#include <Metric.h>

Public Member Functions
	Metric ()

	Metric (const EigenMetric &)

	Metric (double a)

	Metric (double a, double b, double c)

	Metric (double a, const Metric ma, double b, const Metric mb)

	Metric (const double a[3], const Metric m0, const Metric m1, const Metric m2)

void	Echo ()

double	det () const

int	IntersectWith (const Metric &M2)

void	Box (double &hx, double &hy) const

R2	Orthogonal (const R2 x)

R2	Orthogonal (const I2 x)

double	Length (double Ax, double Ay) const

Metric	operator* (double c) const

Metric	operator/ (double c) const

	operator D2xD2 ()

double	operator() (R2 x, R2 y) const

Data Fields
double	a11

double	a21

double	a22

Friends
class	EigenMetric

Detailed Description

Definition at line 17 of file Metric.h.

Constructor & Destructor Documentation

◆ Metric() [1/6]

bamg::Metric::Metric ( )

inline

Definition at line 28 of file Metric.h.

28 :a11(0),a21(0),a22(0){};

◆ Metric() [2/6]

bamg::Metric::Metric ( const EigenMetric & M )

inline

Definition at line 115 of file Metric.h.

                                              {
       double v00=M.vx*M.vx;
       double v11=M.vy*M.vy;
       double v01=M.vx*M.vy;
       a11=v00*M.lambda1+v11*M.lambda2;
       a21=v01*(M.lambda1-M.lambda2);
       a22=v00*M.lambda2+v11*M.lambda1;
    }

◆ Metric() [3/6]

bamg::Metric::Metric ( double a )

Definition at line 15 of file Metric.cpp.

                          {/*{{{*/
  
       /*Isotropic metric for a length of a as unit*/
       this->a11 = 1./(a*a);
       this->a21 = 0.;
       this->a22 = 1./(a*a);
  
    }/*}}}*/

◆ Metric() [4/6]

bamg::Metric::Metric	(	double	a,
		double	b,
		double	c
	)

Definition at line 23 of file Metric.cpp.

                                                           {/*{{{*/
  
       this->a11 = a11_in;
       this->a21 = a21_in;
       this->a22 = a22_in;
  
    }/*}}}*/

◆ Metric() [5/6]

bamg::Metric::Metric	(	double	a,
		const Metric	ma,
		double	b,
		const Metric	mb
	)

Definition at line 59 of file Metric.cpp.

                                                                      { /*{{{*/
  
       /*Compute metric (linear combination of ma and mb)*/
       Metric mab(a*ma.a11+b*mb.a11,a*ma.a21+b*mb.a21,a*ma.a22+b*mb.a22);
  
       /*Get Eigen values and vectors*/
       EigenMetric vab(mab);
       double v1x = + vab.vx;
       double v1y = + vab.vy;
       double v2x = - vab.vy;
       double v2y = + vab.vx;
  
       /*Modify eigen values (a+b=1)*/
       double h1 = a/ma.Length(v1x,v1y) + b/mb.Length(v1x,v1y);
       double h2 = a/ma.Length(v2x,v2y) + b/mb.Length(v2x,v2y);
       vab.lambda1 =  1./(h1*h1);
       vab.lambda2 =  1./(h2*h2);
  
       /*Build metric from vab*/
       double v00=vab.vx*vab.vx;
       double v11=vab.vy*vab.vy;
       double v01=vab.vx*vab.vy;
       this->a11=v00*vab.lambda1+v11*vab.lambda2;
       this->a21=v01*(vab.lambda1-vab.lambda2);
       this->a22=v00*vab.lambda2+v11*vab.lambda1;
    }

◆ Metric() [6/6]

bamg::Metric::Metric	(	const double	a[3],
		const Metric	m0,
		const Metric	m1,
		const Metric	m2
	)

Definition at line 30 of file Metric.cpp.

                                                                                     {/*{{{*/
  
       /*Create metric using 3 inputs*/
       Metric mab(a[0]*m0.a11 + a[1]*m1.a11 + a[2]*m2.a11,
                a[0]*m0.a21 + a[1]*m1.a21 + a[2]*m2.a21,
                a[0]*m0.a22 + a[1]*m1.a22 + a[2]*m2.a22);
  
       /*Convert to eigen metric*/
       EigenMetric vab(mab);
       double v1x = + vab.vx;
       double v1y = + vab.vy;
       double v2x = - vab.vy;
       double v2y = + vab.vx;
  
       double h1=a[0] / m0.Length(v1x,v1y) + a[1] / m1.Length(v1x,v1y) + a[2] / m2.Length(v1x,v1y);
       double h2=a[0] / m0.Length(v2x,v2y) + a[1] / m1.Length(v2x,v2y) + a[2] / m2.Length(v2x,v2y);
  
       vab.lambda1 =  1. / (h1*h1);
       vab.lambda2 =  1. / (h2*h2);
  
       /*Build metric from vab*/
       double v00=vab.vx*vab.vx;
       double v11=vab.vy*vab.vy;
       double v01=vab.vx*vab.vy;
       this->a11=v00*vab.lambda1+v11*vab.lambda2;
       this->a21=v01*(vab.lambda1-vab.lambda2);
       this->a22=v00*vab.lambda2+v11*vab.lambda1;
  
    } /*}}}*/

Member Function Documentation

◆ Echo()

void bamg::Metric::Echo ( void )

Definition at line 91 of file Metric.cpp.

                         {/*{{{*/
  
       _printf_("Metric:\n");
       _printf_("   [a11 a21 a22]: [" << a11 << " " << a21 << " " << a22 << "]\n");
  
       return;
    }

◆ det()

double bamg::Metric::det ( ) const

Definition at line 88 of file Metric.cpp.

                             {/*{{{*/
       return a11*a22-a21*a21;
    }  /*}}}*/

◆ IntersectWith()

int bamg::Metric::IntersectWith ( const Metric & M2 )

Definition at line 99 of file Metric.cpp.

                                              {/*{{{*/
       /*Original code from Frederic Hecht <hecht@ann.jussieu.fr> (BAMG v1.01, Metric.cpp/IntersectWith)*/
  
       /*Get a new metric from an existing metric (M1=this)
        * and a new metric given in input M2 using a 
        * Simultaneous Matrix Reduction:
        * If M1 and M2 are 2 metrics, we must build N=M1^-1 M2 (Alauzet2003 p16) 
        * the eigen vectors of N form a matrix P
        * The new metric M = M1 inter M2 is then given by:
        *
        *      -T [ max(lambda1, mu1)          0         ]  -1            
        * M = P   [                                      ] P     
        *         [        0            max(lambda2, mu2)] 
        *
        * where lambdai and mui can be computed using Rayleigh formula: 
        *    lambdai = vi' M1 vi
        * with vi eigen vectors of N (columns of P)
        */
  
       int         change=0;
       Metric &M1=*this;
       D2xD2       P;
  
       //Get P, eigen vectors of N=inv(M1) M2
       SimultaneousMatrixReduction(*this,M2,P);
  
       //extract the eigen vectors of P (columns)
       R2 v1(P.x.x,P.y.x);
       R2 v2(P.x.y,P.y.y);
  
       //compute lambdai mui
       double lambda1=M1(v1,v1);
       double lambda2=M1(v2,v2);
       double mu1=M2(v1,v1);
       double mu2=M2(v2,v2);
  
       //check where any change needs to be done on M1
       if ( lambda1 < mu1 )  change=1,lambda1=mu1;
       if ( lambda2 < mu2 )  change=1,lambda2=mu2; 
  
       //update M1 if necessary
       if (change) {
          D2xD2 invP(P.inv());
          D2xD2 D(lambda1,0,0,lambda2); 
          D2xD2 M(invP.t()*D*invP);
          a11=M.x.x;
          a21=0.5*(M.x.y+M.y.x);
          a22=M.y.y;
       }
       return change;
    }

◆ Box()

void bamg::Metric::Box	(	double &	hx,
		double &	hy
	)		const

inline

Definition at line 123 of file Metric.h.

                                                          {
       double d=  a11*a22-a21*a21;
       hx = sqrt(a22/d);
       hy = sqrt(a11/d);
    }

◆ Orthogonal() [1/2]

R2 bamg::Metric::Orthogonal ( const R2 x )

inline

Definition at line 41 of file Metric.h.

41 { return R2(-(a21*x.x+a22*x.y),a11*x.x+a21*x.y); }

◆ Orthogonal() [2/2]

R2 bamg::Metric::Orthogonal ( const I2 x )

inline

Definition at line 42 of file Metric.h.

42 { return R2(-(a21*x.x+a22*x.y),a11*x.x+a21*x.y); }

◆ Length()

double bamg::Metric::Length	(	double	Ax,
		double	Ay
	)		const

Definition at line 151 of file Metric.cpp.

                                                  {/*{{{*/
       /*Length of A in the current metric*/
       return sqrt(Ax*Ax*a11+2*Ax*Ay*a21+Ay*Ay*a22);
    }

◆ operator*()

Metric bamg::Metric::operator* ( double c ) const

inline

Definition at line 46 of file Metric.h.

46 {double c2=c*c;return Metric(a11*c2,a21*c2,a22*c2);}

◆ operator/()

Metric bamg::Metric::operator/ ( double c ) const

inline

Definition at line 47 of file Metric.h.

47 {double c2=1/(c*c);return Metric(a11*c2,a21*c2,a22*c2);}

◆ operator D2xD2()

bamg::Metric::operator D2xD2 ( )

inline

Definition at line 48 of file Metric.h.

48 { return D2xD2(a11,a21,a21,a22);}

◆ operator()()

double bamg::Metric::operator()	(	R2	x,
		R2	y
	)		const

inline

Definition at line 50 of file Metric.h.

50 { return x.x*y.x*a11+(x.x*x.y+x.y*y.x)*a21+x.y*y.y*a22;};

Friends And Related Function Documentation

◆ EigenMetric

friend class EigenMetric

friend

Definition at line 25 of file Metric.h.

Field Documentation

◆ a11

double bamg::Metric::a11

Definition at line 22 of file Metric.h.

◆ a21

double bamg::Metric::a21

Definition at line 22 of file Metric.h.

◆ a22

double bamg::Metric::a22

Definition at line 22 of file Metric.h.

The documentation for this class was generated from the following files:

src/c/bamg/Metric.h
src/c/bamg/Metric.cpp

Public Member Functions

Data Fields

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Metric() [1/6]

◆ Metric() [2/6]

◆ Metric() [3/6]

◆ Metric() [4/6]

◆ Metric() [5/6]

◆ Metric() [6/6]

Member Function Documentation

◆ Echo()

◆ det()

◆ IntersectWith()

◆ Box()

◆ Orthogonal() [1/2]

◆ Orthogonal() [2/2]

◆ Length()

◆ operator*()

◆ operator/()

◆ operator D2xD2()

◆ operator()()

Friends And Related Function Documentation

◆ EigenMetric

Field Documentation

◆ a11

◆ a21

◆ a22