Gaussian_Elimination.h File Reference

Gaussian elimination implementation. More...

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Defines
#define	Gaussian_Elimination_h
#define	English_dox   "Doxygen English documentation"
	Doxygen English documentation.
Functions
template<class E >
E	abs (const E &r)
	Returns the absolute value for r.
template<class Matrix >
Matrix::value_type	Gaussian_Elimination (const Matrix &M, Matrix &X, const Matrix &B)
	Gaussianan Elimination.

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Detailed Description

Gaussian elimination implementation.

Author:

Adolfo Di Mare adolf.nosp@m.o@di.nosp@m.-mare.nosp@m..com

Date:

2009

Definition in file Gaussian_Elimination.h.

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Define Documentation

#define Gaussian_Elimination_h

Definition at line 17 of file Gaussian_Elimination.h.

#define English_dox   "Doxygen English documentation"

Doxygen English documentation.

---

Function Documentation

template<class E >

template< class E > inline E abs

(

const E &

r

)

[inline]

Returns the absolute value for r.

Definition at line 35 of file Gaussian_Elimination.h.

template<class Matrix >

template< class Matrix > typename Matrix::value_type Gaussian_Elimination	(	const Matrix &	M,
		Matrix &	X,
		const Matrix &	B
	)

Gaussianan Elimination.

• Solves a system of "n" linear equations with "n" unknowns ussign "Gaussianan Elimination".
• The system has the matricial form MxX = B:

        M0,0    M1,0    M2,0    ....  Mn-1,0  ==   B0,0
        M0,1    M1,1    M2,1    ....  Mn-1,1  ==   B0,1
        M0,2    M1,2    M2,2    ....  Mn-1,2  ==   B0,2
        :       :       :             :            :
        :       :       :             :            :
        M0,n-1  M1,n-1  M2,n-1  ....  Mn-1,n-1 ==  B0,n-1
  

• If matrix "M" is not singular, Gaussian_Elimination() returns its determinant.
  • If matrix "M" is singular, Gaussian_Elimination() returns 0 (cero).
  • The calculated result is returned as the value of vector "X".

Acknowledgments

Adapted from Internet code written by:

• Paul Bourke, 1997
  • http://astronomy.swin.edu.au/pbourke/analysis/gausselim/
  • http://www.gilsinan.com/thesis/gaussian.c
• Jim Gilsinan IV
  • http://www.fas.harvard.edu/~gilsinan/

Definition at line 41 of file Gaussian_Elimination.h.