Brief description of the program. LSM program performs the Least Squares Nonlinear Regression Analysis. The method is also called: Curve Fitting, Least Squares Fitting, Least Squares Method, Least Squares Estimation, Least Squares Approximation. The program fits parameters of curve(s) given analytically to given points. LSM program can carry out the nonlinear regression analysis (curve fitting):
in many
dimensions,
with input
uncertainties in the directions of all axes,
using
input covariances, if needed,
using
many curves approximated simultaneously,
curves may be stuck with some their parameters as well as with some points.
Tens of
elementary functions are available (to create any curve equation).
The goodness of fit can be controled by the chi-sqr quantity.
Adjusted (estimated)
points and their uncertainties can be shown.
Data in
spreadsheet format.
LSM 2 - the latest version improved in its core algorithm.
Now, the LSM 2 program works very precisely.
Nonlinear Least Squares Regression Analysis, Curve Fitting, Nonlinear Weighted Least Squares Estimation Approximation
Hints Each function must have the form of an expression obtained by transferring all terms to one side of an equation. Example: replace your fitting formula
z = a1*x2 + a2*y + a3 with x3= a1*x1^2 + a2*x2 + a3
and write it in the involved form F(x1,x2,x3)=0,without the "=0" part:
a1*x1^2 + a2*x2 + a3 - x3
Curve Fitting, Least Squares Method, Least Squares Fitting, Least Squares Estimation
This form enables applying complicated curves that are not a graph of any function, applying complicated curve equations from which none of variables can be derived
as well as transforming equations to be always computable.
The last case may be useful when some point coordinate or a parameter value being changed during computation temporarily go beyond domain boundary.
Nonlinear Least Squares Regression Analysis, Nonlinear Weighted Least Squares Estimation Approximation
Use the LSM program especially when the point uncertainties are in many axes and they are all known, or point covariance matrix is known,
or the problem is in more than two dimensions, or the curve is not a graph of any function (e.g. a circle), or the curve is given by an equation from which no variable can be
derived, or you use a combination of curves stuck with points or parameters. Least Squares Method, Nonlinear Weighted Least Squares Approximation Estimation
On the basis of input uncertainties, the chi-sqr parameter and its standard deviation
is calculated (chi-sqr expected value equals the number of degrees of freedom). If the chi-sqr value obtained is close to the number of degrees of freedom (i.e. the number of points minus the number of parameters), it is likely that the model assumed fits the points and the point uncertainties.
Curve Fitting, Least Squares Fitting, Least Squares Approximation
The method used in LSM program gives exactly the same values of parameter uncertainties as "other programs" that do not accept X uncertainties
if in LSM program all input X (or X1, X2, ... for many dimensions) uncertainties are fixed at zero and input Y uncertainties are such that
the output chi-sqr parameter(the GInf menu item) is equal to the number of degrees of freedom.
More precise description can also be found in
readme file in the program package.
LSM program requires
MS-DOS 3.0 (or later) or Microsoft Windows 3.0 (or later 95/98/2000/XP/Vista).
In case of a straight line and input uncertainties in x and y axes, the LSM-2 program gives exactly the same results, though it does it in a different way, as the last-minute method for a straight line described in: D. York, N.M. Evensen, M.L. Martinez, J. Delgado, Unified equations for the slope, intercept and standard errors of the best straight line, Am. J. Phys., Vol. 72, No 3.
Two
different approximating curves with common parameter (i.e. asymptote abscissa);
Input covariance matrix - error ellipses
(red).
Least Squares Nonlinear Regression Analysis, Curve Fitting, Least Squares Fitting
Each function must have the form
of an expression obtained by transferring all terms to one side of equation!
Every parameter must be denoted by a1,
a2, a3, ...,
and every point coordinate - by x1, x2,
x3, ... (instead of x ,y, z, ...).
Calculation time is significantly longer due to method nonlinearity
caused by the assumption of errors for all coordinates of points. Such a regression is nonlinear even in case of fitting a straight line.
Curve Fitting, Least Squares Method, Least Squares Fitting, Nonlinear Weighted Least Squares Estimation Approximation
Nonlinear Least Squares Regression Analysis, Nonlinear Weighted Least Squares Approximation Estimation
Curve Fitting, Least Squares Fitting, Least Squares Approximation
Installation and use
Unpack the contents
of the package to anywhere on the hard disc.
Use LSM2-demo.exe as a demo. Use LSM2-r.exe for real precision of calculation. Use LSM2-d.exe for double precision of calculation. The program not even touches Windows registers.
Adapting to newer systems
In Windows 2000/XP/Vista full screen is more recommended
mode of displaying (switch with Ctrl Tab); unfortunately the mouse doesn't work, please use the keyboard.
Curve Fitting, Least Squares Method, Least Squares Fitting
Least Squares Estimation, Least Squares Approximation Least Squares Nonlinear Regression Analysis, Curve Fitting, Maximum Likelihood Estimation
Registering Since the program is free now, there is no need to register it.
Nonlinear Least Squares Regression Analysis, Maximum Likelihood Estimation
Please
forward questions or suggestions to the author:
IMPORTANT: READ CAREFULLY BEFORE DOWNLOADING SOFTWARE. Since the program is free now, the restrictions
concerning non-commercial using and spreading the program are canceled.
BY DOWNLOADING LSM PROGRAM YOU
ARE AGREEING TO BIND YOUR COMPANY AND YOURSELF TO THE TERMS OF THIS AGREEMENT.
A LICENSE TO USE THE SOFTWARE WILL NOT BE GRANTED UNLESS YOU AND YOUR COMPANY
AGREE TO THE TERMS OF THIS AGREEMENT. DOWNLOADING AND INSTALLING THE PROGRAM
WILL BE AN IRREVOCABLE ACCEPTANCE OF THE TERMS OF THIS AGREEMENT.
YOU MAY: 1. use the registered version of the Program for evaluation
purposes on a single computer or network, and only by a single user at
a time regardless of the number of original copies of the Program included
with the Program. If you wish to use the Program for more users, you will
need an additional license for each user;
2. make one copy of the registered version of the Program
for archive or back-up purposes.
YOU MAY NOT: 1. use the Program or make copies of it except as permitted
in this License;
2. translate, reverse engineer, decompile or disassemble
the Program, except to the extent the foregoing restriction is expressly
prohibited by applicable law;
3. rent, lease, assign or transfer the Program;
4. modify the Program or merge all or any part of the
Program in another program.
5. make both the registered version of the Program and
the registration code available over a network for multiple users, access,
distribute them in any form or provide them in conjunction with any other
product.
Disclaimers LSM Program is provided without warranty of any kind,
express or implied, and the user assumes the entire risk of using it.
The author does not assume responsibility for any expense,
damage or loss caused by your use of this software, however it comes down.
All the registered trademarks used herein are registered.
This notification is given in lieu of any specific list
of trademarks and their owners, which would not be as inclusive and would
probably take a lot longer to type.
If you register software, we will assume that you are
doing so having tested the shareware version and ascertained that it's
suitable for your hardware and requirements.
We cannot provide refunds for shareware registration
if you subsequently change your mind.
The shareware version is limited regarding the maximum
number of used points.
Nothing more in the shareware version is suppressed or
crippled nor will suddenly stop working after a predetermined period of
time. If something isn't working as you think it should in the shareware,
this will not change in the registered version.
No portion of the documentation for this software or any
of its attendant files may be reproduced in whole or in part in any medium
or form of transmission.
Registering Registering this software buys you a single-user license
to use it in perpetuity, subject to the terms discussed herein. This means
that your registered software can only be used by one person at a time.
You might, for example, have a copy on your computer at home and a copy
on your computer at work. If you have taken reasonable precautions to ensure
that no one else will use your software on one machine while you're working
with the other, your use of the registered software is in keeping with
the license you have purchased.
A single-user license does not permit you to make the
registered software available over a network for multiple users to access,
to distribute it in any form or to provide it in conjunction with any other
product.
This license extends only to the registered software
itself, and in no way affects any files or documents you might create with
it.
The registered cost of this software does not include
payment for technical support.
Since the program is free now, the restrictions
concerning non-commercial spreading and using of the program are canceled.
creation date: 1998.01.01 last change: 2009.08.31
Key phrases:
multidimensional nonlinear weighted least squares regression analysis,
multidimensional nonlinear weighted least squares estimation,
multidimensional nonlinear weighted least squares approximation,
nonlinear weighted least squares method, nonlinear weighted least square
method, nonlinear weighted least squares fitting, nonlinear weighted least square fitting,
weighted least squares fit, weighted least square fit, non-linear least
squares method, non-linear least square method, non-linear least squares
fitting, non-linear least square fitting, non-linear least squares fit,
non-linear least square fit, non-linear regression analysis, nonlinear least
squares method, nonlinear least square method, nonlinear least squares
fitting, nonlinear least square fitting, nonlinear least squares fit,
nonlinear least square fit, maximum likelihood estimation,
fitting curve to points, fit curve to points,
fitting a curve to points, fit a curve to points, fitting the curve to
the points, fit the curve to the points, fitting curves to points, fit
curves to points.
LEAST
SQUARES METHOD 
