def uvw_unc(req_dict, opt_dict):
cov_radec = np.zeros((2, 2))
cov_radec[0, 0] = opt_dict['epmra']**2
cov_radec[1, 1] = opt_dict['epmdec']**2
covar_pmllbb = b_c.cov_pmrapmdec_to_pmllpmbb(cov_radec,
req_dict['ra'],
req_dict['dec'],
degree=True,
epoch=2000.0)
cov_vxvyvz = b_c.cov_dvrpmllbb_to_vxyz(req_dict['dist'],
opt_dict['edist'],
opt_dict['erv'],
req_dict['pml'],
req_dict['pmb'],
covar_pmllbb,
req_dict['l'],
req_dict['b'],
plx=False,
degree=True)
du = vx_e = m.sqrt(cov_vxvyvz[0, 0])
dv = vy_e = m.sqrt(cov_vxvyvz[1, 1])
dw = vz_e = m.sqrt(cov_vxvyvz[2, 2])
return du, dv, dw
def calc_covar_pmllpmbb(self):
covpmllbb = bcoords.cov_pmrapmdec_to_pmllpmbb(self.covar_pmradec,
self.get_col('RA'),
self.get_col('DEC'),
degree=self.degree,
epoch=2000.0)
self.covar_pmllpmbb = covpmllbb
def test_cov_pmradec_to_pmllbb():
# This is the NGP at 1950., for this the parallactic angle is 180
ra, dec= 192.25, 27.4
cov_pmrapmdec= numpy.array([[100.,100.],[100.,400.]])
cov_pmllpmbb= bovy_coords.cov_pmrapmdec_to_pmllpmbb(cov_pmrapmdec,
ra,dec,
degree=True,
epoch=1950.)
assert numpy.fabs(cov_pmllpmbb[0,0]-100.) < 10.**-10., 'cov_pmradec_to_pmllbb conversion did not work as expected'
assert numpy.fabs(cov_pmllpmbb[0,1]-100.) < 10.**-10., 'cov_pmradec_to_pmllbb conversion did not work as expected'
assert numpy.fabs(cov_pmllpmbb[1,0]-100.) < 10.**-10., 'cov_pmradec_to_pmllbb conversion did not work as expected'
assert numpy.fabs(cov_pmllpmbb[1,1]-400.) < 10.**-10., 'cov_pmradec_to_pmllbb conversion did not work as expected'
# This is a random position, check that the conversion makes sense
ra, dec= 132.25, -23.4
cov_pmrapmdec= numpy.array([[100.,100.],[100.,400.]])
cov_pmllpmbb= bovy_coords.cov_pmrapmdec_to_pmllpmbb(cov_pmrapmdec,
ra/180.*numpy.pi,
dec/180.*numpy.pi,
degree=False,
epoch=1950.)
assert numpy.fabs(numpy.linalg.det(cov_pmllpmbb)-numpy.linalg.det(cov_pmrapmdec)) < 10.**-10., 'cov_pmradec_to_pmllbb conversion did not work as expected'
assert numpy.fabs(numpy.trace(cov_pmllpmbb)-numpy.trace(cov_pmrapmdec)) < 10.**-10., 'cov_pmradec_to_pmllbb conversion did not work as expected'
# This is a random position, check that the conversion makes sense, arrays
ra, dec= 132.25, -23.4
icov_pmrapmdec= numpy.array([[100.,100.],[100.,400.]])
cov_pmrapmdec= numpy.empty((3,2,2))
for ii in range(3): cov_pmrapmdec[ii,:,:]= icov_pmrapmdec
os= numpy.ones(3)
cov_pmllpmbb= bovy_coords.cov_pmrapmdec_to_pmllpmbb(cov_pmrapmdec,
os*ra,
os*dec,
degree=True,
epoch=1950.)
for ii in range(3):
assert numpy.fabs(numpy.linalg.det(cov_pmllpmbb[ii,:,:])-numpy.linalg.det(cov_pmrapmdec[ii,:,:])) < 10.**-10., 'cov_pmradec_to_pmllbb conversion did not work as expected'
assert numpy.fabs(numpy.trace(cov_pmllpmbb[ii,:,:])-numpy.trace(cov_pmrapmdec[ii,:,:])) < 10.**-10., 'cov_pmradec_to_pmllbb conversion did not work as expected'
return None
def add_gaia_galactic_pm_errors(df):
"""Add errors in proper motions in galactic coordinates to a Gaia DR2 pandas DataFrame"""
off_diag = df['pmra_error'] * df['pmdec_error'] * df['pmra_pmdec_corr']
covpmrapmdec = np.array([[df['pmra_error']**2, off_diag],
[off_diag, df['pmdec_error']**2]])
try:
ra_deg = np.array(df['ra_gaia'] / u.deg)
dec_deg = np.array(df['dec_gaia'] / u.deg)
except KeyError:
ra_deg = np.array(df['ra'] / u.deg)
dec_deg = np.array(df['dec'] / u.deg)
cov = bovy_coords.cov_pmrapmdec_to_pmllpmbb(np.transpose(
covpmrapmdec, [2, 0, 1]),
ra_deg,
dec_deg,
degree=True)
df['pml_error'] = np.sqrt(cov[:, 0, 0])
df['pmb_error'] = np.sqrt(cov[:, 1, 1])
df['pml_pmb_corr'] = cov[:, 0, 1] / (np.sqrt(cov[:, 0, 0]) *
np.sqrt(cov[:, 1, 1]))
def obs_to_galcen(ra,
dec,
dist,
pmra,
pmdec,
rv,
pmra_err,
pmdec_err,
pmra_pmdec_corr,
dist_err,
rv_err,
return_cov=True,
verbose=True,
return_rphiz=True,
ro=8.,
vo=220.,
zo=0.025,
parallax=False):
vxvv = np.dstack([ra, dec, dist, pmra, pmdec, rv])[0]
ra, dec = vxvv[:, 0], vxvv[:, 1]
lb = bovy_coords.radec_to_lb(ra, dec, degree=True)
pmra, pmdec = vxvv[:, 3], vxvv[:, 4]
pmllpmbb = bovy_coords.pmrapmdec_to_pmllpmbb(pmra,
pmdec,
ra,
dec,
degree=True)
d, vlos = vxvv[:, 2], vxvv[:, 5]
if parallax:
d = 1. / d
rectgal = bovy_coords.sphergal_to_rectgal(lb[:, 0],
lb[:, 1],
d,
vlos,
pmllpmbb[:, 0],
pmllpmbb[:, 1],
degree=True)
vsolar = np.array([-10.1, 4.0, 6.7])
vsun = np.array([
0.,
1.,
0.,
]) + vsolar / vo
X = rectgal[:, 0] / ro
Y = rectgal[:, 1] / ro
Z = rectgal[:, 2] / ro
vx = rectgal[:, 3] / vo
vy = rectgal[:, 4] / vo
vz = rectgal[:, 5] / vo
XYZ = np.dstack([X, Y, Z])[0]
vxyz = np.dstack([vx, vy, vz])[0]
if return_rphiz:
Rpz = bovy_coords.XYZ_to_galcencyl(XYZ[:, 0],
XYZ[:, 1],
XYZ[:, 2],
Zsun=zo / ro)
vRvTvz = bovy_coords.vxvyvz_to_galcencyl(vxyz[:, 0],
vxyz[:, 1],
vxyz[:, 2],
Rpz[:, 0],
Rpz[:, 1],
Rpz[:, 2],
vsun=vsun,
Xsun=1.,
Zsun=zo / ro,
galcen=True)
if return_cov == True:
cov_pmradec = np.empty([len(pmra_err), 2, 2])
cov_pmradec[:, 0, 0] = pmra_err**2
cov_pmradec[:, 1, 1] = pmdec_err**2
cov_pmradec[:, 0, 1] = pmra_pmdec_corr * pmra_err * pmdec_err
cov_pmradec[:, 1, 0] = pmra_pmdec_corr * pmra_err * pmdec_err
if verbose:
print('propagating covariance in pmra pmdec -> pmll pmbb')
cov_pmllbb = bovy_coords.cov_pmrapmdec_to_pmllpmbb(cov_pmradec,
vxvv[:, 0],
vxvv[:, 1],
degree=True,
epoch='J2015')
if verbose:
print('propagating covariance in pmll pmbb -> vx vy vz')
cov_vxyz = bovy_coords.cov_dvrpmllbb_to_vxyz(vxvv[:, 2], dist_err,
rv_err, pmllpmbb[:, 0],
pmllpmbb[:,
1], cov_pmllbb,
lb[:, 0], lb[:, 1])
if not return_rphiz:
return XYZ, vxyz, cov_vxyz
if verbose:
print('propagating covariance in vx vy vz -> vR vT vz')
cov_galcencyl = bovy_coords.cov_vxyz_to_galcencyl(cov_vxyz,
Rpz[:, 1],
Xsun=1.,
Zsun=zo / ro)
return XYZ, vxyz, cov_vxyz, Rpz, vRvTvz, cov_galcencyl
if not return_rphiz:
return XYZ, vxyz
return XYZ, vxyz, Rpz, vRvTvz
def dat_to_galcen(
dat,
return_cov=True,
return_rphiz=True,
verbose=False,
ro=8.,
vo=220.,
zo=0.025,
keys=['ra', 'dec', 'BPG_meandist', 'pmra', 'pmdec', 'VHELIO_AVG'],
cov_keys=[
'pmra_error', 'pmdec_error', 'pmra_pmdec_corr', 'BPG_diststd',
'VERR'
],
parallax=False):
vxvv = np.dstack([dat[keys[i]] for i in range(len(keys))])[0]
ra, dec = vxvv[:, 0], vxvv[:, 1]
lb = bovy_coords.radec_to_lb(ra, dec, degree=True)
pmra, pmdec = vxvv[:, 3], vxvv[:, 4]
pmllpmbb = bovy_coords.pmrapmdec_to_pmllpmbb(pmra,
pmdec,
ra,
dec,
degree=True)
d, vlos = vxvv[:, 2], vxvv[:, 5]
if parallax:
d = 1. / d
rectgal = bovy_coords.sphergal_to_rectgal(lb[:, 0],
lb[:, 1],
d,
vlos,
pmllpmbb[:, 0],
pmllpmbb[:, 1],
degree=True)
vsolar = np.array([-11.1, 245.6,
7.25]) #use SBD10 vR and vZ and SGR proper motion vT
vsun = np.array([
0.,
0.,
0.,
]) + vsolar / vo
X = rectgal[:, 0] / ro
Y = rectgal[:, 1] / ro
Z = rectgal[:, 2] / ro
vx = rectgal[:, 3] / vo
vy = rectgal[:, 4] / vo
vz = rectgal[:, 5] / vo
XYZ = np.dstack([X, Y, Z])[0]
vxyz = np.dstack([vx, vy, vz])[0]
if return_rphiz:
Rpz = bovy_coords.XYZ_to_galcencyl(XYZ[:, 0],
XYZ[:, 1],
XYZ[:, 2],
Zsun=zo / ro)
vRvTvz = bovy_coords.vxvyvz_to_galcencyl(vxyz[:, 0],
vxyz[:, 1],
vxyz[:, 2],
Rpz[:, 0],
Rpz[:, 1],
Rpz[:, 2],
vsun=vsun,
Xsun=1.,
Zsun=zo / ro,
galcen=True)
if return_cov == True:
cov_pmradec = np.array([[[
dat[cov_keys[0]][i]**2,
dat[cov_keys[2]][i] * dat[cov_keys[0]][i] * dat[cov_keys[1]][i]
],
[
dat[cov_keys[2]][i] *
dat[cov_keys[0]][i] * dat[cov_keys[1]][i],
dat[cov_keys[1]][i]**2
]] for i in range(len(dat))])
if verbose:
print('propagating covariance in pmra pmdec -> pmll pmbb')
cov_pmllbb = bovy_coords.cov_pmrapmdec_to_pmllpmbb(cov_pmradec,
vxvv[:, 0],
vxvv[:, 1],
degree=True,
epoch='J2015')
if verbose:
print('propagating covariance in pmll pmbb -> vx vy vz')
cov_vxyz = bovy_coords.cov_dvrpmllbb_to_vxyz(vxvv[:,
2], dat[cov_keys[3]],
dat[cov_keys[4]],
pmllpmbb[:,
0], pmllpmbb[:,
1],
cov_pmllbb, lb[:,
0], lb[:,
1])
if not return_rphiz:
return XYZ, vxyz, cov_vxyz
if verbose:
print('propagating covariance in vx vy vz -> vR vT vz')
cov_galcencyl = bovy_coords.cov_vxyz_to_galcencyl(cov_vxyz,
Rpz[:, 1],
Xsun=1.,
Zsun=zo / ro)
return XYZ, vxyz, cov_vxyz, Rpz, vRvTvz, cov_galcencyl
if not return_rphiz:
return XYZ, vxyz
return XYZ, vxyz, Rpz, vRvTvz
def plot_distsystematic(options,args):
if options.sample.lower() == 'g':
if options.select.lower() == 'program':
raw= read_gdwarfs(_GDWARFFILE,logg=True,ebv=True,sn=options.snmin)
else:
raw= read_gdwarfs(logg=True,ebv=True,sn=options.snmin)
elif options.sample.lower() == 'k':
if options.select.lower() == 'program':
raw= read_kdwarfs(_KDWARFFILE,logg=True,ebv=True,sn=options.snmin)
else:
raw= read_kdwarfs(logg=True,ebv=True,sn=options.snmin)
if not options.bmin is None:
#Cut on |b|
raw= raw[(numpy.fabs(raw.b) > options.bmin)]
#Bin the data
binned= pixelAfeFeh(raw,dfeh=options.dfeh,dafe=options.dafe)
if options.tighten:
tightbinned= pixelAfeFeh(raw,dfeh=options.dfeh,dafe=options.dafe,
fehmin=-1.6,fehmax=0.5,afemin=-0.05,
afemax=0.55)
else:
tightbinned= binned
plotthis= numpy.zeros((tightbinned.npixfeh(),tightbinned.npixafe()))+numpy.nan
#Run through the bins
for ii in range(tightbinned.npixfeh()):
for jj in range(tightbinned.npixafe()):
data= binned(tightbinned.feh(ii),tightbinned.afe(jj))
if len(data) < options.minndata:
jj+= 1
if jj == len(binned.afeedges)-1:
jj= 0
ii+= 1
break
continue
#Create XYZ and R, vxvyvz, cov_vxvyvz
R= ((8.-data.xc)**2.+data.yc**2.)**0.5
#Confine to R-range?
if not options.rmin is None and not options.rmax is None:
dataindx= (R >= options.rmin)*\
(R < options.rmax)
data= data[dataindx]
R= R[dataindx]
XYZ= numpy.zeros((len(data),3))
XYZ[:,0]= data.xc
XYZ[:,1]= data.yc
XYZ[:,2]= data.zc+_ZSUN
vxvyvz= numpy.zeros((len(data),3))
vxvyvz[:,0]= data.vxc
vxvyvz[:,1]= data.vyc
vxvyvz[:,2]= data.vzc
"""
cov_vxvyvz= numpy.zeros((len(data),3,3))
cov_vxvyvz[:,0,0]= data.vxc_err**2.
cov_vxvyvz[:,1,1]= data.vyc_err**2.
cov_vxvyvz[:,2,2]= data.vzc_err**2.
cov_vxvyvz[:,0,1]= data.vxvyc_rho*data.vxc_err*data.vyc_err
cov_vxvyvz[:,0,2]= data.vxvzc_rho*data.vxc_err*data.vzc_err
cov_vxvyvz[:,1,2]= data.vyvzc_rho*data.vyc_err*data.vzc_err
"""
cosphi= (8.-XYZ[:,0])/R
sinphi= XYZ[:,1]/R
sinbeta= XYZ[:,2]/numpy.sqrt(R*R+XYZ[:,2]*XYZ[:,2])
cosbeta= R/numpy.sqrt(R*R+XYZ[:,2]*XYZ[:,2])
ndata= len(data.ra)
cov_pmradec= numpy.zeros((ndata,2,2))
cov_pmradec[:,0,0]= data.pmra_err**2.
cov_pmradec[:,1,1]= data.pmdec_err**2.
cov_pmllbb= bovy_coords.cov_pmrapmdec_to_pmllpmbb(cov_pmradec,data.ra,
data.dec,degree=True)
"""
vR= -vxvyvz[:,0]*cosphi+vxvyvz[:,1]*sinphi
vT= vxvyvz[:,0]*sinphi+vxvyvz[:,1]*cosphi
vz= vxvyvz[:,2]
vxvyvz[:,0]= vR
vxvyvz[:,1]= vT
for rr in range(len(XYZ[:,0])):
rot= numpy.array([[cosphi[rr],sinphi[rr]],
[-sinphi[rr],cosphi[rr]]])
sxy= cov_vxvyvz[rr,0:2,0:2]
sRT= numpy.dot(rot,numpy.dot(sxy,rot.T))
cov_vxvyvz[rr,0:2,0:2]= sRT
"""
#calculate x and y
lb= bovy_coords.radec_to_lb(data.ra,data.dec,degree=True)
lb*= _DEGTORAD
tuu= 1.-numpy.cos(lb[:,1])**2.*numpy.cos(lb[:,0])**2.
tuv= -0.5*numpy.cos(lb[:,1])**2.*numpy.sin(2.*lb[:,0])
tuw= -0.5*numpy.cos(lb[:,0])*numpy.sin(2.*lb[:,1])
tvv= 1.-numpy.cos(lb[:,1])**2.*numpy.sin(lb[:,0])**2.
tvw= -0.5*numpy.sin(2.*lb[:,1])*numpy.sin(lb[:,0])
tww= numpy.cos(lb[:,1])**2.
#x= tuu*_VRSUN+tuv*vxvyvz[:,1]+tuw*vxvyvz[:,2]
#y= -tww*_VZSUN+tuw*vxvyvz[:,0]+tvw*vxvyvz[:,1]
x= -tuu*numpy.mean(vxvyvz[:,0])+tuv*vxvyvz[:,1]+tuw*vxvyvz[:,2]
y= -tww*numpy.mean(vxvyvz[:,2])+tuw*vxvyvz[:,0]+tvw*vxvyvz[:,1]
if options.type.lower() == 'u':
corcorr=0.
plotthis[ii,jj]= (numpy.mean(vxvyvz[:,0]*x)-numpy.mean(vxvyvz[:,0])*numpy.mean(x))/(numpy.var(x)+numpy.mean(tuv**2.+tuw**2.)*numpy.var(vxvyvz[:,0]))
elif options.type.lower() == 'meanu':
plotthis[ii,jj]= numpy.mean(vxvyvz[:,0])
elif options.type.lower() == 'meanw':
plotthis[ii,jj]= numpy.mean(vxvyvz[:,2])
else:
corcorr= 0.25*numpy.mean(2.*sinbeta*cosbeta*numpy.sin(2.*lb[:,1])*numpy.cos(lb[:,0])*cosphi)*(numpy.var(vxvyvz[:,0])-numpy.var(vxvyvz[:,2]))\
-0.25*numpy.mean(2.*sinbeta*cosbeta*numpy.sin(2.*lb[:,1])*numpy.sin(lb[:,0])*sinphi)*(numpy.var(vxvyvz[:,0])-numpy.var(vxvyvz[:,2]))\
+0.25*numpy.mean(numpy.sin(lb[:,1])**2.*(cov_pmllbb[:,1,1]*data.dist**2.*4.74**2.-data.vr_err**2.))
plotthis[ii,jj]= (numpy.mean(vxvyvz[:,2]*y)-numpy.mean(vxvyvz[:,2])*numpy.mean(y)-corcorr)/(numpy.var(y)+numpy.mean(tvw**2.+tuw**2.)*numpy.var(vxvyvz[:,2]))
#print ii, jj, plotthis[ii,jj], corcorr, numpy.mean(vxvyvz[:,2]*y)-numpy.mean(vxvyvz[:,2])*numpy.mean(y)-corcorr
jj+= 1
if jj == len(binned.afeedges)-1:
jj= 0
ii+= 1
if jj == 0: #this means we've reset the counter
break
#print plotthis
#Set up plot
if options.type.lower() == 'meanu':
vmin, vmax= -20.,20.
zlabel=r'$\mathrm{mean}\ U$'
elif options.type.lower() == 'meanw':
vmin, vmax= -20.,20.
zlabel=r'$\mathrm{mean}\ W$'
else:
vmin, vmax= -0.2,0.2
zlabel=r'$\mathrm{fractional\ distance\ overestimate}$'
if options.tighten:
xrange=[-1.6,0.5]
yrange=[-0.05,0.55]
else:
xrange=[-2.,0.5]
yrange=[-0.2,0.6]
bovy_plot.bovy_print()
bovy_plot.bovy_dens2d(plotthis.T,origin='lower',cmap='jet',
interpolation='nearest',
xlabel=r'$[\mathrm{Fe/H}]$',
ylabel=r'$[\alpha/\mathrm{Fe}]$',
zlabel=zlabel,
xrange=xrange,yrange=yrange,
vmin=vmin,vmax=vmax,
contours=False,
colorbar=True,shrink=0.78)
bovy_plot.bovy_text(r'$\mathrm{median} = %.2f$' % (numpy.median(plotthis[numpy.isfinite(plotthis)])),
bottom_left=True,size=14.)
bovy_plot.bovy_end_print(options.outfilename)
return None
