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include <mach.h>
include <math/nlfit.h>
include "../lib/fitsky.h"
define TOL .001 # Fitting tolerance
# AP_GAUSS -- Procedure to compute the peak, width and skew of the histogram
# by fitting a skewed Gaussian function to the histogram.
int procedure ap_gauss (skypix, coords, wgt, index, nskypix, snx, sny, maxfit,
k1, hwidth, binsize, smooth, losigma, hisigma, rgrow, maxiter,
sky_mode, sky_sigma, sky_skew, nsky, nsky_reject)
real skypix[ARB] # array of unsorted sky pixels
int coords[ARB] # array of coordinates for region growing
real wgt[ARB] # weights for pixel rejection
int index[ARB] # array of sort indices
int nskypix # the number of sky pixels
int snx, sny # the maximum dimensions of sky raster
int maxfit # maximum number of iterations per fit
real k1 # extent of the histogram in skysigma
real hwidth # width of the histogram
real binsize # the size of the histogram in sky sigma
int smooth # smooth the histogram before fitting
real losigma, hisigma # upper and lower sigma rejection criterion
real rgrow # region growing radius in pixels
int maxiter # maximum number of rejection cycles
real sky_mode # computed sky value
real sky_sigma # computed sigma of the sky pixels
real sky_skew # skew of sky pixels
int nsky # number of sky pixels used in fit
int nsky_reject # number of sky pixels rejected
double dsky, sumpx, sumsqpx, sumcbpx
int i, j, nreject, nbins, nker, ier
pointer sp, x, hgm, shgm, w
real sky_mean, sky_msigma, dmin, dmax, hmin, hmax, dh, locut, hicut, cut
real sky_zero
int ap_grow_hist2(), aphigmr()
real ap_asumr(), apmedr()
begin
# Initialize.
nsky = nskypix
nsky_reject = 0
sky_mode = INDEFR
sky_sigma = INDEFR
sky_skew = INDEFR
if (nskypix <= 0)
return (AP_NOSKYAREA)
# Compute initial guess for sky statistics.
sky_zero = ap_asumr (skypix, index, nskypix) / nskypix
call ap_ialimr (skypix, index, nskypix, dmin, dmax)
call apfimoments (skypix, index, nskypix, sky_zero, sumpx, sumsqpx,
sumcbpx, sky_mean, sky_msigma, sky_skew)
sky_mean = apmedr (skypix, index, nskypix)
sky_mean = max (dmin, min (sky_mean, dmax))
# Compute the width and bin size of the sky histogram.
if (! IS_INDEFR(hwidth) && hwidth > 0.0) {
hmin = sky_mean - k1 * hwidth
hmax = sky_mean + k1 * hwidth
dh = binsize * hwidth
} else {
cut = min (sky_mean - dmin, dmax - sky_mean, k1 * sky_msigma)
hmin = sky_mean - cut
hmax = sky_mean + cut
dh = binsize * cut / k1
}
# Compute the number of histogram bins and width of smoothing kernel.
if (dh <= 0.0) {
nbins = 1
dh = 0.0
} else {
nbins = 2 * nint ((hmax - sky_mean) / dh) + 1
dh = (hmax - hmin) / (nbins - 1)
}
# Test for a valid histogram.
if (sky_msigma <= dh || dh <= 0.0 || k1 <= 0.0 || sky_msigma <= 0.0 ||
nbins < 4) {
sky_mode = sky_mean
sky_sigma = 0.0
sky_skew = 0.0
return (AP_NOHISTOGRAM)
}
# Allocate temporary working space.
call smark (sp)
call salloc (x, nbins, TY_REAL)
call salloc (hgm, nbins, TY_REAL)
call salloc (shgm, nbins, TY_REAL)
call salloc (w, nbins, TY_REAL)
# Compute the x array.
do i = 1, nbins
Memr[x+i-1] = i
call amapr (Memr[x], Memr[x], nbins, 1.0, real (nbins),
hmin + 0.5 * dh, hmax + 0.5 * dh)
# Accumulate the histogram.
call aclrr (Memr[hgm], nbins)
nsky_reject = nsky_reject + aphigmr (skypix, wgt, index, nskypix,
Memr[hgm], nbins, hmin, hmax)
nsky = nskypix - nsky_reject
# Do the initial rejection.
if (nsky_reject > 0) {
do i = 1, nskypix {
if (wgt[index[i]] <= 0.0) {
dsky = skypix[index[i]] - sky_zero
sumpx = sumpx - dsky
sumsqpx = sumsqpx - dsky ** 2
sumcbpx = sumcbpx - dsky ** 3
}
}
call apmoments (sumpx, sumsqpx, sumcbpx, nsky, sky_zero,
sky_mean, sky_msigma, sky_skew)
}
# Find the mode, sigma and skew of the histogram.
if (smooth == YES) {
nker = max (1, nint (sky_msigma / dh))
#call ap_lucy_smooth (Memr[hgm], Memr[shgm], nbins, nker, 2)
call ap_bsmooth (Memr[hgm], Memr[shgm], nbins, nker, 2)
call ap_hist_mode (Memr[x], Memr[shgm], Memr[w], nbins,
sky_mode, sky_sigma, sky_skew, maxfit, TOL, ier)
} else
call ap_hist_mode (Memr[x], Memr[hgm], Memr[w], nbins,
sky_mode, sky_sigma, sky_skew, maxfit, TOL, ier)
sky_mode = max (dmin, min (sky_mode, dmax))
if (ier != AP_OK) {
call sfree (sp)
return (ier)
}
if ((IS_INDEFR(losigma) && IS_INDEFR(hisigma)) || sky_sigma <= dh ||
maxiter < 1) {
call sfree (sp)
return (AP_OK)
}
# Fit histogram with pixel rejection and optional region growing.
do i = 1, maxiter {
# Compute the new rejection limits.
if (IS_INDEFR(losigma))
locut = -MAX_REAL
else
locut = sky_mode - losigma * sky_msigma
if (IS_INDEFR(hisigma))
hicut = MAX_REAL
else
hicut = sky_mode + hisigma * sky_msigma
# Detect and reject pixels.
nreject = 0
do j = 1, nskypix {
if (skypix[index[j]] >= locut && skypix[index[j]] <= hicut)
next
if (rgrow > 0.0)
nreject = nreject + ap_grow_hist2 (skypix, coords,
wgt, nskypix, sky_zero, index[j], snx, sny, Memr[hgm],
nbins, hmin, hmax, rgrow, sumpx, sumsqpx, sumcbpx)
else if (wgt[index[j]] > 0.0) {
call ap_hgmsub2 (Memr[hgm], nbins, hmin, hmax,
skypix[index[j]], sky_zero, sumpx, sumsqpx, sumcbpx)
wgt[index[j]] = 0.0
nreject = nreject + 1
}
}
if (nreject == 0)
break
nsky_reject = nsky_reject + nreject
nsky = nskypix - nsky_reject
if (nsky <= 0)
break
call apmoments (sumpx, sumsqpx, sumcbpx, nsky, sky_zero,
sky_mean, sky_msigma, sky_skew)
# Recompute mean, mode, sigma and skew.
if (smooth == YES) {
nker = max (1, nint (sky_msigma / dh))
#call ap_lucy_smooth (Memr[hgm], Memr[shgm], nbins, nker, 2)
call ap_bsmooth (Memr[hgm], Memr[shgm], nbins, nker, 2)
call ap_hist_mode (Memr[x], Memr[shgm], Memr[w], nbins,
sky_mode, sky_sigma, sky_skew, maxfit, TOL, ier)
} else
call ap_hist_mode (Memr[x], Memr[hgm], Memr[w], nbins,
sky_mode, sky_sigma, sky_skew, maxfit, TOL, ier)
sky_mode = max (dmin, min (sky_mode, dmax))
if (ier != AP_OK)
break
if (sky_sigma <= dh)
break
}
# Return appropriate error code.
call sfree (sp)
if (nsky == 0 || nsky_reject == nskypix) {
nsky = 0
nsky_reject = nskypix
sky_mode = INDEFR
sky_sigma = INDEFR
sky_skew = INDEFR
return (AP_NSKY_TOO_SMALL)
} else if (ier == AP_NSKY_TOO_SMALL) {
return (AP_NSKY_TOO_SMALL)
} else if (ier != AP_OK) {
return (ier)
} else
return (AP_OK)
end
# AP_HIST_MODE -- Procedure to fit the skewed Gaussian function to the histogram
# of the sky pixels.
procedure ap_hist_mode (x, hgm, w, nbins, sky_mode, sky_sigma, sky_skew,
maxiter, tol, ier)
real x[ARB] # x array
real hgm[ARB] # histogram
real w[ARB] # weights
int nbins # number of bins
real sky_mode # sky value
real sky_sigma # sky sigma
real sky_skew # sky skew
int maxiter # max number of iterations
real tol # tolerances
int ier # error code
extern gausskew, dgausskew
int i, imin, imax, np, fier
pointer sp, list, fit, nl
real p[4], dp[4], dummy1
int locpr()
begin
# Allocate working memory.
call smark (sp)
call salloc (list, 4, TY_INT)
call salloc (fit, nbins, TY_REAL)
# Initialize.
do i = 1, 4
Memi[list+i-1] = i
# Compute initial guesses for the parameters.
call ap_alimr (hgm, nbins, dummy1, p[1], imin, imax)
p[2] = x[imax]
#p[3] = max (sky_sigma ** 2, abs (x[2] - x[1]) ** 2)
p[3] = abs ((x[nbins] - x[1]) / 6.0) ** 2
p[4] = 0.0
np = 4
# Fit the histogram.
call nlinitr (nl, locpr (gausskew), locpr (dgausskew), p, dp, np,
Memi[list], 4, tol, maxiter)
call nlfitr (nl, x, hgm, w, nbins, 1, WTS_UNIFORM, fier)
call nlvectorr (nl, x, Memr[fit], nbins, 1)
call nlpgetr (nl, p, np)
call nlfreer (nl)
call sfree (sp)
# Return the appropriate error code.
ier = AP_OK
if (fier == NO_DEG_FREEDOM) {
sky_mode = INDEFR
sky_sigma = INDEFR
sky_skew = INDEFR
ier = AP_NSKY_TOO_SMALL
} else {
if (fier == SINGULAR)
ier = AP_SKY_SINGULAR
else if (fier == NOT_DONE)
ier = AP_SKY_NOCONVERGE
if (p[2] < x[1] || p[2] > x[nbins]) {
sky_mode = x[imax]
ier = AP_BADPARAMS
} else
sky_mode = p[2]
if (p[3] <= 0.0) {
sky_sigma = 0.0
sky_skew = 0.0
ier = AP_BADPARAMS
} else {
sky_sigma = sqrt (p[3])
sky_skew = 1.743875281 * abs (p[4]) ** (1.0 / 3.0) * sky_sigma
if (p[4] < 0.0)
sky_skew = - sky_skew
}
}
end
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