bandmat.cpp

非常好用的用C编写的矩阵类,可在不同编译器下编译使用.

   // while (i--) { sum *= *a; a += w; }
   if (i) for (;;) { sum *= *a; if (!(--i)) break; a += w; }
   if (!d) sum.ChangeSign(); return sum;
}

GeneralMatrix* BandMatrix::MakeSolver()
{
   REPORT
   GeneralMatrix* gm = new BandLUMatrix(*this);
   MatrixErrorNoSpace(gm); gm->ReleaseAndDelete(); return gm;
}


void BandLUMatrix::ludcmp()
{
   REPORT
   Real* a = store2; int i = storage2;
   // clear store2 - so unused locations are always zero -
   // required by operator==
   while (i--) *a++ = 0.0;
   a = store;
   i = m1; int j = m2; int k; int n = nrows_val; int w = m1 + 1 + m2;
   while (i)
   {
      Real* ai = a + i;
      k = ++j; while (k--) *a++ = *ai++;
      k = i--; while (k--) *a++ = 0.0;
   }

   a = store; int l = m1;
   for (k=0; k<n; k++)
   {
      Real x = *a; i = k; Real* aj = a;
      if (l < n) l++;
      for (j=k+1; j<l; j++)
         { aj += w; if (fabs(x) < fabs(*aj)) { x = *aj; i = j; } }
      indx[k] = i;
      if (x==0) { sing = true; return; }
      if (i!=k)
      {
         d = !d; Real* ak = a; Real* ai = store + i * w; j = w;
         while (j--) { x = *ak; *ak++ = *ai; *ai++ = x; }
      }
      aj = a + w; Real* m = store2 + m1 * k;
      for (j=k+1; j<l; j++)
      {
         *m++ = x = *aj / *a; i = w; Real* ak = a;
         while (--i) { Real* aj1 = aj++; *aj1 = *aj - x * *(++ak); }
         *aj++ = 0.0;
      }
      a += w;
   }
}

void BandLUMatrix::lubksb(Real* B, int mini)
{
   REPORT
   Tracer tr("BandLUMatrix::lubksb");
   if (sing) Throw(SingularException(*this));
   int n = nrows_val; int l = m1; int w = m1 + 1 + m2;

   for (int k=0; k<n; k++)
   {
      int i = indx[k];
      if (i!=k) { Real x=B[k]; B[k]=B[i]; B[i]=x; }
      if (l<n) l++;
      Real* m = store2 + k*m1; Real* b = B+k; Real* bi = b;
      for (i=k+1; i<l; i++)  *(++bi) -= *m++ * *b;
   }

   l = -m1;
   for (int i = n-1; i>=mini; i--)
   {
      Real* b = B + i; Real* bk = b; Real x = *bk;
      Real* a = store + w*i; Real y = *a;
      int k = l+m1; while (k--) x -=  *(++a) * *(++bk);
      *b = x / y;
      if (l < m2) l++;
   }
}

void BandLUMatrix::Solver(MatrixColX& mcout, const MatrixColX& mcin)
{
   REPORT
   int i = mcin.skip; Real* el = mcin.data-i; Real* el1=el;
   while (i--) *el++ = 0.0;
   el += mcin.storage; i = nrows_val - mcin.skip - mcin.storage;
   while (i--) *el++ = 0.0;
   lubksb(el1, mcout.skip);
}

// Do we need check for entirely zero output?


void UpperBandMatrix::Solver(MatrixColX& mcout,
   const MatrixColX& mcin)
{
   REPORT
   int i = mcin.skip-mcout.skip; Real* elx = mcin.data-i;
   while (i-- > 0) *elx++ = 0.0;
   int nr = mcin.skip+mcin.storage;
   elx = mcin.data+mcin.storage; Real* el = elx;
   int j = mcout.skip+mcout.storage-nr; i = nr-mcout.skip;
   while (j-- > 0) *elx++ = 0.0;

   Real* Ael = store + (upper_val+1)*(i-1)+1; j = 0;
   if (i > 0) for(;;)
   {
      elx = el; Real sum = 0.0; int jx = j;
      while (jx--) sum += *(--Ael) * *(--elx);
      elx--; *elx = (*elx - sum) / *(--Ael);
      if (--i <= 0) break;
      if (j<upper_val) Ael -= upper_val - (++j); else el--;
   }
}

void LowerBandMatrix::Solver(MatrixColX& mcout,
   const MatrixColX& mcin)
{
   REPORT
   int i = mcin.skip-mcout.skip; Real* elx = mcin.data-i;
   while (i-- > 0) *elx++ = 0.0;
   int nc = mcin.skip; i = nc+mcin.storage; elx = mcin.data+mcin.storage;
   int nr = mcout.skip+mcout.storage; int j = nr-i; i = nr-nc;
   while (j-- > 0) *elx++ = 0.0;

   Real* el = mcin.data;
   Real* Ael = store + (lower_val+1)*nc + lower_val;
   j = 0;
   if (i > 0) for(;;)
   {
      elx = el; Real sum = 0.0; int jx = j;
      while (jx--) sum += *Ael++ * *elx++;
      *elx = (*elx - sum) / *Ael++;
      if (--i <= 0) break;
      if (j<lower_val) Ael += lower_val - (++j); else el++;
   }
}


LogAndSign BandMatrix::log_determinant() const
{
   REPORT
   BandLUMatrix C(*this); return C.log_determinant();
}

LogAndSign LowerBandMatrix::log_determinant() const
{
   REPORT
   int i = nrows_val; LogAndSign sum;
   Real* s = store + lower_val; int j = lower_val + 1;
//   while (i--) { sum *= *s; s += j; }
   if (i) for (;;) { sum *= *s; if (!(--i)) break; s += j; }
   ((GeneralMatrix&)*this).tDelete(); return sum;
}

LogAndSign UpperBandMatrix::log_determinant() const
{
   REPORT
   int i = nrows_val; LogAndSign sum; Real* s = store; int j = upper_val + 1;
//   while (i--) { sum *= *s; s += j; }
   if (i) for (;;) { sum *= *s; if (!(--i)) break; s += j; }
   ((GeneralMatrix&)*this).tDelete(); return sum;
}

GeneralMatrix* SymmetricBandMatrix::MakeSolver()
{
   REPORT
   GeneralMatrix* gm = new BandLUMatrix(*this);
   MatrixErrorNoSpace(gm); gm->ReleaseAndDelete(); return gm;
}

SymmetricBandMatrix::SymmetricBandMatrix(const BaseMatrix& M)
{
   REPORT  // CheckConversion(M);
   // MatrixConversionCheck mcc;
   GeneralMatrix* gmx=((BaseMatrix&)M).Evaluate(MatrixType::SB);
   GetMatrix(gmx);
}

GeneralMatrix* SymmetricBandMatrix::Transpose(TransposedMatrix*, MatrixType mt)
{ REPORT  return Evaluate(mt); }

LogAndSign SymmetricBandMatrix::log_determinant() const
{
   REPORT
   BandLUMatrix C(*this); return C.log_determinant();
}

void SymmetricBandMatrix::SetParameters(const GeneralMatrix* gmx)
{ REPORT lower_val = gmx->bandwidth().lower_val; }

void SymmetricBandMatrix::resize(int n, int lb)
{
   REPORT
   Tracer tr("SymmetricBandMatrix::resize");
   if (lb<0) Throw(ProgramException("Undefined bandwidth"));
   lower_val = (lb<=n) ? lb : n-1;
   GeneralMatrix::resize(n,n,n*(lower_val+1));
}

void SymmetricBandMatrix::resize(const GeneralMatrix& A)
{
   REPORT
   int n = A.Nrows();
   if (n != A.Ncols())
   {
      Tracer tr("SymmetricBandMatrix::resize(GM)");
      Throw(NotSquareException(*this));
   }
   MatrixBandWidth mbw = A.bandwidth(); int b = mbw.Lower();
   if (b != mbw.Upper())
   {
      Tracer tr("SymmetricBandMatrix::resize(GM)");
      Throw(ProgramException("Upper and lower band-widths not equal"));
   }
   resize(n, b);
}
/*
bool SymmetricBandMatrix::SameStorageType(const GeneralMatrix& A) const
{
   if (type() != A.type()) { REPORT return false; }
   REPORT
   return bandwidth() == A.bandwidth();
}

void SymmetricBandMatrix::resizeForAdd(const GeneralMatrix& A,
   const GeneralMatrix& B)
{
   REPORT
   Tracer tr("SymmetricBandMatrix::resizeForAdd");
   MatrixBandWidth A_BW = A.bandwidth(); MatrixBandWidth B_BW = B.bandwidth();
   if ((A_BW.Lower() < 0) | (B_BW.Lower() < 0))
         Throw(ProgramException("Can't resize to SymmetricBandMatrix" ));
   // already know A and B are square
   resize(A.Nrows(), my_max(A_BW.Lower(), B_BW.Lower()));
}

void SymmetricBandMatrix::resizeForSP(const GeneralMatrix& A,
   const GeneralMatrix& B)
{
   REPORT
   Tracer tr("SymmetricBandMatrix::resizeForSP");
   MatrixBandWidth A_BW = A.bandwidth(); MatrixBandWidth B_BW = B.bandwidth();
   if ((A_BW.Lower() < 0) | (B_BW.Lower() < 0))
         Throw(ProgramException("Can't resize to SymmetricBandMatrix" ));
   // already know A and B are square
   resize(A.Nrows(), my_min(A_BW.Lower(), B_BW.Lower()));
}
*/

void SymmetricBandMatrix::operator=(const BaseMatrix& X)
{
   REPORT // CheckConversion(X);
   // MatrixConversionCheck mcc;
   Eq(X,MatrixType::SB);
}

void SymmetricBandMatrix::CornerClear() const
{
   // set unused parts of BandMatrix to zero
   REPORT
   int i = lower_val; Real* s = store; int bw = lower_val + 1;
   if (i) for(;;)
   {
      int j = i;
      Real* sj = s;
      while (j--) *sj++ = 0.0;
      if (!(--i)) break;
      s += bw;
   }
}

MatrixBandWidth SymmetricBandMatrix::bandwidth() const
   { REPORT return MatrixBandWidth(lower_val,lower_val); }

GeneralMatrix* BandMatrix::Image() const
{
   REPORT
   GeneralMatrix* gm = new BandMatrix(*this); MatrixErrorNoSpace(gm);
   return gm;
}

GeneralMatrix* UpperBandMatrix::Image() const
{
   REPORT
   GeneralMatrix* gm = new UpperBandMatrix(*this); MatrixErrorNoSpace(gm);
   return gm;
}

GeneralMatrix* LowerBandMatrix::Image() const
{
   REPORT
   GeneralMatrix* gm = new LowerBandMatrix(*this); MatrixErrorNoSpace(gm);
   return gm;
}

GeneralMatrix* SymmetricBandMatrix::Image() const
{
   REPORT
   GeneralMatrix* gm = new SymmetricBandMatrix(*this); MatrixErrorNoSpace(gm);
   return gm;
}

GeneralMatrix* BandLUMatrix::Image() const
{
   REPORT
   GeneralMatrix* gm = new BandLUMatrix(*this); MatrixErrorNoSpace(gm);
   return gm;
}


inline Real square(Real x) { return x*x; }

Real SymmetricBandMatrix::sum_square() const
{
   REPORT
   CornerClear();
   Real sum1=0.0; Real sum2=0.0; Real* s=store; int i=nrows_val;
   int l=lower_val;
   while (i--)
      { int j = l; while (j--) sum2 += square(*s++); sum1 += square(*s++); }
   ((GeneralMatrix&)*this).tDelete(); return sum1 + 2.0 * sum2;
}

Real SymmetricBandMatrix::sum_absolute_value() const
{
   REPORT
   CornerClear();
   Real sum1=0.0; Real sum2=0.0; Real* s=store; int i=nrows_val;
   int l=lower_val;
   while (i--)
      { int j = l; while (j--) sum2 += fabs(*s++); sum1 += fabs(*s++); }
   ((GeneralMatrix&)*this).tDelete(); return sum1 + 2.0 * sum2;
}

Real SymmetricBandMatrix::sum() const
{
   REPORT
   CornerClear();
   Real sum1=0.0; Real sum2=0.0; Real* s=store; int i=nrows_val;
   int l=lower_val;
   while (i--)
      { int j = l; while (j--) sum2 += *s++; sum1 += *s++; }
   ((GeneralMatrix&)*this).tDelete(); return sum1 + 2.0 * sum2;
}





#ifdef use_namespace
}
#endif

///@}