Package org.biojava.nbio.structure.jama

Class QRDecomposition

java.lang.Object
org.biojava.nbio.structure.jama.QRDecomposition
All Implemented Interfaces:
Serializable
public class QRDecomposition extends Object implements 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:

  • Constructor Details

    • QRDecomposition

      public QRDecomposition(Matrix A)
      QR Decomposition, computed by Householder reflections. provides a data structure to access R and the Householder vectors and compute Q.
      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:
      IllegalArgumentException - Matrix row dimensions must agree.
      RuntimeException - Matrix is rank deficient.