# -*- coding: utf-8 -*-
from numpy import *
def deg2rad(degrees):
return degrees*pi/180.
def rad2deg(radians):
return radians*180./pi
[docs]def baryvel(dje, deq=0):
"""
NAME:
BARYVEL
PURPOSE:
Calculates heliocentric and barycentric velocity components of Earth.
EXPLANATION:
BARYVEL takes into account the Earth-Moon motion, and is useful for
radial velocity work to an accuracy of ~1 m/s.
CALLING SEQUENCE:
dvel_hel, dvel_bary = baryvel(dje, deq)
INPUTS:
DJE - (scalar) Julian ephemeris date.
DEQ - (scalar) epoch of mean equinox of dvelh and dvelb. If deq=0
then deq is assumed to be equal to dje.
OUTPUTS:
DVELH: (vector(3)) heliocentric velocity component. in km/s
DVELB: (vector(3)) barycentric velocity component. in km/s
The 3-vectors DVELH and DVELB are given in a right-handed coordinate
system with the +X axis toward the Vernal Equinox, and +Z axis
toward the celestial pole.
OPTIONAL KEYWORD SET:
JPL - if /JPL set, then BARYVEL will call the procedure JPLEPHINTERP
to compute the Earth velocity using the full JPL ephemeris.
The JPL ephemeris FITS file JPLEPH.405 must exist in either the
current directory, or in the directory specified by the
environment variable ASTRO_DATA. Alternatively, the JPL keyword
can be set to the full path and name of the ephemeris file.
A copy of the JPL ephemeris FITS file is available in
http://idlastro.gsfc.nasa.gov/ftp/data/
PROCEDURES CALLED:
Function PREMAT() -- computes precession matrix
JPLEPHREAD, JPLEPHINTERP, TDB2TDT - if /JPL keyword is set
NOTES:
Algorithm taken from FORTRAN program of Stumpff (1980, A&A Suppl, 41,1)
Stumpf claimed an accuracy of 42 cm/s for the velocity. A
comparison with the JPL FORTRAN planetary ephemeris program PLEPH
found agreement to within about 65 cm/s between 1986 and 1994
If /JPL is set (using JPLEPH.405 ephemeris file) then velocities are
given in the ICRS system; otherwise in the FK4 system.
EXAMPLE:
Compute the radial velocity of the Earth toward Altair on 15-Feb-1994
using both the original Stumpf algorithm and the JPL ephemeris
IDL> jdcnv, 1994, 2, 15, 0, jd ;==> JD = 2449398.5
IDL> baryvel, jd, 2000, vh, vb ;Original algorithm
==> vh = [-17.07243, -22.81121, -9.889315] ;Heliocentric km/s
==> vb = [-17.08083, -22.80471, -9.886582] ;Barycentric km/s
IDL> baryvel, jd, 2000, vh, vb, /jpl ;JPL ephemeris
==> vh = [-17.07236, -22.81126, -9.889419] ;Heliocentric km/s
==> vb = [-17.08083, -22.80484, -9.886409] ;Barycentric km/s
IDL> ra = ten(19,50,46.77)*15/!RADEG ;RA in radians
IDL> dec = ten(08,52,3.5)/!RADEG ;Dec in radians
IDL> v = vb[0]*cos(dec)*cos(ra) + $ ;Project velocity toward star
vb[1]*cos(dec)*sin(ra) + vb[2]*sin(dec)
REVISION HISTORY:
Jeff Valenti, U.C. Berkeley Translated BARVEL.FOR to IDL.
W. Landsman, Cleaned up program sent by Chris McCarthy (SfSU) June 1994
Converted to IDL V5.0 W. Landsman September 1997
Added /JPL keyword W. Landsman July 2001
Documentation update W. Landsman Dec 2005
Converted to Python S. Koposov 2009-2010
"""
#Define constants
dc2pi = 2 * pi
cc2pi = 2 * pi
dc1 = 1.0e0
dcto = 2415020.0e0
dcjul = 36525.0e0 #days in Julian year
dcbes = 0.313e0
dctrop = 365.24219572e0 #days in tropical year (...572 insig)
dc1900 = 1900.0e0
au = 1.4959787e8
#Constants dcfel(i,k) of fast changing elements.
dcfel = array([1.7400353e00, 6.2833195099091e02, 5.2796e-6, 6.2565836e00, 6.2830194572674e02, -2.6180e-6, 4.7199666e00, 8.3997091449254e03, -1.9780e-5, 1.9636505e-1, 8.4334662911720e03, -5.6044e-5, 4.1547339e00, 5.2993466764997e01, 5.8845e-6, 4.6524223e00, 2.1354275911213e01, 5.6797e-6, 4.2620486e00, 7.5025342197656e00, 5.5317e-6, 1.4740694e00, 3.8377331909193e00, 5.6093e-6])
dcfel = reshape(dcfel, (8, 3))
#constants dceps and ccsel(i,k) of slowly changing elements.
dceps = array([4.093198e-1, -2.271110e-4, -2.860401e-8])
ccsel = array([1.675104e-2, -4.179579e-5, -1.260516e-7, 2.220221e-1, 2.809917e-2, 1.852532e-5, 1.589963e00, 3.418075e-2, 1.430200e-5, 2.994089e00, 2.590824e-2, 4.155840e-6, 8.155457e-1, 2.486352e-2, 6.836840e-6, 1.735614e00, 1.763719e-2, 6.370440e-6, 1.968564e00, 1.524020e-2, -2.517152e-6, 1.282417e00, 8.703393e-3, 2.289292e-5, 2.280820e00, 1.918010e-2, 4.484520e-6, 4.833473e-2, 1.641773e-4, -4.654200e-7, 5.589232e-2, -3.455092e-4, -7.388560e-7, 4.634443e-2, -2.658234e-5, 7.757000e-8, 8.997041e-3, 6.329728e-6, -1.939256e-9, 2.284178e-2, -9.941590e-5, 6.787400e-8, 4.350267e-2, -6.839749e-5, -2.714956e-7, 1.348204e-2, 1.091504e-5, 6.903760e-7, 3.106570e-2, -1.665665e-4, -1.590188e-7])
ccsel = reshape(ccsel, (17, 3))
#Constants of the arguments of the short-period perturbations.
dcargs = array([5.0974222e0, -7.8604195454652e2, 3.9584962e0, -5.7533848094674e2, 1.6338070e0, -1.1506769618935e3, 2.5487111e0, -3.9302097727326e2, 4.9255514e0, -5.8849265665348e2, 1.3363463e0, -5.5076098609303e2, 1.6072053e0, -5.2237501616674e2, 1.3629480e0, -1.1790629318198e3, 5.5657014e0, -1.0977134971135e3, 5.0708205e0, -1.5774000881978e2, 3.9318944e0, 5.2963464780000e1, 4.8989497e0, 3.9809289073258e1, 1.3097446e0, 7.7540959633708e1, 3.5147141e0, 7.9618578146517e1, 3.5413158e0, -5.4868336758022e2])
dcargs = reshape(dcargs, (15, 2))
#Amplitudes ccamps(n,k) of the short-period perturbations.
ccamps = array([-2.279594e-5, 1.407414e-5, 8.273188e-6, 1.340565e-5, -2.490817e-7, -3.494537e-5, 2.860401e-7, 1.289448e-7, 1.627237e-5, -1.823138e-7, 6.593466e-7, 1.322572e-5, 9.258695e-6, -4.674248e-7, -3.646275e-7, 1.140767e-5, -2.049792e-5, -4.747930e-6, -2.638763e-6, -1.245408e-7, 9.516893e-6, -2.748894e-6, -1.319381e-6, -4.549908e-6, -1.864821e-7, 7.310990e-6, -1.924710e-6, -8.772849e-7, -3.334143e-6, -1.745256e-7, -2.603449e-6, 7.359472e-6, 3.168357e-6, 1.119056e-6, -1.655307e-7, -3.228859e-6, 1.308997e-7, 1.013137e-7, 2.403899e-6, -3.736225e-7, 3.442177e-7, 2.671323e-6, 1.832858e-6, -2.394688e-7, -3.478444e-7, 8.702406e-6, -8.421214e-6, -1.372341e-6, -1.455234e-6, -4.998479e-8, -1.488378e-6, -1.251789e-5, 5.226868e-7, -2.049301e-7, 0.e0, -8.043059e-6, -2.991300e-6, 1.473654e-7, -3.154542e-7, 0.e0, 3.699128e-6, -3.316126e-6, 2.901257e-7, 3.407826e-7, 0.e0, 2.550120e-6, -1.241123e-6, 9.901116e-8, 2.210482e-7, 0.e0, -6.351059e-7, 2.341650e-6, 1.061492e-6, 2.878231e-7, 0.e0])
ccamps = reshape(ccamps, (15, 5))
#Constants csec3 and ccsec(n,k) of the secular perturbations in longitude.
ccsec3 = -7.757020e-8
ccsec = array([1.289600e-6, 5.550147e-1, 2.076942e00, 3.102810e-5, 4.035027e00, 3.525565e-1, 9.124190e-6, 9.990265e-1, 2.622706e00, 9.793240e-7, 5.508259e00, 1.559103e01])
ccsec = reshape(ccsec, (4, 3))
#Sidereal rates.
dcsld = 1.990987e-7 #sidereal rate in longitude
ccsgd = 1.990969e-7 #sidereal rate in mean anomaly
#Constants used in the calculation of the lunar contribution.
cckm = 3.122140e-5
ccmld = 2.661699e-6
ccfdi = 2.399485e-7
#Constants dcargm(i,k) of the arguments of the perturbations of the motion
# of the moon.
dcargm = array([5.1679830e0, 8.3286911095275e3, 5.4913150e0, -7.2140632838100e3, 5.9598530e0, 1.5542754389685e4])
dcargm = reshape(dcargm, (3, 2))
#Amplitudes ccampm(n,k) of the perturbations of the moon.
ccampm = array([1.097594e-1, 2.896773e-7, 5.450474e-2, 1.438491e-7, -2.223581e-2, 5.083103e-8, 1.002548e-2, -2.291823e-8, 1.148966e-2, 5.658888e-8, 8.249439e-3, 4.063015e-8])
ccampm = reshape(ccampm, (3, 4))
#ccpamv(k)=a*m*dl,dt (planets), dc1mme=1-mass(earth+moon)
ccpamv = array([8.326827e-11, 1.843484e-11, 1.988712e-12, 1.881276e-12])
dc1mme = 0.99999696e0
#Time arguments.
dt = (dje - dcto) / dcjul
tvec = array([1e0, dt, dt * dt])
#Values of all elements for the instant(aneous?) dje.
temp = (transpose(dot(transpose(tvec), transpose(dcfel)))) % dc2pi
dml = temp[0]
forbel = temp[1:8]
g = forbel[0] #old fortran equivalence
deps = (tvec * dceps).sum() % dc2pi
sorbel = (transpose(dot(transpose(tvec), transpose(ccsel)))) % dc2pi
e = sorbel[0] #old fortran equivalence
#Secular perturbations in longitude.
dummy = cos(2.0)
sn = sin((transpose(dot(transpose(tvec[0:2]), transpose(ccsec[:,1:3])))) % cc2pi)
#Periodic perturbations of the emb (earth-moon barycenter).
pertl = (ccsec[:,0] * sn).sum() + dt * ccsec3 * sn[2]
pertld = 0.0
pertr = 0.0
pertrd = 0.0
for k in range(0, 15):
a = (dcargs[k,0] + dt * dcargs[k,1]) % dc2pi
cosa = cos(a)
sina = sin(a)
pertl = pertl + ccamps[k,0] * cosa + ccamps[k,1] * sina
pertr = pertr + ccamps[k,2] * cosa + ccamps[k,3] * sina
if k < 11:
pertld = pertld + (ccamps[k,1] * cosa - ccamps[k,0] * sina) * ccamps[k,4]
pertrd = pertrd + (ccamps[k,3] * cosa - ccamps[k,2] * sina) * ccamps[k,4]
#Elliptic part of the motion of the emb.
phi = (e * e / 4e0) * (((8e0 / e) - e) * sin(g) + 5 * sin(2 * g) + (13 / 3e0) * e * sin(3 * g))
f = g + phi
sinf = sin(f)
cosf = cos(f)
dpsi = (dc1 - e * e) / (dc1 + e * cosf)
phid = 2 * e * ccsgd * ((1 + 1.5 * e * e) * cosf + e * (1.25 - 0.5 * sinf * sinf))
psid = ccsgd * e * sinf / sqrt(dc1 - e * e)
#Perturbed heliocentric motion of the emb.
d1pdro = dc1 + pertr
drd = d1pdro * (psid + dpsi * pertrd)
drld = d1pdro * dpsi * (dcsld + phid + pertld)
dtl = (dml + phi + pertl) % dc2pi
dsinls = sin(dtl)
dcosls = cos(dtl)
dxhd = drd * dcosls - drld * dsinls
dyhd = drd * dsinls + drld * dcosls
#Influence of eccentricity, evection and variation on the geocentric
# motion of the moon.
pertl = 0.0
pertld = 0.0
pertp = 0.0
pertpd = 0.0
for k in range(0, 3):
a = (dcargm[k,0] + dt * dcargm[k,1]) % dc2pi
sina = sin(a)
cosa = cos(a)
pertl = pertl + ccampm[k,0] * sina
pertld = pertld + ccampm[k,1] * cosa
pertp = pertp + ccampm[k,2] * cosa
pertpd = pertpd - ccampm[k,3] * sina
#Heliocentric motion of the earth.
tl = forbel[1] + pertl
sinlm = sin(tl)
coslm = cos(tl)
sigma = cckm / (1.0 + pertp)
a = sigma * (ccmld + pertld)
b = sigma * pertpd
dxhd = dxhd + a * sinlm + b * coslm
dyhd = dyhd - a * coslm + b * sinlm
dzhd = -sigma * ccfdi * cos(forbel[2])
#Barycentric motion of the earth.
dxbd = dxhd * dc1mme
dybd = dyhd * dc1mme
dzbd = dzhd * dc1mme
for k in range(0, 4):
plon = forbel[k + 3]
pomg = sorbel[k + 1]
pecc = sorbel[k + 9]
tl = (plon + 2.0 * pecc * sin(plon - pomg)) % cc2pi
dxbd = dxbd + ccpamv[k] * (sin(tl) + pecc * sin(pomg))
dybd = dybd - ccpamv[k] * (cos(tl) + pecc * cos(pomg))
dzbd = dzbd - ccpamv[k] * sorbel[k + 13] * cos(plon - sorbel[k + 5])
#Transition to mean equator of date.
dcosep = cos(deps)
dsinep = sin(deps)
dyahd = dcosep * dyhd - dsinep * dzhd
dzahd = dsinep * dyhd + dcosep * dzhd
dyabd = dcosep * dybd - dsinep * dzbd
dzabd = dsinep * dybd + dcosep * dzbd
#Epoch of mean equinox (deq) of zero implies that we should use
# Julian ephemeris date (dje) as epoch of mean equinox.
if deq == 0:
dvelh = au * (array([dxhd, dyahd, dzahd]))
dvelb = au * (array([dxbd, dyabd, dzabd]))
return (dvelh,dvelb)
#General precession from epoch dje to deq.
deqdat = (dje - dcto - dcbes) / dctrop + dc1900
prema = premat(deqdat, deq, fk4=True)
dvelh = au * (transpose(dot(transpose(prema), transpose(array([dxhd, dyahd, dzahd])))))
dvelb = au * (transpose(dot(transpose(prema), transpose(array([dxbd, dyabd, dzabd])))))
return (dvelh, dvelb)
[docs]def bprecess(ra0, dec0, mu_radec=None, parallax=None, rad_vel=None, epoch=None):
"""
NAME:
BPRECESS
PURPOSE:
Precess positions from J2000.0 (FK5) to B1950.0 (FK4)
EXPLANATION:
Calculates the mean place of a star at B1950.0 on the FK4 system from
the mean place at J2000.0 on the FK5 system.
CALLING SEQUENCE:
bprecess, ra, dec, ra_1950, dec_1950, [ MU_RADEC = , PARALLAX =
RAD_VEL =, EPOCH = ]
INPUTS:
RA,DEC - Input J2000 right ascension and declination in *degrees*.
Scalar or N element vector
OUTPUTS:
RA_1950, DEC_1950 - The corresponding B1950 right ascension and
declination in *degrees*. Same number of elements as
RA,DEC but always double precision.
OPTIONAL INPUT-OUTPUT KEYWORDS
MU_RADEC - 2xN element double precision vector containing the proper
motion in seconds of arc per tropical *century* in right
ascension and declination.
PARALLAX - N_element vector giving stellar parallax (seconds of arc)
RAD_VEL - N_element vector giving radial velocity in km/s
The values of MU_RADEC, PARALLAX, and RADVEL will all be modified
upon output to contain the values of these quantities in the
B1950 system. The parallax and radial velocity will have a very
minor influence on the B1950 position.
EPOCH - scalar giving epoch of original observations, default 2000.0d
This keyword value is only used if the MU_RADEC keyword is not set.
NOTES:
The algorithm is taken from the Explanatory Supplement to the
Astronomical Almanac 1992, page 186.
Also see Aoki et al (1983), A&A, 128,263
BPRECESS distinguishes between the following two cases:
(1) The proper motion is known and non-zero
(2) the proper motion is unknown or known to be exactly zero (i.e.
extragalactic radio sources). In this case, the reverse of
the algorithm in Appendix 2 of Aoki et al. (1983) is used to
ensure that the output proper motion is exactly zero. Better
precision can be achieved in this case by inputting the EPOCH
of the original observations.
The error in using the IDL procedure PRECESS for converting between
B1950 and J1950 can be up to 12", mainly in right ascension. If
better accuracy than this is needed then BPRECESS should be used.
An unsystematic comparison of BPRECESS with the IPAC precession
routine (http://nedwww.ipac.caltech.edu/forms/calculator.html) always
gives differences less than 0.15".
EXAMPLE:
The SAO2000 catalogue gives the J2000 position and proper motion for
the star HD 119288. Find the B1950 position.
RA(2000) = 13h 42m 12.740s Dec(2000) = 8d 23' 17.69''
Mu(RA) = -.0257 s/yr Mu(Dec) = -.090 ''/yr
IDL> mu_radec = 100D* [ -15D*.0257, -0.090 ]
IDL> ra = ten(13, 42, 12.740)*15.D
IDL> dec = ten(8, 23, 17.69)
IDL> bprecess, ra, dec, ra1950, dec1950, mu_radec = mu_radec
IDL> print, adstring(ra1950, dec1950,2)
===> 13h 39m 44.526s +08d 38' 28.63"
REVISION HISTORY:
Written, W. Landsman October, 1992
Vectorized, W. Landsman February, 1994
Treat case where proper motion not known or exactly zero November 1994
Handling of arrays larger than 32767 Lars L. Christensen, march, 1995
Converted to IDL V5.0 W. Landsman September 1997
Fixed bug where A term not initialized for vector input
W. Landsman February 2000
Converted to python Sergey Koposov july 2010
"""
scal = True
if isinstance(ra0, ndarray):
ra = ra0
dec = dec0
n = ra.size
scal = False
else:
n = 1
ra = array([ra0])
dec = array([dec0])
if rad_vel is None:
rad_vel = zeros(n)
else:
if not isinstance(rad_vel, ndarray):
rad_vel = array([rad_vel],dtype=float)
if rad_vel.size != n:
raise Exception('ERROR - RAD_VEL keyword vector must be of the same length as RA and DEC')
if (mu_radec is not None):
if (array(mu_radec).size != 2 * n):
raise Exception('ERROR - MU_RADEC keyword (proper motion) be dimensioned (2,' + strtrim(n, 2) + ')')
mu_radec = mu_radec * 1.
if parallax is None:
parallax = zeros(n)
else:
if not isinstance(parallax, ndarray):
parallax = array([parallax],dtype=float)
if epoch is None:
epoch = 2000.0e0
radeg = 180.e0 / pi
sec_to_radian = lambda x : deg2rad(x/3600.)
m = array([array([+0.9999256795e0, -0.0111814828e0, -0.0048590040e0, -0.000551e0, -0.238560e0, +0.435730e0]),
array([+0.0111814828e0, +0.9999374849e0, -0.0000271557e0, +0.238509e0, -0.002667e0, -0.008541e0]),
array([+0.0048590039e0, -0.0000271771e0, +0.9999881946e0, -0.435614e0, +0.012254e0, +0.002117e0]),
array([-0.00000242389840e0, +0.00000002710544e0, +0.00000001177742e0, +0.99990432e0, -0.01118145e0, -0.00485852e0]),
array([-0.00000002710544e0, -0.00000242392702e0, +0.00000000006585e0, +0.01118145e0, +0.99991613e0, -0.00002716e0]),
array([-0.00000001177742e0, +0.00000000006585e0, -0.00000242404995e0, +0.00485852e0, -0.00002717e0, +0.99996684e0])])
a_dot = 1e-3 * array([1.244e0, -1.579e0, -0.660e0]) #in arc seconds per century
ra_rad = deg2rad(ra)
dec_rad = deg2rad(dec)
cosra = cos(ra_rad)
sinra = sin(ra_rad)
cosdec = cos(dec_rad)
sindec = sin(dec_rad)
dec_1950 = dec * 0.
ra_1950 = ra * 0.
for i in range(n):
# Following statement moved inside loop in Feb 2000.
a = 1e-6 * array([-1.62557e0, -0.31919e0, -0.13843e0]) #in radians
r0 = array([cosra[i] * cosdec[i], sinra[i] * cosdec[i], sindec[i]])
if (mu_radec is not None):
mu_a = mu_radec[i,0]
mu_d = mu_radec[i,1]
r0_dot = array([-mu_a * sinra[i] * cosdec[i] - mu_d * cosra[i] * sindec[i], mu_a * cosra[i] * cosdec[i] - mu_d * sinra[i] * sindec[i], mu_d * cosdec[i]]) + 21.095e0 * rad_vel[i] * parallax[i] * r0
else:
r0_dot = array([0.0e0, 0.0e0, 0.0e0])
r_0 = concatenate((r0, r0_dot))
r_1 = transpose(dot(transpose(m), transpose(r_0)))
# Include the effects of the E-terms of aberration to form r and r_dot.
r1 = r_1[0:3]
r1_dot = r_1[3:6]
if mu_radec is None:
r1 = r1 + sec_to_radian ( r1_dot * (epoch - 1950.0e0) / 100. )
a = a + sec_to_radian ( a_dot * (epoch - 1950.0e0) / 100. )
x1 = r_1[0] ; y1 = r_1[1] ; z1 = r_1[2]
rmag = sqrt(x1 ** 2 + y1 ** 2 + z1 ** 2)
s1 = r1 / rmag ; s1_dot = r1_dot / rmag
s = s1
for j in arange(0, 3):
r = s1 + a - ((s * a).sum()) * s
s = r / rmag
x = r[0] ; y = r[1] ; z = r[2]
r2 = x ** 2 + y ** 2 + z ** 2
rmag = sqrt(r2)
if mu_radec is not None:
r_dot = s1_dot + a_dot - ((s * a_dot).sum()) * s
x_dot = r_dot[0] ; y_dot = r_dot[1] ; z_dot = r_dot[2]
mu_radec[i,0] = (x * y_dot - y * x_dot) / (x ** 2 + y ** 2)
mu_radec[i,1] = (z_dot * (x ** 2 + y ** 2) - z * (x * x_dot + y * y_dot)) / (r2 * sqrt(x ** 2 + y ** 2))
dec_1950[i] = arcsin(z / rmag)
ra_1950[i] = arctan2(y, x)
if parallax[i] > 0.:
rad_vel[i] = (x * x_dot + y * y_dot + z * z_dot) / (21.095 * parallax[i] * rmag)
parallax[i] = parallax[i] / rmag
neg = (ra_1950 < 0)
if neg.any() > 0:
ra_1950[neg] = ra_1950[neg] + 2.e0 * pi
ra_1950 = rad2deg(ra_1950)
dec_1950 = rad2deg(dec_1950)
# Make output scalar if input was scalar
if scal:
return ra_1950[0],dec_1950[0]
else:
return ra_1950, dec_1950
[docs]def convolve(image, psf, ft_psf=None, ft_image=None, no_ft=None, correlate=None, auto_correlation=None):
"""
NAME:
CONVOLVE
PURPOSE:
Convolution of an image with a Point Spread Function (PSF)
EXPLANATION:
The default is to compute the convolution using a product of
Fourier transforms (for speed).
CALLING SEQUENCE:
imconv = convolve( image1, psf, FT_PSF = psf_FT )
or:
correl = convolve( image1, image2, /CORREL )
or:
correl = convolve( image, /AUTO )
INPUTS:
image = 2-D array (matrix) to be convolved with psf
psf = the Point Spread Function, (size < or = to size of image).
OPTIONAL INPUT KEYWORDS:
FT_PSF = passes out/in the Fourier transform of the PSF,
(so that it can be re-used the next time function is called).
FT_IMAGE = passes out/in the Fourier transform of image.
/CORRELATE uses the conjugate of the Fourier transform of PSF,
to compute the cross-correlation of image and PSF,
(equivalent to IDL function convol() with NO rotation of PSF)
/AUTO_CORR computes the auto-correlation function of image using FFT.
/NO_FT overrides the use of FFT, using IDL function convol() instead.
(then PSF is rotated by 180 degrees to give same result)
METHOD:
When using FFT, PSF is centered & expanded to size of image.
HISTORY:
written, Frank Varosi, NASA/GSFC 1992.
Appropriate precision type for result depending on input image
Markus Hundertmark February 2006
Fix the bug causing the recomputation of FFT(psf) and/or FFT(image)
Sergey Koposov December 2006
"""
from numpy.fft import fft2, ifft2
n_params = 2
psf_ft = ft_psf
imft = ft_image
noft = no_ft
auto = auto_correlation
sp = array(shape(psf_ft))
sif = array(shape(imft))
sim = array(shape(image))
sc = sim / 2
npix = array(image, copy=0).size
if image.ndim!=2 or noft!=None:
if (auto is not None):
message("auto-correlation only for images with FFT", inf=True)
return image
else:
if (correlate is not None):
return convol(image, psf)
else:
return convol(image, rotate(psf, 2))
if imft==None or (imft.ndim!=2) or imft.shape!=im.shape: #add the type check
imft = ifft2(image)
if (auto is not None):
return roll(roll(npix * real(fft2(imft * conjugate(imft))), sc[0], 0),sc[1],1)
if (ft_psf==None or ft_psf.ndim!=2 or ft_psf.shape!=image.shape or
ft_psf.dtype!=image.dtype):
sp = array(shape(psf))
loc = maximum((sc - sp / 2), 0) #center PSF in new array,
s = maximum((sp / 2 - sc), 0) #handle all cases: smaller or bigger
l = minimum((s + sim - 1), (sp - 1))
psf_ft = conjugate(image) * 0 #initialise with correct size+type according
#to logic of conj and set values to 0 (type of ft_psf is conserved)
psf_ft[loc[1]:loc[1]+l[1]-s[1]+1,loc[0]:loc[0]+l[0]-s[0]+1] = \
psf[s[1]:(l[1])+1,s[0]:(l[0])+1]
psf_ft = ifft2(psf_ft)
if (correlate is not None):
conv = npix * real(fft2(imft * conjugate(psf_ft)))
else:
conv = npix * real(fft2(imft * psf_ft))
sc = sc + (sim % 2) #shift correction for odd size images.
return roll(roll(conv, sc[0],0), sc[1],1)
def cv_coord(a,b,c,fr=None,to=None,degr=False):
import numpy
if degr:
degrad = numpy.deg2rad
raddeg = numpy.rad2deg
else:
degrad = lambda x: x
raddeg = lambda x: x
if fr=='sph':
cosa = numpy.cos(degrad(a))
sina = numpy.sin(degrad(a))
cosb = numpy.cos(degrad(b))
sinb = numpy.sin(degrad(b))
x=c*cosa*cosb
y=c*sina*cosb
z=c*sinb
elif fr=='rect':
x=a
y=b
z=c
elif fr is None:
raise Exception('You must specify the input coordinate system')
else:
raise Exception('Unknown input coordinate system')
if to=='rect':
return (x,y,z)
elif to=='sph':
ra = raddeg(numpy.arctan2(y,x))
dec = raddeg(numpy.arctan2(z,numpy.sqrt(x**2+y**2)))
rad = numpy.sqrt(x**2+y**2+z**2)
return (ra,dec,rad)
elif to is None:
raise Exception('You must specify the output coordinate system')
else:
raise Exception('Unknown output coordinate system')
[docs]def daycnv(xjd):
"""
NAME:
DAYCNV
PURPOSE:
Converts Julian dates to Gregorian calendar dates
CALLING SEQUENCE:
DAYCNV, XJD, YR, MN, DAY, HR
INPUTS:
XJD = Julian date, positive double precision scalar or vector
OUTPUTS:
YR = Year (Integer)
MN = Month (Integer)
DAY = Day (Integer)
HR = Hours and fractional hours (Real). If XJD is a vector,
then YR,MN,DAY and HR will be vectors of the same length.
EXAMPLE:
IDL> DAYCNV, 2440000.D, yr, mn, day, hr
yields yr = 1968, mn =5, day = 23, hr =12.
WARNING:
Be sure that the Julian date is specified as double precision to
maintain accuracy at the fractional hour level.
METHOD:
Uses the algorithm of Fliegel and Van Flandern (1968) as reported in
the "Explanatory Supplement to the Astronomical Almanac" (1992), p. 604
Works for all Gregorian calendar dates with XJD > 0, i.e., dates after
-4713 November 23.
REVISION HISTORY:
Converted to IDL from Yeoman's Comet Ephemeris Generator,
B. Pfarr, STX, 6/16/88
Converted to IDL V5.0 W. Landsman September 1997
"""
# Adjustment needed because Julian day starts at noon, calendar day at midnight
jd = array(xjd).astype(int) #Truncate to integral day
frac = array(xjd).astype(float) - jd + 0.5 #Fractional part of calendar day
after_noon = (frac >= 1.0)
if after_noon.any(): #Is it really the next calendar day?
if frac.ndim>0: # proper array
frac[after_noon] = frac[after_noon] - 1.0
jd[after_noon] = jd[after_noon] + 1
else: # scalar
frac = frac - 1.0
jd = jd + 1
hr = frac * 24.0
l = jd + 68569
n = 4 * l / 146097
l = l - (146097 * n + 3) / 4
yr = 4000 * (l + 1) / 1461001
l = l - 1461 * yr / 4 + 31 #1461 = 365.25 * 4
mn = 80 * l / 2447
day = l - 2447 * mn / 80
l = mn / 11
mn = mn + 2 - 12 * l
yr = 100 * (n - 49) + yr + l
return (yr, mn, day, hr)
[docs]def euler(ai, bi, select=1, fk4=False):
"""
NAME:
EULER
PURPOSE:
Transform between Galactic, celestial, and ecliptic coordinates.
EXPLANATION:
Use the procedure ASTRO to use this routine interactively
CALLING SEQUENCE:
AO, BO = EULER(AI, BI, [SELECT=1, FK4=False])
INPUTS:
AI - Input Longitude in DEGREES, scalar or vector. If only two
parameters are supplied, then AI and BI will be modified to
contain the output longitude and latitude.
BI - Input Latitude in DEGREES
OPTIONAL INPUT:
SELECT - Integer (1-6) specifying type of coordinate transformation.
SELECT From To | SELECT From To
1 RA-Dec (2000) Galactic | 4 Ecliptic RA-Dec
2 Galactic RA-DEC | 5 Ecliptic Galactic
3 RA-Dec Ecliptic | 6 Galactic Ecliptic
If not supplied as a parameter or keyword, then EULER will prompt for
the value of SELECT
Celestial coordinates (RA, Dec) should be given in equinox J2000
unless the /FK4 keyword is set.
OUTPUTS:
AO - Output Longitude in DEGREES
BO - Output Latitude in DEGREES
INPUT KEYWORD:
/FK4 - If this keyword is set and non-zero, then input and output
celestial and ecliptic coordinates should be given in equinox
B1950.
/SELECT - The coordinate conversion integer (1-6) may alternatively be
specified as a keyword
NOTES:
EULER was changed in December 1998 to use J2000 coordinates as the
default, ** and may be incompatible with earlier versions***.
REVISION HISTORY:
Written W. Landsman, February 1987
Adapted from Fortran by Daryl Yentis NRL
Converted to IDL V5.0 W. Landsman September 1997
Made J2000 the default, added /FK4 keyword W. Landsman December 1998
Add option to specify SELECT as a keyword W. Landsman March 2003
"""
import numpy
twopi = 2.0e0 * numpy.pi
fourpi = 4.0e0 * numpy.pi
# J2000 coordinate conversions are based on the following constants
# (see the Hipparcos explanatory supplement).
# eps = 23.4392911111d Obliquity of the ecliptic
# alphaG = 192.85948d Right Ascension of Galactic North Pole
# deltaG = 27.12825d Declination of Galactic North Pole
# lomega = 32.93192d Galactic longitude of celestial equator
# alphaE = 180.02322d Ecliptic longitude of Galactic North Pole
# deltaE = 29.811438523d Ecliptic latitude of Galactic North Pole
# Eomega = 6.3839743d Galactic longitude of ecliptic equator
if fk4:
equinox = '(B1950)'
psi = numpy.array ([0.57595865315e0, 4.9261918136e0, 0.00000000000e0, 0.0000000000e0, 0.11129056012e0, 4.7005372834e0])
stheta = numpy.array ([0.88781538514e0, -0.88781538514e0, 0.39788119938e0, -0.39788119938e0, 0.86766174755e0, -0.86766174755e0])
ctheta = numpy.array([0.46019978478e0, 0.46019978478e0, 0.91743694670e0, 0.91743694670e0, 0.49715499774e0, 0.49715499774e0])
phi = numpy.array([4.9261918136e0, 0.57595865315e0, 0.0000000000e0, 0.00000000000e0, 4.7005372834e0, 0.11129056012e0])
else:
equinox = '(J2000)'
psi = numpy.array([0.57477043300e0, 4.9368292465e0, 0.00000000000e0, 0.0000000000e0, 0.11142137093e0, 4.71279419371e0])
stheta = numpy.array([0.88998808748e0, -0.88998808748e0, 0.39777715593e0, -0.39777715593e0, 0.86766622025e0, -0.86766622025e0])
ctheta = numpy.array([0.45598377618e0, 0.45598377618e0, 0.91748206207e0, 0.91748206207e0, 0.49714719172e0, 0.49714719172e0])
phi = numpy.array([4.9368292465e0, 0.57477043300e0, 0.0000000000e0, 0.00000000000e0, 4.71279419371e0, 0.11142137093e0])
i = select - 1
a = numpy.deg2rad(ai) - phi[i]
b = numpy.deg2rad(bi)
sb = numpy.sin(b)
cb = numpy.cos(b)
cbsa = cb * numpy.sin(a)
b = -stheta[i] * cbsa + ctheta[i] * sb
bo = numpy.rad2deg(numpy.arcsin(numpy.minimum(b, 1.0)))
del b
a = numpy.arctan2(ctheta[i] * cbsa + stheta[i] * sb, cb * numpy.cos(a))
del cb, cbsa, sb
ao = numpy.rad2deg(((a + psi[i] + fourpi) % twopi) )
return (ao, bo)
[docs]def gal_uvw(distance=None, lsr=None, ra=None, dec=None, pmra=None, pmdec=None, vrad=None, plx=None):
"""
NAME:
GAL_UVW
PURPOSE:
Calculate the Galactic space velocity (U,V,W) of star
EXPLANATION:
Calculates the Galactic space velocity U, V, W of star given its
(1) coordinates, (2) proper motion, (3) distance (or parallax), and
(4) radial velocity.
CALLING SEQUENCE:
GAL_UVW [/LSR, RA=, DEC=, PMRA= ,PMDEC=, VRAD= , DISTANCE=
PLX= ]
OUTPUT PARAMETERS:
U - Velocity (km/s) positive toward the Galactic *anti*center
V - Velocity (km/s) positive in the direction of Galactic rotation
W - Velocity (km/s) positive toward the North Galactic Pole
REQUIRED INPUT KEYWORDS:
User must supply a position, proper motion,radial velocity and distance
(or parallax). Either scalars or vectors can be supplied.
(1) Position:
RA - Right Ascension in *Degrees*
Dec - Declination in *Degrees*
(2) Proper Motion
PMRA = Proper motion in RA in arc units (typically milli-arcseconds/yr)
PMDEC = Proper motion in Declination (typically mas/yr)
(3) Radial Velocity
VRAD = radial velocity in km/s
(4) Distance or Parallax
DISTANCE - distance in parsecs
or
PLX - parallax with same distance units as proper motion measurements
typically milliarcseconds (mas)
OPTIONAL INPUT KEYWORD:
/LSR - If this keyword is set, then the output velocities will be
corrected for the solar motion (U,V,W)_Sun = (-10.00,+5.25,+7.17)
(Dehnen & Binney, 1998) to the local standard of rest
EXAMPLE:
(1) Compute the U,V,W coordinates for the halo star HD 6755.
Use values from Hipparcos catalog, and correct to the LSR
ra = ten(1,9,42.3)*15. & dec = ten(61,32,49.5)
pmra = 627.89 & pmdec = 77.84 ;mas/yr
dis = 144 & vrad = -321.4
gal_uvw,u,v,w,ra=ra,dec=dec,pmra=pmra,pmdec=pmdec,vrad=vrad,dis=dis,/lsr
===> u=154 v = -493 w = 97 ;km/s
(2) Use the Hipparcos Input and Output Catalog IDL databases (see
http://idlastro.gsfc.nasa.gov/ftp/zdbase/) to obtain space velocities
for all stars within 10 pc with radial velocities > 10 km/s
dbopen,'hipparcos,hic' ;Need Hipparcos output and input catalogs
list = dbfind('plx>100,vrad>10') ;Plx > 100 mas, Vrad > 10 km/s
dbext,list,'pmra,pmdec,vrad,ra,dec,plx',pmra,pmdec,vrad,ra,dec,plx
ra = ra*15. ;Need right ascension in degrees
GAL_UVW,u,v,w,ra=ra,dec=dec,pmra=pmra,pmdec=pmdec,vrad=vrad,plx = plx
forprint,u,v,w ;Display results
METHOD:
Follows the general outline of Johnson & Soderblom (1987, AJ, 93,864)
except that U is positive outward toward the Galactic *anti*center, and
the J2000 transformation matrix to Galactic coordinates is taken from
the introduction to the Hipparcos catalog.
REVISION HISTORY:
Written, W. Landsman December 2000
fix the bug occuring if the input arrays are longer than 32767
and update the Sun velocity Sergey Koposov June 2008
vectorization of the loop -- performance on large arrays
is now 10 times higher Sergey Koposov December 2008
"""
import numpy
n_params = 3
if n_params == 0:
print 'Syntax - GAL_UVW, U, V, W, [/LSR, RA=, DEC=, PMRA= ,PMDEC=, VRAD='
print ' Distance=, PLX='
print ' U, V, W - output Galactic space velocities (km/s)'
return None
if ra is None or dec is None:
raise Exception('ERROR - The RA, Dec (J2000) position keywords must be supplied (degrees)')
if plx is None and distance is None:
raise Exception('ERROR - Either a parallax or distance must be specified')
if distance is not None:
if numpy.any(distance==0):
raise Exception('ERROR - All distances must be > 0')
plx = 1e3 / distance #Parallax in milli-arcseconds
if plx is not None and numpy.any(plx==0):
raise Exception('ERROR - Parallaxes must be > 0')
cosd = numpy.cos(numpy.deg2rad(dec))
sind = numpy.sin(numpy.deg2rad(dec))
cosa = numpy.cos(numpy.deg2rad(ra))
sina = numpy.sin(numpy.deg2rad(ra))
k = 4.74047 #Equivalent of 1 A.U/yr in km/s
a_g = numpy.array([[0.0548755604, +0.4941094279, -0.8676661490],
[0.8734370902, -0.4448296300, -0.1980763734],
[0.4838350155, 0.7469822445, +0.4559837762]])
vec1 = vrad
vec2 = k * pmra / plx
vec3 = k * pmdec / plx
u = (a_g[0,0] * cosa * cosd + a_g[1,0] * sina * cosd + a_g[2,0] * sind) * vec1 + (-a_g[0,0] * sina + a_g[1,0] * cosa) * vec2 + (-a_g[0,0] * cosa * sind - a_g[1,0] * sina * sind + a_g[2,0] * cosd) * vec3
v = (a_g[0,1] * cosa * cosd + a_g[1,1] * sina * cosd + a_g[2,1] * sind) * vec1 + (-a_g[0,1] * sina + a_g[1,1] * cosa) * vec2 + (-a_g[0,1] * cosa * sind - a_g[1,1] * sina * sind + a_g[2,1] * cosd) * vec3
w = (a_g[0,2] * cosa * cosd + a_g[1,2] * sina * cosd + a_g[2,2] * sind) * vec1 + (-a_g[0,2] * sina + a_g[1,2] * cosa) * vec2 + (-a_g[0,2] * cosa * sind - a_g[1,2] * sina * sind + a_g[2,2] * cosd) * vec3
lsr_vel = numpy.array([-10.00, 5.25, 7.17])
if (lsr is not None):
u = u + lsr_vel[0]
v = v + lsr_vel[1]
w = w + lsr_vel[2]
return (u,v,w)
#def helcorr(obs_long, obs_lat, obs_alt, ra2000, dec2000, jd, debug=False):
# """
# calculates heliocentric Julian date, baricentric and heliocentric radial
# velocity corrections from:
#
# INPUT:
# <OBSLON> Longitude of observatory (degrees, western direction is positive)
# <OBSLAT> Latitude of observatory (degrees)
# <OBSALT> Altitude of observatory (meters)
# <RA2000> Right ascension of object for epoch 2000.0 (hours)
# <DE2000> Declination of object for epoch 2000.0 (degrees)
# <JD> Julian date for the middle of exposure
# [DEBUG=] set keyword to get additional results for debugging
#
# OUTPUT:
# <CORRECTION> baricentric correction - correction for rotation of earth,
# rotation of earth center about the eart-moon barycenter, eart-moon
# barycenter about the center of the Sun.
# <HJD> Heliocentric Julian date for middle of exposure
#
# Algorithms used are taken from the IRAF task noao.astutils.rvcorrect
# and some procedures of the IDL Astrolib are used as well.
# Accuracy is about 0.5 seconds in time and about 1 m/s in velocity.
#
# History:
# written by Peter Mittermayer, Nov 8,2003
# 2005-January-13 Kudryavtsev Made more accurate calculation of the sideral time.
# Conformity with MIDAS compute/barycorr is checked.
# 2005-June-20 Kochukhov Included precession of RA2000 and DEC2000 to current epoch
# """
#
# _radeg = 180.0 / pi
#
#
# #covert JD to Gregorian calendar date
# xjd = array(2400000.).astype(float) + jd
# year,month,day,ut=daycnv(xjd)
#
# #current epoch
# epoch = year + month / 12. + day / 365.
#
# #precess ra2000 and dec2000 to current epoch
# ra,dec=precess(ra2000*15., dec2000, 2000.0, epoch)
# #calculate heliocentric julian date
# hjd = array(helio_jd(jd, ra, dec)).astype(float)
#
# #DIURNAL VELOCITY (see IRAF task noao.astutil.rvcorrect)
# #convert geodetic latitude into geocentric latitude to correct
# #for rotation of earth
# dlat = -(11. * 60. + 32.743) * sin(2 * obs_lat / _radeg) + 1.1633 * sin(4 * obs_lat / _radeg) - 0.0026 * sin(6 * obs_lat / _radeg)
# lat = obs_lat + dlat / 3600
#
# #calculate distance of observer from earth center
# r = 6378160.0 * (0.998327073 + 0.001676438 * cos(2 * lat / _radeg) - 0.00000351 * cos(4 * lat / _radeg) + 0.000000008 * cos(6 * lat / _radeg)) + obs_alt
#
# #calculate rotational velocity (perpendicular to the radius vector) in km/s
# #23.934469591229 is the siderial day in hours for 1986
# v = 2. * pi * (r / 1000.) / (23.934469591229 * 3600.)
#
# #calculating local mean siderial time (see astronomical almanach)
# tu = (jd - 51545.0) / 36525
# gmst = 6.697374558 + ut + (236.555367908 * (jd - 51545.0) + 0.093104 * tu ** 2 - 6.2e-6 * tu ** 3) / 3600
# lmst = (gmst - obs_long / 15) % 24
#
# #projection of rotational velocity along the line of sight
# vdiurnal = v * cos(lat / _radeg) * cos(dec / _radeg) * sin((ra - lmst * 15) / _radeg)
#
# #BARICENTRIC and HELIOCENTRIC VELOCITIES
# vh,vb=baryvel(xjd, 0)
#
# #project to line of sight
# vbar = vb[0] * cos(dec / _radeg) * cos(ra / _radeg) + vb[1] * cos(dec / _radeg) * sin(ra / _radeg) + vb[2] * sin(dec / _radeg)
# vhel = vh[0] * cos(dec / _radeg) * cos(ra / _radeg) + vh[1] * cos(dec / _radeg) * sin(ra / _radeg) + vh[2] * sin(dec / _radeg)
#
# corr = (vdiurnal + vbar) #using baricentric velocity for correction
#
# if debug:
# print ''
# print '----- HELCORR.PRO - DEBUG INFO - START ----'
# print '(obs_long,obs_lat,obs_alt) Observatory coordinates [deg,m]: ', obs_long, obs_lat, obs_alt
# print '(ra,dec) Object coordinates (for epoch 2000.0) [deg]: ', ra, dec
# print '(ut) Universal time (middle of exposure) [hrs]: ', ut#, format='(A,F20.12)'
# print '(jd) Julian date (middle of exposure) (JD-2400000): ', jd#, format='(A,F20.12)'
# print '(hjd) Heliocentric Julian date (middle of exposure) (HJD-2400000): ', hjd#, format='(A,F20.12)'
# print '(gmst) Greenwich mean siderial time [hrs]: ', gmst % 24
# print '(lmst) Local mean siderial time [hrs]: ', lmst
# print '(dlat) Latitude correction [deg]: ', dlat
# print '(lat) Geocentric latitude of observer [deg]: ', lat
# print '(r) Distance of observer from center of earth [m]: ', r
# print '(v) Rotational velocity of earth at the position of the observer [km/s]: ', v
# print '(vdiurnal) Projected earth rotation and earth-moon revolution [km/s]: ', vdiurnal
# print '(vbar) Baricentric velocity [km/s]: ', vbar
# print '(vhel) Heliocentric velocity [km/s]: ', vhel
# print '(corr) Vdiurnal+vbar [km/s]: ', corr#, format='(A,F12.9)'
# print '----- HELCORR.PRO - DEBUG INFO - END -----'
# print ''
#
#
# return (corr, hjd)
[docs]def helio_jd(date, ra, dec, b1950=False, time_diff=False):
"""
NAME:
HELIO_JD
PURPOSE:
Convert geocentric (reduced) Julian date to heliocentric Julian date
EXPLANATION:
This procedure correct for the extra light travel time between the Earth
and the Sun.
An online calculator for this quantity is available at
http://www.physics.sfasu.edu/astro/javascript/hjd.html
CALLING SEQUENCE:
jdhelio = HELIO_JD( date, ra, dec, /B1950, /TIME_DIFF)
INPUTS
date - reduced Julian date (= JD - 2400000), scalar or vector, MUST
be double precision
ra,dec - scalars giving right ascension and declination in DEGREES
Equinox is J2000 unless the /B1950 keyword is set
OUTPUTS:
jdhelio - heliocentric reduced Julian date. If /TIME_DIFF is set, then
HELIO_JD() instead returns the time difference in seconds
between the geocentric and heliocentric Julian date.
OPTIONAL INPUT KEYWORDS
/B1950 - if set, then input coordinates are assumed to be in equinox
B1950 coordinates.
/TIME_DIFF - if set, then HELIO_JD() returns the time difference
(heliocentric JD - geocentric JD ) in seconds
EXAMPLE:
What is the heliocentric Julian date of an observation of V402 Cygni
(J2000: RA = 20 9 7.8, Dec = 37 09 07) taken June 15, 1973 at 11:40 UT?
IDL> juldate, [1973,6,15,11,40], jd ;Get geocentric Julian date
IDL> hjd = helio_jd( jd, ten(20,9,7.8)*15., ten(37,9,7) )
==> hjd = 41848.9881
Wayne Warren (Raytheon ITSS) has compared the results of HELIO_JD with the
FORTRAN subroutines in the STARLINK SLALIB library (see
http://star-www.rl.ac.uk/).
Time Diff (sec)
Date RA(2000) Dec(2000) STARLINK IDL
1999-10-29T00:00:00.0 21 08 25. -67 22 00. -59.0 -59.0
1999-10-29T00:00:00.0 02 56 33.4 +00 26 55. 474.1 474.1
1940-12-11T06:55:00.0 07 34 41.9 -00 30 42. 366.3 370.2
1992-02-29T03:15:56.2 12 56 27.4 +42 10 17. 350.8 350.9
2000-03-01T10:26:31.8 14 28 36.7 -20 42 11. 243.7 243.7
2100-02-26T09:18:24.2 08 26 51.7 +85 47 28. 104.0 108.8
PROCEDURES CALLED:
bprecess, xyz
REVISION HISTORY:
Algorithm from the book Astronomical Photometry by Henden, p. 114
Written, W. Landsman STX June, 1989
Make J2000 default equinox, add B1950, /TIME_DIFF keywords, compute
variation of the obliquity W. Landsman November 1999
Converted to python Sergey Koposov July 2010
"""
#Because XYZ uses default B1950 coordinates, we'll convert everything to B1950
if not b1950:
ra1, dec1 = bprecess(ra, dec)
else:
ra1 = ra
dec1 = dec
delta_t = (array(date).astype(float) - 33282.42345905e0) / 36525.0e0
epsilon_sec = poly1d([44.836e0, -46.8495, -0.00429, 0.00181][::-1])(delta_t)
epsilon = deg2rad(23.433333e0 + epsilon_sec / 3600.0e0)
ra1 = deg2rad(ra1)
dec1 = deg2rad(dec1)
x, y, z, tmp, tmp, tmp = xyz(date)
#Find extra distance light must travel in AU, multiply by 1.49598e13 cm/AU,
#and divide by the speed of light, and multiply by 86400 second/year
time = -499.00522e0 * (cos(dec1) * cos(ra1) * x + (tan(epsilon) * sin(dec1) + cos(dec1) * sin(ra1)) * y)
if time_diff:
return time
else:
return array(date).astype(float) + time / 86400.0e0
[docs]def mwrfits(filename, arraylist, namelist=None, header=None):
"""
Writes the list of numpy.arrays arraylist as a FITS table filename
using namelist as list of names.
Arraylist can be dictionary with arrays as values and names as keys.
Also Arraylist can be numpy-record-array.
Example:
mwrfits('/tmp/xx.fits',[arr,arr1],['X','Y'])
Or :
mwrfits('test.fits',{'X':arr,'Y':arr1})
Or:
data = numpy.zeros((4,),dtype=[('run','i4'),('rerun','f8'),('zz','b')])
mwfits('test1.fits',data)
Keep in mind that when you used a dictionary, the order of columns in the
fits file is not guaranteed
"""
import numpy, pyfits, types, itertools
tmplist=[]
if isinstance(arraylist,numpy.ndarray):
if arraylist.dtype.type is numpy.void:
iter=itertools.izip(arraylist.dtype.names, itertools.imap (arraylist.__getitem__ , arraylist.dtype.names))
else:
if isinstance(arraylist,types.ListType):
iter= zip(namelist, arraylist)
elif isinstance(arraylist,types.DictType):
iter= arraylist.iteritems()
for name, arr in iter:
if arr.dtype.type==numpy.int8:
format='I'
elif arr.dtype.type==numpy.int16:
format='I'
elif arr.dtype.type==numpy.int32:
format='J'
elif arr.dtype.type==numpy.int64:
format='K'
elif arr.dtype.type==numpy.float32:
format='E'
elif arr.dtype.type==numpy.float64:
format='D'
elif arr.dtype.type==numpy.string_:
format='%dA'%arr.dtype.itemsize
else:
raise Exception("Oops unknown datatype %s"%arr.dtype)
tmplist.append(pyfits.Column(name=name, array=arr, format=format))
hdu = pyfits.new_table(tmplist)
hdu.writeto(filename,clobber=True)
[docs]def precess(ra0, dec0, equinox1, equinox2, doprint=False, fk4=False, radian=False):
"""
NAME:
PRECESS
PURPOSE:
Precess coordinates from EQUINOX1 to EQUINOX2.
EXPLANATION:
For interactive display, one can use the procedure ASTRO which calls
PRECESS or use the /PRINT keyword. The default (RA,DEC) system is
FK5 based on epoch J2000.0 but FK4 based on B1950.0 is available via
the /FK4 keyword.
Use BPRECESS and JPRECESS to convert between FK4 and FK5 systems
CALLING SEQUENCE:
PRECESS, ra, dec, [ equinox1, equinox2, /PRINT, /FK4, /RADIAN ]
INPUT - OUTPUT:
RA - Input right ascension (scalar or vector) in DEGREES, unless the
/RADIAN keyword is set
DEC - Input declination in DEGREES (scalar or vector), unless the
/RADIAN keyword is set
The input RA and DEC are modified by PRECESS to give the
values after precession.
OPTIONAL INPUTS:
EQUINOX1 - Original equinox of coordinates, numeric scalar. If
omitted, then PRECESS will query for EQUINOX1 and EQUINOX2.
EQUINOX2 - Equinox of precessed coordinates.
OPTIONAL INPUT KEYWORDS:
/PRINT - If this keyword is set and non-zero, then the precessed
coordinates are displayed at the terminal. Cannot be used
with the /RADIAN keyword
/FK4 - If this keyword is set and non-zero, the FK4 (B1950.0) system
will be used otherwise FK5 (J2000.0) will be used instead.
/RADIAN - If this keyword is set and non-zero, then the input and
output RA and DEC vectors are in radians rather than degrees
RESTRICTIONS:
Accuracy of precession decreases for declination values near 90
degrees. PRECESS should not be used more than 2.5 centuries from
2000 on the FK5 system (1950.0 on the FK4 system).
EXAMPLES:
(1) The Pole Star has J2000.0 coordinates (2h, 31m, 46.3s,
89d 15' 50.6"); compute its coordinates at J1985.0
IDL> precess, ten(2,31,46.3)*15, ten(89,15,50.6), 2000, 1985, /PRINT
====> 2h 16m 22.73s, 89d 11' 47.3"
(2) Precess the B1950 coordinates of Eps Ind (RA = 21h 59m,33.053s,
DEC = (-56d, 59', 33.053") to equinox B1975.
IDL> ra = ten(21, 59, 33.053)*15
IDL> dec = ten(-56, 59, 33.053)
IDL> precess, ra, dec ,1950, 1975, /fk4
PROCEDURE:
Algorithm from Computational Spherical Astronomy by Taff (1983),
p. 24. (FK4). FK5 constants from "Astronomical Almanac Explanatory
Supplement 1992, page 104 Table 3.211.1.
PROCEDURE CALLED:
Function PREMAT - computes precession matrix
REVISION HISTORY
Written, Wayne Landsman, STI Corporation August 1986
Correct negative output RA values February 1989
Added /PRINT keyword W. Landsman November, 1991
Provided FK5 (J2000.0) I. Freedman January 1994
Precession Matrix computation now in PREMAT W. Landsman June 1994
Added /RADIAN keyword W. Landsman June 1997
Converted to IDL V5.0 W. Landsman September 1997
Correct negative output RA values when /RADIAN used March 1999
Work for arrays, not just vectors W. Landsman September 2003
Convert to Python Sergey Koposov July 2010
"""
scal = True
if isinstance(ra0, ndarray):
ra = ra0.copy()
dec = dec0.copy()
scal = False
else:
ra=array([ra0])
dec=array([dec0])
npts = ra.size
if not radian:
ra_rad = deg2rad(ra) #Convert to double precision if not already
dec_rad = deg2rad(dec)
else:
ra_rad = ra
dec_rad = dec
a = cos(dec_rad)
x = zeros((npts, 3))
x[:,0] = a * cos(ra_rad)
x[:,1] = a * sin(ra_rad)
x[:,2] = sin(dec_rad)
# Use PREMAT function to get precession matrix from Equinox1 to Equinox2
r = premat(equinox1, equinox2, fk4=fk4)
x2 = transpose(dot(transpose(r), transpose(x))) #rotate to get output direction cosines
ra_rad = zeros(npts) + arctan2(x2[:,1], x2[:,0])
dec_rad = zeros(npts) + arcsin(x2[:,2])
if not radian:
ra = rad2deg(ra_rad)
ra = ra + (ra < 0.) * 360.e0 #RA between 0 and 360 degrees
dec = rad2deg(dec_rad)
else:
ra = ra_rad
dec = dec_rad
ra = ra + (ra < 0.) * 2.0e0 * pi
if doprint:
print 'Equinox (%.2f): %f,%f' % (equinox2, ra, dec)
if scal:
ra, dec = ra[0], dec[0]
return ra, dec
[docs]def precess_xyz(x, y, z, equinox1, equinox2):
"""
+
NAME:
PRECESS_XYZ
PURPOSE:
Precess equatorial geocentric rectangular coordinates.
CALLING SEQUENCE:
precess_xyz, x, y, z, equinox1, equinox2
INPUT/OUTPUT:
x,y,z: scalars or vectors giving heliocentric rectangular coordinates
THESE ARE CHANGED UPON RETURNING.
INPUT:
EQUINOX1: equinox of input coordinates, numeric scalar
EQUINOX2: equinox of output coordinates, numeric scalar
OUTPUT:
x,y,z are changed upon return
NOTES:
The equatorial geocentric rectangular coords are converted
to RA and Dec, precessed in the normal way, then changed
back to x, y and z using unit vectors.
EXAMPLE:
Precess 1950 equinox coords x, y and z to 2000.
IDL> precess_xyz,x,y,z, 1950, 2000
HISTORY:
Written by P. Plait/ACC March 24 1999
(unit vectors provided by D. Lindler)
Use /Radian call to PRECESS W. Landsman November 2000
Use two parameter call to ATAN W. Landsman June 2001
-
"""
#check inputs
#take input coords and convert to ra and dec (in radians)
ra = arctan2(y, x)
_del = sqrt(x * x + y * y + z * z) #magnitude of distance to Sun
dec = arcsin(z / _del)
# precess the ra and dec
ra,dec = precess(ra, dec, equinox1, equinox2, radian=True)
#convert back to x, y, z
xunit = cos(ra) * cos(dec)
yunit = sin(ra) * cos(dec)
zunit = sin(dec)
x = xunit * _del
y = yunit * _del
z = zunit * _del
return x,y,z
# -*- coding: utf-8 -*-
[docs]def premat(equinox1, equinox2, fk4=False):
"""
NAME:
PREMAT
PURPOSE:
Return the precession matrix needed to go from EQUINOX1 to EQUINOX2.
EXPLANTION:
This matrix is used by the procedures PRECESS and BARYVEL to precess
astronomical coordinates
CALLING SEQUENCE:
matrix = PREMAT( equinox1, equinox2, [ /FK4 ] )
INPUTS:
EQUINOX1 - Original equinox of coordinates, numeric scalar.
EQUINOX2 - Equinox of precessed coordinates.
OUTPUT:
matrix - double precision 3 x 3 precession matrix, used to precess
equatorial rectangular coordinates
OPTIONAL INPUT KEYWORDS:
/FK4 - If this keyword is set, the FK4 (B1950.0) system precession
angles are used to compute the precession matrix. The
default is to use FK5 (J2000.0) precession angles
EXAMPLES:
Return the precession matrix from 1950.0 to 1975.0 in the FK4 system
IDL> matrix = PREMAT( 1950.0, 1975.0, /FK4)
PROCEDURE:
FK4 constants from "Computational Spherical Astronomy" by Taff (1983),
p. 24. (FK4). FK5 constants from "Astronomical Almanac Explanatory
Supplement 1992, page 104 Table 3.211.1.
REVISION HISTORY
Written, Wayne Landsman, HSTX Corporation, June 1994
Converted to IDL V5.0 W. Landsman September 1997
"""
deg_to_rad = pi / 180.0e0
sec_to_rad = deg_to_rad / 3600.e0
t = 0.001e0 * (equinox2 - equinox1)
if not fk4:
st = 0.001e0 * (equinox1 - 2000.e0)
# Compute 3 rotation angles
a = sec_to_rad * t * (23062.181e0 + st * (139.656e0 + 0.0139e0 * st) + t * (30.188e0 - 0.344e0 * st + 17.998e0 * t))
b = sec_to_rad * t * t * (79.280e0 + 0.410e0 * st + 0.205e0 * t) + a
c = sec_to_rad * t * (20043.109e0 - st * (85.33e0 + 0.217e0 * st) + t * (-42.665e0 - 0.217e0 * st - 41.833e0 * t))
else:
st = 0.001e0 * (equinox1 - 1900.e0)
# Compute 3 rotation angles
a = sec_to_rad * t * (23042.53e0 + st * (139.75e0 + 0.06e0 * st) + t * (30.23e0 - 0.27e0 * st + 18.0e0 * t))
b = sec_to_rad * t * t * (79.27e0 + 0.66e0 * st + 0.32e0 * t) + a
c = sec_to_rad * t * (20046.85e0 - st * (85.33e0 + 0.37e0 * st) + t * (-42.67e0 - 0.37e0 * st - 41.8e0 * t))
sina = sin(a)
sinb = sin(b)
sinc = sin(c)
cosa = cos(a)
cosb = cos(b)
cosc = cos(c)
r = zeros((3, 3))
r[0,:] = array([cosa * cosb * cosc - sina * sinb, sina * cosb + cosa * sinb * cosc, cosa * sinc])
r[1,:] = array([-cosa * sinb - sina * cosb * cosc, cosa * cosb - sina * sinb * cosc, -sina * sinc])
r[2,:] = array([-cosb * sinc, -sinb * sinc, cosc])
return r
[docs]def readcol(filename, delimiter=' ', format=None, skiprows=0, **kw):
""" This routine reads the data from the ascii file
a,b,c=readcol('dat.txt',delimiter='|')
you can skip a certain number of rows in the top of the file by
specifying skiprows=X option.
The format option is needed if you have datatypes different from float in your table
In that case format string should be comma delimted set of I (int) F(float) D (double)
S (string) characters. E.g.
a,b,c=readcol('dat.txt',format='I,S,D')
"""
import scipy.io
import numpy
if format==None:
res=numpy.loadtxt(filename, delimiter=delimiter, skiprows=skiprows, **kw)
nrows = res.shape[0]
if res.ndim==2:
ncols = res.shape[1]
elif res.ndim==1:
ncols=1
res.shape=(nrows,1)
else:
raise "Exception: wrong array dimensions"
stor=[]
for i in range(ncols):
stor.append(res[:,i])
return tuple(stor)
else:
types=[]
i=0
formats=format.split(',')
convs={}
retnull = lambda s: numpy.float(s or 0)
for i, a in enumerate(formats):
if a=='I':
curtype=numpy.int32
convs[i]=retnull
elif a=='F':
curtype=numpy.float32
convs[i]=retnull
elif a=='D':
curtype=numpy.float64
convs[i]=retnull
elif a=='S':
curtype="S100"#numpy.str
else:
raise Exception("Sorry, Unknown type in the format string\n The allowed types are S,I,F,D (string, int, float, double)")
types.append(("a%d"%i,curtype))
rec=numpy.loadtxt(file(filename),dtype=types, delimiter=delimiter,
skiprows=skiprows,converters=convs)
ncols=len(rec[0])
nrows=len(rec)
buf="("
stor=[]
for a in formats:
if a=='I':
tmp=numpy.zeros(nrows,dtype=numpy.int32)
elif a=='F':
tmp=numpy.zeros(nrows,dtype=numpy.float32)
elif a=='D':
tmp=numpy.zeros(nrows,dtype=numpy.float64)
elif a=='S':
tmp=numpy.zeros(nrows,dtype="S100")
stor.append(tmp)
for i in range(ncols):
for j in range(nrows):
stor[i][j]=rec[j][i]
return tuple(stor)
[docs]def sphdist (ra1, dec1, ra2, dec2):
"""measures the spherical distance in degrees
The input has to be in degrees too
"""
dec1_r = deg2rad(dec1)
dec2_r = deg2rad(dec2)
return 2 *\
rad2deg \
(
arcsin
(
sqrt
(
(
sin((dec1_r - dec2_r) / 2)
)**2
+
cos(dec1_r) * cos(dec2_r) *
(
sin((deg2rad(ra1 - ra2)) / 2)
)**2
)
)
)
[docs]def xyz(date, equinox=None):
"""
NAME:
XYZ
PURPOSE:
Calculate geocentric X,Y, and Z and velocity coordinates of the Sun
EXPLANATION:
Calculates geocentric X,Y, and Z vectors and velocity coordinates
(dx, dy and dz) of the Sun. (The positive X axis is directed towards
the equinox, the y-axis, towards the point on the equator at right
ascension 6h, and the z axis toward the north pole of the equator).
Typical position accuracy is <1e-4 AU (15000 km).
CALLING SEQUENCE:
XYZ, date, x, y, z, [ xvel, yvel, zvel, EQUINOX = ]
INPUT:
date: reduced julian date (=JD - 2400000), scalar or vector
OUTPUT:
x,y,z: scalars or vectors giving heliocentric rectangular coordinates
(in A.U) for each date supplied. Note that sqrt(x^2 + y^2
+ z^2) gives the Earth-Sun distance for the given date.
xvel, yvel, zvel: velocity vectors corresponding to X, Y and Z.
OPTIONAL KEYWORD INPUT:
EQUINOX: equinox of output. Default is 1950.
EXAMPLE:
What were the rectangular coordinates and velocities of the Sun on
Jan 22, 1999 0h UT (= JD 2451200.5) in J2000 coords? NOTE:
Astronomical Almanac (AA) is in TDT, so add 64 seconds to
UT to convert.
IDL> xyz,51200.5+64.d/86400.d,x,y,z,xv,yv,zv,equinox = 2000
Compare to Astronomical Almanac (1999 page C20)
X (AU) Y (AU) Z (AU)
XYZ: 0.51456871 -0.76963263 -0.33376880
AA: 0.51453130 -0.7697110 -0.3337152
abs(err): 0.00003739 0.00007839 0.00005360
abs(err)
(km): 5609 11759 8040
NOTE: Velocities in AA are for Earth/Moon barycenter
(a very minor offset) see AA 1999 page E3
X VEL (AU/DAY) YVEL (AU/DAY) Z VEL (AU/DAY)
XYZ: -0.014947268 -0.0083148382 -0.0036068577
AA: -0.01494574 -0.00831185 -0.00360365
abs(err): 0.000001583 0.0000029886 0.0000032077
abs(err)
(km/sec): 0.00265 0.00519 0.00557
PROCEDURE CALLS:
PRECESS_XYZ
REVISION HISTORY
Original algorithm from Almanac for Computers, Doggett et al. USNO 1978
Adapted from the book Astronomical Photometry by A. Henden
Written W. Landsman STX June 1989
Correct error in X coefficient W. Landsman HSTX January 1995
Added velocities, more terms to positions and EQUINOX keyword,
some minor adjustments to calculations
P. Plait/ACC March 24, 1999
"""
picon = pi / 180.0e0
t = (date - 15020.0e0) / 36525.0e0 #Relative Julian century from 1900
# NOTE: longitude arguments below are given in *equinox* of date.
# Precess these to equinox 1950 to give everything an even footing.
# Compute argument of precession from equinox of date back to 1950
pp = (1.396041e0 + 0.000308e0 * (t + 0.5e0)) * (t - 0.499998e0)
# Compute mean solar longitude, precessed back to 1950
el = 279.696678e0 + 36000.76892e0 * t + 0.000303e0 * t * t - pp
# Compute Mean longitude of the Moon
c = 270.434164e0 + 480960.e0 * t + 307.883142e0 * t - 0.001133e0 * t * t - pp
# Compute longitude of Moon's ascending node
n = 259.183275e0 - 1800.e0 * t - 134.142008e0 * t + 0.002078e0 * t * t - pp
# Compute mean solar anomaly
g = 358.475833e0 + 35999.04975e0 * t - 0.00015e0 * t * t
# Compute the mean jupiter anomaly
j = 225.444651e0 + 2880.0e0 * t + 154.906654e0 * t * t
# Compute mean anomaly of Venus
v = 212.603219e0 + 58320.e0 * t + 197.803875e0 * t + 0.001286e0 * t * t
# Compute mean anomaly of Mars
m = 319.529425e0 + 19080.e0 * t + 59.8585e0 * t + 0.000181e0 * t * t
# Convert degrees to radians for trig functions
el = el * picon
g = g * picon
j = j * picon
c = c * picon
v = v * picon
n = n * picon
m = m * picon
# Calculate X,Y,Z using trigonometric series
x = 0.999860e0 * cos(el) - 0.025127e0 * cos(g - el) + 0.008374e0 * cos(g + el) + 0.000105e0 * cos(g + g + el) + 0.000063e0 * t * cos(g - el) + 0.000035e0 * cos(g + g - el) - 0.000026e0 * sin(g - el - j) - 0.000021e0 * t * cos(g + el) + 0.000018e0 * sin(2.e0 * g + el - 2.e0 * v) + 0.000017e0 * cos(c) - 0.000014e0 * cos(c - 2.e0 * el) + 0.000012e0 * cos(4.e0 * g + el - 8.e0 * m + 3.e0 * j) - 0.000012e0 * cos(4.e0 * g - el - 8.e0 * m + 3.e0 * j) - 0.000012e0 * cos(g + el - v) + 0.000011e0 * cos(2.e0 * g + el - 2.e0 * v) + 0.000011e0 * cos(2.e0 * g - el - 2.e0 * j)
y = 0.917308e0 * sin(el) + 0.023053e0 * sin(g - el) + 0.007683e0 * sin(g + el) + 0.000097e0 * sin(g + g + el) - 0.000057e0 * t * sin(g - el) - 0.000032e0 * sin(g + g - el) - 0.000024e0 * cos(g - el - j) - 0.000019e0 * t * sin(g + el) - 0.000017e0 * cos(2.e0 * g + el - 2.e0 * v) + 0.000016e0 * sin(c) + 0.000013e0 * sin(c - 2.e0 * el) + 0.000011e0 * sin(4.e0 * g + el - 8.e0 * m + 3.e0 * j) + 0.000011e0 * sin(4.e0 * g - el - 8.e0 * m + 3.e0 * j) - 0.000011e0 * sin(g + el - v) + 0.000010e0 * sin(2.e0 * g + el - 2.e0 * v) - 0.000010e0 * sin(2.e0 * g - el - 2.e0 * j)
z = 0.397825e0 * sin(el) + 0.009998e0 * sin(g - el) + 0.003332e0 * sin(g + el) + 0.000042e0 * sin(g + g + el) - 0.000025e0 * t * sin(g - el) - 0.000014e0 * sin(g + g - el) - 0.000010e0 * cos(g - el - j)
#Precess_to new equator?
if equinox is not None:
x, y, z = precess_xyz(x, y, z, 1950, equinox)
xvel = -0.017200e0 * sin(el) - 0.000288e0 * sin(g + el) - 0.000005e0 * sin(2.e0 * g + el) - 0.000004e0 * sin(c) + 0.000003e0 * sin(c - 2.e0 * el) + 0.000001e0 * t * sin(g + el) - 0.000001e0 * sin(2.e0 * g - el)
yvel = 0.015780 * cos(el) + 0.000264 * cos(g + el) + 0.000005 * cos(2.e0 * g + el) + 0.000004 * cos(c) + 0.000003 * cos(c - 2.e0 * el) - 0.000001 * t * cos(g + el)
zvel = 0.006843 * cos(el) + 0.000115 * cos(g + el) + 0.000002 * cos(2.e0 * g + el) + 0.000002 * cos(c) + 0.000001 * cos(c - 2.e0 * el)
#Precess to new equator?
if equinox is not None:
xvel, yvel, zvel = precess_xyz(xvel, yvel, zvel, 1950, equinox)
return x, y, z, xvel, yvel, zvel