public CCS CalculateRref(CCS a)
{
var singleMemberColumns = 00;
var aTran = a.Transpose();
var n = a.ColumnCount;
for (var i = 0; i < n; i++)
{
if (a.GetNnzcForColumn(i) == 1)
{
singleMemberColumns++;
}
}
if (singleMemberColumns == a.RowCount)
{
return(a.Clonee());
}
var pat = new CoordinateStorage <double>(a.RowCount, a.ColumnCount - 1, 1);
var bCrd = new CoordinateStorage <double>(a.RowCount, a.ColumnCount - 1, 1);//a matrix without last column
a.EnumerateMembers((row, col, val) =>
{
if (col != a.ColumnCount - 1)
{
pat.At(row, col, 1);
bCrd.At(row, col, val);
}
});
//nonzero pattern of a, except last column
var b = bCrd.ToCCs();
var bTran = b.Transpose();
var patt = pat.ToCCs();
var pattTr = patt.Transpose();
var varGraph = pattTr.Multiply(patt);
varGraph.Values.SetAllMembers(1);
var eqnGraph = patt.Multiply(pattTr);
eqnGraph.Values.SetAllMembers(1);
if (!varGraph.IsSymmetric() || !eqnGraph.IsSymmetric())
{
throw new Exception();
}
var eqnParts = CalcUtil.EnumerateGraphParts(eqnGraph);
var varParts = CalcUtil.EnumerateGraphParts(varGraph);
var varVisited = new bool[varGraph.ColumnCount];
foreach (var eqnPart in eqnParts)
{
//i'th independent system.
var firstEq = eqnPart.First();
int firstVarOfFirstEq = -1;
/*
* patt.EnumerateRowMembers(firstEq, (row, col, val) => {
* if (firstValOfFirstEq != -1)
* firstValOfFirstEq = col;
* );
*/
pattTr.EnumerateColumnMembers(firstEq, (row, col, val) =>
{
if (firstVarOfFirstEq == -1)
{
firstVarOfFirstEq = row;
}
});
//var firstVar = patt.EnumerateColumnMembers()
var connectedVariables = CalcUtil.DepthFirstSearch(varGraph, varVisited, firstVarOfFirstEq);
connectedVariables.Sort();
var vp = new Dictionary <int, int>();//variablePermute
//vp[a] = b, a: number of variable in original system
// b: index of variable in connectedVariables
for (var i = 0; i < connectedVariables.Count; i++)
{
vp[connectedVariables[i]] = i;
}
var denseSubSytem = new Matrix(eqnPart.Count, connectedVariables.Count + 1);////i'th independent system as dense
var dns = aTran.ToDenseMatrix();
for (var i = 0; i < eqnPart.Count; i++)
{
//insert i'th eqn into denseSubSytem
var row = i;
var st = aTran.ColumnPointers[i];
var en = aTran.ColumnPointers[i + 1];
for (int j = st; j < en; j++)
{
var col = aTran.RowIndices[j];
if (col == a.ColumnCount - 1)
{
continue;
}
var val = aTran.Values[j];
denseSubSytem[i, vp[col]] = val;
}
}
}
throw new NotImplementedException();
}