/// <summary>
/// Returns the nxn outer product of two nd-vectors, or [v1]^T*[v2].\ O(n).
/// </summary>
/// <param name="v1"></param>
/// <param name="v2"></param>
/// <returns></returns>
public static MatrixFixed OuterProduct(Vector v1, Vector v2)
{
MatrixFixed outp = new MatrixFixed(v1.size(), v2.size());
for (int i = 0; i < outp.Rows; i++) // v1.column() * v2.row()
for (int j = 0; j < outp.Columns; j++)
outp[i,j] = v1[i] * v2[j];
return outp;
}
/// <summary>
/// Solve the matrix-vector system M x = y, returning x.
/// </summary>
/// <param name="y"></param>
/// <returns></returns>
public Vector Solve(Vector y)
{
// fsm sanity check :
if (y.size() != U_.Rows)
{
Debug.WriteLine("__FILE__ : size of rhs is incompatible with no. of rows in U_ " +
"y =" + Convert.ToString(y) + "\n" +
"m_=" + Convert.ToString(m_) + "\n" +
"n_=" + Convert.ToString(n_) + "\n" +
"U_=\n" + Convert.ToString(U_) + "V_=\n" + Convert.ToString(V_) +
"W_=\n" + W_);
}
Vector x = new Vector(V_.Rows); // Solution matrix.
if (U_.Rows < U_.Columns)
{ // Augment y with extra rows of
Vector yy = new Vector(U_.Rows); // zeros, so that it matches
yy.Fill(0);
if (yy.size() < y.size())
{ // fsm
Debug.WriteLine("yy=" + Convert.ToString(yy));
Debug.WriteLine("y =" + Convert.ToString(y));
// the update() call on the next line will abort...
}
yy.Update(y); // cols of u.transpose.
x = U_.ConjugateTranspose() * yy;
}
else
x = U_.ConjugateTranspose() * y;
for (int i = 0; i < x.size(); i++)
{ // multiply with diagonal 1/W
float weight = W_[i, i], zero_ = 0.0f;
if (weight != zero_)
x[i] /= weight;
else
x[i] = zero_;
}
return V_ * x; // premultiply with v.
}
/// <summary>
/// Replaces elements with index begining at start, by values of v.
/// </summary>
/// <param name="v"></param>
/// <param name="start"></param>
/// <returns></returns>
public Vector Update (Vector v, int start)
{
int end = start + v.size();
if ((start < data.Length) && (end <= data.Length))
{
for (int i = start; i < end; i++)
{
data[i] = v.data[i - start];
}
}
return this;
}
