def plotE(self,*args,**kwargs):
"""
NAME:
plotE
PURPOSE:
plot E(.) along the orbit
INPUT:
pot - Potential instance or list of instances in which the orbit was
integrated
d1= - plot Ez vs d1: e.g., 't', 'R', 'vR', 'vT'
+bovy_plot.bovy_plot inputs
OUTPUT:
figure to output device
HISTORY:
2010-07-10 - Written - Bovy (NYU)
"""
labeldict= {'t':r'$t$','R':r'$R$','vR':r'$v_R$','vT':r'$v_T$',
'z':r'$z$','vz':r'$v_z$','phi':r'$\phi$',
'x':r'$x$','y':r'$y$','vx':r'$v_x$','vy':r'$v_y$'}
if not kwargs.has_key('pot'):
try:
pot= self._pot
except AttributeError:
raise AttributeError("Integrate orbit first or specify pot=")
else:
pot= kwargs['pot']
kwargs.pop('pot')
if kwargs.has_key('d1'):
d1= kwargs['d1']
kwargs.pop('d1')
else:
d1= 't'
if len(self.vxvv) == 4:
self.Es= [evaluateplanarPotentials(self.orbit[ii,0],pot,
phi=self.orbit[ii,3],
t=self.t[ii])+
self.orbit[ii,1]**2./2.+self.orbit[ii,2]**2./2.
for ii in range(len(self.t))]
else:
self.Es= [evaluateplanarPotentials(self.orbit[ii,0],pot,
t=self.t[ii])+
self.orbit[ii,1]**2./2.+self.orbit[ii,2]**2./2.
for ii in range(len(self.t))]
if not kwargs.has_key('xlabel'):
kwargs['xlabel']= labeldict[d1]
if not kwargs.has_key('ylabel'):
kwargs['ylabel']= r'$E$'
if d1 == 't':
plot.bovy_plot(nu.array(self.t),nu.array(self.Es)/self.Es[0],
*args,**kwargs)
elif d1 == 'R':
plot.bovy_plot(self.orbit[:,0],nu.array(self.Es)/self.Es[0],
*args,**kwargs)
elif d1 == 'vR':
plot.bovy_plot(self.orbit[:,1],nu.array(self.Es)/self.Es[0],
*args,**kwargs)
elif d1 == 'vT':
plot.bovy_plot(self.orbit[:,2],nu.array(self.Es)/self.Es[0],
*args,**kwargs)
def _EOM_dxdv(x,t,pot):
"""
NAME:
_EOM_dxdv
PURPOSE:
implements the EOM, i.e., the right-hand side of the differential
equation, for integrating phase space differences, rectangular
INPUT:
x - current phase-space position
t - current time
pot - (list of) Potential instance(s)
OUTPUT:
dy/dt
HISTORY:
2011-10-18 - Written - Bovy (NYU)
"""
#x is rectangular so calculate R and phi
R= nu.sqrt(x[0]**2.+x[1]**2.)
phi= nu.arccos(x[0]/R)
sinphi= x[1]/R
cosphi= x[0]/R
if x[1] < 0.: phi= 2.*nu.pi-phi
#calculate forces
Rforce= evaluateplanarRforces(R,pot,phi=phi,t=t)
phiforce= evaluateplanarphiforces(R,pot,phi=phi,t=t)
R2deriv= evaluateplanarPotentials(R,pot,phi=phi,t=t,dR=2)
phi2deriv= evaluateplanarPotentials(R,pot,phi=phi,t=t,dphi=2)
Rphideriv= evaluateplanarPotentials(R,pot,phi=phi,t=t,dR=1,dphi=1)
#Calculate derivatives and derivatives+time derivatives
dFxdx= -cosphi**2.*R2deriv\
+2.*cosphi*sinphi/R**2.*phiforce\
+sinphi**2./R*Rforce\
+2.*sinphi*cosphi/R*Rphideriv\
-sinphi**2./R**2.*phi2deriv
dFxdy= -sinphi*cosphi*R2deriv\
+(sinphi**2.-cosphi**2.)/R**2.*phiforce\
-cosphi*sinphi/R*Rforce\
-(cosphi**2.-sinphi**2.)/R*Rphideriv\
+cosphi*sinphi/R**2.*phi2deriv
dFydx= -cosphi*sinphi*R2deriv\
+(sinphi**2.-cosphi**2.)/R**2.*phiforce\
+(sinphi**2.-cosphi**2.)/R*Rphideriv\
-sinphi*cosphi/R*Rforce\
+sinphi*cosphi/R**2.*phi2deriv
dFydy= -sinphi**2.*R2deriv\
-2.*sinphi*cosphi/R**2.*phiforce\
-2.*sinphi*cosphi/R*Rphideriv\
+cosphi**2./R*Rforce\
-cosphi**2./R**2.*phi2deriv
return nu.array([x[2],x[3],
cosphi*Rforce-1./R*sinphi*phiforce,
sinphi*Rforce+1./R*cosphi*phiforce,
x[6],x[7],
dFxdx*x[4]+dFxdy*x[5],
dFydx*x[4]+dFydy*x[5]])
def _EOM_dxdv(x, t, pot):
"""
NAME:
_EOM_dxdv
PURPOSE:
implements the EOM, i.e., the right-hand side of the differential
equation, for integrating phase space differences, rectangular
INPUT:
x - current phase-space position
t - current time
pot - (list of) Potential instance(s)
OUTPUT:
dy/dt
HISTORY:
2011-10-18 - Written - Bovy (NYU)
"""
#x is rectangular so calculate R and phi
R = nu.sqrt(x[0]**2. + x[1]**2.)
phi = nu.arccos(x[0] / R)
sinphi = x[1] / R
cosphi = x[0] / R
if x[1] < 0.: phi = 2. * nu.pi - phi
#calculate forces
Rforce = evaluateplanarRforces(R, pot, phi=phi, t=t)
phiforce = evaluateplanarphiforces(R, pot, phi=phi, t=t)
R2deriv = evaluateplanarPotentials(R, pot, phi=phi, t=t, dR=2)
phi2deriv = evaluateplanarPotentials(R, pot, phi=phi, t=t, dphi=2)
Rphideriv = evaluateplanarPotentials(R, pot, phi=phi, t=t, dR=1, dphi=1)
#Calculate derivatives and derivatives+time derivatives
dFxdx= -cosphi**2.*R2deriv\
+2.*cosphi*sinphi/R**2.*phiforce\
+sinphi**2./R*Rforce\
+2.*sinphi*cosphi/R*Rphideriv\
-sinphi**2./R**2.*phi2deriv
dFxdy= -sinphi*cosphi*R2deriv\
+(sinphi**2.-cosphi**2.)/R**2.*phiforce\
-cosphi*sinphi/R*Rforce\
-(cosphi**2.-sinphi**2.)/R*Rphideriv\
+cosphi*sinphi/R**2.*phi2deriv
dFydx= -cosphi*sinphi*R2deriv\
+(sinphi**2.-cosphi**2.)/R**2.*phiforce\
+(sinphi**2.-cosphi**2.)/R*Rphideriv\
-sinphi*cosphi/R*Rforce\
+sinphi*cosphi/R**2.*phi2deriv
dFydy= -sinphi**2.*R2deriv\
-2.*sinphi*cosphi/R**2.*phiforce\
-2.*sinphi*cosphi/R*Rphideriv\
+cosphi**2./R*Rforce\
-cosphi**2./R**2.*phi2deriv
return nu.array([
x[2], x[3], cosphi * Rforce - 1. / R * sinphi * phiforce,
sinphi * Rforce + 1. / R * cosphi * phiforce, x[6], x[7],
dFxdx * x[4] + dFxdy * x[5], dFydx * x[4] + dFydy * x[5]
])
def E(self, *args, **kwargs):
"""
NAME:
E
PURPOSE:
calculate the energy
INPUT:
pot=
t= time at which to evaluate E
OUTPUT:
energy
HISTORY:
2010-09-15 - Written - Bovy (NYU)
"""
if not kwargs.has_key('pot') or kwargs['pot'] is None:
try:
pot = self._pot
except AttributeError:
raise AttributeError("Integrate orbit or specify pot=")
if kwargs.has_key('pot') and kwargs['pot'] is None:
kwargs.pop('pot')
else:
pot = kwargs['pot']
kwargs.pop('pot')
if isinstance(pot, Potential):
thispot = RZToplanarPotential(pot)
elif isinstance(pot, list):
thispot = []
for p in pot:
if isinstance(p, Potential):
thispot.append(RZToplanarPotential(p))
else:
thispot.append(p)
else:
thispot = pot
if len(args) > 0:
t = args[0]
else:
t = 0.
#Get orbit
thiso = self(*args, **kwargs)
onet = (len(thiso.shape) == 1)
if onet:
return evaluateplanarPotentials(thiso[0],thispot,
phi=thiso[3],t=t)\
+thiso[1]**2./2.\
+thiso[2]**2./2.
else:
return nu.array([evaluateplanarPotentials(thiso[0,ii],thispot,
phi=thiso[3,ii],
t=t[ii])\
+thiso[1,ii]**2./2.\
+thiso[2,ii]**2./2. for ii in range(len(t))])
def E(self,*args,**kwargs):
"""
NAME:
E
PURPOSE:
calculate the energy
INPUT:
pot=
t= time at which to evaluate E
OUTPUT:
energy
HISTORY:
2010-09-15 - Written - Bovy (NYU)
"""
if not kwargs.has_key('pot') or kwargs['pot'] is None:
try:
pot= self._pot
except AttributeError:
raise AttributeError("Integrate orbit or specify pot=")
if kwargs.has_key('pot') and kwargs['pot'] is None:
kwargs.pop('pot')
else:
pot= kwargs['pot']
kwargs.pop('pot')
if isinstance(pot,Potential):
thispot= RZToplanarPotential(pot)
elif isinstance(pot,list):
thispot= []
for p in pot:
if isinstance(p,Potential): thispot.append(RZToplanarPotential(p))
else: thispot.append(p)
else:
thispot= pot
if len(args) > 0:
t= args[0]
else:
t= 0.
#Get orbit
thiso= self(*args,**kwargs)
onet= (len(thiso.shape) == 1)
if onet:
return evaluateplanarPotentials(thiso[0],thispot,
phi=thiso[3],t=t)\
+thiso[1]**2./2.\
+thiso[2]**2./2.
else:
return nu.array([evaluateplanarPotentials(thiso[0,ii],thispot,
phi=thiso[3,ii],
t=t[ii])\
+thiso[1,ii]**2./2.\
+thiso[2,ii]**2./2. for ii in range(len(t))])
def _wrap_pot_func(self,attribute):
if attribute == '_evaluate':
return evaluateplanarPotentials
elif attribute == '_Rforce':
return evaluateplanarRforces
elif attribute == '_phiforce':
return evaluateplanarphiforces
elif attribute == '_R2deriv':
return evaluateplanarR2derivs
elif attribute == '_phi2deriv':
return lambda p,R,phi=0.,t=0.: \
evaluateplanarPotentials(p,R,phi=phi,t=t,dphi=2)
elif attribute == '_Rphideriv':
return lambda p,R,phi=0.,t=0.: \
evaluateplanarPotentials(p,R,phi=phi,t=t,dR=1,dphi=1)
else: #pragma: no cover
raise AttributeError("Attribute %s not found in for this WrapperPotential" % attribute)
def _wrap_pot_func(self, attribute):
if attribute == '_evaluate':
return evaluateplanarPotentials
elif attribute == '_Rforce':
return evaluateplanarRforces
elif attribute == '_phiforce':
return evaluateplanarphiforces
elif attribute == '_R2deriv':
return evaluateplanarR2derivs
elif attribute == '_phi2deriv':
return lambda p,R,phi=0.,t=0.: \
evaluateplanarPotentials(p,R,phi=phi,t=t,dphi=2)
elif attribute == '_Rphideriv':
return lambda p,R,phi=0.,t=0.: \
evaluateplanarPotentials(p,R,phi=phi,t=t,dR=1,dphi=1)
else: #pragma: no cover
raise AttributeError(
"Attribute %s not found in for this WrapperPotential" %
attribute)
def potentialAxi(R,pot,vc=1.,ro=1.):
"""
NAME:
potentialAxi
PURPOSE:
return the potential
INPUT:
R - Galactocentric radius (/ro)
pot - potential
vc - circular velocity
ro - reference radius
OUTPUT:
Phi(R)
HISTORY:
2010-11-30 - Written - Bovy (NYU)
"""
return evaluateplanarPotentials(R,pot)
def potentialAxi(R,pot,vc=1.,ro=1.):
"""
NAME:
potentialAxi
PURPOSE:
return the potential
INPUT:
R - Galactocentric radius (/ro)
pot - potential
vc - circular velocity
ro - reference radius
OUTPUT:
Phi(R)
HISTORY:
2010-11-30 - Written - Bovy (NYU)
"""
return evaluateplanarPotentials(R,pot)
def plotE(self, *args, **kwargs):
"""
NAME:
plotE
PURPOSE:
plot E(.) along the orbit
INPUT:
pot - Potential instance or list of instances in which the orbit was
integrated
d1= - plot Ez vs d1: e.g., 't', 'R', 'vR', 'vT', 'phi'
+bovy_plot.bovy_plot inputs
OUTPUT:
figure to output device
HISTORY:
2010-07-10 - Written - Bovy (NYU)
"""
labeldict = {
't': r'$t$',
'R': r'$R$',
'vR': r'$v_R$',
'vT': r'$v_T$',
'z': r'$z$',
'vz': r'$v_z$',
'phi': r'$\phi$',
'x': r'$x$',
'y': r'$y$',
'vx': r'$v_x$',
'vy': r'$v_y$'
}
if not kwargs.has_key('pot'):
try:
pot = self._pot
except AttributeError:
raise AttributeError("Integrate orbit first or specify pot=")
else:
pot = kwargs['pot']
kwargs.pop('pot')
if kwargs.has_key('d1'):
d1 = kwargs['d1']
kwargs.pop('d1')
else:
d1 = 't'
self.Es = [
evaluateplanarPotentials(
self.orbit[ii, 0], pot, phi=self.orbit[ii, 3]) +
self.orbit[ii, 1]**2. / 2. + self.orbit[ii, 2]**2. / 2.
for ii in range(len(self.t))
]
if not kwargs.has_key('xlabel'):
kwargs['xlabel'] = labeldict[d1]
if not kwargs.has_key('ylabel'):
kwargs['ylabel'] = r'$E$'
if d1 == 't':
plot.bovy_plot(nu.array(self.t),
nu.array(self.Es) / self.Es[0], *args, **kwargs)
elif d1 == 'R':
plot.bovy_plot(self.orbit[:, 0],
nu.array(self.Es) / self.Es[0], *args, **kwargs)
elif d1 == 'vR':
plot.bovy_plot(self.orbit[:, 1],
nu.array(self.Es) / self.Es[0], *args, **kwargs)
elif d1 == 'vT':
plot.bovy_plot(self.orbit[:, 2],
nu.array(self.Es) / self.Es[0], *args, **kwargs)
elif d1 == 'phi':
plot.bovy_plot(self.orbit[:, 3],
nu.array(self.Es) / self.Es[0], *args, **kwargs)