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<HTML>
<HEAD>
<TITLE>FIT command</TITLE>
</HEAD>
<BODY BGCOLOR="#FFFFFF" TEXT="#000000">
<P><font size="+3" color="green"><B>FIT command</B></font></P>
<TABLE border="1" cols="2" frame="box" rules="all" width="608">
<TR>
<TD width="15%" valign="top"><B>Syntax</B>:</TD>
<TD width="85%" valign="top"><CODE>
FIT y = { expression }<br />
FIT\UPDATE yout</CODE></TD>
</TR><TR>
<TD valign="top"><B>Qualifiers:</B></TD>
<TD valign="top"><CODE>
\NORMAL, \POISSON, \UPDATE, \ITMAX, \WEIGHTS, \TOLERANCE, \ZEROS, \CHISQ,
\VARNAMES, \CORRMAT, \COVMAT, \CL, \E1, \E2, \FREE, \RESET, \MESSAGES</CODE></TD>
</TR><TR>
<TD valign="top"><B>Defaults:</B></TD>
<TD valign="top"><CODE>
\NORMAL, \-ITMAX, \-WEIGHTS, \-TOLERANCE, \ZEROS, \-CHISQ, \-CL, \-VARNAMES,
\-CORRMAT, \-COVMAT, \-E1, \-E2, \-RESET, \-FREE, \MESSAGES</CODE></TD>
</TR><TR>
<TD valign="top"><B>Examples:</B></TD>
<TD valign="top"><CODE>
FIT Y=A*X+B<br />
FIT\CHISQ\CL\ITMAX\WEIGHTS\TOLERANCE W 3 0.001 Y=A*EXP(-B*X)+C<br />
FIT\UPDATE YF</CODE></TD>
</TR>
</TABLE>
<P>
By default, or if the <code>\NORMAL</code> qualifier is used,
it is assumed that each data point has an error that is distributed as a normal distribution,</p>
<P>
<center><IMG SRC="img3.gif"></center></P>
<p>
where <IMG SRC="img4.gif"> is the mean and <IMG SRC="img5.gif">
is the standard deviation of the distribution. The weight is defined as:
<IMG SRC="img6.gif"></P>
<P>
If the <code>\POISSON</code> qualifier is used, the
data errors are assumed to be distributed as a Poisson distribution,</P>
<P>
<CENTER><IMG SRC="img7.gif"></CENTER></P>
<P>
where <IMG SRC="img8.gif"> is the mean and the variance of the distribution.</P>
<P>
<font size="+2" color="green">Expression and parameters</font></P>
<P>
The <code>expression</code> must result in a vector with the same length as
the data vector, <code>y</code>. A maximum of twenty-five (<CODE>25</CODE>) fitting parameters are
allowed in the <code>expression</code>. The fitting parameter values are altered during the fit.
Fit parameters are created with the <code>
<a href="../ScalarCommand/fitparameters.htm">SCALAR\FIT</a></code>
command, and can be converted to fixed value scalars with the <code>SCALAR</code> command. If you use
the <code>\RESET</code> qualifier, the fitting parameters will be reset to their original values
after an unsuccessful fit.</P>
<P>
If the <code>\VARNAMES</code> qualifier is used with the <code>FIT</code> command, a string array
variable named <font color="orange"><code>FIT$VAR</code></font> will be made which will contain the
names of the fitting parameter variables. The array length of <font color="orange"><code>FIT$VAR</code>
</font> will be equal to the number of fit parameters.</P>
<P>
<font size="+2" color="green">Informational messages</font></P>
<P>
By default, information on the progress of the fit, as well as the results,
are displayed on the monitor screen. If the
<CODE>\-MESSAGES</CODE> qualifier is used, these informational messages will be suppressed.</P>
<P>
<a href="method.htm"><font size="+1" color="olive">Method</font></a><br />
<a href="tolerance.htm"><font size="+1" color="olive">Tolerance</font></a><br />
<a href="corrcov.htm"><font size="+1" color="olive">Correlation and covariance</font></a><br />
<a href="confidencelevel.htm"><font size="+1" color="olive">Confidence level</font></a><br />
<a href="numiters.htm"><font size="+1" color="olive">Number of iterations</font></a><br />
<a href="update.htm"><font size="+1" color="olive">Update after a fit</font></a><br />
<a href="normaldist.htm"><font size="+1" color="olive">Normal distribution</font></a><br />
<a href="poissondist.htm"><font size="+1" color="olive">Poisson distribution</font></a></P>
</BODY>
</HTML>
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