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|
include "../lib/daophotdef.h"
define NGL 4
# DP_PROFILE -- Evaluate the analytic part of the psf function and its
# derivatives.
real procedure dp_profile (ipstyp, dx, dy, par, dhdxc, dhdyc, term, ideriv)
int ipstyp # the analytic psf function type
real dx, dy # distance of point from center of function
real par[ARB] # the current parameter values
real dhdxc, dhdyc # derivatives of the function integral wrt x,y
real term[ARB] # derivatives of the function wrt parameters
int ideriv # compute the derivatives ?
int npt, ix, iy
real d[NGL,NGL], w[NGL,NGL], x[NGL], xsq[NGL], p1xsq[NGL]
real p1p2, dhdsx, dhdsy, erfx, erfy, p1sq, p2sq, y, ysq, p2ysq, profile
real xy, wt, denom, alpha, func, p4fod, wp4fod, f, e, rsq, wf
real wfsq, onemp3, dfby, deby, dbyx0, dbyy0
real daoerf()
data d / 0.0, 0.0, 0.0, 0.0,
-0.28867513, 0.28867513, 0.0, 0.0,
-0.38729833, 0.0, 0.38729833, 0.0,
-0.43056816, -0.16999052, 0.16999052, 0.43056816 /
data w / 1.0, 0.0, 0.0, 0.0,
0.5, 0.5, 0.0, 0.0,
0.27777778, 0.44444444, 0.27777778, 0.0,
0.17392742, 0.32607258, 0.32607258, 0.17392742 /
begin
# Initialize.
profile = 0.0
dhdxc = 0.0
dhdyc = 0.0
# Compute the analytic part of the profile for a given x and y.
switch (ipstyp) {
# Evaluate the Gaussian function
# f = erfx * erfy / (par[1] * par[2])
# par[1] is the hwhm in x; sigma(x) = 0.8493218 * hwhm
# par[2] is the hwhm in y; sigma(y) = 0.8493218 * hwhm
case FCTN_GAUSS:
p1p2 = par[1] * par[2]
erfx = daoerf (dx, 0.0, par[1], dhdxc, dhdsx)
erfy = daoerf (dy, 0.0, par[2], dhdyc, dhdsy)
profile = erfx * erfy / p1p2
dhdxc = dhdxc * erfy / p1p2
dhdyc = dhdyc * erfx / p1p2
if (ideriv > 0) {
term[1] = (dhdsx - erfx / par[1]) * erfy / p1p2
term[2] = (dhdsy - erfy / par[2]) * erfx / p1p2
}
# Evaluate the Moffat25 function
#
# f = (beta - 1) / (ax * ay * (1 + (x/ax) ** 2 + (y/ay) ** 2 +
# (xy * axy)) ** beta)
#
# par[1] is the hwhm in x at y = 0.0
# 1/2 = 1 / (1 + (par[1] / ax) ** 2) ** beta
# so
# 2 ** (1/ beta) - 1 = (par[1] / ax) ** 2
# ax ** 2 = par[1] ** 2 / (2 ** (1 / beta) - 1)
#
# when beta = 2.5 ax ** 2 = 3.129813 * par[1] ** 2
#
# f = 1 / par[1] * par[2] * (1 + 0.3195079 * ((x / par[1]) ** 2 +
# (y / par[2]) ** 2 + xy * par[3])) ** 2.5
#
case FCTN_MOFFAT25:
alpha = 0.3195079
#talpha = 0.6390158
p1sq = par[1] ** 2
p2sq = par[2] ** 2
p1p2 = par[1] * par[2]
xy = dx * dy
if (ideriv > 0)
call aclrr (term, 4)
denom = 1.0 + alpha * (dx ** 2 / p1sq + dy ** 2 / p2sq + xy *
par[3])
if (denom > 1.0e4)
return (profile)
func = 1.0 / (p1p2 * denom ** par[4])
if (func >= 0.046) {
npt = 4
} else if (func >= 0.0022) {
npt = 3
} else if (func >= 0.0001) {
npt = 2
} else if (func >= 1.0e-10) {
profile = (par[4] - 1.0) * func
p4fod = par[4] * alpha * profile / denom
dhdxc = p4fod * (2.0 * dx / p1sq + dy * par[3])
dhdyc = p4fod * (2.0 * dy / p2sq + dx * par[3])
if (ideriv > 0) {
term[1] = (2.0 * p4fod * dx ** 2 / p1sq - profile) /
par[1]
term[2] = (2.0 * p4fod * dy ** 2 / p2sq - profile) /
par[2]
term[3] = - p4fod * xy
term[4] = profile * (1.0 / (par[4] - 1.0) - log (denom))
}
return (profile)
} else {
return (profile)
}
do ix = 1, npt {
x[ix] = dx + d[ix,npt]
xsq[ix] = x[ix] ** 2
p1xsq[ix] = xsq[ix] / p1sq
}
do iy = 1, npt {
y = dy + d[iy,npt]
ysq = y ** 2
p2ysq = ysq / p2sq
do ix = 1, npt {
wt = w[iy,npt] * w[ix,npt]
xy = x[ix] * y
denom = 1.0 + alpha * (p1xsq[ix] + p2ysq + xy * par[3])
func = (par[4] - 1.0) / (p1p2 * denom ** par[4])
p4fod = par[4] * alpha * func / denom
wp4fod = wt * p4fod
wf = wt * func
profile = profile + wf
dhdxc = dhdxc + wp4fod * (2.0 * x[ix] / p1sq +
y * par[3])
dhdyc = dhdyc + wp4fod * (2. * y / p2sq + x[ix] *
par[3])
if (ideriv > 0) {
term[1] = term[1] + (2.0 * wp4fod * p1xsq[ix] - wf) /
par[1]
term[2] = term[2] + (2.0 * wp4fod * p2ysq - wf) /
par[2]
term[3] = term[3] - wp4fod * xy
term[4] = term[4] + wf * (1.0 / (par[4] - 1.0) -
log (denom))
}
}
}
#
# Penny function which has a gaussian core and lorentzian wings.
# The lorentzian is elongated along the x and y axes.
case FCTN_PENNY1:
p1sq = par[1] ** 2
p2sq = par[2] ** 2
onemp3 = 1.0 - par[3]
xy = dx * dy
if (ideriv > 0)
call aclrr (term, 4)
rsq = dx ** 2 / p1sq + dy ** 2 / p2sq
if (rsq > 1.0e10)
return (profile)
f = 1.0 / (1.0 + rsq)
rsq = rsq + xy * par[4]
if (rsq < 34.0) {
e = exp (-0.6931472 * rsq)
func = par[3] * e + onemp3 * f
} else {
e = 0.0
func = onemp3 * f
}
if (func >= 0.046) {
npt = 4
} else if (func >= 0.0022) {
npt = 3
} else if (func >= 0.0001) {
npt = 2
} else if (func >= 1.0e-10) {
profile = func
dfby = onemp3 * f ** 2
deby = 0.6931472 * par[3] * e
dbyx0 = 2.0 * dx / p1sq
dbyy0 = 2.0 * dy / p2sq
dhdxc = deby * (dbyx0 + dy * par[4]) + dfby * dbyx0
dhdyc = deby * (dbyy0 + dx * par[4]) + dfby * dbyy0
if (ideriv > 0) {
dbyx0 = dbyx0 * dx / par[1]
dbyy0 = dbyy0 * dy / par[2]
dfby = dfby + deby
term[1] = dfby * dbyx0
term[2] = dfby * dbyy0
term[3] = e - f
term[4] = - deby * xy / (0.5 - abs(par[4]))
}
return (profile)
} else {
return (profile)
}
do ix = 1, npt {
x[ix] = dx + d[ix,npt]
p1xsq[ix] = x[ix] / p1sq
}
do iy = 1, npt {
y = dy + d[iy,npt]
p2ysq = y / p2sq
do ix = 1, npt {
wt = w[iy,npt] * w[ix,npt]
xy = x[ix] * y
rsq = p1xsq[ix] * x[ix] + p2ysq * y
f = 1.0 / (1.0 + rsq)
rsq = rsq + xy * par[4]
if (rsq < 34.0) {
e = exp (- 0.6931472 * rsq)
func = par[3] * e + onemp3 * f
deby = 0.6931472 * wt * par[3] * e
} else {
e = 0.0
func = onemp3 * f
deby = 0.0
}
profile = profile + wt * func
dfby = wt * onemp3 * f ** 2
dbyx0 = 2.0 * p1xsq[ix]
dbyy0 = 2.0 * p2ysq
dhdxc = dhdxc + deby * (dbyx0 + dy * par[4]) + dfby * dbyx0
dhdyc = dhdyc + deby * (dbyy0 + dx * par[4]) + dfby * dbyy0
if (ideriv > 0) {
dbyx0 = dbyx0 * dx / par[1]
dbyy0 = dbyy0 * dy / par[2]
term[1] = term[1] + (dfby + deby) * dbyx0
term[2] = term[2] + (dfby + deby) * dbyy0
term[3] = term[3] + wt * (e - f)
term[4] = term[4] - deby * xy
}
}
}
# Penny function which has a gaussian core and lorentzian wings.
# The gaussian and lorentzian may be tilted in different directions.
case FCTN_PENNY2:
p1sq = par[1] ** 2
p2sq = par[2] ** 2
onemp3 = 1.0 - par[3]
xy = dx * dy
if (ideriv > 0)
call aclrr (term, 5)
rsq = dx ** 2 / p1sq + dy ** 2 / p2sq
dfby = rsq + par[5] * xy
if (dfby > 1.0e10)
return (profile)
f = 1.0 / (1.0 + dfby)
deby = rsq + par[4] * xy
if (deby < 34.0)
e = exp (-0.6931472 * deby)
else
e = 0.0
func = par[3] * e + onemp3 * f
if (func >= 0.046) {
npt = 4
} else if (func >= 0.0022) {
npt = 3
} else if (func >= 0.0001) {
npt = 2
} else if (func >= 1.0e-10) {
profile = func
dfby = onemp3 * f ** 2
deby = 0.6931472 * par[3] * e
dbyx0 = 2.0 * dx / p1sq
dbyy0 = 2.0 * dy / p2sq
dhdxc = deby * (dbyx0 + dy * par[4]) + dfby * (dbyx0 + dy *
par[5])
dhdyc = deby * (dbyy0 + dx * par[4]) + dfby * (dbyy0 + dx *
par[5])
if (ideriv > 0) {
dbyx0 = dbyx0 * dx / par[1]
dbyy0 = dbyy0 * dy / par[2]
term[5] = -dfby * xy
dfby = dfby + deby
term[1] = dfby * dbyx0
term[2] = dfby * dbyy0
term[3] = e - f
term[4] = - deby * xy
}
return (profile)
} else {
return (profile)
}
do ix = 1, npt {
x[ix] = dx + d[ix,npt]
p1xsq[ix] = x[ix] / p1sq
}
do iy = 1, npt {
y = dy + d[iy,npt]
p2ysq = y / p2sq
do ix = 1, npt {
wt = w[iy,npt] * w[ix,npt]
xy = x[ix] * y
rsq = p1xsq[ix] * x[ix] + p2ysq * y
f = 1.0 / (1.0 + rsq + par[5] * xy)
deby = rsq + par[4] * xy
if (deby < 34.0) {
e = exp (- 0.6931472 * deby)
func = par[3] * e + onemp3 * f
deby = 0.6931472 * wt * par[3] * e
} else {
e = 0.0
func = onemp3 * f
deby = 0.0
}
profile = profile + wt * func
dfby = wt * onemp3 * f ** 2
dbyx0 = 2.0 * p1xsq[ix]
dbyy0 = 2.0 * p2ysq
dhdxc = dhdxc + deby * (dbyx0 + dy * par[4]) + dfby *
(dbyx0 + dy * par[5])
dhdyc = dhdyc + deby * (dbyy0 + dx * par[4]) + dfby *
(dbyy0 + dx * par[5])
if (ideriv > 0) {
dbyx0 = dbyx0 * dx / par[1]
dbyy0 = dbyy0 * dy / par[2]
term[1] = term[1] + (dfby + deby) * dbyx0
term[2] = term[2] + (dfby + deby) * dbyy0
term[3] = term[3] + wt * (e - f)
term[4] = term[4] - deby * xy
term[5] = term[5] - dfby * xy
}
}
}
# Evaluate the Moffat15 function
#
# f = (beta - 1) / (ax * ay * (1 + (x/ax) ** 2 + (y/ay) ** 2 +
# (xy * axy)) ** beta)
#
# par[1] is the hwhm in x at y = 0.0
# 1/2 = 1 / (1 + (par[1] / ax) ** 2) ** beta
# so
# 2 ** (1/ beta) - 1 = (par[1] / ax) ** 2
# ax ** 2 = par[1] ** 2 / (2 ** (1 / beta) - 1)
#
# when beta = 1.5 ax ** 2 = 1.7024144 * par[1] ** 2
#
# f = 1 / par[1] * par[2] * (1 + 0.5874011 * ((x / par[1]) ** 2 +
# (y / par[2]) ** 2 + xy * par[3])) ** 2.5
#
case FCTN_MOFFAT15:
alpha = 0.5874011
#talpha = 1.1748021
p1sq = par[1] ** 2
p2sq = par[2] ** 2
p1p2 = par[1] * par[2]
xy = dx * dy
if (ideriv > 0)
call aclrr (term, 4)
denom = 1.0 + alpha * (dx ** 2 / p1sq + dy ** 2 / p2sq + xy *
par[3])
if (denom > 5.0e6)
return (profile)
func = 1.0 / (p1p2 * denom ** par[4])
if (func >= 0.046) {
npt = 4
} else if (func >= 0.0022) {
npt = 3
} else if (func >= 0.0001) {
npt = 2
} else if (func >= 1.0e-10) {
profile = (par[4] - 1.0) * func
p4fod = par[4] * alpha * profile / denom
dhdxc = p4fod * (2.0 * dx / p1sq + dy * par[3])
dhdyc = p4fod * (2.0 * dy / p2sq + dx * par[3])
if (ideriv > 0) {
term[1] = (2.0 * p4fod * dx ** 2 / p1sq - profile) /
par[1]
term[2] = (2.0 * p4fod * dy ** 2 / p2sq - profile) /
par[2]
term[3] = - p4fod * xy
term[4] = profile * (1.0 / (par[4] - 1.0) - log (denom))
}
return (profile)
} else {
return (profile)
}
do ix = 1, npt {
x[ix] = dx + d[ix,npt]
xsq[ix] = x[ix] ** 2
p1xsq[ix] = xsq[ix] / p1sq
}
do iy = 1, npt {
y = dy + d[iy,npt]
ysq = y ** 2
p2ysq = ysq / p2sq
do ix = 1, npt {
wt = w[iy,npt] * w[ix,npt]
xy = x[ix] * y
denom = 1.0 + alpha * (p1xsq[ix] + p2ysq + xy *
par[3])
func = (par[4] - 1.0) / (p1p2 * denom ** par[4])
p4fod = par[4] * alpha * func / denom
wp4fod = wt * p4fod
wf = wt * func
profile = profile + wf
dhdxc = dhdxc + wp4fod * (2.0 * x[ix] / p1sq + y *
par[3])
dhdyc = dhdyc + wp4fod * (2. * y / p2sq + x[ix] *
par[3])
if (ideriv > 0) {
term[1] = term[1] + (2.0 * wp4fod * p1xsq[ix] - wf) /
par[1]
term[2] = term[2] + (2.0 * wp4fod * p2ysq - wf) /
par[2]
term[3] = term[3] - wp4fod * xy
term[4] = term[4] + wf * (1.0 / (par[4] - 1.0) -
log (denom))
}
}
}
case FCTN_LORENTZ:
p1sq = par[1] ** 2
p2sq = par[2] ** 2
p1p2 = par[1] * par[2]
xy = dx * dy
if (ideriv > 0)
call aclrr (term, 3)
denom = 1.0 + dx ** 2 / p1sq + dy ** 2 / p2sq + xy * par[3]
if (denom > 1.0e10)
return (profile)
func = 1.0 / denom
if (func >= 0.046) {
npt = 4
} else if (func >= 0.0022) {
npt = 3
} else if (func >= 0.0001) {
npt = 2
} else if (func >= 1.0e-10) {
profile = func
wfsq = func ** 2
dhdxc = wfsq * (2.0 * dx / p1sq + dy * par[3])
dhdyc = wfsq * (2.0 * dy / p2sq + dx * par[3])
if (ideriv > 0) {
term[1] = wfsq * (2.0 * dx ** 2 / p1sq) / par[1]
term[2] = wfsq * (2.0 * dy ** 2 / p2sq) / par[2]
term[3] = - wfsq * xy
}
return (profile)
} else {
return (profile)
}
do ix = 1, npt {
x[ix] = dx + d[ix,npt]
xsq[ix] = x[ix] ** 2
p1xsq[ix] = xsq[ix] / p1sq
}
do iy = 1, npt {
y = dy + d[iy,npt]
ysq = y ** 2
p2ysq = ysq / p2sq
do ix = 1, npt {
wt = w[iy,npt] * w[ix,npt]
xy = x[ix] * y
denom = 1.0 + p1xsq[ix] + p2ysq + xy * par[3]
func = 1.0 / denom
wf = wt * func
wfsq = wf * func
profile = profile + wf
dhdxc = dhdxc + wfsq * (2.0 * x[ix] / p1sq + y * par[3])
dhdyc = dhdyc + wfsq * (2.0 * y / p2sq + x[ix] * par[3])
if (ideriv > 0) {
term[1] = term[1] + wfsq * (2.0 * p1xsq[ix]) / par[1]
term[2] = term[2] + wfsq * (2.0 * p2ysq) / par[2]
term[3] = term[3] - wfsq * xy
}
}
}
default:
profile = INDEFR
}
return (profile)
end
|
