#ifndef NAVIERSTOKES_H
#define NAVIERSTOKES_H

#include <complex.h>
#include <stdbool.h>
#include <stdint.h>
#include <fftw3.h>

#define M_PI 3.14159265358979323846

// abort signal
extern volatile bool g_abort;

// arrays on which the ffts are performed
typedef struct fft_vects {
  fftw_complex* fft;
  fftw_plan fft_plan;
} fft_vect;

// compute u_k
int uk( int K1, int K2, int N1, int N2, uint64_t nsteps, double nu, double delta, double L, _Complex double* u0, _Complex double* g, bool irreversible, unsigned int algorithm, uint64_t print_freq, uint64_t starting_time, unsigned int nthreadsl, FILE* savefile);

// compute enstrophy and alpha
int enstrophy( int K1, int K2, int N1, int N2, uint64_t nsteps, double nu, double delta, double L, _Complex double* u0, _Complex double* g, bool irreversible, unsigned int algorithm, uint64_t print_freq, uint64_t starting_time, unsigned int nthreads, FILE* savefile, char* cmd_string, char* params_string, char* savefile_string);

// compute solution as a function of time, but do not print anything (useful for debugging)
int quiet( int K1, int K2, int N1, int N2, uint64_t nsteps, double nu, double delta, double L, uint64_t starting_time, _Complex double* u0, _Complex double* g, bool irreversible, unsigned int algorithm, unsigned int nthreads, FILE* savefile);


// initialize vectors for computation
int  ns_init_tmps( _Complex double **u, _Complex double ** tmp1, _Complex double **tmp2, _Complex double **tmp3, fft_vect* fft1, fft_vect *fft2, fft_vect *ifft, int K1, int K2, int N1, int N2, unsigned int nthreads);
// release vectors
int ns_free_tmps( _Complex double* u, _Complex double* tmp1, _Complex double *tmp2,_Complex double *tmp3, fft_vect fft1, fft_vect fft2, fft_vect ifft);

// copy u0 to u
int copy_u( _Complex double* u, _Complex double* u0, int K1, int K2);

// next time step for Irreversible/reversible Navier-Stokes equation
// RK4
int ns_step_rk4( _Complex double* u, int K1, int K2, int N1, int N2, double nu, double delta, double L, _Complex double* g, fft_vect fft1, fft_vect fft2,fft_vect ifft, _Complex double* tmp1, _Complex double *tmp2, _Complex double *tmp3, bool irreversible);
// RK2
int ns_step_rk2( _Complex double* u, int K1, int K2, int N1, int N2, double nu, double delta, double L, _Complex double* g, fft_vect fft1, fft_vect fft2,fft_vect ifft, _Complex double* tmp1, _Complex double *tmp2, bool irreversible);

// right side of Irreversible/reversible Navier-Stokes equation
int ns_rhs( _Complex double* out, _Complex double* u, int K1, int K2, int N1, int N2, double nu, double L, _Complex double* g, fft_vect fft1, fft_vect fft2, fft_vect ifft, bool irreversible);

// convolution term in right side of equation
int ns_T( _Complex double* u, int K1, int K2, int N1, int N2, fft_vect fft1, fft_vect fft2, fft_vect ifft);

// convolution term in right side of equation (computed without fft)
int ns_T_nofft( _Complex double* out, _Complex double* u, int K1, int K2, int N1, int N2);

// compute alpha
double compute_alpha( _Complex double* u, int K1, int K2, _Complex double* g, double L);
// compute energy
double compute_energy( _Complex double* u, int K1, int K2);
// compute enstrophy
double compute_enstrophy( _Complex double* u, int K1, int K2, double L);

// get index for kx,ky in array of size S
int klookup( int kx, int ky, int S1, int S2);
// get index for kx,ky in array of size K1,K2 in which only the terms with kx>=0 are stored
int klookup_sym( int kx, int ky, int K2);
// get u_{kx,ky} from a vector u in which only the values for kx>=0 are stored, assuming u_{-k}=u_k^*
_Complex double getval_sym( _Complex double* u, int kx, int ky, int K2);

#endif