def getdRAdY(rvec, rvecdot, R, delta, t, t0):
rvec = list(rvec)
rvec1 = rvec[:]
rvec2 = rvec[:]
rvec1[1] = rvec1[1] + delta
rvec2[1] = rvec2[1] - delta
OE = babyOD2(rvec1, rvecdot, t)
dec1, ra1 = ephemeris2(OE[0], OE[1], OE[2], OE[3], OE[4], OE[5], t0, t, R)
OE = babyOD2(rvec2, rvecdot, t)
dec2, ra2 = ephemeris2(OE[0], OE[1], OE[2], OE[3], OE[4], OE[5], t0, t, R)
return (ra1 - ra2) / (2 * delta), (dec1 - dec2) / (2 * delta)
def getdRAdZdot(rvec, rvecdot, R, delta, t, t0):
rvecdot = list(rvecdot)
rvecdot1 = rvecdot[:]
rvecdot2 = rvecdot[:]
rvecdot1[2] = rvecdot1[2] + delta
rvecdot2[2] = rvecdot2[2] - delta
OE = babyOD2(rvec, rvecdot1, t)
dec1, ra1 = ephemeris2(OE[0], OE[1], OE[2], OE[3], OE[4], OE[5], t0, t, R)
OE = babyOD2(rvec, rvecdot2, t)
dec2, ra2 = ephemeris2(OE[0], OE[1], OE[2], OE[3], OE[4], OE[5], t0, t, R)
return (ra1 - ra2) / (2 * delta), (dec1 - dec2) / (2 * delta)
def correct(rvec, rvecdot, R, delta, t, t0):
rvecdot = list(rvecdot)
rvec = list(rvec)
for i in range(len(t)):
OE = babyOD2(rvec, rvecdot, t[i])
DECfit, RAfit = ephemeris2(OE[0], OE[1], OE[2], OE[3], OE[4], OE[5],
t0, t[i], R[i])
parX.extend(getdRAdX(rvec, rvecdot, R[i], delta, t[i], t0))
parY.extend(getdRAdY(rvec, rvecdot, R[i], delta, t[i], t0))
parZ.extend(getdRAdZ(rvec, rvecdot, R[i], delta, t[i], t0))
parXdot.extend(getdRAdXdot(rvec, rvecdot, R[i], delta, t[i], t0))
parYdot.extend(getdRAdYdot(rvec, rvecdot, R[i], delta, t[i], t0))
parZdot.extend(getdRAdZdot(rvec, rvecdot, R[i], delta, t[i], t0))
deltas.extend([abs(ra[i] - RAfit), abs(dec[i] - DECfit)])
masterArr = [[parX, parY, parZ, parXdot, parYdot, parZdot],
[parX, parY, parZ, parXdot, parYdot, parZdot],
[parX, parY, parZ, parXdot, parYdot, parZdot],
[parX, parY, parZ, parXdot, parYdot, parZdot],
[parX, parY, parZ, parXdot, parYdot, parZdot],
[parX, parY, parZ, parXdot, parYdot, parZdot]]
partialArr = [[parX], [parY], [parZ], [parXdot], [parYdot], [parZdot]]
for i in range(6):
for j in range(6):
masterArr[i][j] = np.dot(masterArr[i][j], partialArr[i][0])
for i in range(6):
partialArr[i][0] = np.dot(partialArr[i][0], deltas)
xyzArr = np.matmul(np.linalg.pinv(masterArr), partialArr)
return xyzArr
def RMS(r2, r2dot, R, t, t0):
deltalist = []
r2 = list(r2)
r2dot = list(r2dot)
for i in range(len(t)):
OE = babyOD2(r2, r2dot, t[i])
a, e, I, o, w, M, MP = babyOD3(r2, r2dot, t[i])
DECfit, RAfit = ephemeris2(OE[0], OE[1], OE[2], OE[3], OE[4], OE[5],
t0, t[i], R[i])
deltalist.extend([abs(ra[i] - RAfit), abs(dec[i] - DECfit)])
return sqrt(np.dot(deltalist, deltalist) / (len(t) * 2 - 6))