QRDecomposition (ejml-core 0.39 API)

All Superinterfaces:

DecompositionInterface<T>

All Known Subinterfaces:

QRPDecomposition<T>, QRPDecomposition_F32<T>, QRPDecomposition_F64<T>, QRSparseDecomposition<T>
```
public interface QRDecomposition<T extends Matrix>
extends DecompositionInterface<T>
```
QR decompositions decompose a rectangular matrix 'A' such that 'A=QR'. Where A ∈ ℜ ^{n × m} , n ≥ m, Q ∈ ℜ ^{n × n} is an orthogonal matrix, and R ∈ ℜ ^{n × m} is an upper triangular matrix. Some implementations of QR decomposition require that A has full rank.
Some features of QR decompositions:
- Can decompose rectangular matrices.
- Numerically stable solutions to least-squares problem, but not as stable as SVD
- Can incrementally add and remove columns from the decomposed matrix. See org.ejml.dense.row.linsol.qr.AdjLinearSolverQr_DDRM
Orthogonal matrices have the following properties:
- QQ^T=I
- Q^T=Q^-1

Method Summary

All Methods Instance Methods Abstract Methods
Modifier and Type	Method	Description
`T`	`getQ(T Q, boolean compact)`	Returns the Q matrix from the decomposition.
`T`	`getR(T R, boolean compact)`	Returns the R matrix from the decomposition.

Methods inherited from interface org.ejml.interfaces.decomposition.DecompositionInterface
decompose, inputModified

- Method Detail
  - getQ
```
T getQ(T Q,
       boolean compact)
```
    Returns the Q matrix from the decomposition. Should only be called after DecompositionInterface.decompose(org.ejml.data.Matrix) has been called.
    
    If parameter Q is not null, then that matrix is used to store the Q matrix. Otherwise a new matrix is created.
    
    Parameters:
    
    Q - If not null then the Q matrix is written to it. Modified.
    
    compact - If true an m by n matrix is created, otherwise n by n.
    
    Returns:
    
    The Q matrix.
  - getR
```
T getR(T R,
       boolean compact)
```
    Returns the R matrix from the decomposition. Should only be called after DecompositionInterface.decompose(org.ejml.data.Matrix) has been.
    
    If setZeros is true then an n × m matrix is required and all the elements are set. If setZeros is false then the matrix must be at least m × m and only the upper triangular elements are set.
    
    If parameter R is not null, then that matrix is used to store the R matrix. Otherwise a new matrix is created.
    
    Parameters:
    
    R - If not null then the R matrix is written to it. Modified.
    
    compact - If true only the upper triangular elements are set
    
    Returns:
    
    The R matrix.