/// <summary>
/// Construct packed versions of input matrices, and then use sparse row/column dot
/// to compute elements of output matrix. This is faster. But still relatively expensive.
/// </summary>
void multiply_fast(SymmetricSparseMatrix M2in, ref SymmetricSparseMatrix Rin, bool bParallel)
{
int N = Rows;
if (M2in.Rows != N)
{
throw new Exception("SymmetricSparseMatrix.Multiply: matrices have incompatible dimensions");
}
if (Rin == null)
{
Rin = new SymmetricSparseMatrix();
}
SymmetricSparseMatrix R = Rin; // require alias for use in lambda below
PackedSparseMatrix M = new PackedSparseMatrix(this);
M.Sort();
PackedSparseMatrix M2 = new PackedSparseMatrix(M2in, true);
M2.Sort();
// Parallel variant is vastly faster, uses spinlock to control access to R
if (bParallel)
{
// goddamn SpinLock is in .Net 4
//SpinLock spin = new SpinLock();
gParallel.ForEach(Interval1i.Range(N), (r1i) => {
for (int c2i = r1i; c2i < N; c2i++)
{
double v = M.DotRowColumn(r1i, c2i, M2);
if (Math.Abs(v) > math.MathUtil.ZeroTolerance)
{
//bool taken = false;
//spin.Enter(ref taken);
//Debug.Assert(taken);
//R[r1i, c2i] = v;
//spin.Exit();
lock (R) {
R[r1i, c2i] = v;
}
}
}
});
}
else
{
for (int r1i = 0; r1i < N; r1i++)
{
for (int c2i = r1i; c2i < N; c2i++)
{
double v = M.DotRowColumn(r1i, c2i, M2);
if (Math.Abs(v) > math.MathUtil.ZeroTolerance)
{
R[r1i, c2i] = v;
}
}
}
}
}
/// <summary>
/// Compute dot product of this.row[r] and M.col[c], where the
/// column is stored as MTranspose.row[c]
/// </summary>
public double DotRowColumn(int r, int c, PackedSparseMatrix MTranspose)
{
Debug.Assert(Sorted && MTranspose.Sorted);
Debug.Assert(Rows.Length == MTranspose.Rows.Length);
int a = 0;
int b = 0;
nonzero[] Row = Rows[r];
nonzero[] Col = MTranspose.Rows[c];
int NA = Row.Length;
int NB = Col.Length;
double sum = 0;
while (a < NA && b < NB)
{
if (Row[a].j == Col[b].j)
{
sum += Row[a].d * Col[b].d;
a++;
b++;
}
else if (Row[a].j < Col[b].j)
{
a++;
}
else
{
b++;
}
}
return(sum);
}
// returns this*this (requires less memory)
public SymmetricSparseMatrix Square(bool bParallel = true)
{
SymmetricSparseMatrix R = new SymmetricSparseMatrix();
PackedSparseMatrix M = new PackedSparseMatrix(this);
M.Sort();
// Parallel variant is vastly faster, uses spinlock to control access to R
if (bParallel)
{
// goddamn SpinLock is in .Net 4
//SpinLock spin = new SpinLock();
gParallel.ForEach(Interval1i.Range(N), (r1i) => {
for (int c2i = r1i; c2i < N; c2i++)
{
double v = M.DotRowColumn(r1i, c2i, M);
if (Math.Abs(v) > math.MathUtil.ZeroTolerance)
{
//bool taken = false;
//spin.Enter(ref taken);
//Debug.Assert(taken);
//R[r1i, c2i] = v;
//spin.Exit();
lock (R) {
R[r1i, c2i] = v;
}
}
}
});
}
else
{
for (int r1i = 0; r1i < N; r1i++)
{
for (int c2i = r1i; c2i < N; c2i++)
{
double v = M.DotRowColumn(r1i, c2i, M);
if (Math.Abs(v) > math.MathUtil.ZeroTolerance)
{
R[r1i, c2i] = v;
}
}
}
}
return(R);
}
/// <summary>
/// Compute dot product of this.row[r] with all columns of M,
/// where columns are stored in MTranspose rows.
/// In theory more efficient than doing DotRowColumn(r,c) for each c,
/// however so far the difference is negligible...perhaps because
/// there are quite a few more branches in the inner loop
/// </summary>
public void DotRowAllColumns(int r, double[] sums, int[] col_indices, PackedSparseMatrix MTranspose)
{
Debug.Assert(Sorted && MTranspose.Sorted);
Debug.Assert(Rows.Length == MTranspose.Rows.Length);
int N = Rows.Length;
int a = 0;
nonzero[] Row = Rows[r];
int NA = Row.Length;
Array.Clear(sums, 0, N);
Array.Clear(col_indices, 0, N);
while (a < NA)
{
int aj = Row[a].j;
for (int ci = 0; ci < N; ++ci)
{
nonzero[] Col = MTranspose.Rows[ci];
int b = col_indices[ci];
if (b >= Col.Length)
{
continue;
}
while (b < Col.Length && Col[b].j < aj)
{
b++;
}
if (b < Col.Length && aj == Col[b].j)
{
sums[ci] += Row[a].d * Col[b].d;
b++;
}
col_indices[ci] = b;
}
a++;
}
}