9.6.p02/html/_g4_error_sym_matrix_8hh_source.html

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// $Id: G4ErrorSymMatrix.hh 69766 2013-05-14 14:33:55Z gcosmo $

//

// Class Description:

//

// Simplified version of CLHEP HepSymMatrix class.


// History:

// - Imported from CLHEP and modified:   P. Arce    May 2007

// --------------------------------------------------------------------


#ifndef G4ErrorSymMatrix_hh

#define G4ErrorSymMatrix_hh


#include <vector>


class G4ErrorMatrix;


class G4ErrorSymMatrix

{

 public:  //with description


   inline G4ErrorSymMatrix();

   // Default constructor. Gives 0x0 symmetric matrix.

   // Another G4ErrorSymMatrix can be assigned to it.


   explicit G4ErrorSymMatrix(G4int p);

   G4ErrorSymMatrix(G4int p, G4int);

   // Constructor. Gives p x p symmetric matrix.

   // With a second argument, the matrix is initialized. 0 means a zero

   // matrix, 1 means the identity matrix.


   G4ErrorSymMatrix(const G4ErrorSymMatrix &m1);

   // Copy constructor.


   // Constructor from DiagMatrix


   virtual ~G4ErrorSymMatrix();

   // Destructor.


   inline G4int num_row() const;

   inline G4int num_col() const;

   // Returns number of rows/columns.


   const G4double & operator()(G4int row, G4int col) const;

   G4double & operator()(G4int row, G4int col);

   // Read and write a G4ErrorSymMatrix element.

   // ** Note that indexing starts from (1,1). **


   const G4double & fast(G4int row, G4int col) const;

   G4double & fast(G4int row, G4int col);

   // fast element access.

   // Must be row>=col;

   // ** Note that indexing starts from (1,1). **


   void assign(const G4ErrorMatrix &m2);

   // Assigns m2 to s, assuming m2 is a symmetric matrix.


   void assign(const G4ErrorSymMatrix &m2);

   // Another form of assignment. For consistency.


   G4ErrorSymMatrix & operator*=(G4double t);

   // Multiply a G4ErrorSymMatrix by a floating number.


   G4ErrorSymMatrix & operator/=(G4double t);

   // Divide a G4ErrorSymMatrix by a floating number.


   G4ErrorSymMatrix & operator+=( const G4ErrorSymMatrix &m2);

   G4ErrorSymMatrix & operator-=( const G4ErrorSymMatrix &m2);

   // Add or subtract a G4ErrorSymMatrix.


   G4ErrorSymMatrix & operator=( const G4ErrorSymMatrix &m2);

   // Assignment operators. Notice that there is no G4ErrorSymMatrix = Matrix.


   G4ErrorSymMatrix operator- () const;

   // unary minus, ie. flip the sign of each element.


   G4ErrorSymMatrix T() const;

   // Returns the transpose of a G4ErrorSymMatrix (which is itself).


   G4ErrorSymMatrix apply(G4double (*f)(G4double, G4int, G4int)) const;

   // Apply a function to all elements of the matrix.


   G4ErrorSymMatrix similarity(const G4ErrorMatrix &m1) const;

   G4ErrorSymMatrix similarity(const G4ErrorSymMatrix &m1) const;

   // Returns m1*s*m1.T().


   G4ErrorSymMatrix similarityT(const G4ErrorMatrix &m1) const;

   // temporary. test of new similarity.

   // Returns m1.T()*s*m1.


   G4ErrorSymMatrix sub(G4int min_row, G4int max_row) const;

   // Returns a sub matrix of a G4ErrorSymMatrix.


   void sub(G4int row, const G4ErrorSymMatrix &m1);

   // Sub matrix of this G4ErrorSymMatrix is replaced with m1.


   G4ErrorSymMatrix sub(G4int min_row, G4int max_row);

   // SGI CC bug. I have to have both with/without const. I should not need

   // one without const.


   inline G4ErrorSymMatrix inverse(G4int &ifail) const;

   // Invert a Matrix. The matrix is not changed

   // Returns 0 when successful, otherwise non-zero.


   void invert(G4int &ifail);

   // Invert a Matrix.

   // N.B. the contents of the matrix are replaced by the inverse.

   // Returns ierr = 0 when successful, otherwise non-zero.

   // This method has less overhead then inverse().


   G4double determinant() const;

   // calculate the determinant of the matrix.


   G4double trace() const;

   // calculate the trace of the matrix (sum of diagonal elements).


   class G4ErrorSymMatrix_row

   {

     public:

      inline G4ErrorSymMatrix_row(G4ErrorSymMatrix&,G4int);

      inline G4double & operator[](G4int);

     private:

      G4ErrorSymMatrix& _a;

      G4int _r;

   };

   class G4ErrorSymMatrix_row_const

   {

     public:

      inline G4ErrorSymMatrix_row_const(const G4ErrorSymMatrix&,G4int);

      inline const G4double & operator[](G4int) const;

     private:

      const G4ErrorSymMatrix& _a;

      G4int _r;

   };

   // helper class to implement m[i][j]


   inline G4ErrorSymMatrix_row operator[] (G4int);

   inline G4ErrorSymMatrix_row_const operator[] (G4int) const;

   // Read or write a matrix element.

   // While it may not look like it, you simply do m[i][j] to get an

   // element.

   // ** Note that the indexing starts from [0][0]. **


   // Special-case inversions for 5x5 and 6x6 symmetric positive definite:

   // These set ifail=0 and invert if the matrix was positive definite;

   // otherwise ifail=1 and the matrix is left unaltered.


   void invertCholesky5 (G4int &ifail);

   void invertCholesky6 (G4int &ifail);


   // Inversions for 5x5 and 6x6 forcing use of specific methods:  The

   // behavior (though not the speed) will be identical to invert(ifail).


   void invertHaywood4 (G4int & ifail);

   void invertHaywood5 (G4int &ifail);

   void invertHaywood6 (G4int &ifail);

   void invertBunchKaufman (G4int &ifail);


 protected:


   inline G4int num_size() const;


 private:


   friend class G4ErrorSymMatrix_row;

   friend class G4ErrorSymMatrix_row_const;

   friend class G4ErrorMatrix;


   friend void tridiagonal(G4ErrorSymMatrix *a, G4ErrorMatrix *hsm);

   friend G4double condition(const G4ErrorSymMatrix &m);

   friend void diag_step(G4ErrorSymMatrix *t, G4int begin, G4int end);

   friend void diag_step(G4ErrorSymMatrix *t, G4ErrorMatrix *u,

                         G4int begin, G4int end);

   friend G4ErrorMatrix diagonalize(G4ErrorSymMatrix *s);

   friend void house_with_update2(G4ErrorSymMatrix *a, G4ErrorMatrix *v,

                                  G4int row, G4int col);


   friend G4ErrorSymMatrix operator+(const G4ErrorSymMatrix &m1,

                                     const G4ErrorSymMatrix &m2);

   friend G4ErrorSymMatrix operator-(const G4ErrorSymMatrix &m1,

                                     const G4ErrorSymMatrix &m2);

   friend G4ErrorMatrix operator*(const G4ErrorSymMatrix &m1,

                                  const G4ErrorSymMatrix &m2);

   friend G4ErrorMatrix operator*(const G4ErrorSymMatrix &m1,

                                  const G4ErrorMatrix &m2);

   friend G4ErrorMatrix operator*(const G4ErrorMatrix &m1,

                                  const G4ErrorSymMatrix &m2);

   // Multiply a Matrix by a Matrix or Vector.


   // Returns v * v.T();


   std::vector<G4double > m;


   G4int nrow;

   G4int size;   // total number of elements


   static G4double posDefFraction5x5;

   static G4double adjustment5x5;

   static const  G4double CHOLESKY_THRESHOLD_5x5;

   static const  G4double CHOLESKY_CREEP_5x5;


   static G4double posDefFraction6x6;

   static G4double adjustment6x6;

   static const G4double CHOLESKY_THRESHOLD_6x6;

   static const G4double CHOLESKY_CREEP_6x6;


   void invert4  (G4int & ifail);

   void invert5  (G4int & ifail);

   void invert6  (G4int & ifail);

};


//

// Operations other than member functions for Matrix, G4ErrorSymMatrix,

// DiagMatrix and Vectors

//


std::ostream& operator<<(std::ostream &s, const G4ErrorSymMatrix &q);

// Write out Matrix, G4ErrorSymMatrix, DiagMatrix and Vector into ostream.


G4ErrorMatrix operator*(const G4ErrorMatrix &m1,

                        const G4ErrorSymMatrix &m2);

G4ErrorMatrix operator*(const G4ErrorSymMatrix &m1,

                        const G4ErrorMatrix &m2);

G4ErrorMatrix operator*(const G4ErrorSymMatrix &m1,

                        const G4ErrorSymMatrix &m2);

G4ErrorSymMatrix operator*(G4double t, const G4ErrorSymMatrix &s1);

G4ErrorSymMatrix operator*(const G4ErrorSymMatrix &s1, G4double t);

// Multiplication operators.

// Note that m *= m1 is always faster than m = m * m1


G4ErrorSymMatrix operator/(const G4ErrorSymMatrix &m1, G4double t);

// s = s1 / t. (s /= t is faster if you can use it.)


G4ErrorMatrix operator+(const G4ErrorMatrix &m1,

                        const G4ErrorSymMatrix &s2);

G4ErrorMatrix operator+(const G4ErrorSymMatrix &s1,

                        const G4ErrorMatrix &m2);

G4ErrorSymMatrix operator+(const G4ErrorSymMatrix &s1,

                           const G4ErrorSymMatrix &s2);

// Addition operators


G4ErrorMatrix operator-(const G4ErrorMatrix &m1,

                        const G4ErrorSymMatrix &s2);

G4ErrorMatrix operator-(const G4ErrorSymMatrix &m1,

                        const G4ErrorMatrix &m2);

G4ErrorSymMatrix operator-(const G4ErrorSymMatrix &s1,

                           const G4ErrorSymMatrix &s2);

// subtraction operators


G4ErrorSymMatrix dsum(const G4ErrorSymMatrix &s1,

                      const G4ErrorSymMatrix &s2);

// Direct sum of two symmetric matrices;


G4double condition(const G4ErrorSymMatrix &m);

// Find the conditon number of a symmetric matrix.


void diag_step(G4ErrorSymMatrix *t, G4int begin, G4int end);

void diag_step(G4ErrorSymMatrix *t, G4ErrorMatrix *u, G4int begin, G4int end);

// Implicit symmetric QR step with Wilkinson Shift


G4ErrorMatrix diagonalize(G4ErrorSymMatrix *s);

// Diagonalize a symmetric matrix.

// It returns the matrix U so that s_old = U * s_diag * U.T()


void house_with_update2(G4ErrorSymMatrix *a, G4ErrorMatrix *v,

                        G4int row=1, G4int col=1);

// Finds and does Householder reflection on matrix.


void tridiagonal(G4ErrorSymMatrix *a, G4ErrorMatrix *hsm);

G4ErrorMatrix tridiagonal(G4ErrorSymMatrix *a);

// Does a Householder tridiagonalization of a symmetric matrix.


#include "G4ErrorSymMatrix.icc"


#endif