protected void SwapRowDuringPivoting(int PivotRow, int relativeRow, ref MatrixColumn PivotColumn, ref MatrixRow[] localRows)
{
if (relativeRow > 0)
{
int PivotIndex = PivotRow + relativeRow;
MatrixElement a = Rows[PivotRow].FirsElement;
Rows[PivotRow].FirsElement = Rows[PivotIndex].FirsElement;
Rows[PivotIndex].FirsElement = a;
/*
* double rhs = rightHandSide[PivotRow];
* rightHandSide[PivotRow] = rightHandSide[PivotIndex];
* rightHandSide[PivotIndex] = rhs;
* */
MatrixElement b = localRows[0].FirsElement;
localRows[0].FirsElement = localRows[relativeRow].FirsElement;
localRows[relativeRow].FirsElement = b;
det = -det;
int temp = RowOrder[PivotRow];
RowOrder[PivotRow] = RowOrder[PivotIndex];
RowOrder[PivotIndex] = temp;
SwapLocalRowDuringPivoting(PivotRow, relativeRow, ref PivotColumn);
}
}
protected void ScalePivotColumnToPivot(ref MatrixColumn pivotColumn)
{
MatrixColumnElement a = pivotColumn.FirsElement;
double pivotValue = a.RowElement.Value;
while (a.NotLastItem)
{
a = a.NextElement;
a.RowElement.Value /= pivotValue;
}
}
protected int GetRowOfMaxElementInColumn(ref MatrixColumn column)
{
if (column.ColumnNotPopulated)
{
return(-1);
}
else
{
return(GetRowOfMaxElementInColumn(column.FirsElement));
}
}
private int LUDecomposition_CountElements(MatrixColumn Column)
{
MatrixColumnElement a = Column.FirsElement;
int count = 1;
while (a.NotLastItem)
{
count++;
a = a.NextElement;
}
return(count);
}
protected void SwapLocalRowDuringPivoting(int PivotRow, int relativeRow, ref MatrixColumn PivotColumn)
{
MatrixColumnElement FirstRow = PivotColumn.FirsElement;
MatrixColumnElement a = FirstRow;
MatrixColumnElement aLast;
while (a.NotLastItem)
{
aLast = a;
a = a.NextElement;
if (a.Index == relativeRow)
{
if (FirstRow.NextElement.Index == a.Index)
{
FirstRow.Index = a.Index;
if (a.NotLastItem)
{
FirstRow.NextElement = a.NextElement;
}
else
{
FirstRow.NotLastItem = false;
FirstRow.NextElement = null;
}
a.Index = 0;
a.NextElement = FirstRow;
a.NotLastItem = true;
PivotColumn.FirsElement = a;
}
else
{
MatrixColumnElement SecondElement = FirstRow.NextElement;
aLast.NextElement = FirstRow;
FirstRow.Index = a.Index;
if (a.NotLastItem)
{
FirstRow.NextElement = a.NextElement;
}
else
{
FirstRow.NotLastItem = false;
FirstRow.NextElement = null;
}
a.Index = 0;
a.NextElement = SecondElement;
a.NotLastItem = true;
PivotColumn.FirsElement = a;
}
return;
}
}
}
protected int GetRowOfMaxElementInColumn(ref MatrixColumn column, out MatrixColumnElement MaxColumnElement)
{
if (column.ColumnNotPopulated)
{
MaxColumnElement = null;
return(-1);
}
else
{
return(GetRowOfMaxElementInColumn(column.FirsElement, out MaxColumnElement));
}
}
public void LUDecomposition()
{
DiagonalElements = new MatrixRow[n];
InitializeLocalRows();
for (int i = 0; i < n - 1; i++)
{
MatrixColumn PivotColumn = GetColumn(ref LocalRows, i);
MatrixColumnElement MaxColumnElement;
int newRelativePivotRow = GetRowOfMaxElementInColumn(ref PivotColumn, out MaxColumnElement);
SwapRowDuringPivoting(i, newRelativePivotRow, ref PivotColumn, ref LocalRows);
ScalePivotColumnToPivot(ref PivotColumn);
DiagonalElements[i] = new MatrixRow();
DiagonalElements[i].RowNotPopulated = false;
DiagonalElements[i].FirsElement = PivotColumn.FirsElement.RowElement;
MatrixColumnElement a = PivotColumn.FirsElement;
MatrixElement b = PivotColumn.FirsElement.RowElement;
double colVal;
double change;
MatrixElement StartRowSearch;
MatrixElement c;
if (b.NotLastItem)
{
if (a.NotLastItem)
{
//normal
while (a.NotLastItem)
{
a = a.NextElement;
StartRowSearch = LocalRows[a.Index].FirsElement;
colVal = a.RowElement.Value;
c = b;
while (c.NotLastItem)
{
c = c.NextItem;
change = -colVal * c.Value;
StartRowSearch = AddToElementInRow(ref StartRowSearch, c.Index, change);
}
}
}
}
LocalRows = GetLocalRows(LocalRows, i + 1);
}
DiagonalElements[n - 1].FirsElement = LocalRows[0].FirsElement;
}
private int LUDecomposition_CountElementsColumn(MatrixColumn Column, out MatrixColumnElement[] ColumnArray)
{
MatrixColumnElement a = Column.FirsElement;
int count = 1;
while (a.NotLastItem)
{
count++;
a = a.NextElement;
}
ColumnArray = new MatrixColumnElement[count - 1];
a = Column.FirsElement;
for (int i = 0; i < count - 1; i++)
{
a = a.NextElement;
ColumnArray[i] = a;
}
return(count);
}
public MatrixColumn GetColumn(ref MatrixRow[] rows, int col)//, int numberOfElements)
{
MatrixColumn NewColumn = new MatrixColumn();
NewColumn.ColumnNotPopulated = true;
int lenght = rows.Length;
//numberOfElements = 0;
//MatrixElement FirstElement;
MatrixElement a;
MatrixColumnElement b = new MatrixColumnElement();
for (int i = 0; i < rows.Length; i++)
{
a = GetElementInRow(ref rows[i], col);
if (!(a == null))
{
MatrixColumnElement c = new MatrixColumnElement();
c.Index = i;
c.NotLastItem = false;
c.RowElement = a;
if (NewColumn.ColumnNotPopulated)
{
NewColumn.FirsElement = c;
b = c;
NewColumn.ColumnNotPopulated = false;
}
else
{
b.NextElement = c;
b.NotLastItem = true;
b = c;
}
}
}
return(NewColumn);
}
public void LUDecomposition_Parallel()
{
// LUDecomposition with Parallel operations conducted for multi-processors
// M. Negahban
// 5-8-2011
DiagonalElements = new MatrixRow[n];
InitializeLocalRows();
//For parallel
double[] A_values = new double[n];
int[] A_Indecies = new int[n];
int NumberOfRows;
for (int i = 0; i < n - 1; i++)
{
MatrixColumn PivotColumn = GetColumn(ref LocalRows, i);
MatrixColumnElement MaxColumnElement;
int newRelativePivotRow = GetRowOfMaxElementInColumn(ref PivotColumn, out MaxColumnElement);
SwapRowDuringPivoting(i, newRelativePivotRow, ref PivotColumn, ref LocalRows);
ScalePivotColumnToPivot(ref PivotColumn);
DiagonalElements[i] = new MatrixRow();
DiagonalElements[i].RowNotPopulated = false;
DiagonalElements[i].FirsElement = PivotColumn.FirsElement.RowElement;
MatrixColumnElement a = PivotColumn.FirsElement;
MatrixElement b = PivotColumn.FirsElement.RowElement;
if (b.NotLastItem)
{
if (a.NotLastItem)
{
//Parallel
NumberOfRows = 0;
while (a.NotLastItem)
{
a = a.NextElement;
A_values[NumberOfRows] = a.RowElement.Value;
A_Indecies[NumberOfRows] = a.Index;
NumberOfRows++;
}
//If you want to control level of parallelism Add
//ParallelOptions po = new ParallelOptions();
//po.MaxDegreeOfParallelism = 100; // select any number grater than 0
//Parallel.For(0, NumberOfRows, po, j =>
Parallel.For(0, NumberOfRows, j =>
{
double colValJ = A_values[j];
MatrixElement StartRowSearchJ = LocalRows[A_Indecies[j]].FirsElement;
MatrixElement cJ = b;
while (cJ.NotLastItem)
{
cJ = cJ.NextItem;
double changeJ = -colValJ * cJ.Value;
StartRowSearchJ = AddToElementInRow(ref StartRowSearchJ, cJ.Index, changeJ);
}
});
}
}
LocalRows = GetLocalRows(LocalRows, i + 1);
}
DiagonalElements[n - 1].FirsElement = LocalRows[0].FirsElement;
}
protected void SwapRowDuringPivoting(int PivotRow, int relativeRow, MatrixColumnElement MaxColumnElement, ref MatrixColumn PivotColumn, ref MatrixRow[] localRows)
{
if (relativeRow > 0)
{
// Swap Rows
int PivotIndex = PivotRow + relativeRow;
MatrixElement a = Rows[PivotRow].FirsElement;
Rows[PivotRow].FirsElement = Rows[PivotIndex].FirsElement;
Rows[PivotIndex].FirsElement = a;
// Swap localRows
MatrixElement b = localRows[0].FirsElement;
localRows[0].FirsElement = localRows[relativeRow].FirsElement;
localRows[relativeRow].FirsElement = b;
// Change sign of determinant
det = -det;
// Swap RowOrder
int temp = RowOrder[PivotRow];
RowOrder[PivotRow] = RowOrder[PivotIndex];
RowOrder[PivotIndex] = temp;
// Swap PivotColumn
SwapLocalRowDuringPivoting(PivotRow, relativeRow, MaxColumnElement, ref PivotColumn);
}
}
