Package Jama

Class QRDecomposition

java.lang.Object
Jama.QRDecomposition
All Implemented Interfaces:
java.io.Serializable
public class QRDecomposition
extends java.lang.Object
implements java.io.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 Summary

    Constructors 
    Constructor Description
    QRDecomposition​(Matrix A)
    QR Decomposition, computed by Householder reflections.

  • Method Summary

    Modifier and Type Method Description
    Matrix getH()
    Return the Householder vectors
    Matrix getQ()
    Generate and return the (economy-sized) orthogonal factor
    Matrix getR()
    Return the upper triangular factor
    boolean isFullRank()
    Is the matrix full rank?
    Matrix solve​(Matrix B)
    Least squares solution of A*X = B

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • QRDecomposition

      public QRDecomposition​(Matrix A)
      QR Decomposition, computed by Householder reflections.
      Parameters:
      A - Rectangular matrix

  • Method Details

    • 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:
      java.lang.IllegalArgumentException - Matrix row dimensions must agree.
      java.lang.RuntimeException - Matrix is rank deficient.