profit.c

 /*
 				profit.c

*%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
*
*	Part of:	SExtractor
*
*	Authors:	E.BERTIN (IAP)
*
*	Contents:	Fit an arbitrary profile combination to a detection.
*
*	Last modify:	20/03/2009
*
*%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
*/

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

#ifdef HAVE_MATHIMF_H
#include <mathimf.h>
#else
#define _GNU_SOURCE
#include <math.h>
#endif

#ifdef HAVE_LOGF
#define	LOGF	logf
#else
#define	LOGF	log
#endif

#include	<stdio.h>
#include	<stdlib.h>
#include	<string.h>

#include	"define.h"
#include	"globals.h"
#include	"prefs.h"
#include	"fits/fitscat.h"
#include	"levmar/lm.h"
#include	"fft.h"
#include	"fitswcs.h"
#include	"check.h"
#include	"pattern.h"
#include	"psf.h"
#include	"profit.h"

static double	prof_interpolate(profstruct *prof, double *posin);
static double	interpolate_pix(double *posin, double *pix, int *naxisn,
		interpenum interptype);

static void	make_kernel(double pos, double *kernel, interpenum interptype);

/*------------------------------- variables ---------------------------------*/

char		profname[][32]={"background offset", "Sersic spheroid",
		"De Vaucouleurs spheroid", "exponential disk", "spiral arms",
		"bar", "inner ring", "outer ring", "tabulated model",
		""};

int		interp_kernwidth[5]={1,2,4,6,8};
int theniter, the_gal;
/* "Local" global variables; it seems dirty but it simplifies a lot */
/* interfacing to the LM routines */
static picstruct	*the_field, *the_wfield;
profitstruct		*theprofit;

/****** profit_init ***********************************************************
PROTO	profitstruct profit_init(psfstruct *psf)
PURPOSE	Allocate and initialize a new profile-fitting structure.
INPUT	Pointer to PSF structure.
OUTPUT	A pointer to an allocated profit structure.
NOTES	-.
AUTHOR	E. Bertin (IAP)
VERSION	26/04/2008
 ***/
profitstruct	*profit_init(psfstruct *psf)
  {
   profitstruct		*profit;
   int			p, nprof,
			backflag, spheroidflag, diskflag, barflag, armsflag;

  QCALLOC(profit, profitstruct, 1);
  profit->psf = psf;
  profit->psfdft = NULL;

  profit->nparam = 0;
  QMALLOC(profit->prof, profstruct *, PROF_NPROF);
  backflag = spheroidflag = diskflag = barflag = armsflag = 0;
  nprof = 0;
  for (p=0; p<PROF_NPROF; p++)
    if (!backflag && FLAG(obj2.prof_offset_flux))
      {
      profit->prof[p] = prof_init(profit, PROF_BACK);
      backflag = 1;
      nprof++;
      }
    else if (!spheroidflag && FLAG(obj2.prof_spheroid_flux))
      {
      profit->prof[p] = prof_init(profit,
	FLAG(obj2.prof_spheroid_sersicn)? PROF_SERSIC : PROF_DEVAUCOULEURS);
      spheroidflag = 1;
      nprof++;
      }
    else if (!diskflag && FLAG(obj2.prof_disk_flux))
      {
      profit->prof[p] = prof_init(profit, PROF_EXPONENTIAL);
      diskflag = 1;
      nprof++;
      }
    else if (diskflag && !barflag && FLAG(obj2.prof_bar_flux))
      {
      profit->prof[p] = prof_init(profit, PROF_BAR);
      barflag = 1;
      nprof++;
      }
    else if (barflag && !armsflag && FLAG(obj2.prof_arms_flux))
      {
      profit->prof[p] = prof_init(profit, PROF_ARMS);
      armsflag = 1;
      nprof++;
      }

  QMALLOC(profit->covar, double, profit->nparam*profit->nparam);
  profit->nprof = nprof;

  return profit;
  }  


/****** profit_end ************************************************************
PROTO	void prof_end(profstruct *prof)
PURPOSE	End (deallocate) a profile-fitting structure.
INPUT	Prof structure.
OUTPUT	-.
NOTES	-.
AUTHOR	E. Bertin (IAP)
VERSION	26/04/2008
 ***/
void	profit_end(profitstruct *profit)
  {
   int	p;

  for (p=0; p<profit->nprof; p++)
    prof_end(profit->prof[p]);
  free(profit->prof);
  free(profit->covar);
  free(profit->psfdft);
  free(profit);

  return;
  }


/****** profit_fit ************************************************************
PROTO	void profit_fit(profitstruct *profit, picstruct *field,
		picstruct *wfield, objstruct *obj, obj2struct *obj2)
PURPOSE	Fit profile(s) convolved with the PSF to a detected object.
INPUT	Array of profile structures,
	Number of profiles,
	Pointer to the profile-fitting structure,
	Pointer to the field,
	Pointer to the field weight,
	Pointer to the obj.
OUTPUT	Pointer to an allocated fit structure (containing details about the
	fit).
NOTES	It is a modified version of the lm_minimize() of lmfit.
AUTHOR	E. Bertin (IAP)
VERSION	20/03/2009
 ***/
void	profit_fit(profitstruct *profit,
		picstruct *field, picstruct *wfield,
		objstruct *obj, obj2struct *obj2)
  {
    profitstruct	pprofit;
    patternstruct *pattern;
    psfstruct		*psf;
    checkstruct		*check;
    double		*oldparaminit,
			psf_fwhm, oldchi2, a , cp,sp, emx2,emy2,emxy, dchi2;
    int			i,j,p, oldniter, nparam, ncomp;

  nparam = profit->nparam;
  if (profit->psfdft)
    {
    QFREE(profit->psfdft);
    }

  psf = profit->psf;
  profit->pixstep = psf->pixstep;

/* Create pixmaps at image resolution */
  psf_fwhm = psf->masksize[0]*psf->pixstep;
  profit->objnaxisn[0] = (((int)((obj->xmax-obj->xmin+1) + psf_fwhm + 0.499)
		*1.2)/2)*2 + 1;
  profit->objnaxisn[1] = (((int)((obj->ymax-obj->ymin+1) + psf_fwhm + 0.499)
		*1.2)/2)*2 + 1;
  profit->ix = (int)(obj->mx + 0.49999);/* internal convention: 1st pix = 0 */
  profit->iy = (int)(obj->my + 0.49999);/* internal convention: 1st pix = 0 */

  if (profit->objnaxisn[1]<profit->objnaxisn[0])
    profit->objnaxisn[1] = profit->objnaxisn[0];
  else
    profit->objnaxisn[0] = profit->objnaxisn[1];

/* Use (dirty) global variables to interface with lmfit */
  the_field = field;
  the_wfield = wfield;
  theprofit = profit;
  profit->obj = obj;
  profit->obj2 = obj2;

  QMALLOC(profit->objpix, PIXTYPE, profit->objnaxisn[0]*profit->objnaxisn[1]);
  QMALLOC(profit->objweight, PIXTYPE,profit->objnaxisn[0]*profit->objnaxisn[1]);
  QMALLOC(profit->lmodpix, PIXTYPE, profit->objnaxisn[0]*profit->objnaxisn[1]);
  profit->nresi = profit_copyobjpix(profit, field, wfield);
  if (profit->nresi < nparam)
    {
    if (FLAG(obj2.prof_vector))
      for (p=0; p<nparam; p++)
        obj2->prof_vector[p] = 0.0;
    obj2->prof_niter = 0;
    return;
    }

  QMALLOC(profit->resi, double, profit->nresi);

/* Create pixmap at PSF resolution */
  profit->modnaxisn[0] =
	((int)(profit->objnaxisn[0]/profit->pixstep +0.4999)/2+1)*2; 
  profit->modnaxisn[1] =
	((int)(profit->objnaxisn[1]/profit->pixstep +0.4999)/2+1)*2; 
  if (profit->modnaxisn[1] < profit->modnaxisn[0])
    profit->modnaxisn[1] = profit->modnaxisn[0];
  else
    profit->modnaxisn[0] = profit->modnaxisn[1];

/* Allocate memory for the complete model */
  QCALLOC(profit->modpix, double, profit->modnaxisn[0]*profit->modnaxisn[1]);
  QMALLOC(profit->psfpix, double, profit->modnaxisn[0]*profit->modnaxisn[1]);
/* Allocate memory for the partial model */
  QMALLOC(profit->pmodpix, float, profit->modnaxisn[0]*profit->modnaxisn[1]);

/* Compute the local PSF */
  profit_psf(profit);

/* Set initial guesses and boundaries */
  obj2->prof_flag = 0;
  profit->sigma = obj->sigbkg;

  profit_resetparams(profit);

the_gal++;

/* Actual minimisation */
  profit->niter = profit_minimize(profit, PROFIT_MAXITER);
  profit_residuals(profit,field,wfield, 0.0, profit->param,profit->resi);

/*
  QMEMCPY(profit->paraminit, oldparaminit, double, nparam);
  if (profit_setparam(profit, PARAM_ARMS_PITCH, 160.0, 130.0, 175.0)==RETURN_OK)
    {
    oldchi2 = profit->chi2;
    oldniter = profit->niter;
    profit_resetparams(profit);
    profit_setparam(profit, PARAM_ARMS_PITCH, 160.0, 130.0, 175.0);
    profit->niter = profit_minimize(profit, PROFIT_MAXITER);
    if (profit->chi2 > oldchi2)
      {
      memcpy(profit->paraminit, oldparaminit, nparam*sizeof(double));
      profit->chi2 = oldchi2;
      profit->niter = oldniter;
      }
    else
      obj2->prof_flag |= PROFIT_FLIPPED;
    }  
*/

/* Convert covariance matrix to bound space */
  profit_covarunboundtobound(profit);
  for (p=0; p<nparam; p++)
    profit->paramerr[p]= sqrt(profit->covar[p*(nparam+1)]);

/* Equate param and paraminit vectors to avoid confusion later on */
  for (p=0; p<profit->nparam; p++)
    profit->param[p] = profit->paraminit[p];

/* CHECK-Images */
  if ((check = prefs.check[CHECK_SUBPROFILES]))
    {
    profit_residuals(profit,field,wfield, 0.0, profit->param,profit->resi);
    addcheck(check, profit->lmodpix, profit->objnaxisn[0],profit->objnaxisn[1],
		profit->ix,profit->iy, -1.0);
    }
  if ((check = prefs.check[CHECK_PROFILES]))
    {
    profit_residuals(profit,field,wfield, 0.0, profit->param,profit->resi);
    addcheck(check, profit->lmodpix, profit->objnaxisn[0],profit->objnaxisn[1],
		profit->ix,profit->iy, 1.0);
    }
/* Fill measurement parameters */
  if (FLAG(obj2.prof_vector))
    {
    for (p=0; p<nparam; p++)
      obj2->prof_vector[p]= profit->param[p];
    }
  if (FLAG(obj2.prof_errvector))
    {
    for (p=0; p<nparam; p++)
      obj2->prof_errvector[p]= profit->paramerr[p];
    }

  obj2->prof_niter = profit->niter;
  obj2->flux_prof = profit->flux;
  obj2->prof_chi2 = (profit->nresi > profit->nparam)?
		profit->chi2 / (profit->nresi - profit->nparam) : 0.0;

  if (FLAG(obj2.x_prof))
    {
    i = profit->paramindex[PARAM_X];
    j = profit->paramindex[PARAM_Y];
/*-- Model coordinates follow the FITS convention (first pixel at 1,1) */
    if (profit->paramlist[PARAM_X])
      {
      obj2->x_prof = profit->ix + *profit->paramlist[PARAM_X] + 1.0;
      obj2->poserrmx2_prof = emx2 = profit->covar[i*(nparam+1)];
      }
    else
      emx2 = 0.0;
    if (profit->paramlist[PARAM_Y])
      {
      obj2->y_prof = profit->iy + *profit->paramlist[PARAM_Y] + 1.0;
      obj2->poserrmy2_prof = emy2 = profit->covar[j*(nparam+1)];
      }
    else
      emy2 = 0.0;
    if (profit->paramlist[PARAM_X] && profit->paramlist[PARAM_Y])
      obj2->poserrmxy_prof = emxy = profit->covar[i+j*nparam];
    else
      emxy = 0.0;

/*-- Error ellipse parameters */
    if (FLAG(obj2.poserra_prof))
      {
       double	pmx2,pmy2,temp,theta;

      if (fabs(temp=emx2-emy2) > 0.0)
        theta = atan2(2.0 * emxy,temp) / 2.0;
      else
        theta = PI/4.0;

      temp = sqrt(0.25*temp*temp+ emxy*emxy);
      pmy2 = pmx2 = 0.5*(emx2+emy2);
      pmx2+=temp;
      pmy2-=temp;

      obj2->poserra_prof = (float)sqrt(pmx2);
      obj2->poserrb_prof = (float)sqrt(pmy2);
      obj2->poserrtheta_prof = theta*180.0/PI;
      }

    if (FLAG(obj2.poserrcxx_prof))
      {
       double	temp;

      obj2->poserrcxx_prof = (float)(emy2/(temp=emx2*emy2-emxy*emxy));
      obj2->poserrcyy_prof = (float)(emx2/temp);
      obj2->poserrcxy_prof = (float)(-2*emxy/temp);
      }
    }


  if (FLAG(obj2.prof_mx2))
    {
    memset(profit->modpix, 0,
	profit->modnaxisn[0]*profit->modnaxisn[1]*sizeof(double));
    for (p=0; p<profit->nprof; p++)
      prof_add(profit->prof[p], profit);
    profit_moments(profit);
    }

/* Bulge */
  if (FLAG(obj2.prof_spheroid_flux))
    {
    obj2->prof_spheroid_flux = *profit->paramlist[PARAM_SPHEROID_FLUX];
    obj2->prof_spheroid_fluxerr =
		profit->paramerr[profit->paramindex[PARAM_SPHEROID_FLUX]];
    obj2->prof_spheroid_reff = *profit->paramlist[PARAM_SPHEROID_REFF];
    obj2->prof_spheroid_refferr = 
		profit->paramerr[profit->paramindex[PARAM_SPHEROID_REFF]];
    obj2->prof_spheroid_aspect = *profit->paramlist[PARAM_SPHEROID_ASPECT];
    obj2->prof_spheroid_aspecterr = 
		profit->paramerr[profit->paramindex[PARAM_SPHEROID_ASPECT]];
    obj2->prof_spheroid_theta =
			fmod_m90_p90(*profit->paramlist[PARAM_SPHEROID_POSANG]);
    obj2->prof_spheroid_thetaerr = 
		profit->paramerr[profit->paramindex[PARAM_SPHEROID_POSANG]];
    if (FLAG(obj2.prof_spheroid_sersicn))
      {
      obj2->prof_spheroid_sersicn = *profit->paramlist[PARAM_SPHEROID_SERSICN];
      obj2->prof_spheroid_sersicnerr = 
		profit->paramerr[profit->paramindex[PARAM_SPHEROID_SERSICN]];
      }
    }

/* Disk */
  if (FLAG(obj2.prof_disk_flux))
    {
    obj2->prof_disk_flux = *profit->paramlist[PARAM_DISK_FLUX];
    obj2->prof_disk_fluxerr =
		profit->paramerr[profit->paramindex[PARAM_DISK_FLUX]];
    obj2->prof_disk_scale = *profit->paramlist[PARAM_DISK_SCALE];
    obj2->prof_disk_scaleerr =
		profit->paramerr[profit->paramindex[PARAM_DISK_SCALE]];
    obj2->prof_disk_aspect = *profit->paramlist[PARAM_DISK_ASPECT];
    obj2->prof_disk_aspecterr =
		profit->paramerr[profit->paramindex[PARAM_DISK_ASPECT]];
    obj2->prof_disk_theta = fmod_m90_p90(*profit->paramlist[PARAM_DISK_POSANG]);
    obj2->prof_disk_thetaerr =
		profit->paramerr[profit->paramindex[PARAM_DISK_POSANG]];
    if (FLAG(obj2.prof_disk_inclination))
      {
      obj2->prof_disk_inclination = acos(obj2->prof_disk_aspect) / DEG;
      if (FLAG(obj2.prof_disk_inclinationerr))
        {
        a = sqrt(1.0-obj2->prof_disk_aspect*obj2->prof_disk_aspect);
        obj2->prof_disk_inclinationerr = obj2->prof_disk_aspecterr
					/(a>0.1? a : 0.1)/DEG;
        }
      }

/* Disk pattern */
    if (prefs.pattern_flag)
      {
      profit_residuals(profit,field,wfield, PROFIT_DYNPARAM,
			profit->param,profit->resi);
      pattern = pattern_init(profit, prefs.pattern_type,
		prefs.prof_disk_patternncomp);
      pattern_fit(pattern, profit);
      if (FLAG(obj2.prof_disk_patternspiral))
        obj2->prof_disk_patternspiral = pattern_spiral(pattern);
      if (FLAG(obj2.prof_disk_patternvector))
        {
        ncomp = pattern->size[2];
        for (p=0; p<ncomp; p++)
          obj2->prof_disk_patternvector[p] = (float)pattern->coeff[p];
        }
      if (FLAG(obj2.prof_disk_patternmodvector))
        {
        ncomp = pattern->ncomp*pattern->nfreq;
        for (p=0; p<ncomp; p++)
          obj2->prof_disk_patternmodvector[p] = (float)pattern->mcoeff[p];
        }
      if (FLAG(obj2.prof_disk_patternargvector))
        {
        ncomp = pattern->ncomp*pattern->nfreq;
        for (p=0; p<ncomp; p++)
          obj2->prof_disk_patternargvector[p] = (float)pattern->acoeff[p];
        }
      pattern_end(pattern);
      }

/* Bar */
    if (FLAG(obj2.prof_bar_flux))
      {
      obj2->prof_bar_flux = *profit->paramlist[PARAM_BAR_FLUX];
      obj2->prof_bar_fluxerr =
		profit->paramerr[profit->paramindex[PARAM_BAR_FLUX]];
      obj2->prof_bar_length = *profit->paramlist[PARAM_ARMS_START]
				**profit->paramlist[PARAM_DISK_SCALE];
      obj2->prof_bar_lengtherr = *profit->paramlist[PARAM_ARMS_START]
		  * profit->paramerr[profit->paramindex[PARAM_DISK_SCALE]]
		+ *profit->paramlist[PARAM_DISK_SCALE]
		  * profit->paramerr[profit->paramindex[PARAM_ARMS_START]];
      obj2->prof_bar_aspect = *profit->paramlist[PARAM_BAR_ASPECT];
      obj2->prof_bar_aspecterr =
		profit->paramerr[profit->paramindex[PARAM_BAR_ASPECT]];
      obj2->prof_bar_posang = 
			fmod_m90_p90(*profit->paramlist[PARAM_ARMS_POSANG]);
      obj2->prof_bar_posangerr =
		profit->paramerr[profit->paramindex[PARAM_ARMS_POSANG]];
      if (FLAG(obj2.prof_bar_theta))
        {
        cp = cos(obj2->prof_bar_posang*DEG);
        sp = sin(obj2->prof_bar_posang*DEG);
        a = obj2->prof_disk_aspect;
        obj2->prof_bar_theta = fmod_m90_p90(atan2(a*sp,cp)/DEG
				+ obj2->prof_disk_theta);
        obj2->prof_bar_thetaerr = obj2->prof_bar_posangerr*a/(cp*cp+a*a*sp*sp);
        }

/* Arms */
      if (FLAG(obj2.prof_arms_flux))
        {
        obj2->prof_arms_flux = *profit->paramlist[PARAM_ARMS_FLUX];
        obj2->prof_arms_fluxerr =
		profit->paramerr[profit->paramindex[PARAM_ARMS_FLUX]];
        obj2->prof_arms_pitch =
		fmod_m90_p90(*profit->paramlist[PARAM_ARMS_PITCH]);
        obj2->prof_arms_pitcherr =
		profit->paramerr[profit->paramindex[PARAM_ARMS_PITCH]];
        obj2->prof_arms_start = *profit->paramlist[PARAM_ARMS_START]
				**profit->paramlist[PARAM_DISK_SCALE];
        obj2->prof_arms_starterr = *profit->paramlist[PARAM_ARMS_START]
		  * profit->paramerr[profit->paramindex[PARAM_DISK_SCALE]]
		+ *profit->paramlist[PARAM_DISK_SCALE]
		  * profit->paramerr[profit->paramindex[PARAM_ARMS_START]];
        obj2->prof_arms_quadfrac = *profit->paramlist[PARAM_ARMS_QUADFRAC];
        obj2->prof_arms_quadfracerr =
		profit->paramerr[profit->paramindex[PARAM_ARMS_QUADFRAC]];
        obj2->prof_arms_posang =
			fmod_m90_p90(*profit->paramlist[PARAM_ARMS_POSANG]);
        obj2->prof_arms_posangerr =
		profit->paramerr[profit->paramindex[PARAM_ARMS_POSANG]];
        }
      }
    }

  if (FLAG(obj2.prof_class_star))
    {
    pprofit = *profit;
    memset(pprofit.paramindex, 0, PARAM_NPARAM*sizeof(int));
    memset(pprofit.paramlist, 0, PARAM_NPARAM*sizeof(double *));
    pprofit.nparam = 0;
    QMALLOC(pprofit.prof, profstruct *, 1);
    pprofit.prof[0] = prof_init(&pprofit, PROF_DIRAC);
    QMALLOC(pprofit.covar, double, pprofit.nparam*pprofit.nparam);
    pprofit.nprof = 1;
    profit_resetparams(&pprofit);
    if (profit->paramlist[PARAM_X] && profit->paramlist[PARAM_Y])
      {
      pprofit.paraminit[pprofit.paramindex[PARAM_X]] = *profit->paramlist[PARAM_X];
      pprofit.paraminit[pprofit.paramindex[PARAM_Y]] = *profit->paramlist[PARAM_Y];
      }
    pprofit.paraminit[pprofit.paramindex[PARAM_DISK_FLUX]] = profit->flux;
    pprofit.niter = profit_minimize(&pprofit, PROFIT_MAXITER);
    profit_residuals(&pprofit,field,wfield, 0.0, pprofit.param,pprofit.resi);
    dchi2 = 0.5*(pprofit.chi2 - profit->chi2);
    obj2->prof_class_star = dchi2 < 50.0?
	(dchi2 > -50.0? 2.0/(1.0+exp(dchi2)) : 2.0) : 0.0;
    if (profit->flux > 0.0 && pprofit.flux > 0.0)
      obj2->prof_concentration = -2.5*log10(pprofit.flux / profit->flux);
    else  if (profit->flux > 0.0)
      obj2->prof_concentration = 99.0;
    else  if (pprofit.flux > 0.0)
      obj2->prof_concentration = -99.0;
    prof_end(pprofit.prof[0]);
    free(pprofit.prof);
    free(pprofit.covar);
    }

/* clean up. */
  free(profit->modpix);
  free(profit->psfpix);
  free(profit->pmodpix);
  free(profit->lmodpix);
  free(profit->objpix);
  free(profit->objweight);
  free(profit->resi);
/*
  free(oldparaminit);
*/
  return;
  }


/****** profit_psf ************************************************************
PROTO	void	profit_psf(profitstruct *profit)
PURPOSE	Build the local PSF at a given resolution.
INPUT	Profile-fitting structure.
OUTPUT	-.
NOTES	-.
AUTHOR	E. Bertin (IAP)
VERSION	22/10/2008
 ***/
void	profit_psf(profitstruct *profit)
  {
   double	posin[2], posout[2], dnaxisn[2],
		*pixout,
		xcout,ycout, xcin,ycin, invpixstep, flux, norm;
   int		d,i;

  psf = profit->psf;
  psf_build(psf);

  xcout = (double)(profit->modnaxisn[0]/2) + 1.0;	/* FITS convention */
  ycout = (double)(profit->modnaxisn[1]/2) + 1.0;	/* FITS convention */
  xcin = (psf->masksize[0]/2) + 1.0;			/* FITS convention */
  ycin = (psf->masksize[1]/2) + 1.0;			/* FITS convention */
  invpixstep = profit->pixstep / psf->pixstep;

/* Initialize multi-dimensional counters */
  for (d=0; d<2; d++)
    {
    posout[d] = 1.0;					/* FITS convention */
    dnaxisn[d] = profit->modnaxisn[d]+0.5;
    }

/* Remap each pixel */
  pixout = profit->psfpix;
  flux = 0.0;
  for (i=profit->modnaxisn[0]*profit->modnaxisn[1]; i--;)
    {
    posin[0] = (posout[0] - xcout)*invpixstep + xcin;
    posin[1] = (posout[1] - ycout)*invpixstep + ycin;
    flux += ((*(pixout++) = interpolate_pix(posin, psf->maskloc,
		psf->masksize, INTERP_LANCZOS3)));
    for (d=0; d<2; d++)
      if ((posout[d]+=1.0) < dnaxisn[d])
        break;
      else
        posout[d] = 1.0;
    }

/* Normalize PSF flux (just in case...) */
  flux *= psf->pixstep*psf->pixstep;
  if (fabs(flux) > 0.0)
    {
    norm = 1.0/flux;
    pixout = profit->psfpix;
    for (i=profit->modnaxisn[0]*profit->modnaxisn[1]; i--;)
      *(pixout++) *= norm;
    }

  return;
  }


/****** profit_findinit *******************************************************
PROTO	void profit_findinit(profitstruct *profit)
PURPOSE	Find a suitable set of initialisation parameters
INPUT	Pointer to the profit structure involved in the fit.
OUTPUT	-.
NOTES	-.
AUTHOR	E. Bertin (IAP)
VERSION	16/04/2008
 ***/
void	profit_findinit(profitstruct *profit)
  {
   int	p;

  for (p=0; p<profit->nprof; p++)
    switch (profit->prof[p]->code)
      {
      default:
      break;
      }

  return;
  }


/****** profit_minimize *******************************************************
PROTO	void profit_minimize(profitstruct *profit)
PURPOSE	Provide a function returning residuals to lmfit.
INPUT	Pointer to the profit structure involved in the fit,
	maximum number of iterations.
OUTPUT	Number of iterations used.
NOTES	-.
AUTHOR	E. Bertin (IAP)
VERSION	23/05/2008
 ***/
int	profit_minimize(profitstruct *profit, int niter)
  {
   double		lm_opts[5], info[LM_INFO_SZ];
   int			m,n;

/* Allocate work space */
  n = profit->nparam;
  m = profit->nresi;

  memset(profit->resi, 0, profit->nresi*sizeof(double));
  memset(profit->covar, 0, profit->nparam*profit->nparam*sizeof(double));
  profit_boundtounbound(profit, profit->paraminit);

/* Perform fit */
  lm_opts[0] = 1.0e-3;
  lm_opts[1] = 1.0e-17;
  lm_opts[2] = 1.0e-17;
  lm_opts[3] = 1.0e-17;
  lm_opts[4] = 1.0e-6;

  niter = dlevmar_dif(profit_evaluate, profit->paraminit, profit->resi,
	n, m, niter, lm_opts, info, NULL, profit->covar, profit);

  profit_unboundtobound(profit, profit->paraminit);


  return niter;
  }


/****** profit_printout *******************************************************
PROTO	void profit_printout(int n_par, double* par, int m_dat, double* fvec,
		void *data, int iflag, int iter, int nfev )
PURPOSE	Provide a function to print out results to lmfit.
INPUT	Number of fitted parameters,
	pointer to the vector of parameters,
	number of data points,
	pointer to the vector of residuals (output),
	pointer to the data structure (unused),
	0 (init) 1 (outer loop) 2(inner loop) -1(terminated),
	outer loop counter,
	number of calls to evaluate().
OUTPUT	-.
NOTES	Input arguments are there only for compatibility purposes (unused)
AUTHOR	E. Bertin (IAP)
VERSION	17/09/2008
 ***/
void	profit_printout(int n_par, double* par, int m_dat, double* fvec,
		void *data, int iflag, int iter, int nfev )
  {
   checkstruct	*check;
   profitstruct	*profit;
   char		filename[256];
   static int	itero;

  profit = (profitstruct *)data;

  if (0 && (iter!=itero || iter<0))
    {
    if (iter<0)
      itero++;
    else
      itero = iter;
    sprintf(filename, "check_%d_%04d.fits", the_gal, itero);
    check=initcheck(filename, CHECK_PROFILES, 0);
    reinitcheck(the_field, check);
    addcheck(check, profit->lmodpix, profit->objnaxisn[0],profit->objnaxisn[1],
		profit->ix,profit->iy, 1.0);

    reendcheck(the_field, check);
    endcheck(check);
    }

  return;
  }


/****** profit_evaluate ******************************************************
PROTO	void profit_evaluate(double *par, double *fvec, int m, int n,
		void *adata)
PURPOSE	Provide a function returning residuals to levmar.
INPUT	Pointer to the vector of parameters,
	pointer to the vector of residuals (output),
	number of model parameters,
	number of data points,
	pointer to a data structure (unused).
OUTPUT	-.
NOTES	Input arguments are there only for compatibility purposes (unused)
AUTHOR	E. Bertin (IAP)
VERSION	18/09/2008
 ***/
void	profit_evaluate(double *par, double *fvec, int m, int n,
			void *adata)
  {
   profitstruct	*profit;

  profit = (profitstruct *)adata;
  profit_unboundtobound(profit, par);
  profit_residuals(profit, the_field, the_wfield, PROFIT_DYNPARAM, par, fvec);
  profit_boundtounbound(profit, par);
  profit_printout(m, par, n, fvec, adata, 0, -1, 0 );
  return;
  }


/****** profit_residuals ******************************************************
PROTO	double *prof_residuals(profitstruct *profit, picstruct *field,
		picstruct *wfield, double dynparam, double *param, double *resi)
PURPOSE	Compute the vector of residuals between the data and the galaxy
	profile model.
INPUT	Profile-fitting structure,
	pointer to the field,
	pointer to the field weight,
	dynamic compression parameter (0=no compression),
	pointer to the model parameters (output),
	pointer to the computed residuals (output).
OUTPUT	Vector of residuals.
NOTES	-.
AUTHOR	E. Bertin (IAP)
VERSION	20/03/2009
 ***/
double	*profit_residuals(profitstruct *profit, picstruct *field,
		picstruct *wfield, double dynparam, double *param, double *resi)
  {
   int		p;

  memset(profit->modpix, 0,
	profit->modnaxisn[0]*profit->modnaxisn[1]*sizeof(double));
  for (p=0; p<profit->nparam; p++)
    profit->param[p] = param[p];
/* Simple PSF shortcut */
  if (profit->nprof == 1 && profit->prof[0]->code == PROF_DIRAC)
    profit_resample(profit, profit->psfpix, profit->lmodpix,
		*profit->prof[0]->flux);
  else
    {
    for (p=0; p<profit->nprof; p++)
      prof_add(profit->prof[p], profit);
    profit_convolve(profit, profit->modpix);
    profit_resample(profit, profit->modpix, profit->lmodpix, 1.0);
    }
  profit_compresi(profit, dynparam, resi);

  return resi;
  }


/****** profit_compresi ******************************************************
PROTO	double *prof_compresi(profitstruct *profit, double dynparam,
			double *resi)
PURPOSE	Compute the vector of residuals between the data and the galaxy
	profile model.
INPUT	Profile-fitting structure,
	dynamic-compression parameter (0=no compression),
	vector of residuals (output).
OUTPUT	Vector of residuals.
NOTES	-.
AUTHOR	E. Bertin (IAP)
VERSION	20/03/2009
 ***/
double	*profit_compresi(profitstruct *profit, double dynparam, double *resi)
  {
   double	*resit,
		error, x1c,x1,x2,rmin;
   PIXTYPE	*objpix, *objweight, *lmodpix,
		val,val2,wval, invsig;
   int		npix, i;
  
/* Compute vector of residuals */
  resit = resi;
  objpix = profit->objpix;
  objweight = profit->objweight;
  lmodpix = profit->lmodpix;
  error = 0.0;
  x1c = (double)(profit->objnaxisn[0]/2);
  rmin = profit->obj2->hl_radius / 2.0;
  x2 = -(double)(profit->objnaxisn[1]/2);
  npix = profit->objnaxisn[0]*profit->objnaxisn[1];
  if (dynparam > 0.0)
    {
    invsig = (PIXTYPE)(1.0/dynparam);
    for (i=npix; i--; lmodpix++)
      {
      val = *(objpix++);
      if ((wval=*(objweight++))>0.0)
        {
        val2 = (val - *lmodpix)*wval*invsig;
        val2 = val2>0.0? LOGF(1.0+val2) : -LOGF(1.0-val2);
        *(resit++) = val2*dynparam;
        error += val2*val2;
        }
      }
    profit->chi2 = dynparam*dynparam*error;
    }
  else
    {
    for (i=npix; i--; lmodpix++)
      {
      val = *(objpix++);
      if ((wval=*(objweight++))>0.0)
        {
        val2 = (val - *lmodpix)*wval;
        *(resit++) = val2;
        error += val2*val2;
        }
      }
    profit->chi2 = error;
    }

  return resi;
  }


/****** profit_resample ******************************************************
PROTO	void	prof_resample(profitstruct *profit, double *inpix,
		PIXTYPE *outpix)
PURPOSE	Resample the current full resolution model to image resolution.
INPUT	Profile-fitting structure.
OUTPUT	-.
NOTES	-.
AUTHOR	E. Bertin (IAP)
VERSION	18/03/2009
 ***/
void	profit_resample(profitstruct *profit, double *inpix, PIXTYPE *outpix,
	double factor)
  {
   double	posin[2], posout[2], dnaxisn[2],
		*dx,*dy,
		xcout,ycout, xcin,ycin, invpixstep, flux;
   int		d,i;

  xcout = (double)(profit->objnaxisn[0]/2) + 1.0;	/* FITS convention */
  if ((dx=(profit->paramlist[PARAM_X])))
    xcout += *dx;
  ycout = (double)(profit->objnaxisn[1]/2) + 1.0;	/* FITS convention */
  if ((dy=(profit->paramlist[PARAM_Y])))
    ycout += *dy;
  xcin = (profit->modnaxisn[0]/2) + 1.0;		/* FITS convention */
  ycin = (profit->modnaxisn[1]/2) + 1.0;		/* FITS convention */
  invpixstep = 1.0/profit->pixstep;

/* Initialize multi-dimensional counters */
  for (d=0; d<2; d++)
    {
    posout[d] = 1.0;					/* FITS convention */
    dnaxisn[d] = profit->objnaxisn[d]+0.5;
    }

/* Remap each pixel */
  flux = 0.0;
  for (i=profit->objnaxisn[0]*profit->objnaxisn[1]; i--;)
    {
    posin[0] = (posout[0] - xcout)*invpixstep + xcin;
    posin[1] = (posout[1] - ycout)*invpixstep + ycin;
    flux += ((*(outpix++) = (PIXTYPE)(factor*interpolate_pix(posin, inpix,
		profit->modnaxisn, INTERP_LANCZOS3))));
    for (d=0; d<2; d++)
      if ((posout[d]+=1.0) < dnaxisn[d])
        break;
      else
        posout[d] = 1.0;
    }

  profit->flux = flux;

  return;
  }


/****** profit_convolve *******************************************************
PROTO	void profit_convolve(profitstruct *profit, double *modpix)
PURPOSE	Convolve a model image with the local PSF.
INPUT	Pointer to the profit structure,
	Pointer to the image raster.
OUTPUT	-.
NOTES	-.
AUTHOR	E. Bertin (IAP)
VERSION	15/09/2008
 ***/
void	profit_convolve(profitstruct *profit, double *modpix)
  {
  if (!profit->psfdft)
    profit_makedft(profit);

  fft_conv(modpix, profit->psfdft, profit->modnaxisn);

  return;
  }


/****** profit_makedft *******************************************************
PROTO	void profit_makedft(profitstruct *profit)
PURPOSE	Create the Fourier transform of the descrambled PSF component.
INPUT	Pointer to the profit structure.
OUTPUT	-.
NOTES	-.
AUTHOR	E. Bertin (IAP)
VERSION	22/04/2008
 ***/
void	profit_makedft(profitstruct *profit)
  {
   psfstruct	*psf;
   double      *mask,*maskt, *ppix;
   double       dx,dy, r,r2,rmin,rmin2,rmax,rmax2,rsig,invrsig2;
   int          width,height,npix,offset, psfwidth,psfheight,psfnpix,
                cpwidth, cpheight,hcpwidth,hcpheight, i,j,x,y;

  if (!(psf=profit->psf))
    return;

  psfwidth = profit->modnaxisn[0];
  psfheight = profit->modnaxisn[1];
  psfnpix = psfwidth*psfheight;
  width = profit->modnaxisn[0];
  height = profit->modnaxisn[1];
  npix = width*height;
  QCALLOC(mask, double, npix);
  cpwidth = (width>psfwidth)?psfwidth:width;
  hcpwidth = cpwidth>>1;
  cpwidth = hcpwidth<<1;
  offset = width - cpwidth;
  cpheight = (height>psfheight)?psfheight:height;
  hcpheight = cpheight>>1;
  cpheight = hcpheight<<1;

/* Frame and descramble the PSF data */
  ppix = profit->psfpix + (psfheight/2)*psfwidth + psfwidth/2;
  maskt = mask;
  for (j=hcpheight; j--; ppix+=psfwidth)
    {
    for (i=hcpwidth; i--;)
      *(maskt++) = *(ppix++);      
    ppix -= cpwidth;
    maskt += offset;
    for (i=hcpwidth; i--;)
      *(maskt++) = *(ppix++);