GAUSSFIT

Purpose:

Fits y(x) = A e-B(x-C)2 using linearization.

Syntax:

GAUSSFIT(series)

(fit, coef) = GAUSSFIT(series)

(fit, A, B, C) = GAUSSFIT(series)

series

-

Input series or array.

Returns:

A series.

 

(fit, coef) = GAUSSFIT(series) returns both the fit and the coefficients as a series.

 

(fit, A, B, C) = GAUSSFIT(series) returns both the fit as a series and the coefficients as separate coefficients.

Example:

W1: 10 * exp(-0.5 * ((-10..0.01..10) - 2)^2)

W2: gaussfit(w1);overp(w1, lred)

 

overplots the original data with the calculated Gaussian fit.

Example:

(fit, coef) = gaussfit(w1)

 

fit is the same series as in W2,

 

coef == {10.0, 0.5, 2}

Example:

(fit, A, B, C) = gaussfit(w1)

 

fit is the same series as in W2,

 

A == 10.0

B == 0.5

C == 2

Remarks:

GAUSSFIT fits an exponential curve of the form:

 

image\gaussfit01.gif

 

The fit is accomplished by fitting a polynomial to the following equation:

 

image\gaussfit02.gif

 

The fitted Gaussian curve (fit, coef) = gaussfit(series) returns both the fit and the coefficients as a series where coef is in the form {A, B, C}.

 

If y is not positive, the result will be complex.

See Also:

EXPFIT

LINFIT

POLYFIT

POWFIT

TREND