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include <mach.h>
include <math/nlfit.h>
$if (datatype == r)
include "nlfitdefr.h"
$else
include "nlfitdefd.h"
$endif
# NLFIT -- Routine to perform a non-linear least squares fit. At least MINITER
# iterations must be performed before the fit is complete.
procedure nlfit$t (nl, x, z, w, npts, nvars, wtflag, stat)
pointer nl # pointer to nlfit structure
PIXEL x[ARB] # independent variables (npts * nvars)
PIXEL z[ARB] # function values (npts)
PIXEL w[ARB] # weights (npts)
int npts # number of points
int nvars # number of independent variables
int wtflag # weighting type
int stat # error code
int i, miniter, ier
PIXEL scatter, dscatter
PIXEL nlscatter$t()
begin
# Initialize.
NL_ITER(nl) = 0
NL_LAMBDA(nl) = PIXEL (.001)
NL_REFSQ(nl) = PIXEL (0.0)
NL_SCATTER(nl) = PIXEL(0.0)
# Initialize the weights.
switch (wtflag) {
case WTS_UNIFORM:
do i = 1, npts
w[i] = PIXEL (1.0)
case WTS_SCATTER:
;
case WTS_USER:
;
case WTS_CHISQ:
do i = 1, npts {
if (z[i] > PIXEL (0.0))
w[i] = PIXEL (1.0) / z[i]
else if (z[i] < PIXEL (0.0))
w[i] = PIXEL (-1.0) / z[i]
else
w[i] = PIXEL (0.0)
}
default:
do i = 1, npts
w[i] = PIXEL (1.0)
}
# Initialize.
scatter = PIXEL(0.0)
if (wtflag == WTS_SCATTER)
miniter = MINITER + 1
else
miniter = MINITER
repeat {
# Perform a single iteration.
call nliter$t (nl, x, z, w, npts, nvars, ier)
NL_ITER(nl) = NL_ITER(nl) + 1
#call eprintf ("niter=%d refsq=%g oldsq=%g sumsq=%g\n")
#call pargi (NL_ITER(nl))
#call parg$t (NL_REFSQ(nl))
#call parg$t (NL_OLDSQ(nl))
#call parg$t (NL_SUMSQ(nl))
stat = ier
if (stat == NO_DEG_FREEDOM)
break
# Make the convergence checks.
if (NL_ITER(nl) < miniter)
stat = NOT_DONE
else if (NL_SUMSQ(nl) <= PIXEL (10.0) * EPSILON$T)
stat = DONE
else if (NL_REFSQ(nl) < NL_SUMSQ(nl))
stat = NOT_DONE
else if (((NL_REFSQ(nl) - NL_SUMSQ(nl)) / NL_SUMSQ(nl)) <
NL_TOL(nl))
stat = DONE
else
stat = NOT_DONE
# Check for a singular solution.
if (stat == DONE) {
if (ier == SINGULAR)
stat = ier
break
}
# Quit if the lambda parameter goes to zero.
if (NL_LAMBDA(nl) <= 0.0)
break
# Check the number of iterations.
if ((NL_ITER(nl) >= miniter) && (NL_ITER(nl) >= NL_ITMAX(nl)))
break
# Adjust the weights if necessary.
switch (wtflag) {
case WTS_SCATTER:
dscatter = nlscatter$t (nl, x, z, w, npts, nvars)
if ((NL_ITER(nl) >= MINITER) && (dscatter >= PIXEL (10.0) *
EPSILON$T)) {
do i = 1, npts {
if (w[i] <= PIXEL(0.0))
w[i] = PIXEL(0.0)
else {
w[i] = PIXEL(1.0) / (PIXEL(1.0) / w[i] + dscatter)
}
}
scatter = scatter + dscatter
}
default:
;
}
# Get ready for next iteration.
NL_REFSQ(nl) = min (NL_OLDSQ(nl), NL_SUMSQ(nl))
}
NL_SCATTER(nl) = NL_SCATTER(nl) + scatter
end
# NLSCATTER -- Routine to estimate the original scatter in the fit.
PIXEL procedure nlscatter$t (nl, x, z, w, npts, nvars)
pointer nl # Pointer to nl fitting structure
PIXEL x[ARB] # independent variables (npts * nvars)
PIXEL z[ARB] # function values (npts)
PIXEL w[ARB] # weights (npts)
int npts # number of points
int nvars # number of independent variables
pointer sp, zfit, errors
PIXEL scatter, variance, chisqr
int nlstati()
begin
# Allocate working memory.
call smark (sp)
call salloc (zfit, npts, TY_PIXEL)
call salloc (errors, nlstati (nl, NLNPARAMS), TY_PIXEL)
# Initialize
scatter = PIXEL (0.0)
# Compute the fit and the errors.
call nlvector$t (nl, x, Mem$t[zfit], npts, nvars)
call nlerrors$t (nl, z, Mem$t[zfit], w, npts, variance, chisqr,
Mem$t[errors])
# Estimate the scatter.
if (chisqr <= PIXEL(0.0) || variance <= PIXEL(0.0))
scatter = PIXEL (0.0)
else
scatter = PIXEL(0.5) * variance * (chisqr - PIXEL(1.0)) / chisqr
call sfree (sp)
return (scatter)
end
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