Lapack_Cholesky.h

// -*- c++ -*-

//     Copyright (C) 2009 Tom Drummond (twd20@cam.ac.uk)
//
// This file is part of the TooN Library.  This library 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, or (at your option)
// any later version.

// This library 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 library; see the file COPYING.  If not, write to the Free
// Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307,
// USA.

// As a special exception, you may use this file as part of a free software
// library without restriction.  Specifically, if other files instantiate
// templates or use macros or inline functions from this file, or you compile
// this file and link it with other files to produce an executable, this
// file does not by itself cause the resulting executable to be covered by
// the GNU General Public License.  This exception does not however
// invalidate any other reasons why the executable file might be covered by
// the GNU General Public License.


#ifndef TOON_INCLUDE_LAPACK_CHOLESKY_H
#define TOON_INCLUDE_LAPACK_CHOLESKY_H

#include <TooN/TooN.h>

#include <TooN/lapack.h>

#include <assert.h>

namespace TooN {


/**
Decomposes a positive-semidefinite symmetric matrix A (such as a covariance) into L*L^T, where L is lower-triangular.
Also can compute A = S*S^T, with S lower triangular.  The LDL^T form is faster to compute than the class Cholesky decomposition.
The decomposition can be used to compute A^-1*x, A^-1*M, M*A^-1*M^T, and A^-1 itself, though the latter rarely needs to be explicitly represented.
Also efficiently computes det(A) and rank(A).
It can be used as follows:
@code
// Declare some matrices.
Matrix<3> A = ...; // we'll pretend it is pos-def
Matrix<2,3> M;
Matrix<2> B;
Vector<3> y = make_Vector(2,3,4);
// create the Cholesky decomposition of A
Cholesky<3> chol(A);
// compute x = A^-1 * y
x = cholA.backsub(y);
//compute A^-1
Matrix<3> Ainv = cholA.get_inverse();
@endcode
@ingroup gDecomps

Cholesky decomposition of a symmetric matrix.
Only the lower half of the matrix is considered
This uses the non-sqrt version of the decomposition
giving symmetric M = L*D*L.T() where the diagonal of L contains ones
@param Size the size of the matrix
@param Precision the precision of the entries in the matrix and its decomposition
**/
template <int Size, typename Precision=DefaultPrecision>
class Lapack_Cholesky {
public:

    Lapack_Cholesky(){}
    
    template<class P2, class B2>
    Lapack_Cholesky(const Matrix<Size, Size, P2, B2>& m) 
      : my_cholesky(m), my_cholesky_lapack(m) {
        SizeMismatch<Size,Size>::test(m.num_rows(), m.num_cols());
        do_compute();
    }

    /// Constructor for Size=Dynamic
    Lapack_Cholesky(int size) : my_cholesky(size,size), my_cholesky_lapack(size,size) {}

    template<class P2, class B2> void compute(const Matrix<Size, Size, P2, B2>& m){
        SizeMismatch<Size,Size>::test(m.num_rows(), m.num_cols());
        SizeMismatch<Size,Size>::test(m.num_rows(), my_cholesky.num_rows());
        my_cholesky_lapack=m;
        do_compute();
    }



    void do_compute(){
        FortranInteger N = my_cholesky.num_rows();
        FortranInteger info;
        potrf_("L", &N, my_cholesky_lapack.my_data, &N, &info);
        for (int i=0;i<N;i++) {
          int j;
          for (j=0;j<=i;j++) {
            my_cholesky[i][j]=my_cholesky_lapack[j][i];
          }
          // LAPACK does not set upper triangle to zero, 
          // must be done here
          for (;j<N;j++) {
            my_cholesky[i][j]=0;
          }
        }
        assert(info >= 0);
        if (info > 0) {
            my_rank = info-1;
        } else {
            my_rank = N;
        }
    }

    int rank() const { return my_rank; }

    template <int Size2, typename P2, typename B2>
        Vector<Size, Precision> backsub (const Vector<Size2, P2, B2>& v) const {
        SizeMismatch<Size,Size2>::test(my_cholesky.num_cols(), v.size());

        Vector<Size, Precision> result(v);
        FortranInteger N=my_cholesky.num_rows();
        FortranInteger NRHS=1;
        FortranInteger info;
        potrs_("L", &N, &NRHS, my_cholesky_lapack.my_data, &N, result.my_data, &N, &info);     
        assert(info==0);
        return result;
    }

    template <int Size2, int Cols2, typename P2, typename B2>
        Matrix<Size, Cols2, Precision, ColMajor> backsub (const Matrix<Size2, Cols2, P2, B2>& m) const {
        SizeMismatch<Size,Size2>::test(my_cholesky.num_cols(), m.num_rows());

        Matrix<Size, Cols2, Precision, ColMajor> result(m);
        FortranInteger N=my_cholesky.num_rows();
        FortranInteger NRHS=m.num_cols();
        FortranInteger info;
        potrs_("L", &N, &NRHS, my_cholesky_lapack.my_data, &N, result.my_data, &N, &info);     
        assert(info==0);
        return result;
    }

    template <int Size2, typename P2, typename B2>
        Precision mahalanobis(const Vector<Size2, P2, B2>& v) const {
        return v * backsub(v);
    }

    Matrix<Size,Size,Precision> get_L() const {
        return my_cholesky;
    }

    Precision determinant() const {
        Precision det = my_cholesky[0][0];
        for (int i=1; i<my_cholesky.num_rows(); i++)
            det *= my_cholesky[i][i];
        return det*det;
    }

    Matrix<> get_inverse() const {
        Matrix<Size, Size, Precision> M(my_cholesky.num_rows(),my_cholesky.num_rows());
        M=my_cholesky_lapack;
        FortranInteger N = my_cholesky.num_rows();
        FortranInteger info;
        potri_("L", &N, M.my_data, &N, &info);
        assert(info == 0);
        for (int i=1;i<N;i++) {
          for (int j=0;j<i;j++) {
            M[i][j]=M[j][i];
          }
        }
        return M;
    }

private:
    Matrix<Size,Size,Precision> my_cholesky;     
    Matrix<Size,Size,Precision> my_cholesky_lapack;     
    FortranInteger my_rank;
};


}

#endif