#include <Metric.h>

Public Member Functions
	EigenMetric (const Metric &)

	EigenMetric (double r1, double r2, const D2 &vp1)

void	Echo ()

void	Abs ()

void	pow (double p)

void	Min (double a)

void	Max (double a)

void	Minh (double h)

void	Maxh (double h)

double	hmin () const

double	hmax () const

double	lmax () const

double	lmin () const

double	Aniso2 () const

void	BoundAniso2 (const double coef)

void	operator*= (double coef)

Data Fields
double	lambda1

double	lambda2

double	vx

double	vy

Friends
class	Metric

Detailed Description

Definition at line 54 of file Metric.h.

Constructor & Destructor Documentation

◆ EigenMetric() [1/2]

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

Definition at line 12 of file EigenMetric.cpp.

                                           {/*{{{*/
       /*From a metric (a11,a21,a22), get eigen values lambda1 and lambda2 and one eigen vector v*/
  
       /*Intermediaries*/
       double a11=M.a11,a21=M.a21,a22=M.a22;
       double normM;
       double delta,b;
  
       /*To get the eigen values, we must solve the following equation:
        *     | a11 - lambda    a21        |
        * det |                            | = 0
        *     | a21             a22-lambda |
        *
        * We have to solve the following polynom:
        *  lamda^2 + ( -a11 -a22)*lambda + (a11*a22-a21*a21) = 0*/
  
       /*Compute polynom determinant*/
       b=-a11-a22;
       delta=b*b - 4*(a11*a22-a21*a21);
  
       /*Compute norm of M to avoid round off errors*/
       normM=a11*a11 + a22*a22 + a21*a21;
  
       /*1: normM too small: eigen values = 0*/
       if(normM<1.e-30){
          lambda1=0;
          lambda2=0;
          vx=1;
          vy=0;
       }
       /*2: delta is small -> double root*/
       else if (delta < 1.e-5*normM){
          lambda1=-b/2;
          lambda2=-b/2;
          vx=1;
          vy=0;
       }
       /*3: general case -> two roots*/
       else{
          delta     = sqrt(delta);
          lambda1   = (-b-delta)/2.0;
          lambda2   = (-b+delta)/2.0;
  
          /*Now, one must find the eigen vectors. For that we use the following property of the inner product
           *    <Ax,y> = <x,tAy>
           * Here, M'(M-lambda*Id) is symmetrical, which gives:
           *    ∀(x,y)∈R²xR² <M'x,y> = <M'y,x>
           * And we have the following:
           *    if y∈Ker(M'), ∀x∈R² <M'x,y> = <x,M'y> = 0
           * We have shown that
           *    Im(M') ⊥ Ker(M')
           *
           * To find the eigen vectors of M, we only have to find two vectors
           * of the image of M' and take their perpendicular as long as they are
           * not 0.
           * To do that, we take the images (1,0) and (0,1):
           *  x1 = (a11 - lambda)      x2 = a21
           *  y1 = a21                 y2 = (a22-lambda)
           *
           * We take the vector that has the larger norm and take its perpendicular.*/
  
          double norm1 = (a11-lambda1)*(a11-lambda1) + a21*a21; 
          double norm2 = a21*a21 + (a22-lambda1)*(a22-lambda1);
  
          if (norm2<norm1){
             norm1=sqrt(norm1);
             vx = - a21/norm1;
             vy = (a11-lambda1)/norm1;
          }
          else{
             norm2=sqrt(norm2);
             vx = - (a22-lambda1)/norm2;
             vy = a21/norm2;
          }
       }
  
    }

◆ EigenMetric() [2/2]

bamg::EigenMetric::EigenMetric	(	double	r1,
		double	r2,
		const D2 &	vp1
	)

Definition at line 90 of file EigenMetric.cpp.

                                                             {/*{{{*/
       this->lambda1 = r1;
       this->lambda2 = r2;
       this->vx = vp1.x;
       this->vy = vp1.y;
    }/*}}}*/

Member Function Documentation

◆ Echo()

void bamg::EigenMetric::Echo ( void )

Definition at line 104 of file EigenMetric.cpp.

                              {/*{{{*/
  
       _printf_("EigenMetric:\n");
       _printf_("   lambda1: " << lambda1 << "\n");
       _printf_("   lambda2: " << lambda2 << "\n");
       _printf_("   vx: " << vx << "\n");
       _printf_("   vy: " << vy << "\n");
  
       return;
    }

◆ Abs()

void bamg::EigenMetric::Abs ( )

Definition at line 98 of file EigenMetric.cpp.

                           {/*{{{*/
       lambda1=bamg::Abs(lambda1),lambda2=bamg::Abs(lambda2);
    }/*}}}*/

◆ pow()

void bamg::EigenMetric::pow ( double p )

Definition at line 141 of file EigenMetric.cpp.

                                   {/*{{{*/
       lambda1=::pow(lambda1,p);lambda2=::pow(lambda2,p);
    }/*}}}*/

◆ Min()

void bamg::EigenMetric::Min ( double a )

Definition at line 127 of file EigenMetric.cpp.

                                    { /*{{{*/
       lambda1=bamg::Min(a,lambda1); lambda2=bamg::Min(a,lambda2) ;
    }/*}}}*/

◆ Max()

void bamg::EigenMetric::Max ( double a )

Definition at line 130 of file EigenMetric.cpp.

                                    { /*{{{*/
       //change eigen values
       lambda1=bamg::Max(a,lambda1); lambda2=bamg::Max(a,lambda2) ;
    }/*}}}*/

◆ Minh()

void bamg::EigenMetric::Minh ( double h )

Definition at line 134 of file EigenMetric.cpp.

                                     {/*{{{*/
       Min(1.0/(h*h));
    }/*}}}*/

◆ Maxh()

void bamg::EigenMetric::Maxh ( double h )

Definition at line 137 of file EigenMetric.cpp.

                                     {/*{{{*/
       //Call Max function
       Max(1.0/(h*h));
    }/*}}}*/

◆ hmin()

double bamg::EigenMetric::hmin ( ) const

Definition at line 115 of file EigenMetric.cpp.

                                   {/*{{{*/
       return sqrt(1/bamg::Max3(lambda1,lambda2,1e-30));
    }/*}}}*/

◆ hmax()

double bamg::EigenMetric::hmax ( ) const

Definition at line 118 of file EigenMetric.cpp.

                                   {/*{{{*/
       return sqrt(1/bamg::Max(bamg::Min(lambda1,lambda2),1e-30));
    }/*}}}*/

◆ lmax()

double bamg::EigenMetric::lmax ( ) const

Definition at line 121 of file EigenMetric.cpp.

                                   {/*{{{*/
       return bamg::Max3(lambda1,lambda2,1e-30);
    }/*}}}*/

◆ lmin()

double bamg::EigenMetric::lmin ( ) const

Definition at line 124 of file EigenMetric.cpp.

                                   {/*{{{*/
       return bamg::Max(bamg::Min(lambda1,lambda2),1e-30);
    }/*}}}*/

◆ Aniso2()

double bamg::EigenMetric::Aniso2 ( ) const

Definition at line 101 of file EigenMetric.cpp.

                                      { /*{{{*/
       return lmax()/lmin();
    }/*}}}*/

◆ BoundAniso2()

void bamg::EigenMetric::BoundAniso2 ( const double coef )

inline

Definition at line 101 of file Metric.h.

                                                          {
       if (coef<=1.00000000001){
          if (lambda1 < lambda2)
           lambda1 = bamg::Max(lambda1,lambda2*coef);
          else
           lambda2 = bamg::Max(lambda2,lambda1*coef);
       }
       else{  //TO BE CHECKED
          if (lambda1 > lambda2)
           lambda1 = bamg::Min(lambda1,lambda2*coef);
          else
           lambda2 = bamg::Min(lambda2,lambda1*coef);
       }
    }

◆ operator*=()

void bamg::EigenMetric::operator*= ( double coef )

inline

Definition at line 82 of file Metric.h.

82 { lambda1*=coef;lambda2*=coef;}

Friends And Related Function Documentation

◆ Metric

friend class Metric

friend

Definition at line 62 of file Metric.h.

Field Documentation

◆ lambda1

double bamg::EigenMetric::lambda1

Definition at line 58 of file Metric.h.

◆ lambda2

double bamg::EigenMetric::lambda2