Class OLSSolverByQR

  • Direct Known Subclasses:
    OLSSolver

    public class OLSSolverByQR
    extends Object
    This class solves an over-determined system of linear equations in the ordinary least square sense. An over-determined system, represented by
    Ax = y
    has more rows than columns. That is, there are more equations than unknowns. One important application is linear regression, where A is the independent factors, y the dependent observations. The solution x^ minimizes:
    |Ax - y|2
    That is, x^ is the best approximation that minimizes the sum of squared differences between the data values and their corresponding modeled values. The approach is called "linear" least squares since the solution depends linearly on the data.
    x^ = (AtA)-1Aty,
    This implementation does not use the above formula to solve for x^ because of the numerical stability problem in computing AtA. Instead, we use QR decomposition, an orthogonal decomposition method that is numerically stable.
    See Also:
    • Constructor Detail

      • OLSSolverByQR

        public OLSSolverByQR​(double epsilon)
        Construct an OLS solver for an over-determined system of linear equations.
        Parameters:
        epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0
    • Method Detail

      • solve

        public Vector solve​(LSProblem problem)
        In the ordinary least square sense, solve
        Ax = y
        Parameters:
        problem - a system of linear equations
        Returns:
        a solution x^ that minimizes
        |Ax - y|2