profit.c

  txstart = -hw;
  ty = -hh;
  QMALLOC(dx, float, npix);
  pix = dx;
  for (j=profit->objnaxisn[1]; j--; ty+=1.0)
    {
    tx = txstart;
    y = ty < -0.5? ty + hh : ty - ohh;
    for (i=profit->objnaxisn[0]; i--; tx+=1.0)
      {
      x = tx < -0.5? tx + hw : tx - ohw;
      *(pix++) = exp(invtwosigma2*((x+sep)*(x+sep)+y*y))
		- exp(invtwosigma2*((x-sep)*(x-sep)+y*y));
      }
    }
  QMALLOC(dy, float, npix);
  pix = dy;
  ty = -hh;
  for (j=profit->objnaxisn[1]; j--; ty+=1.0)
    {
    tx = txstart;
    y = ty < -0.5? ty + hh : ty - ohh;
    for (i=profit->objnaxisn[0]; i--; tx+=1.0)
      {
      x = tx < -0.5? tx + hw : tx - ohw;
      *(pix++) = exp(invtwosigma2*(x*x+(y+sep)*(y+sep)))
		- exp(invtwosigma2*(x*x+(y-sep)*(y-sep)));
      }
    }

  QMALLOC(gdx, float, npix);
  gdxt = gdx;
  fpix = profit->objpix;
  invsig = npix/profit->sigma;
  for (i=npix; i--; fpix++)
    {
    val = *fpix > -1e29? *fpix*invsig : 0.0;
    *(gdxt++) = (val>0.0? log(1.0+val) : -log(1.0-val));
    }
  gdy = NULL;			/* to avoid gcc -Wall warnings */
  QMEMCPY(gdx, gdy, float, npix);
  fdx = fft_rtf(dx, profit->objnaxisn);
  fft_conv(gdx, fdx, profit->objnaxisn);
  fdy = fft_rtf(dy, profit->objnaxisn);
  fft_conv(gdy, fdy, profit->objnaxisn);

/* Compute estimator */
  invtwosigma2 = -1.18*1.18 / (2.0*obj2->hl_radius*obj2->hl_radius);
  xstart = -hw - obj->mx + (int)(obj->mx+0.49999);
  y = -hh -  obj->my + (int)(obj->my+0.49999);;
  spirindex = 0.0;
  gdxt = gdx;
  gdyt = gdy;
  for (j=profit->objnaxisn[1]; j--; y+=1.0)
    {
    x = xstart;
    for (i=profit->objnaxisn[0]; i--; x+=1.0)
      {
      gx = *(gdxt++);
      gy = *(gdyt++);
      if ((r2=x*x+y*y)>0.0)
        spirindex += (x*y*(gx*gx-gy*gy)+gx*gy*(y*y-x*x))/r2
			* exp(invtwosigma2*r2);
      }
    }

  free(dx);
  free(dy);
  free(fdx);
  free(fdy);
  free(gdx);
  free(gdy);

  return spirindex;
  }


/****** profit_moments ****************************************************
PROTO	void profit_moments(profitstruct *profit, obj2struct *obj2)
PURPOSE	Compute the 2nd order moments from the unconvolved object model.
INPUT	Profile-fitting structure,
	Pointer to obj2 structure.
OUTPUT	-.
NOTES	-.
AUTHOR	E. Bertin (IAP)
VERSION	20/08/2010
 ***/
void	 profit_moments(profitstruct *profit, obj2struct *obj2)
  {
   profstruct	*prof;
   double	dpdmx2[6], cov[4],
		*jac,*jact, *pjac,*pjact, *dcovar,*dcovart,
		*dmx2,*dmy2,*dmxy,
		m0,invm0, mx2,my2,mxy, den,invden,
		temp, temp2,invtemp2,invstemp2,
		pmx2,theta, flux, dval;
   float	 *covart;
   int		findex[PROF_NPROF],
		i,j,p, nparam;

/*  hw = (float)(profit->modnaxisn[0]/2);*/
/*  hh = (float)(profit->modnaxisn[1]/2);*/
/*  r2max = hw<hh? hw*hw : hh*hh;*/
/*  xstart = -hw;*/
/*  y = -hh;*/
/*  pix = profit->modpix;*/
/*  mx2 = my2 = mxy = mx = my = sum = 0.0;*/
/*  for (iy=profit->modnaxisn[1]; iy--; y+=1.0)*/
/*    {*/
/*    x = xstart;*/
/*    for (ix=profit->modnaxisn[0]; ix--; x+=1.0)*/
/*      if (y*y+x*x <= r2max)*/
/*        {*/
/*        val = *(pix++);*/
/*        sum += val;*/
/*        mx  += val*x;*/
/*        my  += val*y;*/
/*        mx2 += val*x*x;*/
/*        mxy += val*x*y;*/
/*        my2 += val*y*y;*/
/*        }*/
/*      else*/
/*        pix++;*/
/*    }*/

/*  if (sum <= 1.0/BIG)*/
/*    sum = 1.0;*/
/*  mx /= sum;*/
/*  my /= sum;*/
/*  obj2->prof_mx2 = mx2 = mx2/sum - mx*mx;*/
/*  obj2->prof_my2 = my2 = my2/sum - my*my;*/
/*  obj2->prof_mxy = mxy = mxy/sum - mx*my;*/

  nparam = profit->nparam;
  if (FLAG(obj2.prof_e1err) || FLAG(obj2.prof_pol1err))
    {
/*-- Set up Jacobian matrices */
    QCALLOC(jac, double, nparam*3);
    QMALLOC(pjac, double, (nparam<2? 6 : nparam*3));
    QMALLOC(dcovar, double, nparam*nparam);
    dcovart = dcovar;
    covart = profit->covar;
    for (i=nparam*nparam; i--;)
      *(dcovart++) = (double)(*(covart++));
    dmx2 = jac;
    dmy2 = jac+nparam;
    dmxy = jac+2*nparam;
    }
  else
    jac = pjac = dcovar = dmx2 = dmy2 = dmxy = NULL;

  m0 = mx2 = my2 = mxy = 0.0;
  for (p=0; p<profit->nprof; p++)
    {
    prof = profit->prof[p];
    findex[p] = prof_moments(profit, prof, pjac);
    flux = *prof->flux;
    m0 += flux;
    mx2 += prof->mx2*flux;
    my2 += prof->my2*flux;
    mxy += prof->mxy*flux;
    if (jac)
      {
      jact = jac;
      pjact = pjac;
      for (j=nparam*3; j--;)
        *(jact++) += flux * *(pjact++);
      }
    }
  invm0 = 1.0 / m0;
  obj2->prof_mx2 = (mx2 *= invm0);
  obj2->prof_my2 = (my2 *= invm0);
  obj2->prof_mxy = (mxy *= invm0);
/* Complete the flux derivative of moments */
  if (jac)
    {
    for (p=0; p<profit->nprof; p++)
      {
      prof = profit->prof[p];
      dmx2[findex[p]] = prof->mx2 - mx2;
      dmy2[findex[p]] = prof->my2 - my2;
      dmxy[findex[p]] = prof->mxy - mxy;
      }
    jact = jac;
    for (j=nparam*3; j--;)
      *(jact++) *= invm0;
    }

/* Handle fully correlated profiles (which cause a singularity...) */
  if ((temp2=mx2*my2-mxy*mxy)<0.00694)
    {
    mx2 += 0.0833333;
    my2 += 0.0833333;
    temp2 = mx2*my2-mxy*mxy;
    }

/* Use the Jacobians to compute the moment covariance matrix */
  if (jac)
    propagate_covar(dcovar, jac, obj2->prof_mx2cov, nparam, 3,
						pjac);	/* We re-use pjac */

  if (FLAG(obj2.prof_pol1))
    {
/*--- "Polarisation", i.e. module = (a^2-b^2)/(a^2+b^2) */
    if (mx2+my2 > 1.0/BIG)
      {
      obj2->prof_pol1 = (mx2 - my2) / (mx2+my2);
      obj2->prof_pol2 = 2.0*mxy / (mx2 + my2);
      if (FLAG(obj2.prof_pol1err))
        {
/*------ Compute the Jacobian of polarisation */
        invden = 1.0/(mx2+my2);
        dpdmx2[0] =  2.0*my2*invden*invden;
        dpdmx2[1] = -2.0*mx2*invden*invden;
        dpdmx2[2] =  0.0;
        dpdmx2[3] = -2.0*mxy*invden*invden;
        dpdmx2[4] = -2.0*mxy*invden*invden;
        dpdmx2[5] =  2.0*invden;

/*------ Use the Jacobian to compute the polarisation covariance matrix */
        propagate_covar(obj2->prof_mx2cov, dpdmx2, cov, 3, 2,
						pjac);	/* We re-use pjac */
        obj2->prof_pol1err = (float)sqrt(cov[0]<0.0? 0.0: cov[0]);
        obj2->prof_pol2err = (float)sqrt(cov[3]<0.0? 0.0: cov[3]);
        obj2->prof_pol12corr = (dval=cov[0]*cov[3]) > 0.0?
					(float)(cov[1]/sqrt(dval)) : 0.0;
        }
      }
    else
      obj2->prof_pol1 = obj2->prof_pol2
	= obj2->prof_pol1err = obj2->prof_pol2err = obj2->prof_pol12corr = 0.0;
    }

  if (FLAG(obj2.prof_e1))
    {
/*--- "Ellipticity", i.e. module = (a-b)/(a+b) */
    if (mx2+my2 > 1.0/BIG)
      {
      den = (temp2>=0.0) ? mx2+my2+2.0*sqrt(temp2) : mx2+my2;
      invden = 1.0/den;
      obj2->prof_e1 = (float)(invden * (mx2 - my2));
      obj2->prof_e2 = (float)(2.0 * invden * mxy);
      if (FLAG(obj2.prof_e1err))
        {
/*------ Compute the Jacobian of ellipticity */
        invstemp2 = (temp2>=0.0) ? 1.0/sqrt(temp2) : 0.0;
        dpdmx2[0] = ( den - (1.0+my2*invstemp2)*(mx2-my2))*invden*invden;
        dpdmx2[1] = (-den - (1.0+mx2*invstemp2)*(mx2-my2))*invden*invden;
        dpdmx2[2] = 2.0*mxy*invstemp2*(mx2-my2)*invden*invden;
        dpdmx2[3] = -2.0*mxy*(1.0+my2*invstemp2)*invden*invden;
        dpdmx2[4] = -2.0*mxy*(1.0+mx2*invstemp2)*invden*invden;
        dpdmx2[5] =  (2.0*den+4.0*mxy*mxy*invstemp2)*invden*invden;

/*------ Use the Jacobian to compute the ellipticity covariance matrix */
        propagate_covar(obj2->prof_mx2cov, dpdmx2, cov, 3, 2,
					pjac);	/* We re-use pjac */
        obj2->prof_e1err = (float)sqrt(cov[0]<0.0? 0.0: cov[0]);
        obj2->prof_e2err = (float)sqrt(cov[3]<0.0? 0.0: cov[3]);
        obj2->prof_e12corr = (dval=cov[0]*cov[3]) > 0.0?
					(float)(cov[1]/sqrt(dval)) : 0.0;
        }
      }
    else
      obj2->prof_e1 = obj2->prof_e2
	= obj2->prof_e1err = obj2->prof_e2err = obj2->prof_e12corr = 0.0;
    }

  if (FLAG(obj2.prof_cxx))
    {
    invtemp2 = (temp2>=0.0) ? 1.0/temp2 : 0.0;
    obj2->prof_cxx = (float)(my2*invtemp2);
    obj2->prof_cyy = (float)(mx2*invtemp2);
    obj2->prof_cxy = (float)(-2*mxy*invtemp2);
    }

  if (FLAG(obj2.prof_a))
    {
    if ((fabs(temp=mx2-my2)) > 0.0)
      theta = atan2(2.0 * mxy,temp) / 2.0;
    else
      theta = PI/4.0;

    temp = sqrt(0.25*temp*temp+mxy*mxy);
    pmx2 = 0.5*(mx2+my2);
    obj2->prof_a = (float)sqrt(pmx2 + temp);
    obj2->prof_b = (float)sqrt(pmx2 - temp);
    obj2->prof_theta = theta*180.0/PI;
    }

/* Free memory used by Jacobians */
  free(jac);
  free(pjac);
  free(dcovar);

  return;
  }


/****** profit_surface ****************************************************
PROTO	void profit_surface(profitstruct *profit, obj2struct *obj2)
PURPOSE	Compute surface brightnesses from the unconvolved object model.
INPUT	Pointer to the profile-fitting structure,
	Pointer to obj2 structure.
OUTPUT	-.
NOTES	-.
AUTHOR	E. Bertin (IAP)
VERSION	08/07/2010
 ***/
void	 profit_surface(profitstruct *profit, obj2struct *obj2)
  {
   profitstruct	hdprofit;
   double	dsum,dhsum,dsumoff, dhval, frac, seff;
   float	*spix, *spixt,
		val,vmax,
		scalefac, imsizefac, flux, lost, sum, lostfluxfrac;
   int		i,p, imax, npix, neff;

/* Allocate "high-definition" raster only to make measurements */
  hdprofit.oversamp = PROFIT_OVERSAMP;
  hdprofit.modnaxisn[0] = hdprofit.modnaxisn[1] = PROFIT_HIDEFRES;
  npix = hdprofit.nmodpix = hdprofit.modnaxisn[0]*hdprofit.modnaxisn[1];
/* Find best image size factor from fitting results */
  imsizefac = 2.0*profit_minradius(profit, PROFIT_REFFFAC)/profit->pixstep
	/ (float)profit->modnaxisn[0];
  if (imsizefac<0.01)
    imsizefac = 0.01;
  else if (imsizefac>100.0)
    imsizefac = 100.0;
  scalefac = (float)hdprofit.modnaxisn[0] / (float)profit->modnaxisn[0]
	/ imsizefac;
  hdprofit.pixstep = profit->pixstep / scalefac;
  hdprofit.fluxfac = scalefac*scalefac;
  QCALLOC(hdprofit.modpix, float,npix*sizeof(float));

  for (p=0; p<profit->nparam; p++)
    profit->param[p] = profit->paraminit[p];
  lost = sum = 0.0;

  for (p=0; p<profit->nprof; p++)
    {
    sum += (flux = prof_add(&hdprofit, profit->prof[p],0));
    lost += flux*profit->prof[p]->lostfluxfrac;
    }
  lostfluxfrac = sum > 0.0? lost / sum : 0.0;

/*
char filename[256];
sprintf(filename, "raster_%02d.fits", the_gal);
check=initcheck(filename, CHECK_OTHER, 0);
check->width = hdprofit.modnaxisn[0];
check->height = hdprofit.modnaxisn[1];
reinitcheck(the_field, check);
memcpy(check->pix,hdprofit.modpix,check->npix*sizeof(float));


int r,t;
double ratio,ratio0,ang,ang0, x,x0,y,y0;
list = profit->paramlist;
index = profit->paramindex;
for (p=0; p<nparam; p++)
param[p] = profit->paraminit[p];

ratio0 = profit->paraminit[index[PARAM_SPHEROID_ASPECT]];
ang0 = profit->paraminit[index[PARAM_SPHEROID_POSANG]];
x0 = profit->paraminit[index[PARAM_X]];
y0 = profit->paraminit[index[PARAM_Y]];
for (r=0;r<check->height;r++)
for (t=0; t<check->width;t++)
{
//x = (r-10.0)/100.0 + x0;
//y = (t-10.0)/100.0 + y0;
ratio = ratio0*exp((r-10.0)/400.0);
ang = ang0+(t-10.0)/3.0;

for (i=0; i<PARAM_NPARAM; i++)
{
//if (list[i] && i==PARAM_X)
//param[index[i]] = x;
//if (list[i] && i==PARAM_Y)
//param[index[i]] = y;
if (list[i] && i==PARAM_SPHEROID_ASPECT)
param[index[i]] = ratio;
if (list[i] && i==PARAM_SPHEROID_POSANG)
param[index[i]] = ang;
//if (list[i] && i==PARAM_SPHEROID_REFF)
//param[index[i]] = profit->paraminit[index[i]]*sqrt(ratio0/ratio);
}
profit_residuals(profit,field,wfield, PROFIT_DYNPARAM, param,profit->resi);
*((float *)check->pix + t + r*check->width) = profit->chi2;
}
reendcheck(the_field, check);
endcheck(check);
*/

  if (FLAG(obj2.fluxeff_prof))
    {
/*-- Sort model pixel values */
    spix = NULL;			/* to avoid gcc -Wall warnings */
    QMEMCPY(hdprofit.modpix, spix, float, npix);
    fqmedian(spix, npix);
/*-- Build a cumulative distribution */
    dsum = 0.0;
    spixt = spix;
    for (i=npix; i--;)
      dsum += (double)*(spixt++);
/*-- Find matching surface brightness */
    if (lostfluxfrac > 1.0)
      lostfluxfrac = 0.0;
    dhsum = 0.5 * dsum / (1.0-lostfluxfrac);
    dsum = lostfluxfrac * dsum / (1.0-lostfluxfrac);
    neff = 0;
    spixt = spix;
    for (i=npix; i--;)
      if ((dsum += (double)*(spixt++)) >= dhsum)
        {
        neff = i;
        break;
        }
    dhval = (double)*(spixt-1);
    seff = neff;
    dsumoff = 0.0;
    if (spixt>=spix+2)
      if (dhval > 0.0 && (frac = (dsum - dhsum) / dhval) < 1.0)
        {
        seff += frac;
        dsumoff = frac*dhval;
        dhval = dsumoff + (1.0 - frac)*(double)*(spixt-2);
        }
    obj2->fluxeff_prof = dhval;
    if (FLAG(obj2.fluxmean_prof))
      {
      dsum = dsumoff;
      for (i=neff; i--;)
        dsum += (double)*(spixt++);
      obj2->fluxmean_prof = seff > 0.0? dsum / seff : 0.0;
      }
    free(spix);
    }

/* Compute model peak (overwrites oversampled model!!) */
  if (FLAG(obj2.peak_prof))
    {
/*-- Find position of maximum pixel in current hi-def raster */
    imax = 0;
    vmax = -BIG;
    spixt = hdprofit.modpix;
    for (i=npix; i--;)
      if ((val=*(spixt++))>vmax)
        {
        vmax = val;
        imax = i;
        }
    imax = npix-1 - imax;
/*-- Recompute hi-def model raster without oversampling */
/*-- and with the same flux correction factor */
    hdprofit.oversamp = 0;
    memset(hdprofit.modpix,0, npix*sizeof(float));
    for (p=0; p<profit->nprof; p++)
      prof_add(&hdprofit, profit->prof[p], 1);
    obj2->peak_prof = hdprofit.modpix[imax];
    }

/* Free hi-def model raster */
  free(hdprofit.modpix);

  return;
  }


/****** profit_addparam *******************************************************
PROTO	void profit_addparam(profitstruct *profit, paramenum paramindex,
		float **param)
PURPOSE	Add a profile parameter to the list of fitted items.
INPUT	Pointer to the profit structure,
	Parameter index,
	Pointer to the parameter pointer.
OUTPUT	-.
NOTES	-.
AUTHOR	E. Bertin (IAP)
VERSION	29/03/2010
 ***/
void	profit_addparam(profitstruct *profit, paramenum paramindex,
		float **param)
  {
/* Check whether the parameter has already be registered */
  if (profit->paramlist[paramindex])
/*-- Yes */
    *param = profit->paramlist[paramindex];
  else
/*-- No */
    {
    *param = profit->paramlist[paramindex] = &profit->param[profit->nparam];
    profit->paramindex[paramindex] = profit->nparam;
    profit->paramrevindex[profit->nparam++] = paramindex;
    }

  return;
  }


/****** profit_resetparam ****************************************************
PROTO	void profit_resetparam(profitstruct *profit, paramenum paramtype)
PURPOSE	Set the initial, lower and upper boundary values of a profile parameter.
INPUT	Pointer to the profit structure,
	Parameter index.
OUTPUT	-.
NOTES	-.
AUTHOR	E. Bertin (IAP)
VERSION	08/10/2010
 ***/
void	profit_resetparam(profitstruct *profit, paramenum paramtype)
  {
   objstruct	*obj;
   obj2struct	*obj2;
   float	param, parammin,parammax, range;

  obj = profit->obj;
  obj2 = profit->obj2;
  param = parammin = parammax = 0.0;	/* Avoid gcc -Wall warnings*/

  switch(paramtype)
    {
    case PARAM_BACK:
      param = 0.0;
      parammin = -6.0*obj->sigbkg;
      parammax =  6.0*obj->sigbkg;
      break;
    case PARAM_X:
      param = obj->mx - (int)(obj->mx+0.49999);
      range = obj2->hl_radius*4.0;
      if (range>profit->objnaxisn[0]*2.0)
        range = profit->objnaxisn[0]*2.0;
      parammin = -range;
      parammax =  range;
      break;
    case PARAM_Y:
      param = obj->my - (int)(obj->my+0.49999);
      range = obj2->hl_radius*4.0;
      if (range>profit->objnaxisn[1]*2)
        range = profit->objnaxisn[1]*2;
      parammin = -range;
      parammax =  range;
      break;
    case PARAM_DIRAC_FLUX:
      param = obj2->flux_auto/profit->nprof;
      parammin = -obj2->flux_auto/1000.0;
      parammax = 2*obj2->flux_auto;
      break;
    case PARAM_SPHEROID_FLUX:
      param = obj2->flux_auto/profit->nprof;
      parammin = -obj2->flux_auto/1000.0;
      parammax = 4*obj2->flux_auto;
      break;
    case PARAM_SPHEROID_REFF:
      param = FLAG(obj2.prof_disk_flux)? obj2->hl_radius
				: obj2->hl_radius*sqrtf(obj->a/obj->b);
      parammin = 0.0;
      parammax = param * 4.0;
      break;
    case PARAM_SPHEROID_ASPECT:
      param = FLAG(obj2.prof_disk_flux)? 1.0 : obj->b/obj->a;
      parammin = FLAG(obj2.prof_disk_flux)? 0.5 : 0.01;
      parammax = FLAG(obj2.prof_disk_flux)? 2.0 : 100.0;
      break;
    case PARAM_SPHEROID_POSANG:
      param = obj->theta;
      parammin = 90.0;
      parammax =  90.0;
      break;
    case PARAM_SPHEROID_SERSICN:
      param = 4.0;
      parammin = FLAG(obj2.prof_disk_flux)? 1.0 : 0.3;
      parammax = 10.0;
      break;
    case PARAM_DISK_FLUX:
      param = obj2->flux_auto/profit->nprof;
      parammin = -obj2->flux_auto/1000.0;
      parammax = 2*obj2->flux_auto;
      break;
    case PARAM_DISK_SCALE:	/* From scalelength to Re */
      param = obj2->hl_radius/1.67835*sqrtf(obj->a/obj->b);
      parammin = FLAG(obj2.prof_spheroid_flux)? 0.0 : param/4.0;
      parammax = param * 4.0;
      break;
    case PARAM_DISK_ASPECT:
      param = obj->b/obj->a;
      parammin = 0.01;
      parammax = 100.0;
      break;
    case PARAM_DISK_POSANG:
      param = obj->theta;
      parammin = 90.0;
      parammax =  90.0;
      break;
    case PARAM_ARMS_FLUX:
      param = obj2->flux_auto/2.0;
      parammin = 0.0;
      parammax = obj2->flux_auto*2.0;
      break;
    case PARAM_ARMS_QUADFRAC:
      param = 0.5;
      parammin = 0.0;
      parammax = 1.0;
      break;
    case PARAM_ARMS_SCALE:
      param = 1.0;
      parammin = 0.5;
      parammax = 10.0;
      break;
    case PARAM_ARMS_START:
      param = 0.5;
      parammin = 0.0;
      parammax = 3.0;
      break;
    case PARAM_ARMS_PITCH:
      param = 20.0;
      parammin = 5.0;
      parammax = 50.0;
      break;
    case PARAM_ARMS_PITCHVAR:
      param = 0.0;
      parammin = -1.0;
      parammax = 1.0;
      break;
//      if ((profit->spirindex=profit_spiralindex(profit, obj, obj2)) > 0.0)
//        {
//        param = -param;
//        parammin = -parammax;
//        parammax = -parammin;
//        }
//      printf("spiral index: %g  \n", profit->spirindex);
//      break;
    case PARAM_ARMS_POSANG:
      param = 0.0;
      parammin = 0.0;
      parammax = 0.0;
      break;
    case PARAM_ARMS_WIDTH:
      param = 3.0;
      parammin = 1.5;
      parammax = 11.0;
      break;
    case PARAM_BAR_FLUX:
      param = obj2->flux_auto/10.0;
      parammin = 0.0;
      parammax = 2.0*obj2->flux_auto;
      break;
    case PARAM_BAR_ASPECT:
      param = 0.3;
      parammin = 0.2;
      parammax = 0.5;
      break;
    case PARAM_BAR_POSANG:
      param = 0.0;
      parammin = 0.0;
      parammax = 0.0;
      break;
    case PARAM_INRING_FLUX:
      param = obj2->flux_auto/10.0;
      parammin = 0.0;
      parammax = 2.0*obj2->flux_auto;
      break;
    case PARAM_INRING_WIDTH:
      param = 0.3;
      parammin = 0.0;
      parammax = 0.5;
      break;
    case PARAM_INRING_ASPECT:
      param = 0.8;
      parammin = 0.4;
      parammax = 1.0;
      break;
    case PARAM_OUTRING_FLUX:
      param = obj2->flux_auto/10.0;
      parammin = 0.0;
      parammax = 2.0*obj2->flux_auto;
      break;
    case PARAM_OUTRING_START:
      param = 4.0;
      parammin = 3.5;
      parammax = 6.0;
      break;
    case PARAM_OUTRING_WIDTH:
      param = 0.3;
      parammin = 0.0;
      parammax = 0.5;
      break;
    default:
      error(EXIT_FAILURE, "*Internal Error*: Unknown profile parameter in ",
		"profit_resetparam()");
      break;
   }

  if (parammin!=parammax && (param<=parammin || param>=parammax))
    param = (parammin+parammax)/2.0;
  else if (parammin==0.0 && parammax==0.0)
    parammax = 1.0;
  profit_setparam(profit, paramtype, param, parammin, parammax);

  return;
  }


/****** profit_resetparams ****************************************************
PROTO	void profit_resetparams(profitstruct *profit)
PURPOSE	Set the initial, lower and upper boundary values of profile parameters.
INPUT	Pointer to the profit structure.
OUTPUT	-.
NOTES	-.
AUTHOR	E. Bertin (IAP)
VERSION	18/09/2008
 ***/
void	profit_resetparams(profitstruct *profit)
  {
   int		p;


  for (p=0; p<PARAM_NPARAM; p++)
    profit_resetparam(profit, (paramenum)p);

  return;
  }


/****** profit_setparam ****************************************************
PROTO	void profit_setparam(profitstruct *profit, paramenum paramtype,
		float param, float parammin, float parammax)
PURPOSE	Set the actual, lower and upper boundary values of a profile parameter.
INPUT	Pointer to the profit structure,
	Parameter index,
	Actual value,
	Lower boundary to the parameter,
	Upper boundary to the parameter.
OUTPUT	RETURN_OK if the parameter is registered, RETURN_ERROR otherwise.
AUTHOR	E. Bertin (IAP)
VERSION	15/03/2009
 ***/
int	profit_setparam(profitstruct *profit, paramenum paramtype,
		float param, float parammin, float parammax)
  {
   float	*paramptr;
   int		index;

/* Check whether the parameter has already be registered */
  if ((paramptr=profit->paramlist[(int)paramtype]))
    {
    index = profit->paramindex[(int)paramtype];
    profit->paraminit[index] = param;
    profit->parammin[index] = parammin;
    profit->parammax[index] = parammax;
    return RETURN_OK;
    }
  else
    return RETURN_ERROR;
  }

  
/****** profit_boundtounbound *************************************************
PROTO	void profit_boundtounbound(profitstruct *profit,
				float *param, double *dparam, int index)
PURPOSE	Convert parameters from bounded to unbounded space.
INPUT	Pointer to the profit structure,
	input array of single precision parameters,
	output (incomplete) array of double precision parameters,
	parameter selection index (<0 = all parameters)
OUTPUT	-.
NOTES	-.
AUTHOR	E. Bertin (IAP)
VERSION	29/03/2010
 ***/
void	profit_boundtounbound(profitstruct *profit,
				float *param, double *dparam, int index)
  {
   double	num,den;
   float	tparam;
   int		f,p, pstart,np;

  if (index<0)
    {
    pstart = 0;
    np = profit->nparam;
    }
  else
    {
    pstart = index;
    np = pstart+1;
    }

  f = 0;
  for (p=pstart ; p<np; p++)
    if (profit->freeparam_flag[p])
      {
      tparam = param[p-pstart];
      if (profit->parammin[p]!=profit->parammax[p])
        {
        num = tparam - profit->parammin[p];
        den = profit->parammax[p] - tparam;
        dparam[f] = num>1e-50? (den>1e-50? log(num/den): 50.0) : -50.0;
        }
      else if (profit->parammax[p] > 0.0 || profit->parammax[p] < 0.0)
        dparam[f] = param[p-pstart] / profit->parammax[p];

      f++;
      }

  return;
  }


/****** profit_unboundtobound *************************************************
PROTO	void profit_unboundtobound(profitstruct *profit,
				double *dparam, float *param, int index)
PURPOSE	Convert parameters from unbounded to bounded space.
INPUT	Pointer to the profit structure,
	input (incomplete) array of double precision parameters,
	output array of single precision parameters.
	parameter selection index (<0 = all parameters)
OUTPUT	-.
NOTES	-.
AUTHOR	E. Bertin (IAP)
VERSION	08/07/2010
 ***/
void	profit_unboundtobound(profitstruct *profit,
				double *dparam, float *param, int index)
  {
   int		f,p, pstart,np;

  if (index<0)
    {
    pstart = 0;
    np = profit->nparam;
    }
  else
    {
    pstart = index;
    np = pstart+1;
    }

  f = 0;
  for (p=pstart; p<np; p++)
    {
    if (profit->freeparam_flag[p])
      {
      param[p-pstart] = (profit->parammin[p]!=profit->parammax[p])?
		((profit->parammax[p] - profit->parammin[p])
		/ (1.0 + exp(-(dparam[f]>50.0? 50.0
				: (dparam[f]<-50.0? -50.0: dparam[f]))))
		+ profit->parammin[p])
		:  dparam[f]*profit->parammax[p];
      f++;
      }
    else
      param[p-pstart] = profit->paraminit[p];
    }

  return;
  }


/****** profit_covarunboundtobound ********************************************
PROTO	void profit_covarunboundtobound(profitstruct *profit,
				double *dcovar, float *covar)
PURPOSE	Convert covariance matrix from unbounded to bounded space.
INPUT	Pointer to the profit structure,
	input (incomplete) matrix of double precision covariances,
	output matrix of single precision covariances.
OUTPUT	-.
NOTES	-.
AUTHOR	E. Bertin (IAP)
VERSION	27/07/2010
 ***/
void	profit_covarunboundtobound(profitstruct *profit,
				double *dcovar, float *covar)
  {
   double	*dxdy;
   float	*x,*xmin,*xmax;
   int		*fflag,
		f,f1,f2, nfree, p,p1,p2, nparam;

  nparam = profit->nparam;
  fflag = profit->freeparam_flag;
  nfree = profit->nfreeparam;
  QMALLOC16(dxdy, double, nfree);
  x = profit->paraminit;
  xmin = profit->parammin;
  xmax = profit->parammax;
  f = 0;
  for (p=0; p<profit->nparam; p++)
    if (fflag[p])
      {
      if (xmin[p]!=xmax[p])
        dxdy[f++] = (x[p] - xmin[p]) * (xmax[p] - x[p]) / (xmax[p] - xmin[p]);
      else
        dxdy[f++] = xmax[p];
      }

  memset(profit->covar, 0, nparam*nparam*sizeof(float));
  f2 = 0;
  for (p2=0; p2<nparam; p2++)
    {
    if (fflag[p2])
      {
      f1 = 0;
      for (p1=0; p1<nparam; p1++)
        if (fflag[p1])
          {
          covar[p2*nparam+p1] = (float)(dcovar[f2*nfree+f1]*dxdy[f1]*dxdy[f2]);
          f1++;
          }
      f2++;
      }
    }

  free(dxdy);

  return;
  }


/****** prof_init *************************************************************
PROTO	profstruct prof_init(profitstruct *profit, proftypenum profcode)
PURPOSE	Allocate and initialize a new profile structure.
INPUT	Pointer to the profile-fitting structure,
	profile type.
OUTPUT	A pointer to an allocated prof structure.
NOTES	-.
AUTHOR	E. Bertin (IAP)
VERSION	08/10/2010
 ***/
profstruct	*prof_init(profitstruct *profit, proftypenum profcode)
  {
   profstruct	*prof;
   float	*pix,
		rmax2, re2, dy2,r2, scale, zero, k,n, hinvn;
   int		width,height, ixc,iyc, ix,iy, nsub,
		d,s;

  QCALLOC(prof, profstruct, 1);
  prof->code = profcode;
  switch(profcode)
    {
    case PROF_BACK:
      prof->naxis = 2;
      prof->pix = NULL;
      profit_addparam(profit, PARAM_BACK, &prof->flux);
      prof->typscale = 1.0;
      break;
    case PROF_DIRAC:
      prof->naxis = 2;
      prof->naxisn[0] = PROFIT_MAXMODSIZE;
      prof->naxisn[1] = PROFIT_MAXMODSIZE;
      prof->naxisn[2] = 1;
      prof->npix = prof->naxisn[0]*prof->naxisn[1]*prof->naxisn[2];
      prof->typscale = 1.0;
      profit_addparam(profit, PARAM_X, &prof->x[0]);
      profit_addparam(profit, PARAM_Y, &prof->x[1]);
      profit_addparam(profit, PARAM_DIRAC_FLUX, &prof->flux);
      break;
    case PROF_SERSIC:
      prof->naxis = 2;
      prof->naxisn[0] = PROFIT_MAXMODSIZE;
      prof->naxisn[1] = PROFIT_MAXMODSIZE;
      prof->naxisn[2] = 1;
      prof->npix = prof->naxisn[0]*prof->naxisn[1]*prof->naxisn[2];
      QMALLOC(prof->pix, float, prof->npix);
      prof->typscale = 1.0;
      profit_addparam(profit, PARAM_X, &prof->x[0]);
      profit_addparam(profit, PARAM_Y, &prof->x[1]);
      profit_addparam(profit, PARAM_SPHEROID_FLUX, &prof->flux);
      profit_addparam(profit, PARAM_SPHEROID_REFF, &prof->scale);
      profit_addparam(profit, PARAM_SPHEROID_ASPECT, &prof->aspect);
      profit_addparam(profit, PARAM_SPHEROID_POSANG, &prof->posangle);
      profit_addparam(profit, PARAM_SPHEROID_SERSICN, &prof->extra[0]);
      break;
    case PROF_DEVAUCOULEURS:
      prof->naxis = 2;
      prof->naxisn[0] = PROFIT_MAXMODSIZE;
      prof->naxisn[1] = PROFIT_MAXMODSIZE;
      prof->naxisn[2] = 1;
      prof->npix = prof->naxisn[0]*prof->naxisn[1]*prof->naxisn[2];
      QMALLOC(prof->pix, float, profit->nmodpix);
      prof->typscale = 1.0;
      profit_addparam(profit, PARAM_X, &prof->x[0]);
      profit_addparam(profit, PARAM_Y, &prof->x[1]);
      profit_addparam(profit, PARAM_SPHEROID_FLUX, &prof->flux);
      profit_addparam(profit, PARAM_SPHEROID_REFF, &prof->scale);
      profit_addparam(profit, PARAM_SPHEROID_ASPECT, &prof->aspect);
      profit_addparam(profit, PARAM_SPHEROID_POSANG, &prof->posangle);
      break;
    case PROF_EXPONENTIAL:
      prof->naxis = 2;
      prof->naxisn[0] = PROFIT_MAXMODSIZE;
      prof->naxisn[1] = PROFIT_MAXMODSIZE;
      prof->naxisn[2] = 1;
      prof->npix = prof->naxisn[0]*prof->naxisn[1]*prof->naxisn[2];
      QMALLOC(prof->pix, float, profit->nmodpix);
      prof->typscale = 1.0;
      profit_addparam(profit, PARAM_X, &prof->x[0]);
      profit_addparam(profit, PARAM_Y, &prof->x[1]);
      profit_addparam(profit, PARAM_DISK_FLUX, &prof->flux);