - Written - Aladdin
"""
if not self.isNonAxi and phi is None:
phi= 0.
r, theta, phi = bovy_coords.cyl_to_spher(R,z,phi)
#x = z
dr_dz = nu.divide(z,r); dtheta_dz = nu.divide(-R,r**2); dphi_dz = 0
return self._computeforceArray(dr_dz, dtheta_dz, dphi_dz, R,z,phi)
def density1(R, z=0, phi=0.):
r, theta, phi = bovy_coords.cyl_to_spher(R, z, phi)
h = potential.HernquistPotential(2)
return h.dens(R, z, phi) * (1 + numpy.cos(theta) + numpy.cos(theta)**
2.) * (1 + numpy.cos(phi) + numpy.sin(phi))
def axi_density2(R, z=0, phi=0.):
spherical_coords = bovy_coords.cyl_to_spher(R, z, phi)
theta = spherical_coords[1]
return rho_Zeeuw(R, z, phi) * (1 + numpy.cos(theta) + numpy.cos(theta)**2)
def rho_Zeeuw(R, z, phi, a=1.):
r, theta, phi = bovy_coords.cyl_to_spher(R, z, phi)
return 3. / (4 * numpy.pi) * numpy.power((a + r), -4.) * a
def density1(R, z=0, phi=0.):
r, theta, phi = bovy_coords.cyl_to_spher(R,z, phi)
h = potential.HernquistPotential(2)
return h.dens(R, z, phi)*(1 + numpy.cos(theta) + numpy.cos(theta)**2.)*(1 + numpy.cos(phi) + numpy.sin(phi))
def axi_density2(R, z=0, phi=0.):
spherical_coords = bovy_coords.cyl_to_spher(R,z, phi)
theta = spherical_coords[1]
return rho_Zeeuw(R,z,phi)*(1 + numpy.cos(theta) + numpy.cos(theta)**2)
def rho_Zeeuw(R,z,phi,a=1.):
r, theta, phi = bovy_coords.cyl_to_spher(R,z, phi)
return 3./(4*numpy.pi) * numpy.power((a + r),-4.) * a
