java.lang.Object

org.ejml.dense.row.linsol.LinearSolverAbstract_DDRM

org.ejml.dense.row.linsol.qr.BaseLinearSolverQrp_DDRM

All Implemented Interfaces:: org.ejml.interfaces.linsol.LinearSolver<org.ejml.data.DMatrixRMaj,org.ejml.data.DMatrixRMaj>, org.ejml.interfaces.linsol.LinearSolverDense<org.ejml.data.DMatrixRMaj>

Direct Known Subclasses:: LinearSolverQrpHouseCol_DDRM, SolvePseudoInverseQrp_DDRM

public abstract class BaseLinearSolverQrp_DDRM
extends LinearSolverAbstract_DDRM

Base class for QR pivot based pseudo inverse classes. It will return either the basic of minimal 2-norm solution. See [1] for details. The minimal 2-norm solution refers to the solution 'x' whose 2-norm is the smallest making it unique, not some other error function.

 R = [ R12  R12 ] r      P^T*x = [ y ] r       Q^T*b = [ c ] r
     [  0    0  ] m-r            [ z ] n -r            [ d ] m-r
        r   n-r

 where r is the rank of the matrix and (m,n) is the dimension of the linear system.

 The solution 'x' is found by solving the system below.  The basic solution is found by setting z=0

     [ R_11^-1*(c - R12*z) ]
 x = [          z          ]

NOTE: The matrix rank is determined using the provided QR decomposition. [1] mentions that this will not always work and could cause some problems.

[1] See page 258-259 in Gene H. Golub and Charles F. Van Loan "Matrix Computations" 3rd Ed, 1996

Field Summary

Fields
Modifier and Type	Field	Description
`protected org.ejml.data.DMatrixRMaj`	`I`
`protected org.ejml.interfaces.linsol.LinearSolverDense<org.ejml.data.DMatrixRMaj>`	`internalSolver`
`protected boolean`	`norm2Solution`
`protected org.ejml.data.DMatrixRMaj`	`R`
`protected org.ejml.data.DMatrixRMaj`	`R11`
`protected int`	`rank`
`protected org.ejml.data.DMatrixRMaj`	`Y`

Fields inherited from class org.ejml.dense.row.linsol.LinearSolverAbstract_DDRM

A, numCols, numRows

Constructor Summary

Constructors
Modifier	Constructor	Description
`protected`	`BaseLinearSolverQrp_DDRM(org.ejml.interfaces.decomposition.QRPDecomposition_F64<org.ejml.data.DMatrixRMaj> decomposition, boolean norm2Solution)`	Configures internal parameters.

Method Summary

Modifier and Type	Method	Description
`org.ejml.interfaces.decomposition.QRPDecomposition_F64<org.ejml.data.DMatrixRMaj>`	`getDecomposition()`
`void`	`invert(org.ejml.data.DMatrixRMaj A_inv)`
`double`	`quality()`
`boolean`	`setA(org.ejml.data.DMatrixRMaj A)`
`protected void`	`upgradeSolution(org.ejml.data.DMatrixRMaj X)`	Upgrades the basic solution to the optimal 2-norm solution.

Methods inherited from class org.ejml.dense.row.linsol.LinearSolverAbstract_DDRM

_setA, getA

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface org.ejml.interfaces.linsol.LinearSolver

modifiesA, modifiesB, solve

Field Details
- norm2Solution
  
  protected boolean norm2Solution
- Y
  
  protected org.ejml.data.DMatrixRMaj Y
- R
  
  protected org.ejml.data.DMatrixRMaj R
- R11
  
  protected org.ejml.data.DMatrixRMaj R11
- I
  
  protected org.ejml.data.DMatrixRMaj I
- rank
  
  protected int rank
- internalSolver
  
  protected org.ejml.interfaces.linsol.LinearSolverDense<org.ejml.data.DMatrixRMaj> internalSolver
Constructor Details
- BaseLinearSolverQrp_DDRM
  
  protected BaseLinearSolverQrp_DDRM(org.ejml.interfaces.decomposition.QRPDecomposition_F64<org.ejml.data.DMatrixRMaj> decomposition, boolean norm2Solution)
  
  Configures internal parameters.
  
  Parameters:
  
  decomposition - Used to solve the linear system.
  
  norm2Solution - If true then the optimal 2-norm solution will be computed for degenerate systems.
Method Details
- setA
  
  public boolean setA(org.ejml.data.DMatrixRMaj A)
- quality
  
  public double quality()
- upgradeSolution
  
  protected void upgradeSolution(org.ejml.data.DMatrixRMaj X)
  Upgrades the basic solution to the optimal 2-norm solution.
  
  First solves for 'z' || x_b - P*[ R_11^-1 * R_12 ] * z ||2 min z || [ - I_{n-r} ] ||
  Parameters:
  
  X - basic solution, also output solution
- invert
  
  public void invert(org.ejml.data.DMatrixRMaj A_inv)
  
  Specified by:
  
  invert in interface org.ejml.interfaces.linsol.LinearSolverDense<org.ejml.data.DMatrixRMaj>
  
  Overrides:
  
  invert in class LinearSolverAbstract_DDRM
- getDecomposition
  
  public org.ejml.interfaces.decomposition.QRPDecomposition_F64<org.ejml.data.DMatrixRMaj> getDecomposition()

Class BaseLinearSolverQrp_DDRM