def _integrateRZOrbit(vxvv, pot, t, method, dt):
"""
NAME:
_integrateRZOrbit
PURPOSE:
integrate an orbit in a Phi(R,z) potential in the (R,z) plane
INPUT:
vxvv - array with the initial conditions stacked like
[R,vR,vT,z,vz]; vR outward!
pot - Potential instance
t - list of times at which to output (0 has to be in this!)
method - 'odeint' or 'leapfrog'
dt - if set, force the integrator to use this basic stepsize; must be an integer divisor of output stepsize
OUTPUT:
[:,5] array of [R,vR,vT,z,vz] at each t
HISTORY:
2010-04-16 - Written - Bovy (NYU)
"""
#First check that the potential has C
if '_c' in method:
if not _check_c(pot):
if ('leapfrog' in method or 'symplec' in method):
method = 'leapfrog'
else:
method = 'odeint'
warnings.warn(
"Cannot use C integration because some of the potentials are not implemented in C (using %s instead)"
% (method), galpyWarning)
if method.lower() == 'leapfrog' \
or method.lower() == 'leapfrog_c' or method.lower() == 'rk4_c' \
or method.lower() == 'rk6_c' or method.lower() == 'symplec4_c' \
or method.lower() == 'symplec6_c' or method.lower() == 'dopr54_c':
#We hack this by upgrading to a FullOrbit
this_vxvv = nu.zeros(len(vxvv) + 1)
this_vxvv[0:len(vxvv)] = vxvv
tmp_out = _integrateFullOrbit(this_vxvv, pot, t, method, dt)
#tmp_out is (nt,6)
out = tmp_out[:, 0:5]
elif method.lower() == 'odeint':
l = vxvv[0] * vxvv[2]
l2 = l**2.
init = [vxvv[0], vxvv[1], vxvv[3], vxvv[4]]
intOut = integrate.odeint(_RZEOM,
init,
t,
args=(pot, l2),
rtol=10.**-8.) #,mxstep=100000000)
out = nu.zeros((len(t), 5))
out[:, 0] = intOut[:, 0]
out[:, 1] = intOut[:, 1]
out[:, 3] = intOut[:, 2]
out[:, 4] = intOut[:, 3]
out[:, 2] = l / out[:, 0]
#post-process to remove negative radii
neg_radii = (out[:, 0] < 0.)
out[neg_radii, 0] = -out[neg_radii, 0]
return out
def _integrateRZOrbit(vxvv,pot,t,method,dt):
"""
NAME:
_integrateRZOrbit
PURPOSE:
integrate an orbit in a Phi(R,z) potential in the (R,z) plane
INPUT:
vxvv - array with the initial conditions stacked like
[R,vR,vT,z,vz]; vR outward!
pot - Potential instance
t - list of times at which to output (0 has to be in this!)
method - 'odeint' or 'leapfrog'
dt - if set, force the integrator to use this basic stepsize; must be an integer divisor of output stepsize
OUTPUT:
[:,5] array of [R,vR,vT,z,vz] at each t
HISTORY:
2010-04-16 - Written - Bovy (NYU)
"""
#First check that the potential has C
if '_c' in method:
if isinstance(pot,list):
allHasC= nu.prod([p.hasC for p in pot])
else:
allHasC= pot.hasC
if not allHasC and ('leapfrog' in method or 'symplec' in method):
method= 'leapfrog'
elif not allHasC:
method= 'odeint'
if method.lower() == 'leapfrog' \
or method.lower() == 'leapfrog_c' or method.lower() == 'rk4_c' \
or method.lower() == 'rk6_c' or method.lower() == 'symplec4_c' \
or method.lower() == 'symplec6_c' or method.lower() == 'dopr54_c':
#We hack this by upgrading to a FullOrbit
this_vxvv= nu.zeros(len(vxvv)+1)
this_vxvv[0:len(vxvv)]= vxvv
tmp_out= _integrateFullOrbit(this_vxvv,pot,t,method,dt)
#tmp_out is (nt,6)
out= tmp_out[:,0:5]
elif method.lower() == 'odeint':
l= vxvv[0]*vxvv[2]
l2= l**2.
init= [vxvv[0],vxvv[1],vxvv[3],vxvv[4]]
intOut= integrate.odeint(_RZEOM,init,t,args=(pot,l2),
rtol=10.**-8.)#,mxstep=100000000)
out= nu.zeros((len(t),5))
out[:,0]= intOut[:,0]
out[:,1]= intOut[:,1]
out[:,3]= intOut[:,2]
out[:,4]= intOut[:,3]
out[:,2]= l/out[:,0]
#post-process to remove negative radii
neg_radii= (out[:,0] < 0.)
out[neg_radii,0]= -out[neg_radii,0]
return out
def _integrateRZOrbit(vxvv,pot,t,method):
"""
NAME:
_integrateRZOrbit
PURPOSE:
integrate an orbit in a Phi(R,z) potential in the (R,z) plane
INPUT:
vxvv - array with the initial conditions stacked like
[R,vR,vT,z,vz]; vR outward!
pot - Potential instance
t - list of times at which to output (0 has to be in this!)
method - 'odeint' or 'leapfrog'
OUTPUT:
[:,5] array of [R,vR,vT,z,vz] at each t
HISTORY:
2010-04-16 - Written - Bovy (NYU)
"""
if method.lower() == 'leapfrog' \
or method.lower() == 'leapfrog_c' or method.lower() == 'rk4_c' \
or method.lower() == 'rk6_c' or method.lower() == 'symplec4_c' \
or method.lower() == 'symplec6_c' or method.lower() == 'dopr54_c':
#We hack this by upgrading to a FullOrbit
this_vxvv= nu.zeros(len(vxvv)+1)
this_vxvv[0:len(vxvv)]= vxvv
tmp_out= _integrateFullOrbit(this_vxvv,pot,t,method)
#tmp_out is (nt,6)
out= tmp_out[:,0:5]
elif method.lower() == 'odeint':
l= vxvv[0]*vxvv[2]
l2= l**2.
init= [vxvv[0],vxvv[1],vxvv[3],vxvv[4]]
intOut= integrate.odeint(_RZEOM,init,t,args=(pot,l2),
rtol=10.**-8.)#,mxstep=100000000)
out= nu.zeros((len(t),5))
out[:,0]= intOut[:,0]
out[:,1]= intOut[:,1]
out[:,3]= intOut[:,2]
out[:,4]= intOut[:,3]
out[:,2]= l/out[:,0]
#post-process to remove negative radii
neg_radii= (out[:,0] < 0.)
out[neg_radii,0]= -out[neg_radii,0]
return out