Package org.ejml.dense.row.linsol.qr

Class BaseLinearSolverQrp_DDRM

java.lang.Object
org.ejml.dense.row.linsol.LinearSolverAbstract_DDRM
org.ejml.dense.row.linsol.qr.BaseLinearSolverQrp_DDRM
All Implemented Interfaces:
LinearSolver<DMatrixRMaj,DMatrixRMaj>, LinearSolverDense<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 Details

  • Constructor Details

    • BaseLinearSolverQrp_DDRM

      protected BaseLinearSolverQrp_DDRM(QRPDecomposition_F64<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(DMatrixRMaj A)
      Description copied from interface: LinearSolver

      Specifies the A matrix in the linear equation. A reference might be saved and it might also be modified depending on the implementation. If it is modified then LinearSolver.modifiesA() will return true.

      If this value returns true that does not guarantee a valid solution was generated. This is because some decompositions don't detect singular matrices.

      Parameters:
      A - The 'A' matrix in the linear equation. Might be modified or save the reference.
      Returns:
      true if it can be processed.

    • quality

      public double quality()
      Description copied from interface: LinearSolver

      Returns a very quick to compute measure of how singular the system is. This measure will be invariant to the scale of the matrix and always be positive, with larger values indicating it is less singular. If not supported by the solver then the runtime exception IllegalArgumentException is thrown. This is NOT the matrix's condition.

      How this function is implemented is not specified. One possible implementation is the following: In many decompositions a triangular matrix is extracted. The determinant of a triangular matrix is easily computed and once normalized to be scale invariant and its absolute value taken it will provide functionality described above.

      Returns:
      The quality of the linear system.

    • upgradeSolution

      protected void upgradeSolution(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(DMatrixRMaj A_inv)
      Description copied from interface: LinearSolverDense
      Computes the inverse of of the 'A' matrix passed into LinearSolver.setA(Matrix) and writes the results to the provided matrix. If 'A_inv' needs to be different from 'A' is implementation dependent.
      Specified by:
      invert in interface LinearSolverDense<DMatrixRMaj>
      Overrides:
      invert in class LinearSolverAbstract_DDRM
      Parameters:
      A_inv - Where the inverted matrix saved. Modified.

    • getDecomposition

      public QRPDecomposition_F64<DMatrixRMaj> getDecomposition()
      Description copied from interface: LinearSolver
      If a decomposition class was used internally then this will return that class. Most linear solvers decompose the input matrix into a more simplistic form. However some solutions do not require decomposition, e.g. inverse by minor.
      Returns:
      Internal decomposition class. If there is none then null.