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/*
* gauss.i
*
* $Id: gauss.i,v 1.2 2008/01/04 14:35:40 frigaut Exp $
*
* This file is part of Yutils
* Copyright (C) 2007 Thibaut Paumard <paumard@users.sourceforge.net>
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License along
* with this program; if not, write to the Free Software Foundation, Inc.,
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
*
* $Log: gauss.i,v $
* Revision 1.2 2008/01/04 14:35:40 frigaut
* - changed path for require statement
*
* Revision 1.1 2008/01/04 13:47:48 frigaut
* initial import of thibaut's functions
*
*
*/
func gauss(x,a,&grad,deriv=)
/* DOCUMENT gauss(x,a)
Returns a gaussian:
I0*exp(-0.5*((x-x0)/dx)^2) [+a(4) [+a(5)*x]]
Where:
I0=a(1)
x0=a(2)
dx=a(3) (gaussian sigma)
Works with lmfit, and can return derivates.
Notes: FHWM=sigma*2*sqrt(2*alog(2)); sum(gauss)=I0*sigma*sqrt(2*pi)
SEE ALSO: gauss_fit, asgauss, asgauss_fit
*/
{
nterms=numberof(a);
eps=1e-100;
if (abs(a(3))<eps) a(3)=sign(a(3))*eps;
if (a(3)==0) u1=0; else u1=exp(-0.5*((x-a(2))/a(3))^2);
res=a(1)*u1;
if (deriv) {
grad=array(double,numberof(x),nterms);
grad(,1)=u1;
grad(,2)=res*(x-a(2))/a(3)^2;
grad(,3)=res*(x-a(2))^2/a(3)^3;
if (nterms>3) grad(,4)=1.;
if (nterms==5) grad(,5)=x;
}
if (nterms>3) res=res+a(4);
if (nterms==5) res=res+a(5)*x;
return res;
}
func asgauss(x,a,&grad,deriv=)
/* DOCUMENT asgauss(x,a)
Returns an assymetrical gaussian:
I0*exp(-((x-x0)/dx)^2) [+a(5) [+a(6)*x]]
Where:
I0=a(1)
x0=a(2)
dx=a(3) for x<x0 and dx=a(4) for x>=x0
Works with lmfit, and can return derivates.
SEE ALSO: gauss, gauss_fit, asgauss_fit
*/
{
nterms=numberof(a);
ta=(x<a(2));
tb=(x>=a(2));
u1=exp(-0.5*((x-a(2))*(ta/a(3)+tb/a(4)))^2);
res=a(1)*u1;
if (deriv) {
grad=array(double,numberof(x),nterms);
grad(,1)=u1;
grad(,2)=res*(x-a(2))*(ta/a(3)+tb/a(4))^2;
grad(,3)=res*(x-a(2))^2*(ta/a(3))^3;
grad(,4)=res*(x-a(2))^2*(tb/a(4))^3;
if (nterms>4) grad(,5)=1.; // useless
if (nterms==6) grad(,6)=x;
}
if (nterms>4) res=res+a(5);
if (nterms==6) res=res+a(6)*x;
return res;
}
func gauss_fit(y,x,w,guess=,nterms=,fit=,correl=,stdev=,gain=,tol=,deriv=,itmax=,lambda=,eps=,monte_carlo=) {
/* DOCUMENT gauss_fit(y,x,w,guess=,nterms=)
Fits a gaussian (see gauss) profile on a data set using lmfit (see lmfit).
The set of data points Y is the only mandatory argument, X defaults to
indgen(numberof(y)), weights W are optional (see lmfit). GAUSS_FIT tries
to guess a set of initial parameters, but you can (and should in every
non-trivial case) provide one using the GUESS keyword. In case you don't
provide a guess, you should set NTERMS to 3 (simple gaussian), 4 (adjust
constant baseline) or 5 (adjust linear baseline). The returned fitted
parameters have the same format as GUESS, see gauss.
SEE ALSO: gauss, asgauss, asgauss_fit
*/
require,"lmfit.i";
if (is_void(x)) x=indgen(numberof(y));
if (is_void(guess)) {
if (is_void(nterms)) nterms=3;
if (nterms<3) nterms=3;
if (nterms>5) nterms=5;
guess=array(double,nterms);
if (nterms==4) {
base=median(y);
guess(4)=base;
} else if (nterms==5) {
n=numberof(y);
y1=median(y(1:long(n/2)));
x1=median(x(1:long(n/2)));
y2=median(y(-long(n/2):0));
x2=median(x(-long(n/2):0));
guess(5)=(y2-y1)/(x2-x1);
if (guess(5)!=0) guess(4)=y1-guess(5)*x1;
base=guess(4)+guess(5)*x;
} else base=0.;
y2=y-base;
ind0=abs(y2)(mxx);
guess(2)=x(ind0);
guess(1)=y2(ind0);
if (y2(ind0)==guess(1)) yy=y2;
else yy=-y2;
ind1=ind0;
ind2=ind0;
while (ind1>1 && yy(ind1)>0.5*guess(1)) ind1--;
if (yy(ind1)<0.5*guess(1)) ind1++;
while (ind2<numberof(y)-1 && yy(ind2)>0.5*guess(1)) ind2++;
if (yy(ind2)<0.5*guess(1)) ind2--;
guess(3)=abs(x(ind2)-x(ind1))/sqrt(2.);
} else nterms=numberof(guess);
a=guess;
if (is_void(deriv)) deriv=1;
result=lmfit(gauss,x,a,y,w,deriv=deriv,fit=fit,correl=correl,stdev=stdev,
gain=gain,tol=tol,itmax=itmax,lambda=lambda,
eps=eps,monte_carlo=monte_carlo);
return a;
}
func asgauss_fit(y,x,w,guess=,nterms=){
/* DOCUMENT asgauss_fit(y,x,w,guess=,nterms=)
Fits an assymetrical gaussian (see asgauss) profile on a data set using
lmfit (see lmfit). The set of data points Y is the only mandatory
argument, X defaults to indgen(numberof(y)), weights W are optional (see
lmfit). ASGAUSS_FIT tries to guess a set of initial parameters, but you
can (and should in every non-trivial case) provide one using the GUESS
keyword. In case you don't provide a guess, you should set NTERMS to 6
(simple assymmetrical gaussian), 7 (adjust constant baseline) or 8 (adjust
linear baseline). The returned fitted parameters have the same format as
GUESS, see asgauss.
SEE ALSO: asgauss, gauss, gauss_fit
*/
require,"lmfit.i";
if (is_void(x)) x=indgen(numberof(y));
if (is_void(guess)) {
if (is_void(nterms)) nterms=4;
if (nterms<4) nterms=4;
if (nterms>6) nterms=6;
guess=array(double,nterms);
if (nterms==5) {
base=median(y);
guess(5)=base;
} else if (nterms==6) {
n=numberof(y);
y1=median(y(1:long(n/2)));
x1=median(x(1:long(n/2)));
y2=median(y(-long(n/2):0));
x2=median(x(-long(n/2):0));
guess(6)=(y2-y1)/(x2-x1);
if (guess(6)!=0) guess(5)=y1-guess(6)*x1;
base=guess(5)+guess(6)*x;
} else base=0.;
y2=y-base;
ind0=abs(y2)(mxx);
guess(2)=x(ind0);
guess(1)=y2(ind0);
if (y2(ind0)==guess(1)) yy=y2;
else yy=-y2;
ind1=ind0;
ind2=ind0;
while (ind1>1 && yy(ind1)>0.5*guess(1)) ind1--;
if (yy(ind1)<0.5*guess(1)) ind1++;
while (ind2<numberof(y)-1 && yy(ind2)>0.5*guess(1)) ind2++;
if (yy(ind2)<0.5*guess(1)) ind2--;
guess(3)=2*abs(x(ind0)-x(ind1));
guess(4)=2*abs(x(ind2)-x(ind0));
} else nterms=numberof(guess);
a=guess;
result=lmfit(asgauss,x,a,y,w,deriv=1);
return a;
}
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