def drhonfw(c,delta,z,omegam,omegal,h,alp,bet,renc,Mrenc,rmin,rmax,r):
'''Calculates dlnrhodlnr for a generalised NFW profile'''
rs = findrs(c,delta,z,omegam,omegal,h,alp,bet,renc,Mrenc,rmin,rmax)
print 'rs found:', rs, c, alp, bet
rho = (r/rs)**(-alp)*(1+r/rs)**(alp-bet)
lnr = log(r)
lnrho = log(rho)
return derivative(lambda x: interp(x,lnr,lnrho,left=0,right=0),lnr)
def drhonfw(c, delta, z, omegam, omegal, h, alp, bet, renc, Mrenc, rmin, rmax,
r):
'''Calculates dlnrhodlnr for a generalised NFW profile'''
rs = findrs(c, delta, z, omegam, omegal, h, alp, bet, renc, Mrenc, rmin,
rmax)
print 'rs found:', rs, c, alp, bet
rho = (r / rs)**(-alp) * (1 + r / rs)**(alp - bet)
lnr = log(r)
lnrho = log(rho)
return derivative(lambda x: interp(x, lnr, lnrho, left=0, right=0), lnr)
def dlnrhodlnr(rmin, rmax, alphalim, r, rho, mass, R, sigma, massp, rin):
'''Numerically differentiates the density distribution to obtain a
non-parameteric measure of the power law exponent as a function of
radius'''
lnr = log(r)
lnrho = log(rho)
lnrin = log(rin)
# Find match points:
rmin, rmax, sigc_in, sigc_out, Ain, alpin, Aout, m0 = \
findmatchpoints(rmin,rmax,alphalim,R,sigma,massp)
# Find array elements in r corresponding to rmin/rmax: We use r[1] and not
# r[0] for the low range because interpolation at r[0] is unreliable.
jl = 1 if rmin < r[1] else argmin(abs(r - rmin))
jr = -1 if rmax > r[-1] else argmin(abs(r - rmax))
#print rmin, rmax, r[jl], r[jr]
rmin = r[jl]
rmax = r[jr]
# Calculate inner/outer power law match values:
rhoc_in = rho[jl]
rhoc_out = rho[jr]
# Inner power [consistent with known enclosed mass & smooth rho]
menc_in_real = mass[jl]
gamin = 3 - rhoc_in * 4 * pi / menc_in_real * rmin**3
Ain = rhoc_in * rmin**gamin
# Outer power consistent with alphalim
gamout = alphalim + 1
Aout = rhoc_out * rmax**gamout
# Interpolate for rmin<r<rmax; power law otherwise:
output = empty(len(rin), 'double')
output = derivative(lambda x: interp(x, lnr, lnrho, left=0, right=0),
lnrin)
w = rin > rmax
output[w] = -gamout
w = rin < rmin
output[w] = -gamin
return output
def dSigdR(rmin, rmax, alphalim, R, sigma, massp, rin):
'''dSigdR function to calculate and interpolate derivative of the surface
density. It sews on power laws where there are no data.'''
# Find match points:
rmin, rmax, sigc_in, sigc_out, Ain, alpin, Aout, m0 = \
findmatchpoints(rmin,rmax,alphalim,R,sigma,massp)
# Interpolate for rmin<r<rmax; power law otherwise:
output = empty(len(rin), 'double')
output = derivative(lambda x: interp(x, R, sigma), rin)
w = rin > rmax
output[w] = -alphalim * Aout * rin[w]**(-alphalim - 1)
w = rin < rmin
output[w] = -alpin * Ain * rin[w]**(-alpin - 1)
return output
def dSigdR(rmin,rmax,alphalim,R,sigma,massp,rin):
'''dSigdR function to calculate and interpolate derivative of the surface
density. It sews on power laws where there are no data.'''
# Find match points:
rmin, rmax, sigc_in, sigc_out, Ain, alpin, Aout, m0 = \
findmatchpoints(rmin,rmax,alphalim,R,sigma,massp)
# Interpolate for rmin<r<rmax; power law otherwise:
output = empty(len(rin), 'double')
output = derivative(lambda x: interp(x,R,sigma), rin)
w = rin > rmax
output[w] = -alphalim*Aout*rin[w]**(-alphalim-1)
w = rin < rmin
output[w] = -alpin*Ain*rin[w]**(-alpin-1)
return output
def dlnrhodlnr(rmin,rmax,alphalim,r,rho,mass,R,sigma,massp,rin):
'''Numerically differentiates the density distribution to obtain a
non-parameteric measure of the power law exponent as a function of
radius'''
lnr = log(r)
lnrho = log(rho)
lnrin = log(rin)
# Find match points:
rmin, rmax, sigc_in, sigc_out, Ain, alpin, Aout, m0 = \
findmatchpoints(rmin,rmax,alphalim,R,sigma,massp)
# Find array elements in r corresponding to rmin/rmax: We use r[1] and not
# r[0] for the low range because interpolation at r[0] is unreliable.
jl = 1 if rmin < r[1] else argmin(abs(r-rmin))
jr = -1 if rmax > r[-1] else argmin(abs(r-rmax))
#print rmin, rmax, r[jl], r[jr]
rmin = r[jl]
rmax = r[jr]
# Calculate inner/outer power law match values:
rhoc_in = rho[jl]
rhoc_out = rho[jr]
# Inner power [consistent with known enclosed mass & smooth rho]
menc_in_real = mass[jl]
gamin = 3 - rhoc_in*4*pi/menc_in_real*rmin**3
Ain = rhoc_in * rmin**gamin
# Outer power consistent with alphalim
gamout = alphalim + 1
Aout = rhoc_out * rmax**gamout
# Interpolate for rmin<r<rmax; power law otherwise:
output = empty(len(rin), 'double')
output = derivative(lambda x: interp(x,lnr,lnrho,left=0,right=0),lnrin)
w = rin > rmax
output[w] = -gamout
w = rin < rmin
output[w] = -gamin
return output
def cumsolve(r, imagemin, imagemax, integrator, intpnts, alphalim, R, sigma,
massp):
'''Solve the Abel integral to obtain M(r) and then rho(r). This routine
performs better than abelsolve() and ought to be used instead where
possible.'''
# Some asserts to check the inputs are all sensible:
assert imagemin >= 0,\
'Imagemin %f < 0' % imagemin
assert imagemin < imagemax,\
'Imagemin %f > Imagemax %f' % (imagemin, imagemax)
assert imagemax > 0,\
'Imagemax %f < 0' % imagemax
assert intpnts > 0,\
'inpnts %i <= 0' % intpnts
assert alphalim > 0,\
'alphalim %f < 0' % alphalim
assert alphalim >= 2,\
'alphalim %f < 2 (this alphalim gives > "log-infinite" mass)' % \
alphalim
theta = linspace(0, pi / 2 - 1e-6, num=intpnts)
cth = cos(theta)
sth = sin(theta)
massout = empty(len(r), 'double')
for i in xrange(len(r)):
y = sigmaint(imagemin,imagemax,alphalim,R,sigma,massp,r[i]/cth)*\
(1/cth**2-sth/cth**3*arctan(cth/sth))
massout[i] = -4 * r[i]**2 * integrator(y, theta)
massout = massout + \
masspint(imagemin,imagemax,alphalim,R,sigma,massp,r)
# Calculate the density as the derivative of massout:
rhoout = derivative(lambda x: interp(x,r,massout,right=0),r)/\
(4*pi*r**2)
rhoout[-1] = 0
return rhoout, massout
def cumsolve(r,imagemin,imagemax,integrator,intpnts,alphalim,R,sigma,massp):
'''Solve the Abel integral to obtain M(r) and then rho(r). This routine
performs better than abelsolve() and ought to be used instead where
possible.'''
# Some asserts to check the inputs are all sensible:
assert imagemin >= 0,\
'Imagemin %f < 0' % imagemin
assert imagemin < imagemax,\
'Imagemin %f > Imagemax %f' % (imagemin, imagemax)
assert imagemax > 0,\
'Imagemax %f < 0' % imagemax
assert intpnts > 0,\
'inpnts %i <= 0' % intpnts
assert alphalim > 0,\
'alphalim %f < 0' % alphalim
assert alphalim >= 2,\
'alphalim %f < 2 (this alphalim gives > "log-infinite" mass)' % \
alphalim
theta = linspace(0,pi/2-1e-6,num=intpnts)
cth = cos(theta)
sth = sin(theta)
massout = empty(len(r), 'double')
for i in xrange(len(r)):
y = sigmaint(imagemin,imagemax,alphalim,R,sigma,massp,r[i]/cth)*\
(1/cth**2-sth/cth**3*arctan(cth/sth))
massout[i] = -4*r[i]**2*integrator(y,theta)
massout = massout + \
masspint(imagemin,imagemax,alphalim,R,sigma,massp,r)
# Calculate the density as the derivative of massout:
rhoout = derivative(lambda x: interp(x,r,massout,right=0),r)/\
(4*pi*r**2)
rhoout[-1] = 0
return rhoout, massout
def C(n, u):
num = derivative(lambda z: P(z, u), n, order=5)
den = derivative(lambda z: E(z, u), n, order=5)
return num / den
def P(n, u):
return n * derivative(lambda z: E(z, u), n, order=5, dx=1e-5) - E(n, u)
def dsurf(self, r, pars):
'''Calculates radial derivative of surface density'''
return derivative(lambda x: interp(x, self.rsin, self.sdenin, right=0),
r)
def C(n, u):
num = derivative(lambda z: P(z, u), n, order = 5)
den = derivative(lambda z: E(z, u), n, order = 5)
return num/den
def P(n, u):
return n*derivative(lambda z: E(z, u), n, order = 5, dx=1e-5) - E(n, u)
def dsurf(self, r, pars):
'''Calculates radial derivative of surface density'''
return derivative(lambda x: interp(x,self.rsin,self.sdenin,right=0), r)
def df(x):
return derivative(f, x, dx=1e-6)
def corenfw_tides_dlnrhodlnr(r,M200,c,rc,n,rt,delta):
dden = derivative(\
lambda x: corenfw_tides_den(x,M200,c,rc,n,rt,delta),\
r,dx=1e-6)
dlnrhodlnr = dden / corenfw_tides_den(r,M200,c,rc,n,rt,delta) * r
return dlnrhodlnr
def Vs(wr, n):
return derivative(wr.P, n, dx=1e-1,order = 5)/derivative(wr.E, n, dx=1e-1,order = 5)
def Vs(wr, n):
return derivative(wr.P, n, dx=1e-1, order=5) / derivative(
wr.E, n, dx=1e-1, order=5)