eigenv.c File Reference

Find eigenvalues and eigenvectors of matrix. More...

#include <stdio.h>
#include <string.h>
#include <math.h>
#include <assert.h>
#include "eigenv.h"

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Macros
#define	_MG_EPSD   1.e-13
#define	_MG_EPSD2   1.e-10
#define	_MG_EPS6   5.e-06
#define	_MG_EPS   1.e-06
#define	_MG_EPSX2   2.e-06
#define	MAXTOU   50
#define	egal(x, y)

Functions
static int	newton3 (double p[4], double x[3])
	Find root(s) of a polynomial of degree 3. More...
int	_MMG5_eigenv (int symmat, double *mat, double lambda[3], double v[3][3])
	Find eigenvalues and vectors of a 3x3 matrix. More...
int	_MMG5_eigen2 (double *mm, double *lambda, double vp[2][2])
	Find eigenvalues and vectors of a 2x2 matrix. More...
int	_MMG5_eigensym (double m[3], double lambda[2], double vp[2][2])

Variables
static double	Id [3][3]
	Identity matrix. More...

Detailed Description

Find eigenvalues and eigenvectors of matrix.

Author

Cécile Dobrzynski (Bx INP/Inria/UBordeaux)

Pascal Frey (UPMC)

Version

5

Copyright

GNU Lesser General Public License.

Find eigenvalues and eigenvectors of 2x2 or 3x3 symetric definite positive matrix.

Macro Definition Documentation

_MG_EPS

#define _MG_EPS   1.e-06

_MG_EPS6

#define _MG_EPS6   5.e-06

_MG_EPSD

#define _MG_EPSD   1.e-13

_MG_EPSD2

#define _MG_EPSD2   1.e-10

_MG_EPSX2

#define _MG_EPSX2   2.e-06

egal

#define egal	(		x,
			y
	)

Value:

(                                             \
    (  ((x) == 0.0f) ? (fabs(y) < _MG_EPS) :                      \
       ( ((y) == 0.0f) ? (fabs(x) < _MG_EPS) :                    \
         (fabs((x)-(y)) / (fabs(x) + fabs(y)) < _MG_EPSX2) )  ) )

Check if numbers x and y are equal.

MAXTOU

#define MAXTOU   50

Function Documentation

_MMG5_eigen2()

int _MMG5_eigen2	(	double *	mm,
		double *	lambda,
		double	vp[2][2]
	)

Find eigenvalues and vectors of a 2x2 matrix.

Parameters

mm	pointer toward the matrix.
lambda	pointer toward the output eigenvalues.
vp	eigenvectors.

Returns

1.

Warning

not used for now

_MMG5_eigensym()

int _MMG5_eigensym ( double  m[3], double  lambda[2], double  vp[2][2]  )

inline

Parameters

m	terms of symetric matrix .
lambda	eigenvalues of m.
vp	eigenvectors of m.

Returns

order of the eigenvalues.

Compute eigenelements of a symetric matrix m. Eigenvectors are orthogonal.

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_MMG5_eigenv()

int _MMG5_eigenv	(	int	symmat,
		double *	mat,
		double	lambda[3],
		double	v[3][3]
	)

Find eigenvalues and vectors of a 3x3 matrix.

Parameters

symmat	0 if matrix is not symetric, 1 otherwise.
mat	pointer toward the matrix.
lambda	eigenvalues.
v	eigenvectors.

Returns

order of eigenvalues (1,2,3) or 0 if failed.

Remarks

the i^{th} eigenvector is stored in v[i][.].

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newton3()

static int newton3 ( double  p[4], double  x[3]  )

static

Find root(s) of a polynomial of degree 3.

Parameters

p	polynomial coefficients (b=p[2], c=p[1], d=p[0]).
x	root(s) of polynomial.

Returns

0 if no roots.

1 for 3 roots.

2 for 2 roots.

3 for 1 root.

Find root(s) of a polynomial of degree 3: .

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Variable Documentation

Id

double Id[3][3]

static

Initial value:

= {
  {1.0, 0.0, 0.0},
  {0.0, 1.0, 0.0},
  {0.0, 0.0, 1.0} }

Identity matrix.