/*************************************************************************
Copyright (c) 1992-2007 The University of Tennessee.  All rights reserved.

Contributors:
    * Sergey Bochkanov (ALGLIB project). Translation from FORTRAN to
      pseudocode.

See subroutines comments for additional copyrights.

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modification, are permitted provided that the following conditions are
met:

- Redistributions of source code must retain the above copyright
  notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above copyright
  notice, this list of conditions and the following disclaimer listed
  in this license in the documentation and/or other materials
  provided with the distribution.

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  contributors may be used to endorse or promote products derived from
  this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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*************************************************************************/

#ifndef _cholesky_h
#define _cholesky_h

#include "ap.h"

/*************************************************************************
Cholesky decomposition

The algorithm computes Cholesky decomposition of a symmetric
positive-definite matrix.

The result of an algorithm is a representation of matrix A as A = U'*U or
A = L*L'.

Input parameters:
    A       -   upper or lower triangle of a factorized matrix.
                array with elements [0..N-1, 0..N-1].
    N       -   size of matrix A.
    IsUpper -   if IsUpper=True, then A contains an upper triangle of
                a symmetric matrix, otherwise A contains a lower one.

Output parameters:
    A       -   the result of factorization. If IsUpper=True, then
                the upper triangle contains matrix U, so that A = U'*U,
                and the elements below the main diagonal are not modified.
                Similarly, if IsUpper = False.

Result:
    If the matrix is positive-definite, the function returns True.
    Otherwise, the function returns False. This means that the
    factorization could not be carried out.

  -- LAPACK routine (version 3.0) --
     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
     Courant Institute, Argonne National Lab, and Rice University
     February 29, 1992
*************************************************************************/
bool spdmatrixcholesky(ap::real_2d_array& a, int n, bool isupper);


/*************************************************************************
Obsolete 1-based subroutine.
*************************************************************************/
bool choleskydecomposition(ap::real_2d_array& a, int n, bool isupper);


#endif
