/// <summary>
/// Solves a system of linear equations, <c>Ax = b</c>.
/// </summary>
/// <param name="input">The right hand side vector, <c>b</c>.</param>
/// <param name="result">The left hand side vector, <c>x</c>.</param>
public void Solve(Complex[] input, Complex[] result)
{
if (input == null)
{
throw new ArgumentNullException(nameof(input));
}
if (result == null)
{
throw new ArgumentNullException(nameof(result));
}
var x = this.temp;
Permutation.ApplyInverse(S.pinv, input, x, n); // x = P*b
SolverHelper.SolveLower(L, x); // x = L\x
SolverHelper.SolveLowerTranspose(L, x); // x = L'\x
Permutation.Apply(S.pinv, x, result, n); // b = P'*x
}
/// <summary>
/// Solves a system of linear equations, <c>A'x = b</c>.
/// </summary>
/// <param name="input">The right hand side vector, <c>b</c>.</param>
/// <param name="result">The left hand side vector, <c>x</c>.</param>
public void SolveTranspose(Complex[] input, Complex[] result)
{
if (input == null)
{
throw new ArgumentNullException("input");
}
if (result == null)
{
throw new ArgumentNullException("result");
}
var x = this.temp;
Permutation.Apply(S.q, input, x, n); // x = Q'*b
SolverHelper.SolveUpperTranspose(U, x); // x = U'\x.
SolverHelper.SolveLowerTranspose(L, x); // x = L'\x.
Permutation.Apply(pinv, x, result, n); // b = P'*x
}