public static SparseMatrixMDP GaussianJordenElimination(SparseMatrixMDP smatrixMdp)
{
var r = smatrixMdp.Ngroup;
var groups = smatrixMdp.Groups;
for (int i = 0; i < r; i++) //operating on each group, i can take as pivot position
{
var currentGroup = groups[i];
//rows in ith group should normalized according to the element in its pivot position (ith group, ith column)
Debug.Assert(groups != null, "groups != null");
foreach (Row currentRow1 in currentGroup.RowsInSameGroup)
{
if (currentRow1.col[0] == i) //TODO:I think this info is redundant
{
if (Math.Abs(currentRow1.val[0] - 1) > EPSILON)
{
for (int k = 1; k < currentRow1.val.Count; k++)
{
currentRow1.val[k] = currentRow1.val[k]/currentRow1.val[0];
}
}
currentRow1.col.RemoveAt(0);
currentRow1.val.RemoveAt(0);
}
}
//currentRow1.colIndexCurrentRow = currentRow1.col.BinarySearch(i);
//using current row to deduct every rows in other group if corresponding element (column i in dense matrix) is not zero
//follow upper triangular form.
for (int j = 0; j < r; j++) //scan all groups
{
if (j == i)
{
continue;
}
//update rows in group j
var pivotGroup = groups[j];
var removeCollection = new HashSet<Row>();
var addCollection = new HashSet<Row>();
foreach (Row pivotRow in pivotGroup.RowsInSameGroup)
{
if (pivotRow.col[0] == i)
//index of col for column value in dense matrix equal to pivot element. if value is zero, it will not be found
{
double t = -pivotRow.val[0];
//var hashset1 = new HashSet<int>(pivotRow.col);
//hashset1.UnionWith(new HashSet<int>(currentRow.col));
pivotRow.col.RemoveAt(0);
pivotRow.val.RemoveAt(0);
foreach (Row currentRow in currentGroup.RowsInSameGroup)
{
// bool flag;
if (!CheckDictionarySubset(pivotRow.SelectionMemoryInGroups,
currentRow.SelectionMemoryInGroups))
{
continue;
}
var r3 = new Row
{
diag = pivotRow.diag,
diagCol = pivotRow.diagCol,
// val = new List<double>(hashset1.Count),
// col = hashset1.ToList(),
Index = pivotRow.Index,
};
//add elements in colValuePair
var hashset1 = new HashSet<int>(currentRow.col);
hashset1.UnionWith(new HashSet<int>(pivotRow.col));
var colValuePair =
new Dictionary<int, double>(hashset1.ToDictionary(item => item, item => 0.0));
for (int inneri = 0;
inneri < currentRow.col.Count;
inneri++)
{
if (Math.Abs(currentRow.val[inneri]) > EPSILON)
{
colValuePair[currentRow.col[inneri]] += currentRow.val[inneri]*t;
}
}
//add workingRow to r3
//var hashset2 = new HashSet<int>();
for (int inneri = 0; inneri < pivotRow.col.Count; inneri++)
{
double m = colValuePair[pivotRow.col[inneri]] + pivotRow.val[inneri];
if (Math.Abs(m) > EPSILON)
{
colValuePair[pivotRow.col[inneri]] = m;
}
}
r3.col = new List<int>(colValuePair.Keys);
r3.val = new List<double>(colValuePair.Values);
// r3.SelectionMemoryInGroups = new Dictionary<Group, Row>(pivotRow.SelectionMemoryInGroups);
// r3.SelectionMemoryInGroups[currentGroup] = currentRow;
r3.SelectionMemoryInGroups = new Dictionary<int,int>(pivotRow.SelectionMemoryInGroups);
r3.SelectionMemoryInGroups[currentGroup.Index] = currentRow.Index;
//update diag elements in that row. After row adding, the pivot element/diag info is redundant.
// r3.diag = r3.col.Contains(r3.diagCol) ? colValuePair[r3.diagCol] : 0;
//pivotGroup.RowsInSameGroup.Add(r3);
addCollection.Add(r3);
if(pivotRow.SelectionMemoryInGroups.ContainsKey(currentGroup.Index))
{
break;
}
//If pivotRow contains currentGroup index, and currentRow can work with pivotRow,
//that means the rest of rows in the group are not that useful.
}
removeCollection.Add(pivotRow);
}
}
//update rows in current group
foreach (Row row in removeCollection)
{
pivotGroup.RowsInSameGroup.Remove(row);
}
foreach (Row row in addCollection)
{
pivotGroup.RowsInSameGroup.Add(row);
}
}
Debug.WriteLine(smatrixMdp);
}
return smatrixMdp;
}
public static SparseMatrixMDP GaussianJordenElimination(SparseMatrixMDP smatrixMdp)
{
var r = smatrixMdp.Ngroup;
var groups = smatrixMdp.Groups;
for (int i = 0; i < r; i++) //operating on each group, i can take as pivot position
{
var currentGroup = groups[i];
//rows in ith group should normalized according to the element in its pivot position (ith group, ith column)
Debug.Assert(groups != null, "groups != null");
foreach (Row currentRow1 in currentGroup.RowsInSameGroup)
{
if (currentRow1.col[0] == i) //TODO:I think this info is redundant
{
if (Math.Abs(currentRow1.val[0] - 1) > EPSILON)
{
for (int k = 1; k < currentRow1.val.Count; k++)
{
currentRow1.val[k] = currentRow1.val[k] / currentRow1.val[0];
}
}
currentRow1.col.RemoveAt(0);
currentRow1.val.RemoveAt(0);
}
}
//currentRow1.colIndexCurrentRow = currentRow1.col.BinarySearch(i);
//using current row to deduct every rows in other group if corresponding element (column i in dense matrix) is not zero
//follow upper triangular form.
for (int j = 0; j < r; j++) //scan all groups
{
if (j == i)
{
continue;
}
//update rows in group j
var pivotGroup = groups[j];
var removeCollection = new HashSet <Row>();
var addCollection = new HashSet <Row>();
foreach (Row pivotRow in pivotGroup.RowsInSameGroup)
{
if (pivotRow.col[0] == i)
//index of col for column value in dense matrix equal to pivot element. if value is zero, it will not be found
{
double t = -pivotRow.val[0];
//var hashset1 = new HashSet<int>(pivotRow.col);
//hashset1.UnionWith(new HashSet<int>(currentRow.col));
pivotRow.col.RemoveAt(0);
pivotRow.val.RemoveAt(0);
foreach (Row currentRow in currentGroup.RowsInSameGroup)
{
// bool flag;
if (!CheckDictionarySubset(pivotRow.SelectionMemoryInGroups,
currentRow.SelectionMemoryInGroups))
{
continue;
}
var r3 = new Row
{
diag = pivotRow.diag,
diagCol = pivotRow.diagCol,
// val = new List<double>(hashset1.Count),
// col = hashset1.ToList(),
Index = pivotRow.Index,
};
//add elements in colValuePair
var hashset1 = new HashSet <int>(currentRow.col);
hashset1.UnionWith(new HashSet <int>(pivotRow.col));
var colValuePair =
new Dictionary <int, double>(hashset1.ToDictionary(item => item, item => 0.0));
for (int inneri = 0;
inneri < currentRow.col.Count;
inneri++)
{
if (Math.Abs(currentRow.val[inneri]) > EPSILON)
{
colValuePair[currentRow.col[inneri]] += currentRow.val[inneri] * t;
}
}
//add workingRow to r3
//var hashset2 = new HashSet<int>();
for (int inneri = 0; inneri < pivotRow.col.Count; inneri++)
{
double m = colValuePair[pivotRow.col[inneri]] + pivotRow.val[inneri];
if (Math.Abs(m) > EPSILON)
{
colValuePair[pivotRow.col[inneri]] = m;
}
}
r3.col = new List <int>(colValuePair.Keys);
r3.val = new List <double>(colValuePair.Values);
// r3.SelectionMemoryInGroups = new Dictionary<Group, Row>(pivotRow.SelectionMemoryInGroups);
// r3.SelectionMemoryInGroups[currentGroup] = currentRow;
r3.SelectionMemoryInGroups = new Dictionary <int, int>(pivotRow.SelectionMemoryInGroups);
r3.SelectionMemoryInGroups[currentGroup.Index] = currentRow.Index;
//update diag elements in that row. After row adding, the pivot element/diag info is redundant.
// r3.diag = r3.col.Contains(r3.diagCol) ? colValuePair[r3.diagCol] : 0;
//pivotGroup.RowsInSameGroup.Add(r3);
addCollection.Add(r3);
if (pivotRow.SelectionMemoryInGroups.ContainsKey(currentGroup.Index))
{
break;
}
//If pivotRow contains currentGroup index, and currentRow can work with pivotRow,
//that means the rest of rows in the group are not that useful.
}
removeCollection.Add(pivotRow);
}
}
//update rows in current group
foreach (Row row in removeCollection)
{
pivotGroup.RowsInSameGroup.Remove(row);
}
foreach (Row row in addCollection)
{
pivotGroup.RowsInSameGroup.Add(row);
}
}
Debug.WriteLine(smatrixMdp);
}
return(smatrixMdp);
}