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 intermediate vectors
  DoubleVect my; //solution vector of the system L.y=F
  int i;
  malpha.resize(M);
  mbeta.resize(M);
  my.resize(M);
 
  //The Thomas algorithm (TDMA) relies on the LU decomposition of the tridiagonal
  //matrix to be inverted. Let A.x = y be the linear system to solve with A = LU.
  //We first solve by forward substitution the system L.z = y with z = U.x, then
  //solve by back substitution the system U.x = z.
 
  // The 3 diagonals of the matrix are each stored as a vector:
  // ma: main diagonal; mb: lower sub-diagonal
  // mc: upper super-diagonal
  // M is the order of matrix A
 
  //Matrix L has a main diagonal (malpha) and a lower sub-diagonal (mb).
  //Matrix U has a main diagonal (all elements equal to 1) and an upper
  //super-diagonal (mbeta).
 
  //Verified solution of an antisymmetric 3x3 linear system (23.05.2003)
 
  //Fill malpha and 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);
 
  //Forward substitution to solve the first system
 
  my(0) = sm(0)/malpha(0);
 
  for (i = 1 ; i<M ; i++)
    my(i) = (sm(i)-mb(i-1)*my(i-1))/malpha(i);
 
  //Back substitution to solve the second system
 
  vi(M-1) = my(M-1);
 
  for (i = M-2 ; i>=0 ; i--)
    vi(i) = my(i) - mbeta(i)*vi(i+1);
}