SimpleSimulationEngine/cpp/common/math/elliptic_integral.h at master · ProkopHapala/SimpleSimulationEngine · GitHub

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#ifndef ELLIPTIC_INTEGRAL_H
#define ELLIPTIC_INTEGRAL_H

#ifdef __cplusplus
extern "C" {
#endif

/* Complete elliptic integrals (angle argument) */
double elliptic_ea ( double a );
void   elliptic_ea_values ( int *n_data, double *x, double *fx );

double elliptic_fa ( double a );
void   elliptic_fa_values ( int *n_data, double *x, double *fx );

double elliptic_pia ( double n, double a );
void   elliptic_pia_values ( int *n_data, double *n, double *a, double *pia );

/* Complete elliptic integrals (k or m argument) */
double elliptic_ek ( double k );
void   elliptic_ek_values ( int *n_data, double *x, double *fx );

double elliptic_fk ( double k );
void   elliptic_fk_values ( int *n_data, double *x, double *fx );

double elliptic_em ( double m );
void   elliptic_em_values ( int *n_data, double *x, double *fx );

double elliptic_fm ( double m );
void   elliptic_fm_values ( int *n_data, double *x, double *fx );

double elliptic_pik ( double n, double k );
void   elliptic_pik_values ( int *n_data, double *n, double *k, double *pik );

double elliptic_pim ( double n, double m );
void   elliptic_pim_values ( int *n_data, double *n, double *m, double *pim );

/* Incomplete elliptic integrals (angle + parameter) */
double elliptic_inc_ea ( double phi, double a );
void   elliptic_inc_ea_values ( int *n_data, double *phi, double *a, double *ea );

double elliptic_inc_fa ( double phi, double a );
void   elliptic_inc_fa_values ( int *n_data, double *phi, double *a, double *fa );

double elliptic_inc_pia ( double phi, double n, double a );
void   elliptic_inc_pia_values ( int *n_data, double *phi, double *n, double *a, double *pia );

/* Incomplete elliptic integrals (phi + k/m) */
double elliptic_inc_ek ( double phi, double k );
void   elliptic_inc_ek_values ( int *n_data, double *phi, double *k, double *ek );

double elliptic_inc_fk ( double phi, double k );
void   elliptic_inc_fk_values ( int *n_data, double *phi, double *k, double *fk );

double elliptic_inc_em ( double phi, double m );
void   elliptic_inc_em_values ( int *n_data, double *phi, double *m, double *em );

double elliptic_inc_fm ( double phi, double m );
void   elliptic_inc_fm_values ( int *n_data, double *phi, double *m, double *fm );

double elliptic_inc_pik ( double phi, double n, double k );
void   elliptic_inc_pik_values ( int *n_data, double *phi, double *n, double *k, double *pik );

double elliptic_inc_pim ( double phi, double n, double m );
void   elliptic_inc_pim_values ( int *n_data, double *phi, double *n, double *m, double *pim );

/* Jacobi elliptic functions */
double jacobi_sn ( double u, double m );
void   jacobi_sn_values ( int *n_data, double *u, double *a, double *k, double *m, double *fx );

double jacobi_cn ( double u, double m );
void   jacobi_cn_values ( int *n_data, double *u, double *a, double *k, double *m, double *fx );

double jacobi_dn ( double u, double m );
void   jacobi_dn_values ( int *n_data, double *u, double *a, double *k, double *m, double *fx );

void   sncndn ( double u, double m, double *sn, double *cn, double *dn );

/* Carlson symmetric elliptic integrals */
double rc ( double x, double y, double errtol, int *ierr );
double rd ( double x, double y, double z, double errtol, int *ierr );
double rf ( double x, double y, double z, double errtol, int *ierr );
double rj ( double x, double y, double z, double p, double errtol, int *ierr );

/* Utilities */
double r8_max ( double x, double y );
void   timestamp ( );

#ifdef __cplusplus
}
#endif

#endif /* ELLIPTIC_INTEGRAL_H */