- A Least Squares Curve Fit Python Package

by Ben-chin K Cha

Introduction provides python user with a flexible least square line fit plot package. The fitted curve plot is through using the high quality python plot package matplotlib. The plot window generated by can be easily re-adjusted or saved by user.

The user interface is implemented through using python Tkinter and Pmw widgets. It allows the user freely to load the desired Ascii file and extract the desired vector to be fitted. It is assumed that column oriented data array defined in text file. Any line start with ';' or '#' will be treated as comment and ignored. The Ascii file may or may not contain independent variable vector.

Zero based index sequence number is used in indexing the X and Y vectors. By default it assumed that column oriented vector array defined in the text file and the first column (0) contains the X vector. The remaining columns starting from the second column (1) contain the dependent variable vectors. User can easily to pick the desired Y vector from the column array by entering the column sequence number for Y vector.

At present the following set of fit functions available in for least square fit of the selected Y vector:

	Polynomial Fit 	- y = a0*x**n + a1*x**(n-1)+...+ an
	Sine Fit	- y = a*sin(pi*(x-x0)/w)
	Rtional0 Fit	- y = (b+c*x)/(1+a*x)
	Linear Fit	- y = a + b*x
	Allometric Fit  - y = a*(x-x0)**2 + c	
	Cuadratic Fit	- y = a*(x-x0)**2+b*(x-x0)+c
	Gauss Fit	- y = a*exp(-2*(x-x0)**2/W**2)+y0
	Boltzman Fit	- y = (a1-a2)/(1+exp((x-x0)/dx)) + a2
	ExpGrow Fit	- y = y0 + a*exp((x-x0)/t)
	Lorentz Fit	- y = a*w**2/((x-x0)**2+w**2)
	ExpAssoc Fit	- y = y0 + a1*(1+exp(-x/t1))+a2*(1+exp(-x/t2)) 
	Logistic Fit	- y = (a1-a2)/(1+(x/x0)**p)+a2
	GaussAmp	- y = a*exp(-(x-x0)**2/(2*w**2))+y0
	Pulse Fit	- y = y0 +a*(1+exp(-(x-x0)/t1))*exp(-(x-x0)/t2)
	Hyperbl	Fit	- y = p1*x/(p2+x)
	ExpDecay Fit	- y = y0+a*exp(-(x-x0)/t)
Please refer the
fit.html for avaialbe functions or methods defined in

Download (0.126MB) A collection of 1D/2D/3D graphic programs for python package

Python System Requirement

The following python extensions packages must also be installed with the python system by system administrator. They are already installed for the /APSshare file system.
	Tkinter		- Tk user interface
	Pmw		- python mega widgets
	matplotlib	- python matlab plot library
	Numeric		- python numeic  package
	numarray	- python numarray  package
	Pygtk		- python GTK package
	Scientific	- python scientific package

System Setup Requirement

To access on Unix system, a user only need to do following:
	source /APSshare/setup_apsshare

User Interface

Please refer function definition in fit.html on how to pass data directly to fitting functions defined in

Following interface windows show primary result of loading data from Ascii text file. The active plot window can be easily closed by simply clicking the right mouse button on the plot area. The configuration file fit.config is used for easy restart of

Main Window

Follow window shows the main driver window. First user should use the 'Load Data Array from Ascii...' button to load the column oriented text data in, and the text display window will pop up to show the contents in the text file. The 'Y Vector Column Seq #:' specifies the column vector Y to be extracted.

Text Display Window

Extracted X,Y Vector

Press the 'Pass (X,Y) to Fitting...' button pops up following two figures: text window shows the extracted (X,Y) pair vector and the least square fit dialog. The popup display window allows the user easily to verify the extracted vector against the Ascii file text window.

Least Square Fit Dialog

The 'Polynomial Fit... ' button pops up polynomial fitting dialog. The 'Other Fit...' button pops up other fitting functions dialog.

Polynomial Fit Dialog

Following figure show the setting of polynomial fitting with power of 4. The 'Polynomial Coeffs:' field reflects the result of coefficients obtained from least square fitting.

Follwing figure show the resullt of polynomial fitting with power of 4.

Other Fit Dialog

Following figure show the fitting setup dialog for all other methods defined in The FIT ID #, NAME, EXPRESSION and COEFFS # are tabulated for each method. A user must enter the desired fitting function sequence # in the 'FIT ID #:' text field, then followed with the press of the 'Fitting...' button to accept the current setting. It will perform a least square fitting with used specified fit function . If the fitting does not converge a message window will popup. If the fitting converges, then the COEFFS fields will reflect the coefficients obtained from the calculation and the plot window will be redrawn to reflect the result.

Following figure shows the tabulated text result of 'Gauss' Fit.

Following figure shows the plot result of 'Gauss' Fit.