Class QRDecomposition.Solver

java.lang.Object
org.apache.commons.math3.linear.QRDecomposition.Solver
All Implemented Interfaces:
DecompositionSolver
Enclosing class:
QRDecomposition
private static class QRDecomposition.Solver extends Object implements DecompositionSolver
Specialized solver.
Since:
1.2 (changed to concrete class in 3.0)

  • Field Details

    • qrt

      private final double[][] qrt
      A packed TRANSPOSED representation of the QR decomposition.

      The elements BELOW the diagonal are the elements of the UPPER triangular matrix R, and the rows ABOVE the diagonal are the Householder reflector vectors from which an explicit form of Q can be recomputed if desired.

    • rDiag

      private final double[] rDiag
      The diagonal elements of R.

    • threshold

      private final double threshold
      Singularity threshold.

  • Constructor Details

    • Solver

      private Solver(double[][] qrt, double[] rDiag, double threshold)
      Build a solver from decomposed matrix.
      Parameters:
      qrt - Packed TRANSPOSED representation of the QR decomposition.
      rDiag - Diagonal elements of R.
      threshold - Singularity threshold.

  • 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.