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newmat08.zip
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NEWMAT8.CPP
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1995-01-16
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//$$ newmat8.cpp Advanced LU transform, scalar functions
// Copyright (C) 1991,2,3,4: R B Davies
#define WANT_MATH
#include "include.h"
#include "newmatap.h"
//#define REPORT { static ExeCounter ExeCount(__LINE__,8); ++ExeCount; }
#define REPORT {}
/************************** LU transformation ****************************/
void CroutMatrix::ludcmp()
// LU decomposition - from numerical recipes in C
{
REPORT
Tracer trace("Crout(ludcmp)");
int i,j;
Real* vv=new Real [nrows]; MatrixErrorNoSpace(vv);
MONITOR_REAL_NEW("Make (CroutMat)",nrows,vv)
Real* a;
a=store;
for (i=0;i<nrows;i++)
{
Real big=0.0;
j=nrows; while (j--) { Real temp=fabs(*a++); if (temp > big) big=temp; }
if (big == 0.0)
{
MONITOR_REAL_DELETE("Delete (CroutMt)",nrows,vv)
#ifdef Version21
sing = TRUE; delete [] vv; return;
#else
sing = TRUE; delete [nrows] vv; return;
#endif
}
vv[i]=1.0/big;
}
Real* aj=store;
for (j=0;j<nrows;j++)
{
Real* ai=store;
for (i=0;i<j;i++)
{
Real sum=*(ai+j); Real* aix=ai; Real* ajx=aj;
int k=i; while (k--) { sum -= *aix++ * *ajx; ajx += nrows; }
*ajx = sum; ai += nrows;
}
Real big=0.0; int imax;
for (i=j;i<nrows;i++)
{
Real sum=*(ai+j); Real* aix=ai; Real* ajx=aj;
int k=j; while (k--) { sum -= *aix++ * *ajx; ajx += nrows; }
*aix = sum; ai += nrows;
Real dum=vv[i]*fabs(sum); if (dum >= big) { big=dum; imax=i; }
}
if (j != imax)
{
Real* amax=store+imax*nrows; Real* ajx=store+j*nrows;
int k=nrows; while(k--) { Real dum=*amax; *amax++=*ajx; *ajx++=dum; }
d=!d; vv[imax]=vv[j];
}
indx[j]=imax; ai=aj+j*nrows;
if (*ai == 0.0)
{
MONITOR_REAL_DELETE("Delete (CroutMt)",nrows,vv)
#ifdef Version21
sing = TRUE; delete [] vv; return;
#else
sing = TRUE; delete [nrows] vv; return;
#endif
}
Real dum=1.0/(*ai);
i=nrows-j; while (--i) { ai += nrows; *ai *= dum; }
aj++;
}
MONITOR_REAL_DELETE("Delete (CroutMt)",nrows,vv)
#ifdef Version21
delete [] vv;
#else
delete [nrows] vv;
#endif
}
void CroutMatrix::lubksb(Real* B, int mini)
{
REPORT
Tracer trace("Crout(lubksb)");
if (sing) Throw(SingularException(*this));
int i,j; int ii=-1; Real* ai=store;
for (i=0;i<nrows;i++)
{
int ip=indx[i]; Real sum=B[ip]; B[ip]=B[i];
if (ii>=0)
{
Real* aij=ai+ii; Real* bj=B+ii; j=i-ii;
while (j--) { sum -= *aij++ * *bj; bj++; }
}
else if (sum) ii=i;
B[i]=sum; ai += nrows;
}
for (i=nrows-1;i>=mini;i--)
{
Real* bj=B+i; ai -= nrows; Real* ajx=ai+i; Real sum=*bj; bj++;
j=nrows-i; while(--j) { sum -= *(++ajx) * *bj; bj++; }
B[i]=sum/(*(ai+i));
}
}
/****************************** scalar functions ****************************/
inline Real square(Real x) { return x*x; }
Real GeneralMatrix::SumSquare() const
{
REPORT
Real sum = 0.0; int i = storage; Real* s = store;
while (i--) sum += square(*s++);
((GeneralMatrix&)*this).tDelete(); return sum;
}
Real GeneralMatrix::SumAbsoluteValue() const
{
REPORT
Real sum = 0.0; int i = storage; Real* s = store;
while (i--) sum += fabs(*s++);
((GeneralMatrix&)*this).tDelete(); return sum;
}
Real GeneralMatrix::Sum() const
{
REPORT
Real sum = 0.0; int i = storage; Real* s = store;
while (i--) sum += *s++;
((GeneralMatrix&)*this).tDelete(); return sum;
}
Real GeneralMatrix::MaximumAbsoluteValue() const
{
REPORT
Real maxval = 0.0; int i = storage; Real* s = store;
while (i--) { Real a = fabs(*s++); if (maxval < a) maxval = a; }
((GeneralMatrix&)*this).tDelete(); return maxval;
}
Real SymmetricMatrix::SumSquare() const
{
REPORT
Real sum1 = 0.0; Real sum2 = 0.0; Real* s = store; int nr = nrows;
for (int i = 0; i<nr; i++)
{
int j = i;
while (j--) sum2 += square(*s++);
sum1 += square(*s++);
}
((GeneralMatrix&)*this).tDelete(); return sum1 + 2.0 * sum2;
}
Real SymmetricMatrix::SumAbsoluteValue() const
{
REPORT
Real sum1 = 0.0; Real sum2 = 0.0; Real* s = store; int nr = nrows;
for (int i = 0; i<nr; i++)
{
int j = i;
while (j--) sum2 += fabs(*s++);
sum1 += fabs(*s++);
}
((GeneralMatrix&)*this).tDelete(); return sum1 + 2.0 * sum2;
}
Real SymmetricMatrix::Sum() const
{
REPORT
Real sum1 = 0.0; Real sum2 = 0.0; Real* s = store; int nr = nrows;
for (int i = 0; i<nr; i++)
{
int j = i;
while (j--) sum2 += *s++;
sum1 += *s++;
}
((GeneralMatrix&)*this).tDelete(); return sum1 + 2.0 * sum2;
}
Real BaseMatrix::SumSquare() const
{
REPORT GeneralMatrix* gm = ((BaseMatrix&)*this).Evaluate();
Real s = gm->SumSquare(); return s;
}
Real BaseMatrix::SumAbsoluteValue() const
{
REPORT GeneralMatrix* gm = ((BaseMatrix&)*this).Evaluate();
Real s = gm->SumAbsoluteValue(); return s;
}
Real BaseMatrix::Sum() const
{
REPORT GeneralMatrix* gm = ((BaseMatrix&)*this).Evaluate();
Real s = gm->Sum(); return s;
}
Real BaseMatrix::MaximumAbsoluteValue() const
{
REPORT GeneralMatrix* gm = ((BaseMatrix&)*this).Evaluate();
Real s = gm->MaximumAbsoluteValue(); return s;
}
Real Matrix::Trace() const
{
REPORT
Tracer trace("Trace");
int i = nrows; int d = i+1;
if (i != ncols) Throw(NotSquareException(*this));
Real sum = 0.0; Real* s = store;
while (i--) { sum += *s; s += d; }
((GeneralMatrix&)*this).tDelete(); return sum;
}
Real DiagonalMatrix::Trace() const
{
REPORT
int i = nrows; Real sum = 0.0; Real* s = store;
while (i--) sum += *s++;
((GeneralMatrix&)*this).tDelete(); return sum;
}
Real SymmetricMatrix::Trace() const
{
REPORT
int i = nrows; Real sum = 0.0; Real* s = store; int j = 2;
while (i--) { sum += *s; s += j++; }
((GeneralMatrix&)*this).tDelete(); return sum;
}
Real LowerTriangularMatrix::Trace() const
{
REPORT
int i = nrows; Real sum = 0.0; Real* s = store; int j = 2;
while (i--) { sum += *s; s += j++; }
((GeneralMatrix&)*this).tDelete(); return sum;
}
Real UpperTriangularMatrix::Trace() const
{
REPORT
int i = nrows; Real sum = 0.0; Real* s = store;
while (i) { sum += *s; s += i--; }
((GeneralMatrix&)*this).tDelete(); return sum;
}
Real BandMatrix::Trace() const
{
REPORT
int i = nrows; int w = lower+upper+1;
Real sum = 0.0; Real* s = store+lower;
while (i--) { sum += *s; s += w; }
((GeneralMatrix&)*this).tDelete(); return sum;
}
Real SymmetricBandMatrix::Trace() const
{
REPORT
int i = nrows; int w = lower+1;
Real sum = 0.0; Real* s = store+lower;
while (i--) { sum += *s; s += w; }
((GeneralMatrix&)*this).tDelete(); return sum;
}
Real BaseMatrix::Trace() const
{
REPORT
GeneralMatrix* gm = ((BaseMatrix&)*this).Evaluate(MatrixType::Dg);
Real sum = gm->Trace(); return sum;
}
void LogAndSign::operator*=(Real x)
{
if (x > 0.0) { log_value += log(x); }
else if (x < 0.0) { log_value += log(-x); sign = -sign; }
else sign = 0;
}
Real LogAndSign::Value() const { return sign * exp(log_value); }
LogAndSign::LogAndSign(Real f)
{
if (f == 0.0) { log_value = 0.0; sign = 0; return; }
else if (f < 0.0) { sign = -1; f = -f; }
else sign = 1;
log_value = log(f);
}
LogAndSign DiagonalMatrix::LogDeterminant() const
{
REPORT
int i = nrows; LogAndSign sum; Real* s = store;
while (i--) sum *= *s++;
((GeneralMatrix&)*this).tDelete(); return sum;
}
LogAndSign LowerTriangularMatrix::LogDeterminant() const
{
REPORT
int i = nrows; LogAndSign sum; Real* s = store; int j = 2;
while (i--) { sum *= *s; s += j++; }
((GeneralMatrix&)*this).tDelete(); return sum;
}
LogAndSign UpperTriangularMatrix::LogDeterminant() const
{
REPORT
int i = nrows; LogAndSign sum; Real* s = store;
while (i) { sum *= *s; s += i--; }
((GeneralMatrix&)*this).tDelete(); return sum;
}
LogAndSign BaseMatrix::LogDeterminant() const
{
REPORT GeneralMatrix* gm = ((BaseMatrix&)*this).Evaluate();
LogAndSign sum = gm->LogDeterminant(); return sum;
}
LogAndSign GeneralMatrix::LogDeterminant() const
{
REPORT
Tracer tr("Determinant");
if (nrows != ncols) Throw(NotSquareException(*this));
CroutMatrix C(*this); return C.LogDeterminant();
}
LogAndSign CroutMatrix::LogDeterminant() const
{
REPORT
if (sing) return 0.0;
int i = nrows; int dd = i+1; LogAndSign sum; Real* s = store;
while (i--) { sum *= *s; s += dd; }
if (!d) sum.ChangeSign(); return sum;
}
LinearEquationSolver::LinearEquationSolver(const BaseMatrix& bm)
: gm( ( ((BaseMatrix&)bm).Evaluate() )->MakeSolver() )
{
if (gm==&bm) { REPORT gm = gm->Image(); }
// want a copy if *gm is actually bm
else { REPORT gm->Protect(); }
}