Solv_TDMA.cpp

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#include <Solv_TDMA.h>
#include <TRUSTVect.h>
 
void Solv_TDMA::resoudre(const DoubleVect& ma, const DoubleVect& mb, const DoubleVect& mc, const DoubleVect& sm, DoubleVect& vi, int M)
{
  DoubleVect malpha, mbeta; //2 vecteurs intermediares
  DoubleVect my; //vecteur solution du systeme L.y=F
  int i;
  malpha.resize(M);
  mbeta.resize(M);
  my.resize(M);
 
  //L'algorithme de Thomas (TDMA) repose sur la decomposition LU de la matrice
  //tridiagonale a inverser. Soit A.x = y le systeme lineaire a inverser avec A = LU.
  //On resoud d'abord par descente le syteme L.z = y avec z = U.x et on resoud ensuite
  //par remontee le systeme U.x = z.
 
  // Les 3 diagonales de la matrice sont chacune conservees sous forme de vecteur
  // ma : diagonale principale ; mb : diagonale secondaire inferieure
  // mc : diagonale secondaire superieure
  // M est l'ordre de la matrice A
 
  //La matrice L est composee d'une diagonale principale (malpha) et d'une diagonale
  //secondaire inferieure (mb). La matrice U est composee d'une diagonale principale
  //(dont tous les elements sont egaux a 1) et d'une diagonale secondaire superieure
  //(mbeta).
 
  //Resolution correcte d'un systeme lineaire 3*3 antisymetrique, le 23.05.2003
 
  //Remplissage de malpha et mbeta
 
  malpha(0) = ma(0);
  mbeta(0) = mc(0)/ma(0);
 
  for (i = 1 ; i<M-1 ; i++)
    {
      malpha(i) = ma(i) - mb(i-1)*mbeta(i-1);
      mbeta(i) = mc(i)/malpha(i);
    }
  malpha(M-1) = ma(M-1) - mb(M-2)*mbeta(M-2);
 
  //Resolution du premier systeme par descente
 
  my(0) = sm(0)/malpha(0);
 
  for (i = 1 ; i<M ; i++)
    my(i) = (sm(i)-mb(i-1)*my(i-1))/malpha(i);
 
  //Resolution du premier systeme par remontee
 
  vi(M-1) = my(M-1);
 
  for (i = M-2 ; i>=0 ; i--)
    vi(i) = my(i) - mbeta(i)*vi(i+1);
}