### (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 ------------------------ ... ...
Markdown is supported
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!