scratch_kl_debug.txt

Process for kl_data from Joseph's paper (arxiv:1004.1409):

(1) Calculate weighted Alm(r), Blm(r) -- Eqs. 51, 52
(2) Calculate weighted A(r,n), B(r,n) -- Eqs. 51, 52
(3) Calculate product maps (for each r) AB, BB, ABA, and ABB 
	-- Eqs. 57, 58 (70-73)
(4) Calculate 3-1 and 2-2 power spectra (for each r) ABA,B; ABB,B; AB,AB; 
	and AB,BB -- Eq. 74
(5) Integrate over r (or r1 and r2) -- Eqs. 70-73
(6) Sum integrated power spectra -- Eq. 68, 69

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Process for kl_data used in kl_data.py:

(1) Load Planck power spectrum, alpha, beta, and beam (na_cltt, 
    na_alpha, na_beta, na_bl) (lines 133-209)
(2) Create optimally weighted maps:
    (a) Convert cltt to alm (na_alm) (line 217)
    (b) For each r1, r2 value used in alpha, beta, multiply 
        alpha / Cl * bl by alm (na_Almr1, na_Blmr1, na_Almr2, 
        na_Blmr2) (lines 291-294)
    (c) For each r1, r2 value used in alpha, beta, convert Alm, Blm 
        to maps (na_Ar1n, na_Br1n, na_Ar2n, na_Br2n) (lines 298-310)
(3) Calculate two-two and three-one power spectra
    (a) For each r1, r2 value used in alpha, beta, multiply 
        Alm * B^2lm and convert to cl (similarly for AB * B) 
        (na_Jl_AB_ABr1, etc.) (lines 316-341)
(4) Calculate full kurtosis power spectra
    (a) Sum over all r values (na_kl22_data, na_kl31_data) (lines 345-357)