com.numericalmethod.suanshu.matrix.doubles.factorization.diagonalization

Class TriDiagonalization

java.lang.Object

com.numericalmethod.suanshu.matrix.doubles.factorization.diagonalization.TriDiagonalization

All Implemented Interfaces:

java.io.Serializable

public class TriDiagonalization
extends java.lang.Object
implements java.io.Serializable

A tri-diagonal matrix A is a matrix such that it has non-zero elements only in the main diagonal, the first diagonal below, and the first diagonal above. Successive Householder reflections on columns and then rows gradually transform a symmetric matrix A to the tri-diagonal form. The procedure is essentially the same as in Hessenberg decomposition, c.f., HessenbergDecomposition, except that here we apply the procedure only to symmetric matrix. The trailing elements in rows are also zeroed out, due to symmetry.

See Also:

• Wikipedia: Tridiagonal matrix
• Wikipedia: TriDiagonalization

, Serialized Form

Constructor Summary

Constructors

Constructor and Description
TriDiagonalization(Matrix A) Run the tri-diagonalization process for a symmetric matrix.

Method Summary

Modifier and Type	Method and Description
Matrix	Q() Get Q, such that Q * A * Q = T.
Matrix	T() Get T, such that T = Q * A * Q.

Methods inherited from class java.lang.Object

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

Constructor Detail

TriDiagonalization

public TriDiagonalization(Matrix A)

Run the tri-diagonalization process for a symmetric matrix.

Parameters:

A - a symmetric matrix

Throws:

java.lang.IllegalArgumentException - if A is not symmetric

Method Detail

T

public Matrix T()

Get T, such that T = Q * A * Q. T is triangular. Q is orthogonal.

Returns:

the T matrix

Q

public Matrix Q()

Get Q, such that Q * A * Q = T. Q is orthogonal. T is triangular.

Returns:

the Q matrix