jmathlib.toolbox.jmathlib.matrix._private.Jama
Class QRDecomposition

java.lang.Object
  extended by jmathlib.toolbox.jmathlib.matrix._private.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

Field Summary
private  int m
          Row and column dimensions.
private  int n
          Row and column dimensions.
private  double[][] QR
          Array for internal storage of decomposition.
private  double[] Rdiag
          Array for internal storage of diagonal of R.
 
Constructor Summary
QRDecomposition(double[][] A)
          QR Decomposition, computed by Householder reflections.
QRDecomposition(Matrix A)
           
 
Method Summary
 double[][] getH()
          Return the Householder vectors
 double[][] getQ()
          Generate and return the (economy-sized) orthogonal factor
 double[][] getR()
          Return the upper triangular factor
static double hypot(double a, double b)
           
 boolean isFullRank()
          Is the matrix full rank?
 double[][] solve(double[][] B)
          Least squares solution of A*X = B
 double[][] solve(Matrix B)
          Solve A*X = B
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Field Detail

QR

private double[][] QR
Array for internal storage of decomposition.


m

private int m
Row and column dimensions.


n

private int n
Row and column dimensions.


Rdiag

private double[] Rdiag
Array for internal storage of diagonal of R.

Constructor Detail

QRDecomposition

public QRDecomposition(Matrix A)

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(Matrix B)
Solve A*X = B

Parameters:
B - A Matrix with as many rows as A and any number of columns.
Returns:
X so that L*U*X = B(piv,:)
Throws:
java.lang.IllegalArgumentException - Matrix row dimensions must agree.
java.lang.RuntimeException - Matrix is singular.

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

hypot

public static double hypot(double a,
                           double b)

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