Changeset 1218 in Sophya for trunk/SophyaLib/Samba/lambdaBuilder.h

Timestamp:

Oct 3, 2000, 2:14:14 PM (25 years ago)

Author:

ansari

Message:

doc dans .cc

File:

• trunk/SophyaLib/Samba/lambdaBuilder.h (modified) (7 diffs)

trunk/SophyaLib/Samba/lambdaBuilder.h

@@ -10 +10 @@
 namespace SOPHYA {
 
-/*! 
-generate Legendre polynomials : use in two steps : 
-
-a) instanciate Legendre(\f$x\f$, \f$lmax\f$) ; \f$x\f$ is the value for wich Legendre polynomials will be required (usually equal to \f$\cos \theta\f$) and \f$lmax\f$ is the MAXIMUM value of the order of polynomials wich will be required in the following code (all polynomials, from \f$l=0 to lmax\f$, are computed once for all by an iterative formula).
-
-b) get the value of Legendre polynomial for a particular value of \f$l\f$ by calling the method getPl.
-*/
+/*!  classe pour les polynomes de legendre*/
 class Legendre {
 
@@ -32 +26 @@
 
  private : 
-   /*! compute all \f$P_l(x,l_{max})\f$ for \f$l=1,l_{max}\f$ */
   void array_init(int_4 lmax);
 
@@ -42 +35 @@
 
 
-/*! 
-This class generate the coefficients :
-\f[
-            \lambda_l^m=\sqrt{\frac{2l+1}{4\pi}\frac{(l-m)!}{(l+m)!}}
-            P_l^m(\cos{\theta})
-\f]
-where \f$P_l^m\f$ are the associated Legendre polynomials.  The above coefficients contain the theta-dependance of spheric harmonics : 
-\f[
-            Y_{lm}(\cos{\theta})=\lambda_l^m(\cos{\theta}) e^{im\phi}.
-\f]
-
-Each object has a fixed theta (radians), and maximum l and m to be calculated
-(lmax and mmax).
- use the class in two steps : 
-a) instanciate  LambdaLMBuilder(\f$\theta\f$, \f$lmax\f$, \f$mmax\f$) ;  \f$lmax\f$ and \f$mmax\f$ are  MAXIMUM values for which \f$\lambda_l^m\f$ will be required in the following code (all coefficients, from \f$l=0 to lmax\f$, are computed once for all by an iterative formula).
-b) get the values of coefficients for  particular values of \f$l\f$ and \f$m\f$ by calling the method lamlm.
-*/
  class LambdaLMBuilder {
 
@@ -71 +47 @@
 
  private:
-/*! compute a static array of coefficients independant from theta (common to all instances of the LambdaBuilder Class */
  void updateArrayRecurrence(int_4 lmax);
 
@@ -82 +57 @@
  protected :
 
-/*! compute  static arrays of coefficients independant from theta (common to all instances of the derived  classes */
  void updateArrayLamNorm();
 
@@ -96 +70 @@
 
 
-/*! 
-
-This class generates the coefficients :
-\f[
-            _{w}\lambda_l^m=-2\sqrt{\frac{2(l-2)!}{(l+2)!}\frac{(2l+1)}{4\pi}\frac{(l-m)!}{(l+m)!}} G^+_{lm}
-\f]
-\f[
-            _{x}\lambda_l^m=-2\sqrt{\frac{2(l-2)!}{(l+2)!}\frac{(2l+1)}{4\pi}\frac{(l-m)!}{(l+m)!}}G^-_{lm}
-\f]
-where
-\f[G^+_{lm}(\cos{\theta})=-\left( \frac{l-m^2}{\sin^2{\theta}}+\frac{1}{2}l\left(l-1\right)\right)P_l^m(\cos{\theta})+\left(l+m\right)\frac{\cos{\theta}}{\sin^2{\theta}}P^m_{l-1}(\cos{\theta})
-\f]
-and
-\f[G^-_{lm}(\cos{\theta})=\frac{m}{\sin^2{\theta}}\left(\left(l-1\right)\cos{\theta}P^m_l(\cos{\theta})-\left(l+m\right)P^m_{l-1}(\cos{\theta})\right)
-\f]
- \f$P_l^m\f$ are the associated Legendre polynomials.
-
-The coefficients express the theta-dependance of the \f$W_{lm}(\cos{\theta})\f$ and \f$X_{lm}(\cos{\theta})\f$ functions :
-\f[W_{lm}(\cos{\theta}) = \sqrt{\frac{(l+2)!}{2(l-2)!}}_w\lambda_l^m(\cos{\theta})e^{im\phi}
-\f]
-\f[X_{lm}(\cos{\theta}) = -i\sqrt{\frac{(l+2)!}{2(l-2)!}}_x\lambda_l^m(\cos{\theta})e^{im\phi}
-\f]
- where \f$W_{lm}(\cos{\theta})\f$ and \f$X_{lm}(\cos{\theta})\f$ are defined as :
-
-\f[
-W_{lm}(\cos{\theta})=-\frac{1}{2}\sqrt{\frac{(l+2)!}{(l-2)!}}\left(
-_{+2}Y_l^m(\cos{\theta})+_{-2}Y_l^m(\cos{\theta})\right)
-\f]
-\f[X_{lm}(\cos{\theta})=-\frac{i}{2}\sqrt{\frac{(l+2)!}{(l-2)!}}\left(
-_{+2}Y_l^m(\cos{\theta})-_{-2}Y_l^m(\cos{\theta})\right)
-\f]
-
-*/
 class LambdaWXBuilder : public LambdaLMBuilder
 {
@@ -156 +97 @@
 };
 
-/*! 
-
-This class generates the coefficients
-\f[
-            _{\pm}\lambda_l^m=2\sqrt{\frac{(l-2)!}{(l+2)!}\frac{(2l+1)}{4\pi}\frac{(l-m)!}{(l+m)!}}\left( G^+_{lm} \mp G^-_{lm}\right)
-\f]
-where
-\f[G^+_{lm}(\cos{\theta})=-\left( \frac{l-m^2}{\sin^2{\theta}}+\frac{1}{2}l\left(l-1\right)\right)P_l^m(\cos{\theta})+\left(l+m\right)\frac{\cos{\theta}}{\sin^2{\theta}}P^m_{l-1}(\cos{\theta})
-\f]
-and
-\f[G^-_{lm}(\cos{\theta})=\frac{m}{\sin^2{\theta}}\left(\left(l-1\right)\cos{\theta}P^m_l(\cos{\theta})-\left(l+m\right)P^m_{l-1}(\cos{\theta})\right)
-\f]
-and \f$P_l^m\f$ are the associated Legendre polynomials.
-The coefficients express the theta-dependance of the  spin-2 spherical harmonics :
-\f[_{\pm2}Y_l^m(\cos{\theta})=_\pm\lambda_l^m(\cos{\theta})e^{im\phi}
-\f]
-*/
 class LambdaPMBuilder : public LambdaLMBuilder
 {