SchurTransformer (Hipparchus 3.0 API)

java.lang.Object
- org.hipparchus.linear.SchurTransformer

```
public class SchurTransformer
extends Object
```
Class transforming a general real matrix to Schur form.
A m × m matrix A can be written as the product of three matrices: A = P × T × P^T with P an orthogonal matrix and T an quasi-triangular matrix. Both P and T are m × m matrices.

Transformation to Schur form is often not a goal by itself, but it is an intermediate step in more general decomposition algorithms like eigen decomposition. This class is therefore intended for expert use. As a consequence of this explicitly limited scope, many methods directly returns references to internal arrays, not copies.

This class is based on the method hqr2 in class EigenvalueDecomposition from the JAMA library.

See Also:

Schur Decomposition - MathWorld, Schur Decomposition - Wikipedia, Householder Transformations

Constructor Summary

Constructors
Constructor	Description
`SchurTransformer(RealMatrix matrix)`	Build the transformation to Schur form of a general real matrix.
`SchurTransformer(RealMatrix matrix, double epsilon)`	Build the transformation to Schur form of a general real matrix.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`RealMatrix`	`getP()`	Returns the matrix P of the transform.
`RealMatrix`	`getPT()`	Returns the transpose of the matrix P of the transform.
`RealMatrix`	`getT()`	Returns the quasi-triangular Schur matrix T of the transform.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - SchurTransformer
```
public SchurTransformer(RealMatrix matrix)
```
    Build the transformation to Schur form of a general real matrix.
    
    Parameters:
    
    matrix - matrix to transform
    
    Throws:
    
    MathIllegalArgumentException - if the matrix is not square
  - SchurTransformer
```
public SchurTransformer(RealMatrix matrix,
                        double epsilon)
```
    Build the transformation to Schur form of a general real matrix.
    
    Parameters:
    
    matrix - matrix to transform
    
    epsilon - convergence criteria
    
    Throws:
    
    MathIllegalArgumentException - if the matrix is not square
    
    Since:
    
    3.0
- Method Detail
  - getP
```
public RealMatrix getP()
```
    Returns the matrix P of the transform.
    P is an orthogonal matrix, i.e. its inverse is also its transpose.
    
    Returns:
    
    the P matrix
  - getPT
```
public RealMatrix getPT()
```
    Returns the transpose of the matrix P of the transform.
    P is an orthogonal matrix, i.e. its inverse is also its transpose.
    
    Returns:
    
    the transpose of the P matrix
  - getT
```
public RealMatrix getT()
```
    Returns the quasi-triangular Schur matrix T of the transform.
    
    Returns:
    
    the T matrix