private bool isGaussSeidelAppropriate(IList <double> b, out List <int>[] potentialDiagonals,
ref IList <double> initialGuess)
{
potentialDiagonals = null;
if (NumRows < StarMath.GaussSeidelMinimumMatrixSize)
{
return(false);
}
if (initialGuess == null)
{
initialGuess = makeInitialGuess(b);
}
var error = StarMath.norm1(StarMath.subtract(b, multiply(initialGuess))) / b.norm1();
if (error > StarMath.MaxErrorForUsingGaussSeidel)
{
return(false);
}
return(findPotentialDiagonals(out potentialDiagonals, StarMath.GaussSeidelDiagonalDominanceRatio));
}
public double[] SolveIteratively(IList <double> b,
IList <double> initialGuess = null, List <int>[] potentialDiagonals = null)
{
double[] x;
if (initialGuess == null)
{
x = makeInitialGuess(b);
}
else
{
x = initialGuess.ToArray();
}
if (potentialDiagonals == null &&
!findPotentialDiagonals(out potentialDiagonals, StarMath.GaussSeidelDiagonalDominanceRatio))
{
return(null);
}
var order = Enumerable.Range(0, NumRows).ToArray();
if (!order.All(rowIndex => potentialDiagonals[rowIndex].Contains(rowIndex)))
{
order = reorderMatrixForDiagonalDominance(NumRows, potentialDiagonals);
}
if (order == null)
{
return(null);
}
var bNorm1 = StarMath.norm1(b);
var error = StarMath.norm1(StarMath.subtract(b, multiply(x))) / bNorm1;
var success = error <= StarMath.GaussSeidelMaxError;
var xWentNaN = false;
var iteration = NumRows * StarMath.GaussSeidelMaxIterationFactor;
while (!xWentNaN && !success && iteration-- > 0)
{
for (var i = 0; i < NumRows; i++)
{
var rowI = order[i];
var diagCell = Diagonals[i];
var adjust = b[rowI];
var cell = RowFirsts[rowI];
do
{
if (cell != diagCell)
{
adjust -= cell.Value * x[cell.ColIndex];
}
cell = cell.Right;
} while (cell != null);
x[rowI] = (1 - StarMath.GaussSeidelRelaxationOmega) * x[rowI] +
StarMath.GaussSeidelRelaxationOmega * adjust / this[rowI, i];
}
xWentNaN = x.Any(double.IsNaN);
error = StarMath.norm1(StarMath.subtract(b, multiply(x))) / bNorm1;
success = error <= StarMath.GaussSeidelMaxError;
}
if (!success)
{
return(null);
}
return(x);
}