QRDecomposition
jhplot.math

Class QRDecomposition



  • public class QRDecompositionextends Object
    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.

    • Constructor Summary

      Constructors 
      Constructor and Description
      QRDecomposition(double[][] A)
      QR Decomposition, computed by Householder reflections.
    • Method Summary

      Methods 
      Modifier and TypeMethod and Description
      double[][]getH()
      Return the Householder vectors
      double[][]getQ()
      Generate and return the (economy-sized) orthogonal factor
      double[][]getR()
      Return the upper triangular factor
      booleanisFullRank()
      Is the matrix full rank?
      double[][]solve(double[][] B)
      Least squares solution of A*X = B
    • Constructor Detail

      • QRDecomposition

        public QRDecomposition(double[][] A)
        QR Decomposition, computed by Householder reflections.
        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 double[][] getH()
        Return the Householder vectors
        Returns:
        Lower trapezoidal matrix whose columns define the reflections
      • getR

        public double[][] getR()
        Return the upper triangular factor
        Returns:
        R
      • getQ

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

        public double[][] solve(double[][] 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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