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<H1><A NAME="SECTION001340000000000000000"> </A>
<A NAME="fitting-process"> </A>
<BR>
The Fitting Process.
</H1>
<P>
The typical sequence of operations for a FITting
process would be first to create the approximating function, to choose
relatively to your problem and your needs the <TT>FIT</TT> options, then
to execute the real least squares approximation and finally to store
and view the results. This corresponds to the typical sequence of
MIDAS instructions :
<P>
<BLOCKQUOTE>
<TT>EDIT/FIT fitname <BR>
SET/FIT options <BR>
FIT/... nfeval,prec image (or table and cols) <BR>
COMPUTE/FIT output</TT></BLOCKQUOTE>
<P>
The commands have been designed so that defaults exists for almost all the
parameters, (see description in Volume C of the MIDAS User Guide).
<P>
<TT>EDIT/FIT</TT> has been described in the last section.
<P>
The MIDAS command <TT>SET/FIT</TT> is used
to specify the different options of the <TT>FIT</TT> command, for
instance the method to be applied or the type of used functions.
The instruction<BLOCKQUOTE>
<TT>SET/FIT METHOD=CGNND PRINT=1 WEIGHT=S FUNCT=BLACBODY FCTDEF=USER</TT></BLOCKQUOTE>declares that the Corrected Gauss-Newton no derivatives method is to be
applied, that at each iteration, a display of the intermediate result
will be performed, that the weighting factors are statistical,
that the name of the approximating
function is <TT>BLACBODY</TT>, and that this <TT>BLACBODY</TT> function which
contains user defined functions has already been built
in the user area.
The appendix or the MIDAS interactive <TT>HELP</TT> facility will give you
the complete description of the <TT>SET/FIT</TT> command.
<P>
The command <TT>SHOW/FIT</TT> displays the actual selected <TT>FIT</TT> options.
<P>
The <TT>FIT</TT> instruction is performing the least squares approximation
itself. It has a slightly different syntax if the fitting concerns
a table or an image.
<P>
<BLOCKQUOTE>
<TT>FIT/TABLE nfeval[,prec,[metpar]] table :depcol[,:wgt] :indcol,...
<BR>
FIT/IMAGE nfeval[,prec,[metpar]] image</TT></BLOCKQUOTE>
<P>
<TT>nfeval</TT> is the maximum number of function evaluations that can be
performed, <TT>prec</TT> is the precision on the parameters
i.e. the program stops if
<BR><P></P>
<DIV ALIGN="CENTER">
<!-- MATH: \begin{displaymath}
\|a^{(solution)}-a^{(found)}\| \le prec~(1+\|a^{(found)}\|)~~,
\end{displaymath} -->
<IMG
WIDTH="451" HEIGHT="40"
SRC="img292.gif"
ALT="\begin{displaymath}\Vert a^{(solution)}-a^{(found)}\Vert \le prec~(1+\Vert a^{(found)}\Vert)~~,\end{displaymath}">
</DIV>
<BR CLEAR="ALL">
<P></P>
and <TT>metpar</TT> are the specific method parameters (for instance in NR
: the relaxation factor).
The latter have not generally to be given as they can be
deduced by the program. For
stiff problems, they can thus be overwritten by the user.
Any non-given parameter is defaulted. Consult the appendix or use the
MIDAS interactive <TT>HELP</TT> to get a complete description.
For instance, the instruction<BLOCKQUOTE>
<TT>FIT/IMAGE 100,0.001 PROFILE</TT></BLOCKQUOTE>executed after the preceeding <TT>SET/FIT</TT>, will execute a non-linear
least squares approximation using the <TT>CGNND</TT> method. The program will
stop if more than 100 computations of the approximating function have
been performed or if the solution has been found with a precision of
10<SUP>-3</SUP>.
<P>
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<ADDRESS>
<I>Petra Nass</I>
<BR><I>1999-06-09</I>
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