Package org.apache.commons.math3.linear

Interface FieldDecompositionSolver<T extends FieldElement<T>>

Type Parameters:
T - the type of the field elements
public interface FieldDecompositionSolver<T extends FieldElement<T>>
Interface handling decomposition algorithms that can solve A × X = B.

Decomposition algorithms decompose an A matrix has a product of several specific matrices from which they can solve A × X = B in least squares sense: they find X such that ||A × X - B|| is minimal.

Some solvers like FieldLUDecomposition can only find the solution for square matrices and when the solution is an exact linear solution, i.e. when ||A × X - B|| is exactly 0. Other solvers can also find solutions with non-square matrix A and with non-null minimal norm. If an exact linear solution exists it is also the minimal norm solution.

Since:
2.0

  • Method Details

    • solve

      FieldVector<T> solve(FieldVector<T> b)
      Solve the linear equation A × X = B for matrices A.

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

      Parameters:
      b - right-hand side of the equation A × X = B
      Returns:
      a vector X that minimizes the two norm of A × X - B
      Throws:
      DimensionMismatchException - if the matrices dimensions do not match.
      SingularMatrixException - if the decomposed matrix is singular.

    • solve

      FieldMatrix<T> solve(FieldMatrix<T> b)
      Solve the linear equation A × X = B for matrices A.

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

      Parameters:
      b - right-hand side of the equation A × X = B
      Returns:
      a matrix X that minimizes the two norm of A × X - B
      Throws:
      DimensionMismatchException - if the matrices dimensions do not match.
      SingularMatrixException - if the decomposed matrix is singular.

    • isNonSingular

      boolean isNonSingular()
      Check if the decomposed matrix is non-singular.
      Returns:
      true if the decomposed matrix is non-singular

    • getInverse

      FieldMatrix<T> getInverse()
      Get the inverse (or pseudo-inverse) of the decomposed matrix.
      Returns:
      inverse matrix
      Throws:
      SingularMatrixException - if the decomposed matrix is singular.