Class GaussElimination<C extends edu.jas.structure.RingElem<C>>

  • Type Parameters:
    C - coefficient ring element type

    public class GaussElimination<C extends edu.jas.structure.RingElem<C>>
    extends java.lang.Object
    Algorithms related to Gaussian elimination. Conversion to JLinAlg classes and delegation to JLinAlg algorithms.
    Author:
    Heinz Kredel
    • Method Summary

      All Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      edu.jas.poly.GenPolynomial<C> characteristicPolynomial​(edu.jas.vector.GenMatrix<C> a)
      Characteristic polynomial of a matrix.
      C determinant​(edu.jas.vector.GenMatrix<C> a)
      Determinant of a matrix.
      edu.jas.vector.GenMatrix<C> gaussElimination​(edu.jas.vector.GenMatrix<C> a)
      Gauss elimination of a matrix.
      edu.jas.vector.GenMatrix<C> gaussJordanElimination​(edu.jas.vector.GenMatrix<C> a)
      Gauss-Jordan elimination of a matrix.
      edu.jas.vector.GenMatrix<C> inverse​(edu.jas.vector.GenMatrix<C> a)
      Inverse of a matrix.
      boolean isNullSpace​(edu.jas.vector.GenMatrix<C> a, edu.jas.vector.GenMatrix<C> n)
      Test if n is a null space for the linear system: a n = 0.
      edu.jas.vector.GenMatrix<C> nullSpace​(edu.jas.vector.GenMatrix<C> a)
      Null space, generating system of solutions of a linear system: a x = 0.
      int rank​(edu.jas.vector.GenMatrix<C> a)
      Rank of a matrix.
      edu.jas.vector.GenVector<C> solve​(edu.jas.vector.GenMatrix<C> a, edu.jas.vector.GenVector<C> b)
      Solve a linear system: a x = b.
      C trace​(edu.jas.vector.GenMatrix<C> a)
      Trace of a matrix.
      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
    • Method Detail

      • solve

        public edu.jas.vector.GenVector<Csolve​(edu.jas.vector.GenMatrix<C> a,
                                                 edu.jas.vector.GenVector<C> b)
        Solve a linear system: a x = b.
        Parameters:
        a - matrix
        b - vector of right hand side
        Returns:
        a solution vector x
      • nullSpace

        public edu.jas.vector.GenMatrix<CnullSpace​(edu.jas.vector.GenMatrix<C> a)
        Null space, generating system of solutions of a linear system: a x = 0.
        Parameters:
        a - matrix
        Returns:
        matrix of generating system of solution vectors x
      • isNullSpace

        public boolean isNullSpace​(edu.jas.vector.GenMatrix<C> a,
                                   edu.jas.vector.GenMatrix<C> n)
        Test if n is a null space for the linear system: a n = 0.
        Parameters:
        a - matrix
        n - matrix
        Returns:
        true, if n is a nullspace of a, else false
      • characteristicPolynomial

        public edu.jas.poly.GenPolynomial<CcharacteristicPolynomial​(edu.jas.vector.GenMatrix<C> a)
        Characteristic polynomial of a matrix.
        Parameters:
        a - matrix
        Returns:
        characteristic polynomial of a
      • determinant

        public C determinant​(edu.jas.vector.GenMatrix<C> a)
        Determinant of a matrix.
        Parameters:
        a - matrix
        Returns:
        determinant of a
      • trace

        public C trace​(edu.jas.vector.GenMatrix<C> a)
        Trace of a matrix.
        Parameters:
        a - matrix
        Returns:
        trace of a
      • rank

        public int rank​(edu.jas.vector.GenMatrix<C> a)
        Rank of a matrix.
        Parameters:
        a - matrix
        Returns:
        rank of a
      • gaussElimination

        public edu.jas.vector.GenMatrix<CgaussElimination​(edu.jas.vector.GenMatrix<C> a)
        Gauss elimination of a matrix.
        Parameters:
        a - matrix
        Returns:
        Gauss elimination of a
      • gaussJordanElimination

        public edu.jas.vector.GenMatrix<CgaussJordanElimination​(edu.jas.vector.GenMatrix<C> a)
        Gauss-Jordan elimination of a matrix.
        Parameters:
        a - matrix
        Returns:
        Gauss-Jordan elimination of a
      • inverse

        public edu.jas.vector.GenMatrix<Cinverse​(edu.jas.vector.GenMatrix<C> a)
        Inverse of a matrix.
        Parameters:
        a - matrix
        Returns:
        inverse matrix of a