The Curve Fitting Library is a library of models for data fitting
with the FIT function.
These models are divided into groups according to the type of
equations being modeled.
The groups are
GROUP DESCRIPTION
distribution : distribution models such as Weibull
exponential : models involving exponential terms
fourier : initial terms of fourier series up to eighth order
gaussian : sum of gaussian models up to eighth order
interpolant : interpolants
polynomial : polynomial models up to ninth order
power : power function and sum of two power functions
rational : rational equation models
sin : sum of sin functions up to eighth order
spline : splines
To list only the model equations for a group, type CFLIBHELP
followed by the group name.
Example:
cflibhelp polynomial
All models in the Curve Fitting Library:
DISTRIBUTION MODELS
MODELNAME EQUATION
weibull Y = a*b*x^(b-1)*exp(-a*x^b)
EXPONENTIAL MODELS
MODELNAME EQUATION
exp1 Y = a*exp(b*x)
exp2 Y = a*exp(b*x)+c*exp(d*x)
FOURIER SERIES
MODELNAME EQUATION
fourier1 Y = a0+a1*cos(x*p)+b1*sin(x*p)
fourier2 Y = a0+a1*cos(x*p)+b1*sin(x*p)+a2*cos(2*x*p)+b2*sin(2*x*p)
fourier3 Y = a0+a1*cos(x*p)+b1*sin(x*p)+...+a3*cos(3*x*p)+b3*sin(3*x*p)
...
fourier8 Y = a0+a1*cos(x*p)+b1*sin(x*p)+...+a8*cos(8*x*p)+b8*sin(8*x*p)
where p = 2*pi/(max(xdata)-min(xdata)).
GAUSSIAN SUMS (Peak fitting)
MODELNAME EQUATION
gauss1 Y = a1*exp(-((x-b1)/c1)^2)
gauss2 Y = a1*exp(-((x-b1)/c1)^2)+a2*exp(-((x-b2)/c2)^2)
gauss3 Y = a1*exp(-((x-b1)/c1)^2)+...+a3*exp(-((x-b3)/c3)^2)
...
gauss8 Y = a1*exp(-((x-b1)/c1)^2)+...+a8*exp(-((x-b8)/c8)^2)
poly1 Y = p1*x+p2
poly2 Y = p1*x^2+p2*x+p3
poly3 Y = p1*x^3+p2*x^2+...+p4
...
poly9 Y = p1*x^9+p2*x^8+...+p10
POWER MODELS
MODELNAME EQUATION
power1 Y = a*x^b
power2 Y = a*x^b+c
RATIONAL MODELS
Rational Models are polynomials over polynomials with the leading coefficient
of the denominator set to 1. Model names are ratij, where i is the order of the
numerator and j is the order of the denominator. The orders go up to five for
both the numerator and the denominator. For example:
MODELNAME EQUATION
rat02 Y = (p1)/(x^2+q1*x+q2)
rat21 Y = (p1*x^2+p2*x+p3)/(x+q1)
rat55 Y = (p1*x^5+...+p6)/(x^5+...+q5)
SUM OF SIN FUNCTIONS
MODELNAME EQUATION
sin1 Y = a1*sin(b1*x+c1)
sin2 Y = a1*sin(b1*x+c1)+a2*sin(b2*x+c2)
sin3 Y = a1*sin(b1*x+c1)+...+a3*sin(b3*x+c3)
...
sin8 Y = a1*sin(b1*x+c1)+...+a8*sin(b8*x+c8)