Package org.ejml.dense.row.linsol.svd

Class SolvePseudoInverseSvd_DDRM

java.lang.Object
org.ejml.dense.row.linsol.svd.SolvePseudoInverseSvd_DDRM
All Implemented Interfaces:
LinearSolver<DMatrixRMaj,DMatrixRMaj>, LinearSolverDense<DMatrixRMaj>
public class SolvePseudoInverseSvd_DDRM extends Object implements LinearSolverDense<DMatrixRMaj>

The pseudo-inverse is typically used to solve over determined system for which there is no unique solution.
x=inv(ATA)ATb
where A ∈ ℜ m × n and m ≥ n.

This class implements the Moore-Penrose pseudo-inverse using SVD and should never fail. Alternative implementations can use Cholesky decomposition, but those will fail if the ATA matrix is singular. However the Cholesky implementation is much faster.

  • Constructor Details

    • SolvePseudoInverseSvd_DDRM

      public SolvePseudoInverseSvd_DDRM(int maxRows, int maxCols)
      Creates a new solver targeted at the specified matrix size.
      Parameters:
      maxRows - The expected largest matrix it might have to process. Can be larger.
      maxCols - The expected largest matrix it might have to process. Can be larger.

    • SolvePseudoInverseSvd_DDRM

      public SolvePseudoInverseSvd_DDRM()
      Creates a solver targeted at matrices around 100x100

  • 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.

      Specified by:
      setA in interface LinearSolver<DMatrixRMaj,DMatrixRMaj>
      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.

      Specified by:
      quality in interface LinearSolver<DMatrixRMaj,DMatrixRMaj>
      Returns:
      The quality of the linear system.

    • solve

      public void solve(DMatrixRMaj b, DMatrixRMaj x)
      Description copied from interface: LinearSolver

      Solves for X in the linear system, A*X=B.

      In some implementations 'B' and 'X' can be the same instance of a variable. Call LinearSolver.modifiesB() to determine if 'B' is modified.

      Specified by:
      solve in interface LinearSolver<DMatrixRMaj,DMatrixRMaj>
      Parameters:
      b - A matrix ℜ m × p. Might be modified.
      x - A matrix ℜ n × p, where the solution is written to. Modified.

    • 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>
      Parameters:
      A_inv - Where the inverted matrix saved. Modified.

    • modifiesA

      public boolean modifiesA()
      Description copied from interface: LinearSolver
      Returns true if the passed in matrix to LinearSolver.setA(Matrix) is modified.
      Specified by:
      modifiesA in interface LinearSolver<DMatrixRMaj,DMatrixRMaj>
      Returns:
      true if A is modified in setA().

    • modifiesB

      public boolean modifiesB()
      Description copied from interface: LinearSolver
      Returns true if the passed in 'B' matrix to LinearSolver.solve(Matrix, Matrix) is modified.
      Specified by:
      modifiesB in interface LinearSolver<DMatrixRMaj,DMatrixRMaj>
      Returns:
      true if B is modified in solve(B,X).

    • getDecomposition

      public SingularValueDecomposition_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.
      Specified by:
      getDecomposition in interface LinearSolver<DMatrixRMaj,DMatrixRMaj>
      Returns:
      Internal decomposition class. If there is none then null.

    • setThreshold

      public void setThreshold(double threshold)
      Specify the relative threshold used to select singular values. By default it's UtilEjml.EPS.
      Parameters:
      threshold - The singular value threshold

    • getDecomposer

      public SingularValueDecomposition<DMatrixRMaj> getDecomposer()