org.apache.ignite.ml.math.decompositions

Class QRDSolver

java.lang.Object

org.apache.ignite.ml.math.decompositions.QRDSolver

All Implemented Interfaces:

Serializable

public class QRDSolver
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.

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
QRDSolver(Matrix q, Matrix r) Constructs a new QR decomposition solver object.

Method Summary

Modifier and Type	Method and Description
Matrix	calculateBetaVariance(int p) Calculates the variance-covariance matrix of the regression parameters.
Matrix	calculateHat() Compute the "hat" matrix.
boolean	equals(Object o)
int	hashCode()
Matrix	solve(Matrix mtx) Least squares solution of A*X = B; returns X.
Vector	solve(Vector vec) Least squares solution of A*X = B; returns X.
String	toString() Returns a rough string rendition of a QRD solver.

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Constructor Detail

QRDSolver

public QRDSolver(Matrix q,
                 Matrix r)

Constructs a new QR decomposition solver object.

Parameters:

q - An orthogonal matrix.

r - An upper triangular matrix

Method Detail

solve

public Matrix solve(Matrix mtx)

Least squares solution of A*X = B; returns X.

Parameters:

mtx - A matrix with as many rows as A and any number of cols.

Returns:

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

Throws:

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

solve

public Vector solve(Vector vec)

Least squares solution of A*X = B; returns X.

Parameters:

vec - A vector with as many rows as A.

Returns:

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

Throws:

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

calculateHat

public Matrix calculateHat()

Compute the "hat" matrix.

The hat matrix is defined in terms of the design matrix X by X(X^TX)^-1X^T

The implementation here uses the QR decomposition to compute the hat matrix as Q I_pQ^T where I_p is the p-dimensional identity matrix augmented by 0's. This computational formula is from "The Hat Matrix in Regression and ANOVA", David C. Hoaglin and Roy E. Welsch, The American Statistician, Vol. 32, No. 1 (Feb., 1978), pp. 17-22.

Data for the model must have been successfully loaded using one of the newSampleData methods before invoking this method; otherwise a NullPointerException will be thrown.

Returns:

the hat matrix

Throws:

NullPointerException - unless method newSampleData has been called beforehand.

calculateBetaVariance

public Matrix calculateBetaVariance(int p)

Calculates the variance-covariance matrix of the regression parameters.

Var(b) = (X^TX)^-1

Uses QR decomposition to reduce (X^TX)^-1 to (R^TR)^-1, with only the top p rows of R included, where p = the length of the beta vector.

Data for the model must have been successfully loaded using one of the newSampleData methods before invoking this method; otherwise a NullPointerException will be thrown.

Parameters:

p - Size of the beta variance-covariance matrix

Returns:

The beta variance-covariance matrix

Throws:

SingularMatrixException - if the design matrix is singular

NullPointerException - if the data for the model have not been loaded

equals

public boolean equals(Object o)

Overrides:

equals in class Object

hashCode

public int hashCode()

Overrides:

hashCode in class Object

toString

public String toString()

Returns a rough string rendition of a QRD solver.

Overrides:

toString in class Object