QRDecomposition
Jama

Class QRDecomposition

  • All Implemented Interfaces:
    Serializable


    public class QRDecompositionextends Objectimplements Serializable
    QR Decomposition.

    For an m-by-n matrix A with m >= n, the QR decomposition is an m-by-n orthogonal matrix Q and an n-by-n upper triangular matrix R so that A = Q*R.

    The QR decompostion always exists, even if the matrix does not have full rank, so the constructor will never fail. The primary use of the QR decomposition is in the least squares solution of nonsquare systems of simultaneous linear equations. This will fail if isFullRank() returns false.

    See Also:
    Serialized Form
    • Constructor Detail

      • QRDecomposition

        public QRDecomposition(Matrix A)
        QR Decomposition, computed by Householder reflections. Structure to access R and the Householder vectors and compute Q.
        Parameters:
        A - Rectangular matrix
    • Method Detail

      • isFullRank

        public boolean isFullRank()
        Is the matrix full rank?
        Returns:
        true if R, and hence A, has full rank.
      • getH

        public Matrix getH()
        Return the Householder vectors
        Returns:
        Lower trapezoidal matrix whose columns define the reflections
      • getR

        public Matrix getR()
        Return the upper triangular factor
        Returns:
        R
      • getQ

        public Matrix getQ()
        Generate and return the (economy-sized) orthogonal factor
        Returns:
        Q
      • solve

        public Matrix solve(Matrix B)
        Least squares solution of A*X = B
        Parameters:
        B - A Matrix with as many rows as A and any number of columns.
        Returns:
        X that minimizes the two norm of Q*R*X-B.
        Throws:
        IllegalArgumentException - Matrix row dimensions must agree.
        RuntimeException - Matrix is rank deficient.

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