library: libMatrix #include "TMatrixDSym.h"

# TMatrixDSym

class description - source file - inheritance tree (.pdf)

## class TMatrixDSym : public TMatrixDBase

| Inheritance Chart:
`TObject`
| <- | `TMatrixDBase`
| <- | `TMatrixDSym` |

        protected:

          virtual void Allocate(Int_t nrows, Int_t ncols, Int_t row_lwb = 0, Int_t col_lwb = 0, Int_t init = 0, Int_t nr_nonzeros = -1)
                  void AMultA(const TMatrixDSym& a, Int_t constr = 1)
                  void AtMultA(const TMatrixD& a, Int_t constr = 1)
                  void AtMultA(const TMatrixDSym& a, Int_t constr = 1)
                  void Delete_m(Int_t size, Double_t*&)
                 Int_t Memcpy_m(Double_t* newp, const Double_t* oldp, Int_t copySize, Int_t newSize, Int_t oldSize)
             Double_t* New_m(Int_t size)

        public:

                                  TMatrixDSym()
                                  TMatrixDSym(Int_t nrows)
                                  TMatrixDSym(Int_t row_lwb, Int_t row_upb)
                                  TMatrixDSym(Int_t nrows, const Double_t* data, Option_t* option = "")
                                  TMatrixDSym(Int_t row_lwb, Int_t row_upb, const Double_t* data, Option_t* option = "")
                                  TMatrixDSym(const TMatrixDSym& another)
                                  TMatrixDSym(const TMatrixFSym& another)
                                  TMatrixDSym(TMatrixDBase::EMatrixCreatorsOp1 op, const TMatrixDSym& prototype)
                                  TMatrixDSym(TMatrixDBase::EMatrixCreatorsOp1 op, const TMatrixD& prototype)
                                  TMatrixDSym(const TMatrixDSym& a, TMatrixDBase::EMatrixCreatorsOp2 op, const TMatrixDSym& b)
                                  TMatrixDSym(const TMatrixDSymLazy& lazy_constructor)
                      TMatrixDSym GetSub(Int_t row_lwb, Int_t row_upb, Int_t col_lwb, Int_t col_upb, Option_t* option = "S") const
                          virtual ~TMatrixDSym()
            virtual TMatrixDBase& Apply(const TElementActionD& action)
            virtual TMatrixDBase& Apply(const TElementPosActionD& action)
                   static TClass* Class()
                     virtual void Clear(Option_t* = "")
                 virtual Double_t Determinant() const
                     virtual void Determinant(Double_t& d1, Double_t& d2) const
                   const TMatrixD EigenVectors(TVectorD& eigenValues) const
             virtual const Int_t* GetColIndexArray() const
                   virtual Int_t* GetColIndexArray()
          virtual const Double_t* GetMatrixArray() const
                virtual Double_t* GetMatrixArray()
             virtual const Int_t* GetRowIndexArray() const
                   virtual Int_t* GetRowIndexArray()
                     TMatrixDSym& GetSub(Int_t row_lwb, Int_t row_upb, TMatrixDSym& target, Option_t* option = "S") const
            virtual TMatrixDBase& GetSub(Int_t row_lwb, Int_t row_upb, Int_t col_lwb, Int_t col_upb, TMatrixDBase& target, Option_t* option = "S") const
                     TMatrixDSym& Invert(Double_t* det = 0)
                     TMatrixDSym& InvertFast(Double_t* det = 0)
                  virtual TClass* IsA() const
                   virtual Bool_t IsSymmetric() const
                 virtual Double_t operator()(Int_t rown, Int_t coln) const
                virtual Double_t& operator()(Int_t rown, Int_t coln)
                     TMatrixDSym& operator*=(Double_t val)
                     TMatrixDSym& operator+=(Double_t val)
                     TMatrixDSym& operator+=(const TMatrixDSym& source)
                     TMatrixDSym& operator-=(Double_t val)
                     TMatrixDSym& operator-=(const TMatrixDSym& source)
                     TMatrixDSym& operator=(const TMatrixDSym& source)
                     TMatrixDSym& operator=(const TMatrixFSym& source)
                     TMatrixDSym& operator=(const TMatrixDSymLazy& source)
                     TMatrixDSym& operator=(Double_t val)
          const TMatrixDRow_const operator[](Int_t rown) const
                      TMatrixDRow operator[](Int_t rown)
            virtual TMatrixDBase& Randomize(Double_t alpha, Double_t beta, Double_t& seed)
             virtual TMatrixDSym& RandomizePD(Double_t alpha, Double_t beta, Double_t& seed)
                     TMatrixDSym& Rank1Update(const TVectorD& v, Double_t alpha = 1.0)
            virtual TMatrixDBase& ResizeTo(Int_t nrows, Int_t ncols, Int_t nr_nonzeros = -1)
            virtual TMatrixDBase& ResizeTo(Int_t row_lwb, Int_t row_upb, Int_t col_lwb, Int_t col_upb, Int_t nr_nonzeros = -1)
                    TMatrixDBase& ResizeTo(const TMatrixDSym& m)
            virtual TMatrixDBase& SetColIndexArray(Int_t*)
            virtual TMatrixDBase& SetMatrixArray(const Double_t* data, Option_t* option = "")
            virtual TMatrixDBase& SetRowIndexArray(Int_t*)
                     TMatrixDSym& SetSub(Int_t row_lwb, const TMatrixDBase& source)
            virtual TMatrixDBase& SetSub(Int_t row_lwb, Int_t col_lwb, const TMatrixDBase& source)
            virtual TMatrixDBase& Shift(Int_t row_shift, Int_t col_shift)
                     virtual void ShowMembers(TMemberInspector& insp, char* parent)
                     TMatrixDSym& Similarity(const TMatrixD& n)
                     TMatrixDSym& Similarity(const TMatrixDSym& n)
                     TMatrixDSym& SimilarityT(const TMatrixD& n)
                     virtual void Streamer(TBuffer& b)
                             void StreamerNVirtual(TBuffer& b)
                     TMatrixDSym& T()
                     TMatrixDSym& Transpose(const TMatrixDSym& source)
                     TMatrixDSym& Use(Int_t nrows, Double_t* data)
                     TMatrixDSym& Use(Int_t row_lwb, Int_t row_upb, Double_t* data)
                     TMatrixDSym& Use(TMatrixDSym& a)

### Data Members

        protected:

           Double_t fDataStack[25]  ! data container
          Double_t* fElements       [fNelems] elements themselves

## Class Description

     TMatrixDSym

     Implementation of a symmetric matrix in the linear algebra package

     Note that in this implementation both matrix element m[i][j] and
     m[j][i] are updated and stored in memory . However, when making the
     object persistent only the upper right triangle is stored .

TMatrixDSym(Int_t no_rows)

TMatrixDSym(Int_t row_lwb,Int_t row_upb)

TMatrixDSym(Int_t no_rows,const Double_t *elements,Option_t *option)

     option="F": array elements contains the matrix stored column-wise
                 like in Fortran, so a[i,j] = elements[i+no_rows*j],
     else        it is supposed that array elements are stored row-wise
                 a[i,j] = elements[i*no_cols+j]

     array elements are copied

TMatrixDSym(Int_t row_lwb,Int_t row_upb,const Double_t *elements,Option_t *option)

     array elements are copied

TMatrixDSym(const TMatrixDSym &another) : TMatrixDBase()

TMatrixDSym(const TMatrixFSym &another) : TMatrixDBase()

TMatrixDSym(EMatrixCreatorsOp1 op,const TMatrixDSym &prototype)

     Create a matrix applying a specific operation to the prototype.
     Example: TMatrixDSym a(10,12); ...; TMatrixDSym b(TMatrixDBase::kTransposed, a);
     Supported operations are: kZero, kUnit, kTransposed, kInverted and kAtA.

TMatrixDSym(EMatrixCreatorsOp1 op,const TMatrixD &prototype)

TMatrixDSym(const TMatrixDSym &a,EMatrixCreatorsOp2 op,const TMatrixDSym &b)

TMatrixDSym(const TMatrixDSymLazy &lazy_constructor)

void Delete_m(Int_t size,Double_t *&m)

     delete data pointer m, if it was assigned on the heap

Double_t* New_m(Int_t size)

     return data pointer . if requested size <= kSizeMax, assign pointer
     to the stack space

Int_t Memcpy_m(Double_t *newp,const Double_t *oldp,Int_t copySize, Int_t newSize,Int_t oldSize)

     copy copySize doubles from *oldp to *newp . However take care of the
     situation where both pointers are assigned to the same stack space

void Allocate(Int_t no_rows,Int_t no_cols,Int_t row_lwb,Int_t col_lwb, Int_t init,Int_t /*nr_nonzeros*/)

     Allocate new matrix. Arguments are number of rows, columns, row
     lowerbound (0 default) and column lowerbound (0 default).

void AtMultA(const TMatrixD &a,Int_t constr)

     Create a matrix C such that C = A' * A. In other words,
     c[i,j] = SUM{ a[k,i] * a[k,j] }. Note, matrix C is allocated for constr=1.

void AtMultA(const TMatrixDSym &a,Int_t constr)

     Matrix multiplication, with A symmetric
     Create a matrix C such that C = A' * A = A * A = A * A'
     Note, matrix C is allocated for constr=1.

TMatrixDSym& Use(Int_t row_lwb,Int_t row_upb,Double_t *data)

TMatrixDSym& GetSub(Int_t row_lwb,Int_t row_upb,TMatrixDSym &target,Option_t *option) const

     Get submatrix [row_lwb..row_upb][row_lwb..row_upb]; The indexing range of the
     returned matrix depends on the argument option:

     option == "S" : return [0..row_upb-row_lwb+1][0..row_upb-row_lwb+1] (default)
     else          : return [row_lwb..row_upb][row_lwb..row_upb]

TMatrixDBase& GetSub(Int_t row_lwb,Int_t row_upb,Int_t col_lwb,Int_t col_upb, TMatrixDBase &target,Option_t *option) const

     Get submatrix [row_lwb..row_upb][col_lwb..col_upb]; The indexing range of the
     returned matrix depends on the argument option:

     option == "S" : return [0..row_upb-row_lwb+1][0..col_upb-col_lwb+1] (default)
     else          : return [row_lwb..row_upb][col_lwb..col_upb]

TMatrixDSym& SetSub(Int_t row_lwb,const TMatrixDBase &source)

     Insert matrix source starting at [row_lwb][row_lwb], thereby overwriting the part
     [row_lwb..row_lwb+nrows_source][row_lwb..row_lwb+nrows_source];

TMatrixDBase& SetSub(Int_t row_lwb,Int_t col_lwb,const TMatrixDBase &source)

     Insert matrix source starting at [row_lwb][col_lwb] in a symmetric fashion, thereby overwriting the part
     [row_lwb..row_lwb+nrows_source][row_lwb..row_lwb+nrows_source];

TMatrixDBase& SetMatrixArray(const Double_t *data,Option_t *option)

TMatrixDBase& Shift(Int_t row_shift,Int_t col_shift)

TMatrixDBase& ResizeTo(Int_t nrows,Int_t ncols,Int_t /*nr_nonzeros*/)

     Set size of the matrix to nrows x ncols
     New dynamic elements are created, the overlapping part of the old ones are
     copied to the new structures, then the old elements are deleted.

TMatrixDBase& ResizeTo(Int_t row_lwb,Int_t row_upb,Int_t col_lwb,Int_t col_upb, Int_t /*nr_nonzeros*/)

     Set size of the matrix to [row_lwb:row_upb] x [col_lwb:col_upb]
     New dynamic elemenst are created, the overlapping part of the old ones are
     copied to the new structures, then the old elements are deleted.

Double_t Determinant() const

void Determinant(Double_t &d1,Double_t &d2) const

TMatrixDSym& Invert(Double_t *det)

     Invert the matrix and calculate its determinant
     Notice that we need to invoke an additional LU decomposition in order to
     calculate the determinant beacuse the Bunch-Kaufman does not result in a
     convenient triagularr matrix .

TMatrixDSym& InvertFast(Double_t *det)

     Invert the matrix and calculate its determinant

TMatrixDSym& Transpose(const TMatrixDSym &source)

     Transpose a matrix.

TMatrixDSym& Rank1Update(const TVectorD &v,Double_t alpha)

     Perform a rank 1 operation on the matrix:
         A += alpha * v * v^T

TMatrixDSym& Similarity(const TMatrixD &b)

     Calculate B * (*this) * B^T , final matrix will be (nrowsb x nrowsb)
     This is a similarity transform when B is orthogonal . It is more
     efficient than applying the actual multiplication because this
     routine realizes that  the final matrix is symmetric .

TMatrixDSym& Similarity(const TMatrixDSym &b)

     Calculate B * (*this) * B^T , final matrix will be (nrowsb x nrowsb)
     This is a similarity transform when B is orthogonal . It is more
     efficient than applying the actual multiplication because this
     routine realizes that  the final matrix is symmetric .

TMatrixDSym& SimilarityT(const TMatrixD &b)

     Calculate B^T * (*this) * B , final matrix will be (ncolsb x ncolsb)
     It is more efficient than applying the actual multiplication because this
     routine realizes that  the final matrix is symmetric .

TMatrixDBase& Apply(const TElementActionD &action)

TMatrixDBase& Apply(const TElementPosActionD &action)

     Apply action to each element of the matrix. To action the location
     of the current element is passed.

TMatrixDBase& Randomize(Double_t alpha,Double_t beta,Double_t &seed)

     randomize matrix element values but keep matrix symmetric

TMatrixDSym& RandomizePD(Double_t alpha,Double_t beta,Double_t &seed)

     randomize matrix element values but keep matrix symmetric positive definite

const TMatrixD EigenVectors(TVectorD &eigenValues) const

     Return a matrix containing the eigen-vectors ordered by descending eigen-values.
     For full functionality use TMatrixDSymEigen .

void Streamer(TBuffer &R__b)

     Stream an object of class TMatrixDSym.

### Inline Functions

                               void ~TMatrixDSym()
                               void AMultA(const TMatrixDSym& a, Int_t constr = 1)
                        TMatrixDSym TMatrixDSym(const TMatrixDSymLazy& lazy_constructor)
                    const Double_t* GetMatrixArray() const
                          Double_t* GetMatrixArray()
                       const Int_t* GetRowIndexArray() const
                             Int_t* GetRowIndexArray()
                       const Int_t* GetColIndexArray() const
                             Int_t* GetColIndexArray()
                      TMatrixDBase& SetRowIndexArray(Int_t*)
                      TMatrixDBase& SetColIndexArray(Int_t*)
                               void Clear(Option_t* = "")
                             Bool_t IsSymmetric() const
                       TMatrixDSym& Use(Int_t row_lwb, Int_t row_upb, Double_t* data)
                       TMatrixDSym& Use(TMatrixDSym& a)
                        TMatrixDSym GetSub(Int_t row_lwb, Int_t row_upb, Int_t col_lwb, Int_t col_upb, Option_t* option = "S") const
                      TMatrixDBase& ResizeTo(const TMatrixDSym& m)
                       TMatrixDSym& T()
                           Double_t operator()(Int_t rown, Int_t coln) const
                          Double_t& operator()(Int_t rown, Int_t coln)
            const TMatrixDRow_const operator[](Int_t rown) const
                        TMatrixDRow operator[](Int_t rown)
                       TMatrixDSym& operator=(const TMatrixDSym& source)
                       TMatrixDSym& operator=(const TMatrixFSym& source)
                       TMatrixDSym& operator=(const TMatrixDSymLazy& source)
                       TMatrixDSym& operator=(Double_t val)
                       TMatrixDSym& operator-=(Double_t val)
                       TMatrixDSym& operator+=(Double_t val)
                       TMatrixDSym& operator*=(Double_t val)
                       TMatrixDSym& operator+=(const TMatrixDSym& source)
                       TMatrixDSym& operator-=(const TMatrixDSym& source)
                            TClass* Class()
                            TClass* IsA() const
                               void ShowMembers(TMemberInspector& insp, char* parent)
                               void StreamerNVirtual(TBuffer& b)

Last update: root/matrix:$Name: $:$Id: TMatrixDSym.cxx,v 1.23 2005/03/28 20:38:35 brun Exp $
Copyright (C) 1995-2000, Rene Brun and Fons Rademakers. *