interp.c

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#include "extern.h"

/*
   2d array interpolation routine
   swiped from Darrel, converted to 'C' by Jeff
*/


/*
 version 1.0  mpifr cyber edition  22 MAY 1977.
 see nod 2 manual page m 2.1                                       
 C.G Haslam       mar  1969.                                        
 This routine interpolates the amplitude z at the point y which lies
 between the points b and c. y=0.0 corresponds to b and y=1.0
 corresponds to c. a,b,c,d are the amplitudes at 4 points spaced at
 unit intervals.                                                  
*/



double yintpn(a, b, c, d, y)
double a, b, c, d, y;
{
  double e, f, g;

  if(y == 0.0)
  {
    return((double)b);
  }

  e = b-a;      /* exact copy case */
  f = b-c;
  g = e + f + f + d - c;
  g = g*y- e - f - g;
  g = g*y - a + c;

  return( (double)(0.5*g*y + b));
}

/*
  interp interpolates a 2-d array array into parray.
  uses lots of memory; PC gymnastics deleted
*/
int interp(array, nx, ny, parray, npx, npy )
double *array;
int nx, ny;
double *parray;
int npx, npy;
{
  double *one, *two, *three, *four, *save, *done;
  double *xone, *xtwo, *xthree, *xfour;
  int k, i, iy;
  double y, dy, lasty;
  double oversampy, oversampx, oversamp;

  one   = (double *)malloc( (unsigned)(sizeof(double) * npx));
  two   = (double *)malloc( (unsigned)(sizeof(double) * npx));
  three = (double *)malloc( (unsigned)(sizeof(double) * npx));
  four  = (double *)malloc( (unsigned)(sizeof(double) * npx));

  if(!one || !two || !three || !four)
  {
    st_fail("no memory for interpolation");
    return(1);
  }

  xone   = &array[0];
  xtwo   = &array[nx];
  xthree = &array[nx*2];

  oversampy = (npy-1.0)/(ny-1.0);
  oversampx = (npx-1.0)/(nx-1.0);
  oversamp = oversampx < oversampy ? oversampx:oversampy;

/*
  npx = 1 + (int)rint(oversamp * ((double)nx - 1.0));
  npy = 1 + (int)rint(oversamp * ((double)ny - 1.0));
 */

                                                        /*  check that we need to interpolate */
  if(fabs(oversamp - 1.0) < 0.001 )
  {
     st_report("interpolation not needed - oversamp is %f", oversamp );
     return(0);
  }

  xinterp( xone,    nx, two,   npx );
  xinterp( xtwo,    nx, three, npx );
  xinterp( xthree,  nx, four,  npx );

  lasty = 0;
                                                        /* create first row by extrapolation */
  for( i=0; i< npx; i++ )
  {
    one[i] = two[i] - three[i] + two[i];
  }

  for(k=0;k<npy;k++)                                    /* for each new row, interpolate in y */
  {
    y  = (double)k/oversampy;
    iy = (int)y;

    if(iy != lasty)                                     /* check to see if it is time to move the pointers */
    { 
      save  = one;
      one   = two;
      two   = three;
      three = four;
      four  = save;

      if(iy+2 < ny)                                     /* interpolate along x */
      {
        xfour = &array[(iy+2)*nx];
        xinterp( xfour, nx, four, npx );
      }
      else                                              /* otherwize extrapolate */
      {
        for(i=0;i<npx;i++)
        {
          four[i] = three[i] - two[i] + three[i];
        }
      }

      lasty = iy;
    }

    done = &parray[npx*k];
    dy   = y - (double)iy;

    for(i=0;i<npx;i++) 
    {
      done[i] = yintpn( one[i], two[i], three[i], four[i], dy );
    }
  }

  free((char *)one);
  free((char *)two);
  free((char *)three);
  free((char *)four);

  return(0);
}

/*
  subroutine xinterp interpolates the input array x1 onto the output
  array x2, with nx2 points, oversampling the input array by oversamp
*/
int xinterp(x1, nx1, x2, nx2)
double *x1;
int nx1;
double *x2;
int nx2;
{
  double oversamp, x, a, b, c, d, dx;
  int jx, ix, inx;
  
  oversamp = (double)(nx2-1)/(double)(nx1-1);

  for(jx=0;jx<nx2;jx++)                                 /* jx is address of interpolated array */
  {
    x   = jx/oversamp;
    inx = (int)rint(x);

    if(fabs(x-(double)inx) < 0.0001)
    {
      x2[jx]=x1[inx];
    }
    else
    {
      ix = (int)x;
      dx = x-ix;
      b  = x1[ix];
      c  = x1[ix+1];

      if(ix > 0)
      {
        a = x1[ix-1];
      }
      else
      {
        a = b -c +b;         /* linear extrapolation for first point */
      }

      if(ix+2 < nx1)
      {
        d = x1[ix+2];
      }
      else
      {
        d = c -b +c;         /* linear extrapolation for last point */
      }

      x2[jx] = yintpn(a, b, c, d, dx);
    }
  }

  return(0);
}