public RowBasedMatrix IncompleteCholesky(double droptol)
{
// suppose this matrix is symmetric, square and sorted
int n = this.RowSize;
int nAdd = 0;
RowBasedMatrix L = new RowBasedMatrix(n);
for (int i = 0; i < n; i++)
{
List <Element> r = rows[i];
List <Element> rr1 = L.rows[i];
double drop = 0;
double norm = 0;
foreach (Element e in r)
{
norm += e.value * e.value;
}
norm = Math.Sqrt(norm) * droptol;
int k = 0;
for (int j = 0; j < i; j++)
{
double sum = 0;
if (k < r.Count && r[k].colIndex == j)
{
sum = r[k++].value;
}
int c1 = 0, c2 = 0;
List <Element> rr2 = L.rows[j];
while (c1 < rr1.Count && c2 < rr2.Count)
{
Element e1 = rr1[c1];
Element e2 = rr2[c2];
if (e1.colIndex >= j)
{
break;
}
if (e2.colIndex >= j)
{
break;
}
if (e1.colIndex > e2.colIndex)
{
c2++;
}
else if (e1.colIndex < e2.colIndex)
{
c1++;
}
else
{
sum -= e1.value * e2.value;
c1++;
c2++;
}
}
while (rr2[c2].colIndex < j)
{
c2++;
}
sum /= rr2[c2].value;
if (Math.Abs(sum) > norm)
{
rr1.Add(new Element(j, sum)); nAdd++;
}
else
{
drop += sum;
}
}
if (r[k].colIndex != i)
{
throw new Exception();
}
double diag = r[k].value; // + drop;
for (int c = 0; c < rr1.Count && rr1[c].colIndex < i; c++)
{
diag -= rr1[c].value * rr1[c].value;
}
if (diag > 0.0)
{
rr1.Add(new Element(i, Math.Sqrt(diag)));
}
else
{
throw new Exception();
}
}
OutputText("drops:" + nAdd.ToString());
return(L);
}
public void CG_SolveATA(double[] x, double[] b, int maxIter, double eps, int recompute, RowBasedMatrix inv)
{
int n = x.Length;
int iter = 0;
double[] r = new double[n];
double[] d = new double[n];
double[] q = new double[n];
double[] s = new double[n];
double[] t = new double[n];
double errNew = 0, errold = 0;
for (int i = 0; i < n; i++)
{
r[i] = b[i];
}
for (int i = 0; i < RowSize; i++)
{
double sum = 0;
foreach (Element e in rows[i])
{
sum += e.value * x[e.colIndex];
}
foreach (Element e in rows[i])
{
r[e.colIndex] -= e.value * sum;
}
}
inv.Cholesky_Solve(d, r);
for (int i = 0; i < n; i++)
{
errNew += r[i] * d[i];
}
double tolerance = eps * errNew;
OutputText("0:" + errNew.ToString());
while (iter < maxIter && errNew > tolerance)
{
iter++;
double dAd = 0;
for (int i = 0; i < n; i++)
{
q[i] = 0;
}
for (int i = 0; i < RowSize; i++)
{
double sum = 0;
foreach (Element e in rows[i])
{
sum += e.value * d[e.colIndex];
}
foreach (Element e in rows[i])
{
q[e.colIndex] += e.value * sum;
}
}
for (int i = 0; i < n; i++)
{
dAd += d[i] * q[i];
}
double alpha = errNew / dAd;
for (int i = 0; i < n; i++)
{
x[i] += alpha * d[i];
}
if (iter % recompute == 0)
{
for (int i = 0; i < n; i++)
{
r[i] = b[i];
}
for (int i = 0; i < RowSize; i++)
{
double sum = 0;
foreach (Element e in rows[i])
{
sum += e.value * x[e.colIndex];
}
foreach (Element e in rows[i])
{
r[e.colIndex] -= e.value * sum;
}
}
OutputText(iter + ":" + errNew.ToString());
}
else
{
for (int i = 0; i < n; i++)
{
r[i] -= alpha * q[i];
}
}
inv.Cholesky_Solve(s, r);
errold = errNew;
errNew = 0;
for (int i = 0; i < n; i++)
{
errNew += r[i] * s[i];
}
double beta = errNew / errold;
for (int i = 0; i < n; i++)
{
d[i] = s[i] + beta * d[i];
}
}
double err = 0;
for (int i = 0; i < n; i++)
{
err += r[i] * r[i];
}
OutputText(iter + ":" + err.ToString());
}
public RowBasedMatrix IncompleteCholesky()
{
// suppose this matrix is symmetric, square and sorted
int n = this.RowSize;
RowBasedMatrix L = new RowBasedMatrix(n);
for (int i = 0; i < n; i++)
{
List <Element> r = rows[i];
List <Element> rr1 = L.rows[i];
for (int j = 0; j < r.Count; j++)
{
Element e = r[j];
if (e.colIndex == i)
{
double sum = e.value;
for (int c = 0; c < rr1.Count && rr1[c].colIndex < i; c++)
{
sum -= rr1[c].value * rr1[c].value;
}
if (sum > 0.0)
{
rr1.Add(new Element(i, Math.Sqrt(sum)));
}
else
{
rr1.Add(new Element(i, 10e-12));
}
}
else if (e.colIndex < i)
{
List <Element> rr2 = L.rows[e.colIndex];
double sum = e.value;
int c1 = 0, c2 = 0;
while (c1 < rr1.Count && c2 < rr2.Count)
{
Element e1 = rr1[c1];
Element e2 = rr2[c2];
if (e1.colIndex >= e.colIndex)
{
break;
}
if (e2.colIndex >= e.colIndex)
{
break;
}
if (e1.colIndex > e2.colIndex)
{
c2++;
}
else if (e1.colIndex < e2.colIndex)
{
c1++;
}
else
{
sum -= e1.value * e2.value;
c1++;
c2++;
}
}
while (rr2[c2].colIndex < e.colIndex)
{
c2++;
}
rr1.Add(new Element(e.colIndex, sum / rr2[c2].value));
}
}
}
return(L);
}