void
spSolve(
spMatrix eMatrix,
spREAL RHS[],
spREAL Solution[]
# if spCOMPLEX AND spSEPARATED_COMPLEX_VECTORS
, spREAL iRHS[]
, spREAL iSolution[]
# endif
)
{
MatrixPtr Matrix = (MatrixPtr)eMatrix;
register ElementPtr pElement;
register RealVector Intermediate;
register RealNumber Temp;
register int I, *pExtOrder, Size;
ElementPtr pPivot;
void SolveComplexMatrix();
/* Begin `spSolve'. */
ASSERT_IS_SPARSE( Matrix );
ASSERT_NO_ERRORS( Matrix );
ASSERT_IS_FACTORED( Matrix );
#if spCOMPLEX
if (Matrix->Complex)
{ SolveComplexMatrix( Matrix, RHS, Solution IMAG_VECTORS );
return;
}
#endif
#if REAL
Intermediate = Matrix->Intermediate;
Size = Matrix->Size;
/* Correct array pointers for ARRAY_OFFSET. */
#if NOT ARRAY_OFFSET
--RHS;
--Solution;
#endif
/* Initialize Intermediate vector. */
pExtOrder = &Matrix->IntToExtRowMap[Size];
for (I = Size; I > 0; I--)
Intermediate[I] = RHS[*(pExtOrder--)];
/* Forward elimination. Solves Lc = b.*/
for (I = 1; I <= Size; I++)
{
/* This step of the elimination is skipped if Temp equals zero. */
if ((Temp = Intermediate[I]) != 0.0)
{ pPivot = Matrix->Diag[I];
Intermediate[I] = (Temp *= pPivot->Real);
pElement = pPivot->NextInCol;
while (pElement != NULL)
{ Intermediate[pElement->Row] -= Temp * pElement->Real;
pElement = pElement->NextInCol;
}
}
}
/* Backward Substitution. Solves Ux = c.*/
for (I = Size; I > 0; I--)
{ Temp = Intermediate[I];
pElement = Matrix->Diag[I]->NextInRow;
while (pElement != NULL)
{ Temp -= pElement->Real * Intermediate[pElement->Col];
pElement = pElement->NextInRow;
}
Intermediate[I] = Temp;
}
/* Unscramble Intermediate vector while placing data in to Solution vector. */
pExtOrder = &Matrix->IntToExtColMap[Size];
for (I = Size; I > 0; I--)
Solution[*(pExtOrder--)] = Intermediate[I];
return;
#endif /* REAL */
}
void
spSolve(char *eMatrix, RealVector RHS, RealVector Solution IMAG_VECTORS )
{
MatrixPtr Matrix = (MatrixPtr)eMatrix;
register ElementPtr pElement;
register RealVector Intermediate;
register RealNumber Temp;
register int I, *pExtOrder, Size;
ElementPtr pPivot;
/* Begin `spSolve'. */
ASSERT( IS_VALID(Matrix) AND IS_FACTORED(Matrix) );
#if spCOMPLEX
if (Matrix->Complex)
{
SolveComplexMatrix( Matrix, RHS, Solution IMAG_VECTORS );
return;
}
#endif
#if REAL
Intermediate = Matrix->Intermediate;
Size = Matrix->Size;
/* Correct array pointers for ARRAY_OFFSET. */
#if NOT ARRAY_OFFSET
--RHS;
--Solution;
#endif
/* Initialize Intermediate vector. */
pExtOrder = &Matrix->IntToExtRowMap[Size];
for (I = Size; I > 0; I--)
{
Intermediate[I] = RHS[*(pExtOrder--)];
}
/* Forward elimination. Solves Lc = b.*/
for (I = 1; I <= Size; I++)
{
/* This step of the elimination is skipped if Temp equals zero. */
if ((Temp = Intermediate[I]) != 0.0)
{
pPivot = Matrix->Diag[I];
if ( pPivot != 0 && ELEMENT_MAG(pPivot) > Matrix->AbsThreshold )
{
/*jpc Intermediate[I] = (Temp *= pPivot->Real);*/
Intermediate[I] = (Temp /= pPivot->Real);
pElement = pPivot->NextInCol;
while (pElement != NULL)
{
Intermediate[pElement->Row] -= Temp * pElement->Real;
pElement = pElement->NextInCol;
}
}
else
{
Intermediate[I] = 0.0;
}
}
}
/* Backward Substitution. Solves Ux = c.*/
/* modification for singular matrix a diagonal element can be a null pointer */
for (I = Size ; I > 0; I--)
{
Temp = Intermediate[I];
if ( Matrix->Diag[I] == 0) /* test for nul pointer */
{
Intermediate[I] = 0.0;
}
else
{
pElement = Matrix->Diag[I]->NextInRow;
while (pElement != NULL)
{
Temp -= pElement->Real * Intermediate[pElement->Col];
pElement = pElement->NextInRow;
}
Intermediate[I] = Temp;
}
}
/* Unscramble Intermediate vector while placing data in to Solution vector. */
pExtOrder = &Matrix->IntToExtColMap[Size];
for (I = Size; I > 0; I--)
{
Solution[*(pExtOrder--)] = Intermediate[I];
}
return;
#endif /* REAL */
}
void
spSolve(MatrixPtr Matrix, RealVector RHS, RealVector Solution,
RealVector iRHS, RealVector iSolution)
{
ElementPtr pElement;
RealVector Intermediate;
RealNumber Temp;
int I, *pExtOrder, Size;
ElementPtr pPivot;
/* Begin `spSolve'. */
assert( IS_VALID(Matrix) && IS_FACTORED(Matrix) );
if (Matrix->Complex)
{
SolveComplexMatrix( Matrix, RHS, Solution, iRHS, iSolution );
return;
}
Intermediate = Matrix->Intermediate;
Size = Matrix->Size;
/* Initialize Intermediate vector. */
pExtOrder = &Matrix->IntToExtRowMap[Size];
for (I = Size; I > 0; I--)
Intermediate[I] = RHS[*(pExtOrder--)];
/* Forward elimination. Solves Lc = b.*/
for (I = 1; I <= Size; I++)
{
/* This step of the elimination is skipped if Temp equals zero. */
if ((Temp = Intermediate[I]) != 0.0)
{
pPivot = Matrix->Diag[I];
Intermediate[I] = (Temp *= pPivot->Real);
pElement = pPivot->NextInCol;
while (pElement != NULL)
{
Intermediate[pElement->Row] -= Temp * pElement->Real;
pElement = pElement->NextInCol;
}
}
}
/* Backward Substitution. Solves Ux = c.*/
for (I = Size; I > 0; I--)
{
Temp = Intermediate[I];
pElement = Matrix->Diag[I]->NextInRow;
while (pElement != NULL)
{
Temp -= pElement->Real * Intermediate[pElement->Col];
pElement = pElement->NextInRow;
}
Intermediate[I] = Temp;
}
/* Unscramble Intermediate vector while placing data in to Solution vector. */
pExtOrder = &Matrix->IntToExtColMap[Size];
for (I = Size; I > 0; I--)
Solution[*(pExtOrder--)] = Intermediate[I];
return;
}
