Dinv.h

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// @(#)root/smatrix:$Id$
// Authors: T. Glebe, L. Moneta    2005

#ifndef  ROOT_Math_Dinv
#define  ROOT_Math_Dinv
// ********************************************************************
//
// source:
//
// type:      source code
//
// created:   03. Apr 2001
//
// author:    Thorsten Glebe
//            HERA-B Collaboration
//            Max-Planck-Institut fuer Kernphysik
//            Saupfercheckweg 1
//            69117 Heidelberg
//            Germany
//            E-mail: T.Glebe@mpi-hd.mpg.de
//
// Description: square Matrix inversion
//              Code was taken from CERNLIB::kernlib dfinv function, translated
//              from FORTRAN to C++ and optimized.
//              n:    Order of the square matrix
//              idim: First dimension of array A
//
// changes:
// 03 Apr 2001 (TG) creation
//
// ********************************************************************
#ifdef OLD_IMPL
#include "Math/Dfactir.h"
#include "Math/Dfinv.h"
#include "Math/Dsinv.h"
#endif

#ifndef ROOT_Math_CholeskyDecomp
#include "Math/CholeskyDecomp.h"
#endif

#ifndef ROOT_Math_MatrixRepresentationsStatic
#include "Math/MatrixRepresentationsStatic.h"
#endif

// #ifndef ROOT_Math_QRDecomposition
// #include "Math/QRDecomposition.h"
// #endif

#include "TError.h"

namespace ROOT {

  namespace Math {



/**
    Matrix Inverter class
    Class to specialize calls to Dinv. Dinv computes the inverse of a square
    matrix if dimension idim and order n. The content of the matrix will be
    replaced by its inverse. In case the inversion fails, the matrix content is
    destroyed. Invert specializes Dinv by the matrix order. E.g. if the order
    of the matrix is two, the routine Inverter<2> is called which implements
    Cramers rule.

    @author T. Glebe
*/
//==============================================================================
// Inverter class
//==============================================================================
template <unsigned int idim, unsigned int n = idim>
class Inverter {
public:
  /// matrix inversion for a generic square matrix using LU factorization
  /// (code originally from CERNLIB and then ported in C++ for CLHEP)
  /// implementation is in file Math/MatrixInversion.icc
  template <class MatrixRep>
  static bool Dinv(MatrixRep& rhs) {


      /* Initialized data */
     unsigned int work[n+1] = {0};

     typename MatrixRep::value_type det(0.0);

     if (DfactMatrix(rhs,det,work) != 0) {
        Error("Inverter::Dinv","Dfact_matrix failed!!");
        return false;
     }

     int ifail =  DfinvMatrix(rhs,work);
     if (ifail == 0) return true;
     return false;
  } // Dinv


  ///  symmetric matrix inversion using
  ///   Bunch-kaufman pivoting method
  ///   implementation in Math/MatrixInversion.icc
  template <class T>
  static bool Dinv(MatRepSym<T,idim> & rhs) {
    int ifail = 0;
    InvertBunchKaufman(rhs,ifail);
    if (ifail == 0) return true;
    return false;
  }


  /**
     LU Factorization method for inversion of general square matrices
     (see implementation in Math/MatrixInversion.icc)
   */
  template <class T>
  static int DfactMatrix(MatRepStd<T,idim,n> & rhs, T & det, unsigned int * work);
  /**
     LU inversion of general square matrices. To be called after DFactMatrix
     (see implementation in Math/MatrixInversion.icc)
   */
  template <class T>
  static int DfinvMatrix(MatRepStd<T,idim,n> & rhs, unsigned int * work);

  /**
     Bunch-Kaufman method for inversion of symmetric matrices
   */
  template <class T>
  static void InvertBunchKaufman(MatRepSym<T,idim> & rhs, int &ifail);



}; // class Inverter

// fast inverter class using Cramer inversion
// by default use other default inversion
/**
    Fast Matrix Inverter class
    Class to specialize calls to Dinv. Dinv computes the inverse of a square
    matrix if dimension idim and order n. The content of the matrix will be
    replaced by its inverse. In case the inversion fails, the matrix content is
    destroyed. Invert specializes Dinv by the matrix order. E.g. if the order
    of the matrix is less than 5 , the class implements
    Cramers rule.
    Be careful that for matrix with high condition the accuracy of the Cramer rule is much poorer

    @author L. Moneta
*/
template <unsigned int idim, unsigned int n = idim>
class FastInverter {
public:
  ///
  template <class MatrixRep>
  static bool Dinv(MatrixRep& rhs) {
     return Inverter<idim,n>::Dinv(rhs);
  }
  template <class T>
  static bool Dinv(MatRepSym<T,idim> & rhs) {
     return Inverter<idim,n>::Dinv(rhs);
  }
};


/** Inverter<0>.
    In case of zero order, do nothing.

    @author T. Glebe
*/
//==============================================================================
// Inverter<0>
//==============================================================================
template <>
class Inverter<0> {
public:
  ///
  template <class MatrixRep>
  inline static bool Dinv(MatrixRep&) { return true; }
};


/**
    1x1 matrix inversion \f$a_{11} \to 1/a_{11}\f$

    @author T. Glebe
*/
//==============================================================================
// Inverter<1>
//==============================================================================
template <>
class Inverter<1> {
public:
  ///
  template <class MatrixRep>
  static bool Dinv(MatrixRep& rhs) {

    if (rhs[0] == 0.) {
      return false;
    }
    rhs[0] = 1. / rhs[0];
    return true;
  }
};


/**
    2x2 matrix inversion  using Cramers rule.

    @author T. Glebe
*/
//==============================================================================
// Inverter<2>: Cramers rule
//==============================================================================

template <>
class Inverter<2> {
public:
  ///
  template <class MatrixRep>
  static bool Dinv(MatrixRep& rhs) {

    typedef typename MatrixRep::value_type T;
    T det = rhs[0] * rhs[3] - rhs[2] * rhs[1];

    if (det == T(0.) ) { return false; }

    T s = T(1.0) / det;

    T c11 = s * rhs[3];


    rhs[2] = -s * rhs[2];
    rhs[1] = -s * rhs[1];
    rhs[3] =  s * rhs[0];
    rhs[0] = c11;


    return true;
  }

  // specialization for the symmetric matrices
  template <class T>
  static bool Dinv(MatRepSym<T,2> & rep) {

    T * rhs = rep.Array();

    T det = rhs[0] * rhs[2] - rhs[1] * rhs[1];


    if (det == T(0.)) { return false; }

    T s = T(1.0) / det;
    T c11 = s * rhs[2];

    rhs[1] = -s * rhs[1];
    rhs[2] =  s * rhs[0];
    rhs[0] = c11;
    return true;
  }

};


/**
    3x3 direct matrix inversion  using Cramer Rule
    use only for FastInverter
*/
//==============================================================================
// FastInverter<3>
//==============================================================================

template <>
class FastInverter<3> {
public:
  ///
  // use Cramer Rule
  template <class MatrixRep>
  static bool Dinv(MatrixRep& rhs);

  template <class T>
  static bool Dinv(MatRepSym<T,3> & rhs);

};

/**
    4x4 matrix inversion using Cramers rule.
*/
template <>
class FastInverter<4> {
public:
  ///
  template <class MatrixRep>
  static bool Dinv(MatrixRep& rhs);

  template <class T>
  static bool Dinv(MatRepSym<T,4> & rhs);

};

/**
    5x5 Matrix inversion using Cramers rule.
*/
template <>
class FastInverter<5> {
public:
  ///
  template <class MatrixRep>
  static bool Dinv(MatrixRep& rhs);

  template <class T>
  static bool Dinv(MatRepSym<T,5> & rhs);

};

// inverter for Cholesky
// works only for symmetric matrices and will produce a
// compilation error otherwise

template <unsigned int idim>
class CholInverter {
public:
  ///
  template <class MatrixRep>
  static bool Dinv(MatrixRep&) {
     STATIC_CHECK( false, Error_cholesky_SMatrix_type_is_not_symmetric );
     return false;
  }
  template <class T>
  inline static bool Dinv(MatRepSym<T,idim> & rhs) {
     CholeskyDecomp<T, idim> decomp(rhs);
     return decomp.Invert(rhs);
  }
};


  }  // namespace Math

}  // namespace ROOT

#ifndef ROOT_Math_CramerInversion_icc
#include "CramerInversion.icc"
#endif
#ifndef ROOT_Math_CramerInversionSym_icc
#include "CramerInversionSym.icc"
#endif
#ifndef ROOT_Math_MatrixInversion_icc
#include "MatrixInversion.icc"
#endif

#endif  /* ROOT_Math_Dinv */