def test_elliptical_cold_vt():
# Test that the rotational velocity for the elliptical disk behaves as analytically expected
idf = dehnendf(beta=0., profileParams=(1. / 3., 1., 0.0125))
cp = 0.05
pot = [
LogarithmicHaloPotential(normalize=1.),
EllipticalDiskPotential(cp=cp, sp=0., p=0., tform=-150., tsteady=125.)
]
edf = evolveddiskdf(idf, pot=pot, to=-150.)
#Should be 1.
mvt, grid = edf.meanvT(0.9,
phi=-numpy.pi / 4.,
integrate_method='rk6_c',
grid=True,
returnGrid=True,
gridpoints=_GRIDPOINTS)
assert numpy.fabs(
mvt - 1.
) < 10.**-3., 'Cold elliptical disk does not agree with analytical calculation for vt'
#Should be 1.-cp
mvt, grid = edf.meanvT(0.9,
phi=0.,
integrate_method='rk6_c',
grid=True,
nsigma=7.,
returnGrid=True,
gridpoints=_GRIDPOINTS)
assert numpy.fabs(
mvt - 1. + cp
) < 10.**-3., 'Cold elliptical disk does not agree with analytical calculation for vt'
return None
def test_elliptical_cold_vertexdev():
# Test that the vertex deviations for the elliptical disk behaves as analytically expected
idf = dehnendf(beta=0., profileParams=(1. / 3., 1., 0.0125))
cp = 0.05
pot = [
LogarithmicHaloPotential(normalize=1.),
EllipticalDiskPotential(cp=cp, sp=0., p=0., tform=-150., tsteady=125.)
]
edf = evolveddiskdf(idf, pot=pot, to=-150.)
#Should be -2cp in radians
vdev, grid = edf.vertexdev(0.9,
phi=-numpy.pi / 4.,
integrate_method='rk6_c',
grid=True,
nsigma=7.,
returnGrid=True,
gridpoints=_GRIDPOINTS)
assert numpy.fabs(
vdev + 2. * cp
) < 10.**-3., 'Cold elliptical disk does not agree with analytical calculation for vertexdev'
#Should be 0
vdev, grid = edf.vertexdev(0.9,
phi=0.,
integrate_method='rk6_c',
grid=True,
nsigma=7.,
returnGrid=True,
gridpoints=_GRIDPOINTS)
assert numpy.fabs(
vdev
) < 10.**-2. / 180. * numpy.pi, 'Cold elliptical disk does not agree with analytical calculation for vertexdev'
return None
def test_mildnonaxi_oortA_grid_tlist():
# Test that for a close to axisymmetric potential, the oortA is close to the value of the initial DF
idf = dehnendf(beta=0.)
pot = [
LogarithmicHaloPotential(normalize=1.),
EllipticalDiskPotential(twophio=0.001)
] #very mild non-axi
edf = evolveddiskdf(idf, pot=pot, to=-10.)
oa, grid, dgridR, dgridphi=\
edf.oortA(0.9,t=[0.,-2.5,-5.,-7.5,-10.],
phi=0.2,integrate_method='rk6_c',
grid=True,derivRGrid=True,derivphiGrid=True,
returnGrids=True,
gridpoints=_GRIDPOINTS,derivGridpoints=_GRIDPOINTS)
ioa = idf.oortA(0.9)
assert numpy.all(
numpy.fabs(oa - ioa) < 0.005
), 'oortA of evolveddiskdf for axisymmetric potential is not equal to that of initial DF'
oa = edf.oortA(0.9,
t=[0., -2.5, -5., -7.5, -10.],
phi=0.2,
integrate_method='rk6_c',
grid=grid,
derivRGrid=dgridR,
derivphiGrid=dgridphi,
gridpoints=_GRIDPOINTS,
derivGridpoints=_GRIDPOINTS)
assert numpy.all(
numpy.fabs(oa - ioa) < 0.005
), 'oortA of evolveddiskdf for axisymmetric potential is not equal to that of initial DF when calculated with pre-computed grid'
return None
def test_mildnonaxi_oortK_grid():
# Test that for a close to axisymmetric potential, the oortK is close to zero
idf = dehnendf(beta=0.)
pot = [
LogarithmicHaloPotential(normalize=1.),
EllipticalDiskPotential(twophio=0.001)
] #very mild non-axi
edf = evolveddiskdf(idf, pot=pot, to=-10.)
ok, grid, dgridR, dgridphi=\
edf.oortK(0.9,phi=0.2,integrate_method='rk6_c',
grid=True,derivRGrid=True,derivphiGrid=True,
returnGrids=True,
gridpoints=_GRIDPOINTS,derivGridpoints=_GRIDPOINTS)
assert numpy.fabs(
ok
) < 0.005, 'oortK of evolveddiskdf for axisymmetric potential is not equal to that of initial DF'
ok = edf.oortK(0.9,
phi=0.2,
integrate_method='rk6_c',
grid=grid,
derivRGrid=dgridR,
derivphiGrid=dgridphi,
gridpoints=_GRIDPOINTS,
derivGridpoints=_GRIDPOINTS)
assert numpy.fabs(
ok
) < 0.005, 'oortK of evolveddiskdf for axisymmetric potential is not equal to that of initial DF when calculated with pre-computed grid'
return None
def test_call_marginalizevlos():
from galpy.orbit import Orbit
idf = dehnendf(beta=0.)
pot = [
LogarithmicHaloPotential(normalize=1.),
EllipticalDiskPotential(twophio=0.001)
] #very mild non-axi
edf = evolveddiskdf(idf, pot=pot[0], to=-10.) #one with just one potential
#l=0
R, phi, vT = 0.8, 0., 0.7
vrs = numpy.linspace(-1., 1., 101)
pvrs = numpy.array(
[edf(Orbit([R, vr, vT, phi]), integrate_method='rk6_c') for vr in vrs])
assert numpy.fabs(numpy.log(numpy.sum(pvrs)*(vrs[1]-vrs[0]))\
-edf(Orbit([R,0.,vT,phi]),marginalizeVlos=True,integrate_method='rk6_c',log=True)) < 10.**-4., 'diskdf call w/ marginalizeVlos does not work'
#l=270, this DF has some issues, but it suffices to test the mechanics of the code
edf = evolveddiskdf(idf, pot=pot, to=-10.)
R, phi, vR = numpy.sin(numpy.pi / 6.), -numpy.pi / 3., 0.4 #l=30 degree
vts = numpy.linspace(0.3, 1.5, 101)
pvts = numpy.array(
[edf(Orbit([R, vR, vt, phi]), integrate_method='rk6_c') for vt in vts])
assert numpy.fabs(numpy.sum(pvts)*(vts[1]-vts[0])\
-edf(Orbit([R,vR,0.,phi]),
marginalizeVlos=True,
integrate_method='rk6_c',
nsigma=4)) < 10.**-3.5, 'diskdf call w/ marginalizeVlos does not work'
return None
def test_call_marginalizevperp():
from galpy.orbit import Orbit
idf = dehnendf(beta=0.)
pot = [
LogarithmicHaloPotential(normalize=1.),
EllipticalDiskPotential(twophio=0.001)
] #very mild non-axi
edf = evolveddiskdf(idf, pot=pot[0], to=-10.) #one with just one potential
#l=0
R, phi, vR = 0.8, 0., 0.4
vts = numpy.linspace(0., 1.5, 51)
pvts = numpy.array(
[edf(Orbit([R, vR, vt, phi]), integrate_method='rk6_c') for vt in vts])
assert numpy.fabs(numpy.sum(pvts)*(vts[1]-vts[0])\
-edf(Orbit([R,vR,0.,phi]),marginalizeVperp=True,integrate_method='rk6_c')) < 10.**-3.5, 'evolveddiskdf call w/ marginalizeVperp does not work'
#l=270
edf = evolveddiskdf(idf, pot=pot, to=-10.)
R, phi, vT = numpy.sin(numpy.pi / 6.), -numpy.pi / 3., 0.7 #l=30 degree
vrs = numpy.linspace(-1., 1., 101)
pvrs = numpy.array(
[edf(Orbit([R, vr, vT, phi]), integrate_method='rk6_c') for vr in vrs])
assert numpy.fabs(numpy.log(numpy.sum(pvrs)*(vrs[1]-vrs[0]))\
-edf(Orbit([R,0.,vT,phi]),
marginalizeVperp=True,
integrate_method='rk6_c',log=True,
nsigma=4)) < 10.**-2.5, 'evolveddiskdf call w/ marginalizeVperp does not work'
return None
def test_elliptical_cold_oortABCK_position2():
# Test that the Oort functions A, B, C, and K for the elliptical disk behaves as analytically expected
idf= dehnendf(beta=0.,profileParams=(1./3.,1.,0.0125))
cp= 0.05
pot= [LogarithmicHaloPotential(normalize=1.),
EllipticalDiskPotential(cp=cp,sp=0.,p=0.,tform=-150.,tsteady=125.)]
edf= evolveddiskdf(idf,pot=pot,to=-150.)
#Should be 0.5/0.9+cp/2
oorta, grid, gridr, gridp= edf.oortA(0.9,phi=0.,
integrate_method='rk6_c',grid=True,
nsigma=7.,
derivRGrid=True,derivphiGrid=True,
returnGrids=True,
gridpoints=51,
derivGridpoints=51)
assert numpy.fabs(oorta-cp/2.-0.5/0.9) < 10.**-2.2, 'Cold elliptical disk does not agree with analytical calculation for oortA'
#Should be -cp/2-0.5/0.9
oortb= edf.oortB(0.9,phi=0.,
integrate_method='rk6_c',grid=grid,nsigma=7.,
derivRGrid=gridr,derivphiGrid=gridp)
assert numpy.fabs(oortb+cp/2.+0.5/0.9) < 10.**-2.2, 'Cold elliptical disk does not agree with analytical calculation for oortB'
#Should be 0
oortc= edf.oortC(0.9,phi=0.,
integrate_method='rk6_c',grid=grid,nsigma=7.,
derivRGrid=gridr,derivphiGrid=gridp)
assert numpy.fabs(oortc) < 10.**-3., 'Cold elliptical disk does not agree with analytical calculation for oortC'
#Should be 0
oortk= edf.oortK(0.9,phi=0.,
integrate_method='rk6_c',grid=grid,nsigma=7.,
derivRGrid=gridr,derivphiGrid=gridp)
assert numpy.fabs(oortk) < 10.**-3., 'Cold elliptical disk does not agree with analytical calculation for oortK'
return None
def test_call_special():
from galpy.orbit import Orbit
idf= dehnendf(beta=0.)
pot= [LogarithmicHaloPotential(normalize=1.),
EllipticalDiskPotential(twophio=0.001)] #very mild non-axi
edf= evolveddiskdf(idf,pot=pot,to=-10.)
o= Orbit([0.9,0.1,1.1,2.])
#call w/ and w/o explicit t
assert numpy.fabs(numpy.log(edf(o,0.))-numpy.log(edf(o))) < 10.**-10., 'edf.__call__ w/ explicit t=0. and w/o t do not give the same answer'
#call must get Orbit, otherwise error
try: edf(0.9,0.1,1.1,2.)
except IOError: pass
else: raise AssertionError('edf.__call__ w/o Orbit input did not raise IOError')
#Call w/ list, but just to
assert numpy.fabs(numpy.log(edf(o,[-10.]))-numpy.log(idf(o))) < 10.**-10., 'edf.__call__ w/ tlist set to [to] did not return initial DF'
#Call w/ just to
assert numpy.fabs(numpy.log(edf(o,-10.))-numpy.log(idf(o))) < 10.**-10., 'edf.__call__ w/ tlist set to [to] did not return initial DF'
#also w/ log
assert numpy.fabs(edf(o,[-10.],log=True)-numpy.log(idf(o))) < 10.**-10., 'edf.__call__ w/ tlist set to [to] did not return initial DF (log)'
assert numpy.fabs(edf(o,-10.,log=True)-numpy.log(idf(o))) < 10.**-10., 'edf.__call__ w/ tlist set to [to] did not return initial DF (log)'
# Tests w/ odeint: tlist
codeint= edf(o,[0.,-2.5,-5.,-7.5,-10.],integrate_method='odeint',log=True)
crk6c= edf(o,[0.,-2.5,-5.,-7.5,-10.],integrate_method='rk6_c',log=True)
assert numpy.all(numpy.fabs(codeint-crk6c) < 10.**-4.), 'edf.__call__ w/ odeint and tlist does not give the same result as w/ rk6_c'
# Crazy orbit w/ tlist
crk6c= edf(Orbit([3.,1.,-1.,2.]),[0.],integrate_method='odeint',log=True)
assert crk6c < -20., 'crazy orbit does not have DF equal to zero'
# deriv w/ odeint
codeint= edf(o,[0.,-2.5,-5.,-7.5,-10.],integrate_method='odeint',
deriv='R')
crk6c= edf(o,[0.,-2.5,-5.,-7.5,-10.],integrate_method='rk6_c',deriv='R')
assert numpy.all(numpy.fabs(codeint-crk6c) < 10.**-4.), 'edf.__call__ w/ odeint and tlist does not give the same result as w/ rk6_c (deriv=R)'
# deriv w/ len(tlist)=1
crk6c= edf(o,[0.],integrate_method='rk6_c',deriv='R')
crk6c2= edf(o,0.,integrate_method='rk6_c',deriv='R')
assert numpy.all(numpy.fabs(crk6c-crk6c2) < 10.**-4.), 'edf.__call__ w/ tlist consisting of one time and just a scalar time do not agree'
#Call w/ just to and deriv
assert numpy.fabs(edf(o,-10.,deriv='R')-idf(o)*idf._dlnfdR(o._orb.vxvv[0],o._orb.vxvv[1],o._orb.vxvv[2])) < 10.**-10., 'edf.__call__ w/ to did not return initial DF (deriv=R)'
assert numpy.fabs(edf(o,-10.,deriv='phi')) < 10.**-10., 'edf.__call__ w/ to did not return initial DF (deriv=phi)'
# Call w/ just one t and odeint
codeint= edf(o,0,integrate_method='odeint',log=True)
crk6c= edf(o,0.,integrate_method='rk6_c',log=True)
assert numpy.fabs(codeint-crk6c) < 10.**-4., 'edf.__call__ w/ odeint and tlist does not give the same result as w/ rk6_c'
# Call w/ just one t and fallback to odeint
# turn off C
edf._pot[0].hasC= False
edf._pot[0].hasC_dxdv= False
codeint= edf(o,0,integrate_method='dopr54_c',log=True)
assert numpy.fabs(codeint-crk6c) < 10.**-4., 'edf.__call__ w/ odeint and tlist does not give the same result as w/ rk6_c'
# Call w/ just one t and fallback to leaprog
cleapfrog= edf(o,0,integrate_method='leapfrog_c',log=True)
assert numpy.fabs(cleapfrog-crk6c) < 10.**-4., 'edf.__call__ w/ odeint and tlist does not give the same result as w/ rk6_c'
def plot_vpecvo(filename, plotfilename):
if not os.path.exists(filename):
raise IOError("given filename does not exist")
savefile = open(filename, 'rb')
params = pickle.load(savefile)
savefile.close()
vos = numpy.array([s[0] for s in params]) * _REFV0
ros = numpy.array([s[1] for s in params]) * _REFR0
if _ROTCURVE == 'flat':
vpec = numpy.array([s[7] for s in params
]) * _PMSGRA * ros - vos #7 w/ dwarf
vpecR = numpy.array([s[6] for s in params]) * _VRSUN #6 w/ dwarf
elif _ROTCURVE == 'powerlaw' or _ROTCURVE == 'linear':
vpec = numpy.array([s[8] for s in params
]) * _PMSGRA * ros - vos #7 w/ dwarf
vpecR = numpy.array([s[7] for s in params]) * _VRSUN #6 w/ dwarf
bovy_plot.bovy_print()
levels = list(special.erf(0.5 * numpy.arange(1, 4)))
levels.append(1.01) #HACK to not plot outliers
axScatter, axHistx, axHisty = bovy_plot.scatterplot(
vpecR, #vos/ros+vpec/ros,
vpec,
'k,',
levels=levels,
xlabel=r'$V_{R,\odot}\ [\mathrm{km\ s}^{-1}]$',
ylabel=r'$V_{\phi,\odot}-V_c\ [\mathrm{km\ s}^{-1}]$',
bins=31,
xrange=[-15., 0.],
yrange=[0., 35.],
contours=True,
cntrcolors='k',
onedhists=True,
cmap='gist_yarg',
retAxes=True)
#SBD10 value
bovy_plot.bovy_plot([-20., 40.], [12.24, 12.24],
'--',
color='0.5',
overplot=True)
bovy_plot.bovy_text(-4., 12.7, r'$\mathrm{SBD10}$')
axHisty.plot([0., 100.], [12.24, 12.24], '--', color='0.5')
bovy_plot.bovy_plot([_VRSUN, _VRSUN], [-100., 100.],
'--',
color='0.5',
overplot=True)
bovy_plot.bovy_text(_VRSUN - .75, 7., r'$\mathrm{SBD10}$', rotation=90.)
axHistx.plot([_VRSUN, _VRSUN], [0., 100.], '--', color='0.5')
#Reid / Brunthaler
#bovy_plot.bovy_plot([_PMSGRA,_PMSGRA],[-10.,100.],
# '--',color='0.5',overplot=True)
#axHistx.plot([_PMSGRA,_PMSGRA],[0.,100.],'--',color='0.5')
#bovy_plot.bovy_text(29.4,5.,r'$\mathrm{RB04}$')
#Inset, closed orbit at the Sun
lp = LogarithmicHaloPotential(normalize=1.)
ep = EllipticalDiskPotential(phib=numpy.pi / 2.,
p=0.,
tform=-100.,
tsteady=-100.,
twophio=14. / 220.) #0.072725)
o = Orbit([1., 0., 1. + 14. / 220., 0.])
oc = Orbit([1., 0., 1., 0.])
ts = numpy.linspace(0., 4. * numpy.pi, 1001)
o.integrate(ts, [lp, ep])
print o.e(analytic=True, pot=lp)
oc.integrate(ts, lp)
left, bottom, width, height = 0.45, 0.45, 0.25, 0.25
axInset = pyplot.axes([left, bottom, width, height])
pyplot.sca(axInset)
pyplot.plot(o._orb.orbit[:, 0] * numpy.cos(o._orb.orbit[:, 3]),
o._orb.orbit[:, 0] * numpy.sin(o._orb.orbit[:, 3]), 'k-')
pyplot.plot(oc._orb.orbit[:, 0] * numpy.cos(oc._orb.orbit[:, 3]),
oc._orb.orbit[:, 0] * numpy.sin(oc._orb.orbit[:, 3]),
'--',
color='0.6')
pyplot.xlim(-1.5, 1.5)
pyplot.ylim(-1.5, 1.5)
#pyplot.xlabel(r'$x / R_0$')
#pyplot.ylabel(r'$y / R_0$')
nullfmt = NullFormatter() # no labels
axInset.xaxis.set_major_formatter(nullfmt)
axInset.yaxis.set_major_formatter(nullfmt)
bovy_plot.bovy_end_print(plotfilename)