143 lines
No EOL
5.2 KiB
Python
143 lines
No EOL
5.2 KiB
Python
#pylint: disable=W0401,W0614,W0622
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#All pylint codes: http://pylint.pycqa.org/en/latest/technical_reference/features.html
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from pylab import *
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import h5py
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from density_center import def_dc
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import ellipsoids
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import scipy.optimize
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# Simumation parameters
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h0 = 0.6774
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# Halo parameters
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file_name = 'data/subhalo_411321.hdf5'
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# centers_file_name = 'data/centers_411321.hdf5'
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### Snapshot parameters ###
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snapshot = 99
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a = 1.0 # Should read this value from somewhere!
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# Read the centre from separate file
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# DISABLED: we calculate on our own.
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# f = h5py.File(centers_file_name, 'r')
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# X_center = f[str(snapshot)]['Coordinates'][...]
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# V_center = f[str(snapshot)]['Velocities'][...]
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# f.close()
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# Dictionary of particle types
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particle_types = {}
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particle_types['gas'] = '0'
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particle_types['dm'] = '1'
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particle_types['stars'] = '4'
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particle_types['bhs'] = '5'
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# Read stars
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particle_type = 'stars'
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with h5py.File(file_name, 'r') as f:
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m = f[str(snapshot)][particle_types[particle_type]]['Masses'][...]
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X = f[str(snapshot)][particle_types[particle_type]]['Coordinates'][...] * a / h0
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V = f[str(snapshot)][particle_types[particle_type]]['Velocities'][...] * sqrt(a)
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M_tot = sum(m)
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# Calculate density centre and shift appropriately
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X_center_new, V_center_new = def_dc(m, X, V)
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X -= X_center_new
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V -= V_center_new
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# Rotate such that the short axis is z and medium axis is y
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r = linalg.norm(X, axis=1)
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rh = median(r)
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mask = r < 2*rh
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Q = ellipsoids.quadrupole_tensor(*X[mask].T, m[mask])
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eigenvalues, eigenvectors = np.linalg.eig(Q)
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R = ellipsoids.rotation_matrix_from_eigenvectors(eigenvectors, eigenvalues)
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X_new = (R @ X.T).T
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x, y, z = X_new.T
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# d is the axial distance
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d = sqrt(x**2 + y**2)
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# Cread a two-dimensional grid
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# The grid sizes don't _have to_ be equal in both directions, but there is some
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# logic in keeping them the same.
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n_grid_d, n_grid_z = 16, 16
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d_max = 2*median(d)
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z_max = 2*median(abs(z))
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d_grid = linspace(0, d_max, n_grid_d+1)
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z_grid = linspace(0, z_max, n_grid_z+1)
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# Calculates the mass in each (d,z)-cell
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# We fold negative z-values assuming symmetry with respect to the xy-plane
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values, _, _ = histogram2d(d, abs(z), bins=[d_grid, z_grid], weights=m)
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values = values.T # Needed because how histogram2d workds
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# Calculate the volume of each (d,z)-cell (cylinder subtraction)
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d_edges, z_edges = meshgrid(d_grid, z_grid, indexing='xy')
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volumes = pi*(d_edges[1:,1:]**2 - d_edges[1:,:-1]**2)*(z_edges[1:,1:] - z_edges[:-1,1:])
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# Finally we have the density as a function of d and z. The normalization is to
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# make the numbers easier to work with for the minimization routine.
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rho_measured_normalized = values/volumes/M_tot
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# Define Plummer and Miyamoto-Nagai density
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rho_plummer = lambda r, M, b: (3*M/(4*pi*b**3))*(1+(r/b)**2)**(-2.5)
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rho_mn = lambda d, z, M, a, b: \
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(b**2 * M / (4*pi)) * \
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(a*d**2 + (a + 3*sqrt(z**2+b**2))*(a+sqrt(z**2+b**2))**2) / \
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((d**2 + (a+sqrt(z**2+b**2))**2)**2.5 * (z**2+b**2)**1.5)
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# The minimization procedure
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means = lambda arr: .5*(arr[:-1]+arr[1:]) # small helper function
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# Define a grid of the centre of each cell from the histogram we created earlier
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dd, zz = meshgrid(means(d_grid), means(z_grid), indexing='xy')
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def cost(args):
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a_mn, b_mn = args
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rho = rho_mn(dd, zz, 1, a_mn, b_mn)
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square_diff = (rho - rho_measured_normalized)**2
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return sum(square_diff)
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minimization_result = \
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scipy.optimize.minimize(cost, [median(abs(z)), median(d)], method='Nelder-Mead', tol=1e-6, options={'maxiter':5000})
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a_mn, b_mn = minimization_result.x
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####
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if False:
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print('!!!Setting parameters artificially!!!')
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a_mn, b_mn = 2.98, 1.61
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####
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rho_best_fit = rho_mn(dd, zz, 1, a_mn, b_mn)
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print(f'a_mn = {a_mn:.4f} kpc b_mn = {b_mn:.4f} kpc')
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print(f'M_mn = {M_tot:.2e} MSun')
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# Compare with Matteo's results
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with h5py.File(file_name, 'r') as f:
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particle_id = f[str(snapshot)][particle_types[particle_type]]['ParticleIDs'][...]
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matteo_id = f[str(snapshot)][particle_types[particle_type]]['IDs_truncated'][...]
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matteo_component_tag = f[str(snapshot)][particle_types[particle_type]]['Component'][...]
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# Find the array indices in the original arrays that appear in Matteo's list
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i = particle_id.argsort()
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matteo_disk_ids = matteo_id[matteo_component_tag==1]
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i_matteo_disk = i[searchsorted(particle_id[i], matteo_disk_ids)]
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matteo_bulge_ids = matteo_id[matteo_component_tag==2]
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i_matteo_bulge = i[searchsorted(particle_id[i], matteo_bulge_ids)]
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# Print Matteo's results
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M_matteo_bulge = sum(m[i_matteo_bulge])
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M_matteo_disk = sum(m[i_matteo_disk])
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rh_matteo_bulge = median(r[i_matteo_bulge])
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print('=== Matteo\'s results ===')
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print(f'M_bulge = {M_matteo_bulge:.2e} MSun M_disk = {M_matteo_disk:.2e} MSun')
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print(f'rh_bulge = {rh_matteo_bulge:.4f} kpc (equivalent Plummer radius: {0.76642*rh_matteo_bulge:.4f}) kpc')
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# Plot the density as a function of d for three values of z.
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rho = lambda d, z: rho_mn(d, z, 1, a_mn, b_mn)
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for c, i in enumerate([0, 3, 6, 9]):
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semilogy(dd[i,:], M_tot*rho_measured_normalized[i,:], c=f'C{c}', ls='-', label=f'h={1000*zz[i,0]:.0f} pc')
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semilogy(dd[i,:], M_tot*rho(dd[i,:], zz[i,0]), c=f'C{c}', ls='--', alpha=0.5)
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legend()
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xlabel('x [kpc]')
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ylabel(r'$\rho\ [\rm M_\odot\ kpc^{-3}]$')
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savefig('subhalo_411321_stellar_fit.png')
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show() |