ubic.basecode.math.linalg

Class QRDecomposition

java.lang.Object

ubic.basecode.math.linalg.QRDecomposition

public class QRDecomposition
extends Object

QR with pivoting. See http://www.netlib.org/lapack/lug/node42.html and http://www.netlib.org/lapack/lug/node27.html, and Golub and VanLoan, section 5.5.6+. Designed to mimic the way R does this by default.

Author:

paul

Constructor Summary

Constructors

Constructor and Description
QRDecomposition(cern.colt.matrix.DoubleMatrix2D A)
QRDecomposition(cern.colt.matrix.DoubleMatrix2D A, boolean pivoting) Construct the QR decomposition of A.

Method Summary

Modifier and Type	Method and Description
cern.colt.matrix.DoubleMatrix2D	chol2inv() Used for computing standard errors of parameter estimates for least squares; copies functionality of R chol2inv.
protected String	diagnose()
cern.colt.matrix.DoubleMatrix1D	effects(cern.colt.matrix.DoubleMatrix1D y) Compute effects matrix Q'y (as in Rb = Q'y).
cern.colt.matrix.DoubleMatrix2D	effects(cern.colt.matrix.DoubleMatrix2D y) Compute effects matrix Q'y (as in Rb = Q'y)
cern.colt.list.IntArrayList	getPivotOrder()
cern.colt.matrix.DoubleMatrix2D	getQ() Generates and returns the (economy-sized - first p columns only) orthogonal factor Q.
protected cern.colt.matrix.DoubleMatrix2D	getQR() For testing.
cern.colt.matrix.DoubleMatrix1D	getQraux()
cern.colt.matrix.DoubleMatrix2D	getR() Returns the upper triangular factor, R.
int	getRank()
double	getTolerance()
boolean	hasFullRank() Returns whether the matrix A has full rank.
boolean	isPivoting()
cern.colt.matrix.DoubleMatrix2D	solve(cern.colt.matrix.DoubleMatrix2D y) Least squares solution of A*X = y; returns X using the stored QR decomposition of A.
String	toString() Returns a String with (propertyName, propertyValue) pairs.

Methods inherited from class java.lang.Object

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

Constructor Detail

QRDecomposition

public QRDecomposition(cern.colt.matrix.DoubleMatrix2D A)

Parameters:

A - the matrix to decompose, pivoting will be used.

QRDecomposition

public QRDecomposition(cern.colt.matrix.DoubleMatrix2D A,
                       boolean pivoting)

Construct the QR decomposition of A. With pivoting = true, this reproduces quite closely the behaviour of R qr().

Parameters:

A - the matrix to decompose

pivoting - set to false to obtain standard QR behaviour.

Method Detail

chol2inv

public cern.colt.matrix.DoubleMatrix2D chol2inv()

Used for computing standard errors of parameter estimates for least squares; copies functionality of R chol2inv.

Returns:

effects

public cern.colt.matrix.DoubleMatrix1D effects(cern.colt.matrix.DoubleMatrix1D y)

Compute effects matrix Q'y (as in Rb = Q'y).

"Tthe effects are the uncorrelated single-degree-of-freedom values obtained by projecting the data onto the successive orthogonal subspaces generated by the QR decomposition during the fitting process. The first r (the rank of the model) are associated with coefficients and the remainder span the space of residuals (but are not associated with particular residuals)."

Parameters:

y - vector Missing values are ignored, otherwise assumed to be of the right size

Returns:

vector of effects - these are the projections of y into Q column space

effects

public cern.colt.matrix.DoubleMatrix2D effects(cern.colt.matrix.DoubleMatrix2D y)

Compute effects matrix Q'y (as in Rb = Q'y)

Parameters:

y - matrix of data, assumed to be of right size, missing values are not supported

Returns:

matrix of effects - these are the projections of y's columns into Q column subspace associated with the parameters, so values are "effects" each basis vector on the data

getPivotOrder

public cern.colt.list.IntArrayList getPivotOrder()

Returns:

getQ

public cern.colt.matrix.DoubleMatrix2D getQ()

Generates and returns the (economy-sized - first p columns only) orthogonal factor Q.

Returns:

first p columns of Q

getQraux

public cern.colt.matrix.DoubleMatrix1D getQraux()

Returns:

getR

public cern.colt.matrix.DoubleMatrix2D getR()

Returns the upper triangular factor, R.

Returns:

R

getRank

public int getRank()

Returns:

rank

getTolerance

public double getTolerance()

hasFullRank

public boolean hasFullRank()

Returns whether the matrix A has full rank.

Returns:

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

isPivoting

public boolean isPivoting()

Returns:

true if pivoting was used (just whether it was set; not whether any actual pivoting happened)

solve

public cern.colt.matrix.DoubleMatrix2D solve(cern.colt.matrix.DoubleMatrix2D y)

Least squares solution of A*X = y; returns X using the stored QR decomposition of A.

Parameters:

y - A matrix with as many rows as A and any number of columns. Least squares is fit for each column of y.

Returns:

X that minimizes the two norm of Q*R*X - B.

Throws:

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

IllegalArgumentException - if !this.hasFullRank() (A is rank deficient). However, rank-deficient cases are handled by pivoting, so if you are using pivoting you should not see this happening.

toString

public String toString()

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

Overrides:

toString in class Object

diagnose

protected String diagnose()

getQR

protected cern.colt.matrix.DoubleMatrix2D getQR()

For testing.

Returns: