newmat7.cpp

各种矩阵算法库。支持UpperTriangularMatrix,LowerTriangularMatrix, DiagonalMatrix, SymmetricMatrix, BandMatrix,U

   Matrix* gm = new Matrix(nr,nc); MatrixErrorNoSpace(gm);

   Real* s1=gm1->Store(); Real* s2=gm2->Store(); Real* s=gm->Store();
   
   if (ncr)
   {
      while (nr--)
      {
         Real* s2x = s2; int j = ncr;
         Real* sx = s; Real f = *s1++; int k = nc;
         while (k--) *sx++ = f * *s2x++;
         while (--j)
            { sx = s; f = *s1++; k = nc; while (k--) *sx++ += f * *s2x++; }
         s = sx;
      }
   }
   else *gm = 0.0;

   gm->ReleaseAndDelete(); gm1->tDelete(); gm2->tDelete(); return gm;
}

static GeneralMatrix* GeneralMult(GeneralMatrix* gm1, GeneralMatrix* gm2,
   MultipliedMatrix* mm, MatrixType mtx)
{
   if ( Rectangular(gm1->Type(), gm2->Type(), mtx)) return mmMult(gm1, gm2);
   else
   {
      Compare(gm1->Type() * gm2->Type(),mtx);
      int nr = gm2->Nrows(); int nc = gm2->Ncols();
      if (nc <= 5 && nr > nc) return GeneralMult1(gm1, gm2, mm, mtx);
      else return GeneralMult2(gm1, gm2, mm, mtx);
   }
}

#ifdef __GNUG__
void SPMatrix::SelectVersion
   (MatrixType mtx, int& c1, int& c2) const
#else
void SPMatrix::SelectVersion
   (MatrixType mtx, bool& c1, bool& c2) const
#endif
// for determining version of SP routines
// will need to modify if further matrix structures are introduced
{
   MatrixBandWidth bw1 = gm1->BandWidth();
   MatrixBandWidth bw2 = gm2->BandWidth();
   MatrixBandWidth bwx(-1);  if (mtx.IsBand()) bwx = bw1.minimum(bw2);
   c1 = (mtx == gm1->Type()) && (bwx == bw1);
   c2 = (mtx == gm2->Type()) && (bwx == bw2);
}

static GeneralMatrix* GeneralSP(GeneralMatrix* gm1, GeneralMatrix* gm2,
   SPMatrix* am, MatrixType mtx)
{
   Tracer tr("GeneralSP");
   int nr=gm1->Nrows(); int nc=gm1->Ncols();
   if (nr!=gm2->Nrows() || nc!=gm2->Ncols()) 
      Throw(IncompatibleDimensionsException(*gm1, *gm2));
   Compare(gm1->Type().SP(gm2->Type()),mtx);
#ifdef __GNUG__
   int c1,c2; am->SelectVersion(mtx,c1,c2);
#else
   bool c1,c2; am->SelectVersion(mtx,c1,c2); // causes problems for g++
#endif
   if (c1 && c2)
   {
      if (gm1->reuse()) { REPORT SP(gm1,gm2); gm2->tDelete(); return gm1; }
      else if (gm2->reuse()) { REPORT SP(gm2,gm1); return gm2; }
      else
      {
         REPORT GeneralMatrix* gmx = gm1->Type().New(nr,nc,am);
         gmx->ReleaseAndDelete(); SP(gmx,gm1,gm2); return gmx;
      }
   }
   else
   {
      if (c1 && gm1->reuse() )               // must have type test first
      { REPORT SPDS(gm1,gm2); gm2->tDelete(); return gm1; }
      else if (c2 && gm2->reuse() )
      { REPORT SPDS(gm2,gm1); if (!c1) gm1->tDelete(); return gm2; }
      else
      {
         REPORT
	 GeneralMatrix* gmx = mtx.New(nr,nc,am); SPDS(gmx,gm1,gm2);
	 if (!c1) gm1->tDelete(); if (!c2) gm2->tDelete();
         gmx->ReleaseAndDelete(); return gmx;
      }
   }
}


static GeneralMatrix* GeneralSolv(GeneralMatrix* gm1, GeneralMatrix* gm2,
   BaseMatrix* sm, MatrixType mtx)
{
   REPORT
   Tracer tr("GeneralSolv");
   Compare(gm1->Type().i() * gm2->Type(),mtx);
   int nr = gm1->Nrows();
   if (nr != gm1->Ncols()) Throw(NotSquareException(*gm1));
   int nc = gm2->Ncols();
   if (gm1->Ncols() != gm2->Nrows())
      Throw(IncompatibleDimensionsException(*gm1, *gm2));
   GeneralMatrix* gmx = mtx.New(nr,nc,sm); MatrixErrorNoSpace(gmx);
   Real* r = new Real [nr]; MatrixErrorNoSpace(r);
   MONITOR_REAL_NEW("Make   (GenSolv)",nr,r)
   GeneralMatrix* gms = gm1->MakeSolver();
   Try
   {

      MatrixColX mcx(gmx, r, StoreOnExit+DirectPart);   // copy to and from r
         // this must be inside Try so mcx is destroyed before gmx
      MatrixColX mc2(gm2, r, LoadOnEntry);
      while (nc--) { gms->Solver(mcx, mc2); mcx.Next(); mc2.Next(); }
   }
   CatchAll
   {
      if (gms) gms->tDelete();
      delete gmx;                   // <--------------------
      gm2->tDelete();
      MONITOR_REAL_DELETE("Delete (GenSolv)",nr,r)
                          // ATandT version 2.1 gives an internal error
      delete [] r;
      ReThrow;
   }
   gms->tDelete(); gmx->ReleaseAndDelete(); gm2->tDelete();
   MONITOR_REAL_DELETE("Delete (GenSolv)",nr,r)
                          // ATandT version 2.1 gives an internal error
   delete [] r;
   return gmx;
}

// version for inverses - gm2 is identity
static GeneralMatrix* GeneralSolvI(GeneralMatrix* gm1, BaseMatrix* sm,
   MatrixType mtx)
{
   REPORT
   Tracer tr("GeneralSolvI");
   Compare(gm1->Type().i(),mtx);
   int nr = gm1->Nrows();
   if (nr != gm1->Ncols()) Throw(NotSquareException(*gm1));
   int nc = nr;
   DiagonalMatrix I(nr); I=1.0;
   GeneralMatrix* gmx = mtx.New(nr,nc,sm); MatrixErrorNoSpace(gmx);
   Real* r = new Real [nr]; MatrixErrorNoSpace(r);
   MONITOR_REAL_NEW("Make   (GenSolvI)",nr,r)
   GeneralMatrix* gms = gm1->MakeSolver();
   Try
   {

      MatrixColX mcx(gmx, r, StoreOnExit+DirectPart);   // copy to and from r
         // this must be inside Try so mcx is destroyed before gmx
      MatrixColX mc2(&I, r, LoadOnEntry);
      while (nc--) { gms->Solver(mcx, mc2); mcx.Next(); mc2.Next(); }
   }
   CatchAll
   {
      if (gms) gms->tDelete();
      delete gmx;
      MONITOR_REAL_DELETE("Delete (GenSolvI)",nr,r)
                          // ATandT version 2.1 gives an internal error
      delete [] r;
      ReThrow;
   }
   gms->tDelete(); gmx->ReleaseAndDelete();
   MONITOR_REAL_DELETE("Delete (GenSolvI)",nr,r)
                          // ATandT version 2.1 gives an internal error
   delete [] r;
   return gmx;
}

GeneralMatrix* InvertedMatrix::Evaluate(MatrixType mtx)
{
   // Matrix Inversion - use solve routines
   Tracer tr("InvertedMatrix::Evaluate");
   REPORT
   gm=((BaseMatrix*&)bm)->Evaluate();
#ifdef TEMPS_DESTROYED_QUICKLY
	GeneralMatrix* gmx;
	Try { gmx = GeneralSolvI(gm,this,mtx); }
   CatchAll { delete this; ReThrow; }
   delete this; return gmx;
#else
   return GeneralSolvI(gm,this,mtx);
#endif
}


/*************************** norm functions ****************************/

Real BaseMatrix::Norm1() const
{
   // maximum of sum of absolute values of a column
   REPORT
   GeneralMatrix* gm = ((BaseMatrix&)*this).Evaluate();
   int nc = gm->Ncols(); Real value = 0.0;
   MatrixCol mc(gm, LoadOnEntry);
   while (nc--)
      { Real v = mc.SumAbsoluteValue(); if (value < v) value = v; mc.Next(); }
   gm->tDelete(); return value;
}

Real BaseMatrix::NormInfinity() const
{
   // maximum of sum of absolute values of a row
   REPORT
   GeneralMatrix* gm = ((BaseMatrix&)*this).Evaluate();
   int nr = gm->Nrows(); Real value = 0.0;
   MatrixRow mr(gm, LoadOnEntry);
   while (nr--)
      { Real v = mr.SumAbsoluteValue(); if (value < v) value = v; mr.Next(); }
   gm->tDelete(); return value;
}

/********************** Concatenation and stacking *************************/

GeneralMatrix* ConcatenatedMatrix::Evaluate(MatrixType mtx)
{
   REPORT
   Tracer tr("Concatenate");
#ifdef TEMPS_DESTROYED_QUICKLY
      Try
      {
         gm2 = ((BaseMatrix*&)bm2)->Evaluate();
         gm1 = ((BaseMatrix*&)bm1)->Evaluate();
         Compare(gm1->Type() | gm2->Type(),mtx);
         int nr=gm1->Nrows(); int nc = gm1->Ncols() + gm2->Ncols();
         if (nr != gm2->Nrows())
            Throw(IncompatibleDimensionsException(*gm1, *gm2));
         GeneralMatrix* gmx = mtx.New(nr,nc,this);
         MatrixRow mr1(gm1, LoadOnEntry); MatrixRow mr2(gm2, LoadOnEntry);
         MatrixRow mr(gmx, StoreOnExit+DirectPart);
         while (nr--) { mr.ConCat(mr1,mr2); mr1.Next(); mr2.Next(); mr.Next(); }
         gmx->ReleaseAndDelete(); gm1->tDelete(); gm2->tDelete(); delete this;
         return gmx;
      }
      CatchAll  { delete this; ReThrow; }
#ifndef UseExceptions
      return 0;
#endif 
#else
      gm2 = ((BaseMatrix*&)bm2)->Evaluate();
      gm1 = ((BaseMatrix*&)bm1)->Evaluate();
      Compare(gm1->Type() | gm2->Type(),mtx);
      int nr=gm1->Nrows(); int nc = gm1->Ncols() + gm2->Ncols();
      if (nr != gm2->Nrows())
         Throw(IncompatibleDimensionsException(*gm1, *gm2));
      GeneralMatrix* gmx = mtx.New(nr,nc,this);
      MatrixRow mr1(gm1, LoadOnEntry); MatrixRow mr2(gm2, LoadOnEntry);
      MatrixRow mr(gmx, StoreOnExit+DirectPart);
      while (nr--) { mr.ConCat(mr1,mr2); mr1.Next(); mr2.Next(); mr.Next(); }
      gmx->ReleaseAndDelete(); gm1->tDelete(); gm2->tDelete(); return gmx;
#endif
}

GeneralMatrix* StackedMatrix::Evaluate(MatrixType mtx)
{
   REPORT
   Tracer tr("Stack");
#ifdef TEMPS_DESTROYED_QUICKLY
      Try
      {
         gm2 = ((BaseMatrix*&)bm2)->Evaluate();
         gm1 = ((BaseMatrix*&)bm1)->Evaluate();
         Compare(gm1->Type() & gm2->Type(),mtx);
         int nc=gm1->Ncols();
         int nr1 = gm1->Nrows(); int nr2 = gm2->Nrows();
         if (nc != gm2->Ncols())
            Throw(IncompatibleDimensionsException(*gm1, *gm2));
         GeneralMatrix* gmx = mtx.New(nr1+nr2,nc,this);
         MatrixRow mr1(gm1, LoadOnEntry); MatrixRow mr2(gm2, LoadOnEntry);
         MatrixRow mr(gmx, StoreOnExit+DirectPart);
         while (nr1--) { mr.Copy(mr1); mr1.Next(); mr.Next(); }
         while (nr2--) { mr.Copy(mr2); mr2.Next(); mr.Next(); }
         gmx->ReleaseAndDelete(); gm1->tDelete(); gm2->tDelete(); delete this;
         return gmx;
      }
      CatchAll  { delete this; ReThrow; }
#ifndef UseExceptions
      return 0;
#endif
#else
      gm2 = ((BaseMatrix*&)bm2)->Evaluate();
      gm1 = ((BaseMatrix*&)bm1)->Evaluate();
      Compare(gm1->Type() & gm2->Type(),mtx);
      int nc=gm1->Ncols();
      int nr1 = gm1->Nrows(); int nr2 = gm2->Nrows();
      if (nc != gm2->Ncols())
         Throw(IncompatibleDimensionsException(*gm1, *gm2));
      GeneralMatrix* gmx = mtx.New(nr1+nr2,nc,this);
      MatrixRow mr1(gm1, LoadOnEntry); MatrixRow mr2(gm2, LoadOnEntry);
      MatrixRow mr(gmx, StoreOnExit+DirectPart);
      while (nr1--) { mr.Copy(mr1); mr1.Next(); mr.Next(); }
      while (nr2--) { mr.Copy(mr2); mr2.Next(); mr.Next(); }
      gmx->ReleaseAndDelete(); gm1->tDelete(); gm2->tDelete(); return gmx;
#endif
}

// ************************* equality of matrices ******************** //

static bool RealEqual(Real* s1, Real* s2, int n)
{
   int i = n >> 2;
   while (i--)
   {
      if (*s1++ != *s2++) return false; if (*s1++ != *s2++) return false;
      if (*s1++ != *s2++) return false; if (*s1++ != *s2++) return false;
   }
   i = n & 3; while (i--) if (*s1++ != *s2++) return false;
   return true;
}

static bool intEqual(int* s1, int* s2, int n)
{
   int i = n >> 2;
   while (i--)
   {
      if (*s1++ != *s2++) return false; if (*s1++ != *s2++) return false;
      if (*s1++ != *s2++) return false; if (*s1++ != *s2++) return false;
   }
   i = n & 3; while (i--) if (*s1++ != *s2++) return false;
   return true;
}


bool operator==(const BaseMatrix& A, const BaseMatrix& B)
{
   Tracer tr("BaseMatrix ==");
   REPORT
   GeneralMatrix* gmA = ((BaseMatrix&)A).Evaluate();
   GeneralMatrix* gmB = ((BaseMatrix&)B).Evaluate();

   if (gmA == gmB)                            // same matrix
      { REPORT gmA->tDelete(); return true; }

   if ( gmA->Nrows() != gmB->Nrows() || gmA->Ncols() != gmB->Ncols() )
                                              // different dimensions
      { REPORT gmA->tDelete(); gmB->tDelete(); return false; }

   // check for CroutMatrix or BandLUMatrix
   MatrixType AType = gmA->Type(); MatrixType BType = gmB->Type();
   if (AType.CannotConvert() || BType.CannotConvert() )
   {
      REPORT
      bool bx = gmA->IsEqual(*gmB);
      gmA->tDelete(); gmB->tDelete();
      return bx;
   }

   // is matrix storage the same
   // will need to modify if further matrix structures are introduced
   if (AType == BType && gmA->BandWidth() == gmB->BandWidth())
   {                                          // compare store
      REPORT
      bool bx = RealEqual(gmA->Store(),gmB->Store(),gmA->Storage());
      gmA->tDelete(); gmB->tDelete();
      return bx;
   }

   // matrix storage different - just subtract
   REPORT  return IsZero(*gmA-*gmB);
}

bool operator==(const GeneralMatrix& A, const GeneralMatrix& B)
{
   Tracer tr("GeneralMatrix ==");
   // May or may not call tDeletes
   REPORT

   if (&A == &B)                              // same matrix
      { REPORT return true; }

   if ( A.Nrows() != B.Nrows() || A.Ncols() != B.Ncols() )
      { REPORT return false; }                // different dimensions

   // check for CroutMatrix or BandLUMatrix
   MatrixType AType = A.Type(); MatrixType BType = B.Type();
   if (AType.CannotConvert() || BType.CannotConvert() )
      { REPORT  return A.IsEqual(B); }

   // is matrix storage the same
   // will need to modify if further matrix structures are introduced
   if (AType == BType && A.BandWidth() == B.BandWidth())
      { REPORT return RealEqual(A.Store(),B.Store(),A.Storage()); }

   // matrix storage different - just subtract
   REPORT  return IsZero(A-B);
}

bool GeneralMatrix::IsZero() const
{
   REPORT
   Real* s=store; int i = storage >> 2;
   while (i--)
   {
      if (*s++) return false; if (*s++) return false;
      if (*s++) return false; if (*s++) return false;
   }
   i = storage & 3; while (i--) if (*s++) return false;
   return true;
}

bool IsZero(const BaseMatrix& A)
{
   Tracer tr("BaseMatrix::IsZero");
   REPORT
   GeneralMatrix* gm1 = 0; bool bx;
   Try { gm1=((BaseMatrix&)A).Evaluate(); bx = gm1->IsZero(); }
   CatchAll { if (gm1) gm1->tDelete(); ReThrow; }
   gm1->tDelete();
   return bx;
}

// IsEqual functions - insist matrices are of same type
// as well as equal values to be equal

bool GeneralMatrix::IsEqual(const GeneralMatrix& A) const
{
   Tracer tr("GeneralMatrix IsEqual");
   if (A.Type() != Type())                       // not same types
      { REPORT return false; }
   if (&A == this)                               // same matrix
      { REPORT  return true; }
   if (A.nrows != nrows || A.ncols != ncols)
						 // different dimensions
   { REPORT return false; }
   // is matrix storage the same - compare store
   REPORT
   return RealEqual(A.store,store,storage);
}

bool CroutMatrix::IsEqual(const GeneralMatrix& A) const
{
   Tracer tr("CroutMatrix IsEqual");
   if (A.Type() != Type())                       // not same types
      { REPORT return false; }
   if (&A == this)                              // same matrix
      { REPORT  return true; }
   if (A.nrows != nrows || A.ncols != ncols)
						 // different dimensions
   { REPORT return false; }
   // is matrix storage the same - compare store
   REPORT
   return RealEqual(A.store,store,storage)
      && intEqual(((CroutMatrix&)A).indx, indx, nrows);
}


bool BandLUMatrix::IsEqual(const GeneralMatrix& A) const
{
   Tracer tr("BandLUMatrix IsEqual");
   if (A.Type() != Type())                       // not same types
      { REPORT  return false; }
   if (&A == this)                               // same matrix
      { REPORT  return true; }
   if ( A.Nrows() != nrows || A.Ncols() != ncols
      || ((BandLUMatrix&)A).m1 != m1 || ((BandLUMatrix&)A).m2 != m2 )
						 // different dimensions
   { REPORT  return false; }

   // matrix storage the same - compare store
   REPORT
   return RealEqual(A.Store(),store,storage)
      && RealEqual(((BandLUMatrix&)A).store2,store2,storage2)
      && intEqual(((BandLUMatrix&)A).indx, indx, nrows);
}





#ifdef use_namespace
}
#endif