def _Rzderiv(self, R, z, phi=0., t=0.):
"""
NAME:
_Rzderiv
PURPOSE:
evaluate the mixed R,z derivative for this potential
INPUT:
R - Galactocentric cylindrical radius
z - vertical height
phi - azimuth
t- time
OUTPUT:
d2phi/dR/dz
HISTORY:
2015-02-13 - Written - Trick (MPIA)
"""
l, n = bovy_coords.Rz_to_lambdanu(R, z, ac=self._ac, Delta=self._Delta)
jac = bovy_coords.Rz_to_lambdanu_jac(R, z, Delta=self._Delta)
hess = bovy_coords.Rz_to_lambdanu_hess(R, z, Delta=self._Delta)
dldR = jac[0, 0]
dndR = jac[1, 0]
dldz = jac[0, 1]
dndz = jac[1, 1]
d2ldRdz = hess[0, 0, 1]
d2ndRdz = hess[1, 0, 1]
return d2ldRdz * self._lderiv(l,n) + \
d2ndRdz * self._nderiv(l,n) + \
dldR*dldz * self._l2deriv(l,n) + \
dndR*dndz * self._n2deriv(l,n) + \
(dldR*dndz+dldz*dndR)* self._lnderiv(l,n)
def _Rforce(self, R, z, phi=0., t=0.):
"""
NAME:
_Rforce
PURPOSE:
evaluate the radial force for this potential
INPUT:
R - Galactocentric cylindrical radius
z - vertical height
phi - azimuth
t - time
OUTPUT:
the radial force = -dphi/dR
HISTORY:
2015-02-13 - Written - Trick (MPIA)
"""
l, n = bovy_coords.Rz_to_lambdanu(R, z, ac=self._ac, Delta=self._Delta)
jac = bovy_coords.Rz_to_lambdanu_jac(R, z, Delta=self._Delta)
dldR = jac[0, 0]
dndR = jac[1, 0]
return - (dldR * self._lderiv(l,n) + \
dndR * self._nderiv(l,n))
def test_Rz_to_lambdanu_jac():
#coordinate system:
a = 3.
g = 7.
Delta = numpy.sqrt(g - a)
ac = numpy.sqrt(a / g)
#_____test float input (R=0)_____
R, z = 1.4, 0.1
dR = 10.**-8.
dz = 10.**-8.
# R derivatives
tmp = R + dR
dR = tmp - R
num_deriv_lR= (bovy_coords.Rz_to_lambdanu(R+dR,z,ac=ac,Delta=Delta)[0]\
-bovy_coords.Rz_to_lambdanu(R,z,ac=ac,Delta=Delta)[0])/dR
num_deriv_nR= (bovy_coords.Rz_to_lambdanu(R+dR,z,ac=ac,Delta=Delta)[1]\
-bovy_coords.Rz_to_lambdanu(R,z,ac=ac,Delta=Delta)[1])/dR
# z derivatives
tmp = z + dz
dz = tmp - z
num_deriv_lz= (bovy_coords.Rz_to_lambdanu(R,z+dz,ac=ac,Delta=Delta)[0]\
-bovy_coords.Rz_to_lambdanu(R,z,ac=ac,Delta=Delta)[0])/dR
num_deriv_nz= (bovy_coords.Rz_to_lambdanu(R,z+dz,ac=ac,Delta=Delta)[1]\
-bovy_coords.Rz_to_lambdanu(R,z,ac=ac,Delta=Delta)[1])/dR
jac = bovy_coords.Rz_to_lambdanu_jac(R, z, Delta=Delta)
assert numpy.fabs(num_deriv_lR - jac[
0, 0]) < 10.**-6., 'jacobian d((lambda,nu))/d((R,z)) fails for (dl/dR)'
assert numpy.fabs(num_deriv_nR - jac[
1, 0]) < 10.**-6., 'jacobian d((lambda,nu))/d((R,z)) fails for (dn/dR)'
assert numpy.fabs(num_deriv_lz - jac[
0, 1]) < 10.**-6., 'jacobian d((lambda,nu))/d((R,z)) fails for (dl/dz)'
assert numpy.fabs(num_deriv_nz - jac[
1, 1]) < 10.**-6., 'jacobian d((lambda,nu))/d((R,z)) fails for (dn/dz)'
#___Also test for arrays___
R = numpy.arange(1, 4) * 0.5
z = numpy.arange(1, 4) * 0.125
dR = 10.**-8.
dz = 10.**-8.
# R derivatives
tmp = R + dR
dR = tmp - R
num_deriv_lR= (bovy_coords.Rz_to_lambdanu(R+dR,z,ac=ac,Delta=Delta)[0]\
-bovy_coords.Rz_to_lambdanu(R,z,ac=ac,Delta=Delta)[0])/dR
num_deriv_nR= (bovy_coords.Rz_to_lambdanu(R+dR,z,ac=ac,Delta=Delta)[1]\
-bovy_coords.Rz_to_lambdanu(R,z,ac=ac,Delta=Delta)[1])/dR
# z derivatives
tmp = z + dz
dz = tmp - z
num_deriv_lz= (bovy_coords.Rz_to_lambdanu(R,z+dz,ac=ac,Delta=Delta)[0]\
-bovy_coords.Rz_to_lambdanu(R,z,ac=ac,Delta=Delta)[0])/dR
num_deriv_nz= (bovy_coords.Rz_to_lambdanu(R,z+dz,ac=ac,Delta=Delta)[1]\
-bovy_coords.Rz_to_lambdanu(R,z,ac=ac,Delta=Delta)[1])/dR
jac = bovy_coords.Rz_to_lambdanu_jac(R, z, Delta=Delta)
assert numpy.all(numpy.fabs(num_deriv_lR - jac[0, 0]) < 10.**-6.
), 'jacobian d((lambda,nu))/d((R,z)) fails for (dl/dR)'
assert numpy.all(numpy.fabs(num_deriv_nR - jac[1, 0]) < 10.**-6.
), 'jacobian d((lambda,nu))/d((R,z)) fails for (dn/dR)'
assert numpy.all(numpy.fabs(num_deriv_lz - jac[0, 1]) < 10.**-6.
), 'jacobian d((lambda,nu))/d((R,z)) fails for (dl/dz)'
assert numpy.all(numpy.fabs(num_deriv_nz - jac[1, 1]) < 10.**-6.
), 'jacobian d((lambda,nu))/d((R,z)) fails for (dn/dz)'
return None
