#ifdef  HAVE_CONFIG_H
#include "config.h"
#endif

#include <stdio.h>
#include <float.h>
#include <math.h>

#ifndef  M_SQRT2
#define  M_SQRT2  1.41421356237309504880168872420969808
#endif

#include "dmemory.h"
#include "cdi_int.h"


static
void cpledn(size_t kn, size_t kodd, double *pfn, double pdx, int kflag,
            double *pw, double *pdxn, double *pxmod)
{
  /* 1.0 Newton iteration step */

  double zdlx = pdx;
  double zdlk = 0.0;
  if ( kodd == 0 ) zdlk = 0.5*pfn[0];
  double zdlxn  = 0.0;
  double zdlldn = 0.0;

  size_t ik = 1;

  if ( kflag == 0 )
    {
      for ( size_t jn = 2-kodd; jn <= kn; jn += 2 )
	{
	  /* normalised ordinary Legendre polynomial == \overbar{p_n}^0 */
	  zdlk   = zdlk + pfn[ik]*cos((double)(jn)*zdlx);
	  /* normalised derivative == d/d\theta(\overbar{p_n}^0) */
	  zdlldn = zdlldn - pfn[ik]*(double)(jn)*sin((double)(jn)*zdlx);
	  ik++;
	}
      /* Newton method */
      double zdlmod = -(zdlk/zdlldn);
      zdlxn = zdlx + zdlmod;
      *pdxn = zdlxn;
      *pxmod = zdlmod;
    }

  /* 2.0 Compute weights */

  if ( kflag == 1 )
    {
      for ( size_t jn = 2-kodd; jn <= kn; jn += 2 )
	{
	  /* normalised derivative */
	  zdlldn = zdlldn - pfn[ik]*(double)(jn)*sin((double)(jn)*zdlx);
	  ik++;
	}
      *pw = (double)(2*kn+1)/(zdlldn*zdlldn);
    }

  return;
}

static
void gawl(double *pfn, double *pl, double *pw, size_t kn)
{
  double pmod = 0;
  double zw = 0;
  double zdlxn = 0;

  /* 1.0 Initizialization */

  int iflag  =  0;
  int itemax = 20;

  size_t iodd   = (kn % 2);

  double zdlx   =  *pl;

  /* 2.0 Newton iteration */

  for ( int jter = 1; jter <= itemax+1; jter++ )
    {
      cpledn(kn, iodd, pfn, zdlx, iflag, &zw, &zdlxn, &pmod);
      zdlx = zdlxn;
      if (iflag == 1) break;
      if (fabs(pmod) <= DBL_EPSILON*1000.0) iflag = 1;
    }

  *pl = zdlxn;
  *pw = zw;

  return;
}

static
void gauaw(size_t kn, double *restrict pl, double *restrict pw)
{
  /*
   * 1.0 Initialize Fourier coefficients for ordinary Legendre polynomials
   *
   * Belousov, Swarztrauber, and ECHAM use zfn(0,0) = sqrt(2)
   * IFS normalisation chosen to be 0.5*Integral(Pnm**2) = 1 (zfn(0,0) = 2.0)
   */
  double *zfn    = (double *) Malloc((kn+1) * (kn+1) * sizeof(double));
  double *zfnlat = (double *) Malloc((kn/2+1+1)*sizeof(double));

  zfn[0] = M_SQRT2;
  for ( size_t jn = 1; jn <= kn; jn++ )
    {
      double zfnn = zfn[0];
      for (size_t jgl = 1; jgl <= jn; jgl++)
	{
	  zfnn *= sqrt(1.0-0.25/((double)(jgl*jgl)));
	}

      zfn[jn*(kn+1)+jn] = zfnn;

      size_t iodd = jn % 2;
      for ( size_t jgl = 2; jgl <= jn-iodd; jgl += 2 )
	{
	  zfn[jn*(kn+1)+jn-jgl] = zfn[jn*(kn+1)+jn-jgl+2]
	    *((double)((jgl-1)*(2*jn-jgl+2)))/((double)(jgl*(2*jn-jgl+1)));
	}
    }


  /* 2.0 Gaussian latitudes and weights */

  size_t iodd = kn % 2;
  size_t ik = iodd;
  for ( size_t jgl = iodd; jgl <= kn; jgl += 2 )
    {
      zfnlat[ik] = zfn[kn*(kn+1)+jgl];
      ik++;
    }

  /* 2.1 Find first approximation of the roots of the Legendre polynomial of degree kn */

  size_t ins2 = kn/2+(kn % 2);
  double z;

  for ( size_t jgl = 1; jgl <= ins2; jgl++ )
    {
      z = ((double)(4*jgl-1))*M_PI/((double)(4*kn+2));
      pl[jgl-1] = z+1.0/(tan(z)*((double)(8*kn*kn)));
    }

  /* 2.2 Computes roots and weights for transformed theta */

  for ( size_t jgl = ins2; jgl >= 1 ; jgl-- )
    {
      size_t jglm1 = jgl-1;
      gawl(zfnlat, &(pl[jglm1]), &(pw[jglm1]), kn);
    }

  /* convert to physical latitude */

  for ( size_t jgl = 0; jgl < ins2; jgl++ )
    {
      pl[jgl] = cos(pl[jgl]);
    }

  for ( size_t jgl = 1; jgl <= kn/2; jgl++ )
    {
      size_t jglm1 = jgl-1;
      size_t isym =  kn-jgl;
      pl[isym] =  -pl[jglm1];
      pw[isym] =  pw[jglm1];
    }

  Free(zfnlat);
  Free(zfn);

  return;
}


void gaussianLatitudes(double *latitudes, double *weights, size_t nlat)
{
  //gauaw_old(latitudes, weights, nlat);
  gauaw(nlat, latitudes, weights);
}


bool isGaussGrid(size_t ysize, double yinc, const double *yvals)
{
  bool lgauss = false;

  if ( IS_EQUAL(yinc, 0) && ysize > 2 ) // check if gaussian
    {
      size_t i;
      double *yv = (double *) Malloc(ysize*sizeof(double));
      double *yw = (double *) Malloc(ysize*sizeof(double));
      gaussianLatitudes(yv, yw, ysize);
      Free(yw);
      for ( i = 0; i < ysize; i++ )
        yv[i] = asin(yv[i])/M_PI*180.0;

      for ( i = 0; i < ysize; i++ )
        if ( fabs(yv[i] - yvals[i]) > ((yv[0] - yv[1])/500) ) break;

      if ( i == ysize ) lgauss = true;

      // check S->N
      if ( lgauss == false )
        {
          for ( i = 0; i < ysize; i++ )
            if ( fabs(yv[i] - yvals[ysize-i-1]) > ((yv[0] - yv[1])/500) ) break;

          if ( i == ysize ) lgauss = true;
        }

      Free(yv);
    }

  return lgauss;
}

/*
#define NGL  48

int main (int rgc, char *argv[])
{
  int ngl = NGL;
  double plo[NGL], pwo[NGL];
  double pl[NGL], pw[NGL];

  int i;

  gauaw(ngl, pl, pw);
  for (i = 0; i < ngl; i++)
    {
      pl[i]  = asin(pl[i])/M_PI*180.0;
      plo[i] = asin(plo[i])/M_PI*180.0;
    }

  for (i = 0; i < ngl; i++)
    {
      fprintf(stderr, "%4d%25.18f%25.18f%25.18f%25.18f\n", i+1, pl[i], pw[i], pl[i]-plo[i], pw[i]-pwo[i]);
    }

  return 0;
}
*/
/*
 * Local Variables:
 * c-file-style: "Java"
 * c-basic-offset: 2
 * indent-tabs-mode: nil
 * show-trailing-whitespace: t
 * require-trailing-newline: t
 * End:
 */
