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Warning, file /include/root/TMatrixT.h was not indexed or was modified since last indexation (in which case cross-reference links may be missing, inaccurate or erroneous).

0001 // @(#)root/matrix:$Id$
0002 // Authors: Fons Rademakers, Eddy Offermann   Nov 2003
0003 
0004 /*************************************************************************
0005  * Copyright (C) 1995-2000, Rene Brun and Fons Rademakers.               *
0006  * All rights reserved.                                                  *
0007  *                                                                       *
0008  * For the licensing terms see $ROOTSYS/LICENSE.                         *
0009  * For the list of contributors see $ROOTSYS/README/CREDITS.             *
0010  *************************************************************************/
0011 
0012 #ifndef ROOT_TMatrixT
0013 #define ROOT_TMatrixT
0014 
0015 //////////////////////////////////////////////////////////////////////////
0016 //                                                                      //
0017 // TMatrixT                                                             //
0018 //                                                                      //
0019 // Template class of a general matrix in the linear algebra package     //
0020 //                                                                      //
0021 //////////////////////////////////////////////////////////////////////////
0022 
0023 #include "TMatrixTBase.h"
0024 #include "TMatrixTUtils.h"
0025 
0026 #ifdef CBLAS
0027 #include <vecLib/vBLAS.h>
0028 //#include <cblas.h>
0029 #endif
0030 
0031 #include "Rtypes.h"
0032 #include "TError.h"
0033 
0034 
0035 template<class Element> class TMatrixTSym;
0036 template<class Element> class TMatrixTSparse;
0037 template<class Element> class TMatrixTLazy;
0038 
0039 template<class Element> class TMatrixT : public TMatrixTBase<Element> {
0040 
0041 protected:
0042 
0043    Element  fDataStack[TMatrixTBase<Element>::kSizeMax]; //! data container
0044    Element *fElements;                                   //[fNelems] elements themselves
0045 
0046    Element *New_m   (Int_t size);
0047    void     Delete_m(Int_t size,Element*&);
0048    Int_t    Memcpy_m(Element *newp,const Element *oldp,Int_t copySize,
0049                       Int_t newSize,Int_t oldSize);
0050    void     Allocate(Int_t nrows,Int_t ncols,Int_t row_lwb = 0,Int_t col_lwb = 0,Int_t init = 0,
0051                      Int_t /*nr_nonzeros*/ = -1);
0052 
0053 
0054 public:
0055 
0056 
0057    enum {kWorkMax = 100};
0058    enum EMatrixCreatorsOp1 { kZero,kUnit,kTransposed,kInverted,kAtA };
0059    enum EMatrixCreatorsOp2 { kMult,kTransposeMult,kInvMult,kMultTranspose,kPlus,kMinus };
0060 
0061    TMatrixT(): fDataStack(), fElements(nullptr) { }
0062    TMatrixT(Int_t nrows,Int_t ncols);
0063    TMatrixT(Int_t row_lwb,Int_t row_upb,Int_t col_lwb,Int_t col_upb);
0064    TMatrixT(Int_t nrows,Int_t ncols,const Element *data,Option_t *option="");
0065    TMatrixT(Int_t row_lwb,Int_t row_upb,Int_t col_lwb,Int_t col_upb,const Element *data,Option_t *option="");
0066    TMatrixT(const TMatrixT      <Element> &another);
0067    TMatrixT(const TMatrixTSym   <Element> &another);
0068    TMatrixT(const TMatrixTSparse<Element> &another);
0069    template <class Element2> TMatrixT(const TMatrixT<Element2> &another): fElements(nullptr)
0070    {
0071       R__ASSERT(another.IsValid());
0072       Allocate(another.GetNrows(),another.GetNcols(),another.GetRowLwb(),another.GetColLwb());
0073       *this = another;
0074    }
0075 
0076    TMatrixT(EMatrixCreatorsOp1 op,const TMatrixT<Element> &prototype);
0077    TMatrixT(const TMatrixT    <Element> &a,EMatrixCreatorsOp2 op,const TMatrixT   <Element> &b);
0078    TMatrixT(const TMatrixT    <Element> &a,EMatrixCreatorsOp2 op,const TMatrixTSym<Element> &b);
0079    TMatrixT(const TMatrixTSym <Element> &a,EMatrixCreatorsOp2 op,const TMatrixT   <Element> &b);
0080    TMatrixT(const TMatrixTSym <Element> &a,EMatrixCreatorsOp2 op,const TMatrixTSym<Element> &b);
0081    TMatrixT(const TMatrixTLazy<Element> &lazy_constructor);
0082 
0083    ~TMatrixT() override { TMatrixT::Clear(); }
0084 
0085    // Elementary constructors
0086 
0087    void Plus (const TMatrixT   <Element> &a,const TMatrixT   <Element> &b);
0088    void Plus (const TMatrixT   <Element> &a,const TMatrixTSym<Element> &b);
0089    void Plus (const TMatrixTSym<Element> &a,const TMatrixT   <Element> &b) { Plus(b,a); }
0090 
0091    void Minus(const TMatrixT   <Element> &a,const TMatrixT   <Element> &b);
0092    void Minus(const TMatrixT   <Element> &a,const TMatrixTSym<Element> &b);
0093    void Minus(const TMatrixTSym<Element> &a,const TMatrixT   <Element> &b) { Minus(b,a); }
0094 
0095    void Mult (const TMatrixT   <Element> &a,const TMatrixT   <Element> &b);
0096    void Mult (const TMatrixT   <Element> &a,const TMatrixTSym<Element> &b);
0097    void Mult (const TMatrixTSym<Element> &a,const TMatrixT   <Element> &b);
0098    void Mult (const TMatrixTSym<Element> &a,const TMatrixTSym<Element> &b);
0099 
0100    void TMult(const TMatrixT   <Element> &a,const TMatrixT   <Element> &b);
0101    void TMult(const TMatrixT   <Element> &a,const TMatrixTSym<Element> &b);
0102    void TMult(const TMatrixTSym<Element> &a,const TMatrixT   <Element> &b) { Mult(a,b); }
0103    void TMult(const TMatrixTSym<Element> &a,const TMatrixTSym<Element> &b) { Mult(a,b); }
0104 
0105    void MultT(const TMatrixT   <Element> &a,const TMatrixT   <Element> &b);
0106    void MultT(const TMatrixT   <Element> &a,const TMatrixTSym<Element> &b) { Mult(a,b); }
0107    void MultT(const TMatrixTSym<Element> &a,const TMatrixT   <Element> &b);
0108    void MultT(const TMatrixTSym<Element> &a,const TMatrixTSym<Element> &b) { Mult(a,b); }
0109 
0110    const Element *GetMatrixArray  () const override;
0111          Element *GetMatrixArray  () override;
0112    const Int_t   *GetRowIndexArray() const override { return nullptr; }
0113          Int_t   *GetRowIndexArray() override       { return nullptr; }
0114    const Int_t   *GetColIndexArray() const override { return nullptr; }
0115          Int_t   *GetColIndexArray() override       { return nullptr; }
0116 
0117          TMatrixTBase<Element> &SetRowIndexArray(Int_t * /*data*/) override { MayNotUse("SetRowIndexArray(Int_t *)"); return *this; }
0118          TMatrixTBase<Element> &SetColIndexArray(Int_t * /*data*/) override { MayNotUse("SetColIndexArray(Int_t *)"); return *this; }
0119 
0120    void Clear(Option_t * /*option*/ ="") override
0121    {
0122       if (this->fIsOwner)
0123          Delete_m(this->fNelems, fElements);
0124       else
0125          fElements = nullptr;
0126       this->fNelems = 0;
0127    }
0128 
0129            TMatrixT    <Element> &Use     (Int_t row_lwb,Int_t row_upb,Int_t col_lwb,Int_t col_upb,Element *data);
0130    const   TMatrixT    <Element> &Use     (Int_t row_lwb,Int_t row_upb,Int_t col_lwb,Int_t col_upb,const Element *data) const
0131                                             { return (const TMatrixT<Element>&)
0132                                                      ((const_cast<TMatrixT<Element> *>(this))->Use(row_lwb,row_upb,col_lwb,col_upb, const_cast<Element *>(data))); }
0133            TMatrixT    <Element> &Use     (Int_t nrows,Int_t ncols,Element *data);
0134    const   TMatrixT    <Element> &Use     (Int_t nrows,Int_t ncols,const Element *data) const;
0135            TMatrixT    <Element> &Use     (TMatrixT<Element> &a);
0136    const   TMatrixT    <Element> &Use     (const TMatrixT<Element> &a) const;
0137 
0138    TMatrixTBase<Element> &GetSub  (Int_t row_lwb,Int_t row_upb,Int_t col_lwb,Int_t col_upb,
0139                                            TMatrixTBase<Element> &target,Option_t *option="S") const override;
0140            TMatrixT    <Element>  GetSub  (Int_t row_lwb,Int_t row_upb,Int_t col_lwb,Int_t col_upb,Option_t *option="S") const;
0141    TMatrixTBase<Element> &SetSub  (Int_t row_lwb,Int_t col_lwb,const TMatrixTBase<Element> &source) override;
0142 
0143    TMatrixTBase<Element> &ResizeTo(Int_t nrows,Int_t ncols,Int_t /*nr_nonzeros*/ =-1) override;
0144    TMatrixTBase<Element> &ResizeTo(Int_t row_lwb,Int_t row_upb,Int_t col_lwb,Int_t col_upb,Int_t /*nr_nonzeros*/ =-1) override;
0145    inline  TMatrixTBase<Element> &ResizeTo(const TMatrixT<Element> &m) {
0146                                             return ResizeTo(m.GetRowLwb(),m.GetRowUpb(),m.GetColLwb(),m.GetColUpb());
0147                                  }
0148 
0149    Double_t Determinant  () const override;
0150    void     Determinant  (Double_t &d1,Double_t &d2) const override;
0151 
0152            TMatrixT<Element> &Invert      (Double_t *det = nullptr);
0153            TMatrixT<Element> &InvertFast  (Double_t *det = nullptr);
0154            TMatrixT<Element> &Transpose   (const TMatrixT<Element> &source);
0155    inline  TMatrixT<Element> &T           () { return this->Transpose(*this); }
0156            TMatrixT<Element> &Rank1Update (const TVectorT<Element> &v,Element alpha=1.0);
0157            TMatrixT<Element> &Rank1Update (const TVectorT<Element> &v1,const TVectorT<Element> &v2,Element alpha=1.0);
0158            Element            Similarity  (const TVectorT<Element> &v) const;
0159 
0160    TMatrixT<Element> &NormByColumn(const TVectorT<Element> &v,Option_t *option="D");
0161    TMatrixT<Element> &NormByRow   (const TVectorT<Element> &v,Option_t *option="D");
0162 
0163    // Either access a_ij as a(i,j)
0164    inline       Element                     operator()(Int_t rown,Int_t coln) const override;
0165    inline       Element                    &operator()(Int_t rown,Int_t coln) override;
0166 
0167    // or as a[i][j]
0168    inline const TMatrixTRow_const<Element>  operator[](Int_t rown) const { return TMatrixTRow_const<Element>(*this,rown); }
0169    inline       TMatrixTRow      <Element>  operator[](Int_t rown)       { return TMatrixTRow      <Element>(*this,rown); }
0170 
0171    TMatrixT<Element> &operator= (const TMatrixT      <Element> &source);
0172    TMatrixT<Element> &operator= (const TMatrixTSym   <Element> &source);
0173    TMatrixT<Element> &operator= (const TMatrixTSparse<Element> &source);
0174    TMatrixT<Element> &operator= (const TMatrixTLazy  <Element> &source);
0175    template <class Element2> TMatrixT<Element> &operator= (const TMatrixT<Element2> &source)
0176    {
0177       if (!AreCompatible(*this,source)) {
0178          Error("operator=(const TMatrixT2 &)","matrices not compatible");
0179          return *this;
0180       }
0181 
0182      TObject::operator=(source);
0183      const Element2 * const ps = source.GetMatrixArray();
0184            Element  * const pt = this->GetMatrixArray();
0185      for (Int_t i = 0; i < this->fNelems; i++)
0186         pt[i] = ps[i];
0187      this->fTol = source.GetTol();
0188      return *this;
0189    }
0190 
0191    TMatrixT<Element> &operator= (Element val);
0192    TMatrixT<Element> &operator-=(Element val);
0193    TMatrixT<Element> &operator+=(Element val);
0194    TMatrixT<Element> &operator*=(Element val);
0195 
0196    TMatrixT<Element> &operator+=(const TMatrixT   <Element> &source);
0197    TMatrixT<Element> &operator+=(const TMatrixTSym<Element> &source);
0198    TMatrixT<Element> &operator-=(const TMatrixT   <Element> &source);
0199    TMatrixT<Element> &operator-=(const TMatrixTSym<Element> &source);
0200 
0201    TMatrixT<Element> &operator*=(const TMatrixT            <Element> &source);
0202    TMatrixT<Element> &operator*=(const TMatrixTSym         <Element> &source);
0203    TMatrixT<Element> &operator*=(const TMatrixTDiag_const  <Element> &diag);
0204    TMatrixT<Element> &operator/=(const TMatrixTDiag_const  <Element> &diag);
0205    TMatrixT<Element> &operator*=(const TMatrixTRow_const   <Element> &row);
0206    TMatrixT<Element> &operator/=(const TMatrixTRow_const   <Element> &row);
0207    TMatrixT<Element> &operator*=(const TMatrixTColumn_const<Element> &col);
0208    TMatrixT<Element> &operator/=(const TMatrixTColumn_const<Element> &col);
0209 
0210    const TMatrixT<Element> EigenVectors(TVectorT<Element> &eigenValues) const;
0211 
0212    ClassDefOverride(TMatrixT,4) // Template of General Matrix class
0213 };
0214 
0215 // When building with -fmodules, it instantiates all pending instantiations,
0216 // instead of delaying them until the end of the translation unit.
0217 // We 'got away with' probably because the use and the definition of the
0218 // explicit specialization do not occur in the same TU.
0219 //
0220 // In case we are building with -fmodules, we need to forward declare the
0221 // specialization in order to compile the dictionary G__Matrix.cxx.
0222 template <> TClass *TMatrixT<double>::Class();
0223 
0224 
0225 template <class Element> inline const Element           *TMatrixT<Element>::GetMatrixArray() const { return fElements; }
0226 template <class Element> inline       Element           *TMatrixT<Element>::GetMatrixArray()       { return fElements; }
0227 
0228 template <class Element> inline       TMatrixT<Element> &TMatrixT<Element>::Use           (Int_t nrows,Int_t ncols,Element *data)
0229                                                                                           { return Use(0,nrows-1,0,ncols-1,data); }
0230 template <class Element> inline const TMatrixT<Element> &TMatrixT<Element>::Use           (Int_t nrows,Int_t ncols,const Element *data) const
0231                                                                                           { return Use(0,nrows-1,0,ncols-1,data); }
0232 template <class Element> inline       TMatrixT<Element> &TMatrixT<Element>::Use           (TMatrixT &a)
0233                                                                                           {
0234                                                                                             R__ASSERT(a.IsValid());
0235                                                                                             return Use(a.GetRowLwb(),a.GetRowUpb(),
0236                                                                                                        a.GetColLwb(),a.GetColUpb(),a.GetMatrixArray());
0237                                                                                           }
0238 template <class Element> inline const TMatrixT<Element> &TMatrixT<Element>::Use           (const TMatrixT &a) const
0239                                                                                           {
0240                                                                                             R__ASSERT(a.IsValid());
0241                                                                                             return Use(a.GetRowLwb(),a.GetRowUpb(),
0242                                                                                                        a.GetColLwb(),a.GetColUpb(),a.GetMatrixArray());
0243                                                                                           }
0244 
0245 template <class Element> inline       TMatrixT<Element>  TMatrixT<Element>::GetSub        (Int_t row_lwb,Int_t row_upb,Int_t col_lwb,Int_t col_upb,
0246                                                                                            Option_t *option) const
0247                                                                                           {
0248                                                                                             TMatrixT tmp;
0249                                                                                             this->GetSub(row_lwb,row_upb,col_lwb,col_upb,tmp,option);
0250                                                                                             return tmp;
0251                                                                                           }
0252 
0253 template <class Element> inline Element TMatrixT<Element>::operator()(Int_t rown,Int_t coln) const
0254 {
0255    R__ASSERT(this->IsValid());
0256    const Int_t arown = rown-this->fRowLwb;
0257    const Int_t acoln = coln-this->fColLwb;
0258    if (arown >= this->fNrows || arown < 0) {
0259       Error("operator()","Request row(%d) outside matrix range of %d - %d",rown,this->fRowLwb,this->fRowLwb+this->fNrows);
0260       return TMatrixTBase<Element>::NaNValue();
0261    }
0262    if (acoln >= this->fNcols || acoln < 0) {
0263       Error("operator()","Request column(%d) outside matrix range of %d - %d",coln,this->fColLwb,this->fColLwb+this->fNcols);
0264       return TMatrixTBase<Element>::NaNValue();
0265 
0266    }
0267    return (fElements[arown*this->fNcols+acoln]);
0268 }
0269 
0270 template <class Element> inline Element &TMatrixT<Element>::operator()(Int_t rown,Int_t coln)
0271 {
0272    R__ASSERT(this->IsValid());
0273    const Int_t arown = rown-this->fRowLwb;
0274    const Int_t acoln = coln-this->fColLwb;
0275    if (arown >= this->fNrows || arown < 0) {
0276       Error("operator()","Request row(%d) outside matrix range of %d - %d",rown,this->fRowLwb,this->fRowLwb+this->fNrows);
0277       return TMatrixTBase<Element>::NaNValue();
0278    }
0279    if (acoln >= this->fNcols || acoln < 0) {
0280       Error("operator()","Request column(%d) outside matrix range of %d - %d",coln,this->fColLwb,this->fColLwb+this->fNcols);
0281       return TMatrixTBase<Element>::NaNValue();
0282    }
0283    return (fElements[arown*this->fNcols+acoln]);
0284 }
0285 
0286 inline namespace TMatrixTAutoloadOps {
0287 
0288 template <class Element> TMatrixT<Element>  operator+  (const TMatrixT   <Element> &source1,const TMatrixT   <Element> &source2);
0289 template <class Element> TMatrixT<Element>  operator+  (const TMatrixT   <Element> &source1,const TMatrixTSym<Element> &source2);
0290 template <class Element> TMatrixT<Element>  operator+  (const TMatrixTSym<Element> &source1,const TMatrixT   <Element> &source2);
0291 template <class Element> TMatrixT<Element>  operator+  (const TMatrixT   <Element> &source ,      Element               val    );
0292 template <class Element> TMatrixT<Element>  operator+  (      Element               val    ,const TMatrixT   <Element> &source );
0293 template <class Element> TMatrixT<Element>  operator-  (const TMatrixT   <Element> &source1,const TMatrixT   <Element> &source2);
0294 template <class Element> TMatrixT<Element>  operator-  (const TMatrixT   <Element> &source1,const TMatrixTSym<Element> &source2);
0295 template <class Element> TMatrixT<Element>  operator-  (const TMatrixTSym<Element> &source1,const TMatrixT   <Element> &source2);
0296 template <class Element> TMatrixT<Element>  operator-  (const TMatrixT   <Element> &source ,      Element               val    );
0297 template <class Element> TMatrixT<Element>  operator-  (      Element               val    ,const TMatrixT   <Element> &source );
0298 template <class Element> TMatrixT<Element>  operator*  (      Element               val    ,const TMatrixT   <Element> &source );
0299 template <class Element> TMatrixT<Element>  operator*  (const TMatrixT   <Element> &source ,      Element               val    );
0300 template <class Element> TMatrixT<Element>  operator*  (const TMatrixT   <Element> &source1,const TMatrixT   <Element> &source2);
0301 template <class Element> TMatrixT<Element>  operator*  (const TMatrixT   <Element> &source1,const TMatrixTSym<Element> &source2);
0302 template <class Element> TMatrixT<Element>  operator*  (const TMatrixTSym<Element> &source1,const TMatrixT   <Element> &source2);
0303 template <class Element> TMatrixT<Element>  operator*  (const TMatrixTSym<Element> &source1,const TMatrixTSym<Element> &source2);
0304 // Preventing warnings with -Weffc++ in GCC since overloading the || and && operators was a design choice.
0305 #if (__GNUC__ * 10000 + __GNUC_MINOR__ * 100 + __GNUC_PATCHLEVEL__) >= 40600
0306 #pragma GCC diagnostic push
0307 #pragma GCC diagnostic ignored "-Weffc++"
0308 #endif
0309 template <class Element> TMatrixT<Element>  operator&& (const TMatrixT   <Element> &source1,const TMatrixT   <Element> &source2);
0310 template <class Element> TMatrixT<Element>  operator&& (const TMatrixT   <Element> &source1,const TMatrixTSym<Element> &source2);
0311 template <class Element> TMatrixT<Element>  operator&& (const TMatrixTSym<Element> &source1,const TMatrixT   <Element> &source2);
0312 template <class Element> TMatrixT<Element>  operator|| (const TMatrixT   <Element> &source1,const TMatrixT   <Element> &source2);
0313 template <class Element> TMatrixT<Element>  operator|| (const TMatrixT   <Element> &source1,const TMatrixTSym<Element> &source2);
0314 template <class Element> TMatrixT<Element>  operator|| (const TMatrixTSym<Element> &source1,const TMatrixT   <Element> &source2);
0315 #if (__GNUC__ * 10000 + __GNUC_MINOR__ * 100 + __GNUC_PATCHLEVEL__) >= 40600
0316 #pragma GCC diagnostic pop
0317 #endif
0318 template <class Element> TMatrixT<Element>  operator>  (const TMatrixT   <Element> &source1,const TMatrixT   <Element> &source2);
0319 template <class Element> TMatrixT<Element>  operator>  (const TMatrixT   <Element> &source1,const TMatrixTSym<Element> &source2);
0320 template <class Element> TMatrixT<Element>  operator>  (const TMatrixTSym<Element> &source1,const TMatrixT   <Element> &source2);
0321 template <class Element> TMatrixT<Element>  operator>= (const TMatrixT   <Element> &source1,const TMatrixT   <Element> &source2);
0322 template <class Element> TMatrixT<Element>  operator>= (const TMatrixT   <Element> &source1,const TMatrixTSym<Element> &source2);
0323 template <class Element> TMatrixT<Element>  operator>= (const TMatrixTSym<Element> &source1,const TMatrixT   <Element> &source2);
0324 template <class Element> TMatrixT<Element>  operator<= (const TMatrixT   <Element> &source1,const TMatrixT   <Element> &source2);
0325 template <class Element> TMatrixT<Element>  operator<= (const TMatrixT   <Element> &source1,const TMatrixTSym<Element> &source2);
0326 template <class Element> TMatrixT<Element>  operator<= (const TMatrixTSym<Element> &source1,const TMatrixT   <Element> &source2);
0327 template <class Element> TMatrixT<Element>  operator<  (const TMatrixT   <Element> &source1,const TMatrixT   <Element> &source2);
0328 template <class Element> TMatrixT<Element>  operator<  (const TMatrixT   <Element> &source1,const TMatrixTSym<Element> &source2);
0329 template <class Element> TMatrixT<Element>  operator<  (const TMatrixTSym<Element> &source1,const TMatrixT   <Element> &source2);
0330 template <class Element> TMatrixT<Element>  operator!= (const TMatrixT   <Element> &source1,const TMatrixT   <Element> &source2);
0331 template <class Element> TMatrixT<Element>  operator!= (const TMatrixT   <Element> &source1,const TMatrixTSym<Element> &source2);
0332 template <class Element> TMatrixT<Element>  operator!= (const TMatrixTSym<Element> &source1,const TMatrixT   <Element> &source2);
0333 
0334 template <class Element> TMatrixT<Element> &Add        (TMatrixT<Element> &target,      Element               scalar,const TMatrixT   <Element> &source);
0335 template <class Element> TMatrixT<Element> &Add        (TMatrixT<Element> &target,      Element               scalar,const TMatrixTSym<Element> &source);
0336 template <class Element> TMatrixT<Element> &ElementMult(TMatrixT<Element> &target,const TMatrixT   <Element> &source);
0337 template <class Element> TMatrixT<Element> &ElementMult(TMatrixT<Element> &target,const TMatrixTSym<Element> &source);
0338 template <class Element> TMatrixT<Element> &ElementDiv (TMatrixT<Element> &target,const TMatrixT   <Element> &source);
0339 template <class Element> TMatrixT<Element> &ElementDiv (TMatrixT<Element> &target,const TMatrixTSym<Element> &source);
0340 
0341 template <class Element> void AMultB (const Element * const ap,Int_t na,Int_t ncolsa,
0342                                       const Element * const bp,Int_t nb,Int_t ncolsb,Element *cp);
0343 template <class Element> void AtMultB(const Element * const ap,Int_t ncolsa,
0344                                       const Element * const bp,Int_t nb,Int_t ncolsb,Element *cp);
0345 template <class Element> void AMultBt(const Element * const ap,Int_t na,Int_t ncolsa,
0346                                       const Element * const bp,Int_t nb,Int_t ncolsb,Element *cp);
0347 } // inline namespace TMatrixTAutoloadOps
0348 #endif
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