// Statics //
public static CellArray Clone(CellArray A)
{
CellArray x = new CellArray();
foreach (Cell c in A)
{
if (c.IsArray)
{
x.Append(CellArray.Clone(c));
}
else
{
x.Append(c);
}
}
return(x);
}
public LUDecomposition(CellArray A)
{
// Use a "left-looking", dot-product, Crout/Doolittle algorithm.
LU = CellArray.Clone(A);
m = A.Count;
n = ColumnCount(A);
piv = new int[m];
for (int i = 0; i < m; i++)
{
piv[i] = i;
}
pivsign = 1;
Cell[] LUcolj = new Cell[m];
// Outer loop.
for (int j = 0; j < n; j++)
{
// Make a copy of the j-th column to localize references.
for (int i = 0; i < m; i++)
{
LUcolj[i] = LU[i].ARRAY[j];
}
// Apply previous transformations.
for (int i = 0; i < m; i++)
{
// Most of the time is spent in the following dot product.
int kmax = Math.Min(i, j);
Cell s = this._zero;
for (int k = 0; k < kmax; k++)
{
s += LU[i].ARRAY[k] * LUcolj[k];
}
LU[i].ARRAY[j] = LUcolj[i] -= s;
}
// Find pivot and exchange if necessary.
int p = j;
for (int i = j + 1; i < m; i++)
{
if (CellFunctions.Abs(LUcolj[i]) > CellFunctions.Abs(LUcolj[p]))
{
p = i;
}
}
if (p != j)
{
for (int k = 0; k < n; k++)
{
Cell t = LU[p, k];
LU[p].ARRAY[k] = LU[j].ARRAY[k];
LU[j].ARRAY[k] = t;
}
int l = piv[p];
piv[p] = piv[j];
piv[j] = l;
pivsign = -pivsign;
}
// Compute multipliers.
if (j < m && LU[j].ARRAY[j] != this._zero)
{
for (int i = j + 1; i < m; i++)
{
LU[i].ARRAY[j] /= LU[j].ARRAY[j];
}
}
}
}