Package edu.jas.jlinalg
Class GaussElimination<C extends edu.jas.structure.RingElem<C>>
- java.lang.Object
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- edu.jas.jlinalg.GaussElimination<C>
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- 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
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Constructor Summary
Constructors Constructor Description GaussElimination()
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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.
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Constructor Detail
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GaussElimination
public GaussElimination()
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Method Detail
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solve
public 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.- Parameters:
a
- matrixb
- vector of right hand side- Returns:
- a solution vector x
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nullSpace
public 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.- Parameters:
a
- matrix- Returns:
- matrix of generating system of solution vectors x
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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
- matrixn
- matrix- Returns:
- true, if n is a nullspace of a, else false
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characteristicPolynomial
public edu.jas.poly.GenPolynomial<C> characteristicPolynomial(edu.jas.vector.GenMatrix<C> a)
Characteristic polynomial of a matrix.- Parameters:
a
- matrix- Returns:
- characteristic polynomial of a
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determinant
public C determinant(edu.jas.vector.GenMatrix<C> a)
Determinant of a matrix.- Parameters:
a
- matrix- Returns:
- determinant of a
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trace
public C trace(edu.jas.vector.GenMatrix<C> a)
Trace of a matrix.- Parameters:
a
- matrix- Returns:
- trace of a
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rank
public int rank(edu.jas.vector.GenMatrix<C> a)
Rank of a matrix.- Parameters:
a
- matrix- Returns:
- rank of a
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gaussElimination
public edu.jas.vector.GenMatrix<C> gaussElimination(edu.jas.vector.GenMatrix<C> a)
Gauss elimination of a matrix.- Parameters:
a
- matrix- Returns:
- Gauss elimination of a
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gaussJordanElimination
public edu.jas.vector.GenMatrix<C> gaussJordanElimination(edu.jas.vector.GenMatrix<C> a)
Gauss-Jordan elimination of a matrix.- Parameters:
a
- matrix- Returns:
- Gauss-Jordan elimination of a
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