def generalIntOverMassFn(beta, mExponent, extra_integrand, h, whichp = 0):
""" beta
Computes I (k) (as in Cooray & Hu (2001)), integrating over the halo mass function.
mu
beta: order of bias coefficient (b_beta in the integrand)
mExponent: additional (over the power of m from the logarithmic integration)
mass exponent (put mu here)
extra_integrand: e.g. halo density profiles
h: halo model instance
e.g. i11[k] = integralOverMassFn(1,1, g.int(h.fthp[k,:,:]),h)
where the two : indices in h.fthp are for mass and concentration parameter;
g.int integrates over concentration parameter, so g.int(h.fthp[k,:,:]) is an array
for each mass.
"""
if whichp == 0:
whichp == h.p.whichp
if whichp == 'gg':
integrand = h.b[beta,:]*h.m*hodMoment(mExponent,h)*h.nmz * extra_integrand
elif whichp == 'mm':
integrand = h.b[beta,:]*h.m*h.m**(mExponent)*h.nmz * extra_integrand
ans = utils.simpsonRule(integrand, h.dlogm)
return ans
def intOverMassFn(beta, mExponent, karrayunnumed, h, whichp = 0, plot = 0, show = 0,colstr = ''):
"""
Get an integral of, e.g., halo density profiles over the mass function.
More automatic than generalIntOverMassFn.
beta
Computes I (k) (as in Cooray & Hu (2001)), integrating over the halo mass function.
mu
beta: order of bias coefficient (b_beta in the integrand)
mExponent: additional (over the power of m from the logarithmic integration)
mass exponent (put mu here).
karrayunnumed: Array of k indices to evaluate Fourier-transformed halo density profile
h: halo model instance
whichp: for now, 'gg' -> galaxy statistics.
'mm' -> matter stats. Default: h.p.whichp
"""
if whichp == 0:
whichp = h.p.whichp
karray = M.array(karrayunnumed)
if len(karray) != mExponent:
print "Warning! Different number of k indices than mExponent!"
g = utils.HGQ(5) # 5-pt Hermite-Gauss quadrature class
uM = h.fthp[0,:,:]*0. + 1.
g_integrand = h.fthp[0,:,:]*0. + 1.
if whichp == 'gg':
"""
Right now, we've only implemented the Kravtsov-style 'satellite' halo occupation distribution,
i.e. the HOD excluding the central galaxy. For example, in Smith, Watts & Sheth 2006, sect. 5.4, the
halo integrands simplify in the case of a satellite HOD in eq. 72 (one-halo P_gg) to
<Ns(Ns-1)> |u(k)|^2 + 2 <Ns> u(k). This second term includes the contribution of the central galaxy.
In general, using SWS's notation, the n-galaxy convolution kernel (e.g. eq. 76) is
W^ng(k_0, ..., k_n) = <Ns(Ns-1)...(Ns-n)> u(k_0)...u(k_n) + Sum_i <Ns...(Ns-(n-1))> u(k_0)...u(k_n)/u(k_i).
"""
hodNsMomentM = M.outer(hodNsMoment(mExponent,h),1.*M.ones(5))
hodNsMomentMminus1 = M.outer(hodNsMoment(mExponent-1,h),1.*M.ones(5))
# Leading term in mExponent; fthp(k)^mExponent
for ki in karray:
uM *= h.fthp[ki,:,:]
g_integrand = hodNsMomentM*uM*1.
#mExponent * fthp^(mExponent-1) term
for ki in karray:
g_integrand += hodNsMomentMminus1 * uM/h.fthp[ki,:,:]
extra_integrand = g.int(g_integrand)
elif whichp == 'mm':
for ki in karray:
g_integrand *= h.fthp[ki,:,:]
extra_integrand = h.m**(mExponent)* g.int(g_integrand)
integrand = h.b[beta,:]*h.m*h.nmz * extra_integrand
if plot == 1:
M.loglog(h.m[::10],integrand[::10],colstr)
#M.semilogx(h.m,integrand)
if show == 1:
M.show()
ans = utils.simpsonRule(integrand[:h.integratetoindex], h.dlogm)
if whichp == 'gg':
ans /= h.ngalbar**mExponent
return ans
