/// <summary>
/// Ordering and symbolic analysis for a Cholesky factorization.
/// </summary>
/// <param name="A">Matrix to factorize.</param>
/// <param name="p">Permutation.</param>
private void SymbolicAnalysis(CompressedColumnStorage <Complex> A, int[] p)
{
int n = A.ColumnCount;
var sym = this.S = new SymbolicFactorization();
// Find inverse permutation.
sym.pinv = Permutation.Invert(p);
// C = spones(triu(A(P,P)))
var C = PermuteSym(A, sym.pinv, false);
// Find etree of C.
sym.parent = GraphHelper.EliminationTree(n, n, C.ColumnPointers, C.RowIndices, false);
// Postorder the etree.
var post = GraphHelper.TreePostorder(sym.parent, n);
// Find column counts of chol(C)
var c = GraphHelper.ColumnCounts(SymbolicColumnStorage.Create(C, false), sym.parent, post, false);
sym.cp = new int[n + 1];
// Find column pointers for L
sym.unz = sym.lnz = Helper.CumulativeSum(sym.cp, c, n);
}
/// <summary>
/// Symbolic ordering and analysis for QR.
/// </summary>
/// <param name="A">Matrix to factorize.</param>
/// <param name="p">Permutation.</param>
protected void SymbolicAnalysis(CompressedColumnStorage <T> A, int[] p, bool natural)
{
int m = A.RowCount;
int n = A.ColumnCount;
var sym = this.S = new SymbolicFactorization();
// Fill-reducing ordering
sym.q = p;
var C = natural ? SymbolicColumnStorage.Create(A) : Permute(A, null, sym.q);
// etree of C'*C, where C=A(:,q)
sym.parent = GraphHelper.EliminationTree(m, n, C.ColumnPointers, C.RowIndices, true);
int[] post = GraphHelper.TreePostorder(sym.parent, n);
sym.cp = GraphHelper.ColumnCounts(C, sym.parent, post, true); // col counts chol(C'*C)
bool ok = C != null && sym.parent != null && sym.cp != null && CountV(C, sym);
if (ok)
{
sym.unz = 0;
for (int k = 0; k < n; k++)
{
sym.unz += sym.cp[k];
}
}
}
/// <summary>
/// Symbolic ordering and analysis for QR.
/// </summary>
private void SymbolicAnalysis(ColumnOrdering order, CompressedColumnStorage <double> A)
{
int m = A.RowCount;
int n = A.ColumnCount;
var sym = this.symFactor = new SymbolicFactorization();
// Fill-reducing ordering
sym.q = AMD.Generate(A, order);
var C = order > 0 ? Permute(A, null, sym.q) : SymbolicColumnStorage.Create(A);
// etree of C'*C, where C=A(:,q)
sym.parent = GraphHelper.EliminationTree(m, n, C.ColumnPointers, C.RowIndices, true);
int[] post = GraphHelper.TreePostorder(sym.parent, n);
sym.cp = GraphHelper.ColumnCounts(C, sym.parent, post, true); // col counts chol(C'*C)
bool ok = C != null && sym.parent != null && sym.cp != null && CountV(C);
if (ok)
{
sym.unz = 0;
for (int k = 0; k < n; k++)
{
sym.unz += sym.cp[k];
}
}
}