def a2(m, x, y, nbin):
rcil = np.sqrt(x**2 + y**2)
rbin, nodos = bines.rbin1(rcil, nbin)
A2v = np.ndarray(nbin)
phiv = np.ndarray(nbin)
n = len(x)
delta = n / nbin
r_sort = np.sort(rcil)
for j in range(0, nbin):
mask, = np.where((rcil > r_sort[j * (delta - 1)])
& (rcil <= r_sort[(delta - 1) * (j + 1)]))
xn = x[mask]
yn = y[mask]
titaj = np.arctan2(yn, xn)
a0 = np.sum(m[mask])
a2 = np.sum(m[mask] * np.cos(2. * titaj))
b2 = np.sum(m[mask] * np.sin(2. * titaj))
A2v[j] = np.sqrt(a2**2 + b2**2) / a0
phiv[j] = np.arctan2(b2, a2) / 2.
return A2v, phiv, rbin
def a2max(m,x,y,nbin):
rcil = np.sqrt(x**2 + y**2)
rbin, nodos = bines.rbin1(rcil, nbin)
A2v = np.ndarray(nbin)
phiv = np.ndarray(nbin)
n = len(x)
delta = n / nbin
r_sort = np.sort(rcil)
for j in range(0, nbin):
mask, = np.where((rcil > r_sort[j*(delta-1)]) & (rcil <= r_sort[(delta-1)*(j+1)]))
xn = x[mask]
yn = y[mask]
titaj = np.arctan2(yn,xn)
a0 = np.sum(m[mask])
a2 = np.sum(m[mask]*np.cos(2.*titaj))
b2 = np.sum(m[mask]*np.sin(2.*titaj))
A2v[j] = np.sqrt(a2**2 + b2**2) / a0
phiv[j] = np.arctan2(b2,a2) / 2.
A2max_arg = np.argmax(A2v)
A2max = A2v[A2max_arg]
rbinmax = rbin[A2max_arg]
phimax = phiv[A2max_arg]
phimed = np.mean([phiv[A2max_arg],phiv[A2max_arg+1],phiv[A2max_arg-1],phiv[A2max_arg+2],phiv[A2max_arg-2]])
return A2max, rbinmax, phimax, phimed
def a2max(m, x, y, nbin):
Rcil = np.sqrt(x**2 + y**2)
rbin = bines.rbin1(Rcil, nbin)
A2v = np.ndarray(nbin)
phiv = np.ndarray(nbin)
for j in range(0, nbin - 1):
mask, = np.where((Rcil > rbin[j]) & (Rcil <= rbin[j + 1]))
xn = x[mask]
yn = y[mask]
titaj = np.arctan2(yn, xn)
a0 = sum(m[mask])
a2 = sum(m[mask] * np.cos(2. * titaj))
b2 = sum(m[mask] * np.sin(2. * titaj))
A2v[j] = np.sqrt(a2**2 + b2**2) / a0
phiv[j] = np.arctan2(b2, a2) / 2.
A2max_arg = np.argmax(A2v)
A2max = max(A2v)
rbinmax = rbin[A2max_arg]
phimax = phiv[A2max_arg]
return A2max, rbinmax, phimax
def met(R, z, FeH, nbin):
med, nodos = bines2.rbin1(R, nbin)
Fe_H = np.zeros(nbin)
for i in range(nbin):
mask, = np.where((R < nodos[i + 1]) & (R > nodos[i]) & (z > 0))
Fe_H[i] = np.median(FeH[mask])
return med, Fe_H
def vol_density(r, m, nbin):
med, nodos = bines2.rbin1(r, nbin)
rho = np.zeros(nbin)
for i in range(nbin):
vol = (4/3.)*np.pi*(nodos[i+1]**3 - nodos[i]**3)
mask, = np.where((r < nodos[i+1]) & (r > nodos[i]))
rho[i] = np.sum(m[mask])/vol
return rho, med
def Vc_bin(r, m, nbin, G=4.299e-6):
med, nodos = bines2.rbin1(r, nbin)
Vcir = np.zeros(nbin)
for i in range(nbin):
limit = np.where(r < med[i])
M = np.sum(m[limit])
Vcir[i] = np.sqrt(G * M / med[i])
return Vcir, med
def surf_density(R,m,nbin):
med, nodos = bines2.rbin1(R, nbin)
sigma = np.zeros(nbin)
for i in range(nbin):
area = np.pi*(nodos[i+1]**2 - nodos[i]**2)
mask, = np.where((R < nodos[i+1]) & (R > nodos[i]))
sigma[i] = np.sum(m[mask])/area
return sigma, med
def surf_density(R,m,nbin):
if len(R) != len(m):
print ('Error: vector lengths do not match')
med, nodos = bines2.rbin1(R, nbin)
sigma = np.zeros(nbin)
for i in range(nbin):
area = np.pi*np.abs(nodos[i+1]**2 - nodos[i]**2)
mask, = np.where((R < nodos[i+1]) & (R > nodos[i]))
sigma[i] = np.sum(m[mask])/area
return sigma, med
def HMSH(R,z,m,nbin):
med, nodos = bines2.rbin1(R, nbin)
z50 = np.zeros(nbin)
for i in range(nbin):
mask, = np.where((R < nodos[i+1]) & (R > nodos[i]) & (z>0))
zorder = np.argsort(z[mask])
zsort = z[mask][zorder]
msort = m[mask][zorder]
mtot = np.cumsum(msort)
m_mean, = np.where(mtot < mtot[-1]/2.)
z50[i] = zsort[m_mean][-1]
return med, z50
def elipsoide2(x,y,z,vx,vy,vz,m,radio, nbin=20):
if np.isnan(radio)== True:
omegabar = np.nan
goto .end
r = np.sqrt(x**2 + y**2 + z**2)
limit, = np.where(r < radio)
jx = sum(m[limit]*(y[limit]*vz[limit]-z[limit]*vy[limit]))
jy = sum(m[limit]*(z[limit]*vx[limit]-x[limit]*vz[limit]))
jz = sum(m[limit]*(x[limit]*vy[limit]-y[limit]*vx[limit]))
j = np.sqrt(jx**2 + jy**2 + jz**2)
Jt = np.ndarray(3)
Jt[0] = jx
Jt[1] = jy
Jt[2] = jz
tensor = ten.tenf(x[limit], y[limit], z[limit]) #calculo el tensor de forma
matriz = np.linalg.eig(tensor) #saco los autovalores
autoval = matriz[0]
autovec = matriz[1]
asort = np.argsort(autoval) #los ordeno de menor a mayor
A = np.sqrt(autoval[asort][2]) #semiejes
B = np.sqrt(autoval[asort][1])
C = np.sqrt(autoval[asort][0])
V1 = autovec[:,asort][:,2]
V2 = autovec[:,asort][:,1]
V3 = autovec[:,asort][:,0]
modV = np.sqrt(np.dot(V3,V3))
tita = np.arccos(np.dot(Jt,V3)/(j*modV))
if tita > np.pi/2.:
V3 = -V3
cruz = np.cross(V3,V1)
test = np.sign(cruz) == np.sign(V2)
if test.all() == False:
V2 = cruz
aa = radio #normalizo al radio que yo quiero
bb = (B/A)*radio
cc = (C/A)*radio
pos = np.ndarray([len(x[limit]),3])
pos[:,0] = x[limit]
pos[:,1] = y[limit]
pos[:,2] = z[limit]
xx = np.zeros(len(x[limit]))
yy = np.zeros(len(x[limit]))
zz = np.zeros(len(x[limit]))
xx[:] = np.dot(pos[:],V1)
yy[:] = np.dot(pos[:],V2)
zz[:] = np.dot(pos[:],V3)
Relip = np.sqrt((xx/aa)**2 + (yy/bb)**2 + (zz/cc)**2) # formula del elipsoide
mask, = np.where(Relip <= 1.)
xn = xx[mask]
yn = yy[mask]
zn = zz[mask]
vel = np.ndarray([len(x[limit]),3])
vel[:,0] = vx[limit]
vel[:,1] = vy[limit]
vel[:,2] = vz[limit]
vxx = np.zeros(len(x[limit]))
vyy = np.zeros(len(x[limit]))
vzz = np.zeros(len(x[limit]))
vxx[:] = np.dot(vel[:],V1)
vyy[:] = np.dot(vel[:],V2)
vzz[:] = np.dot(vel[:],V3)
vxn = vxx[mask]
vyn = vyy[mask]
vzn = vzz[mask]
rn = np.sqrt(xn**2 + yn**2 + zn**2)
Rn = np.sqrt(xn**2 + yn**2)
Vtg = (-yn*vxn + xn*vyn)/Rn
omega = Vtg/Rn
med, nodos = bine.rbin1(rn,nbin)
omega_mean = np.zeros(nbin)
for i in range(0,nbin):
inbin, = np.where((rn > nodos[i]) & (rn < nodos[i+1]))
omega_mean[i] = np.mean(omega[inbin])
finterp = sint.interp1d(med,omega_mean,fill_value="extrapolate")
omegabar = finterp(radio)
label .end
return omegabar #xn, yn, zn, V1, V2, V3, A, B, C
def elipsoide(x, y, z, vx, vy, vz, radio, phi=0, nbin=20):
if radio == np.nan:
omegabar = np.nan
else:
xx = x * np.cos(phi) + y * np.sin(phi)
yy = x * -np.sin(phi) + y * np.cos(phi)
zz = z
r = np.sqrt(xx**2 + yy**2 + zz**2)
limit, = np.where(r < radio)
tensor = ten.tenf(xx[limit], yy[limit],
zz[limit]) #calculo el tensor de forma
matriz = np.linalg.eig(tensor) #saco los autovalores
autoval = matriz[0]
autovec = matriz[1]
# print autovec, '\n'
asort = np.sort(autoval) #los ordeno de menor a mayor
A = np.sqrt(asort[2]) #semiejes
B = np.sqrt(asort[1])
C = np.sqrt(asort[0])
aa = radio #normalizo al radio que yo quiero
bb = (B / A) * radio
cc = (C / A) * radio
Relip = np.sqrt((xx / aa)**2 + (yy / bb)**2 +
(zz / cc)**2) # formula del elipsoide
mask, = np.where(Relip <= 1.)
xn = x[mask]
yn = y[mask]
zn = z[mask]
vxn = vx[mask]
vyn = vy[mask]
vzn = vz[mask]
rn = np.sqrt(xn**2 + yn**2 + zn**2)
Rn = np.sqrt(xn**2 + yn**2)
Vtg = (-yn * vxn + xn * vyn) / Rn
omega = Vtg / Rn
med, nodos = bine.rbin1(rn, nbin)
omega_mean = np.zeros(nbin)
for i in range(0, nbin):
inbin, = np.where((rn > nodos[i]) & (rn < nodos[i + 1]))
omega_mean[i] = np.mean(omega[inbin])
finterp = sint.interp1d(med, omega_mean, fill_value="extrapolate")
omegabar = finterp(radio)
return omegabar, xn, yn, zn, autovec, A, B, C
