I am recently studying correlation function method to calculate
lensed C_l following the calculation of arXiv: astro-ph/0502425 . In that paper the flat sky correlation function for temperature anisotropy is given by equation(17) which is an integral over "l". The integrand consists of [tex][ l/(2\pi) C_l \exp(-l^2 \sigma^2(r)/2)(.......)][/tex]. My question is how to perform the numerical integration for a given value of "r" as C_ls are known at integer points (l=2,3,4...) only.
Also what should be the range of [l] in that integration and when we calculate the lensed C_l's we need to perform an integration over "r"
what should be range of r.
I have looked into CAMB: lensing.f90 CorrFuncFlatSky subroutine
but did not understand the program specifically how the evaluation of
"sigmasq", "cgl2" are done
Code: Select all
do i=1,npoints-1
theta = i * dtheta
sigmasq =0
Cgl2=0
fac = theta /dbessel
do l=lmin,CP%Max_l
!Interpolate the Bessel functions, and compute sigma^2 and C_{gl,2}
b0 = l*fac
b_lo = int(b0) +1
a0= b_lo - b0
b0= 1._dl - a0
fac1 = a0*b0*dbessfac
fac2 = fac1*(a0-2)
fac1 = fac1*(b0-2)
Bessel0(l) = a0*Bess0(b_lo)+ b0*Bess0(b_lo+1) +fac1*ddBess0(b_lo) &
+fac2*ddBess0(b_lo+1)
sigmasq = sigmasq + (1-Bessel0(l))*Cphil3(l)
Bessel2(l) = a0*Bess2(b_lo)+ b0*Bess2(b_lo+1) +fac1*ddBess2(b_lo) &
+fac2*ddBess2(b_lo+1)
Cgl2 = Cgl2 + Bessel2(l)*Cphil3(l)
Bessel4(l) = a0*Bess4(b_lo)+ b0*Bess4(b_lo+1) +fac1*ddBess4(b_lo) &
+fac2*ddBess4(b_lo+1)
Bessel6(l) = a0*Bess6(b_lo)+ b0*Bess6(b_lo+1) +fac1*ddBess6(b_lo) &
+fac2*ddBess6(b_lo+1)
end do