cern.colt.matrix.tdouble.algo.decomposition

Class DenseDoubleQRDecomposition

java.lang.Object

cern.colt.matrix.tdouble.algo.decomposition.DenseDoubleQRDecomposition

All Implemented Interfaces:

Serializable

public class DenseDoubleQRDecomposition
extends Object
implements Serializable

For an m x n matrix A with m >= n, the QR decomposition is an m x n orthogonal matrix Q and an n x 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.

Author:

Piotr Wendykier (piotr.wendykier@gmail.com)

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
DenseDoubleQRDecomposition(DoubleMatrix2D A) Constructs and returns a new QR decomposition object; computed by Householder reflections; The decomposed matrices can be retrieved via instance methods of the returned decomposition object.

Method Summary

Methods

Modifier and Type	Method and Description
DoubleMatrix2D	getQ(boolean economySize) Generates and returns a copy of the orthogonal factor Q.
DoubleMatrix2D	getR(boolean economySize) Returns a copy of the upper triangular factor, R.
boolean	hasFullRank() Returns whether the matrix A has full rank.
void	solve(DoubleMatrix1D b) Least squares solution of A*x = b (in-place).
void	solve(DoubleMatrix2D B) Least squares solution of A*X = B(in-place).
String	toString() Returns a String with (propertyName, propertyValue) pairs.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

DenseDoubleQRDecomposition

public DenseDoubleQRDecomposition(DoubleMatrix2D A)

Constructs and returns a new QR decomposition object; computed by Householder reflections; The decomposed matrices can be retrieved via instance methods of the returned decomposition object.

Parameters:

A - A rectangular matrix.

Throws:

IllegalArgumentException - if A.rows() < A.columns().

Method Detail

getQ

public DoubleMatrix2D getQ(boolean economySize)

Generates and returns a copy of the orthogonal factor Q.

Parameters:

economySize - if true, then Q is m-by-n, otherwise, Q is m-by-m

Returns:

Q

getR

public DoubleMatrix2D getR(boolean economySize)

Returns a copy of the upper triangular factor, R.

Parameters:

economySize - if true, then R is n-by-n, otherwise, R is m-by-n

Returns:

R

hasFullRank

public boolean hasFullRank()

Returns whether the matrix A has full rank.

Returns:

true if R, and hence A, has full rank.

solve

public void solve(DoubleMatrix1D b)

Least squares solution of A*x = b (in-place). Upon return b is overridden with the result x.

Parameters:

b - right-hand side.

Throws:

IllegalArgumentException - if b.size() != A.rows().

IllegalArgumentException - if !this.hasFullRank() (A is rank deficient).

solve

public void solve(DoubleMatrix2D B)

Least squares solution of A*X = B(in-place). Upon return B is overridden with the result X.

Parameters:

B - A matrix with as many rows as A and any number of columns.

Throws:

IllegalArgumentException - if B.rows() != A.rows().

IllegalArgumentException - if !this.hasFullRank() (A is rank deficient).

toString

public String toString()

Returns a String with (propertyName, propertyValue) pairs. Useful for debugging or to quickly get the rough picture. For example,

   rank          : 3
   trace         : 0
 
 

Overrides:

toString in class Object