[GENERAL INFORMATION]
Function Name=Giddings
Brief Description=Giddings peak function for use in Chromatography
Function Source=fgroup.Giddings
Function Type=Built-in
Function Form=Expression
Number Of Parameters=4
Number Of Independent Variables=1
Number Of Dependent Variables=1


[FITTING PARAMETERS]
Naming Method=User-Defined
Names=y0,xc,w,A
Meanings=offset,center,width,area
Lower Bounds=--(I,Off),--(I,Off),0(X,On),--(I,Off)
Upper Bounds=--(I,Off),--(I,Off),--(I,Off),--(I,Off)
Number Of Significant Digits=


[FORMULA]
// Note: I1() is the modified Bessel function of the first kind
y = y0 + (A/w)*sqrt(xc/x)*I1(2*sqrt(xc*x)/w) * exp((-x-xc)/w)


[CONSTRAINTS]



[CONSTANTS]


[Parameters Initialization]
sort(x_y_curve);
//smooth(x_y_curve, 2);
y0 = yatxmax( x_y_curve );
w = 0.1 * fwhm( x_y_curve, y0 );
A = area( x_y_curve, y0 );
if ( A > 0 ) xc = xatymax( x_y_curve );
else xc = xatymin( x_y_curve );


[INITIALIZATIONS]



[AFTER FITTING]



[INDEPENDENT VARIABLES]
x=


[DEPENDENT VARIABLES]
y=


[CONTROLS]
General Linear Constraints=Off
Initialization Scripts=Off
Scripts After Fitting=Off
Number Of Duplicates=0
Duplicate Offset=2
Duplicate Unit=3
Peak Center=2
Peak Width=3
Peak Amplitude=4