/*
 The MIT License (MIT)
 
 Copyright (c) 2015 Tony Saad
 
 Permission is hereby granted, free of charge, to any person obtaining a copy
 of this software and associated documentation files (the "Software"), to deal
 in the Software without restriction, including without limitation the rights
 to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 copies of the Software, and to permit persons to whom the Software is
 furnished to do so, subject to the following conditions:
 
 The above copyright notice and this permission notice shall be included in all
 copies or substantial portions of the Software.
 
 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 SOFTWARE.
*/

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <math.h>
#include <time.h>
#include <ctype.h>
#ifndef M_PI
    #define M_PI 3.14159265358979323846
#endif
double karman_spec(const double k)
{
  // INPUTS
  const double ke_ = 40.0;   // ke - peak wave number
  const double nu = 1.0e-5;
  const double urms = 0.25;
  
  // computed from inputs to satisfy isotropic turbulence properties
  const double ke = sqrt(5.0/12)*ke_;
  const double L = 0.746834/ke;     //integral length scale - sqrt(Pi)*Gamma(5/6)/Gamma(1/3)*1/ke
  const double alpha = 1.452762113; // 55/(9 Sqrt[Pi]) Gamma[5/6]/Gamma[1/3]
  const double epsilone = urms*urms*urms/L;
  const double keta = pow(epsilone, 0.25)*pow(nu,-3.0/4.0);
  const double r1 = k/ke;
  const double r2 = k/keta;
  const double tke = alpha*(urms*urms/ke)*(r1*r1*r1*r1 / pow(1.0 + r1*r1, 17.0/6.0))*exp(-2.0*r2*r2);
  return tke;
}

void help()
{
  printf("Usage: TurboGen -n number_of_points -m number_of_modes -l domain_length -o \n");
}

int main(int argc, char ** argv) {
  //__________________________________
  // Parse arguments
  int N = 32;
  int nModes = 5000;
  double L = 9.0*2.0*M_PI/100;
  bool enableIO = false;
  for (int i=0; i<argc; ++i) {
    if (argv[i][1] == 'n') {
      N = atoi(argv[i+1]);
    }  else if (argv[i][1] == 'm') {
      nModes = atoi(argv[i+1]);
    }  else if (argv[i][1] == 'l') {
      L = atoi(argv[i+1]);
    } else if (argv[i][1] == 'o') {
      enableIO = true;
    } else if (argv[i][1] == 'h') {
      help();
      return 0;
    }
  }
  
  // specify which spectrum to use.
  double (*which_spec)(const double);
  which_spec = &karman_spec;
  
  // start timer
  printf("starting clock...\n");
  clock_t begin, end;
  double time_spent;
  begin = clock();

  // lowest wave number. This is generally set to 2*Pi/L
  // In some cases, however, such as those when you have experimental
  // spectra, the minimum wave number may not correspond to the length of
  // the domain chosen
  const double km0 = 2.0*M_PI/L;
  
  // specify domain size
  const double lx = L;
  const double ly = L;
  const double lz = L;

  // set the x, y, and z resolutions. Currently support same res in all directions
  const int nx = N;
  const int ny = N;
  const int nz = N;
  
  // find dx and half dx (hdx) et al.
  const double dx  = lx/nx;
  const double hdx = dx/2.0;
  const double dy  = ly/ny;
  const double hdy = dy/2.0;
  const double dz  = lz/nz;
  const double hdz = dz/2.0;

  //______________________________________________________________________
  // compute wave arrays using standard random number generation
  double* phi   = (double*) malloc(sizeof(double)*(nModes+1));
  double* nu    = (double*) malloc(sizeof(double)*(nModes+1));
  double* theta = (double*) malloc(sizeof(double)*(nModes+1));
  double* psi   = (double*) malloc(sizeof(double)*(nModes+1));
  
  // seed the random number generator
  //time_t t;
  //srand((unsigned) time(&t));
  srand(0);
  for (int i=0; i<=nModes; ++i) {
    phi[i]   = 2.0*M_PI* (double) rand()/RAND_MAX;
    nu[i]    = (double) rand()/RAND_MAX;
    theta[i] = acos(2.0*nu[i] -1.0);
    psi[i]   = M_PI* (double) rand()/RAND_MAX - M_PI/2.0;
  }
  
  // maximum wave number supported on this grid
  const double kmmax = M_PI/dx;
  printf ("I will generate data up to wave number: %f\n", kmmax);

  // find spacing in wave-space
  const double dk = (kmmax-km0)/nModes;
  // create an array of wave numbers
  double* km = malloc(sizeof(double)*(nModes+1));
  for (int i=0; i<=nModes; ++i) {
    km[i] = km0 + i*dk;
  }
  
  // create wave vector (kx, ky, kz)
  double* kx = (double*) malloc(sizeof(double)*(nModes+1));
  double* ky = (double*) malloc(sizeof(double)*(nModes+1));
  double* kz = (double*) malloc(sizeof(double)*(nModes+1));
  for (int i=0; i<=nModes; ++i) {
    kx[i] = sin(theta[i])*cos(phi[i])*km[i];
    ky[i] = sin(theta[i])*sin(phi[i])*km[i];
    kz[i] = cos(theta[i])*km[i];
  }
  
  //________________________________________________________
  // ENFORCE MASS CONSERVATION
  double* ktx = (double*) malloc(sizeof(double)*(nModes+1));
  double* kty = (double*) malloc(sizeof(double)*(nModes+1));
  double* ktz = (double*) malloc(sizeof(double)*(nModes+1));
  
  for (int i=0; i<=nModes; ++i) {
    ktx[i] = sin(kx[i]*hdx)/dx;
    kty[i] = sin(ky[i]*hdy)/dy;
    ktz[i] = sin(kz[i]*hdz)/dz;
  }
  
  // find the direction vector sigma
  double* sxm = (double*) malloc(sizeof(double)*(nModes+1));
  double* sym = (double*) malloc(sizeof(double)*(nModes+1));
  double* szm = (double*) malloc(sizeof(double)*(nModes+1));
  
  // CREATE VECTOR ZETA AND MAKE SIGMA = ZETA x K
  for (int i=0; i<=nModes; ++i) {
    phi[i] = 2.0*M_PI* (double) rand()/RAND_MAX;
    nu[i]    = (double) rand()/RAND_MAX;
    theta[i] = acos(2.0*nu[i] -1.0);
  }
  for (int i=0; i<=nModes; ++i) {
    double zetax = sin(theta[i])*cos(phi[i]);
    double zetay = sin(theta[i])*sin(phi[i]);
    double zetaz = cos(theta[i]);
    // take cross product of zeta with k_tilde
    sxm[i] =  (zetay*ktz[i] - zetaz*kty[i]);
    sym[i] = -(zetax*ktz[i] - zetaz*ktx[i]);
    szm[i] =  (zetax*kty[i] - zetay*ktx[i]);
    // now make sigma a unit vector
    double smag = 1.0/sqrt(sxm[i]*sxm[i] + sym[i]*sym[i] + szm[i]*szm[i]);
    sxm[i] = sxm[i]*smag;
    sym[i] = sym[i]*smag;
    szm[i] = szm[i]*smag;
  }

  //________________________________________________________
  // update the sigma vector with the amplitude (reduces amount of computation)
  double espec;
  for (int i=0; i<=nModes; ++i) {
    espec = 2.0*sqrt(which_spec(km[i]) * dk);
    sxm[i] *= espec;
    sym[i] *= espec;
    szm[i] *= espec;
  }

  //___________________________________________________________________________________________
  // cell centered coordinates
  double* xc = (double*) malloc(sizeof(double)*nx);
  double* yc = (double*) malloc(sizeof(double)*ny);
  double* zc = (double*) malloc(sizeof(double)*nz);

  for (int i=0; i<nx; ++i) {
    xc[i] = hdx + i*dx;
  }
  for (int j=0; j<ny; ++j) {
    yc[j] = hdy + j*dy;
  }
  for (int k=0; k<nz; ++k) {
    zc[k] = hdz + k*dz;
  }

  //___________________________________________________________________________________________
  // compute the Fourier series at each point!
  const double nt = nx*ny*nz; // total number of points on this processor
  double* u = (double*) malloc(sizeof(double)*nt);
  double* v = (double*) malloc(sizeof(double)*nt);
  double* w = (double*) malloc(sizeof(double)*nt);

  for (int k=0; k<nz; ++k) {
    const int knxny = k*nx*ny;
    for (int j=0; j<ny; ++j) {
      const int jnx = j*nx;
      for (int i=0; i<nx; ++i) {
        const int flat = i + jnx + knxny; // compute flat index
        u[flat] = 0.0;
        v[flat] = 0.0;
        w[flat] = 0.0;
        for (int m=0; m<=nModes; ++m) {
          const double arg = kx[m]*xc[i] + ky[m]*yc[j] + kz[m]*zc[k] - psi[m];
          u[flat] += cos(arg - kx[m]*hdx)*sxm[m];
          v[flat] += cos(arg - ky[m]*hdy)*sym[m];
          w[flat] += cos(arg - kz[m]*hdz)*szm[m];
        }
      }
    }
  }
  
  // after Fourier series is computed, get the average time spend on computing
  end = clock();
  time_spent = (double)(end - begin) / CLOCKS_PER_SEC;
  printf("Done generating Turbulence in %f s \n", time_spent);
  
  //___________________________________________________________________________________________
  // write to disk
  if (enableIO) {
    
    begin = clock();
    char fname[50];
    
    sprintf(fname, "u_n%i_m%i.txt", N, nModes);
    FILE *uFile = fopen(fname, "w");
    fprintf(uFile, "FLAT\n");
    fprintf(uFile, "%i \t %i \t %i \t \n", nx, ny, nz);
    for (int i =0; i<nx*ny*nz; ++i) {
      fprintf(uFile, "%.32f\n",u[i]);
    }
    fclose(uFile);

    sprintf(fname, "v_n%i_m%i.txt", N, nModes);
    FILE *vFile = fopen(fname, "w");
    fprintf(vFile, "FLAT\n");
    fprintf(vFile, "%i \t %i \t %i \t \n", nx, ny, nz);
    for (int i =0; i<nx*ny*nz; ++i) {
      fprintf(vFile, "%.32f\n",v[i]);
    }
    fclose(vFile);

    sprintf(fname, "w_n%i_m%i.txt", N, nModes);
    FILE *wFile = fopen(fname, "w");
    fprintf(wFile, "FLAT\n");
    fprintf(wFile, "%i \t %i \t %i \t \n", nx, ny, nz);
    for (int i =0; i<nx*ny*nz; ++i) {
      fprintf(wFile, "%.32f\n",w[i]);
    }
    fclose(wFile);

    end = clock();
    time_spent = (double)(end - begin) / CLOCKS_PER_SEC;
    printf("Done writing to disk in %f s \n", time_spent);
  }
  
#ifdef DEBUG
// check for divergence
  int count = 0;
  double src = 0.0;
  for (int k = 0; k < nz-1; ++k) {
    for (int j = 0; j < ny-1; ++j) {
      for (int i = 0; i < nx-1; ++i) {
        const int flat = i + j*nx + k*nx*ny;
        const int ip1 = flat + 1;
        const int jp1 = flat + nx;
        const int kp1 = flat + nx*ny;
        src = (u[ip1] - u[flat])/dx + (v[jp1] - v[flat])/dy + (w[kp1]-w[flat])/dz;
        if (src > 1.0e-10) {
          count++;
        }
      }
    }
  }
  printf("cells with divergence = %i\n", count);
#endif // DEBUG
  
  // cleanup
  free(phi);
  free(nu);
  free(theta);
  free(psi);

  free(km);
  free(kx);
  free(ky);
  free(kz);

  free(ktx);
  free(kty);
  free(ktz);

  free(sxm);
  free(sym);
  free(szm);
  
  free(xc);
  free(yc);
  free(zc);

  free(u);
  free(v);
  free(w);

  return 0;
}