alm2dl

Description

alm2dl reads $a_{{\ell}m}$ and calculates $C_{{\ell}}$ and $D_{{\ell}}$ where

$$C_{{\ell}}=\frac{1}{2{\ell}+1}\sum_{m=-{\ell}}^{{\ell}} \vert a_{{\ell}m}\vert^2.$$ (1)

$$D_{{\ell}}=\frac{ {\ell}({\ell}+1)C_{{\ell}}}{2 \pi T_0^2}.$$ (2)

where $T_0 = 2.726$K, $C_{{\ell}}$ is output in unit of $T^2$ and $D_{{\ell}}$ is unitless. alm2dl can read the input $a_{{\ell}m}$ file either in FITS or in ASCII formats. The FITS binary format should contain 3 fields: index= ${\ell}\times {\ell}+{\ell}+m+1$ (in HEALPix definition), $a_{{\ell}m}$ real part ($\Re$) and imaginary part ($\Im$). The ASCII format should contain 4 entries : L, M, Re, Im, where L is the ${\ell}$-multipole and M is the $m$-multipole.

alm2dl calculates $a_{{\ell}m}$ amplitudes: $\vert a_{{\ell}m}\vert$ and phases defined as $\arctan(\Im/\Re)$ in $[0,2\pi]$.

alm2dl also lists the values of the FITS $a_{{\ell}m}$ coefficients, which can be output either to a file or to the standard output device for display.

Examples

1. Calculating $C_{{\ell}}$ or $D_{{\ell}}$:
   • alm2dl alm.txt -lmax 25
     reads ASCII ' alm.txt' and displays $D_{{\ell}}$ up to 25.

   • alm2dl -cl alm.fits -lmax 1000 -o cl.txt
     calculates $C_{{\ell}}$ up to ${\ell}=1000$ from ' alm.fits' and outputs in 'cl.txt'.

2. Listing $a_{{\ell}m}$:
   • alm2dl -g alm.fits | less
     reads FITS file ' alm.fits' and displays in standard output device the $a_{{\ell}m}$ coefficients in 4 columns: ${\ell}$, $m$, real and imaginary parts.

   • alm2dl -p alm.fits -o nlmalm.txt
     reads ' alm.fits' and outputs $a_{{\ell}m}$ and phases to file ' nlmalm.txt' with 6 entries: nlm index (= ${\ell}\times {\ell}+{\ell}+m+1$), ${\ell}$, $m$, real, imaginary part and the phase.

3. Calculating amplitudes:
   • alm2dl -amp alm.fits -lmax 10
     reads ' alm.fits' and calculates amplitudes up to ${\ell}=10$.

   • alm2dl -amp -a alm.txt -lmax 50 -o amp.txt
     reads ASCII ' alm.txt' and outputs ASCII amplitudes up to ${\ell}=50$ in ' amp.txt'.

4. Calculating phases:
   • alm2dl -ph alm.fits -lmax 10
     reads ' alm.fits' and displays phases up to ${\ell}=10$.