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include <math.h>
include <mach.h>
# FUNCS - File to contain all of the functional models and derivatives.
# Models currently supported are:
# - Gaussian on a constant background
# - N-th order polynomial
# - Lorentzian on a constant background
# CGAUSS1D - Procedure to compute the value of a 1-D Gaussian function
# sitting on top of a constant background.
procedure cgauss1d (x, nvars, p, np, z)
real x # position coordinate
int nvars # number of variables
real p[ARB] # p[1]=amplitude p[2]=center p[3]=sigma p[4]=background
int np # number of parameters np = 4
real z # function return
real r2
begin
r2 = (x - p[2]) ** 2 / (2. * p[3])
if (abs (r2) > 25.0)
z = p[4]
else
z = p[1] * exp (-r2) + p[4]
end
# CDGAUSS1D -- Procedure to compute a 1-D Gaussian profile and its derivatives.
# The Gaussian is assumed to sitting on top of a constant background.
procedure cdgauss1d (x, nvars, p, dp, np, z, der)
real x # position coordinate
int nvars # number of variables
real p[ARB] # p[1]=amplitude, p[2]=center, p[3]=sky, p[4]=sigma
real dp[ARB] # parameter derivatives
int np # number of parameters np=4
real z # function value
real der[ARB] # derivatives
real dx, r2
begin
dx = x - p[2]
r2 = dx * dx / (2.0 * p[3])
if (abs (r2) > 25.0) {
z = p[4]
der[1] = 0.0
der[2] = 0.0
der[3] = 0.0
der[4] = 1.0
} else {
der[1] = exp (-r2)
z = p[1] * der[1]
der[2] = z * dx / p[3]
der[3] = z * r2 / p[3]
der[4] = 1.0
z = z + p[4]
}
end
# D_CGAUSS1D - Procedure to compute the value of a 1-D Gaussian function
# sitting on top of a constant background.
procedure d_cgauss1d (x, nvars, p, np, z)
double x # position coordinate
int nvars # number of variables
double p[ARB] # p[1]=amplitude p[2]=center p[3]=sigma p[4]=background
int np # number of parameters np = 4
double z # function return
double r2
begin
r2 = (x - p[2]) ** 2 / (2. * p[3])
if (abs (r2) > 25.0)
z = p[4]
else
z = p[1] * exp (-r2) + p[4]
end
# D_CDGAUSS1D -- Procedure to compute a 1-D Gaussian profile and its deriv-
# atives. The Gaussian is assumed to sitting on top of a constant background.
procedure d_cdgauss1d (x, nvars, p, dp, np, z, der)
double x # position coordinate
int nvars # number of variables
double p[ARB] # p[1]=amplitude, p[2]=center, p[3]=sky, p[4]=sigma
double dp[ARB] # parameter derivatives
int np # number of parameters np=4
double z # function value
double der[ARB] # derivatives
double dx, r2
begin
dx = x - p[2]
r2 = dx * dx / (2.0 * p[3])
if (abs (r2) > 25.0) {
z = p[4]
der[1] = 0.0
der[2] = 0.0
der[3] = 0.0
der[4] = 1.0
} else {
der[1] = exp (-r2)
z = p[1] * der[1]
der[2] = z * dx / p[3]
der[3] = z * r2 / p[3]
der[4] = 1.0
z = z + p[4]
}
end
# POLYFIT -- Procedure to compute the fit of an N-order polynomial
procedure polyfit (x, nvars, p, np, z)
real x # position coordinate
int nvars # number of variables
real p[ARB] # coefficients of polynomial
int np # number of parameters
real z # function return
int i
real r
begin
r = 0.0
do i = 2, np
r = r + x**(i-1) * p[i]
z = p[1] + r
end
# DPOLYFIT -- Procedure to compute the function value and derivatives of
# a N-order polynomial.
procedure dpolyfit (x, nvars, p, dp, np, z, der)
real x # position coordinate
int nvars # number of variables
real p[ARB] # p[1]=amplitude, p[2]=center, p[3]=sigma
real dp[ARB] # parameter derivatives
int np # number of parameters
real z # function value
real der[ARB] # derivatives
int i
begin
der[1] = 1.0
z = 0.0
do i = 2, np {
der[i] = x ** (i-1)
z = z + x**(i-1) * p[i]
}
z = p[1] + z
end
# LORENTZ -- Procedure to compute a Lorentzian profile
procedure lorentz (x, nvars, p, np, z)
real x # position coordinate
int nvars # number of variables
real p[ARB] # p[1]=amplitude p[2]=center p[3]=fwhm p[4]=background
int np # number of parameters np = 4
real z # function return
real r2
begin
r2 = (x - p[2])**2 + (p[3] / 2.0)**2
if (r2 != 0.0)
z = p[1] * ((p[3]/2.0) / r2) + p[4]
else
z = p[4]
end
# DLORENTZ -- Procedure to compute the function value and derivatives of
# a Lorentzian profile
procedure dlorentz (x, nvars, p, dp, np, z, der)
real x # position coordinate
int nvars # number of variables
real p[ARB] # p[1]=amplitude, p[2]=center, p[3]=fwhm, [4]=background
real dp[ARB] # parameter derivatives
int np # number of parameters
real z # function value
real der[ARB] # derivatives
real dl, dr, d2
begin
dl = (x - p[2]) * (x - p[2])
dr = (0.5 * p[3]) * (0.5 * p[3])
d2 = dl + dr
if (d2 == 0.0) {
der[1] = 0.0
der[2] = 0.0
der[3] = 0.0
der[4] = 1.0
z = p[4]
} else {
der[1] = ((p[3]/2.0) / d2)
der[2] = (p[1]*p[3]/2.0) * (2.0 * (x - p[2])) / (d2 * d2)
der[3] = ((p[1] / (2.0 * d2)) - (((p[1]*p[3]*p[3])/2.0)/(d2*d2)))
der[4] = 1.0
z = p[1] * ((p[3]/2.0) / d2) + p[4]
}
end
# LORENTZ -- Procedure to compute a Lorentzian profile
procedure lorentz_old (x, nvars, p, np, z)
real x # position coordinate
int nvars # number of variables
real p[ARB] # p[1]=amplitude p[2]=center p[3]=fwhm p[4]=background
int np # number of parameters np = 4
real z # function return
begin
if (p[3] != 0.0)
z = p[1] / (1. + ((x-p[2])/p[3])**2) + p[4]
else
z = p[4]
end
# DLORENTZ -- Procedure to compute the function value and derivatives of
# a Lorentzian profile
procedure dlorentz_old (x, nvars, p, dp, np, z, der)
real x # position coordinate
int nvars # number of variables
real p[ARB] # p[1]=amplitude, p[2]=center, p[3]=fwhm, [4]=background
real dp[ARB] # parameter derivatives
int np # number of parameters
real z # function value
real der[ARB] # derivatives
real dx, D
begin
#dx = (x - p[2]) / p[3] # Frank's derivs
dx = (x - p[2])
D = 1. + (dx/p[3])**2
if (p[3] == 0.0) {
der[1] = 0.0
der[2] = 0.0
der[3] = 0.0
der[4] = 1.0
z = p[4]
} else {
der[1] = 1. / D
der[2] = p[1] / D**2 * (2. * dx / p[3]**2)
der[3] = p[1] / D**2 * (2. * dx * dx / p[3]**3)
#der[2] = p[1] / D**2 * (2. * dx / p[3]) # Frank's derivs
#der[3] = -p[1] / D**2 * (2. * dx * dx / p[3])
der[4] = 1.0
if (p[3] != 0.0)
z = p[1] / (1. + ((x-p[2])/p[3])**2) + p[4]
else
z = p[4]
}
end
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