Class RealBackSolver

java.lang.Object
org.flag4j.linalg.solvers.exact.triangular.BackSolver<Matrix,Vector,double[]>
org.flag4j.linalg.solvers.exact.triangular.RealBackSolver
All Implemented Interfaces:
LinearMatrixSolver<Matrix,Vector>, LinearSolver<Matrix>
public class RealBackSolver extends BackSolver<Matrix,Vector,double[]>
This solver solves linear systems of the form \( Ux = b \) or \( UX = B \) where \( U \) is an upper triangular matrix. This system is solved in an exact sense.
See Also:

  • Field Details

    • det

      protected double det
      For computing determinant of coefficient matrix during solve.

  • Constructor Details

    • RealBackSolver

      public RealBackSolver()
      Creates a solver for solving linear systems for upper triangular coefficient matrices. By default, an explicit check will be made that the coefficient matrix is upper triangular. To toggle this, use RealBackSolver(boolean).

    • RealBackSolver

      public RealBackSolver(boolean enforceTriU)
      Creates a solver for solving linear systems for upper triangular coefficient matrices.
      Parameters:
      enforceTriU - Flag indicating if an explicit check should be made that the coefficient matrix is upper triangular.

  • Method Details

    • setCheckSingular

      public RealBackSolver setCheckSingular(boolean checkSingular)
      Sets a flag indicating if an explicit check should be made that the coefficient matrix is singular.
      Overrides:
      setCheckSingular in class BackSolver<Matrix,Vector,double[]>
      Parameters:
      checkSingular - Flag indicating if an explicit check should be made that the matrix is singular (or near singular).
      • If true, an explicit singularity check will be made.
      • If false, no check will be made.
      Returns:
      A reference to this back solver instance.

    • getDet

      public double getDet()
      Gets the determinant computed during the last solve.

    • solve

      public Vector solve(Matrix U, Vector b)
      Solves the linear system of equations given by \( Ux = b \) where the coefficient matrix \( U \) is an upper triangular matrix.
      Parameters:
      U - Upper triangular coefficient matrix in the linear system. If enforceTriU was set to false when this solver instance was created and U is not actually upper triangular, it will be treated as if it were.
      b - Vector of constants in the linear system.
      Returns:
      The solution to x in the linear system \( Ux = b \).
      Throws:
      SingularMatrixException - If the matrix U is singular (i.e. has a zero on the principle diagonal).

    • solve

      public Matrix solve(Matrix U, Matrix B)
      Solves the linear system of equations given by \( UX = B \) where the coefficient matrix \( U \) is an upper triangular matrix.
      Parameters:
      U - Upper triangular coefficient matrix in the linear system. If enforceTriU was set to false when this solver instance was created and U is not actually upper triangular, it will be treated as if it were.
      B - Matrix of constants in the linear system.
      Returns:
      The solution to X in the linear system \( UX = B \).
      Throws:
      SingularMatrixException - If the matrix U is singular (i.e. has a zero on the principle diagonal).

    • solveIdentity

      public Matrix solveIdentity(Matrix U)
      Solves the linear system of equations given by \( UX = I \) where the coefficient matrix \( U \) is an upper triangular matrix and I is the identity matrix of appropriate size. This essentially inverts the upper triangular matrix since \( UU^{-1} = I \).
      Parameters:
      U - Upper triangular coefficient matrix in the linear system. If enforceTriU was set to false when this solver instance was created and U is not actually upper triangular, it will be treated as if it were.
      Returns:
      The solution to X in the linear system \( UX = B \).
      Throws:
      SingularMatrixException - If the matrix U is singular (i.e. has a zero on the principle diagonal).

    • solveLower

      public Matrix solveLower(Matrix U, Matrix L)
      Solves a special case of the linear system \( UX = L \) for \( X \) where the coefficient matrix \( U \) is an upper triangular matrix and the constant matrix \( L \) is lower triangular.
      Parameters:
      U - Upper triangular coefficient matrix in the linear system. If enforceTriU was set to false when this solver instance was created and U is not actually upper triangular, it will be treated as if it were.
      L - Lower triangular constant matrix. This is not explicit checked. If L is not lower triangular, values above the principle diagonal will be ignored and the result will still be correctly computed.
      Returns:
      The result of solving the linear system \( UX = L \) for the matrix \( X \).