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alm2dl

Description

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

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


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

  2. Listing $a_{{\ell}m}$:

  3. Calculating amplitudes:

  4. Calculating phases:


next up previous
Next: cl2map Up: GLESP Description and Examples Previous: GLESP Description and Examples
Gauss Legendre Sky Pixelization