public class QRDecompositionHouseholder_CDRM
extends java.lang.Object
implements org.ejml.interfaces.decomposition.QRDecomposition<org.ejml.data.CMatrixRMaj>
This variation of complex QR decomposition uses reflections to compute the Q matrix. Each reflection uses a householder operations, hence its name. To provide a meaningful solution the original matrix must have full rank. This is intended for processing of small to medium matrices.
Both Q and R are stored in the same m by n matrix. Q is not stored directly, instead the u from Qk=(I-γ*u*uH) is stored. Decomposition requires about 2n*m2-2m2/3 flops.
See the QR reflections algorithm described in:
David S. Watkins, "Fundamentals of Matrix Computations" 2nd Edition, 2002
For the most part this is a straight forward implementation. To improve performance on large matrices a column is written to an array and the order of some of the loops has been changed. This will degrade performance noticeably on small matrices. Since it is unlikely that the QR decomposition would be a bottle neck when small matrices are involved only one implementation is provided.
Modifier and Type | Field and Description |
---|---|
protected float[] |
dataQR |
protected boolean |
error |
protected float[] |
gammas |
protected int |
minLength |
protected int |
numCols |
protected int |
numRows |
protected org.ejml.data.CMatrixRMaj |
QR
Where the Q and R matrices are stored.
|
protected org.ejml.data.Complex_F32 |
tau |
protected float[] |
u |
protected float[] |
v |
Constructor and Description |
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QRDecompositionHouseholder_CDRM() |
Modifier and Type | Method and Description |
---|---|
protected void |
commonSetup(org.ejml.data.CMatrixRMaj A)
This function performs sanity check on the input for decompose and sets up the QR matrix.
|
boolean |
decompose(org.ejml.data.CMatrixRMaj A)
In order to decompose the matrix 'A' it must have full rank.
|
float[] |
getGammas() |
org.ejml.data.CMatrixRMaj |
getQ(org.ejml.data.CMatrixRMaj Q,
boolean compact)
Computes the Q matrix from the information stored in the QR matrix.
|
org.ejml.data.CMatrixRMaj |
getQR()
Returns a single matrix which contains the combined values of Q and R.
|
org.ejml.data.CMatrixRMaj |
getR(org.ejml.data.CMatrixRMaj R,
boolean compact)
Returns an upper triangular matrix which is the R in the QR decomposition.
|
protected void |
householder(int j)
Computes the householder vector "u" for the first column of submatrix j.
|
boolean |
inputModified() |
void |
setExpectedMaxSize(int numRows,
int numCols) |
protected org.ejml.data.CMatrixRMaj QR
protected float[] u
protected float[] v
protected int numCols
protected int numRows
protected int minLength
protected float[] dataQR
protected float[] gammas
protected org.ejml.data.Complex_F32 tau
protected boolean error
public void setExpectedMaxSize(int numRows, int numCols)
public org.ejml.data.CMatrixRMaj getQR()
public org.ejml.data.CMatrixRMaj getQ(org.ejml.data.CMatrixRMaj Q, boolean compact)
getQ
in interface org.ejml.interfaces.decomposition.QRDecomposition<org.ejml.data.CMatrixRMaj>
Q
- The orthogonal Q matrix.public org.ejml.data.CMatrixRMaj getR(org.ejml.data.CMatrixRMaj R, boolean compact)
getR
in interface org.ejml.interfaces.decomposition.QRDecomposition<org.ejml.data.CMatrixRMaj>
R
- An upper triangular matrix.compact
- public boolean decompose(org.ejml.data.CMatrixRMaj A)
In order to decompose the matrix 'A' it must have full rank. 'A' is a 'm' by 'n' matrix. It requires about 2n*m2-2m2/3 flops.
The matrix provided here can be of different dimension than the one specified in the constructor. It just has to be smaller than or equal to it.
decompose
in interface org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.CMatrixRMaj>
public boolean inputModified()
inputModified
in interface org.ejml.interfaces.decomposition.DecompositionInterface<org.ejml.data.CMatrixRMaj>
protected void householder(int j)
Computes the householder vector "u" for the first column of submatrix j. Note this is a specialized householder for this problem. There is some protection against overflow and underflow.
Q = I - γuuH
This function finds the values of 'u' and 'γ'.
j
- Which submatrix to work off of.protected void commonSetup(org.ejml.data.CMatrixRMaj A)
A
- public float[] getGammas()