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include <mach.h>
include <math.h>
# APTOPT - One-dimensional centering routine using repeated convolutions to
# locate image center.
define MAX_SEARCH 3 # Max initial search steps
int procedure aptopt (data, npix, center, sigma, tol, maxiter, ortho)
real data[ARB] # initial data
int npix # number of pixels
real center # initial guess at center
real sigma # sigma of Gaussian
real tol # gap tolerance for sigma
int maxiter # maximum number of iterations
int ortho # orthogonalize weighting vector
int i, iter
pointer sp, wgt
real newx, x[3], news, s[3], delx
real adotr(), apqzero()
begin
if (sigma <= 0.0)
return (-1)
# Allocate working space.
call smark (sp)
call salloc (wgt, npix, TY_REAL)
# Initialize.
x[1] = center
call mkt_prof_derv (Memr[wgt], npix, x[1], sigma, ortho)
s[1] = adotr (Memr[wgt], data, npix)
#if (abs (s[1]) <= EPSILONR) {
if (s[1] == 0.0) {
center = x[1]
call sfree (sp)
return (0)
} else
s[3] = s[1]
# Search for the correct interval.
for (i = 1; (s[3] * s[1] >= 0.0) && (i <= MAX_SEARCH); i = i + 1) {
s[3] = s[1]
x[3] = x[1]
x[1] = x[3] + sign (sigma, s[3])
call mkt_prof_derv (Memr[wgt], npix, x[1], sigma, ortho)
s[1] = adotr (Memr[wgt], data, npix)
#if (abs (s[1]) <= EPSILONR) {
if (s[1] == 0.0) {
center = x[1]
call sfree (sp)
return (0)
}
}
# Location not bracketed.
if (s[3] * s[1] > 0.0) {
call sfree (sp)
return (-1)
}
# Intialize the quadratic search.
delx = x[1] - x[3]
x[2] = x[3] - s[3] * delx / (s[1] - s[3])
call mkt_prof_derv (Memr[wgt], npix, x[2], sigma, ortho)
s[2] = adotr (Memr[wgt], data, npix)
#if (abs (s[2]) <= EPSILONR) {
if (s[2] == 0.0) {
center = x[2]
call sfree (sp)
return (1)
}
# Search quadratically.
for (iter = 2; iter <= maxiter; iter = iter + 1) {
# Check for completion.
#if (abs (s[2]) <= EPSILONR)
if (s[2] == 0.0)
break
if (abs (x[2] - x[1]) <= tol)
break
if (abs (x[3] - x[2]) <= tol)
break
# Compute new intermediate value.
newx = x[1] + apqzero (x, s)
call mkt_prof_derv (Memr[wgt], npix, newx, sigma, ortho)
news = adotr (Memr[wgt], data, npix)
if (s[1] * s[2] > 0.0) {
s[1] = s[2]
x[1] = x[2]
s[2] = news
x[2] = newx
} else {
s[3] = s[2]
x[3] = x[2]
s[2] = news
x[2] = newx
}
}
# Evaluate the center.
center = x[2]
call sfree (sp)
return (iter)
end
# AP_TPROFDER -- Procedure to estimate the approximating triangle function
# and its derivatives.
procedure ap_tprofder (data, der, npix, center, sigma, ampl)
real data[ARB] # input data
real der[ARB] # derivatives
int npix # number of pixels
real center # center of input Gaussian function
real sigma # sigma of input Gaussian function
real ampl # amplitude
int i
real x, xabs, width
begin
width = sigma * 2.35
do i = 1, npix {
x = (i - center) / width
xabs = abs (x)
if (xabs <= 1.0) {
data[i] = ampl * (1.0 - xabs)
der[i] = x * data[i]
} else {
data[i] = 0.0
der[i] = 0.0
}
}
end
# MKT_PROF_DERV - Make orthogonal profile derivative vector.
procedure mkt_prof_derv (weight, npix, center, sigma, norm)
real weight[ARB] # input weight
int npix # number of pixels
real center # center
real sigma # center
int norm # orthogonalise weight
pointer sp, der
real coef
real asumr(), adotr()
begin
call smark (sp)
call salloc (der, npix, TY_REAL)
# Fetch the weighting function and derivatives.
call ap_tprofder (Memr[der], weight, npix, center, sigma, 1.0)
if (norm == YES) {
# Make orthogonal to level background.
coef = -asumr (weight, npix) / npix
call aaddkr (weight, coef, weight, npix)
coef = -asumr (Memr[der], npix) / npix
call aaddkr (Memr[der], coef, Memr[der], npix)
# Make orthogonal to profile vector.
coef = adotr (Memr[der], Memr[der], npix)
if (coef <= 0.0)
coef = 1.0
else
coef = adotr (weight, Memr[der], npix) / coef
call amulkr (Memr[der], coef, Memr[der], npix)
call asubr (weight, Memr[der], weight, npix)
# Normalize the final vector.
coef = adotr (weight, weight, npix)
if (coef <= 0.0)
coef = 1.0
else
coef = sqrt (1.0 / coef)
call amulkr (weight, coef, weight, npix)
}
call sfree (sp)
end
define QTOL .125
# APQZERO - Solve for the root of a quadratic function defined by three
# points.
real procedure apqzero (x, y)
real x[3]
real y[3]
real a, b, c, det, dx
real x2, x3, y2, y3
begin
# Compute the determinant.
x2 = x[2] - x[1]
x3 = x[3] - x[1]
y2 = y[2] - y[1]
y3 = y[3] - y[1]
det = x2 * x3 * (x2 - x3)
# Compute the shift in x.
#if (abs (det) > 100.0 * EPSILONR) {
if (abs (det) > 0.0) {
a = (x3 * y2 - x2 * y3) / det
b = - (x3 * x3 * y2 - x2 * x2 * y3) / det
c = a * y[1] / (b * b)
if (abs (c) > QTOL)
dx = (-b / (2.0 * a)) * (1.0 - sqrt (1.0 - 4.0 * c))
else
dx = - (y[1] / b) * (1.0 + c)
return (dx)
#} else if (abs (y3) > EPSILONR)
} else if (abs (y3) > 0.0)
return (-y[1] * x3 / y3)
else
return (0.0)
end
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