Commit dcf66d72 authored by Jean-Eric Campagne's avatar Jean-Eric Campagne
Browse files

(JEC) 7/5/15 polish doc

parent 2c360460
......@@ -61,7 +61,7 @@ The analysis process starts by gathering the 3D pixels real values \f$f_{ijk} \e
+ for the \f$k\f$th-radial shell, one performs a Spherical Harmonic decomposition using for instance the `map2alm` routine of `libsharp` to get the set of complex coefficients \f$a_{lmk}=a_{lm}(r_k)\f$ with \f$l\in\{0,\dots,L-1\}\f$ and \f$m \in\{0,\dots,l\}\f$ (the notation remind the underlying 2D Spherical Harmonic transform and the usual way to note the resulting coefficients \f$a_{lm}\f$);
+ for each \f$(l,m)\f$, one uses the set of values \f$a_{lmk}\f$ with \f$k\in\{0,\dots,N-1\}\f$ to determine the \f$f_{lmn}\f$ complex coefficients thanks to the following simplified relation
\f[
f_{lmn} = \sum_{k=0}^{N-1}w_k\ a_{lmk}\ {\cal L}_n(r_k) \quad\quad n\in\{0,\dots,N-1\}
f_{lmn} = \sum_{k=0}^{N-1}w_k\ a_{lmk}\ {\cal L}_n^{(\alpha)}(r_k) \quad\quad n\in\{0,\dots,N-1\}
\f]
+ **Synthesis**:
......@@ -72,7 +72,7 @@ a_{lmk} = \sum_{n=0}^{N-1} f_{lmn}\ {\cal L}_n^{(\alpha)}(r_k)
\f]
+ then, thanks to the Inverse Spherical Harmonic Transform, `alm2map` routine of `libsharp`, ones determines the real \f$f_{ijk}\f$ pixel values.
We take advantage from the Matrix Multiplication writing of the \f$f_{lmn} \leftrightarrow a_{lmk}\f$ passage to use efficient algorithm or even more efficient the BLAS-like libraries (OpenBLAS for Linux and the native Accelerate framework on Mac OS X).
We take advantage from the Matrix Multiplication writing of the \f$f_{lmn} \leftrightarrow a_{lmk}\f$ passage to use efficient algorithm or even more efficiently the BLAS-like libraries (OpenBLAS for Linux and the native Accelerate framework on Mac OS X).
The main classes in brief
------------------------
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