cholesky.h

/*
This file is distributed as part of the BIAS library (Basic ImageAlgorithmS)
but it has not been developed by the authors of BIAS.

For copyright, author and license information see below.
*/


/*
*
* Template Numerical Toolkit (TNT): Linear Algebra Module
*
* Mathematical and Computational Sciences Division
* National Institute of Technology,
* Gaithersburg, MD USA
*
*
* This software was developed at the National Institute of Standards and
* Technology (NIST) by employees of the Federal Government in the course
* of their official duties. Pursuant to title 17 Section 105 of the
* United States Code, this software is not subject to copyright protection
* and is in the public domain.  The Template Numerical Toolkit (TNT) is
* an experimental system.  NIST assumes no responsibility whatsoever for
* its use by other parties, and makes no guarantees, expressed or implied,
* about its quality, reliability, or any other characteristic.
*
* BETA VERSION INCOMPLETE AND SUBJECT TO CHANGE
* see http://math.nist.gov/tnt for latest updates.
*
*/



#ifndef CHOLESKY_H
#define CHOLESKY_H

#include <cmath>

// index method

namespace TNT
{


  //
  // Only upper part of A is used.  Cholesky factor is returned in
  // lower part of L.  Returns 0 if successful, 1 otherwise.
  //
  template <class SPDMatrix, class SymmMatrix>
    int Cholesky_upper_factorization(SPDMatrix &A, SymmMatrix &L)
  {
    Subscript M = A.dim(1);
    Subscript N = A.dim(2);

    BIASASSERT(M == N);                 // make sure A is square

    // readjust size of L, if necessary

    if (M != L.dim(1) || N != L.dim(2))
      L = SymmMatrix(N,N);

    Subscript i,j,k;


    typename SPDMatrix::element_type dot=0;


    for (j=1; j<=N; j++)                // form column j of L
    {
      dot= 0;

      for (i=1; i<j; i++)             // for k= 1 TO j-1
        dot = dot +  L(j,i)*L(j,i);

      L(j,j) = A(j,j) - dot;

      for (i=j+1; i<=N; i++)
      {
        dot = 0;
        for (k=1; k<j; k++)
          dot = dot +  L(i,k)*L(j,k);
        L(i,j) = A(j,i) - dot;
      }

      if (L(j,j) <= 0.0) return 1;

      L(j,j) = sqrt( L(j,j) );

      for (i=j+1; i<=N; i++)
        L(i,j) = L(i,j) / L(j,j);

    }

    return 0;
  }




}  
// namespace TNT

#endif
// CHOLESKY_H