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 ext_loaded or not _check_c(pot):
if ('leapfrog' in method or 'symplec' in method):
method= 'leapfrog'
else:
method= 'odeint'
if not ext_loaded: # pragma: no cover
warnings.warn("Cannot use C integration because C extension not loaded (using %s instead)" % (method), galpyWarning)
else:
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' or method.lower() == 'dop853_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' or method.lower() == 'dop853':
l= vxvv[0]*vxvv[2]
l2= l**2.
init= [vxvv[0],vxvv[1],vxvv[3],vxvv[4]]
if method.lower() == "dop853":
intOut = dop853(_RZEOM, init, t, args=(pot, l2))
else:
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 _integrateLinearOrbit(vxvv,pot,t,method,dt):
"""
NAME:
integrateLinearOrbit
PURPOSE:
integrate a one-dimensional orbit
INPUT:
vxvv - initial condition [x,vx]
pot - linearPotential or list of linearPotentials
t - list of times at which to output (0 has to be in this!)
method - 'odeint' or 'leapfrog'
OUTPUT:
[:,2] array of [x,vx] at each t
HISTORY:
2010-07-13- Written - Bovy (NYU)
2018-10-05- Added support for C integration - Bovy (UofT)
"""
#First check that the potential has C
if '_c' in method:
if not ext_loaded or not _check_c(pot):
if ('leapfrog' in method or 'symplec' in method):
method= 'leapfrog'
else:
method= 'odeint'
if not ext_loaded: # pragma: no cover
warnings.warn("Cannot use C integration because C extension not loaded (using %s instead)" % (method), galpyWarning)
else:
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':
return symplecticode.leapfrog(lambda x,t=t: _evaluatelinearForces(pot,x,
t=t),
nu.array(vxvv),
t,rtol=10.**-8)
elif method.lower() == 'dop853':
return dop853(func=_linearEOM, x=vxvv, t=t, args=(pot,))
elif ext_loaded and \
(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' \
or method.lower() == 'dop853_c'):
warnings.warn("Using C implementation to integrate orbits",
galpyWarningVerbose)
out, msg= integrateLinearOrbit_c(pot,nu.array(vxvv),t,method,dt=dt)
return out
elif method.lower() == 'odeint' or not ext_loaded:
return integrate.odeint(_linearEOM,vxvv,t,args=(pot,),rtol=10.**-8.)
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 ext_loaded or not _check_c(pot):
if ('leapfrog' in method or 'symplec' in method):
method = 'leapfrog'
else:
method = 'odeint'
if not ext_loaded: # pragma: no cover
warnings.warn(
"Cannot use C integration because C extension not loaded (using %s instead)"
% (method), galpyWarning)
else:
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' or method.lower() == 'dop853_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' or method.lower() == 'dop853':
l = vxvv[0] * vxvv[2]
l2 = l**2.
init = [vxvv[0], vxvv[1], vxvv[3], vxvv[4]]
if method.lower() == "dop853":
intOut = dop853(_RZEOM, init, t, args=(pot, l2))
else:
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 _integrateFullOrbit(vxvv, pot, t, method, dt):
"""
NAME:
_integrateFullOrbit
PURPOSE:
integrate an orbit in a Phi(R,z,phi) potential
INPUT:
vxvv - array with the initial conditions stacked like
[R,vR,vT,z,vz,phi]; 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,phi] at each t
HISTORY:
2010-08-01 - Written - Bovy (NYU)
"""
#First check that the potential has C
if '_c' in method:
if not ext_loaded or not _check_c(pot):
if ('leapfrog' in method or 'symplec' in method):
method = 'leapfrog'
else:
method = 'odeint'
if not ext_loaded: # pragma: no cover
warnings.warn(
"Cannot use C integration because C extension not loaded (using %s instead)"
% (method), galpyWarning)
else:
warnings.warn(
"Cannot use C integration because some of the potentials are not implemented in C (using %s instead)"
% (method), galpyWarning)
# Now check that we aren't trying to integrate a dissipative force
# with a symplectic integrator
if _isDissipative(pot) and ('leapfrog' in method or 'symplec' in method):
if '_c' in method:
method = 'dopr54_c'
else:
method = 'odeint'
warnings.warn(
"Cannot use symplectic integration because some of the included forces are dissipative (using non-symplectic integrator %s instead)"
% (method), galpyWarning)
if method.lower() == 'leapfrog':
#go to the rectangular frame
this_vxvv = nu.array([
vxvv[0] * nu.cos(vxvv[5]), vxvv[0] * nu.sin(vxvv[5]), vxvv[3],
vxvv[1] * nu.cos(vxvv[5]) - vxvv[2] * nu.sin(vxvv[5]),
vxvv[2] * nu.cos(vxvv[5]) + vxvv[1] * nu.sin(vxvv[5]), vxvv[4]
])
#integrate
out = symplecticode.leapfrog(_rectForce,
this_vxvv,
t,
args=(pot, ),
rtol=10.**-8)
#go back to the cylindrical frame
R = nu.sqrt(out[:, 0]**2. + out[:, 1]**2.)
phi = nu.arccos(out[:, 0] / R)
phi[(out[:, 1] < 0.)] = 2. * nu.pi - phi[(out[:, 1] < 0.)]
vR = out[:, 3] * nu.cos(phi) + out[:, 4] * nu.sin(phi)
vT = out[:, 4] * nu.cos(phi) - out[:, 3] * nu.sin(phi)
out[:, 3] = out[:, 2]
out[:, 4] = out[:, 5]
out[:, 0] = R
out[:, 1] = vR
out[:, 2] = vT
out[:, 5] = phi
elif ext_loaded and \
(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' \
or method.lower() == 'dop853_c'):
warnings.warn("Using C implementation to integrate orbits",
galpyWarningVerbose)
#go to the rectangular frame
this_vxvv = nu.array([
vxvv[0] * nu.cos(vxvv[5]), vxvv[0] * nu.sin(vxvv[5]), vxvv[3],
vxvv[1] * nu.cos(vxvv[5]) - vxvv[2] * nu.sin(vxvv[5]),
vxvv[2] * nu.cos(vxvv[5]) + vxvv[1] * nu.sin(vxvv[5]), vxvv[4]
])
#integrate
tmp_out, msg = integrateFullOrbit_c(pot, this_vxvv, t, method, dt=dt)
#go back to the cylindrical frame
R = nu.sqrt(tmp_out[:, 0]**2. + tmp_out[:, 1]**2.)
phi = nu.arccos(tmp_out[:, 0] / R)
phi[(tmp_out[:, 1] < 0.)] = 2. * nu.pi - phi[(tmp_out[:, 1] < 0.)]
vR = tmp_out[:, 3] * nu.cos(phi) + tmp_out[:, 4] * nu.sin(phi)
vT = tmp_out[:, 4] * nu.cos(phi) - tmp_out[:, 3] * nu.sin(phi)
out = nu.zeros((len(t), 6))
out[:, 0] = R
out[:, 1] = vR
out[:, 2] = vT
out[:, 5] = phi
out[:, 3] = tmp_out[:, 2]
out[:, 4] = tmp_out[:, 5]
elif method.lower() == 'odeint' or method.lower(
) == 'dop853' or not ext_loaded:
vphi = vxvv[2] / vxvv[0]
init = [vxvv[0], vxvv[1], vxvv[5], vphi, vxvv[3], vxvv[4]]
if method == 'dop853':
intOut = dop853(_FullEOM, init, t, args=(pot, ))
else:
intOut = integrate.odeint(_FullEOM,
init,
t,
args=(pot, ),
rtol=10.**-8.) #,mxstep=100000000)
out = nu.zeros((len(t), 6))
out[:, 0] = intOut[:, 0]
out[:, 1] = intOut[:, 1]
out[:, 2] = out[:, 0] * intOut[:, 3]
out[:, 3] = intOut[:, 4]
out[:, 4] = intOut[:, 5]
out[:, 5] = intOut[:, 2]
#post-process to remove negative radii
neg_radii = (out[:, 0] < 0.)
out[neg_radii, 0] = -out[neg_radii, 0]
out[neg_radii, 5] += m.pi
return out
def _integrateOrbit_dxdv(vxvv, dxdv, pot, t, method, rectIn, rectOut):
"""
NAME:
_integrateOrbit_dxdv
PURPOSE:
integrate an orbit and area of phase space in a Phi(R) potential
in the (R,phi)-plane
INPUT:
vxvv - array with the initial conditions stacked like
[R,vR,vT,phi]; vR outward!
dxdv - difference to integrate [dR,dvR,dvT,dphi]
pot - Potential instance
t - list of times at which to output (0 has to be in this!)
method - 'odeint' or 'leapfrog'
rectIn= (False) if True, input dxdv is in rectangular coordinates
rectOut= (False) if True, output dxdv (that in orbit_dxdv) is in rectangular coordinates
OUTPUT:
[:,8] array of [R,vR,vT,phi,dR,dvR,dvT,dphi] at each t
error message from integrator
HISTORY:
2010-10-17 - Written - Bovy (IAS)
"""
#First check that the potential has C
if '_c' in method:
allHasC = _check_c(pot) and _check_c(pot, dxdv=True)
if not ext_loaded or \
(not allHasC and not 'leapfrog' in method and not 'symplec' in method):
method = 'odeint'
if not ext_loaded: # pragma: no cover
warnings.warn("Using odeint because C extension not loaded",
galpyWarning)
else:
warnings.warn(
"Using odeint because not all used potential have adequate C implementations to integrate phase-space volumes",
galpyWarning)
#go to the rectangular frame
this_vxvv = nu.array([
vxvv[0] * nu.cos(vxvv[3]), vxvv[0] * nu.sin(vxvv[3]),
vxvv[1] * nu.cos(vxvv[3]) - vxvv[2] * nu.sin(vxvv[3]),
vxvv[2] * nu.cos(vxvv[3]) + vxvv[1] * nu.sin(vxvv[3])
])
if not rectIn:
this_dxdv = nu.array([
nu.cos(vxvv[3]) * dxdv[0] - vxvv[0] * nu.sin(vxvv[3]) * dxdv[3],
nu.sin(vxvv[3]) * dxdv[0] + vxvv[0] * nu.cos(vxvv[3]) * dxdv[3],
-(vxvv[1] * nu.sin(vxvv[3]) + vxvv[2] * nu.cos(vxvv[3])) * dxdv[3]
+ nu.cos(vxvv[3]) * dxdv[1] - nu.sin(vxvv[3]) * dxdv[2],
(vxvv[1] * nu.cos(vxvv[3]) - vxvv[2] * nu.sin(vxvv[3])) * dxdv[3] +
nu.sin(vxvv[3]) * dxdv[1] + nu.cos(vxvv[3]) * dxdv[2]
])
else:
this_dxdv = dxdv
if 'leapfrog' in method.lower() or 'symplec' in method.lower():
raise TypeError(
'Symplectic integration for phase-space volume is not possible')
elif ext_loaded and \
(method.lower() == 'rk4_c' or method.lower() == 'rk6_c' \
or method.lower() == 'dopr54_c' or method.lower() == 'dop853_c'):
warnings.warn("Using C implementation to integrate orbits",
galpyWarningVerbose)
#integrate
tmp_out, msg = integratePlanarOrbit_dxdv_c(pot, this_vxvv, this_dxdv,
t, method)
elif method.lower() == 'odeint' or not ext_loaded or method.lower(
) == 'dop853':
init = [
this_vxvv[0], this_vxvv[1], this_vxvv[2], this_vxvv[3],
this_dxdv[0], this_dxdv[1], this_dxdv[2], this_dxdv[3]
]
#integrate
if method.lower() == "dop853":
tmp_out = dop853(_EOM_dxdv, init, t, args=(pot, ))
else:
tmp_out = integrate.odeint(_EOM_dxdv,
init,
t,
args=(pot, ),
rtol=10.**-8.) #,mxstep=100000000)
msg = 0
else:
raise NotImplementedError(
"requested integration method does not exist")
#go back to the cylindrical frame
R = nu.sqrt(tmp_out[:, 0]**2. + tmp_out[:, 1]**2.)
phi = nu.arccos(tmp_out[:, 0] / R)
phi[(tmp_out[:, 1] < 0.)] = 2. * nu.pi - phi[(tmp_out[:, 1] < 0.)]
vR = tmp_out[:, 2] * nu.cos(phi) + tmp_out[:, 3] * nu.sin(phi)
vT = tmp_out[:, 3] * nu.cos(phi) - tmp_out[:, 2] * nu.sin(phi)
cp = nu.cos(phi)
sp = nu.sin(phi)
dR = cp * tmp_out[:, 4] + sp * tmp_out[:, 5]
dphi = (cp * tmp_out[:, 5] - sp * tmp_out[:, 4]) / R
dvR = cp * tmp_out[:, 6] + sp * tmp_out[:, 7] + vT * dphi
dvT = cp * tmp_out[:, 7] - sp * tmp_out[:, 6] - vR * dphi
out = nu.zeros((len(t), 8))
out[:, 0] = R
out[:, 1] = vR
out[:, 2] = vT
out[:, 3] = phi
if rectOut:
out[:, 4:] = tmp_out[:, 4:]
else:
out[:, 4] = dR
out[:, 7] = dphi
out[:, 5] = dvR
out[:, 6] = dvT
_parse_warnmessage(msg)
return (out, msg)
def _integrateOrbit_dxdv(vxvv,dxdv,pot,t,method,rectIn,rectOut):
"""
NAME:
_integrateOrbit_dxdv
PURPOSE:
integrate an orbit and area of phase space in a Phi(R) potential
in the (R,phi)-plane
INPUT:
vxvv - array with the initial conditions stacked like
[R,vR,vT,phi]; vR outward!
dxdv - difference to integrate [dR,dvR,dvT,dphi]
pot - Potential instance
t - list of times at which to output (0 has to be in this!)
method - 'odeint' or 'leapfrog'
rectIn= (False) if True, input dxdv is in rectangular coordinates
rectOut= (False) if True, output dxdv (that in orbit_dxdv) is in rectangular coordinates
OUTPUT:
[:,8] array of [R,vR,vT,phi,dR,dvR,dvT,dphi] at each t
error message from integrator
HISTORY:
2010-10-17 - Written - Bovy (IAS)
"""
#First check that the potential has C
if '_c' in method:
allHasC= _check_c(pot) and _check_c(pot,dxdv=True)
if not ext_loaded or \
(not allHasC and not 'leapfrog' in method and not 'symplec' in method):
method= 'odeint'
if not ext_loaded: # pragma: no cover
warnings.warn("Using odeint because C extension not loaded",galpyWarning)
else:
warnings.warn("Using odeint because not all used potential have adequate C implementations to integrate phase-space volumes",galpyWarning)
#go to the rectangular frame
this_vxvv= nu.array([vxvv[0]*nu.cos(vxvv[3]),
vxvv[0]*nu.sin(vxvv[3]),
vxvv[1]*nu.cos(vxvv[3])-vxvv[2]*nu.sin(vxvv[3]),
vxvv[2]*nu.cos(vxvv[3])+vxvv[1]*nu.sin(vxvv[3])])
if not rectIn:
this_dxdv= nu.array([nu.cos(vxvv[3])*dxdv[0]
-vxvv[0]*nu.sin(vxvv[3])*dxdv[3],
nu.sin(vxvv[3])*dxdv[0]
+vxvv[0]*nu.cos(vxvv[3])*dxdv[3],
-(vxvv[1]*nu.sin(vxvv[3])
+vxvv[2]*nu.cos(vxvv[3]))*dxdv[3]
+nu.cos(vxvv[3])*dxdv[1]-nu.sin(vxvv[3])*dxdv[2],
(vxvv[1]*nu.cos(vxvv[3])
-vxvv[2]*nu.sin(vxvv[3]))*dxdv[3]
+nu.sin(vxvv[3])*dxdv[1]+nu.cos(vxvv[3])*dxdv[2]])
else:
this_dxdv= dxdv
if 'leapfrog' in method.lower() or 'symplec' in method.lower():
raise TypeError('Symplectic integration for phase-space volume is not possible')
elif ext_loaded and \
(method.lower() == 'rk4_c' or method.lower() == 'rk6_c' \
or method.lower() == 'dopr54_c' or method.lower() == 'dop853_c'):
warnings.warn("Using C implementation to integrate orbits",galpyWarningVerbose)
#integrate
tmp_out, msg= integratePlanarOrbit_dxdv_c(pot,this_vxvv,this_dxdv,
t,method)
elif method.lower() == 'odeint' or not ext_loaded or method.lower() == 'dop853':
init= [this_vxvv[0],this_vxvv[1],this_vxvv[2],this_vxvv[3],
this_dxdv[0],this_dxdv[1],this_dxdv[2],this_dxdv[3]]
#integrate
if method.lower() == "dop853":
tmp_out = dop853(_EOM_dxdv, init, t, args=(pot,))
else:
tmp_out= integrate.odeint(_EOM_dxdv,init,t,args=(pot,),
rtol=10.**-8.)#,mxstep=100000000)
msg= 0
else:
raise NotImplementedError("requested integration method does not exist")
#go back to the cylindrical frame
R= nu.sqrt(tmp_out[:,0]**2.+tmp_out[:,1]**2.)
phi= nu.arccos(tmp_out[:,0]/R)
phi[(tmp_out[:,1] < 0.)]= 2.*nu.pi-phi[(tmp_out[:,1] < 0.)]
vR= tmp_out[:,2]*nu.cos(phi)+tmp_out[:,3]*nu.sin(phi)
vT= tmp_out[:,3]*nu.cos(phi)-tmp_out[:,2]*nu.sin(phi)
cp= nu.cos(phi)
sp= nu.sin(phi)
dR= cp*tmp_out[:,4]+sp*tmp_out[:,5]
dphi= (cp*tmp_out[:,5]-sp*tmp_out[:,4])/R
dvR= cp*tmp_out[:,6]+sp*tmp_out[:,7]+vT*dphi
dvT= cp*tmp_out[:,7]-sp*tmp_out[:,6]-vR*dphi
out= nu.zeros((len(t),8))
out[:,0]= R
out[:,1]= vR
out[:,2]= vT
out[:,3]= phi
if rectOut:
out[:,4:]= tmp_out[:,4:]
else:
out[:,4]= dR
out[:,7]= dphi
out[:,5]= dvR
out[:,6]= dvT
_parse_warnmessage(msg)
return (out,msg)
def _integrateOrbit(vxvv,pot,t,method,dt):
"""
NAME:
_integrateOrbit
PURPOSE:
integrate an orbit in a Phi(R) potential in the (R,phi)-plane
INPUT:
vxvv - array with the initial conditions stacked like
[R,vR,vT,phi]; 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:
[:,4] array of [R,vR,vT,phi] at each t
HISTORY:
2010-07-20 - Written - Bovy (NYU)
"""
#First check that the potential has C
if '_c' in method:
if not ext_loaded or not _check_c(pot):
if ('leapfrog' in method or 'symplec' in method):
method= 'leapfrog'
else:
method= 'odeint'
if not ext_loaded: # pragma: no cover
warnings.warn("Cannot use C integration because C extension not loaded (using %s instead)" % (method), galpyWarning)
else:
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':
#go to the rectangular frame
this_vxvv= nu.array([vxvv[0]*nu.cos(vxvv[3]),
vxvv[0]*nu.sin(vxvv[3]),
vxvv[1]*nu.cos(vxvv[3])-vxvv[2]*nu.sin(vxvv[3]),
vxvv[2]*nu.cos(vxvv[3])+vxvv[1]*nu.sin(vxvv[3])])
#integrate
tmp_out= symplecticode.leapfrog(_rectForce,this_vxvv,
t,args=(pot,),rtol=10.**-8)
#go back to the cylindrical frame
R= nu.sqrt(tmp_out[:,0]**2.+tmp_out[:,1]**2.)
phi= nu.arccos(tmp_out[:,0]/R)
phi[(tmp_out[:,1] < 0.)]= 2.*nu.pi-phi[(tmp_out[:,1] < 0.)]
vR= tmp_out[:,2]*nu.cos(phi)+tmp_out[:,3]*nu.sin(phi)
vT= tmp_out[:,3]*nu.cos(phi)-tmp_out[:,2]*nu.sin(phi)
out= nu.zeros((len(t),4))
out[:,0]= R
out[:,1]= vR
out[:,2]= vT
out[:,3]= phi
msg= 0
elif ext_loaded and \
(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' \
or method.lower() == 'dop853_c'):
warnings.warn("Using C implementation to integrate orbits",galpyWarningVerbose)
#go to the rectangular frame
this_vxvv= nu.array([vxvv[0]*nu.cos(vxvv[3]),
vxvv[0]*nu.sin(vxvv[3]),
vxvv[1]*nu.cos(vxvv[3])-vxvv[2]*nu.sin(vxvv[3]),
vxvv[2]*nu.cos(vxvv[3])+vxvv[1]*nu.sin(vxvv[3])])
#integrate
tmp_out, msg= integratePlanarOrbit_c(pot,this_vxvv,
t,method,dt=dt)
#go back to the cylindrical frame
R= nu.sqrt(tmp_out[:,0]**2.+tmp_out[:,1]**2.)
phi= nu.arccos(tmp_out[:,0]/R)
phi[(tmp_out[:,1] < 0.)]= 2.*nu.pi-phi[(tmp_out[:,1] < 0.)]
vR= tmp_out[:,2]*nu.cos(phi)+tmp_out[:,3]*nu.sin(phi)
vT= tmp_out[:,3]*nu.cos(phi)-tmp_out[:,2]*nu.sin(phi)
out= nu.zeros((len(t),4))
out[:,0]= R
out[:,1]= vR
out[:,2]= vT
out[:,3]= phi
elif method.lower() == 'odeint' or method.lower() == 'dop853' or not ext_loaded:
vphi= vxvv[2]/vxvv[0]
init= [vxvv[0],vxvv[1],vxvv[3],vphi]
if method == 'dop853':
intOut = dop853(_EOM, init, t, args=(pot,))
else:
intOut= integrate.odeint(_EOM,init,t,args=(pot,),
rtol=10.**-8.)#,mxstep=100000000)
out= nu.zeros((len(t),4))
out[:,0]= intOut[:,0]
out[:,1]= intOut[:,1]
out[:,3]= intOut[:,2]
out[:,2]= out[:,0]*intOut[:,3]
msg= 0
else:
raise NotImplementedError("requested integration method does not exist")
#post-process to remove negative radii
neg_radii= (out[:,0] < 0.)
out[neg_radii,0]= -out[neg_radii,0]
out[neg_radii,3]+= m.pi
_parse_warnmessage(msg)
return (out,msg)