RAMSES	Systems Ecology
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DEFINITION MODULE JacobiL;

  (*******************************************************************

    Module  JacobiL     (Version 1.0)

      Copyright (c) 1992-2006 by Dimitrios Gyalistras and ETH Zurich.

    Purpose   Compute the eigenvalues and eigenvectors of
              a real symmetric matrix.

    Remarks   Algorithms taken from Press, W.H. et al. (1988).
              Numerical Recipes, Cambridge, pp 335 and 748-750
              (ISBN 0521 30811 9).


    Programming

      o Design
        Dimitrios Gyalistras      03/04/1992

      o Implementation
        Dimitrios Gyalistras      03/04/1992


    ETH Zurich
    Systems Ecology
    CHN E 35.1
    Universitaetstrasse 16
    8092 Zurich
    SWITZERLAND

    URLs:
        <mailto:RAMSES@env.ethz.ch>
        <http://www.sysecol.ethz.ch>
        <http://www.sysecol.ethz.ch/SimSoftware/RAMSES>


    Last revision of definition:  14/09/1999  AF

  *******************************************************************)


  FROM LMatrices IMPORT MaxElems, LMatrix, LVector;

  CONST
    VecSize = MaxElems;

  TYPE
    Vector  = LVector;
    Matrix  = LMatrix;


  PROCEDURE Jacobi( VAR mat     : Matrix;
                        dim     : INTEGER;
                    VAR eigVals : Vector;
  					VAR eigVecs : Matrix;
  					VAR numRot  : INTEGER );
  (*
    Calculates all eigenvectors and eigenvalues of the dim x dim
    -matrix stored in 'mat'. 'eigVals' returns in its first 'dim'
    elements the eigenvalues of 'mat'. 'eigVecs' is a dim x dim
    -matrix returning the normalized eigenvectors of 'mat' (sum of
    squares of vector elements = 1). 'numRot' returns the number of
    jacobi rotations which were required.
    NOTE: After calling the procedure, all elements of 'mat' above
    the diagonal will have been overwritten with 0!
  *)

  PROCEDURE EigSort( VAR eigVals : Vector;
                     VAR eigVecs : Matrix;
                     dim         : INTEGER );
  (*
    Given 'dim' eigenvalues in vector 'eigVals' and the dim x
    dim -matrix 'eigVecs' containing the corresponding
    eigenvectors (as obtained both from procedure Jacobi), this
    routine sorts the eigenvalues in descending order. The columns
    of the 'eigVecs'-matrix are rearranged correspondingly. The
    method used is straight insertion.
  *)

END JacobiL.