/// <summary>
/// Returns the upper triagonal matrix that was created during the LU decomposition.
/// </summary>
/// <remarks>
/// This method is used for debugging purposes only and should normally not be used.
/// </remarks>
/// <returns>A new matrix containing the upper triagonal elements.</returns>
internal Matrix <Complex> UpperTriangle()
{
return(_upper.Clone());
}
public static Status Solve(int NumberOfEquations, SparseMatrix aMatrix, SparseArray bVector, SparseArray xVector)
{
var aMatrixClone = aMatrix.Clone();
var RowMaximumVector = new Dictionary<int, double>();
int i;
for (i = 0; i < NumberOfEquations; i++)
{
double temp = 0;
for (var j = 0; j < NumberOfEquations; j++)
{
var Test = Math.Abs(aMatrix[i, j]);
if (Test > temp)
temp = Test;
}
RowMaximumVector[i] = temp;
if (temp == 0)
return Status.Singular;
}
var PivotRowArray = new Dictionary<int, int>();
for (var r = 0; r < NumberOfEquations; r++)
{
double MaximumValue = 0;
var RowMaximumValueIndex = r;
double Temp;
for (i = r; i < NumberOfEquations; i++)
{
Temp = aMatrixClone[i, r];
for (var j = 0; j < r; j++) Temp = Temp - aMatrixClone[i, j] * aMatrixClone[j, r];
aMatrixClone[i, r] = Temp;
var test = Math.Abs(Temp / RowMaximumVector[i]);
if (!(test > MaximumValue))
continue;
MaximumValue = test;
RowMaximumValueIndex = i;
}
if (MaximumValue == 0)
return Status.IllConditioned;
RowMaximumVector[RowMaximumValueIndex] = RowMaximumVector[r];
PivotRowArray[r] = RowMaximumValueIndex;
for (i = 0; i < NumberOfEquations; i++)
{
Temp = aMatrixClone[r, i];
aMatrixClone[r, i] = aMatrixClone[RowMaximumValueIndex, i];
aMatrixClone[RowMaximumValueIndex, i] = Temp;
}
for (i = r + 1; i < NumberOfEquations; i++)
{
Temp = aMatrixClone[r, i];
for (var j = 0; j < r; j++) Temp = Temp - aMatrixClone[r, j] * aMatrixClone[j, i];
aMatrixClone[r, i] = Temp / aMatrixClone[r, r];
}
}
var ResidualVector = new Dictionary<int, double>();
for (i = 0; i < NumberOfEquations; i++)
{
xVector[i] = 0;
ResidualVector[i] = bVector[i];
}
var Iteration = 0;
var NotConverged = true;
do
{
for (i = 0; i < NumberOfEquations; i++)
{
var PivotRowIndex = PivotRowArray[i];
var Temp = ResidualVector[PivotRowIndex];
ResidualVector[PivotRowIndex] = ResidualVector[i];
for (var j = 0; j < i; j++) Temp -= aMatrixClone[i, j] * ResidualVector[j];
ResidualVector[i] = Temp / aMatrixClone[i, i];
}
for (i = NumberOfEquations - 1; i >= 0; i--)
{
var Temp = ResidualVector[i];
for (var j = i + 1; j < NumberOfEquations; j++) Temp -= aMatrixClone[i, j] * ResidualVector[j];
ResidualVector[i] = Temp;
}
double NormOfX = 0;
double NormOfError = 0;
for (i = 0; i < NumberOfEquations; i++)
{
var Test = Math.Abs(xVector[i]);
if (Test > NormOfX) NormOfX = Test;
Test = Math.Abs(ResidualVector[i]);
if (Test > NormOfError) NormOfError = Test;
}
if (Iteration != 0)
{
if ((Iteration == 1) && (NormOfError / NormOfX > 0.5))
return Status.IllConditioned;
NotConverged = NormOfError / NormOfX >= Epsilon;
}
for (i = 0; i < NumberOfEquations; i++) xVector[i] = xVector[i] + ResidualVector[i];
for (i = 0; i < NumberOfEquations; i++)
{
var Temp = bVector[i];
for (var j = 0; j < NumberOfEquations; j++) Temp = Temp - aMatrix[i, j] * xVector[j];
ResidualVector[i] = Temp;
}
Iteration++;
}
while (NotConverged);
return Status.Success;
}
/// <summary>
/// Returns the upper triagonal matrix that was created during the LU decomposition.
/// </summary>
/// <remarks>
/// This method is used for debugging purposes only and should normally not be used.
/// </remarks>
/// <returns>A new matrix containing the upper triagonal elements.</returns>
internal Matrix <float> UpperTriangle()
{
return(_upper.Clone());
}
/// <summary>
/// Returns the lower triagonal matrix that was created during the LU decomposition.
/// </summary>
/// <remarks>
/// This method is used for debugging purposes only and should normally not be used.
/// </remarks>
/// <returns>A new matrix containing the lower triagonal elements.</returns>
internal Matrix <float> LowerTriangle()
{
return(_lower.Clone());
}
/// <summary>
/// Returns the upper triagonal matrix that was created during the LU decomposition.
/// </summary>
/// <remarks>
/// This method is used for debugging purposes only and should normally not be used.
/// </remarks>
/// <returns>A new matrix containing the upper triagonal elements.</returns>
internal Matrix UpperTriangle()
{
return((Matrix)_upper.Clone());
}
/// <summary>
/// Returns the lower triagonal matrix that was created during the LU decomposition.
/// </summary>
/// <remarks>
/// This method is used for debugging purposes only and should normally not be used.
/// </remarks>
/// <returns>A new matrix containing the lower triagonal elements.</returns>
internal Matrix LowerTriangle()
{
return((Matrix)_lower.Clone());
}
/// <summary>
/// Returns the lower triagonal matrix that was created during the LU decomposition.
/// </summary>
/// <remarks>
/// This method is used for debugging purposes only and should normally not be used.
/// </remarks>
/// <returns>A new matrix containing the lower triagonal elements.</returns>
internal Matrix <double> LowerTriangle()
{
return(_lower.Clone());
}
/// <summary>
/// Returns the lower triagonal matrix that was created during the LU decomposition.
/// </summary>
/// <remarks>
/// This method is used for debugging purposes only and should normally not be used.
/// </remarks>
/// <returns>A new matrix containing the lower triagonal elements.</returns>
internal Matrix <Complex> LowerTriangle()
{
return(_lower.Clone());
}
/// <summary>
/// Returns the upper triagonal matrix that was created during the LU decomposition.
/// </summary>
/// <remarks>
/// This method is used for debugging purposes only and should normally not be used.
/// </remarks>
/// <returns>A new matrix containing the upper triagonal elements.</returns>
internal Matrix <double> UpperTriangle()
{
return(_upper.Clone());
}
private static void TestRandomSymmetric(IDisposableSolver <Complex> solver, SparseMatrix matrix, string name)
{
Console.Write("Testing {0} (symmetric) ... ", name);
RunTest(solver, (SparseMatrix)matrix.Clone(), true);
}
protected virtual void TestRandomMulti(SparseMatrix matrix)
{
Console.Write("Testing {0} (multi) ... ", name);
var A = (SparseMatrix)matrix.Clone();
int count = 3;
int n = A.RowCount;
var b = Vector.Create(n, 0.0);
var x = Vector.Create(n, 0.0);
var s = Vector.Create(n, 0.0);
var X = new DenseMatrix(n, count);
var S = new DenseMatrix(n, count);
var B = new DenseMatrix(n, count);
for (int i = 0; i < count; i++)
{
x = Vector.Create(n, i + 1);
X.SetColumn(i, x);
S.SetColumn(i, x);
A.Multiply(x, b);
B.SetColumn(i, b);
}
X.Clear();
try
{
timer.Restart();
using (var solver = CreateSolver(A, false))
{
//solver.Solve(B, X);
}
timer.Stop();
Display.Time(timer.ElapsedTicks);
double error = 0.0;
for (int i = 0; i < count; i++)
{
X.Column(i, x);
S.Column(i, s);
error += Helper.ComputeError(x, s);
}
if (error / count > ERROR_THRESHOLD)
{
Display.Warning("relative error too large");
}
else
{
Display.Ok("OK");
}
}
catch (DllNotFoundException)
{
throw;
}
catch (Exception e)
{
Display.Error(e.Message);
}
}
protected virtual void TestRandomSymmetric(SparseMatrix matrix)
{
Console.Write("Testing {0} (symmetric) ... ", name);
RunTest((SparseMatrix)matrix.Clone(), true);
}
protected virtual void TestRandom(SparseMatrix matrix)
{
Console.Write("Testing {0} ... ", name);
RunTest((SparseMatrix)matrix.Clone(), false);
}