nodastro.py
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import numpy as np
import novas
import time
RAD = np.pi/180.0
GRD = 180.0/np.pi
class nodtrafo:
def __init__(self, JD=None):
if JD == None:
JD = self.JulDat()
else:
JD = self.str_JD(JD)
epsm, eps, eqeq, dpsi, deps = novas.etilt(JD)
self.eps = eps
self.JD = JD
# old nod2 matrix
self.LBAD2000 = [[-0.0548777625376, 0.4941083214789, -0.8676666398013], \
[-0.8734369590694, -0.4448308611625, -0.1980741868317], \
[-0.4838350025685, 0.7469822431643, 0.4559837921317]]
self.lbad2000 = [[-0.054875539, 0.494109454, -0.867666136], \
[-0.873437105, -0.444829594, -0.198076390], \
[-0.483834992, 0.746982249, 0.455983795]]
# old nod2 matrix
self.AD50AD00 = [[ 0.9999257079524, -0.0111789381378, -0.0048590038154], \
[ 0.0111789381264, 0.9999375133500, -0.0000271625947],
[ 0.0048590038415, -0.0000271579263, 0.9999881946024]]
self.ad50ad00 = [[ 0.9999256782, -0.0111820611, -0.0048579477], \
[ 0.0111820610, 0.9999374784, -0.0000271765],
[ 0.0048579479, -0.0000271474, 0.9999881997]]
self.ekad2000 = [[ 1.0000000000000, 0.0000000000000, 0.0000000000000], \
[ 0.0000000000000, 0.9174820583615, -0.3977771644837], \
[ 0.0000000000000, 0.3977771644837, 0.9174820583615]]
self.ekadnow = [[ 1.0, 0.0, 0.0], \
[ 0.0, np.cos(eps*RAD), -np.sin(eps*RAD)], \
[ 0.0, np.sin(eps*RAD), np.cos(eps*RAD)]]
self.unit = [[1.0, 0.0, 0.0], \
[0.0, 1.0, 0.0], \
[0.0, 0.0, 1.0]]
self.lbad1950 = np.dot(np.array(self.ad50ad00).transpose(), self.lbad2000)
self.adnow2000 = self.premat(JD, 2451545.0)
self.adnow1950 = self.premat(JD, 2433282.4235)
def azel(self, phi, az, el):
x = np.sin(el*RAD)*np.cos(phi*RAD) - np.cos(el*RAD)*np.cos(az*RAD)*np.sin(phi*RAD)
y = -np.cos(el*RAD)*np.sin(az*RAD)
z = np.sin(el*RAD)*np.sin(phi*RAD) + np.cos(el*RAD)*np.cos(az*RAD)*np.cos(phi*RAD)
stw = np.arctan2(y,x)*GRD
delta = np.arctan2(z, np.sqrt(x*x+y*y))*GRD
return stw, delta
def horizon2equator(self, phi):
sinphi = np.sin(phi*RAD)
cosphi = np.cos(phi*RAD)
mat = [[-sinphi, 0.0, cosphi], [0.0, -1.0, 0.0], [cosphi, 0.0, sinphi]]
return np.array(mat)
def sidereal(self, t):
sint = np.sin(t*RAD)
cost = np.cos(t*RAD)
mat = [[cost, sint, 0.0], [sint, -cost, 0.0], [0.0, 0.0, 1.0]]
return np.array(mat)
def str_JD(self, date):
if type(date) == float:
ja = int(0.01*int(date))
jy = int(date)
days = (date - int(date)) * 365.25
jd = int(365.25*jy) - 678576 - ja + int(0.25*ja) + days + 2400000.5
return jd
x = date.split("T")
if len(x) == 1:
t = time.strptime(date)
year = t.tm_year
month = t.tm_mon
day = t.tm_mday
hour = float(t.tm_hour) + float(t.tm_min)/60.0 + float(t.tm_sec)/3600.0
else:
day, month, year = x[0].split("-")
if int(day) > 1000:
y = day
day = year
year = y
h, m, s = x[1].split(":")
hour = float(h) + float(m)/60.0 + float(s)/3600.0
jd = novas.juldat(int(year), int(month), int(day), hour)
return jd
def JulDat(self):
""" calculates the Julian day from the computer time signal """
jd = 2440587.5 + time.time() / 86400.0
return jd
def invert(self, mat):
return mat.transpose()
def get_trafo_matrix(self, coord_in, equinox_in, coord_out, equinox_out):
""" Calculates coordinate transformation matix """
c_in = coord_in.split("-")[0]
c_out = coord_out.split("-")[0]
if c_in[:2] == "GL" and c_out[:2] == "RA" and int(equinox_out) == 2000:
return self.lbad2000
elif c_in[:2] == "GL" and c_out[:2] == "RA" and int(equinox_out) == 1950:
return self.lbad1950
elif c_in[:2] == "RA" and int(equinox_in) == 2000 and c_out[:2] == "GL":
return np.array(self.lbad2000).transpose()
elif c_in[:2] == "RA" and int(equinox_in) == 1950 and c_out[:2] == "GL":
return np.array(self.lbad1950).transpose()
elif c_in[:2] == "RA" and int(equinox_in) == 2000 and \
c_out[:2] == "RA" and int(equinox_out) == 1950:
return np.array(self.ad50ad00).transpose()
elif c_in[:2] == "RA" and int(equinox_in) == 1950 and \
c_out[:2] == "RA" and int(equinox_out) == 2000:
return self.ad50ad00
elif c_in == c_out:
return self.unit
else:
return []
def trafo(self, lam, bet, mat):
x = np.cos(lam*RAD)*np.cos(bet*RAD)
y = np.sin(lam*RAD)*np.cos(bet*RAD)
z = np.sin(bet*RAD)
x1, y1, z1 = np.dot(mat, (x,y,z))
lam1 = np.arctan2(y1, x1)/RAD
bet1 = np.arctan2(z1, np.sqrt(x1*x1+y1*y1))/RAD
return lam1, bet1
def premat(self, jd1, jd2):
""" Computation of the precession matrix for transformations
between the epochs "jd1" and "jd2".
The coefficients in the precession angles are those given by J.H.Lieske
et al., Astron.Astrophys. 58, 1-16, 1977, Table 5; they were accepted
by the IAU as the present standard.
jd1 = Jul.Date of given mean equator and equinox
jd2 = Jul.Date of new mean equator and equinox
precmat = Matrix of precession from jd1 to jd2"""
dczet = [2306.2181, 1.39656, 1.39e-4, 3.0188e-1, 3.44e-4, 1.7998e-2]
dcztt = [7.928e-1, 4.1e-4, 2.05e-4]
dcthe = [2004.3109, 8.533e-1, 2.17e-4, 4.2665e-1, 2.17e-4, 4.1833e-2]
dcj20c = 2451545.0
dcjcen = 36525.0
dcsar = np.pi/(180.0*3600.0)
t0 = (jd1-dcj20c)/dcjcen
t = (jd2-jd1)/dcjcen
t0sq = t0*t0
tsq = t*t
tcb = tsq*t
zeta = ((dczet[0]+t0*dczet[1]-t0sq*dczet[2])*t \
+(dczet[3]-t0*dczet[4])*tsq +tcb*dczet[5])*dcsar
zett = zeta+((dcztt[0]+t0*dcztt[1])*tsq +tcb*dcztt[2])*dcsar
thet = ((dcthe[0]-t0*dcthe[1]-t0sq*dcthe[2])*t \
-(dcthe[3] +t0*dcthe[4])*tsq -tcb*dcthe[5])*dcsar
szeta = np.sin(zeta)
czeta = np.cos(zeta)
szett = np.sin(zett)
czett = np.cos(zett)
sthet = np.sin(thet)
cthet = np.cos(thet)
a = szeta*szett
b = czeta*szett
c = szeta*czett
d = czeta*czett
# and save it in the precession matrix
premat = []
premat.append(+d*cthet - a)
premat.append(-c*cthet - b)
premat.append(-sthet*czett)
premat.append(+b*cthet + c)
premat.append(-a*cthet + d)
premat.append(-sthet*szett)
premat.append(+czeta*sthet)
premat.append(-szeta*sthet)
premat.append(cthet)
return np.reshape(premat, (3,3))
def rotmat(self, l, b, a):
""" this subroutine calculates the rotation matrix
l = longitude of origin
b = latitude of origin
a = tilt angle
rotmat = Matrix of rotation"""
zrot = [[np.cos(l*RAD), -np.sin(l*RAD), 0.0], \
[np.sin(l*RAD), np.cos(l*RAD), 0.0], \
[0.0, 0.0, 1.0]]
yrot = [[np.cos(b*RAD), 0.0, -np.sin(b*RAD)], \
[0.0, 1.0, 0.0], \
[np.sin(b*RAD), 0.0, np.cos(b*RAD)]]
xrot = [[1.0, 0.0, 0.0], \
[0.0, np.cos(a*RAD), -np.sin(a*RAD)], \
[0.0, np.sin(a*RAD), np.cos(a*RAD)]]
return np.dot(np.dot(zrot, yrot), xrot)
def rotmat_pst(self, l, b, a):
""" this subroutine calculates the rotation matrix
l = longitude of origin
b = latitude of origin
a = tilt angle
rotmat = Matrix of rotation"""
cosl = np.cos(l*RAD)
sinl = np.sin(l*RAD)
cosb = np.cos(b*RAD)
sinb = np.sin(b*RAD)
cosa = np.cos(a*RAD)
sina = np.sin(a*RAD)
rotmat = []
rotmat.append(cosb*cosl)
rotmat.append(-sina*sinb*cosl - cosa*sinl)
rotmat.append(-cosa*sinb*cosl + sina*sinl)
rotmat.append(cosb*sinl)
rotmat.append(-sina*sinb*sinl + cosa*cosl)
rotmat.append(-cosa*sinb*sinl - sina*cosl)
rotmat.append(sinb)
rotmat.append(sina*cosb)
rotmat.append(cosa*cosb)
return np.reshape(rotmat, (3,3))
def getCoord(self, l, b, mat):
x = np.cos(RAD*b)*np.cos(RAD*l)
y = np.cos(RAD*b)*np.sin(RAD*l)
z = np.sin(RAD*b)
xyz = np.dot(np.array(mat), np.array([x,y,z]))
l1 = np.arctan2(xyz[1], xyz[0])
b1 = np.arctan2(xyz[2], np.sqrt(xyz[1]**2 + xyz[0]**2))
return l1/RAD, b1/RAD
def getPosAng(self, l, b, rot, coord, equinox):
if coord[:2] == "GL":
mat = np.dot(self.lbad2000, self.adnow2000)
elif int(equinox) == 1950:
mat = self.adnow1950
elif int(equinox) == 2000:
mat = self.adnow2000
else:
return 0.0
mat = np.dot(mat, self.rotmat(0.0, 0.0, rot))
ra_mean, dec_mean = self.getCoord(l, b, mat)
ra = ra_mean*RAD
dec = dec_mean*RAD
sin_pos = mat[0][2]*np.sin(ra) - mat[1][2]*np.cos(ra)
cos_pos = mat[0][2]*np.cos(ra) + mat[1][2]*np.sin(ra)
cos_pos = -cos_pos*np.sin(dec) + mat[2][2]*np.cos(dec)
pos = np.arctan2(sin_pos, cos_pos) * GRD
return pos
def Osmose(self, U, Q, FacU, FacQ, Angle):
def parmat(p):
return np.array([[np.cos(p), -np.sin(p)], [np.sin(p), np.cos(p)]])
ly, lx = U.parmap.shape
if 'CROTA2' in U.header: rot = U.header['CROTA2']
else: rot = 0.0
if 'EPOCH' in U.header: equinox = U.header['EPOCH']
else: equinox = None
coord = U.header['CTYPE1']
for j in range(ly):
b = U.header['CRVAL2'] + (j-U.header['CRPIX2'])*U.header['CDELT2']
for i in range(lx):
l = U.header['CRVAL1'] + (i-U.header['CRPIX1'])*U.header['CDELT1']
omega = self.getPosAng(l, b, rot, coord, equinox)
eta = (Angle -U.parmap[j][i] - omega)*RAD*2
U.data[j][i], Q.data[j][i] = np.dot(parmat(eta),
[FacU*U.data[j][i], FacQ*Q.data[j][i]])
return U, Q