trisolve.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.
*
*/



// Triangular Solves

#ifndef TRISLV_H
#define TRISLV_H


#include "triang.h"

namespace TNT
{

  template <class MaTriX, class VecToR>
    VecToR Lower_triangular_solve(/*const*/ MaTriX &A, /*const*/ VecToR &b)
  {
    Subscript N = A.num_rows();

    // make sure matrix sizes agree; A must be square

    BIASASSERT(A.num_cols() == N);
    BIASASSERT(b.dim() == N);

    VecToR x(N);

    Subscript i;
    for (i=1; i<=N; i++)
    {
      typename MaTriX::element_type tmp=0;

      for (Subscript j=1; j<i; j++)
        tmp = tmp + A(i,j)*x(j);

      x(i) =  (b(i) - tmp)/ A(i,i);
    }

    return x;
  }


  template <class MaTriX, class VecToR>
    VecToR Unit_lower_triangular_solve(/*const*/ MaTriX &A, /*const*/ VecToR &b)
  {
    Subscript N = A.num_rows();

    // make sure matrix sizes agree; A must be square

    BIASASSERT(A.num_cols() == N);
    BIASASSERT(b.dim() == N);

    VecToR x(N);

    Subscript i;
    for (i=1; i<=N; i++)
    {

      typename MaTriX::element_type tmp=0;

      for (Subscript j=1; j<i; j++)
        tmp = tmp + A(i,j)*x(j);

      x(i) =  b(i) - tmp;
    }

    return x;
  }


  template <class MaTriX, class VecToR>
    VecToR linear_solve(/*const*/ LowerTriangularView<MaTriX> &A, 
    /*const*/ VecToR &b)
  {
    return Lower_triangular_solve(A, b);
  }

  template <class MaTriX, class VecToR>
    VecToR linear_solve(/*const*/ UnitLowerTriangularView<MaTriX> &A, 
    /*const*/ VecToR &b)
  {
    return Unit_lower_triangular_solve(A, b);
  }



  //********************** Upper triangular section ****************

  template <class MaTriX, class VecToR>
    VecToR Upper_triangular_solve(/*const*/ MaTriX &A, /*const*/ VecToR &b)
  {
    Subscript N = A.num_rows();

    // make sure matrix sizes agree; A must be square

    BIASASSERT(A.num_cols() == N);
    BIASASSERT(b.dim() == N);

    VecToR x(N);

    Subscript i;
    for (i=N; i>=1; i--)
    {

      typename MaTriX::element_type tmp=0;

      for (Subscript j=i+1; j<=N; j++)
        tmp = tmp + A(i,j)*x(j);

      x(i) =  (b(i) - tmp)/ A(i,i);
    }

    return x;
  }


  template <class MaTriX, class VecToR>
    VecToR Unit_upper_triangular_solve(/*const*/ MaTriX &A, /*const*/ VecToR &b)
  {
    Subscript N = A.num_rows();

    // make sure matrix sizes agree; A must be square

    BIASASSERT(A.num_cols() == N);
    BIASASSERT(b.dim() == N);

    VecToR x(N);

    Subscript i;
    for (i=N; i>=1; i--)
    {

      typename MaTriX::element_type tmp=0;

      for (Subscript j=i+1; j<i; j++)
        tmp = tmp + A(i,j)*x(j);

      x(i) =  b(i) - tmp;
    }

    return x;
  }


  template <class MaTriX, class VecToR>
    VecToR linear_solve(/*const*/ UpperTriangularView<MaTriX> &A, 
    /*const*/ VecToR &b)
  {
    return Upper_triangular_solve(A, b);
  }

  template <class MaTriX, class VecToR>
    VecToR linear_solve(/*const*/ UnitUpperTriangularView<MaTriX> &A, 
    /*const*/ VecToR &b)
  {
    return Unit_upper_triangular_solve(A, b);
  }


} // namespace TNT

#endif
// TRISLV_H