java.lang.Object
- org.ojalgo.matrix.decomposition.AbstractDecomposition<N,DecompositionStore<N>>
- - org.ojalgo.matrix.decomposition.InPlaceDecomposition<N>
  - - org.ojalgo.matrix.decomposition.DenseQR<N>

All Implemented Interfaces:

MatrixDecomposition<N>, MatrixDecomposition.Determinant<N>, MatrixDecomposition.EconomySize<N>, MatrixDecomposition.Ordered<N>, MatrixDecomposition.RankRevealing<N>, MatrixDecomposition.Solver<N>, MatrixDecomposition.Updatable<N>, QR<N>, Provider2D, Provider2D.Determinant<N>, Provider2D.Inverse<java.util.Optional<MatrixStore<N>>>, Provider2D.Rank, Provider2D.Solution<java.util.Optional<MatrixStore<N>>>, DeterminantTask<N>, InverterTask<N>, MatrixTask<N>, SolverTask<N>, InvertibleFactor<N>, Structure1D, Structure2D

Direct Known Subclasses:

DenseQR.C128, DenseQR.H256, DenseQR.Q128, DenseQR.R064, DenseQR.R128
```
abstract class DenseQR<N extends java.lang.Comparable<N>>
extends InPlaceDecomposition<N>
implements QR<N>
```

Nested Class Summary

Nested Classes
Modifier and Type	Class	Description
`(package private) static class`	`DenseQR.C128`
`(package private) static class`	`DenseQR.H256`
`(package private) static class`	`DenseQR.Q128`
`(package private) static class`	`DenseQR.R064`
`(package private) static class`	`DenseQR.R128`

Nested classes/interfaces inherited from interface org.ojalgo.matrix.transformation.InvertibleFactor
InvertibleFactor.IdentityFactor<N extends java.lang.Comparable<N>>

Nested classes/interfaces inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition
MatrixDecomposition.Determinant<N extends java.lang.Comparable<N>>, MatrixDecomposition.EconomySize<N extends java.lang.Comparable<N>>, MatrixDecomposition.Factory<D extends MatrixDecomposition<?>>, MatrixDecomposition.Hermitian<N extends java.lang.Comparable<N>>, MatrixDecomposition.Ordered<N extends java.lang.Comparable<N>>, MatrixDecomposition.Pivoting<N extends java.lang.Comparable<N>>, MatrixDecomposition.RankRevealing<N extends java.lang.Comparable<N>>, MatrixDecomposition.Solver<N extends java.lang.Comparable<N>>, MatrixDecomposition.Updatable<N extends java.lang.Comparable<N>>, MatrixDecomposition.Values<N extends java.lang.Comparable<N>>

Nested classes/interfaces inherited from interface org.ojalgo.matrix.Provider2D
Provider2D.Condition, Provider2D.Determinant<N extends java.lang.Comparable<N>>, Provider2D.Eigenpairs, Provider2D.Hermitian, Provider2D.Inverse<M>, Provider2D.Rank, Provider2D.Solution<M>, Provider2D.Symmetric, Provider2D.Trace<N extends java.lang.Comparable<N>>

Nested classes/interfaces inherited from interface org.ojalgo.matrix.decomposition.QR
QR.Factory<N extends java.lang.Comparable<N>>

Nested classes/interfaces inherited from interface org.ojalgo.structure.Structure1D
Structure1D.BasicMapper<T>, Structure1D.IndexMapper<T>, Structure1D.IntIndex, Structure1D.LongIndex, Structure1D.LoopCallback

Nested classes/interfaces inherited from interface org.ojalgo.structure.Structure2D
Structure2D.IntRowColumn, Structure2D.Logical<S extends Structure2D,B extends Structure2D.Logical<S,B>>, Structure2D.LongRowColumn, Structure2D.ReducibleTo1D<R extends Structure1D>, Structure2D.Reshapable, Structure2D.RowColumnKey<R,C>, Structure2D.RowColumnMapper<R,C>

Field Summary

Fields
Modifier and Type Field Description

private boolean myFullSize

private int myNumberOfHouseholderTransformations
- Fields inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition
  TYPICAL
- Fields inherited from interface org.ojalgo.matrix.decomposition.QR
  C128, H256, Q128, R064, R128

Constructor Summary

Constructors
Modifier Constructor Description

protected DenseQR(PhysicalStore.Factory<N,? extends DecompositionStore<N>> factory, boolean fullSize)

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`void`	`btran(PhysicalStore<N> arg)`	Backwards-transformation
`N`	`calculateDeterminant(Access2D<?> matrix)`
`protected boolean`	`checkSolvability()`
`int`	`countSignificant(double threshold)`
`boolean`	`decompose(Access2D.Collectable<N,? super TransformableRegion<N>> matrix)`
`N`	`getDeterminant()`	A matrix' determinant is the product of its eigenvalues.
`MatrixStore<N>`	`getInverse(PhysicalStore<N> preallocated)`	Implementing this method is optional.
`protected DecompositionStore<N>`	`getL()`
`MatrixStore<N>`	`getQ()`
`MatrixStore<N>`	`getR()`
`double`	`getRankThreshold()`
`MatrixStore<N>`	`getSolution(Access2D.Collectable<N,? super PhysicalStore<N>> rhs, PhysicalStore<N> preallocated)`	Solve [A][X]=[B] by first solving [Q][Y]=[B] and then [R]*[X]=[Y].
`MatrixStore<N>`	`invert(Access2D<?> original)`	The output must be a "right inverse" and a "generalised inverse".
`MatrixStore<N>`	`invert(Access2D<?> original, PhysicalStore<N> preallocated)`	Exactly how (if at all) a specific implementation makes use of `preallocated` is not specified by this interface.
`boolean`	`isFullSize()`
`boolean`	`isSolvable()`	Please note that producing a pseudoinverse and/or a least squares solution is ok! The return value, of this method, is not an indication of if the decomposed matrix is square, has full rank, is postive definite or whatever.
`PhysicalStore<N>`	`preallocate(int nbEquations, int nbVariables, int nbSolutions)`
`void`	`reset()`	Delete computed results, and resets attributes to default values
`MatrixStore<N>`	`solve(Access2D<?> body, Access2D<?> rhs, PhysicalStore<N> preallocated)`	Exactly how (if at all) a specific implementation makes use of `preallocated` is not specified by this interface.

Methods inherited from class org.ojalgo.matrix.decomposition.InPlaceDecomposition
getColDim, getInPlace, getInverse, getRowDim, setInPlace

Methods inherited from class org.ojalgo.matrix.decomposition.AbstractDecomposition
aggregator, applyPivotOrder, applyReverseOrder, collect, computed, function, getDimensionalEpsilon, isAspectRatioNormal, isComputed, makeArray, makeDiagonal, makeEye, makeHouseholder, makeIdentity, makeRotation, makeRotation, makeZero, makeZero, scalar, wrap

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

Methods inherited from interface org.ojalgo.matrix.task.InverterTask
preallocate

Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition
isComputed

Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Determinant
toDeterminantProvider

Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.RankRevealing
getRank, isFullRank

Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Solver
compute, getInverse, getSolution, invert, preallocate, solve, toInverseProvider, toSolutionProvider

Methods inherited from interface org.ojalgo.matrix.decomposition.QR
ftran, isOrdered, reconstruct, updateColumn

Methods inherited from interface org.ojalgo.matrix.task.SolverTask
preallocate, solve

Methods inherited from interface org.ojalgo.structure.Structure2D
count, countColumns, countRows, firstInColumn, firstInRow, getColDim, getMaxDim, getMinDim, getRowDim, isEmpty, isFat, isScalar, isSquare, isTall, isVector, limitOfColumn, limitOfRow, size

- Field Detail
  - myFullSize
```
private final boolean myFullSize
```
  - myNumberOfHouseholderTransformations
```
private int myNumberOfHouseholderTransformations
```
- Constructor Detail
  - DenseQR
```
protected DenseQR(PhysicalStore.Factory<N,? extends DecompositionStore<N>> factory,
                  boolean fullSize)
```
- Method Detail
  - btran
```
public void btran(PhysicalStore<N> arg)
```
    Description copied from interface: InvertibleFactor
    
    Backwards-transformation
    Solve [x]^T[A] = [b]^T (equivalent to [A]^T[x] = [b]) by transforming [b] into [x] in-place.
    
    Specified by:
    
    btran in interface InvertibleFactor<N extends java.lang.Comparable<N>>
    
    Parameters:
    
    arg - [b] transformed into [x]
  - calculateDeterminant
```
public N calculateDeterminant(Access2D<?> matrix)
```
    Specified by:
    
    calculateDeterminant in interface DeterminantTask<N extends java.lang.Comparable<N>>
  - countSignificant
```
public int countSignificant(double threshold)
```
    Specified by:
    
    countSignificant in interface MatrixDecomposition.RankRevealing<N extends java.lang.Comparable<N>>
    
    Parameters:
    
    threshold - Significance limit
    
    Returns:
    
    The number of elements in the diagonal matrix that are greater than the threshold
  - decompose
```
public boolean decompose(Access2D.Collectable<N,? super TransformableRegion<N>> matrix)
```
    Specified by:
    
    decompose in interface MatrixDecomposition<N extends java.lang.Comparable<N>>
    
    Parameters:
    
    matrix - A matrix to decompose
    
    Returns:
    
    true if decomposition suceeded; false if not
  - getDeterminant
```
public N getDeterminant()
```
    Description copied from interface: MatrixDecomposition.Determinant
    
    A matrix' determinant is the product of its eigenvalues.
    
    Specified by:
    
    getDeterminant in interface MatrixDecomposition.Determinant<N extends java.lang.Comparable<N>>
    
    Specified by:
    
    getDeterminant in interface Provider2D.Determinant<N extends java.lang.Comparable<N>>
    
    Returns:
    
    The matrix' determinant
  - getInverse
```
public MatrixStore<N> getInverse(PhysicalStore<N> preallocated)
```
    Description copied from interface: MatrixDecomposition.Solver
    
    Implementing this method is optional.
    
    Exactly how a specific implementation makes use of preallocated is not specified by this interface. It must be documented for each implementation.
    
    Should produce the same results as calling MatrixDecomposition.Solver.getInverse().
    
    Specified by:
    
    getInverse in interface MatrixDecomposition.Solver<N extends java.lang.Comparable<N>>
    
    Overrides:
    
    getInverse in class InPlaceDecomposition<N extends java.lang.Comparable<N>>
    
    Parameters:
    
    preallocated - Preallocated memory for the results, possibly some intermediate results. You must assume this is modified, but you cannot assume it will contain the full/final/correct solution. Use MatrixDecomposition.Solver.preallocate(int, int) or InverterTask.preallocate(Structure2D) to get a suitable instance.
    
    Returns:
    
    The inverse, this is where you get the solution
  - getQ
```
public MatrixStore<N> getQ()
```
    Specified by:
    
    getQ in interface QR<N extends java.lang.Comparable<N>>
  - getR
```
public MatrixStore<N> getR()
```
    Specified by:
    
    getR in interface QR<N extends java.lang.Comparable<N>>
  - getRankThreshold
```
public double getRankThreshold()
```
    Specified by:
    
    getRankThreshold in interface MatrixDecomposition.RankRevealing<N extends java.lang.Comparable<N>>
  - getSolution
```
public MatrixStore<N> getSolution(Access2D.Collectable<N,? super PhysicalStore<N>> rhs,
                                  PhysicalStore<N> preallocated)
```
    Solve [A]*[X]=[B] by first solving [Q]*[Y]=[B] and then [R]*[X]=[Y]. [X] minimises the 2-norm of [Q]*[R]*[X]-[B].
    
    Specified by:
    
    getSolution in interface MatrixDecomposition.Solver<N extends java.lang.Comparable<N>>
    
    Parameters:
    
    rhs - The right hand side [B]
    
    preallocated - Preallocated memory for the results, possibly some intermediate results. You must assume this is modified, but you cannot assume it will contain the full/final/correct solution. Use SolverTask.preallocate(int, int, int) or SolverTask.preallocate(Structure2D, Structure2D) to get a suitable instance.
    
    Returns:
    
    [X] "preallocated" is used to form the results, but the solution is in the returned MatrixStore.
  - invert
```
public MatrixStore<N> invert(Access2D<?> original)
                      throws RecoverableCondition
```
    Description copied from interface: InverterTask
    
    The output must be a "right inverse" and a "generalised inverse".
    
    Specified by:
    
    invert in interface InverterTask<N extends java.lang.Comparable<N>>
    
    Throws:
    
    RecoverableCondition
  - invert
```
public MatrixStore<N> invert(Access2D<?> original,
                             PhysicalStore<N> preallocated)
                      throws RecoverableCondition
```
    Description copied from interface: InverterTask
    
    Exactly how (if at all) a specific implementation makes use of preallocated is not specified by this interface. It must be documented for each implementation.
    
    Should produce the same results as calling InverterTask.invert(Access2D).
    
    Use InverterTask.preallocate(Structure2D) to obtain a suitbale preallocated.
    
    Specified by:
    
    invert in interface InverterTask<N extends java.lang.Comparable<N>>
    
    preallocated - Preallocated memory for the results, possibly some intermediate results. You must assume this is modified, but you cannot assume it will contain the full/final/correct solution.
    
    Returns:
    
    The inverse
    
    Throws:
    
    RecoverableCondition - TODO
  - isFullSize
```
public boolean isFullSize()
```
    Specified by:
    
    isFullSize in interface MatrixDecomposition.EconomySize<N extends java.lang.Comparable<N>>
    
    Returns:
    
    True if it will generate a full sized decomposition.
  - isSolvable
```
public boolean isSolvable()
```
    Description copied from interface: MatrixDecomposition.Solver
    
    Please note that producing a pseudoinverse and/or a least squares solution is ok! The return value, of this method, is not an indication of if the decomposed matrix is square, has full rank, is postive definite or whatever. It's that in combination with the specific decomposition algorithm's capabilities.
    
    Specified by:
    
    isSolvable in interface MatrixDecomposition.Solver<N extends java.lang.Comparable<N>>
    
    Overrides:
    
    isSolvable in class AbstractDecomposition<N extends java.lang.Comparable<N>,DecompositionStore<N extends java.lang.Comparable<N>>>
    
    Returns:
    
    true if this matrix decomposition is in a state to be able to deliver an inverse or an equation system solution (with some degree of numerical stability).
  - preallocate
```
public PhysicalStore<N> preallocate(int nbEquations,
                                    int nbVariables,
                                    int nbSolutions)
```
    Specified by:
    
    preallocate in interface SolverTask<N extends java.lang.Comparable<N>>
  - reset
```
public void reset()
```
    Description copied from interface: MatrixDecomposition
    
    Delete computed results, and resets attributes to default values
    
    Specified by:
    
    reset in interface MatrixDecomposition<N extends java.lang.Comparable<N>>
    
    Overrides:
    
    reset in class AbstractDecomposition<N extends java.lang.Comparable<N>,DecompositionStore<N extends java.lang.Comparable<N>>>
  - solve
```
public MatrixStore<N> solve(Access2D<?> body,
                            Access2D<?> rhs,
                            PhysicalStore<N> preallocated)
                     throws RecoverableCondition
```
    Description copied from interface: SolverTask
    
    Exactly how (if at all) a specific implementation makes use of preallocated is not specified by this interface. It must be documented for each implementation.
    
    Should produce the same results as calling SolverTask.solve(Access2D, Access2D).
    
    Use SolverTask.preallocate(Structure2D, Structure2D) to obtain a suitbale preallocated.
    
    Specified by:
    
    solve in interface SolverTask<N extends java.lang.Comparable<N>>
    
    rhs - The Right Hand Side, wont be modfied
    
    preallocated - Preallocated memory for the results, possibly some intermediate results. You must assume this is modified, but you cannot assume it will contain the full/ /correct solution.
    
    Returns:
    
    The solution
    
    Throws:
    
    RecoverableCondition
  - checkSolvability
```
protected boolean checkSolvability()
```
    Overrides:
    
    checkSolvability in class AbstractDecomposition<N extends java.lang.Comparable<N>,DecompositionStore<N extends java.lang.Comparable<N>>>
  - getL
```
protected DecompositionStore<N> getL()
```
    Returns:
    
    L as in R^T.

Modifier and Type	Field	Description
`private boolean`	`myFullSize`
`private int`	`myNumberOfHouseholderTransformations`

Class DenseQR<N extends java.lang.Comparable<N>>

Nested Class Summary

Nested classes/interfaces inherited from interface org.ojalgo.matrix.transformation.InvertibleFactor

Nested classes/interfaces inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition

Nested classes/interfaces inherited from interface org.ojalgo.matrix.Provider2D

Nested classes/interfaces inherited from interface org.ojalgo.matrix.decomposition.QR

Nested classes/interfaces inherited from interface org.ojalgo.structure.Structure1D

Nested classes/interfaces inherited from interface org.ojalgo.structure.Structure2D

Field Summary

Fields inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition

Fields inherited from interface org.ojalgo.matrix.decomposition.QR

Constructor Summary

Method Summary

Methods inherited from class org.ojalgo.matrix.decomposition.InPlaceDecomposition

Methods inherited from class org.ojalgo.matrix.decomposition.AbstractDecomposition

Methods inherited from class java.lang.Object

Methods inherited from interface org.ojalgo.matrix.task.InverterTask

Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition

Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Determinant

Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.RankRevealing

Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Solver

Methods inherited from interface org.ojalgo.matrix.decomposition.QR

Methods inherited from interface org.ojalgo.matrix.task.SolverTask

Methods inherited from interface org.ojalgo.structure.Structure2D

Field Detail

myFullSize

myNumberOfHouseholderTransformations

Constructor Detail

DenseQR

Method Detail

btran

calculateDeterminant

countSignificant

decompose

getDeterminant

getInverse

getQ

getR

getRankThreshold

getSolution

invert

invert

isFullSize

isSolvable

preallocate

reset

solve

checkSolvability

getL