def equatorial_to_galactic(alpha, delta):
"""
Convert equatorial coordinates to galactic system.
"""
cbcX, cbsX, sb = np.dot(MATRIXT, [cosd(delta)*cosd(alpha),
cosd(delta)*sind(alpha),
sind(delta)])
b = np.arcsin(sb)
l = np.arctan2(cbsX/cosd(b),cbcX/cosd(b))
if l < 0.:
l = l + np.pi * 2
return np.degrees(l), np.degrees(b)
def convert_all(ra, de, pmra, pmde, dpmra, dpmde,
vr, dvr, distance, e_distance):
"""
"""
rotRA = np.array([[cosd(ra), -sind(ra), 0.],
[sind(ra), cosd(ra), 0.],
[0., 0., 1.]])
rotDE = np.array([[cosd(de), 0., -sind(de)],
[0., 1., 0.],
[sind(de), 0., cosd(de)]])
l, b = equatorial_to_galactic(ra, de)
pos = np.array([cosd(b)*cosd(l),
cosd(b)*sind(l),
sind(b)])
matrixA = np.dot(rotRA, rotDE)
XYZ = distance * np.dot(MATRIXT, pos)
UVW = np.dot(MATRIXT, np.dot(matrixA, np.array([vr,
K*distance * pmra,
K*distance * pmde])))
#print cov_pmrapmdec_to_pmllpmbb(np.array([[dpmra**2, 0.], [0., dpmde**2]]), ra ,de, degree=True)
# Now to uncertainces:
#sinb = XYZ[2] / distance
#cosb = np.sqrt(1. - sinb**2)
#matrixP = get_P_matrix(ra, de, sinb, cosb)
# eq. 76
#cov_mu = np.dot(matrixP,
# np.dot(np.diag([dpmra * cosd(de), dpmde]), matrixP.T))
# eq. 70
jac_vavd = K * np.array([[pmra, distance, 0.],
[pmde, 0., distance]])
# eq. 71
cov_d_pm = np.diag([e_distance**2, dpmra**2, dpmde**2])
cov_vpm = doubledot(jac_vavd, cov_d_pm)
# eq. 72
cov_v = block_diag(dvr**2, cov_vpm)
cov_UVW = doubledot(MATRIXT, doubledot(matrixA, cov_v))
return XYZ, UVW, cov_UVW
def get_P_matrix(ra, de, sinb, cosb):
cos_phi = (SIN_DEC_NGP - sind(de)*sinb)/(cosd(de)*cosb)
sin_phi = sind(ra - RA_NGP) * COS_DEC_NGP / cosb
return np.array([[cos_phi, sin_phi], [-sin_phi, cos_phi]])
"""
Created on Mon Oct 26 14:28:40 2015
@author: mints
"""
import numpy as np
from sage.convert import R_SUN, V_SUN, cosd, sind, K
from scipy.linalg import block_diag
from galpy.util.bovy_coords import cov_pmrapmdec_to_pmllpmbb, cov_dvrpmllbb_to_vxyz
THETA = 122.932
RA_NGP = 192.85948
DEC_NGP = 27.12825
COS_THETA = cosd(THETA)
SIN_THETA = sind(THETA)
COS_RA_NGP = cosd(RA_NGP)
SIN_RA_NGP = sind(RA_NGP)
COS_DEC_NGP = cosd(DEC_NGP)
SIN_DEC_NGP = sind(DEC_NGP)
MATRIXT = np.dot(np.array([[COS_THETA, SIN_THETA, 0.],
[SIN_THETA, -COS_THETA, 0.],
[0., 0., 1.]]),
np.dot(np.array([[-SIN_DEC_NGP, 0., COS_DEC_NGP],
[0., 1., 0.],
[COS_DEC_NGP, 0., SIN_DEC_NGP]]),
np.array([[ COS_RA_NGP, SIN_RA_NGP, 0.],