public static SparseEqSystem Generate(CSparse.Double.SparseMatrix eqSystem)
{
var buf = new SparseEqSystem();
var lastCol = eqSystem.ColumnCount;
var eqs = buf.Equations = new SparseRow[eqSystem.RowCount];
var colNnzs = buf.ColumnNonzeros = new int[eqSystem.ColumnCount];
buf.RowNonzeros = new int[eqSystem.RowCount];
for (var i = 0; i < eqs.Length; i++)
{
buf.Equations[i] = new SparseRow(1);
}
foreach (var tuple in eqSystem.EnumerateIndexed())
{
var rw = tuple.Item1; //tuple.Item1;
var col = tuple.Item2; //tuple.Item2;
var val = tuple.Item3;
eqs[rw].Add(col, val);
if (col != lastCol)
{
colNnzs[col]++;
}
}
for (var i = 0; i < eqs.Length; i++)
{
buf.RowNonzeros[i] = buf.Equations[i].CalcNnz(lastCol);
}
buf.RowCount = eqSystem.RowCount;
buf.ColumnCount = eqSystem.ColumnCount;
return(buf);
}
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((CCS)a.Clone());
}
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.EnumerateIndexed((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.FillWith(1);
var eqnGraph = patt.Multiply(pattTr);
eqnGraph.Values.FillWith(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
// Convert sparse to dense.
//var dns = Matrix.OfMatrix(aTran);
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();
}
public Tuple <CCS, double[]> CalculateDisplacementPermutation(CCS a)
{
//based on this solution : https://github.com/wo80/CSparse.NET/issues/7#issuecomment-317268696
if (a.RowCount < a.ColumnCount)
{
//For a matrix A with rows < columns, SparseQR does a factorization of the transpose A'
//so we add zero rows to A and make it rectangular!
var a2 = new CoordinateStorage <double>(a.ColumnCount, a.ColumnCount, a.NonZerosCount);
foreach (var t in a.EnumerateIndexed())
{
a2.At(t.Item1, t.Item2, t.Item3);
}
a = a2.ToCCs();
}
SparseMatrix buf;
var n = a.RowCount;
var m = a.ColumnCount;
var order = ColumnOrdering.MinimumDegreeAtA;
var sp = System.Diagnostics.Stopwatch.StartNew();
var qr = SparseQR.Create(a, order);
var t2 = sp.ElapsedMilliseconds;
var r = GetFactorR(qr);
var q = GetFactorQ(qr);
var leads = new int[a.RowCount];
leads.FillWith(-1);
var epsilon = 1e-8;
foreach (var t in r.EnumerateIndexed())
{
if (Math.Abs(t.Item3) > epsilon)
{
if (leads[t.Item1] == -1)
{
leads[t.Item1] = t.Item2;
}
else
{
leads[t.Item1] = Math.Min(leads[t.Item1], t.Item2);
}
}
}
var leadCount = leads.Count(i => i != -1);
{
var nnzApprox = leadCount;
var p1Crd = new CoordinateStorage <double>(leadCount, r.RowCount, nnzApprox);
var p2Crd = new CoordinateStorage <double>(r.ColumnCount, leadCount, nnzApprox);
var p2pCrd = new CoordinateStorage <double>(r.ColumnCount, r.ColumnCount - leadCount, nnzApprox);
var cnt1 = 0;
var cnt2 = 0;
for (var i = 0; i < leads.Length; i++)
{
if (leads[i] != -1)
{
var j = leads[i];
p1Crd.At(cnt1, i, 1);
p2Crd.At(j, cnt1, 1);
cnt1++;
}
if (leads[i] == -1)
{
var j = i;// leads[i];
p2pCrd.At(j, cnt2, 1);
cnt2++;
}
}
var p1 = p1Crd.ToCCs();
var p2 = p2Crd.ToCCs();
var p2p = p2pCrd.ToCCs();
//var rp = r.Transpose();
var rdep = p1.Multiply(r).Multiply(p2);
var rinDep = p1.Multiply(r).Multiply(p2p);
var qr2 = SparseQR.Create(rdep, order);
var t = sp.ElapsedMilliseconds;
var right = new double[rinDep.RowCount];
var sol = new double[rinDep.RowCount];
var bufCrd = new CoordinateStorage <double>(leadCount, a.ColumnCount - leadCount, leadCount);
for (var j = 0; j < rinDep.ColumnCount; j++)
{
//put the j'th column of r into the rightSide
right.FillWith(0);
{
var col = j;
var st = rinDep.ColumnPointers[j];
var end = rinDep.ColumnPointers[j + 1];
for (var ii = st; ii < end; ii++)
{
var row = rinDep.RowIndices[ii];
var val = rinDep.Values[ii];
right[row] = val;
}
}
qr2.Solve(right, sol);
for (var i = 0; i < rdep.RowCount; i++)
{
bufCrd.At(i, j, sol[i]);
}
}
buf = bufCrd.ToCCs();
}
//var top = buf.ToDenseMatrix();
var buft = buf.Transpose();
var masterCount = a.ColumnCount - 1 - leadCount;
//var p_d_dense = new Matrix(a.ColumnCount - 1, masterCount);
var p_d = new CoordinateStorage <double>(a.ColumnCount - 1, masterCount, 1);
var rightSideDense = new double[a.ColumnCount - 1];
var rightSide = new double[a.ColumnCount - 1];
var cnt = 0;
var cnt3 = 0;
for (var i = 0; i < a.ColumnCount - 1; i++)
{
if (leads[i] != -1)
{
/*{//dense
* var rw = top.ExtractRow(cnt).CoreArray;
*
* var right = rw.Last();
* Array.Resize(ref rw, rw.Length - 1);
*
* for (var j = 0; j < rw.Length; j++)
* {
* p_d_dense[i, j] = -rw[j];
* }
*
* rightSideDense[i] = -right;
* }*/
{//sparse
var right = 0.0;
foreach (var t in buft.EnumerateColumnMembers(cnt))//enumerate column members of transposed matrix
{
if (t.Item1 != p_d.ColumnCount)
{
p_d.At(i, t.Item1, -t.Item2);
}
else
{
right = t.Item2;
}
}
rightSide[i] = -right;
}
cnt++;
}
else
{
{
var t = cnt3++;
//p_d_dense[i, t] = 1;
p_d.At(i, t, 1);
}
}
}
//var top2 = p_d_dense;//.ToDenseMatrix();
//var top3 = p_d.ToCCs().ToDenseMatrix();
//var d = (top2 - top3);
//var d2 = rightSide.Plus(rightSideDense, -1);
var pdd = (CCS)p_d.ToCCs();
return(Tuple.Create(pdd, rightSide));
var tol = 1e-6;
throw new NotImplementedException();
}
public Tuple <CCS, double[]> CalculateDisplacementPermutation(CCS a)
{
//based on this solution : https://github.com/wo80/CSparse.NET/issues/7#issuecomment-317268696
if (a.RowCount < a.ColumnCount)
{
//For a matrix A with rows < columns, SparseQR does a factorization of the transpose A'
//so we add zero rows to A and make it rectangular!
var a2 = new CoordinateStorage <double>(a.ColumnCount, a.ColumnCount, a.NonZerosCount);
foreach (var t in a.EnumerateIndexed())
{
a2.At(t.Item1, t.Item2, t.Item3);
}
a = a2.ToCCs();
}
//var adense = a.ToDenseMatrix();
SparseMatrix buf;
var n = a.RowCount;
var m = a.ColumnCount;
var order = ColumnOrdering.Natural;
var sp = System.Diagnostics.Stopwatch.StartNew();
var qr = SparseQR.Create(a, order);
var t2 = sp.ElapsedMilliseconds;
var r = GetFactorR(qr);
var q = GetFactorQ(qr);
var s = GetSymbolicFactorization(qr);
var leads = new int[a.RowCount];
leads.FillWith(-1);
//leads[i] = columnIndex of first nonzero in i'th row of r fasctor
//if leads[i] == -1, then there is no nonzero in row[i] then i'th equation in original a matrix in non usable
//this will be used for rdep and rindep
var epsilon = 1e-8;
foreach (var r_item in r.EnumerateIndexed())
{
var rowNum = r_item.Item1;
var colNum = r_item.Item2;
var val = r_item.Item3;
if (Math.Abs(val) <= epsilon)
{
; //then row at
}
if (Math.Abs(val) > epsilon) //Then, if abs(R[i, i]) > tol, you found an independent row
//Make sure to take row permutations into account (again, you can get the SymbolicFactorization containing row and column permutations using reflection)
{
if (leads[rowNum] == -1)
{
leads[rowNum] = colNum;
}
else
{
leads[rowNum] = Math.Min(leads[rowNum], colNum);
}
}
}
//throw new NotImplementedException("above section not right");
var leadCount = leads.Count(i => i != -1);
{
var nnzApprox = leadCount;
var p1Crd = new CoordinateStorage <double>(leadCount, r.RowCount, nnzApprox);
var p2Crd = new CoordinateStorage <double>(r.ColumnCount, leadCount, nnzApprox);
var p2pCrd = new CoordinateStorage <double>(r.ColumnCount, r.ColumnCount - leadCount, nnzApprox);
var cnt1 = 0;
var cnt2 = 0;
for (var i = 0; i < leads.Length; i++)
{
if (leads[i] != -1)
{
var j = leads[i];
p1Crd.At(cnt1, i, 1);
p2Crd.At(j, cnt1, 1);
cnt1++;
}
if (leads[i] == -1)
{
var j = i;// leads[i];
p2pCrd.At(j, cnt2, 1);
cnt2++;
}
}
var p1 = p1Crd.ToCCs();
var p2 = p2Crd.ToCCs();
var p2p = p2pCrd.ToCCs();
//var rp = r.Transpose();
var rdep = p1.Multiply(r).Multiply(p2);
var rinDep = p1.Multiply(r).Multiply(p2p);
var qr2 = SparseQR.Create(rdep, order);
var t = sp.ElapsedMilliseconds;
var right = new double[rinDep.RowCount];
var sol = new double[rinDep.RowCount];
var bufCrd = new CoordinateStorage <double>(leadCount, a.ColumnCount - leadCount, leadCount);
for (var j = 0; j < rinDep.ColumnCount; j++)
{
//put the j'th column of r into the rightSide
right.FillWith(0);
{
var col = j;
var st = rinDep.ColumnPointers[j];
var end = rinDep.ColumnPointers[j + 1];
for (var ii = st; ii < end; ii++)
{
var row = rinDep.RowIndices[ii];
var val = rinDep.Values[ii];
right[row] = val;
}
}
qr2.Solve(right, sol);
for (var i = 0; i < rdep.RowCount; i++)
{
bufCrd.At(i, j, sol[i]);
}
}
buf = bufCrd.ToCCs();
}
//var top = buf.ToDenseMatrix();
var buft = buf.Transpose();
var masterCount = a.ColumnCount - 1 - leadCount;
//var p_d_dense = new Matrix(a.ColumnCount - 1, masterCount);
var p_d = new CoordinateStorage <double>(a.ColumnCount - 1, masterCount, 1);
var rightSideDense = new double[a.ColumnCount - 1];
var rightSide = new double[a.ColumnCount - 1];
var cnt = 0;
var cnt3 = 0;
for (var i = 0; i < a.ColumnCount - 1; i++)
{
if (leads[i] != -1)
{
/*{//dense
* var rw = top.ExtractRow(cnt).CoreArray;
*
* var right = rw.Last();
* Array.Resize(ref rw, rw.Length - 1);
*
* for (var j = 0; j < rw.Length; j++)
* {
* p_d_dense[i, j] = -rw[j];
* }
*
* rightSideDense[i] = -right;
* }*/
{//sparse
var right = 0.0;
//var rowNum = s.pinv[i];
foreach (var t in buft.EnumerateColumnMembers(cnt))//enumerate column members of transposed matrix
{
var rowNum = i;
var colNum = t.Item1;
//var colNum = s.q[t.Item1];
var value = t.Item2;
if (t.Item1 != p_d.ColumnCount)
{
p_d.At(rowNum, colNum, -value);
}
else
{
right = value;
}
}
//rightSide[s.cp[i]] = -right;
rightSide[i] = -right;
}
cnt++;
}
else
{
var t = cnt3++;
var rowNum = i; // s.pinv[ i];
var colNum = t; // s.q[ t];
p_d.At(rowNum, colNum, 1);
}
}
//var top2 = p_d_dense;//.ToDenseMatrix();
//var top3 = p_d.ToCCs().ToDenseMatrix();
//var d = (top2 - top3);
//var d2 = rightSide.Plus(rightSideDense, -1);
var pdd = (CCS)p_d.ToCCs();
return(Tuple.Create(pdd, rightSide));
var tol = 1e-6;
throw new NotImplementedException();
}