CURVEFIT Function

Standard Library function that performs a nonlinear least-squares fit to a function of an arbitrary number of parameters.

TIP: These initial estimates for parms can be calculated from the result of the POLY_FIT function when it is used to fit a straight line through data.

The function to be fit must be defined and called with FUNCT.

CURVEFIT is modified from the program CURFIT found in Data Reduction and Error Analysis for the Physical Sciences, by Philip Bevington, McGraw-Hill, New York, 1969. It combines a gradient search with an analytical solution developed from linearizing the fitting function. This method is termed a "gradient-expansion algorithm."

Weighting Factor

Weighting is useful when you want to correct for potential errors in the data you are fitting to a curve. The weighting factor, wt, adjusts the parameters of the curve so that the error at each point of the curve is minimized.

wt can have any value, as long as its size is correct. Some possible ways to weight a curve are suggested below (where i is an index into y, the vector of Y values):

For statistical weighting, use wt = 1/y_i
For instrumental weighting, use wt = 1/(Std dev of y_i)
For no weighting, use wt = 1
Statistical Weighting Statistical weighting is useful when you arrived at your dependent values by measuring a number of discrete events with respect to the independent variable, such as counting the number of cars passing through an intersection over 10-minute intervals.
Instrumental Weighting Instrumental weighting is useful when you are measuring things from a scale, such as length, mass, voltage, or current, and you suspect that unequal errors have been introduced into the data by the measuring device. For example, if an ohm meter has three different scales (one for 0 to 1 ohm, one for 2 to 99 ohms, and one for 100 ohms or more), the weighting factor would be the same for each measurement taken with the same scale.

TIP: In most cases, you would use a different weighting factor for each scale or instrument that was used to measure your original data.

No Weighting If you feel that fluctuations in your data are due to instrument error but that the uncertainties of the measuring device used are equal for all the data collected, you would probably specify no weighting (wt = 1).

Example

For an example, refer to the gaussfit.pro file in the Standard Library.

CURVEFIT Function

Usage

Input Parameters

Output Parameters

Returned Value

Keywords

Discussion

Weighting Factor

Example

See Also