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 allHasC and not 'leapfrog' in method and not 'symplec' in method:
method = 'odeint'
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 method.lower() == 'rk4_c' or method.lower() == 'rk6_c' \
or method.lower() == 'dopr54_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':
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
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 allHasC and not 'leapfrog' in method and not 'symplec' in method:
method= 'odeint'
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 method.lower() == 'rk4_c' or method.lower() == 'rk6_c' \
or method.lower() == 'dopr54_c':
warnings.warn("Using C implementation to integrate orbits",galpyWarning)
#integrate
tmp_out, msg= integratePlanarOrbit_dxdv_c(pot,this_vxvv,this_dxdv,
t,method)
elif method.lower() == 'odeint':
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
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):
"""
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'
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)
"""
#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])])
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]])
if 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':
#raise NotImplementedError("C implementation of phase space integration not implemented yet")
warnings.warn("Using C implementation to integrate orbits",galpyWarning)
#integrate
tmp_out, msg= integratePlanarOrbit_dxdv_c(pot,this_vxvv,this_dxdv,
t,method)
elif method.lower() == 'odeint':
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
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
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):
"""
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'
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)
"""
#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])
])
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]
])
if 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':
#raise NotImplementedError("C implementation of phase space integration not implemented yet")
warnings.warn("Using C implementation to integrate orbits")
#integrate
tmp_out, msg = integratePlanarOrbit_dxdv_c(pot, this_vxvv, this_dxdv,
t, method)
elif method.lower() == 'odeint':
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
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
out[:, 4] = dR
out[:, 7] = dphi
out[:, 5] = dvR
out[:, 6] = dvT
_parse_warnmessage(msg)
return (out, msg)