def test_rphi_to_dl_2d():
#This is a tangent point
r,phi= 6., numpy.arccos(0.75)
d,l= bovy_coords.rphi_to_dl_2d(r,phi,degree=False,ro=8.,phio=0.)
l= numpy.arcsin(0.75)
d= 6./numpy.tan(l)
assert numpy.fabs(d-6./numpy.tan(numpy.arcsin(0.75))) < 10.**-10., 'dl_to_rphi_2d conversion did not work as expected'
assert numpy.fabs(l-numpy.arcsin(0.75)) < 10.**-10., 'rphi_to_dl_2d conversion did not work as expected'
#This is another point
r,phi= 2., 55.
d,l= bovy_coords.rphi_to_dl_2d(r,phi,degree=True,ro=2.*numpy.sqrt(2.),
phio=10.)
assert numpy.fabs(d-2.) < 10.**-10., 'rphi_to_dl_2d conversion did not work as expected'
assert numpy.fabs(l-45.) < 10.**-10., 'rphi_to_dl_2d conversion did not work as expected'
#This is another point, for arrays
r,phi= 2., 45.
os= numpy.ones(2)
d,l= bovy_coords.rphi_to_dl_2d(os*r,os*phi,
degree=True,ro=2.*numpy.sqrt(2.),
phio=0.)
assert numpy.all(numpy.fabs(d-2.) < 10.**-10.), 'rphi_to_dl_2d conversion did not work as expected'
assert numpy.all(numpy.fabs(l-45.) < 10.**-10.), 'rphi_to_dl_2d conversion did not work as expected'
#This is another point, for lists, which for some reason I support
r,phi= 2., 45.
d,l= bovy_coords.rphi_to_dl_2d([r,r],[phi,phi],
degree=True,ro=2.*numpy.sqrt(2.),
phio=0.)
d= numpy.array(d)
l= numpy.array(l)
assert numpy.all(numpy.fabs(d-2.) < 10.**-10.), 'rphi_to_dl_2d conversion did not work as expected'
assert numpy.all(numpy.fabs(l-45.) < 10.**-10.), 'rphi_to_dl_2d conversion did not work as expected'
return None
def simulate_vlos_spiral(alpha=-7.,m=2.,gamma=0.7853981633974483,omegas=0.65,
xmin=None,xmax=None,ymin=None,ymax=None,
dx=None,returnvrvt=False):
"""Perform a simple simulation of the effect of spiral structure on the velocity field; use the WKB approximation; if returnvrvt == True, return (vr,vt), otherwise return vlos"""
#Set up galpy spiral
sp= SteadyLogSpiralPotential(alpha=alpha,m=m,gamma=gamma,omegas=omegas)
#Now evaluate on the grid
nx= int(numpy.ceil((xmax-xmin)/dx))
ny= int(numpy.ceil((ymax-ymin)/dx))
xs= numpy.arange(xmin+dx/2.,xmax-dx/2.+0.000001,dx)
ys= numpy.arange(ymin+dx/2.,ymax-dx/2.+0.000001,dx)
xv,yv= numpy.meshgrid(xs,ys,indexing='ij')
rs= numpy.sqrt(xv**2.+yv**2.)/8.
phis= numpy.arctan2(yv,xv)
(d,l)= bovy_coords.rphi_to_dl_2d(rs,phis)
cospl= numpy.cos(phis+l)
sinpl= numpy.sin(phis+l)
vlos= numpy.empty((nx,ny))
vr= numpy.empty((nx,ny))
vt= numpy.empty((nx,ny))
Delta= 2.-m**2.*(omegas-1.)**2.
for ii in range(nx):
for jj in range(ny):
pot= sp(rs[ii,jj],phi=phis[ii,jj])
vr[ii,jj]= m*(omegas-1.)/Delta*rs[ii,jj]*alpha/1.\
*reduction_factor(alpha/1.)*pot
vt[ii,jj]= -2.*-0.5/Delta*rs[ii,jj]*alpha/1.\
*reduction_factor(alpha/1.)*pot
vlos[ii,jj]= -vr[ii,jj]*cospl[ii,jj]+vt[ii,jj]*sinpl[ii,jj]
if returnvrvt:
return (vr,vt)
else:
return vlos
def vlos_polar(savefile):
dvr,dvt= read_dmeanvrvt(savefile)
resx, resy= dvr.shape[0], dvr.shape[1]
#Project onto the line-of-sight
xgrid= numpy.linspace(0.,2.*numpy.pi*(1.-1./resy/2.),resx)
ygrid= numpy.linspace(0.5,2.,resy)
phis,rs= numpy.meshgrid(xgrid,ygrid,indexing='ij')
(d,l)= bovy_coords.rphi_to_dl_2d(rs,phis)
cospl= numpy.cos(phis+l)
sinpl= numpy.sin(phis+l)
vlos= -cospl*dvr+sinpl*dvt
return vlos[:,:]
def vlos_centraldiskrect(savefile):
dvr,dvt= read_dmeanvrvt(savefile)
resx, resy= dvr.shape[0], dvr.shape[1]
#Project onto the line-of-sight
xgrid= numpy.linspace(-16./8.+0.8/8./2.,
0./8.-0.8/8./2.,
resx)
ygrid= numpy.linspace(-8./8.+0.8/8./2.,
8./8.-0.8/8./2.,
resy)
xv,yv= numpy.meshgrid(xgrid,ygrid,indexing='ij')
rs= numpy.sqrt((1.+xv)**2.+yv**2.)
phis= numpy.arctan2(yv,1.+xv)
(d,l)= bovy_coords.rphi_to_dl_2d(rs,phis)
cospl= numpy.cos(phis+l)
sinpl= numpy.sin(phis+l)
vlos= -cospl*dvr+sinpl*dvt
return vlos[:,:]
def vlos_altrect(savefile):
dvr,dvt= read_dmeanvrvt(savefile)
resx, resy= dvr.shape[0], dvr.shape[1]
#Project onto the line-of-sight
from plot_psd import _RCXMIN, _RCXMAX, _RCYMIN, _RCYMAX, _RCDX
xgrid= numpy.linspace((_RCXMIN-2.25-8.)/8.+_RCDX/8./2.,
(_RCXMAX+2.25-8.)/8.-_RCDX/8./2.,
resx)
ygrid= numpy.linspace(_RCYMIN/8.-2.25/8.+_RCDX/8./2.,
_RCYMAX/8.+2.25/8.-_RCDX/8./2.,
resy)
xv,yv= numpy.meshgrid(xgrid,ygrid,indexing='ij')
rs= numpy.sqrt((1.+xv)**2.+yv**2.)
phis= numpy.arctan2(yv,1.+xv)
(d,l)= bovy_coords.rphi_to_dl_2d(rs,phis)
cospl= numpy.cos(phis+l)
sinpl= numpy.sin(phis+l)
vlos= -cospl*dvr+sinpl*dvt
return vlos[:,:]
def vlos_elliptical(res=19,cp=0.05,sp=0.,p=0.,beta=0.,xgrid=None,ygrid=None):
sr= 31.4
dvramp= 1./(1.-beta)*(1.+0.5*p)*(1.-8.*(sr/220.)**2.)
dvtamp= 1./(1.-beta)*(1.+0.25*p*(1.+beta))*(1.-2.5*(sr/220.)**2.)
#Project onto the line-of-sight
if xgrid is None:
from plot_psd import _RCXMIN, _RCXMAX, _RCYMIN, _RCYMAX, _RCDX
xgrid= numpy.linspace((_RCXMIN-8.)/8.+_RCDX/8./2.,
(_RCXMAX-8.)/8.-_RCDX/8./2.,
res)
ygrid= numpy.linspace(_RCYMIN/8.+_RCDX/8./2.,
_RCYMAX/8.-_RCDX/8./2.,
res)
xv,yv= numpy.meshgrid(xgrid,ygrid,indexing='ij')
rs= numpy.sqrt((1.+xv)**2.+yv**2.)
phis= numpy.arctan2(yv,1.+xv)
(d,l)= bovy_coords.rphi_to_dl_2d(rs,phis)
cospl= numpy.cos(phis+l)
sinpl= numpy.sin(phis+l)
dvr= -dvramp*(numpy.sin(2.*phis)*cp-numpy.cos(2.*phis)*sp)
dvt= -dvtamp*(numpy.cos(2.*phis)*cp+numpy.sin(2.*phis)*sp)
vlos= (-cospl*dvr+sinpl*dvt)*rs**(p-2.*beta)
return vlos
def plot_rckinematics(plotfilename,subsun=False):
#Set up 3 axes
bovy_plot.bovy_print(fig_width=8.,axes_labelsize=14)
axdx= 1./3.
#APOGEE-RC observations
tdy= (_RCYMAX-_RCYMIN+4.5)/(_RCXMAX-_RCXMIN+4.5)*axdx
obsAxes= pyplot.axes([0.1,(1.-tdy)/2.,axdx,tdy])
pyplot.sca(obsAxes)
data= apread.rcsample()
if _ADDLLOGGCUT:
data= data[data['ADDL_LOGG_CUT'] == 1]
#Cut
indx= (numpy.fabs(data['RC_GALZ']) < 0.25)*(data['METALS'] > -1000.)
data= data[indx]
#Get velocity field
pixrc= pixelize_sample.pixelXY(data,
xmin=_RCXMIN-2.25,xmax=_RCXMAX+2.25,
ymin=_RCYMIN-2.25,ymax=_RCYMAX+2.25,
dx=_RCDX,dy=_RCDX)
if subsun:
vmin, vmax= 0., 250.
pixrc.plot(lambda x: vlosgal(x),
func=lambda x: numpy.fabs(numpy.median(x)),
zlabel=r'$|\mathrm{median}\ V^{\mathrm{GC}}_{\mathrm{los}}|\,(\mathrm{km\,s}^{-1})$',
vmin=vmin,vmax=vmax)
else:
vmin, vmax= -75., 75.
img= pixrc.plot('VHELIO_AVG',
vmin=vmin,vmax=vmax,overplot=True,
colorbar=False)
resv= pixrc.plot('VHELIO_AVG',
justcalc=True,returnz=True) #for later
bovy_plot.bovy_text(r'$\mathrm{typical\ uncertainty\!:}\ 3\,\mathrm{km\,s}^{-1}$',
bottom_left=True,size=8.25)
bovy_plot.bovy_text(r'$|Z| < 250\,\mathrm{pc}$',top_right=True,size=10.)
pyplot.annotate(r'$\mathrm{APOGEE\!-\!RC\ data}$',
(0.5,1.09),xycoords='axes fraction',
horizontalalignment='center',
verticalalignment='top',size=10.)
pyplot.axis([pixrc.xmin,pixrc.xmax,pixrc.ymin,pixrc.ymax])
bovy_plot._add_ticks()
bovy_plot._add_axislabels(r'$X_{\mathrm{GC}}\,(\mathrm{kpc})$',
r'$Y_{\mathrm{GC}}\,(\mathrm{kpc})$')
#Colorbar
cbaxes = pyplot.axes([0.1625,(1.-tdy)/2.+tdy+0.065,2.*axdx-0.195,0.02])
CB1= pyplot.colorbar(img,orientation='horizontal',
cax=cbaxes)#,ticks=[-16.,-8.,0.,8.,16.])
CB1.set_label(r'$\mathrm{median}\ V_{\mathrm{los}}\,(\mathrm{km\,s}^{-1})$',labelpad=-35,fontsize=14.)
#Now calculate the expected field
xgrid= numpy.arange(_RCXMIN-2.25+_RCDX/2.,_RCXMAX+2.25+_RCDX/2.,_RCDX)
ygrid= numpy.arange(_RCYMIN-2.25+_RCDX/2.,_RCYMAX+2.25+_RCDX/2.,_RCDX)
xv,yv= numpy.meshgrid(xgrid,ygrid,indexing='ij')
rs= numpy.sqrt(xv**2.+yv**2.)
phis= numpy.arctan2(yv,xv)
d,l= bovy_coords.rphi_to_dl_2d(rs/8.,phis)
expec_vlos= numpy.empty((len(xgrid),len(ygrid)))
for ii in range(len(xgrid)):
for jj in range(len(ygrid)):
expec_vlos[ii,jj]= modelvlosgal(rs[ii,jj],phis[ii,jj],l[ii,jj],
vc=218.,vtsun=242.)
modelAxes= pyplot.axes([0.03+axdx,(1.-tdy)/2.,axdx,tdy])
pyplot.sca(modelAxes)
xlabel=r'$X_{\mathrm{GC}}\,(\mathrm{kpc})$'
ylabel=r'$Y_{\mathrm{GC}}\,(\mathrm{kpc})$'
indx= True-numpy.isnan(resv)
plotthis= copy.copy(expec_vlos)
plotthis[numpy.isnan(resv)]= numpy.nan #turn these off
bovy_plot.bovy_dens2d(plotthis.T,origin='lower',cmap='jet',
interpolation='nearest',
xlabel=xlabel,ylabel=ylabel,
xrange=[_RCXMIN-2.25,_RCXMAX+2.25],
yrange=[_RCYMIN-2.25,_RCYMAX+2.25],
contours=False,
vmin=vmin,vmax=vmax,overplot=True,zorder=3)
if True:
#Now plot the pixels outside the APOGEE data set
plotthis= copy.copy(expec_vlos)
plotthis[True-numpy.isnan(resv)]= numpy.nan #turn these off
bovy_plot.bovy_dens2d(plotthis.T,origin='lower',cmap='jet',
interpolation='nearest',
alpha=0.3,
xrange=[_RCXMIN-2.25,_RCXMAX+2.25],
yrange=[_RCYMIN-2.25,_RCYMAX+2.25],
contours=False,
vmin=vmin,vmax=vmax,overplot=True,
zorder=0)
pyplot.annotate(r'$\mathrm{Bovy\ et.\ al\ (2012)\ model}$',
(1.02,1.09),xycoords='axes fraction',
horizontalalignment='center',
verticalalignment='top',size=10.,zorder=3)
pyplot.axis([_RCXMIN-2.25,_RCXMAX+2.25,_RCYMIN-2.25,_RCYMAX+2.25])
bovy_plot._add_ticks()
bovy_plot._add_axislabels(xlabel,r'$ $')
#Finally, add a polar plot of the whole disk
res= 51
rmin, rmax= 0.2, 2.4
xgrid= numpy.linspace(0.,2.*numpy.pi*(1.-1./res/2.),
2.*res)
ygrid= numpy.linspace(rmin,rmax,res)
nx= len(xgrid)
ny= len(ygrid)
savefile= 'expec_vlos.sav'
if os.path.exists(savefile):
savefile= open(savefile,'rb')
expec_vlos= pickle.load(savefile)
savefile.close()
else:
expec_vlos= numpy.zeros((nx,ny))
for ii in range(nx):
for jj in range(ny):
R, phi= ygrid[jj], xgrid[ii]
d,l= bovy_coords.rphi_to_dl_2d(R,phi)
expec_vlos[ii,jj]= modelvlosgal(R*8.,phi,l,
vc=218.,vtsun=242.)
save_pickles(savefile,expec_vlos)
plotxgrid= numpy.linspace(xgrid[0]-(xgrid[1]-xgrid[0])/2.,
xgrid[-1]+(xgrid[1]-xgrid[0])/2.,
len(xgrid)+1)
plotygrid= numpy.linspace(ygrid[0]-(ygrid[1]-ygrid[0])/2.,
ygrid[-1]+(ygrid[1]-ygrid[0])/2.,
len(ygrid)+1)
fullmodelAxes= pyplot.axes([-0.05+2.*axdx,(1.-tdy)/2.,axdx,tdy],polar=True)
ax= fullmodelAxes
pyplot.sca(fullmodelAxes)
vmin, vmax= -150., 150.
zlabel= r'$\mathrm{line\!-\!of\!-\!sight\ velocity}\ (\mathrm{km\,s}^{-1})$'
out= ax.pcolor(plotxgrid,plotygrid,expec_vlos.T,cmap='jet',
vmin=vmin,vmax=vmax,clip_on=False)
shrink= 0.8
if False:
CB1= pyplot.colorbar(out,shrink=shrink)
bbox = CB1.ax.get_position().get_points()
CB1.ax.set_position(transforms.Bbox.from_extents(bbox[0,0]+0.025,
bbox[0,1],
bbox[1,0],
bbox[1,1]))
CB1.set_label(zlabel)
from matplotlib.patches import FancyArrowPatch
arr= FancyArrowPatch(posA=(numpy.pi+0.1,1.8),
posB=(3*numpy.pi/2.+0.1,1.8),
arrowstyle='->',
connectionstyle='arc3,rad=%4.2f' % (numpy.pi/8.-0.05),
shrinkA=2.0, shrinkB=2.0, mutation_scale=20.0,
mutation_aspect=None,fc='k')
ax.add_patch(arr)
bovy_plot.bovy_text(numpy.pi+0.17,1.7,r'$\mathrm{Galactic\ rotation}$',
rotation=-30.,size=9.)
radii= numpy.array([0.5,1.,1.5,2.,2.5])
labels= []
for r in radii:
ax.plot(numpy.linspace(0.,2.*numpy.pi,501,),
numpy.zeros(501)+r,ls='-',color='0.65',zorder=1,lw=0.5)
labels.append(r'$%i$' % int(r*8.))
pyplot.rgrids(radii,labels=labels,angle=147.5)
thetaticks = numpy.arange(0,360,45)
# set ticklabels location at x times the axes' radius
ax.set_thetagrids(thetaticks,frac=1.16,backgroundcolor='w',zorder=3)
bovy_plot.bovy_text(3.*numpy.pi/4.+0.06,2.095,r'$\mathrm{kpc}$',size=10.)
pyplot.ylim(0.,2.8)
#Plot the box
xs= numpy.linspace(_RCXMIN-2.25,_RCXMAX+2.25,101)
ys= numpy.ones(101)*(_RCYMIN-2.25)
rs= numpy.sqrt(xs**2.+ys**2.)/8.
phis= numpy.arctan2(ys,xs)
ax.plot(phis,rs,'--',lw=1.25,color='k')
#Plot the box
xs= numpy.linspace(_RCXMIN-2.25,_RCXMAX+2.25,101)
ys= numpy.ones(101)*(_RCYMAX+2.25)
rs= numpy.sqrt(xs**2.+ys**2.)/8.
phis= numpy.arctan2(ys,xs)
ax.plot(phis,rs,'--',lw=1.25,color='k')
#Plot the box
ys= numpy.linspace(_RCYMIN-2.25,_RCYMAX+2.25,101)
xs= numpy.ones(101)*(_RCXMIN-2.25)
rs= numpy.sqrt(xs**2.+ys**2.)/8.
phis= numpy.arctan2(ys,xs)
ax.plot(phis,rs,'--',lw=1.25,color='k')
#Plot the box
ys= numpy.linspace(_RCYMIN-2.25,_RCYMAX+2.25,101)
xs= numpy.ones(101)*(_RCXMAX+2.25)
rs= numpy.sqrt(xs**2.+ys**2.)/8.
phis= numpy.arctan2(ys,xs)
ax.plot(phis,rs,'--',lw=1.25,color='k')
#Plot the connectors on the modelAxes
xlow=-4.*8.
ylow= 2.77*8.
xs= numpy.linspace(xlow,(_RCXMAX+2.25),101)
ys= (ylow-(_RCYMAX+2.25))/(xlow-(_RCXMAX+2.25))*(xs-xlow)+ylow
rs= numpy.sqrt(xs**2.+ys**2.)/8.
phis= numpy.arctan2(ys,xs)
line= ax.plot(phis,rs,':',lw=1.,color='k',zorder=2)
line[0].set_clip_on(False)
xlow=-4.*8.
ylow= -2.77*8.
xs= numpy.linspace(xlow,(_RCXMAX+2.25),101)
ys= (ylow-(_RCYMIN-2.25))/(xlow-(_RCXMAX+2.25))*(xs-xlow)+ylow
rs= numpy.sqrt(xs**2.+ys**2.)/8.
phis= numpy.arctan2(ys,xs)
line= ax.plot(phis,rs,':',lw=1.,color='k',zorder=2)
line[0].set_clip_on(False)
#Colorbar
cbaxes = pyplot.axes([0.01+2.*axdx,(1.-tdy)/2.+tdy+0.065,axdx-0.125,0.02])
CB1= pyplot.colorbar(out,orientation='horizontal',
cax=cbaxes,ticks=[-150.,-75.,0.,75.,150.])
#CB1.set_label(r'$\mathrm{median}\ V_{\mathrm{los}}\,(\mathrm{km\,s}^{-1})$',labelpad=-35,fontsize=14.)
bovy_plot.bovy_end_print(plotfilename,dpi=300)
return None