Package org.ejml.dense.row.linsol.qr

Class BaseLinearSolverQrp_FDRM

java.lang.Object
org.ejml.dense.row.linsol.LinearSolverAbstract_FDRM
org.ejml.dense.row.linsol.qr.BaseLinearSolverQrp_FDRM
All Implemented Interfaces:
org.ejml.interfaces.linsol.LinearSolver<org.ejml.data.FMatrixRMaj,org.ejml.data.FMatrixRMaj>, org.ejml.interfaces.linsol.LinearSolverDense<org.ejml.data.FMatrixRMaj>
Direct Known Subclasses:
LinearSolverQrpHouseCol_FDRM, SolvePseudoInverseQrp_FDRM
@Generated("org.ejml.dense.row.linsol.qr.BaseLinearSolverQrp_DDRM") public abstract class BaseLinearSolverQrp_FDRM extends LinearSolverAbstract_FDRM

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.FMatrixRMaj
    I
     
    protected org.ejml.interfaces.linsol.LinearSolverDense<org.ejml.data.FMatrixRMaj>
    internalSolver
     
    protected boolean
    norm2Solution
     
    protected org.ejml.data.FMatrixRMaj
    R
     
    protected org.ejml.data.FMatrixRMaj
    R11
     
    protected int
    rank
     
    protected org.ejml.data.FMatrixRMaj
    Y
     

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

    A, numCols, numRows

  • Constructor Summary

    Constructors
    Modifier
    Constructor
    Description
    protected
    BaseLinearSolverQrp_FDRM(org.ejml.interfaces.decomposition.QRPDecomposition_F32<org.ejml.data.FMatrixRMaj> decomposition, boolean norm2Solution)
    Configures internal parameters.

  • Method Summary

    Modifier and Type
    Method
    Description
    org.ejml.interfaces.decomposition.QRPDecomposition_F32<org.ejml.data.FMatrixRMaj>
    getDecomposition()
     
    void
    invert(org.ejml.data.FMatrixRMaj A_inv)
     
    double
    quality()
     
    boolean
    setA(org.ejml.data.FMatrixRMaj A)
     
    protected void
    upgradeSolution(org.ejml.data.FMatrixRMaj X)
    Upgrades the basic solution to the optimal 2-norm solution.

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

    _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.FMatrixRMaj Y

    • R

      protected org.ejml.data.FMatrixRMaj R

    • R11

      protected org.ejml.data.FMatrixRMaj R11

    • I

      protected org.ejml.data.FMatrixRMaj I

    • rank

      protected int rank

    • internalSolver

      protected org.ejml.interfaces.linsol.LinearSolverDense<org.ejml.data.FMatrixRMaj> internalSolver

  • Constructor Details

    • BaseLinearSolverQrp_FDRM

      protected BaseLinearSolverQrp_FDRM(org.ejml.interfaces.decomposition.QRPDecomposition_F32<org.ejml.data.FMatrixRMaj> 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.FMatrixRMaj A)

    • quality

      public double quality()

    • upgradeSolution

      protected void upgradeSolution(org.ejml.data.FMatrixRMaj 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.FMatrixRMaj A_inv)
      Specified by:
      invert in interface org.ejml.interfaces.linsol.LinearSolverDense<org.ejml.data.FMatrixRMaj>
      Overrides:
      invert in class LinearSolverAbstract_FDRM

    • getDecomposition

      public org.ejml.interfaces.decomposition.QRPDecomposition_F32<org.ejml.data.FMatrixRMaj> getDecomposition()