lambda2.h

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#ifndef VA_LAMBDA2_H
#define VA_LAMBDA2_H
 
#include "common_defs.h"
#include "linalg3.h"
 
/***************************************************************************/
VA_DEVICE_FUN void valib_lambda2(VA_REAL *A, VA_REAL *lambda_2)
{
    VA_REAL SO[9];      // velocity gradient
    VA_REAL O[9];       // Omega
    VA_REAL SSOO[9];    // S*S + Omega*Omega
    VA_REAL eigSSOO[3]; // eigenvalues of SSOO
 
    // make a local copy of the velocity gradient
    valib_mat_copy3(A, SO);
 
    // find symmetric and antisymmetric parts
    valib_sym_antisym3(SO);
 
    // create full antisymmetric part and mirror
    // the lower part with the oposite sign
    O[1] = SO[1]; // (2,1)
    O[2] = SO[2]; // (3,1)
    O[5] = SO[5]; // (3,2)
 
    // antisymmetrize
    O[0] = 0.;    // (1,1)
    O[3] = -O[1]; // (1,2)
    O[4] = 0.;    // (2,2)
    O[6] = -O[2]; // (1,3)
    O[7] = -O[5]; // (2,3)
    O[8] = 0.;    // (3,3)
 
    // create the full symmetric part
    SO[1] = SO[3]; // (2,1)
    SO[2] = SO[6]; // (3,1)
    SO[5] = SO[7]; // (3,2)
 
    // zero resulting values together
    valib_mat_zero3(SSOO);
    // SSOO = S*S
    valib_matmat3_prod(0, 0, SO, SO, SSOO);
    // SSOO = SSOO + O*O
    valib_matmat3_prod(0, 0, O,  O,  SSOO);
 
    // find sorted eigenvalues
    valib_eigenvalues_sym3(SSOO, eigSSOO);
 
    // extract the second eigenvalue
    *lambda_2 = eigSSOO[1];
    //printf("eigenvalues: %lf, %lf, %lf \n", eigSSOO[0], eigSSOO[1], eigSSOO[2]);
}
 
#endif // VA_LAMBDA2_H