def plotlinearPotentials(Pot,
t=0.,
min=-15.,
max=15,
ns=21,
savefilename=None):
"""
NAME:
plotlinearPotentials
PURPOSE:
plot a combination of potentials
INPUT:
t - time to evaluate potential at
min - minimum x
max - maximum x
ns - grid in x
savefilename - save to or restore from this savefile (pickle)
OUTPUT:
plot to output device
HISTORY:
2010-07-13 - Written - Bovy (NYU)
"""
Pot = flatten(Pot)
if not savefilename == None and os.path.exists(savefilename):
print("Restoring savefile " + savefilename + " ...")
savefile = open(savefilename, 'rb')
potx = pickle.load(savefile)
xs = pickle.load(savefile)
savefile.close()
else:
xs = nu.linspace(min, max, ns)
potx = nu.zeros(ns)
for ii in range(ns):
potx[ii] = evaluatelinearPotentials(Pot, xs[ii], t=t)
if not savefilename == None:
print("Writing savefile " + savefilename + " ...")
savefile = open(savefilename, 'wb')
pickle.dump(potx, savefile)
pickle.dump(xs, savefile)
savefile.close()
return plot.bovy_plot(xs,
potx,
xlabel=r"$x/x_0$",
ylabel=r"$\Phi(x)$",
xrange=[min, max])
def LinShuReductionFactor(axiPot,R,sigmar,nonaxiPot=None,
k=None,m=None,OmegaP=None):
"""
NAME:
LinShuReductionFactor
PURPOSE:
Calculate the Lin & Shu (1966) reduction factor: the reduced linear response of a kinematically-warm stellar disk to a perturbation
INPUT:
axiPot - The background, axisymmetric potential
R - Cylindrical radius (can be Quantity)
sigmar - radial velocity dispersion of the population (can be Quantity)
Then either provide:
1) m= m in the perturbation's m x phi (number of arms for a spiral)
k= wavenumber (see Binney & Tremaine 2008)
OmegaP= pattern speed (can be Quantity)
2) nonaxiPot= a non-axisymmetric Potential instance (such as SteadyLogSpiralPotential) that has functions that return OmegaP, m, and wavenumber
OUTPUT:
reduction factor
HISTORY:
2014-08-23 - Written - Bovy (IAS)
"""
axiPot= flatten(axiPot)
from galpy.potential import omegac, epifreq
if nonaxiPot is None and (OmegaP is None or k is None or m is None):
raise IOError("Need to specify either nonaxiPot= or m=, k=, OmegaP= for LinShuReductionFactor")
elif not nonaxiPot is None:
OmegaP= nonaxiPot.OmegaP()
k= nonaxiPot.wavenumber(R)
m= nonaxiPot.m()
tepif= epifreq(axiPot,R)
s= m*(OmegaP-omegac(axiPot,R))/tepif
chi= sigmar**2.*k**2./tepif**2.
return (1.-s**2.)/nu.sin(nu.pi*s)\
*integrate.quad(lambda t: nu.exp(-chi*(1.+nu.cos(t)))\
*nu.sin(s*t)*nu.sin(t),
0.,nu.pi)[0]
def LinShuReductionFactor(axiPot,R,sigmar,nonaxiPot=None,
k=None,m=None,OmegaP=None):
"""
NAME:
LinShuReductionFactor
PURPOSE:
Calculate the Lin & Shu (1966) reduction factor: the reduced linear response of a kinematically-warm stellar disk to a perturbation
INPUT:
axiPot - The background, axisymmetric potential
R - Cylindrical radius (can be Quantity)
sigmar - radial velocity dispersion of the population (can be Quantity)
Then either provide:
1) m= m in the perturbation's m x phi (number of arms for a spiral)
k= wavenumber (see Binney & Tremaine 2008)
OmegaP= pattern speed (can be Quantity)
2) nonaxiPot= a non-axisymmetric Potential instance (such as SteadyLogSpiralPotential) that has functions that return OmegaP, m, and wavenumber
OUTPUT:
reduction factor
HISTORY:
2014-08-23 - Written - Bovy (IAS)
"""
axiPot= flatten(axiPot)
from galpy.potential import omegac, epifreq
if nonaxiPot is None and (OmegaP is None or k is None or m is None):
raise IOError("Need to specify either nonaxiPot= or m=, k=, OmegaP= for LinShuReductionFactor")
elif not nonaxiPot is None:
OmegaP= nonaxiPot.OmegaP()
k= nonaxiPot.wavenumber(R)
m= nonaxiPot.m()
tepif= epifreq(axiPot,R)
s= m*(OmegaP-omegac(axiPot,R))/tepif
chi= sigmar**2.*k**2./tepif**2.
return (1.-s**2.)/nu.sin(nu.pi*s)\
*integrate.quad(lambda t: nu.exp(-chi*(1.+nu.cos(t)))\
*nu.sin(s*t)*nu.sin(t),
0.,nu.pi)[0]
def plotlinearPotentials(Pot,t=0.,min=-15.,max=15,ns=21,savefilename=None):
"""
NAME:
plotlinearPotentials
PURPOSE:
plot a combination of potentials
INPUT:
t - time to evaluate potential at
min - minimum x
max - maximum x
ns - grid in x
savefilename - save to or restore from this savefile (pickle)
OUTPUT:
plot to output device
HISTORY:
2010-07-13 - Written - Bovy (NYU)
"""
Pot= flatten(Pot)
if not savefilename == None and os.path.exists(savefilename):
print("Restoring savefile "+savefilename+" ...")
savefile= open(savefilename,'rb')
potx= pickle.load(savefile)
xs= pickle.load(savefile)
savefile.close()
else:
xs= nu.linspace(min,max,ns)
potx= nu.zeros(ns)
for ii in range(ns):
potx[ii]= evaluatelinearPotentials(Pot,xs[ii],t=t)
if not savefilename == None:
print("Writing savefile "+savefilename+" ...")
savefile= open(savefilename,'wb')
pickle.dump(potx,savefile)
pickle.dump(xs,savefile)
savefile.close()
return plot.bovy_plot(xs,potx,
xlabel=r"$x/x_0$",ylabel=r"$\Phi(x)$",
xrange=[min,max])
def toPlanarPotential(Pot):
"""
NAME:
toPlanarPotential
PURPOSE:
convert an Potential to a planarPotential in the mid-plane (z=0)
INPUT:
Pot - Potential instance or list of such instances (existing planarPotential instances are just copied to the output)
OUTPUT:
planarPotential instance(s)
HISTORY:
2016-06-11 - Written - Bovy (UofT)
"""
Pot= flatten(Pot)
if isinstance(Pot,list):
out= []
for pot in Pot:
if isinstance(pot,planarPotential):
out.append(pot)
elif pot.isNonAxi:
out.append(planarPotentialFromFullPotential(pot))
else:
out.append(planarPotentialFromRZPotential(pot))
return out
elif isinstance(Pot,Potential) and Pot.isNonAxi:
return planarPotentialFromFullPotential(Pot)
elif isinstance(Pot,Potential):
return planarPotentialFromRZPotential(Pot)
elif isinstance(Pot,planarPotential):
return Pot
else:
raise PotentialError("Input to 'toPlanarPotential' is neither an Potential-instance or a list of such instances")
def toPlanarPotential(Pot):
"""
NAME:
toPlanarPotential
PURPOSE:
convert an Potential to a planarPotential in the mid-plane (z=0)
INPUT:
Pot - Potential instance or list of such instances (existing planarPotential instances are just copied to the output)
OUTPUT:
planarPotential instance(s)
HISTORY:
2016-06-11 - Written - Bovy (UofT)
"""
Pot= flatten(Pot)
if isinstance(Pot,list):
out= []
for pot in Pot:
if isinstance(pot,planarPotential):
out.append(pot)
elif pot.isNonAxi:
out.append(planarPotentialFromFullPotential(pot))
else:
out.append(planarPotentialFromRZPotential(pot))
return out
elif isinstance(Pot,Potential) and Pot.isNonAxi:
return planarPotentialFromFullPotential(Pot)
elif isinstance(Pot,Potential):
return planarPotentialFromRZPotential(Pot)
elif isinstance(Pot,planarPotential):
return Pot
else:
raise PotentialError("Input to 'toPlanarPotential' is neither an Potential-instance or a list of such instances")
def RZToplanarPotential(RZPot):
"""
NAME:
RZToplanarPotential
PURPOSE:
convert an RZPotential to a planarPotential in the mid-plane (z=0)
INPUT:
RZPot - RZPotential instance or list of such instances (existing planarPotential instances are just copied to the output)
OUTPUT:
planarPotential instance(s)
HISTORY:
2010-07-13 - Written - Bovy (NYU)
"""
RZPot= flatten(RZPot)
if isinstance(RZPot,list):
out= []
for pot in RZPot:
if isinstance(pot,planarPotential):
out.append(pot)
else:
out.append(planarPotentialFromRZPotential(pot))
return out
elif isinstance(RZPot,Potential):
return planarPotentialFromRZPotential(RZPot)
elif isinstance(RZPot,planarPotential):
return RZPot
else:
raise PotentialError("Input to 'RZToplanarPotential' is neither an RZPotential-instance or a list of such instances")
def RZToplanarPotential(RZPot):
"""
NAME:
RZToplanarPotential
PURPOSE:
convert an RZPotential to a planarPotential in the mid-plane (z=0)
INPUT:
RZPot - RZPotential instance or list of such instances (existing planarPotential instances are just copied to the output)
OUTPUT:
planarPotential instance(s)
HISTORY:
2010-07-13 - Written - Bovy (NYU)
"""
RZPot= flatten(RZPot)
if isinstance(RZPot,list):
out= []
for pot in RZPot:
if isinstance(pot,planarPotential):
out.append(pot)
else:
out.append(planarPotentialFromRZPotential(pot))
return out
elif isinstance(RZPot,Potential):
return planarPotentialFromRZPotential(RZPot)
elif isinstance(RZPot,planarPotential):
return RZPot
else:
raise PotentialError("Input to 'RZToplanarPotential' is neither an RZPotential-instance or a list of such instances")
def plotplanarPotentials(Pot,*args,**kwargs):
"""
NAME:
plotplanarPotentials
PURPOSE:
plot a planar potential
INPUT:
Rrange - range (can be Quantity)
xrange, yrange - if relevant (can be Quantity)
grid, gridx, gridy - number of points to plot
savefilename - save to or restore from this savefile (pickle)
ncontours - number of contours to plot (if applicable)
+bovy_plot(*args,**kwargs) or bovy_dens2d(**kwargs)
OUTPUT:
plot to output device
HISTORY:
2010-07-13 - Written - Bovy (NYU)
"""
Pot= flatten(Pot)
Rrange= kwargs.pop('Rrange',[0.01,5.])
xrange= kwargs.pop('xrange',[-5.,5.])
yrange= kwargs.pop('yrange',[-5.,5.])
if _APY_LOADED:
if hasattr(Pot,'_ro'):
tro= Pot._ro
else:
tro= Pot[0]._ro
if isinstance(Rrange[0],units.Quantity):
Rrange[0]= Rrange[0].to(units.kpc).value/tro
if isinstance(Rrange[1],units.Quantity):
Rrange[1]= Rrange[1].to(units.kpc).value/tro
if isinstance(xrange[0],units.Quantity):
xrange[0]= xrange[0].to(units.kpc).value/tro
if isinstance(xrange[1],units.Quantity):
xrange[1]= xrange[1].to(units.kpc).value/tro
if isinstance(yrange[0],units.Quantity):
yrange[0]= yrange[0].to(units.kpc).value/tro
if isinstance(yrange[1],units.Quantity):
yrange[1]= yrange[1].to(units.kpc).value/tro
grid= kwargs.pop('grid',100)
gridx= kwargs.pop('gridx',100)
gridy= kwargs.pop('gridy',gridx)
savefilename= kwargs.pop('savefilename',None)
isList= isinstance(Pot,list)
nonAxi= ((isList and Pot[0].isNonAxi) or (not isList and Pot.isNonAxi))
if not savefilename is None and os.path.exists(savefilename):
print("Restoring savefile "+savefilename+" ...")
savefile= open(savefilename,'rb')
potR= pickle.load(savefile)
if nonAxi:
xs= pickle.load(savefile)
ys= pickle.load(savefile)
else:
Rs= pickle.load(savefile)
savefile.close()
else:
if nonAxi:
xs= nu.linspace(xrange[0],xrange[1],gridx)
ys= nu.linspace(yrange[0],yrange[1],gridy)
potR= nu.zeros((gridx,gridy))
for ii in range(gridx):
for jj in range(gridy):
thisR= nu.sqrt(xs[ii]**2.+ys[jj]**2.)
if xs[ii] >= 0.:
thisphi= nu.arcsin(ys[jj]/thisR)
else:
thisphi= -nu.arcsin(ys[jj]/thisR)+nu.pi
potR[ii,jj]= evaluateplanarPotentials(Pot,thisR,
phi=thisphi,
use_physical=False)
else:
Rs= nu.linspace(Rrange[0],Rrange[1],grid)
potR= nu.zeros(grid)
for ii in range(grid):
potR[ii]= evaluateplanarPotentials(Pot,Rs[ii],
use_physical=False)
if not savefilename is None:
print("Writing planar savefile "+savefilename+" ...")
savefile= open(savefilename,'wb')
pickle.dump(potR,savefile)
if nonAxi:
pickle.dump(xs,savefile)
pickle.dump(ys,savefile)
else:
pickle.dump(Rs,savefile)
savefile.close()
if nonAxi:
if not 'orogin' in kwargs:
kwargs['origin']= 'lower'
if not 'cmap' in kwargs:
kwargs['cmap']= 'gist_yarg'
if not 'contours' in kwargs:
kwargs['contours']= True
if not 'xlabel' in kwargs:
kwargs['xlabel']= r"$x / R_0$"
if not 'ylabel' in kwargs:
kwargs['ylabel']= "$y / R_0$"
if not 'aspect' in kwargs:
kwargs['aspect']= 1.
if not 'cntrls' in kwargs:
kwargs['cntrls']= '-'
ncontours= kwargs.pop('ncontours',10)
if not 'levels' in kwargs:
kwargs['levels']= nu.linspace(nu.nanmin(potR),nu.nanmax(potR),ncontours)
return plot.bovy_dens2d(potR.T,
xrange=xrange,
yrange=yrange,**kwargs)
else:
kwargs['xlabel']=r"$R/R_0$"
kwargs['ylabel']=r"$\Phi(R)$"
kwargs['xrange']=Rrange
return plot.bovy_plot(Rs,potR,*args,**kwargs)
def plotplanarPotentials(Pot,*args,**kwargs):
"""
NAME:
plotplanarPotentials
PURPOSE:
plot a planar potential
INPUT:
Rrange - range (can be Quantity)
xrange, yrange - if relevant (can be Quantity)
grid, gridx, gridy - number of points to plot
savefilename - save to or restore from this savefile (pickle)
ncontours - number of contours to plot (if applicable)
+bovy_plot(*args,**kwargs) or bovy_dens2d(**kwargs)
OUTPUT:
plot to output device
HISTORY:
2010-07-13 - Written - Bovy (NYU)
"""
Pot= flatten(Pot)
Rrange= kwargs.pop('Rrange',[0.01,5.])
xrange= kwargs.pop('xrange',[-5.,5.])
yrange= kwargs.pop('yrange',[-5.,5.])
if _APY_LOADED:
if hasattr(Pot,'_ro'):
tro= Pot._ro
else:
tro= Pot[0]._ro
if isinstance(Rrange[0],units.Quantity):
Rrange[0]= Rrange[0].to(units.kpc).value/tro
if isinstance(Rrange[1],units.Quantity):
Rrange[1]= Rrange[1].to(units.kpc).value/tro
if isinstance(xrange[0],units.Quantity):
xrange[0]= xrange[0].to(units.kpc).value/tro
if isinstance(xrange[1],units.Quantity):
xrange[1]= xrange[1].to(units.kpc).value/tro
if isinstance(yrange[0],units.Quantity):
yrange[0]= yrange[0].to(units.kpc).value/tro
if isinstance(yrange[1],units.Quantity):
yrange[1]= yrange[1].to(units.kpc).value/tro
grid= kwargs.pop('grid',100)
gridx= kwargs.pop('gridx',100)
gridy= kwargs.pop('gridy',gridx)
savefilename= kwargs.pop('savefilename',None)
isList= isinstance(Pot,list)
nonAxi= ((isList and Pot[0].isNonAxi) or (not isList and Pot.isNonAxi))
if not savefilename is None and os.path.exists(savefilename):
print("Restoring savefile "+savefilename+" ...")
savefile= open(savefilename,'rb')
potR= pickle.load(savefile)
if nonAxi:
xs= pickle.load(savefile)
ys= pickle.load(savefile)
else:
Rs= pickle.load(savefile)
savefile.close()
else:
if nonAxi:
xs= nu.linspace(xrange[0],xrange[1],gridx)
ys= nu.linspace(yrange[0],yrange[1],gridy)
potR= nu.zeros((gridx,gridy))
for ii in range(gridx):
for jj in range(gridy):
thisR= nu.sqrt(xs[ii]**2.+ys[jj]**2.)
if xs[ii] >= 0.:
thisphi= nu.arcsin(ys[jj]/thisR)
else:
thisphi= -nu.arcsin(ys[jj]/thisR)+nu.pi
potR[ii,jj]= evaluateplanarPotentials(Pot,thisR,
phi=thisphi,
use_physical=False)
else:
Rs= nu.linspace(Rrange[0],Rrange[1],grid)
potR= nu.zeros(grid)
for ii in range(grid):
potR[ii]= evaluateplanarPotentials(Pot,Rs[ii],
use_physical=False)
if not savefilename is None:
print("Writing planar savefile "+savefilename+" ...")
savefile= open(savefilename,'wb')
pickle.dump(potR,savefile)
if nonAxi:
pickle.dump(xs,savefile)
pickle.dump(ys,savefile)
else:
pickle.dump(Rs,savefile)
savefile.close()
if nonAxi:
if not 'orogin' in kwargs:
kwargs['origin']= 'lower'
if not 'cmap' in kwargs:
kwargs['cmap']= 'gist_yarg'
if not 'contours' in kwargs:
kwargs['contours']= True
if not 'xlabel' in kwargs:
kwargs['xlabel']= r"$x / R_0$"
if not 'ylabel' in kwargs:
kwargs['ylabel']= "$y / R_0$"
if not 'aspect' in kwargs:
kwargs['aspect']= 1.
if not 'cntrls' in kwargs:
kwargs['cntrls']= '-'
ncontours= kwargs.pop('ncontours',10)
if not 'levels' in kwargs:
kwargs['levels']= nu.linspace(nu.nanmin(potR),nu.nanmax(potR),ncontours)
return plot.bovy_dens2d(potR.T,
xrange=xrange,
yrange=yrange,**kwargs)
else:
kwargs['xlabel']=r"$R/R_0$"
kwargs['ylabel']=r"$\Phi(R)$"
kwargs['xrange']=Rrange
return plot.bovy_plot(Rs,potR,*args,**kwargs)