smile.math.matrix

Class FloatMatrix.QR

java.lang.Object

smile.math.matrix.FloatMatrix.QR

All Implemented Interfaces:

java.io.Serializable

Enclosing class:

FloatMatrix

public static class FloatMatrix.QR
extends java.lang.Object
implements java.io.Serializable

The 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 such that A = Q*R.

The QR decomposition always exists, even if the matrix does not have full rank. The primary use of the QR decomposition is in the least squares solution of non-square systems of simultaneous linear equations.

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
FloatMatrix	qr The QR decomposition.
float[]	tau The scalar factors of the elementary reflectors

Constructor Summary

Constructors

Constructor and Description
QR(FloatMatrix qr, float[] tau) Constructor.

Method Summary

Modifier and Type	Method and Description
FloatMatrix.Cholesky	CholeskyOfAtA() Returns the Cholesky decomposition of A'A.
FloatMatrix	Q() Returns the orthogonal factor.
FloatMatrix	R() Returns the upper triangular factor.
float[]	solve(float[] b) Solves the least squares min || B - A*X ||.
void	solve(FloatMatrix B) Solves the least squares min || B - A*X ||.

Methods inherited from class java.lang.Object

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

Field Detail

qr

public final FloatMatrix qr

The QR decomposition.

tau

public final float[] tau

The scalar factors of the elementary reflectors

Constructor Detail

QR

public QR(FloatMatrix qr,
          float[] tau)

Constructor.

Method Detail

CholeskyOfAtA

public FloatMatrix.Cholesky CholeskyOfAtA()

Returns the Cholesky decomposition of A'A.

R

public FloatMatrix R()

Returns the upper triangular factor.

Q

public FloatMatrix Q()

Returns the orthogonal factor.

solve

public float[] solve(float[] b)

Solves the least squares min || B - A*X ||.

Parameters:

b - the right hand side of overdetermined linear system.

Returns:

the solution vector beta that minimizes ||Y - X*beta||.

Throws:

java.lang.RuntimeException - if matrix is rank deficient.

solve

public void solve(FloatMatrix B)

Solves the least squares min || B - A*X ||.

Parameters:

B - the right hand side of overdetermined linear system. B will be overwritten with the solution matrix on output.

Throws:

java.lang.RuntimeException - if matrix is rank deficient.