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coords.py
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coords.py
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###############################################################################
#
# coords: module for coordinate transformations between the equatorial
# and Galactic coordinate frame
#
#
# Main included functions:
# radec_to_lb
# lb_to_radec
# radec_to_custom
# custom_to_radec
# lbd_to_XYZ
# XYZ_to_lbd
# rectgal_to_sphergal
# sphergal_to_rectgal
# vrpmllpmbb_to_vxvyvz
# vxvyvz_to_vrpmllpmbb
# pmrapmdec_to_pmllpmbb
# pmllpmbb_to_pmrapmdec
# pmrapmdec_to_custom
# custom_to_pmrapmdec
# cov_pmrapmdec_to_pmllpmbb
# cov_dvrpmllbb_to_vxyz
# XYZ_to_galcenrect
# XYZ_to_galcencyl
# galcenrect_to_XYZ
# galcencyl_to_XYZ
# rect_to_cyl
# cyl_to_rect
# rect_to_cyl_vec
# cyl_to_rect_vec
# vxvyvz_to_galcenrect
# vxvyvz_to_galcencyl
# galcenrect_to_vxvyvz
# galcencyl_to_vxvyvz
# dl_to_rphi_2d
# rphi_to_dl_2d
# Rz_to_coshucosv
# Rz_to_uv
# uv_to_Rz
# Rz_to_lambdanu
# Rz_to_lambdanu_jac
# Rz_to_lambdanu_hess
# lambdanu_to_Rz
#
##############################################################################
#############################################################################
#Copyright (c) 2010 - 2020, Jo Bovy
#All rights reserved.
#
#Redistribution and use in source and binary forms, with or without
#modification, are permitted provided that the following conditions are met:
#
# Redistributions of source code must retain the above copyright notice,
# this list of conditions and the following disclaimer.
# Redistributions in binary form must reproduce the above copyright notice,
# this list of conditions and the following disclaimer in the
# documentation and/or other materials provided with the distribution.
# The name of the author may not be used to endorse or promote products
# derived from this software without specific prior written permission.
#
#THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
#"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
#LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
#A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
#HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
#INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
#BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
#OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
#AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
#LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY
#WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
#POSSIBILITY OF SUCH DAMAGE.
#############################################################################
from functools import wraps
import numpy
from ..util import _rotate_to_arbitrary_vector
from ..util.config import __config__
_APY_COORDS= __config__.getboolean('astropy','astropy-coords')
_APY_LOADED= True
try:
import astropy.coordinates as apycoords
from astropy import units
except ImportError:
_APY_LOADED= False
_APY_COORDS*= _APY_LOADED
_DEGTORAD= numpy.pi/180.
if _APY_LOADED:
_K= (1.*units.mas/units.yr).to(units.km/units.s/units.kpc,
equivalencies=units.dimensionless_angles())\
.value
else:
_K=4.74047
# numpy 1.14 einsum bug causes astropy conversions to fail in py2.7 -> turn off
if _APY_COORDS:
ra, dec= numpy.array([192.25*_DEGTORAD]), numpy.array([27.4*_DEGTORAD])
c= apycoords.SkyCoord(ra*units.rad,dec*units.rad,
equinox='B1950',frame='fk4')
# This conversion fails bc of einsum bug
try:
c= c.transform_to(apycoords.Galactic)
except TypeError: # pragma: no cover
_APY_COORDS= False
def scalarDecorator(func):
"""Decorator to return scalar outputs as a set"""
@wraps(func)
def scalar_wrapper(*args,**kwargs):
if numpy.array(args[0]).shape == ():
scalarOut= True
newargs= ()
for ii in range(len(args)):
newargs= newargs+(numpy.array([args[ii]]),)
args= newargs
else:
scalarOut= False
result= func(*args,**kwargs)
if scalarOut:
out= ()
for ii in range(result.shape[1]):
out= out+(result[0,ii],)
return out
else:
return result
return scalar_wrapper
def degreeDecorator(inDegrees,outDegrees):
"""
NAME:
degreeDecorator
PURPOSE:
Decorator to transform angles from and to degrees if necessary
INPUT:
inDegrees - list specifiying indices of angle arguments (e.g., [0,1])
outDegrees - list, same as inDegrees, but for function return
HISTORY:
____-__-__ - Written - Bovy
2019-03-02 - speedup - Nathaniel Starkman (UofT)
"""
# (modified) old degree decorator
def wrapper(func):
@wraps(func)
def wrapped(*args, **kwargs):
isdeg = kwargs.get('degree', False)
if isdeg:
args = [arg * numpy.pi / 180 if i in inDegrees else arg
for i, arg in enumerate(args)]
out = func(*args, **kwargs)
if isdeg:
for i in outDegrees:
out[:, i] *= 180. / numpy.pi
return out
return wrapped
return wrapper
@scalarDecorator
@degreeDecorator([0,1],[0,1])
def radec_to_lb(ra,dec,degree=False,epoch=2000.0):
"""
NAME:
radec_to_lb
PURPOSE:
transform from equatorial coordinates to Galactic coordinates
INPUT:
ra - right ascension
dec - declination
degree - (Bool) if True, ra and dec are given in degree and l and b will be as well
epoch - epoch of ra,dec (right now only 2000.0 and 1950.0 are supported when not using astropy's transformations internally; when internally using astropy's coordinate transformations, epoch can be None for ICRS, 'JXXXX' for FK5, and 'BXXXX' for FK4)
OUTPUT:
l,b
For vector inputs [:,2]
HISTORY:
2009-11-12 - Written - Bovy (NYU)
2014-06-14 - Re-written w/ numpy functions for speed and w/ decorators for beauty - Bovy (IAS)
2016-05-13 - Added support for using astropy's coordinate transformations and for non-standard epochs - Bovy (UofT)
"""
if _APY_COORDS:
epoch, frame= _parse_epoch_frame_apy(epoch)
c= apycoords.SkyCoord(ra*units.rad,dec*units.rad,
equinox=epoch,frame=frame)
c= c.transform_to(apycoords.Galactic)
return numpy.array([c.l.to(units.rad).value,c.b.to(units.rad).value]).T
#First calculate the transformation matrix T
theta,dec_ngp,ra_ngp= get_epoch_angles(epoch)
T= numpy.dot(numpy.array([[numpy.cos(theta),numpy.sin(theta),0.],[numpy.sin(theta),-numpy.cos(theta),0.],[0.,0.,1.]]),numpy.dot(numpy.array([[-numpy.sin(dec_ngp),0.,numpy.cos(dec_ngp)],[0.,1.,0.],[numpy.cos(dec_ngp),0.,numpy.sin(dec_ngp)]]),numpy.array([[numpy.cos(ra_ngp),numpy.sin(ra_ngp),0.],[-numpy.sin(ra_ngp),numpy.cos(ra_ngp),0.],[0.,0.,1.]])))
#Whether to use degrees and scalar input is handled by decorators
XYZ= numpy.array([numpy.cos(dec)*numpy.cos(ra),
numpy.cos(dec)*numpy.sin(ra),
numpy.sin(dec)])
galXYZ= numpy.dot(T,XYZ)
galXYZ[2][galXYZ[2] > 1.]= 1.
galXYZ[2][galXYZ[2] < -1.]= -1.
b= numpy.arcsin(galXYZ[2])
l= numpy.arctan2(galXYZ[1]/numpy.cos(b),galXYZ[0]/numpy.cos(b))
l[l<0.]+= 2.*numpy.pi
out= numpy.array([l,b])
return out.T
@scalarDecorator
@degreeDecorator([0,1],[0,1])
def lb_to_radec(l,b,degree=False,epoch=2000.0):
"""
NAME:
lb_to_radec
PURPOSE:
transform from Galactic coordinates to equatorial coordinates
INPUT:
l - Galactic longitude
b - Galactic lattitude
degree - (Bool) if True, l and b are given in degree and ra and dec will be as well
epoch - epoch of ra,dec (right now only 2000.0 and 1950.0 are supported when not using astropy's transformations internally; when internally using astropy's coordinate transformations, epoch can be None for ICRS, 'JXXXX' for FK5, and 'BXXXX' for FK4)
OUTPUT:
ra,dec
For vector inputs [:,2]
HISTORY:
2010-04-07 - Written - Bovy (NYU)
2014-06-14 - Re-written w/ numpy functions for speed and w/ decorators for beauty - Bovy (IAS)
2016-05-13 - Added support for using astropy's coordinate transformations and for non-standard epochs - Bovy (UofT)
"""
if _APY_COORDS:
epoch, frame= _parse_epoch_frame_apy(epoch)
c= apycoords.SkyCoord(l*units.rad,b*units.rad,frame='galactic')
if not epoch is None and 'J' in epoch:
c= c.transform_to(apycoords.FK5(equinox=epoch))
elif not epoch is None and 'B' in epoch:
c= c.transform_to(apycoords.FK4(equinox=epoch))
else:
c= c.transform_to(apycoords.ICRS)
return numpy.array([c.ra.to(units.rad).value,c.dec.to(units.rad).value]).T
#First calculate the transformation matrix T'
theta,dec_ngp,ra_ngp= get_epoch_angles(epoch)
T= numpy.dot(numpy.array([[numpy.cos(ra_ngp),-numpy.sin(ra_ngp),0.],[numpy.sin(ra_ngp),numpy.cos(ra_ngp),0.],[0.,0.,1.]]),numpy.dot(numpy.array([[-numpy.sin(dec_ngp),0.,numpy.cos(dec_ngp)],[0.,1.,0.],[numpy.cos(dec_ngp),0.,numpy.sin(dec_ngp)]]),numpy.array([[numpy.cos(theta),numpy.sin(theta),0.],[numpy.sin(theta),-numpy.cos(theta),0.],[0.,0.,1.]])))
#Whether to use degrees and scalar input is handled by decorators
XYZ= numpy.array([numpy.cos(b)*numpy.cos(l),
numpy.cos(b)*numpy.sin(l),
numpy.sin(b)])
eqXYZ= numpy.dot(T,XYZ)
dec= numpy.arcsin(eqXYZ[2])
ra= numpy.arctan2(eqXYZ[1],eqXYZ[0])
ra[ra<0.]+= 2.*numpy.pi
return numpy.array([ra,dec]).T
@scalarDecorator
@degreeDecorator([0,1],[])
def lbd_to_XYZ(l,b,d,degree=False):
"""
NAME:
lbd_to_XYZ
PURPOSE:
transform from spherical Galactic coordinates to rectangular Galactic coordinates (works with vector inputs)
INPUT:
l - Galactic longitude (rad)
b - Galactic lattitude (rad)
d - distance (arbitrary units)
degree - (bool) if True, l and b are in degrees
OUTPUT:
[X,Y,Z] in whatever units d was in
For vector inputs [:,3]
HISTORY:
2009-10-24- Written - Bovy (NYU)
2014-06-14 - Re-written w/ numpy functions for speed and w/ decorators for beauty - Bovy (IAS)
"""
#Whether to use degrees and scalar input is handled by decorators
return numpy.array([d*numpy.cos(b)*numpy.cos(l),
d*numpy.cos(b)*numpy.sin(l),
d*numpy.sin(b)]).T
def rectgal_to_sphergal(X,Y,Z,vx,vy,vz,degree=False):
"""
NAME:
rectgal_to_sphergal
PURPOSE:
transform phase-space coordinates in rectangular Galactic coordinates to spherical Galactic coordinates (can take vector inputs)
INPUT:
X - component towards the Galactic Center (kpc)
Y - component in the direction of Galactic rotation (kpc)
Z - component towards the North Galactic Pole (kpc)
vx - velocity towards the Galactic Center (km/s)
vy - velocity in the direction of Galactic rotation (km/s)
vz - velocity towards the North Galactic Pole (km/s)
degree - (Bool) if True, return l and b in degrees
OUTPUT:
(l,b,d,vr,pmll x cos(b),pmbb) in (rad,rad,kpc,km/s,mas/yr,mas/yr)
HISTORY:
2009-10-25 - Written - Bovy (NYU)
"""
lbd= XYZ_to_lbd(X,Y,Z,degree=degree)
vrpmllpmbb= vxvyvz_to_vrpmllpmbb(vx,vy,vz,X,Y,Z,XYZ=True)
if numpy.array(X).shape == ():
return numpy.array([lbd[0],lbd[1],lbd[2],vrpmllpmbb[0],vrpmllpmbb[1],vrpmllpmbb[2]])
else:
out=numpy.zeros((len(X),6))
out[:,0:3]= lbd
out[:,3:6]= vrpmllpmbb
return out
def sphergal_to_rectgal(l,b,d,vr,pmll,pmbb,degree=False):
"""
NAME:
sphergal_to_rectgal
PURPOSE:
transform phase-space coordinates in spherical Galactic coordinates to rectangular Galactic coordinates (can take vector inputs)
INPUT:
l - Galactic longitude (rad)
b - Galactic lattitude (rad)
d - distance (kpc)
vr - line-of-sight velocity (km/s)
pmll - proper motion in the Galactic longitude direction (mu_l*cos(b) ) (mas/yr)
pmbb - proper motion in the Galactic lattitude (mas/yr)
degree - (bool) if True, l and b are in degrees
OUTPUT:
(X,Y,Z,vx,vy,vz) in (kpc,kpc,kpc,km/s,km/s,km/s)
HISTORY:
2009-10-25 - Written - Bovy (NYU)
"""
XYZ= lbd_to_XYZ(l,b,d,degree=degree)
vxvyvz= vrpmllpmbb_to_vxvyvz(vr,pmll,pmbb,l,b,d,XYZ=False,degree=degree)
if numpy.array(l).shape == ():
return numpy.array([XYZ[0],XYZ[1],XYZ[2],vxvyvz[0],vxvyvz[1],vxvyvz[2]])
else:
out=numpy.zeros((len(l),6))
out[:,0:3]= XYZ
out[:,3:6]= vxvyvz
return out
@scalarDecorator
@degreeDecorator([3,4],[])
def vrpmllpmbb_to_vxvyvz(vr,pmll,pmbb,l,b,d,XYZ=False,degree=False):
"""
NAME:
vrpmllpmbb_to_vxvyvz
PURPOSE:
Transform velocities in the spherical Galactic coordinate frame to the rectangular Galactic coordinate frame (can take vector inputs)
INPUT:
vr - line-of-sight velocity (km/s)
pmll - proper motion in the Galactic longitude (mu_l * cos(b))(mas/yr)
pmbb - proper motion in the Galactic lattitude (mas/yr)
l - Galactic longitude
b - Galactic lattitude
d - distance (kpc)
XYZ - (bool) If True, then l,b,d is actually X,Y,Z (rectangular Galactic coordinates)
degree - (bool) if True, l and b are in degrees
OUTPUT:
(vx,vy,vz) in (km/s,km/s,km/s)
For vector inputs [:,3]
HISTORY:
2009-10-24 - Written - Bovy (NYU)
2014-06-14 - Re-written w/ numpy functions for speed and w/ decorators for beauty - Bovy (IAS)
"""
#Whether to use degrees and scalar input is handled by decorators
if XYZ: #undo the incorrect conversion that the decorator did
if degree:
l*= 180./numpy.pi
b*= 180./numpy.pi
lbd= XYZ_to_lbd(l,b,d,degree=False)
l= lbd[:,0]
b= lbd[:,1]
d= lbd[:,2]
R=numpy.zeros((3,3,len(l)))
R[0,0]= numpy.cos(l)*numpy.cos(b)
R[1,0]= -numpy.sin(l)
R[2,0]= -numpy.cos(l)*numpy.sin(b)
R[0,1]= numpy.sin(l)*numpy.cos(b)
R[1,1]= numpy.cos(l)
R[2,1]= -numpy.sin(l)*numpy.sin(b)
R[0,2]= numpy.sin(b)
R[2,2]= numpy.cos(b)
invr= numpy.array([[vr,vr,vr],
[d*pmll*_K,d*pmll*_K,d*pmll*_K],
[d*pmbb*_K,d*pmbb*_K,d*pmbb*_K]])
return (R.T*invr.T).sum(-1)
@scalarDecorator
@degreeDecorator([3,4],[])
def vxvyvz_to_vrpmllpmbb(vx,vy,vz,l,b,d,XYZ=False,degree=False):
"""
NAME:
vxvyvz_to_vrpmllpmbb
PURPOSE:
Transform velocities in the rectangular Galactic coordinate frame to the spherical Galactic coordinate frame (can take vector inputs)
INPUT:
vx - velocity towards the Galactic Center (km/s)
vy - velocity in the direction of Galactic rotation (km/s)
vz - velocity towards the North Galactic Pole (km/s)
l - Galactic longitude
b - Galactic lattitude
d - distance (kpc)
XYZ - (bool) If True, then l,b,d is actually X,Y,Z (rectangular Galactic coordinates)
degree - (bool) if True, l and b are in degrees
OUTPUT:
(vr,pmll x cos(b),pmbb) in (km/s,mas/yr,mas/yr); pmll = mu_l * cos(b)
For vector inputs [:,3]
HISTORY:
2009-10-24 - Written - Bovy (NYU)
2014-06-14 - Re-written w/ numpy functions for speed and w/ decorators for beauty - Bovy (IAS)
"""
#Whether to use degrees and scalar input is handled by decorators
if XYZ: #undo the incorrect conversion that the decorator did
if degree:
l*= 180./numpy.pi
b*= 180./numpy.pi
lbd= XYZ_to_lbd(l,b,d,degree=False)
l= lbd[:,0]
b= lbd[:,1]
d= lbd[:,2]
R=numpy.zeros((3,3,len(l)))
R[0,0]= numpy.cos(l)*numpy.cos(b)
R[0,1]= -numpy.sin(l)
R[0,2]= -numpy.cos(l)*numpy.sin(b)
R[1,0]= numpy.sin(l)*numpy.cos(b)
R[1,1]= numpy.cos(l)
R[1,2]= -numpy.sin(l)*numpy.sin(b)
R[2,0]= numpy.sin(b)
R[2,2]= numpy.cos(b)
invxyz= numpy.array([[vx,vx,vx],
[vy,vy,vy],
[vz,vz,vz]])
vrvlvb= (R.T*invxyz.T).sum(-1)
vrvlvb[:,1]/= d*_K
vrvlvb[:,2]/= d*_K
return vrvlvb
@scalarDecorator
@degreeDecorator([],[0,1])
def XYZ_to_lbd(X,Y,Z,degree=False):
"""
NAME:
XYZ_to_lbd
PURPOSE:
transform from rectangular Galactic coordinates to spherical Galactic coordinates (works with vector inputs)
INPUT:
X - component towards the Galactic Center (in kpc; though this obviously does not matter))
Y - component in the direction of Galactic rotation (in kpc)
Z - component towards the North Galactic Pole (kpc)
degree - (Bool) if True, return l and b in degrees
OUTPUT:
[l,b,d] in (rad or degree,rad or degree,kpc)
For vector inputs [:,3]
HISTORY:
2009-10-24 - Written - Bovy (NYU)
2014-06-14 - Re-written w/ numpy functions for speed and w/ decorators for beauty - Bovy (IAS)
"""
#Whether to use degrees and scalar input is handled by decorators
d= numpy.sqrt(X**2.+Y**2.+Z**2.)
b= numpy.arcsin(Z/d)
out= numpy.empty((len(d),3))
out[:,0]= numpy.arctan2(Y,X)
out[:,1]= b
out[:,2]= d
return out
@scalarDecorator
@degreeDecorator([2,3],[])
def pmrapmdec_to_pmllpmbb(pmra,pmdec,ra,dec,degree=False,epoch=2000.0):
"""
NAME:
pmrapmdec_to_pmllpmbb
PURPOSE:
rotate proper motions in (ra,dec) into proper motions in (l,b)
INPUT:
pmra - proper motion in ra (multplied with cos(dec)) [mas/yr]
pmdec - proper motion in dec [mas/yr]
ra - right ascension
dec - declination
degree - if True, ra and dec are given in degrees (default=False)
epoch - epoch of ra,dec (right now only 2000.0 and 1950.0 are supported when not using astropy's transformations internally; when internally using astropy's coordinate transformations, epoch can be None for ICRS, 'JXXXX' for FK5, and 'BXXXX' for FK4)
OUTPUT:
(pmll x cos(b),pmbb) for vector inputs [:,2]
HISTORY:
2010-04-07 - Written - Bovy (NYU)
2014-06-14 - Re-written w/ numpy functions for speed and w/ decorators for beauty - Bovy (IAS)
"""
theta,dec_ngp,ra_ngp= get_epoch_angles(epoch)
#Whether to use degrees and scalar input is handled by decorators
dec[dec == dec_ngp]+= 10.**-16 #deal w/ pole.
sindec_ngp= numpy.sin(dec_ngp)
cosdec_ngp= numpy.cos(dec_ngp)
sindec= numpy.sin(dec)
cosdec= numpy.cos(dec)
sinrarangp= numpy.sin(ra-ra_ngp)
cosrarangp= numpy.cos(ra-ra_ngp)
#These were replaced by Poleski (2013)'s equivalent form that is better at the poles
#cosphi= (sindec_ngp-sindec*sinb)/cosdec/cosb
#sinphi= sinrarangp*cosdec_ngp/cosb
cosphi= sindec_ngp*cosdec-cosdec_ngp*sindec*cosrarangp
sinphi= sinrarangp*cosdec_ngp
norm= numpy.sqrt(cosphi**2.+sinphi**2.)
cosphi/= norm
sinphi/= norm
return (numpy.array([[cosphi,-sinphi],[sinphi,cosphi]]).T\
*numpy.array([[pmra,pmra],[pmdec,pmdec]]).T).sum(-1)
@scalarDecorator
@degreeDecorator([2,3],[])
def pmllpmbb_to_pmrapmdec(pmll,pmbb,l,b,degree=False,epoch=2000.0):
"""
NAME:
pmllpmbb_to_pmrapmdec
PURPOSE:
rotate proper motions in (l,b) into proper motions in (ra,dec)
INPUT:
pmll - proper motion in l (multplied with cos(b)) [mas/yr]
pmbb - proper motion in b [mas/yr]
l - Galactic longitude
b - Galactic lattitude
degree - if True, l and b are given in degrees (default=False)
epoch - epoch of ra,dec (right now only 2000.0 and 1950.0 are supported when not using astropy's transformations internally; when internally using astropy's coordinate transformations, epoch can be None for ICRS, 'JXXXX' for FK5, and 'BXXXX' for FK4)
OUTPUT:
(pmra x cos(dec),pmdec), for vector inputs [:,2]
HISTORY:
2010-04-07 - Written - Bovy (NYU)
2014-06-14 - Re-written w/ numpy functions for speed and w/ decorators for beauty - Bovy (IAS)
"""
theta,dec_ngp,ra_ngp= get_epoch_angles(epoch)
#Whether to use degrees and scalar input is handled by decorators
radec = lb_to_radec(l,b,degree=False,epoch=epoch)
ra= radec[:,0]
dec= radec[:,1]
dec[dec == dec_ngp]+= 10.**-16 #deal w/ pole.
sindec_ngp= numpy.sin(dec_ngp)
cosdec_ngp= numpy.cos(dec_ngp)
sindec= numpy.sin(dec)
cosdec= numpy.cos(dec)
sinrarangp= numpy.sin(ra-ra_ngp)
cosrarangp= numpy.cos(ra-ra_ngp)
#These were replaced by Poleski (2013)'s equivalent form that is better at the poles
#cosphi= (sindec_ngp-sindec*sinb)/cosdec/cosb
#sinphi= sinrarangp*cosdec_ngp/cosb
cosphi= sindec_ngp*cosdec-cosdec_ngp*sindec*cosrarangp
sinphi= sinrarangp*cosdec_ngp
norm= numpy.sqrt(cosphi**2.+sinphi**2.)
cosphi/= norm
sinphi/= norm
return (numpy.array([[cosphi,sinphi],[-sinphi,cosphi]]).T\
*numpy.array([[pmll,pmll],[pmbb,pmbb]]).T).sum(-1)
def cov_pmrapmdec_to_pmllpmbb(cov_pmradec,ra,dec,degree=False,epoch=2000.0):
"""
NAME:
cov_pmrapmdec_to_pmllpmbb
PURPOSE:
propagate the proper motions errors through the rotation from (ra,dec) to (l,b)
INPUT:
covar_pmradec - uncertainty covariance matrix of the proper motion in ra (multplied with cos(dec)) and dec [2,2] or [:,2,2]
ra - right ascension
dec - declination
degree - if True, ra and dec are given in degrees (default=False)
epoch - epoch of ra,dec (right now only 2000.0 and 1950.0 are supported when not using astropy's transformations internally; when internally using astropy's coordinate transformations, epoch can be None for ICRS, 'JXXXX' for FK5, and 'BXXXX' for FK4)
OUTPUT:
covar_pmllbb [2,2] or [:,2,2] [pmll here is pmll x cos(b)]
HISTORY:
2010-04-12 - Written - Bovy (NYU)
2020-09-21 - Adapted for array input - Mackereth (UofT)
"""
scalar= not hasattr(ra, '__iter__')
if scalar:
cov_pmradec= cov_pmradec[numpy.newaxis,:,:]
theta,dec_ngp,ra_ngp= get_epoch_angles(epoch)
if degree:
sindec_ngp= numpy.sin(dec_ngp)
cosdec_ngp= numpy.cos(dec_ngp)
sindec= numpy.sin(dec*_DEGTORAD)
cosdec= numpy.cos(dec*_DEGTORAD)
sinrarangp= numpy.sin(ra*_DEGTORAD-ra_ngp)
cosrarangp= numpy.cos(ra*_DEGTORAD-ra_ngp)
else:
sindec_ngp= numpy.sin(dec_ngp)
cosdec_ngp= numpy.cos(dec_ngp)
sindec= numpy.sin(dec)
cosdec= numpy.cos(dec)
sinrarangp= numpy.sin(ra-ra_ngp)
cosrarangp= numpy.cos(ra-ra_ngp)
#These were replaced by Poleski (2013)'s equivalent form that is better at the poles
#cosphi= (sindec_ngp-sindec*sinb)/cosdec/cosb
#sinphi= sinrarangp*cosdec_ngp/cosb
cosphi= sindec_ngp*cosdec-cosdec_ngp*sindec*cosrarangp
sinphi= sinrarangp*cosdec_ngp
norm= numpy.sqrt(cosphi**2.+sinphi**2.)
cosphi/= norm
sinphi/= norm
P = numpy.zeros([len(cov_pmradec),2,2])
P[:,0,0] = cosphi
P[:,0,1] = sinphi
P[:,1,0] = -sinphi
P[:,1,1] = cosphi
out= numpy.einsum('aij,ajk->aik',P,
numpy.einsum('aij,jka->aik',cov_pmradec,P.T))
if scalar:
return out[0]
else:
return out
def cov_dvrpmllbb_to_vxyz(d,e_d,e_vr,pmll,pmbb,cov_pmllbb,l,b,
plx=False,degree=False):
"""
NAME:
cov_dvrpmllbb_to_vxyz
PURPOSE:
propagate distance, radial velocity, and proper motion uncertainties to Galactic coordinates
INPUT:
d - distance [kpc, as/mas for plx]
e_d - distance uncertainty [kpc, [as/mas] for plx]
e_vr - low velocity uncertainty [km/s]
pmll - proper motion in l (*cos(b)) [ [as/mas]/yr ]
pmbb - proper motion in b [ [as/mas]/yr ]
cov_pmllbb - uncertainty covariance for proper motion [pmll is pmll x cos(b)]
l - Galactic longitude
b - Galactic lattitude
KEYWORDS:
plx - if True, d is a parallax, and e_d is a parallax uncertainty
degree - if True, l and b are given in degree
OUTPUT:
cov(vx,vy,vz) [3,3] or [:,3,3]
HISTORY:
2010-04-12 - Written - Bovy (NYU)
2020-09-21 - Adapted for array input - Mackereth (UofT)
"""
if plx:
d= 1./d
e_d*= d**2.
if degree:
l*= _DEGTORAD
b*= _DEGTORAD
scalar= not hasattr(d,'__iter__')
if scalar:
cov_pmllbb= cov_pmllbb[numpy.newaxis,:,:]
ndata= len(cov_pmllbb)
M = numpy.zeros((ndata,2,3))
M[:,0,0] = pmll
M[:,1,0] = pmbb
M[:,0,1] = d
M[:,1,2] = d
M= _K*M
cov_dpmllbb= numpy.zeros((ndata,3,3))
cov_dpmllbb[:,0,0]= e_d**2.
cov_dpmllbb[:,1:3,1:3]= cov_pmllbb
cov_vlvb= numpy.einsum('aij,ajk->aik',M,
numpy.einsum('aij,jka->aik',cov_dpmllbb,M.T))
if scalar:
cov_vlvb= cov_vlvb[0]
cov_vrvlvb= numpy.zeros((ndata,3,3))
cov_vrvlvb[:,0,0]= e_vr**2.
cov_vrvlvb[:,1:3,1:3]= cov_vlvb
R = numpy.zeros((ndata,3,3))
R[:,0,0] = numpy.cos(l)*numpy.cos(b)
R[:,0,1] = numpy.sin(l)*numpy.cos(b)
R[:,0,2] = numpy.sin(b)
R[:,1,0] = -numpy.sin(l)
R[:,1,1] = numpy.cos(l)
R[:,2,0] = -numpy.cos(l)*numpy.sin(b)
R[:,2,1] = -numpy.sin(l)*numpy.sin(b)
R[:,2,2] = numpy.cos(b)
out= numpy.einsum('ija,ajk->aik',R.T,
numpy.einsum('aij,ajk->aik',cov_vrvlvb,R))
if scalar:
return out[0]
else:
return out
def cov_vxyz_to_galcencyl(cov_vxyz, phi, Xsun=1., Zsun=0.):
"""
NAME:
cov_vxyz_to_galcencyl
PURPOSE:
propagate uncertainties in vxyz to galactocentric cylindrical coordinates
INPUT:
cov_vxyz - uncertainty covariance in U,V,W
phi - angular position of star in galactocentric cylindrical coords
OUTPUT:
cov(vR,vT,vz) [3,3]
HISTORY:
2018-03-22 - Written - Mackereth (LJMU)
2020-09-21- Moved to coords.py - Mackereth (UofT)
"""
cov_galcenrect = cov_vxyz_to_galcenrect(cov_vxyz, Xsun=Xsun, Zsun=Zsun)
cov_galcencyl = cov_galcenrect_to_galcencyl(cov_galcenrect, phi)
return cov_galcencyl
def cov_vxyz_to_galcenrect(cov_vxyz,Xsun=1.,Zsun=0.):
"""
NAME:
cov_vxyz_to_galcenrect
PURPOSE:
propagate uncertainties in vxyz to galactocentric rectangular coordinates
INPUT:
cov_vxyz - uncertainty covariance in U,V,W
OUTPUT:
cov(vx,vy,vz) [3,3]
HISTORY:
2018-03-22 - Written - Mackereth (LJMU)
2020-09-21- Moved to coords.py - Mackereth (UofT)
"""
scalar= cov_vxyz.ndim < 3
if scalar:
cov_vxyz= cov_vxyz[numpy.newaxis,:,:]
dgc= numpy.sqrt(Xsun**2.+Zsun**2.)
costheta, sintheta= Xsun/dgc, Zsun/dgc
R = numpy.array([[costheta,0.,-sintheta],
[0.,1.,0.],
[sintheta,0.,costheta]])
R = numpy.ones([len(cov_vxyz),3,3])*R
out= numpy.einsum('ija,ajk->aik',R.T,
numpy.einsum('aij,ajk->aik',cov_vxyz,R))
if scalar:
return out[0]
else:
return out
def cov_galcenrect_to_galcencyl(cov_galcenrect, phi):
"""
NAME:
cov_galcenrect_to_galcencyl
PURPOSE:
propagate uncertainties in galactocentric rectangular to galactocentric cylindrical coordinates
INPUT:
cov_galcenrect - uncertainty covariance in Galactocentric rectangular coords
OUTPUT:
cov(vR,vT,vz) [3,3]
HISTORY:
2018-03-22 - Written - Mackereth (LJMU)
2020-09-21- Moved to coords.py - Mackereth (UofT)
"""
scalar= cov_galcenrect.ndim < 3
if scalar:
cov_galcenrect= cov_galcenrect[numpy.newaxis,:,:]
cosphi = numpy.cos(phi)
sinphi = numpy.sin(phi)
R = numpy.zeros([len(cov_galcenrect),3,3])
R[:,0,0] = cosphi
R[:,0,1] = sinphi
R[:,1,0] = -sinphi
R[:,1,1] = cosphi
R[:,2,2] = 1.
out= numpy.einsum('aij,ajk->aik',R,
numpy.einsum('aij,jka->aik',cov_galcenrect,R.T))
if scalar:
return out[0]
else:
return out
@scalarDecorator
def XYZ_to_galcenrect(X,Y,Z,Xsun=1.,Zsun=0.,_extra_rot=True):
"""
NAME:
XYZ_to_galcenrect
PURPOSE:
transform XYZ coordinates (wrt Sun) to rectangular Galactocentric coordinates
INPUT:
X - X
Y - Y