#include "math.h" 
/*
 * DISUFQ  Is an internal function to spec2nlsdat
 *
 *  CALL:  disufq(rvec,ivec,rA,iA, w,kw,h,g,nmin,nmax,m,n)
 *
 * rvec, ivec = real and imaginary parts of the resultant  (size m X n).
 * rA, iA     = real and imaginary parts of the amplitudes (size m X n). 
 * w          = vector with angular frequencies (w>=0)
 * kw         = vector with wavenumbers (kw>=0)
 * h          = water depth             (h >=0)
 * g          = constant acceleration of gravity
 * nmin       = minimum index where rA(:,nmin) and iA(:,nmin) is 
 *              greater than zero.
 * nmax       = maximum index where rA(:,nmax) and iA(:,nmax) is 
 *              greater than zero.
 * m          = size(rA,1),size(iA,1)
 * n          = size(rA,2),size(iA,2), or size(rvec,2),size(ivec,2)
 *
 * DISUFQ returns the summation of difference frequency and sum 
 * frequency effects in the vector vec = rvec +sqrt(-1)*ivec.
 * The 2'nd order contribution to the Stokes wave is then calculated by
 * a simple 1D Fourier transform, real(FFT(vec)).
 *
 *  Install gfortran and run the following to build the module:
 *   f2py diffsumfunq.pyf disufq1.c -c --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71
 *
 * by Per Andreas Brodtkorb 15.08.2001
 * revised pab 14.03.2002, 01.05.2002 22.07.2002, oct 2008
 */ 

void disufq(double *rvec, double *ivec,
	   double *rA,   double *iA,
	   double *w,    double *kw,
	   double h,     double g,
	   int nmin, int nmax,
	   int m,    int n)
{ 
  double Epij, Edij;
  double tmp1, tmp2, tmp3, tmp4, kfact;
  double w1, w2, kw1, kw2, Cg;
  double rrA, iiA, riA, irA;
  int i,jy,ix,iz1,iv1,ixi,jyi;
  //int iz2, iv2;
  //Initialize rvec and ivec to zero
  for (ix=0;ix<n*m;ix++) {
    rvec[ix] = 0.0;
    ivec[ix] = 0.0;
  }

  // kfact is set to 2 in order to exploit the symmetry.
  // If you set kfact to 1, you must uncomment all statements 
  // including the expressions: rvec[iz2], rvec[iv2], ivec[iz2] and ivec[iv2].

  kfact = 2.0;
  if (h>10000){ /* deep water /Inifinite water depth */
    for (ix = nmin-1;ix<nmax;ix++) {
      ixi = ix*m;
      iz1 = 2*ixi;
      //iz2 = n*m-ixi;
      kw1  = kw[ix];
      Epij = kw1; 
      for (i=0;i<m;i++,ixi++,iz1++) { 
	rrA = rA[ixi]*rA[ixi]; ///
	iiA = iA[ixi]*iA[ixi]; ///
	riA = rA[ixi]*iA[ixi]; ///
	
	/// Sum frequency effects along the diagonal
	tmp1 = kfact*(rrA-iiA)*Epij;
	tmp2 = kfact*2.0*riA*Epij;
	rvec[iz1] += tmp1;
	ivec[iz1] += tmp2;
	
	//rvec[iz2] += tmp1;
	//ivec[iz2] -= tmp2;
	//iz2++;

	/// Difference frequency effects are zero along the diagonal
	/// and are thus not contributing to the mean.
      }
      for (jy = ix+1;jy<nmax;jy++){
	kw2  = kw[jy];
	Epij = 0.5*(kw2 + kw1); 
	Edij = -0.5*(kw2 - kw1);
	//printf("Edij = %f Epij = %f \n", Edij,Epij);
	
	ixi = ix*m;
	jyi = jy*m;
	iz1 = ixi+jyi;
	iv1 = jyi-ixi;
	//iz2 = (n*m-iz1);
	//iv2 = (n*m-iv1);
	for (i = 0;i<m;i++,ixi++,jyi++,iz1++,iv1++) { 
	  
	  rrA = rA[ixi]*rA[jyi]; ///rrA = rA[i][ix]*rA[i][jy];
	  iiA = iA[ixi]*iA[jyi]; ///iiA = iA[i][ix]*iA[i][jy];
	  riA = rA[ixi]*iA[jyi]; ///riA = rA[i][ix]*iA[i][jy];
	  irA = iA[ixi]*rA[jyi]; ///irA = iA[i][ix]*rA[i][jy];
	  
	 /* Sum frequency effects */ 
	  tmp1 = kfact*2.0*(rrA-iiA)*Epij;
	  tmp2 = kfact*2.0*(riA+irA)*Epij;
	  rvec[iz1] += tmp1;///rvec[i][ix+jy] += tmp1;
	  ivec[iz1] += tmp2;///ivec[i][ix+jy] += tmp2;
	  //rvec[iz2] += tmp1;///rvec[i][n*m-(ix+jy)] +=  tmp1;
	  //ivec[iz2] -= tmp2;///ivec[i][n*m-(ix+jy)] -=  tmp2;
	  // iz2++;

	  /* Difference frequency effects */
	  tmp1 = kfact*2.0*(rrA+iiA)*Edij;
	  tmp2 = kfact*2.0*(riA-irA)*Edij;
	  
	  rvec[iv1] += tmp1;///rvec[i][jy-ix] += tmp1;
	  ivec[iv1] += tmp2;///ivec[i][jy-ix] += tmp2;
	  
	  //rvec[iv2] += tmp1;///rvec[i][n*m-(jy-ix)] += tmp1;
	  //ivec[iv2] -= tmp2;///ivec[i][n*m-(jy-ix)] -= tmp2;
	  //iv2++;
	}
      }
   }
  }
  else{ /* Finite water depth */
    for (ix = nmin-1;ix<nmax;ix++) {
     kw1  = kw[ix]; 
     w1   = w[ix];
     tmp1 = tanh(kw1*h);
     /// Cg, wave group velocity
     Cg   = 0.5*g*(tmp1 + kw1*h*(1.0- tmp1*tmp1))/w1; /// OK
     tmp1 = 0.5*g*(kw1/w1)*(kw1/w1);
     tmp2 = 0.5*w1*w1/g;
     tmp3 = g*kw1/(w1*Cg);
     
     if (kw1*h<300.0){
       tmp4 = kw1/sinh(2.0*kw1*h);
     }
     else{ // To ensure sinh does not overflow.
       tmp4 = 0.0;
     }
     // Difference frequency effects finite water depth
     Edij = (tmp1-tmp2+tmp3)/(1.0-g*h/(Cg*Cg))-tmp4; /// OK
     
     // Sum frequency effects finite water depth
     Epij = (3.0*(tmp1-tmp2)/(1.0-tmp1/kw1*tanh(2.0*kw1*h))+3.0*tmp2-tmp1); /// OK
     //printf("Edij = %f Epij = %f \n", Edij,Epij);
     
     ixi = ix*m;
     iz1 = 2*ixi;
     //iz2 = n*m-ixi;
     for (i=0;i<m;i++,ixi++,iz1++) { 
       
       rrA = rA[ixi]*rA[ixi]; ///
       iiA = iA[ixi]*iA[ixi]; ///
       riA = rA[ixi]*iA[ixi]; ///
       
       
       /// Sum frequency effects along the diagonal
       rvec[iz1] +=  kfact*(rrA-iiA)*Epij;
       ivec[iz1] +=  kfact*2.0*riA*Epij;
       //rvec[iz2] +=  kfact*(rrA-iiA)*Epij;
       //ivec[iz2] -=  kfact*2.0*riA*Epij;
       //iz2++;
       
       /// Difference frequency effects along the diagonal
       /// are only contributing to the mean
       rvec[i] +=  2.0*(rrA+iiA)*Edij;
     }
     for (jy = ix+1;jy<nmax;jy++) {
       // w1  = w[ix];
       // kw1 = kw[ix]; 
       w2   = w[jy];
       kw2  = kw[jy];
       tmp1 = g*(kw1/w1)*(kw2/w2);
       tmp2 = 0.5/g*(w1*w1+w2*w2+w1*w2);
       tmp3 = 0.5*g*(w1*kw2*kw2+w2*kw1*kw1)/(w1*w2*(w1+w2));
       tmp4 = (1-g*(kw1+kw2)/(w1+w2)/(w1+w2)*tanh((kw1+kw2)*h));
       Epij = (tmp1-tmp2+tmp3)/tmp4+tmp2-0.5*tmp1; /* OK */
       
       tmp2 = 0.5/g*(w1*w1+w2*w2-w1*w2); /*OK*/
       tmp3 = -0.5*g*(w1*kw2*kw2-w2*kw1*kw1)/(w1*w2*(w1-w2));
       tmp4 = (1.0-g*(kw1-kw2)/(w1-w2)/(w1-w2)*tanh((kw1-kw2)*h));
       Edij = (tmp1-tmp2+tmp3)/tmp4+tmp2-0.5*tmp1; /* OK */
       //printf("Edij = %f Epij = %f \n", Edij,Epij);

       ixi = ix*m;
       jyi = jy*m;
       iz1 = ixi+jyi;
       iv1 = jyi-ixi;
       //       iz2 = (n*m-iz1);
       //       iv2 = n*m-iv1;
       for (i=0;i<m;i++,ixi++,jyi++,iz1++,iv1++) { 
	 rrA = rA[ixi]*rA[jyi]; ///rrA = rA[i][ix]*rA[i][jy];
	 iiA = iA[ixi]*iA[jyi]; ///iiA = iA[i][ix]*iA[i][jy];
	 riA = rA[ixi]*iA[jyi]; ///riA = rA[i][ix]*iA[i][jy];
	 irA = iA[ixi]*rA[jyi]; ///irA = iA[i][ix]*rA[i][jy];
	 
	 /* Sum frequency effects */ 
	 tmp1 = kfact*2.0*(rrA-iiA)*Epij;
	 tmp2 = kfact*2.0*(riA+irA)*Epij;
	 rvec[iz1] += tmp1;///rvec[i][jy+ix] += tmp1;
	 ivec[iz1] += tmp2;///ivec[i][jy+ix] += tmp2;
	 //rvec[iz2] += tmp1;///rvec[i][n*m-(jy+ix)] += tmp1;
	 //ivec[iz2] -= tmp2;///ivec[i][n*m-(jy+ix)] -= tmp2;
	 //iz2++;
	 	 
	 /* Difference frequency effects */
	 tmp1 = kfact*2.0*(rrA+iiA)*Edij;
	 tmp2 = kfact*2.0*(riA-irA)*Edij;
	 rvec[iv1] += tmp1;///rvec[i][jy-ix] += tmp1;
	 ivec[iv1] += tmp2;///ivec[i][jy-ix] -= tmp2;
	 
	 //rvec[iv2] += tmp1;
	 //ivec[iv2] -= tmp2;	 
	 //iv2++;
       }
     }
   }
  }
  //return i;
}
/*
 * DISUFQ2  Is an internal function to spec2nlsdat
 *
 *  CALL:  disufq2(rsvec,isvec,rdvec,idvec,rA,iA, w,kw,h,g,nmin,nmax,m,n)
 *
 * rsvec, isvec = real and imaginary parts of the sum frequency
 *                effects  (size m X n).
 * rdvec, idvec = real and imaginary parts of the difference frequency
 *                effects  (size m X n).
 * rA, iA     = real and imaginary parts of the amplitudes (size m X n). 
 * w          = vector with angular frequencies (w>=0)
 * kw         = vector with wavenumbers (kw>=0)
 * h          = water depth             (h >=0)
 * g          = constant acceleration of gravity
 * nmin       = minimum index where rA(:,nmin) and iA(:,nmin) is 
 *              greater than zero.
 * nmax       = maximum index where rA(:,nmax) and iA(:,nmax) is 
 *              greater than zero.
 * m          = size(rA,1),size(iA,1)
 * n          = size(rA,2),size(iA,2), or size(rvec,2),size(ivec,2)
 *
 * DISUFQ2 returns the summation of sum and difference frequency 
 * frequency effects in the vectors svec = rsvec +sqrt(-1)*isvec and
 * dvec =  rdvec +sqrt(-1)*idvec.
 * The 2'nd order contribution to the Stokes wave is then calculated by
 * a simple 1D Fourier transform, real(FFT(svec+dvec)).
 *
 *
 * This is a MEX-file for MATLAB.
 * by Per Andreas Brodtkorb 15.08.2001
 * revised pab 14.03.2002, 01.05.2002 
 */ 

void disufq2(double *rsvec, double *isvec,
	    double *rdvec, double *idvec,
	    double *rA,   double *iA,
	    double *w,    double *kw,
	    double h,     double g,
	    int nmin, int nmax,
	    int m,    int n)
{ 
  double Epij, Edij;
  double tmp1, tmp2, tmp3, tmp4, kfact;
  double w1, w2, kw1, kw2, Cg;
  double rrA, iiA, riA, irA;
  int i,jy,ix,iz1,iv1,ixi,jyi;
  //int iz2,iv2

  //Initialize rvec and ivec to zero
  for (ix=0;ix<n*m;ix++) {
    rsvec[ix] = 0.0;
    isvec[ix] = 0.0;
    rdvec[ix] = 0.0;
    idvec[ix] = 0.0;
  }

  // kfact is set to 2 in order to exploit the symmetry.
  // If you set kfact to 1, you must uncomment all statements 
  // including the expressions: rvec[iz2], rvec[iv2], ivec[iz2] and ivec[iv2].

  kfact = 2.0;
  if (h>10000){ /* deep water /Inifinite water depth */
    for (ix = nmin-1;ix<nmax;ix++) {
      ixi = ix*m;
      iz1 = 2*ixi;
      //iz2 = n*m-ixi;
      kw1  = kw[ix];
      Epij = kw1; 
      for (i=0;i<m;i++,ixi++,iz1++) { 
	rrA = rA[ixi]*rA[ixi]; ///
	iiA = iA[ixi]*iA[ixi]; ///
	riA = rA[ixi]*iA[ixi]; ///
	
	/// Sum frequency effects along the diagonal
	tmp1 = kfact*(rrA-iiA)*Epij;
	tmp2 = kfact*2.0*riA*Epij;
	rsvec[iz1] += tmp1;
	isvec[iz1] += tmp2;
	
	//rsvec[iz2] += tmp1;
	//isvec[iz2] -= tmp2;
	//iz2++;

	/// Difference frequency effects are zero along the diagonal
	/// and are thus not contributing to the mean.
      }
      for (jy = ix+1;jy<nmax;jy++){
	kw2  = kw[jy];
	Epij = 0.5*(kw2 + kw1); 
	Edij = -0.5*(kw2 - kw1);
	//printf("Edij = %f Epij = %f \n", Edij,Epij);
	
	ixi = ix*m;
	jyi = jy*m;
	iz1 = ixi+jyi;
	iv1 = jyi-ixi;
	//iz2 = (n*m-iz1);
	//iv2 = (n*m-iv1);
	for (i = 0;i<m;i++,ixi++,jyi++,iz1++,iv1++) { 
	  
	  rrA = rA[ixi]*rA[jyi]; ///rrA = rA[i][ix]*rA[i][jy];
	  iiA = iA[ixi]*iA[jyi]; ///iiA = iA[i][ix]*iA[i][jy];
	  riA = rA[ixi]*iA[jyi]; ///riA = rA[i][ix]*iA[i][jy];
	  irA = iA[ixi]*rA[jyi]; ///irA = iA[i][ix]*rA[i][jy];
	  
	 /* Sum frequency effects */ 
	  tmp1 = kfact*2.0*(rrA-iiA)*Epij;
	  tmp2 = kfact*2.0*(riA+irA)*Epij;
	  rsvec[iz1] += tmp1;  ///rvec[i][ix+jy] += tmp1;
	  isvec[iz1] += tmp2;  ///ivec[i][ix+jy] += tmp2;
	  //rsvec[iz2] += tmp1;///rvec[i][n*m-(ix+jy)] += tmp1;
	  //isvec[iz2] -= tmp2;///ivec[i][n*m-(ix+jy)] += tmp2;
	  //iz2++;

	  /* Difference frequency effects */
	  tmp1 = kfact*2.0*(rrA+iiA)*Edij;
	  tmp2 = kfact*2.0*(riA-irA)*Edij;
	  
	  rdvec[iv1] += tmp1;///rvec[i][jy-ix] += tmp1;
	  idvec[iv1] += tmp2;///ivec[i][jy-ix] += tmp2;
	  
	  //rdvec[iv2] += tmp1;///rvec[i][n*m-(jy-ix)] += tmp1;
	  //idvec[iv2] -= tmp2;///ivec[i][n*m-(jy-ix)] -= tmp2;
	  //  iv2++;
	}
      }
   }
  }
  else{ /* Finite water depth */
    for (ix = nmin-1;ix<nmax;ix++) {
     kw1  = kw[ix]; 
     w1   = w[ix];
     tmp1 = tanh(kw1*h);
     /// Cg, wave group velocity
     Cg   = 0.5*g*(tmp1 + kw1*h*(1.0- tmp1*tmp1))/w1; /// OK
     tmp1 = 0.5*g*(kw1/w1)*(kw1/w1);
     tmp2 = 0.5*w1*w1/g;
     tmp3 = g*kw1/(w1*Cg);
     
     if (kw1*h<300.0){
       tmp4 = kw1/sinh(2.0*kw1*h);
     }
     else{ // To ensure sinh does not overflow.
       tmp4 = 0.0;
     }
     // Difference frequency effects finite water depth
     Edij = (tmp1-tmp2+tmp3)/(1.0-g*h/(Cg*Cg))-tmp4; /// OK
     
     // Sum frequency effects finite water depth
     Epij = (3.0*(tmp1-tmp2)/(1.0-tmp1/kw1*tanh(2.0*kw1*h))+3.0*tmp2-tmp1); /// OK
     //printf("Edij = %f Epij = %f \n", Edij,Epij);
     
     ixi = ix*m;
     iz1 = 2*ixi;
     //iz2 = n*m-ixi;
     for (i=0;i<m;i++,ixi++,iz1++) { 
       
       rrA = rA[ixi]*rA[ixi]; ///
       iiA = iA[ixi]*iA[ixi]; ///
       riA = rA[ixi]*iA[ixi]; ///
       
       
       /// Sum frequency effects along the diagonal
       rsvec[iz1] +=  kfact*(rrA-iiA)*Epij;
       isvec[iz1] +=  kfact*2.0*riA*Epij;
       //rsvec[iz2] +=  kfact*(rrA-iiA)*Epij;
       //isvec[iz2] -=  kfact*2.0*riA*Epij;
       
       /// Difference frequency effects along the diagonal
       /// are only contributing to the mean
       //printf(" %f \n",2.0*(rrA+iiA)*Edij);
       rdvec[i] +=  2.0*(rrA+iiA)*Edij;
     }
     for (jy = ix+1;jy<nmax;jy++) {
       // w1  = w[ix];
       // kw1 = kw[ix]; 
       w2   = w[jy];
       kw2  = kw[jy];
       tmp1 = g*(kw1/w1)*(kw2/w2);
       tmp2 = 0.5/g*(w1*w1+w2*w2+w1*w2);
       tmp3 = 0.5*g*(w1*kw2*kw2+w2*kw1*kw1)/(w1*w2*(w1+w2));
       tmp4 = (1-g*(kw1+kw2)/(w1+w2)/(w1+w2)*tanh((kw1+kw2)*h));
       Epij = (tmp1-tmp2+tmp3)/tmp4+tmp2-0.5*tmp1; /* OK */
       
       tmp2 = 0.5/g*(w1*w1+w2*w2-w1*w2); /*OK*/
       tmp3 = -0.5*g*(w1*kw2*kw2-w2*kw1*kw1)/(w1*w2*(w1-w2));
       tmp4 = (1.0-g*(kw1-kw2)/(w1-w2)/(w1-w2)*tanh((kw1-kw2)*h));
       Edij = (tmp1-tmp2+tmp3)/tmp4+tmp2-0.5*tmp1; /* OK */
       //printf("Edij = %f Epij = %f \n", Edij,Epij);

       ixi = ix*m;
       jyi = jy*m;
       iz1 = ixi+jyi;
       iv1 = jyi-ixi;
       //       iz2 = (n*m-iz1);
       //       iv2 = (n*m-iv1);
       for (i=0;i<m;i++,ixi++,jyi++,iz1++,iv1++) { 
	 rrA = rA[ixi]*rA[jyi]; ///rrA = rA[i][ix]*rA[i][jy];
	 iiA = iA[ixi]*iA[jyi]; ///iiA = iA[i][ix]*iA[i][jy];
	 riA = rA[ixi]*iA[jyi]; ///riA = rA[i][ix]*iA[i][jy];
	 irA = iA[ixi]*rA[jyi]; ///irA = iA[i][ix]*rA[i][jy];
	 
	 /* Sum frequency effects */ 
	 tmp1 = kfact*2.0*(rrA-iiA)*Epij;
	 tmp2 = kfact*2.0*(riA+irA)*Epij;
	 rsvec[iz1] += tmp1;///rsvec[i][jy+ix] += tmp1;
	 isvec[iz1] += tmp2;///isvec[i][jy+ix] += tmp2;
	 //rsvec[iz2] += tmp1;///rsvec[i][n*m-(jy+ix)] += tmp1;
	 //isvec[iz2] -= tmp2;///isvec[i][n*m-(jy-ix)] += tmp2;
	 //iz2++;
	 	 
	 /* Difference frequency effects */
	 tmp1 = kfact*2.0*(rrA+iiA)*Edij;
	 tmp2 = kfact*2.0*(riA-irA)*Edij;
	 rdvec[iv1] += tmp1;
	 idvec[iv1] += tmp2;
	 
	 //rdvec[iv2] += tmp1;
	 //idvec[iv2] -= tmp2;	 
	 // iv2++;
       }
     }
   }
  }
 // return i;
}