G4ErrorMatrix.hh

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//
//
// Class Description:
//
// Simplified version of CLHEP HepMatrix class
 
// History:
// - Imported from CLHEP and modified:   P. Arce    May 2007
// --------------------------------------------------------------------
 
#ifndef G4ErrorMatrix_hh
#define G4ErrorMatrix_hh
 
#include <vector>
#include "G4Types.hh"
 
class G4ErrorSymMatrix;
 
typedef std::vector<G4double >::iterator G4ErrorMatrixIter;
typedef std::vector<G4double >::const_iterator G4ErrorMatrixConstIter;
 
class G4ErrorMatrix
{
 
 public:  // with description
 
   G4ErrorMatrix();
   // Default constructor. Gives 0 x 0 matrix.
   // Another G4ErrorMatrix can be assigned to it.
 
   G4ErrorMatrix(G4int p, G4int q);
   // Constructor. Gives an unitialized p x q matrix.
 
   G4ErrorMatrix(G4int p, G4int q, G4int i);
   // Constructor. Gives an initialized p x q matrix. 
   // If i=0, it is initialized to all 0. If i=1, the diagonal elements
   // are set to 1.0.
 
   G4ErrorMatrix(const G4ErrorMatrix &m1);
   G4ErrorMatrix(G4ErrorMatrix &&) = default;
   // Copy and move constructor.
 
   G4ErrorMatrix(const G4ErrorSymMatrix &m1);
   // Constructors from G4ErrorSymG4ErrorMatrix, DiagG4ErrorMatrix and Vector.
 
   virtual ~G4ErrorMatrix();
   // Destructor.
 
   inline virtual G4int num_row() const;
   // Returns the number of rows.
 
   inline virtual G4int num_col() const;
   // Returns the number of columns.
 
   inline virtual const G4double & operator()(G4int row, G4int col) const;
   inline virtual G4double & operator()(G4int row, G4int col);
   // Read or write a matrix element. 
   // ** Note that the indexing starts from (1,1). **
 
   G4ErrorMatrix & operator *= (G4double t);
   // Multiply a G4ErrorMatrix by a floating number.
 
   G4ErrorMatrix & operator /= (G4double t); 
   // Divide a G4ErrorMatrix by a floating number.
 
   G4ErrorMatrix & operator += ( const G4ErrorMatrix &m2);
   G4ErrorMatrix & operator += ( const G4ErrorSymMatrix &m2);
   G4ErrorMatrix & operator -= ( const G4ErrorMatrix &m2);
   G4ErrorMatrix & operator -= ( const G4ErrorSymMatrix &m2);
   // Add or subtract a G4ErrorMatrix. 
   // When adding/subtracting Vector, G4ErrorMatrix must have num_col of one.
 
   G4ErrorMatrix & operator = ( const G4ErrorMatrix &m2);
   G4ErrorMatrix & operator = ( const G4ErrorSymMatrix &m2);
   G4ErrorMatrix & operator = (G4ErrorMatrix &&) = default;
   // Assignment and move operators.
 
   G4ErrorMatrix operator- () const;
   // unary minus, ie. flip the sign of each element.
 
   G4ErrorMatrix apply(G4double (*f)(G4double, G4int, G4int)) const;
   // Apply a function to all elements of the matrix.
 
   G4ErrorMatrix T() const;
   // Returns the transpose of a G4ErrorMatrix.
 
   G4ErrorMatrix sub(G4int min_row, G4int max_row,
                     G4int min_col, G4int max_col) const;
   // Returns a sub matrix of a G4ErrorMatrix.
   // WARNING: rows and columns are numbered from 1
 
   void sub(G4int row, G4int col, const G4ErrorMatrix &m1);
   // Sub matrix of this G4ErrorMatrix is replaced with m1.
   // WARNING: rows and columns are numbered from 1
 
   inline G4ErrorMatrix inverse(G4int& ierr) const;
   // Invert a G4ErrorMatrix. G4ErrorMatrix must be square and is not changed.
   // Returns ierr = 0 (zero) when successful, otherwise non-zero.
 
   virtual void invert(G4int& ierr);
   // Invert a G4ErrorMatrix. G4ErrorMatrix must be square.
   // N.B. the contents of the matrix are replaced by the inverse.
   // Returns ierr = 0 (zero) 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 G4ErrorMatrix_row
   {
     typedef std::vector<G4double >::const_iterator G4ErrorMatrixConstIter;
     public:
       inline G4ErrorMatrix_row(G4ErrorMatrix&,G4int);
       G4double & operator[](G4int);
     private:
       G4ErrorMatrix& _a;
       G4int _r;
   };
   class G4ErrorMatrix_row_const
   {
     public:
       inline G4ErrorMatrix_row_const (const G4ErrorMatrix&,G4int);
       const G4double & operator[](G4int) const;
     private:
       const G4ErrorMatrix& _a;
       G4int _r;
   };
   // helper classes for implementing m[i][j]
 
   inline G4ErrorMatrix_row operator[] (G4int);
   inline const G4ErrorMatrix_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]. **
 
 protected:
 
   virtual inline G4int num_size() const;
   virtual void invertHaywood4(G4int& ierr);
   virtual void invertHaywood5(G4int& ierr);
   virtual void invertHaywood6(G4int& ierr);
 
 public:
 
   static void error(const char *s);
 
 private:
 
   friend class G4ErrorMatrix_row;
   friend class G4ErrorMatrix_row_const;
   friend class G4ErrorSymMatrix;
   // Friend classes.
 
   friend G4ErrorMatrix operator+(const G4ErrorMatrix &m1,
                                  const G4ErrorMatrix &m2);
   friend G4ErrorMatrix operator-(const G4ErrorMatrix &m1,
                                  const G4ErrorMatrix &m2);
   friend G4ErrorMatrix operator*(const G4ErrorMatrix &m1,
                                  const G4ErrorMatrix &m2);
   friend G4ErrorMatrix operator*(const G4ErrorMatrix &m1,
                                  const G4ErrorSymMatrix &m2);
   friend G4ErrorMatrix operator*(const G4ErrorSymMatrix &m1,
                                  const G4ErrorMatrix &m2);
   friend G4ErrorMatrix operator*(const G4ErrorSymMatrix &m1,
                                  const G4ErrorSymMatrix &m2);
   // Multiply a G4ErrorMatrix by a G4ErrorMatrix or Vector.
 
   // solve the system of linear eq
 
   friend G4ErrorMatrix qr_solve(G4ErrorMatrix *, const G4ErrorMatrix &b);
   friend void tridiagonal(G4ErrorSymMatrix *a,G4ErrorMatrix *hsm);
   friend void row_house(G4ErrorMatrix *,const G4ErrorMatrix &, G4double,
                         G4int, G4int, G4int, G4int);
   friend void back_solve(const G4ErrorMatrix &R, G4ErrorMatrix *b);
   friend void col_givens(G4ErrorMatrix *A, G4double c,
                          G4double s, G4int k1, G4int k2, 
                          G4int rowmin, G4int rowmax);
   // Does a column Givens update.
 
   friend void row_givens(G4ErrorMatrix *A, G4double c,
                          G4double s, G4int k1, G4int k2, 
                          G4int colmin, G4int colmax);
   friend void col_house(G4ErrorMatrix *,const G4ErrorMatrix &, G4double,
                         G4int, G4int, G4int, G4int);
   friend void house_with_update(G4ErrorMatrix *a,G4int row,G4int col);
   friend void house_with_update(G4ErrorMatrix *a,G4ErrorMatrix *v,
                                 G4int row, G4int col);
   friend void house_with_update2(G4ErrorSymMatrix *a,G4ErrorMatrix *v,
                                  G4int row, G4int col); 
 
   G4int dfact_matrix(G4double &det, G4int *ir);
   // factorize the matrix. If successful, the return code is 0. On
   // return, det is the determinant and ir[] is row-interchange
   // matrix. See CERNLIB's DFACT routine.
 
   G4int dfinv_matrix(G4int *ir);
   // invert the matrix. See CERNLIB DFINV.
 
   std::vector<G4double > m;
 
   G4int nrow, ncol;
   G4int size;
};
 
// Operations other than member functions for G4ErrorMatrix
 
G4ErrorMatrix operator*(const G4ErrorMatrix &m1, const G4ErrorMatrix &m2);
G4ErrorMatrix operator*(G4double t, const G4ErrorMatrix &m1);
G4ErrorMatrix operator*(const G4ErrorMatrix &m1, G4double t);
// Multiplication operators
// Note that m *= m1 is always faster than m = m * m1.
 
G4ErrorMatrix operator/(const G4ErrorMatrix &m1, G4double t);
// m = m1 / t. (m /= t is faster if you can use it.)
 
G4ErrorMatrix operator+(const G4ErrorMatrix &m1, const G4ErrorMatrix &m2);
// m = m1 + m2;
// Note that m += m1 is always faster than m = m + m1.
 
G4ErrorMatrix operator-(const G4ErrorMatrix &m1, const G4ErrorMatrix &m2);
// m = m1 - m2;
// Note that m -= m1 is always faster than m = m - m1.
 
G4ErrorMatrix dsum(const G4ErrorMatrix&, const G4ErrorMatrix&);
// Direct sum of two matrices. The direct sum of A and B is the matrix 
//        A 0
//        0 B
 
std::ostream& operator<<(std::ostream &s, const G4ErrorMatrix &q);
// Read in, write out G4ErrorMatrix into a stream.
 
//
// Specialized linear algebra functions
//
 
G4ErrorMatrix qr_solve(const G4ErrorMatrix &A, const G4ErrorMatrix &b);
G4ErrorMatrix qr_solve(G4ErrorMatrix *A, const G4ErrorMatrix &b);
// Works like backsolve, except matrix does not need to be upper
// triangular. For nonsquare matrix, it solves in the least square sense.
 
G4ErrorMatrix qr_inverse(const G4ErrorMatrix &A);
G4ErrorMatrix qr_inverse(G4ErrorMatrix *A);
// Finds the inverse of a matrix using QR decomposition.  Note, often what
// you really want is solve or backsolve, they can be much quicker than
// inverse in many calculations.
 
 
void qr_decomp(G4ErrorMatrix *A, G4ErrorMatrix *hsm);
G4ErrorMatrix qr_decomp(G4ErrorMatrix *A);
// Does a QR decomposition of a matrix.
 
void back_solve(const G4ErrorMatrix &R, G4ErrorMatrix *b);
// Solves R*x = b where R is upper triangular.  Also has a variation that
// solves a number of equations of this form in one step, where b is a matrix
// with each column a different vector. See also solve.
 
void col_house(G4ErrorMatrix *a, const G4ErrorMatrix &v, G4double vnormsq,
               G4int row, G4int col, G4int row_start, G4int col_start);
void col_house(G4ErrorMatrix *a, const G4ErrorMatrix &v, G4int row, G4int col,
               G4int row_start, G4int col_start);
// Does a column Householder update.
 
void col_givens(G4ErrorMatrix *A, G4double c, G4double s,
                G4int k1, G4int k2, G4int row_min=1, G4int row_max=0);
// do a column Givens update
 
void row_givens(G4ErrorMatrix *A, G4double c, G4double s,
                G4int k1, G4int k2, G4int col_min=1, G4int col_max=0);
// do a row Givens update
 
// void givens(G4double a, G4double b, G4double *c, G4double *s);
// algorithm 5.1.5 in Golub and Van Loan
 
// Returns a Householder vector to zero elements.
 
void house_with_update(G4ErrorMatrix *a, G4int row=1, G4int col=1);
void house_with_update(G4ErrorMatrix *a, G4ErrorMatrix *v,
                       G4int row=1, G4int col=1);
// Finds and does Householder reflection on matrix.
 
void row_house(G4ErrorMatrix *a, const G4ErrorMatrix &v, G4double vnormsq,
               G4int row, G4int col, G4int row_start, G4int col_start);
void row_house(G4ErrorMatrix *a, const G4ErrorMatrix &v, G4int row, G4int col,
               G4int row_start, G4int col_start);
// Does a row Householder update.
 
#include "G4ErrorMatrix.icc"
 
#endif