/*!
* Solve linear system using Cramer procedure
*
* \throw ExceptionDimension incompatible matrix dimensions
* \throw ExceptionRuntime Equation has either no solution or an infinity of solutions
*
* \param[in] Coefficients matrix of equations' coefficients
* \param[in] ConstantTerms column matrix of constant term
*
* \return solutions packed in a column matrix (SMatrixDouble)
*/
MatrixDouble LinearSystem::Cramer(const SquareMatrixDouble &Coefficients, const MatrixDouble &ConstantTerms)
{
size_t n = Coefficients.GetRows();
if ((ConstantTerms.GetRows() != n) || (ConstantTerms.GetCols() != 1))
{
throw ExceptionDimension(StringUTF8("LinearEquationsSystem::CramerSolver("
"const SquareMatrixDouble *Coefficients, const MatrixDouble *ConstantTerms): ") +
_("invalid or incompatible matrix dimensions"));
}
else
{
double D = Coefficients.Determinant();
if (D == 0.0)
{
throw ExceptionRuntime(_("Equation has either no solution or an infinity of solutions."));
}
MatrixDouble Solutions(n, 1, 0.0);
for (size_t k = 0; k < n; k++)
{
SquareMatrixDouble Mk(Coefficients);
for (size_t r = 0; r < n; r++)
{
Mk.At(r, k) = ConstantTerms.At(r, 0);
}
double Dk = Mk.Determinant();
Solutions.At(k, 0) = Dk / D;
}
return Solutions;
}
}
/*!
* Solve linear system using Gauss-Jordan procedure
*
* \throw ExceptionDimension incompatible matrix dimensions
* \throw ExceptionRuntime Equation has either no solution or an infinity of solutions
*
* \param[in] Coefficients matrix of equations' coefficients
* \param[in] ConstantTerms column matrix of constant terms
*
* \return solutions packed in a column matrix (SMatrixDouble)
*/
MatrixDouble LinearSystem::GaussJordan(const SquareMatrixDouble &Coefficients, const MatrixDouble &ConstantTerms)
{
size_t n = Coefficients.GetRows();
if (ConstantTerms.GetRows() != n)
{
throw ExceptionDimension(StringUTF8("LinearEquationsSystem::GaussJordanSolver("
"const SquareMatrixDouble *Coefficients, const MatrixDouble *ConstantTerms): ") +
_("invalid or incompatible matrix dimensions"));
}
else
{
USquareMatrixDouble CopyCoefficients = CloneAs<SquareMatrixDouble>(Coefficients);
UMatrixDouble CopyConstantTerms = CloneAs<MatrixDouble>(ConstantTerms);
for (size_t c = 0; c < n - 1; c++)
{
// Search the greatest pivot in column
double Pivot = CopyCoefficients->At(c, c);
double AbsMaxPivot = fabs(Pivot);
size_t RowIndex = c;
for (size_t r = c + 1 ; r < n; r++)
{
double Candidate = CopyCoefficients->At(r, c);
if (fabs(Candidate) > AbsMaxPivot)
{
Pivot = Candidate;
AbsMaxPivot = fabs(Pivot);
RowIndex = r;
}
}
// If no non-null pivot found, system may have infinite number of solutions
if (Pivot == 0.0)
{
throw ExceptionRuntime(_("Equation has either no solution or an infinity of solutions."));
}
if (RowIndex != c)
{
CopyCoefficients->SwapRows(c, RowIndex);
CopyConstantTerms->SwapRows(c, RowIndex);
}
// Elimination
for (size_t r = c + 1; r < n; r++)
{
double Coeff = CopyCoefficients->At(r, c);
if (Coeff != 0.0)
{
double Scale = - Coeff / Pivot;
for (size_t k = c; k < n; k++)
{
CopyCoefficients->IncreaseElement(r, k, CopyCoefficients->At(c, k) * Scale);
}
CopyConstantTerms->IncreaseElement(r, 0, CopyConstantTerms->At(c, 0) * Scale);
}
}
}
// End of loop for column
MatrixDouble Solutions(n, 1, 0.0);
Solutions.At(n - 1, 0) = CopyConstantTerms->At(n - 1, 0) / CopyCoefficients->At(n - 1, n - 1);
for (auto r = int(n) - 2; r >= 0; --r)
{
double Cumul = 0.0;
for (auto c = int(n) - 1; c > r; --c)
{
Cumul += CopyCoefficients->At(r, c) * Solutions.At(c, 0);
}
Solutions.At(r, 0) = (CopyConstantTerms->At(r, 0) - Cumul) / CopyCoefficients->At(r, r);
}
return Solutions;
}
}
