** File: TPSht_09.hlp
** Index: 48

** More Sheet View Help
   :: Non-linear Curve Fitting
   :: Model Equation


Û  Nonlinear curve fitting

    The nonlinear curve fitting (or
nonlinear parameter estimation) feature
of TechPlot gives the user the ability to
develop models from experimental data.
TechPlot offers a built-in script language,
model equation editor, and a model
equation parser.  In this section, we
describe how to use them.


Û  Editing a model equation file

    The model equation files used for
nonlinear curve fitting in TechPlot are
ASCII text files with certain conventions.
These files can be saved to disk.  The
suggested filename extension is "*.EQN",
but you can use any name you want.  The
model equation files can be edited by the
equation editor in TechPlot or any other
text editor.  All information required
for a nonlinear curve fitting is entered
in the edit window in the Fitting dialog
box.  To invoke this dialog box, choose
the User Defined fitting command from
the Math Menu in Sheet View.

    The following is a sample of a complete
model equation file:

    //TechPlot Model equation
    //
    [INDVAR]: TIME
    [DEPVAR]: CONCENTRAT
    [PARAMS]: A1, A2, K1, K2
    [EQUATIONS]:
    // T1 and T2 are intermediate variables
    T1=A1*EXP(-K1*TIME)
    T2=A2*EXP(-K2*TIME)
    CONCENTRAT=T1+T2

    [INIT PARAMS]:
    // initial estimates of parameters
    A1=1
    A2=2
    K1=0.1
    K2=0.2

    ENDMODEL

    There are five key fields in this
window: independent variable(s), dependent
variable(s), parameter(s), equation(s), and
initial parameter value(s).  All these
fields are filled by a model template at
the time when the User Fitting dialog box
is shown.  You can simply modify the
variable names, equations and initial
values to suit your needs.  Please do not
modify or delete the key words that are
enclosed in square brackets.

    Comments are placed in the model file
by preceding them with a double back slash,
i.e. '//'.  You can also use them to
comment out equations instead of deleting
them.

    All variables used in model equations
that are not declared as dependent
variables are considered as intermediate
variable.  The intermediate variables are
often used to simplify complex model
equations.  For example, instead of
writing 

  y=sin(x+2*cos(x))
    -a*exp(x+2*cos(x))/(1+sqr(x+2*cos(x)))

you can write

  w=x+2*cos(x)

  y=sin(w)-a*exp(w)/(1+sqr(w))

    Based on the model template, you can
simply modify it to create the model you
want.


Û  Compiling model

    To compile a model, choose the Compile
command in the Fitting dialog box.


Û  Choosing fitting method

    The nonlinear curve fitting techniques
used in TechPlot are the least-square
minimization techniques with three popular
kernel iteration algorithms.

