SymmetricQREigenHelper (Efficient Java Matrix Library 0.25 API)

java.lang.Object
- org.ejml.alg.dense.decomposition.eig.symm.SymmetricQREigenHelper

```
public class SymmetricQREigenHelper
extends Object
```
A helper class for the symmetric matrix implicit QR algorithm for eigenvalue decomposition. Performs most of the basic operations needed to extract eigenvalues and eigenvectors.

Author:

Peter Abeles

Field Summary

Fields
Modifier and Type	Field and Description
`protected double[]`	`diag`
`protected EigenvalueSmall`	`eigenSmall`
`protected int`	`lastExceptional`
`protected int`	`N`
`protected int`	`numExceptional`
`protected int`	`numSplits`
`protected double[]`	`off`
`protected DenseMatrix64F`	`Q`
`protected Random`	`rand`
`protected int[]`	`splits`
`protected int`	`steps`
`protected int`	`x1`
`protected int`	`x2`

Constructor Summary

Constructors
Constructor and Description

SymmetricQREigenHelper()

Constructors
Constructor and Description
`SymmetricQREigenHelper()`

Method Summary

Methods
Modifier and Type	Method and Description
`double`	`computeShift()`
`double`	`computeWilkinsonShift()`
`double[]`	`copyDiag(double[] ret)`
`double[]`	`copyEigenvalues(double[] ret)`
`double[]`	`copyOff(double[] ret)`
`protected void`	`createBulge(int x1, double p, boolean byAngle)` Performs a similar transform on A-pI
`protected void`	`createBulge2by2(int x1, double p, boolean byAngle)`
`protected void`	`eigenvalue2by2(int x1)` Computes the eigenvalue of the 2 by 2 matrix.
`void`	`exceptionalShift()` Perform a shift in a random direction that is of the same magnitude as the elements in the matrix.
`int`	`getMatrixSize()`
`void`	`incrementSteps()`
`void`	`init(double[] diag, double[] off, int numCols)` Sets up and declares internal data structures.
`protected boolean`	`isZero(int index)` Checks to see if the specified off diagonal element is zero using a relative metric.
`boolean`	`nextSplit()` Tells it to process the submatrix at the next split.
`protected void`	`performImplicitSingleStep(double lambda, boolean byAngle)`
`void`	`printMatrix()`
`protected void`	`removeBulge(int x1)`
`protected void`	`removeBulgeEnd(int x1)` Rotator to remove the bulge
`void`	`reset(int N)` Sets the size of the matrix being decomposed, declares new memory if needed, and sets all helper functions to their initial value.
`void`	`resetSteps()`
`void`	`setQ(DenseMatrix64F q)`
`void`	`setSubmatrix(int x1, int x2)` Sets which submatrix is being processed.
`double[]`	`swapDiag(double[] diag)` Exchanges the internal array of the diagonal elements for the provided one.
`double[]`	`swapOff(double[] off)` Exchanges the internal array of the off diagonal elements for the provided one.
`protected void`	`updateQ(int m, int n, double c, double s)`

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

Field Detail

rand
```
protected Random rand
```

steps
```
protected int steps
```

numExceptional
```
protected int numExceptional
```

lastExceptional
```
protected int lastExceptional
```

eigenSmall
```
protected EigenvalueSmall eigenSmall
```

Q
```
protected DenseMatrix64F Q
```

N
```
protected int N
```

diag
```
protected double[] diag
```

off
```
protected double[] off
```

x1
```
protected int x1
```

x2
```
protected int x2
```

splits
```
protected int[] splits
```

numSplits
```
protected int numSplits
```

Constructor Detail
- SymmetricQREigenHelper
```
public SymmetricQREigenHelper()
```

Method Detail
- printMatrix
```
public void printMatrix()
```
- setQ
```
public void setQ(DenseMatrix64F q)
```
- incrementSteps
```
public void incrementSteps()
```
- init
```
public void init(double[] diag,
        double[] off,
        int numCols)
```
  Sets up and declares internal data structures.
  
  Parameters:
  diag - Diagonal elements from tridiagonal matrix. Modified.
  off - Off diagonal elements from tridiagonal matrix. Modified.
  numCols - number of columns (and rows) in the matrix.
- swapDiag
```
public double[] swapDiag(double[] diag)
```
  Exchanges the internal array of the diagonal elements for the provided one.
- swapOff
```
public double[] swapOff(double[] off)
```
  Exchanges the internal array of the off diagonal elements for the provided one.
- reset
```
public void reset(int N)
```
  Sets the size of the matrix being decomposed, declares new memory if needed, and sets all helper functions to their initial value.
- copyDiag
```
public double[] copyDiag(double[] ret)
```
- copyOff
```
public double[] copyOff(double[] ret)
```
- copyEigenvalues
```
public double[] copyEigenvalues(double[] ret)
```
- setSubmatrix
```
public void setSubmatrix(int x1,
                int x2)
```
  Sets which submatrix is being processed.
  
  Parameters:
  x1 - Lower bound, inclusive.
  x2 - Upper bound, inclusive.
- isZero
```
protected boolean isZero(int index)
```
  Checks to see if the specified off diagonal element is zero using a relative metric.
- performImplicitSingleStep
```
protected void performImplicitSingleStep(double lambda,
                             boolean byAngle)
```
- updateQ
```
protected void updateQ(int m,
           int n,
           double c,
           double s)
```
- createBulge
```
protected void createBulge(int x1,
               double p,
               boolean byAngle)
```
  Performs a similar transform on A-pI
- createBulge2by2
```
protected void createBulge2by2(int x1,
                   double p,
                   boolean byAngle)
```
- removeBulge
```
protected void removeBulge(int x1)
```
- removeBulgeEnd
```
protected void removeBulgeEnd(int x1)
```
  Rotator to remove the bulge
- eigenvalue2by2
```
protected void eigenvalue2by2(int x1)
```
  Computes the eigenvalue of the 2 by 2 matrix.
- exceptionalShift
```
public void exceptionalShift()
```
  Perform a shift in a random direction that is of the same magnitude as the elements in the matrix.
- nextSplit
```
public boolean nextSplit()
```
  Tells it to process the submatrix at the next split. Should be called after the current submatrix has been processed.
- computeShift
```
public double computeShift()
```
- computeWilkinsonShift
```
public double computeWilkinsonShift()
```
- getMatrixSize
```
public int getMatrixSize()
```
- resetSteps
```
public void resetSteps()
```

Class SymmetricQREigenHelper

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

rand

steps

numExceptional

lastExceptional

eigenSmall

Q

N

diag

off

x1

x2

splits

numSplits

Constructor Detail

SymmetricQREigenHelper

Method Detail

printMatrix

setQ

incrementSteps

init

swapDiag

swapOff

reset

copyDiag

copyOff

copyEigenvalues

setSubmatrix

isZero

performImplicitSingleStep

updateQ

createBulge

createBulge2by2

removeBulge

removeBulgeEnd

eigenvalue2by2

exceptionalShift

nextSplit

computeShift

computeWilkinsonShift

getMatrixSize

resetSteps