sdpa_jordan.h

/* -------------------------------------------------------------

This file is a component of SDPA
Copyright (C) 2004 SDPA Project

This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307 USA

------------------------------------------------------------- */

#ifndef __sdpa_jordan_h__
#define __sdpa_jordan_h__

#include <sdpa_linear.h>

namespace sdpa {
class WorkVariables;
}

namespace sdpa {

class Jal {
  public:
    static mpf_class trace(DenseLinearSpace &aMat);

    // calculate the minimum eigen value of lMat*xMat*(lMat^T)
    // by Lanczos methods.
    // lMat is lower triangular¡¢xMat is symmetric
    // block size > 20   : Lanczos method
    // block size <= 20  : QR method
    static mpf_class getMinEigen(DenseLinearSpace &lMat, DenseLinearSpace &xMat, WorkVariables &work);

    // calculate the minimum eigen value of xMat by QR method.
    static mpf_class getMinEigen(DenseLinearSpace &xMat, WorkVariables &work);

    static bool getInvChol(DenseLinearSpace &invCholMat, DenseLinearSpace &aMat, DenseLinearSpace &workMat);

    static bool getInvCholAndInv(DenseLinearSpace &invCholMat, DenseLinearSpace &inverseMat, DenseLinearSpace &aMat, DenseLinearSpace &workMat);

    static bool multiply(DenseLinearSpace &retMat, DenseLinearSpace &aMat, DenseLinearSpace &bMat, mpf_class *scalar = NULL);
#if 0
// CAUTION!!! We don't initialize retMat to zero matrix for efficiently.
  static bool multiply(DenseLinearSpace& retMat,
		       SparseLinearSpace& aMat,
		       DenseLinearSpace& bMat,
		       mpf_class* scalar = NULL);
// CAUTION!!! We don't initialize retMat to zero matrix for efficiently.
  static bool multiply(DenseLinearSpace& retMat,
		       DenseLinearSpace& aMat,
		       SparseLinearSpace& bMat,
		       mpf_class* scalar = NULL);
#endif

    //  retMat = L_{A} B = (A * B + B * A)/2
    static bool jordan_product(DenseLinearSpace &retMat, DenseLinearSpace &aMat, DenseLinearSpace &bMat);
    //  retMat = A * B
    static bool ns_jordan_product(DenseLinearSpace &retMat, DenseLinearSpace &aMat, DenseLinearSpace &bMat);

    //  retMat = P_{A} B = A * B * A
    static bool jordan_quadratic_product(DenseLinearSpace &retMat, DenseLinearSpace &aMat, DenseLinearSpace &bMat, DenseLinearSpace &work);

    //  retMat = Q_{A,C} B = (A * B * C + C * B * A)/2
    static bool jordan_triple_product(DenseLinearSpace &retMat, DenseLinearSpace &aMat, DenseLinearSpace &bMat, DenseLinearSpace &cMat, DenseLinearSpace &work);

    //  retMat = A * B * C
    static bool ns_jordan_triple_product(DenseLinearSpace &retMat, DenseLinearSpace &aMat, DenseLinearSpace &bMat, DenseLinearSpace &cMat, DenseLinearSpace &work);
};

} // namespace sdpa

#endif // __sdpa_jordan_h__