/// <summary>
/// Solves Ax=b, where A is square and nonsingular. b overwritten with
/// solution. Partial pivoting if tol = 1.
/// </summary>
/// <param name="b">size n, b on input, x on output</param>
/// <returns>true if successful, false on error</returns>
public bool Solve(Complex[] b)
{
if (b == null || numFactor == null)
{
return(false); // check inputs
}
Complex[] x = new Complex[n]; // get workspace
Common.InversePermute(numFactor.pinv, b, x, n); // x = b(p)
Triangular.SolveL(numFactor.L, x); // x = L\x
Triangular.SolveU(numFactor.U, x); // x = U\x
Common.InversePermute(symFactor.q, x, b, n); // b(q) = x
return(true);
}
/// <summary>
/// Solve a least-squares problem (min ||Ax-b||_2, where A is m-by-n with m
/// >= n) or underdetermined system (Ax=b, where m < n)
/// </summary>
/// <param name="b">size max(m,n), b (size m) on input, x(size n) on output</param>
/// <returns>true if successful, false on error</returns>
public bool Solve(Complex[] b)
{
Complex[] x;
if (b == null)
{
return(false); // check inputs
}
if (m >= n)
{
x = new Complex[symFactor != null ? symFactor.m2 : 1]; // get workspace
Common.InversePermute(symFactor.pinv, b, x, m); // x(0:m-1) = b(p(0:m-1)
for (int k = 0; k < n; k++) // apply Householder refl. to x
{
ApplyHouseholder(numFactor.L, k, numFactor.B[k], x);
}
Triangular.SolveU(numFactor.U, x); // x = R\x
Common.InversePermute(symFactor.q, x, b, n); // b(q(0:n-1)) = x(0:n-1)
}
else
{
x = new Complex[symFactor != null ? symFactor.m2 : 1]; // get workspace
Common.Permute(symFactor.q, b, x, m); // x(q(0:m-1)) = b(0:m-1)
Triangular.SolveUt(numFactor.U, x); // x = R'\x
for (int k = m - 1; k >= 0; k--) // apply Householder refl. to x
{
ApplyHouseholder(numFactor.L, k, numFactor.B[k], x);
}
Common.Permute(symFactor.pinv, x, b, n); // b(0:n-1) = x(p(0:n-1))
}
return(true);
}