def contour_singlebox(phi2, d, mu1, mu2, Vrad, Vc, q):
ro = 8.5
vo = Vc
p = potential.LogarithmicHaloPotential(q=q, normalize=1)
# ---------------------------------------------------------------
# evaluating the x,y,z and vx,vy,vz from the function variables
# ---------------------------------------------------------------
phi1 = 34.776756565525091 # degrees
lf, bf = mw.phi12_to_lb(phi1, phi2, degree=True)
xf, yf, zf = bovy_coords.lbd_to_XYZ(lf, bf, d, degree=True)
# guessed initial position in cylindrical coordinate
Rf, zcylf, phif = xyz_to_cyl(xf, yf, zf)
# convert proper motion in phi1 and phi2 coordinates to
# proper motion in Galactic (vl,vb) coordinate
vl, vb = mw.pmphi12_to_pmllpmbb(mu1, mu2, phi1, phi2, degree=True)
# convert the vl, vb to proper motion in cartesian coordinate
vxf, vyf, vzf = bovy_coords.vrpmllpmbb_to_vxvyvz(Vrad, vl, vb, lf, bf, d, degree=True)
# convert vx,vy,vz to be in cylindrical coordinates
vrf, vtf, vzff = vxvyvz_to_vrvtvz(xf, yf, zf, vxf, vyf, vzf)
o = Orbit(vxvv=[Rf / ro, vrf / vo, vtf / vo, zcylf / ro, vzff / vo, phif], ro=ro, vo=vo)
global time
o.integrate(time, p)
time = np.linspace(0.0, 1e1, 1e4)
# Orbit in Galactic coordinates
lval = o.ll(time, ro=ro, obs=[ro, 0.0, 0.0])
bval = o.bb(time, ro=ro, obs=[ro, 0.0, 0.0])
pmll = o.pmll(time, ro=ro, obs=[ro, 0.0, 0.0, -10.0, vo + 5.25, 7.17])
pmbb = o.pmbb(time, ro=ro, obs=[ro, 0.0, 0.0, -10.0, vo + 5.25, 7.17])
galpy_vel = mw.pmllpmbb_to_pmphi12(pmll, pmbb, lval, bval, degree=True)
vrad_galpy = o.vlos(time, ro=ro, obs=[ro, 0.0, 0.0, -10.0, vo + 5.25, 7.17])
phi12 = mw.lb_to_phi12(lval, bval, degree=True)
phi12[phi12[:, 0] > 180, 0] -= 360.0
L_pos = likelihood_all_test_sum(phi12[:, 0], phi1_pos, x_err_pos, phi12[:, 1], phi2_pos, phi2_err, time)
L_dist = likelihood_all_test_sum(phi12[:, 0], phi1_dist, x_err_dist, o.dist(time), dist, dist_err, time)
L_vrad = likelihood_all_test_sum(phi12[:, 0], phi1_vrad, x_err_vrad, vrad_galpy, Vrad, V_err, time)
L_mu1 = likelihood_all_test_sum(phi12[:, 0], phi1_mu, x_err_mu, galpy_vel.T[0], mu1, sigma_mu, time)
L_mu2 = likelihood_all_test_sum(phi12[:, 0], phi1_mu, x_err_mu, galpy_vel.T[1], mu2, sigma_mu, time)
L_total = L_pos + L_dist + L_vrad + L_mu1 + L_mu2
return L_total
def orb_fit(params, find_posvel):
if find_posvel:
pos, vel = conversion_likelihood_fig(params)
xi,yi,zi = pos[0], pos[1], pos[2]
vxi,vyi,vzi = vel[0], vel[1], vel[2]
else:
xi,yi,zi = np.array([3.41,13.00,9.58])
vxi,vyi,vzi = np.array([200.4,-162.6,13.9])
Ri,zcyli,phii = xyz_to_cyl(xi,yi,zi)
vri,vti,vzcyli = vxvyvz_to_vrvtvz(xi,yi,zi,vxi,vyi,vzi)
p = potential.LogarithmicHaloPotential(q=0.9,normalize=1)
ts = 1000 # number of timesteps
time = np.linspace(0.,1e1,ts)
o = Orbit(vxvv=[Ri/ro,vri/vo,vti/vo,zcyli/ro,vzcyli/vo,phii],ro=ro,vo=vo)
o.integrate(time,p)
lval = o.ll(time,ro = ro,obs= [ro,0.,0.])
bval = o.bb(time,ro = ro,obs= [ro,0.,0.])
phi12 = mw.lb_to_phi12(lval,bval,degree=True)
phi12[phi12[:,0] > 180,0]-= 360.
pmll = o.pmll(time, ro = ro, obs=[ro,0.,0.,0.,vo,0.])
pmbb = o.pmbb(time, ro = ro, obs=[ro,0.,0.,0.,vo,0.])
galpy_vel = mw.pmllpmbb_to_pmphi12(pmll,pmbb,lval,bval,degree=True)
distvals = o.dist(time)
Vrad = o.vlos(time)
mu1 = galpy_vel.T[0]
mu2 = galpy_vel.T[1]
return phi12, distvals, Vrad, mu1, mu2
def vxvyvz_to_pmphi12(x, y, z, vx, vy, vz, degree):
'''
Parameters
----------------------------------------------------
x, y, z :
position in cartesian coordinate
vx, vy, vz :
velocity in cartesian coordinate
Return
----------------------------------------------------
proper motion in stream coordinate as an array
and the radial velocity as a number
'''
l, b, d = bovy_coords.XYZ_to_lbd(x, y, z, degree = degree)
vr, vl, vb = bovy_coords.vxvyvz_to_vrpmllpmbb(vx,vy,vz, l, b, d, degree = degree)
vphi1, vphi2 = mw.pmllpmbb_to_pmphi12(vl, vb, l, b, degree = degree)
return np.array([vphi1,vphi2]), vr
def optimizer_func(input,Vc,q):
'''
Parameters
----------------------------------------------------
phi2:
phi2 in degrees
D:
distance in kpc
mu_phi1, mu_phi2:
proper motion in phi1 and phi2 coordinates
Vrad:
radial velocity
Return
----------------------------------------------------
Log likelihood using the specified Vc,q, phi2,
D, proper motions in stream coordinates and
the radial velocity.
'''
phi2 = input[0]
D = input[1]
mu_phi1 = input[2]
mu_phi2 = input[3]
Vrad = input[4]
print "vc in function:", Vc
print "q in function:" , q
# choose a value of phi2 for the given phi1 (phi1 should stay constant from
# initial conditions obtained above in degrees
phi1i = -30. #phi12i_kop[0]
phi2i = phi2
# convert the phi1 and phi2 to be in cylindrical coordinate
lf, bf = mw.phi12_to_lb(phi1i, phi2i, degree=True)
xf, yf, zf = bovy_coords.lbd_to_XYZ(lf, bf, D, degree = True)
# guessed initial position in cylindrical coordinate
Rf,zcylf,phif = xyz_to_cyl(xf, yf, zf)
# convert proper motion in phi1 and phi2 coordinates to
# proper motion in Galactic (vl,vb) coordinate
vl,vb = mw.pmphi12_to_pmllpmbb(mu_phi1, mu_phi2, phi1i, phi2i, degree = True)
# convert the vl, vb to proper motion in cartesian coordinate
vxf, vyf, vzf = bovy_coords.vrpmllpmbb_to_vxvyvz(Vrad, vl, vb, lf, bf, D, degree = True)
# convert vx,vy,vz to be in cylindrical coordinates
vrf, vtf, vzff = vxvyvz_to_vrvtvz(xf, yf, zf, vxf, vyf, vzf)
# use the above initial positions to calculate the potential and orbit
ro = 8.5
vo = Vc
p = potential.LogarithmicHaloPotential(q = q,normalize = 1)
o = Orbit(vxvv=[Rf/ro, vrf/vo, vtf/vo, zcylf/ro, vzff/vo, phif], ro = ro, vo = vo)
o.integrate(time_glob,p)
time = np.linspace(0.,1e1,1e4)
# compute the likelihood with the above initial position
lval = o.ll(time, ro = ro, obs = [ro,0.,0.])
bval = o.bb(time, ro = ro, obs = [ro,0.,0.])
pmll = o.pmll(time, ro = ro, obs = [ro, 0., 0., -10., vo+5.25, 7.17])
pmbb = o.pmbb(time, ro = ro, obs = [ro, 0., 0., -10., vo+5.25, 7.17])
galpy_vel = mw.pmllpmbb_to_pmphi12(pmll,pmbb,lval,bval,degree = True)
vrad_galpy = o.vlos(time, ro = ro, obs = [ro, 0., 0., -10., vo+5.25, 7.17])
phi12 = mw.lb_to_phi12(lval, bval, degree = True)
phi12[phi12[:,0] > 180,0]-= 360.
# calculating likelihood for each set of parameters
L_pos = likelihood_all_test_sum(phi12[:,0], phi1_pos, x_err_pos, phi12[:,1], phi2_pos, phi2_err, time)
L_dist = likelihood_all_test_sum(phi12[:,0], phi1_dist, x_err_dist, o.dist(time), dist, dist_err, time)
L_vrad = likelihood_all_test_sum(phi12[:,0], phi1_vrad, x_err_vrad, vrad_galpy, Vrad_kop, V_err, time)
L_mu1 = likelihood_all_test_sum(phi12[:,0], phi1_mu, x_err_mu, galpy_vel.T[0], mu1, sigma_mu, time)
L_mu2 = likelihood_all_test_sum(phi12[:,0], phi1_mu, x_err_mu, galpy_vel.T[1], mu2, sigma_mu, time)
print "L position:", L_pos
print "L dist:" , L_dist
print "L vrad:" , L_vrad
print "L mu1:" , L_mu1
print "L mu2:" , L_mu2
print
L_total = L_pos + L_dist + L_vrad + L_mu1 + L_mu2
# chi^2 = -2ln(L) where ln(L) = L_total
chi2 = -2. * L_total
print
print "chi2: ",chi2
print
print "input:", input
return chi2