SolvePseudoInverseSvd
org.ejml.alg.dense.linsol.svd

Class SolvePseudoInverseSvd

  • All Implemented Interfaces:
    LinearSolver<DenseMatrix64F>


    public class SolvePseudoInverseSvdextends Objectimplements LinearSolver<DenseMatrix64F>

    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 Detail

      • SolvePseudoInverseSvd

        public SolvePseudoInverseSvd(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

        public SolvePseudoInverseSvd()
        Creates a solver targeted at matrices around 100x100
    • Method Detail

      • setA

        public boolean setA(DenseMatrix64F 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<DenseMatrix64F>
        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<DenseMatrix64F>
        Returns:
        The quality of the linear system.
      • solve

        public void solve(DenseMatrix64F b,         DenseMatrix64F 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<DenseMatrix64F>
        Parameters:
        b - A matrix ℜ m × p. Might be modified.
        x - A matrix ℜ n × p, where the solution is written to. Modified.

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