Class RRQRDecomposition.Solver

java.lang.Object
org.apache.commons.math3.linear.RRQRDecomposition.Solver
All Implemented Interfaces:
DecompositionSolver
Enclosing class:
RRQRDecomposition
private static class RRQRDecomposition.Solver extends Object implements DecompositionSolver
Specialized solver.
Since:
3.2

  • Field Details

    • upper

      private final DecompositionSolver upper
      Upper level solver.

    • p

      private RealMatrix p
      A permutation matrix for the pivots used in the QR decomposition

  • Constructor Details

    • Solver

      private Solver(DecompositionSolver upper, RealMatrix p)
      Build a solver from decomposed matrix.
      Parameters:
      upper - upper level solver.
      p - permutation matrix

  • Method Details

    • isNonSingular

      public boolean isNonSingular()
      Check if the decomposed matrix is non-singular.
      Specified by:
      isNonSingular in interface DecompositionSolver
      Returns:
      true if the decomposed matrix is non-singular.

    • solve

      public RealVector solve(RealVector b)
      Solve the linear equation A × X = B for matrices A.

      The A matrix is implicit, it is provided by the underlying decomposition algorithm.

      Specified by:
      solve in interface DecompositionSolver
      Parameters:
      b - right-hand side of the equation A × X = B
      Returns:
      a vector X that minimizes the two norm of A × X - B

    • solve

      public RealMatrix solve(RealMatrix b)
      Solve the linear equation A × X = B for matrices A.

      The A matrix is implicit, it is provided by the underlying decomposition algorithm.

      Specified by:
      solve in interface DecompositionSolver
      Parameters:
      b - right-hand side of the equation A × X = B
      Returns:
      a matrix X that minimizes the two norm of A × X - B

    • getInverse

      public RealMatrix getInverse()
      Get the pseudo-inverse of the decomposed matrix.

      This is equal to the inverse of the decomposed matrix, if such an inverse exists.

      If no such inverse exists, then the result has properties that resemble that of an inverse.

      In particular, in this case, if the decomposed matrix is A, then the system of equations \( A x = b \) may have no solutions, or many. If it has no solutions, then the pseudo-inverse \( A^+ \) gives the "closest" solution \( z = A^+ b \), meaning \( \left \| A z - b \right \|_2 \) is minimized. If there are many solutions, then \( z = A^+ b \) is the smallest solution, meaning \( \left \| z \right \|_2 \) is minimized.

      Note however that some decompositions cannot compute a pseudo-inverse for all matrices. For example, the LUDecomposition is not defined for non-square matrices to begin with. The QRDecomposition can operate on non-square matrices, but will throw SingularMatrixException if the decomposed matrix is singular. Refer to the javadoc of specific decomposition implementations for more details.

      Specified by:
      getInverse in interface DecompositionSolver
      Returns:
      pseudo-inverse matrix (which is the inverse, if it exists), if the decomposition can pseudo-invert the decomposed matrix
      Throws:
      SingularMatrixException - if the decomposed matrix is singular.