profit.c

        posout[d] = 1.0;	/* FITS convention */
        dnaxisn[d] = profit->modnaxisn[d] + 0.99999;
        }

      for (e=0; e<prof->naxis - 2; e++)
        {
        d = 2+e;
/*------ Compute position along axis */
        posin[d] = (*prof->extra[e]-prof->extrazero[e])/prof->extrascale[e]+1.0;
/*------ Keep position within boundaries and let interpolation do the rest */
        if (posin[d] < 0.99999)
          {
          if (prof->extracycleflag[e])
            posin[d] += (float)prof->naxisn[d];
          else
            posin[d] = 1.0;
          }
        else if (posin[d] > (float)prof->naxisn[d])
          {
          if (prof->extracycleflag[e])
          posin[d] = (prof->extracycleflag[e])?
		  fmod(posin[d], (float)prof->naxisn[d])
		: (float)prof->naxisn[d];
          }
        }
      x1cin = (float)(prof->naxisn[0]/2);
      x2cin = (float)(prof->naxisn[1]/2);
      pixin = prof->pix;
      for (i=npix; i--;)
        {
        x1 = posout[0] - x1cout - 1.0 - dx1;
        x2 = posout[1] - x2cout - 1.0 - dx2;
        posin[0] = cd11*x1 + cd12*x2 + x1cin + 1.0;
        posin[1] = cd21*x1 + cd22*x2 + x2cin + 1.0;
        *(pixin++) = prof_interpolate(prof, posin);
        for (d=0; d<2; d++)
          if ((posout[d]+=1.0) < dnaxisn[d])
            break;
          else
            posout[d] = 1.0;
        }
      prof->lostfluxfrac = 0.0;
      threshflag = 1;
    break;
    }

/* For complex profiles, threshold to the brightest pixel value at border */
  if (threshflag)
    {
/*-- Now find truncation threshold */
/*-- Find the shortest distance to a vignet border */
    rmax = x1cout;
    if (rmax > (r = x2cout))
      rmax = r;
    rmax += 0.01;
    if (rmax<1.0)
      rmax = 1.0;
    r2max = rmax*rmax;
    rmin = rmax - 1.0;
    r2min = rmin*rmin;

/*-- Find best threshold (the max around the circle with radius rmax */
    dx2 = -x2cout;
    pixin = prof->pix;
    thresh = -BIG;
    for (ix2=profit->modnaxisn[1]; ix2--; dx2 += 1.0)
      {
      dx1 = -x1cout;
      for (ix1=profit->modnaxisn[0]; ix1--; dx1 += 1.0)
        if ((val=*(pixin++))>thresh && (r2=dx1*dx1+dx2*dx2)>r2min && r2<r2max)
          thresh = val;
      }

/*-- Threshold and measure the flux */
    flux = 0.0;
    pixin = prof->pix;
    for (i=npix; i--; pixin++)
      if (*pixin >= thresh)
        flux += (double)*pixin;
      else
        *pixin = 0.0;
    }
  else
    {
    flux = 0.0;
    pixin = prof->pix;
    for (i=npix; i--;)
      flux += (double)*(pixin++);
    }

  if (extfluxfac_flag)
    fluxfac = prof->fluxfac;
  else
    {
    if (prof->lostfluxfrac < 1.0)
      flux /= (1.0 - prof->lostfluxfrac);

    prof->fluxfac = fluxfac = fabs(flux)>0.0? profit->fluxfac/fabs(flux) : 0.0;
    }

  pixin = prof->pix;
  for (i=npix; i--;)
    *(pixin++) *= fluxfac;

/* Correct final flux */
  fluxfac = *prof->flux;
  pixin = prof->pix;
  pixout = profit->modpix;
  for (i=npix; i--;)
    *(pixout++) += fluxfac**(pixin++);

  return *prof->flux;
  }


/****** prof_moments **********************************************************
PROTO	int	prof_moments(profitstruct *profit, profstruct *prof)
PURPOSE	Computes (analytically or numerically) the 2nd moments of a profile.
INPUT	Profile-fitting structure,
	profile structure,
	optional pointer to 3xnparam Jacobian matrix.
OUTPUT	Index to the profile flux for further processing.
NOTES	.
AUTHOR	E. Bertin (IAP)
VERSION	20/08/2010
 ***/
int	prof_moments(profitstruct *profit, profstruct *prof, double *jac)
  {
   double	*dmx2,*dmy2,*dmxy,
		m20, a2, ct,st, mx2fac, my2fac,mxyfac, dc2,ds2,dcs,
		bn,bn2, n,n2, nfac,nfac2, hscale2, dmdn;
   int		nparam, index;

  if (jac)
/*-- Clear output Jacobian */
    {
    nparam = profit->nparam;
    memset(jac, 0, nparam*3*sizeof(double));
    dmx2 = jac;
    dmy2 = jac + nparam;
    dmxy = jac + 2*nparam;
    }
  else
    dmx2 = dmy2 = dmxy = NULL;		/* To avoid gcc -Wall warnings */

  m20 = 0.0;				/* to avoid gcc -Wall warnings */
  index = 0;				/* to avoid gcc -Wall warnings */


  if (prof->posangle)
    {
    a2 = *prof->aspect**prof->aspect;
    ct = cos(*prof->posangle*DEG);
    st = sin(*prof->posangle*DEG);
    mx2fac = ct*ct + st*st*a2;
    my2fac = st*st + ct*ct*a2;
    mxyfac = ct*st * (1.0 - a2);
    if (jac)
      {
      dc2 = -2.0*ct*st*DEG;
      ds2 =  2.0*ct*st*DEG;
      dcs = (ct*ct - st*st)*DEG;
      }
    else
      dc2 = ds2 = dcs = 0.0;		/* To avoid gcc -Wall warnings */
    switch(prof->code)
      {
      case MODEL_SERSIC:
        n = fabs(*prof->extra[0]);
        bn = 2.0*n - 1.0/3.0 + 4.0/(405.0*n) + 46.0/(25515.0*n*n)
		+ 131.0/(1148175*n*n*n);	/* Ciotti & Bertin 1999 */
        nfac  = prof_gamma(4.0*n) / (prof_gamma(2.0*n)*pow(bn, 2.0*n));
        hscale2 = 0.5 * *prof->scale**prof->scale;
        m20 = hscale2 * nfac;
        if (jac)
          {
          dmx2[profit->paramindex[PARAM_SPHEROID_REFF]]
			= *prof->scale * nfac * mx2fac;
          dmy2[profit->paramindex[PARAM_SPHEROID_REFF]]
			= *prof->scale * nfac * my2fac;
          dmxy[profit->paramindex[PARAM_SPHEROID_REFF]]
			= *prof->scale * nfac * mxyfac;
          n2 = n+0.01;
          bn2 = 2.0*n2 - 1.0/3.0 + 4.0/(405.0*n2) + 46.0/(25515.0*n2*n2)
		+ 131.0/(1148175*n2*n2*n2);	/* Ciotti & Bertin 1999 */
          nfac2 = prof_gamma(4.0*n2) / (prof_gamma(2.0*n2)*pow(bn2, 2.0*n2));
          dmdn = 100.0 * hscale2 * (nfac2-nfac);
          dmx2[profit->paramindex[PARAM_SPHEROID_SERSICN]] = dmdn * mx2fac;
          dmy2[profit->paramindex[PARAM_SPHEROID_SERSICN]] = dmdn * my2fac;
          dmxy[profit->paramindex[PARAM_SPHEROID_SERSICN]] = dmdn * mxyfac;
          dmx2[profit->paramindex[PARAM_SPHEROID_ASPECT]]
			= 2.0 * m20 * st*st * *prof->aspect;
          dmy2[profit->paramindex[PARAM_SPHEROID_ASPECT]]
			= 2.0 * m20 * ct*ct * *prof->aspect;
          dmxy[profit->paramindex[PARAM_SPHEROID_ASPECT]]
			= -2.0 * m20 * ct*st * *prof->aspect;
          dmx2[profit->paramindex[PARAM_SPHEROID_POSANG]] = m20 * (dc2+ds2*a2);
          dmy2[profit->paramindex[PARAM_SPHEROID_POSANG]] = m20 * (ds2+dc2*a2);
          dmxy[profit->paramindex[PARAM_SPHEROID_POSANG]] = m20 * (1.0-a2)*dcs;
          }
        index = profit->paramindex[PARAM_SPHEROID_FLUX];
        break; 
      case MODEL_DEVAUCOULEURS:
        m20 = 10.83995 * *prof->scale**prof->scale;
        if (jac)
          {
          dmx2[profit->paramindex[PARAM_SPHEROID_REFF]]
			= 21.680 * *prof->scale * mx2fac;
          dmy2[profit->paramindex[PARAM_SPHEROID_REFF]]
			= 21.680 * *prof->scale * my2fac;
          dmxy[profit->paramindex[PARAM_SPHEROID_REFF]]
			= 21.680 * *prof->scale * mxyfac;
          dmx2[profit->paramindex[PARAM_SPHEROID_ASPECT]]
			= 2.0 * m20 * st*st * *prof->aspect;
          dmy2[profit->paramindex[PARAM_SPHEROID_ASPECT]]
			= 2.0 * m20 * ct*ct * *prof->aspect;
          dmxy[profit->paramindex[PARAM_SPHEROID_ASPECT]]
			= -2.0 * m20 * ct*st * *prof->aspect;
          dmx2[profit->paramindex[PARAM_SPHEROID_POSANG]] = m20 * (dc2+ds2*a2);
          dmy2[profit->paramindex[PARAM_SPHEROID_POSANG]] = m20 * (ds2+dc2*a2);
          dmxy[profit->paramindex[PARAM_SPHEROID_POSANG]] = m20 * (1.0-a2)*dcs;
          }
        index = profit->paramindex[PARAM_SPHEROID_FLUX];
        break;
      case MODEL_EXPONENTIAL:
        m20 = 3.0 * *prof->scale**prof->scale;
        if (jac)
          {
          dmx2[profit->paramindex[PARAM_DISK_SCALE]]
			= 6.0 * *prof->scale * mx2fac;
          dmy2[profit->paramindex[PARAM_DISK_SCALE]]
			= 6.0 * *prof->scale * my2fac;
          dmxy[profit->paramindex[PARAM_DISK_SCALE]]
			= 6.0 * *prof->scale * mxyfac;
          dmx2[profit->paramindex[PARAM_DISK_ASPECT]]
			= 2.0 * m20 * st*st * *prof->aspect;
          dmy2[profit->paramindex[PARAM_DISK_ASPECT]]
			= 2.0 * m20 * ct*ct * *prof->aspect;
          dmxy[profit->paramindex[PARAM_DISK_ASPECT]]
			= -2.0 * m20 * ct*st * *prof->aspect;
          dmx2[profit->paramindex[PARAM_DISK_POSANG]] = m20 * (dc2 + ds2*a2);
          dmy2[profit->paramindex[PARAM_DISK_POSANG]] = m20 * (ds2 + dc2*a2);
          dmxy[profit->paramindex[PARAM_DISK_POSANG]] = m20 * (1.0 - a2) * dcs;
          }
        index = profit->paramindex[PARAM_DISK_FLUX];
        break;
      case MODEL_ARMS:
        m20 = 1.0;
        index = profit->paramindex[PARAM_ARMS_FLUX];
        break;
      case MODEL_BAR:
        m20 = 1.0;
        index = profit->paramindex[PARAM_BAR_FLUX];
        break;
      case MODEL_INRING:
        m20 = 1.0;
        index = profit->paramindex[PARAM_INRING_FLUX];
        break;
      case MODEL_OUTRING:
        m20 = 1.0;
        index = profit->paramindex[PARAM_OUTRING_FLUX];
        break;
      default:
        error(EXIT_FAILURE, "*Internal Error*: Unknown oriented model in ",
		"prof_moments()");
      break;
      }

    prof->mx2 = m20*mx2fac;
    prof->my2 = m20*my2fac;
    prof->mxy = m20*mxyfac;
    
    }
  else
    prof->mx2 = prof->my2 = prof->mxy = 0.0;

  return index;
  }


/****** prof_interpolate ******************************************************
PROTO	float	prof_interpolate(profstruct *prof, float *posin)
PURPOSE	Interpolate a multidimensional model profile at a given position.
INPUT	Profile structure,
	input position vector.
OUTPUT	-.
NOTES	-.
AUTHOR	E. Bertin (IAP)
VERSION	10/12/2006
 ***/
static float	prof_interpolate(profstruct *prof, float *posin)
  {
   float		dpos[2+PROFIT_MAXEXTRA],
			kernel_vector[INTERP_MAXKERNELWIDTH],
			*kvector, *pixin,*pixout,
			val;
   long			step[2+PROFIT_MAXEXTRA],
			start, fac;
   int			linecount[2+PROFIT_MAXEXTRA],
			*naxisn,
			i,j,n, ival, nlines, kwidth,width, badpixflag, naxis;

  naxis = prof->naxis;
  naxisn = prof->naxisn;
  start = 0;
  fac = 1;
  for (n=0; n<naxis; n++)
    {
    val = *(posin++);
    width = *(naxisn++);
/*-- Get the integer part of the current coordinate or nearest neighbour */
    ival = (prof->interptype[n]==INTERP_NEARESTNEIGHBOUR)?
                                        (int)(val-0.50001):(int)val;
/*-- Store the fractional part of the current coordinate */
    dpos[n] = val - ival;
/*-- Check if interpolation start/end exceed image boundary... */
    kwidth = prof->kernelwidth[n];
    ival-=kwidth/2;
    if (ival<0 || ival+kwidth<=0 || ival+kwidth>width)
      return 0.0;

/*-- Update starting pointer */
    start += ival*fac;
/*-- Update step between interpolated regions */
    step[n] = fac*(width-kwidth);
    linecount[n] = 0.0;
    fac *= width;
    }

/* Update Interpolation kernel vectors */
  make_kernel(*dpos, kernel_vector, prof->interptype[0]);
  kwidth = prof->kernelwidth[0];
  nlines = prof->kernelnlines;
/* First step: interpolate along NAXIS1 from the data themselves */
  badpixflag = 0;
  pixin = prof->pix+start;
  pixout = prof->kernelbuf;
  for (j=nlines; j--;)
    {
    val = 0.0;
    kvector = kernel_vector;
    for (i=kwidth; i--;)
       val += *(kvector++)**(pixin++);
    *(pixout++) = val;
    for (n=1; n<naxis; n++)
      {
      pixin+=step[n-1];
      if (++linecount[n]<prof->kernelwidth[n])
        break;
      else
        linecount[n] = 0;       /* No need to initialize it to 0! */
      }
    }

/* Second step: interpolate along other axes from the interpolation buffer */
  for (n=1; n<naxis; n++)
    {
    make_kernel(dpos[n], kernel_vector, prof->interptype[n]);
    kwidth = prof->kernelwidth[n];
    pixout = pixin = prof->kernelbuf;
    for (j = (nlines/=kwidth); j--;)
      {
      val = 0.0;
      kvector = kernel_vector;
      for (i=kwidth; i--;)
        val += *(kvector++)**(pixin++);
      *(pixout++) = val;
     }
    }

  return prof->kernelbuf[0];
  }


/****** interpolate_pix ******************************************************
PROTO	void interpolate_pix(float *posin, float *pix, int naxisn,
		interpenum interptype)
PURPOSE	Interpolate a model profile at a given position.
INPUT	Profile structure,
	input position vector,
	input pixmap dimension vector,
	interpolation type.
OUTPUT	-.
NOTES	-.
AUTHOR	E. Bertin (IAP)
VERSION	07/12/2006
 ***/
static float	interpolate_pix(float *posin, float *pix, int *naxisn,
			interpenum interptype)
  {
   float	buffer[INTERP_MAXKERNELWIDTH],
		kernel[INTERP_MAXKERNELWIDTH], dpos[2],
		*kvector, *pixin, *pixout,
		val;
   int		fac, ival, kwidth, start, width, step,
		i,j, n;

  kwidth = interp_kernwidth[interptype];
  start = 0;
  fac = 1;
  for (n=0; n<2; n++)
    {
    val = *(posin++);
    width = naxisn[n];
/*-- Get the integer part of the current coordinate or nearest neighbour */
    ival = (interptype==INTERP_NEARESTNEIGHBOUR)? (int)(val-0.50001):(int)val;
/*-- Store the fractional part of the current coordinate */
    dpos[n] = val - ival;
/*-- Check if interpolation start/end exceed image boundary... */
    ival-=kwidth/2;
    if (ival<0 || ival+kwidth<=0 || ival+kwidth>width)
      return 0.0;
/*-- Update starting pointer */
    start += ival*fac;
/*-- Update step between interpolated regions */
    fac *= width;
    }

/* First step: interpolate along NAXIS1 from the data themselves */
  make_kernel(dpos[0], kernel, interptype);
  step = naxisn[0]-kwidth;
  pixin = pix+start;
  pixout = buffer;
  for (j=kwidth; j--;)
    {
    val = 0.0;
    kvector = kernel;
    for (i=kwidth; i--;)
      val += *(kvector++)**(pixin++);
    *(pixout++) = val;
    pixin += step;
    }

/* Second step: interpolate along NAXIS2 from the interpolation buffer */
  make_kernel(dpos[1], kernel, interptype);
  pixin = buffer;
  val = 0.0;
  kvector = kernel;
  for (i=kwidth; i--;)
    val += *(kvector++)**(pixin++);

  return val;
  }


/****** make_kernel **********************************************************
PROTO	void make_kernel(float pos, float *kernel, interpenum interptype)
PURPOSE	Conpute interpolation-kernel data
INPUT	Position,
	Pointer to the output kernel data,
	Interpolation method.
OUTPUT	-.
NOTES	-.
AUTHOR	E. Bertin (IAP)
VERSION	07/09/2009
 ***/
void	make_kernel(float pos, float *kernel, interpenum interptype)
  {
   float	x, val, sinx1,sinx2,sinx3,cosx1;

  if (interptype == INTERP_NEARESTNEIGHBOUR)
    *kernel = 1;
  else if (interptype == INTERP_BILINEAR)
    {
    *(kernel++) = 1.0-pos;
    *kernel = pos;
    }
  else if (interptype == INTERP_LANCZOS2)
    {
    if (pos<1e-5 && pos>-1e-5)
      {
      *(kernel++) = 0.0;
      *(kernel++) = 1.0;
      *(kernel++) = 0.0;
      *kernel = 0.0;
      }
    else
      {
      x = -PI/2.0*(pos+1.0);
#ifdef HAVE_SINCOSF
      sincosf(x, &sinx1, &cosx1);
#else
      sinx1 = sinf(x);
      cosx1 = cosf(x);
#endif
      val = (*(kernel++) = sinx1/(x*x));
      x += PI/2.0;
      val += (*(kernel++) = -cosx1/(x*x));
      x += PI/2.0;
      val += (*(kernel++) = -sinx1/(x*x));
      x += PI/2.0;
      val += (*kernel = cosx1/(x*x));
      val = 1.0/val;
      *(kernel--) *= val;
      *(kernel--) *= val;
      *(kernel--) *= val;
      *kernel *= val;
      }
    }
  else if (interptype == INTERP_LANCZOS3)
    {
    if (pos<1e-5 && pos>-1e-5)
      {
      *(kernel++) = 0.0;
      *(kernel++) = 0.0;
      *(kernel++) = 1.0;
      *(kernel++) = 0.0;
      *(kernel++) = 0.0;
      *kernel = 0.0;
      }
    else
      {
      x = -PI/3.0*(pos+2.0);
#ifdef HAVE_SINCOS
      sincosf(x, &sinx1, &cosx1);
#else
      sinx1 = sinf(x);
      cosx1 = cosf(x);
#endif
      val = (*(kernel++) = sinx1/(x*x));
      x += PI/3.0;
      val += (*(kernel++) = (sinx2=-0.5*sinx1-0.866025403785*cosx1)
				/ (x*x));
      x += PI/3.0;
      val += (*(kernel++) = (sinx3=-0.5*sinx1+0.866025403785*cosx1)
				/(x*x));
      x += PI/3.0;
      val += (*(kernel++) = sinx1/(x*x));
      x += PI/3.0;
      val += (*(kernel++) = sinx2/(x*x));
      x += PI/3.0;
      val += (*kernel = sinx3/(x*x));
      val = 1.0/val;
      *(kernel--) *= val;
      *(kernel--) *= val;
      *(kernel--) *= val;
      *(kernel--) *= val;
      *(kernel--) *= val;
      *kernel *= val;
      }
    }
  else if (interptype == INTERP_LANCZOS4)
    {
    if (pos<1e-5 && pos>-1e-5)
      {
      *(kernel++) = 0.0;
      *(kernel++) = 0.0;
      *(kernel++) = 0.0;
      *(kernel++) = 1.0;
      *(kernel++) = 0.0;
      *(kernel++) = 0.0;
      *(kernel++) = 0.0;
      *kernel = 0.0;
      }
    else
      {
      x = -PI/4.0*(pos+3.0);
#ifdef HAVE_SINCOS
      sincosf(x, &sinx1, &cosx1);
#else
      sinx1 = sinf(x);
      cosx1 = cosf(x);
#endif
      val = (*(kernel++) = sinx1/(x*x));
      x += PI/4.0;
      val +=(*(kernel++) = -(sinx2=0.707106781186*(sinx1+cosx1))
				/(x*x));
      x += PI/4.0;
      val += (*(kernel++) = cosx1/(x*x));
      x += PI/4.0;
      val += (*(kernel++) = -(sinx3=0.707106781186*(cosx1-sinx1))/(x*x));
      x += PI/4.0;
      val += (*(kernel++) = -sinx1/(x*x));
      x += PI/4.0;
      val += (*(kernel++) = sinx2/(x*x));
      x += PI/4.0;
      val += (*(kernel++) = -cosx1/(x*x));
      x += PI/4.0;
      val += (*kernel = sinx3/(x*x));
      val = 1.0/val;
      *(kernel--) *= val;
      *(kernel--) *= val;
      *(kernel--) *= val;
      *(kernel--) *= val;
      *(kernel--) *= val;
      *(kernel--) *= val;
      *(kernel--) *= val;
      *kernel *= val;
      }
    }
  else
    error(EXIT_FAILURE, "*Internal Error*: Unknown interpolation type in ",
		"make_kernel()");

  return;
  }