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## nl.liacs.subdisc.Jama
Class QRDecomposition

    java.lang.Object
      nl.liacs.subdisc.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
`QRDecomposition(Matrix A)` QR Decomposition, computed by Householder reflections.

Method Summary
`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
`equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

Constructor Detail

### QRDecomposition

    public QRDecomposition(Matrix 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 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.

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