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#if !defined escript_LocalOps_H |
#if !defined escript_LocalOps_H |
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#define escript_LocalOps_H |
#define escript_LocalOps_H |
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#include <math.h> |
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namespace escript { |
namespace escript { |
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inline |
inline |
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void eigenvalues1(const double A00,double* ev0) { |
void eigenvalues1(const double A00,double* ev0) { |
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*ev0=1.; |
*ev0=A00; |
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} |
} |
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/** |
/** |
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void eigenvalues2(const double A00,const double A01 |
void eigenvalues2(const double A00,const double A01 |
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,const double A11, |
,const double A11, |
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double* ev0, double* ev1) { |
double* ev0, double* ev1) { |
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const register double trA=(A00+A11)/2.; |
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*ev0=1.; |
const register double A_00=A00-trA; |
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*ev1=2.; |
const register double A_11=A11-trA; |
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const register double s=sqrt(A01*A01-A_00*A_11); |
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*ev0=trA-s; |
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*ev1=trA+s; |
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} |
} |
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/** |
/** |
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\brief |
\brief |
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const double A22, |
const double A22, |
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double* ev0, double* ev1,double* ev2) { |
double* ev0, double* ev1,double* ev2) { |
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*ev0=1.; |
const register double trA=(A00+A11+A22)/3.; |
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*ev1=2.; |
const register double A_00=A00-trA; |
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*ev2=3.; |
const register double A_11=A11-trA; |
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const register double A_22=A22-trA; |
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const register double A01_2=A01*A01; |
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const register double A02_2=A02*A02; |
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const register double A12_2=A12*A12; |
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const register double p=A02_2+A12_2+A01_2+(A_00*A_00+A_11*A_11+A_22*A_22)/2.; |
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const register double q=(A02_2*A_11+A12_2*A_00+A01_2*A_22)-(A_00*A_11*A_22+2*A01*A12*A02); |
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const register double sq_p=sqrt(p/3.); |
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register double z=-q/(2*pow(sq_p,3)); |
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if (z<-1.) { |
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z=-1.; |
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} else if (z>1.) { |
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z=1.; |
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} |
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const register double alpha_3=acos(z)/3.; |
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*ev2=trA+2.*sq_p*cos(alpha_3); |
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*ev1=trA-2.*sq_p*cos(alpha_3+M_PI/3.); |
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*ev0=trA-2.*sq_p*cos(alpha_3-M_PI/3.); |
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} |
} |
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} // end of namespace |
} // end of namespace |
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#endif |
#endif |