<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN"> <!--Converted with LaTeX2HTML 98.1p1 release (March 2nd, 1998) originally by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds * revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan * with significant contributions from: Jens Lippmann, Marek Rouchal, Martin Wilck and others --> <HTML> <HEAD> <TITLE>Fitting of Data</TITLE> <META NAME="description" CONTENT="Fitting of Data"> <META NAME="keywords" CONTENT="vol1"> <META NAME="resource-type" CONTENT="document"> <META NAME="distribution" CONTENT="global"> <META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1"> <LINK REL="STYLESHEET" HREF="vol1.css"> <LINK REL="next" HREF="node146.html"> <LINK REL="previous" HREF="node126.html"> <LINK REL="up" HREF="vol1.html"> <LINK REL="next" HREF="node128.html"> </HEAD> <BODY > <!--Navigation Panel--> <A NAME="tex2html2131" HREF="node128.html"> <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="icons.gif/next_motif.gif"></A> <A NAME="tex2html2127" HREF="vol1.html"> <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="icons.gif/up_motif.gif"></A> <A NAME="tex2html2121" HREF="node126.html"> <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="icons.gif/previous_motif.gif"></A> <A NAME="tex2html2129" HREF="node1.html"> <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="icons.gif/contents_motif.gif"></A> <A NAME="tex2html2130" HREF="node216.html"> <IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index" SRC="icons.gif/index_motif.gif"></A> <BR> <B> Next:</B> <A NAME="tex2html2132" HREF="node128.html">Outline of the Available</A> <B> Up:</B> <A NAME="tex2html2128" HREF="vol1.html">No Title</A> <B> Previous:</B> <A NAME="tex2html2122" HREF="node126.html">Bibliography</A> <BR> <BR> <!--End of Navigation Panel--> <H1><A NAME="SECTION001300000000000000000"> </A> <A NAME="fitting-of-data"> </A> <BR> Fitting of Data </H1> <P> This chapter deals with the modelling and the analysis of image and table data by fitting non-linear functions, using least squares approximation. The different non-linear least squares methods implemented in MIDAS are first shortly described and discussed. The MIDAS commands dealing with functions or linear combination of functions and with the modelling process are then presented. <P> The basic scheme under these commands is to provide the necessary tools to define the functions entering in the fit, to give initial guesses for the parameters and, in iterations controlled by the user, find the optimal parameters of the functions. These parameters can be used to generate fitted data either as images or as columns in tabular form. <P> Due to the nature of the methods, it is recommended to use these commands in fitting problems involving small amounts of data. For analysis involving large amounts of data, like full CCD images, there are algorithms, in the context of 2D-photometry, optimized for special purpose analyses. A tutorial command (<TT>TUTORIAL/FIT</TT>) has been introduced in order to show the capabilities of the package. <P> A brief description of the implemented methods is included in section <A HREF="node128.html#fit-methods">8.1</A>. Section <A HREF="node133.html#function-specification">8.2</A> describes how to specify functions in the fit. Section <A HREF="node134.html#external-functions">8.3</A> describes how to include external functions. The usage of the commands is illustrated in section <A HREF="node135.html#fitting-process">8.4</A>. The output of the programs and their possible interpretation are discussed in section <A HREF="node136.html#fit-outputs">8.5</A>. An example is presented in section <A HREF="node137.html#tutorial">8.6</A>, it may be convenient for first time users to run the command <TT>TUTORIAL/FIT</TT> while reading this section. Section <A HREF="node138.html#fit-command-summary">8.7</A> contains a summary of the commands. Finally, the functions supported in the current version are listed in section <A HREF="node139.html#basic-functions">8.8</A>. References can be found in section <A HREF="node145.html#fit-ref">8.9</A>. <P> <BR><HR> <!--Table of Child-Links--> <A NAME="CHILD_LINKS"> </A> <UL> <LI><A NAME="tex2html2133" HREF="node128.html">Outline of the Available Methods</A> <UL> <LI><A NAME="tex2html2134" HREF="node129.html">The Newton-Raphson Method.</A> <LI><A NAME="tex2html2135" HREF="node130.html">The Modified Gauss-Newton Method.</A> <LI><A NAME="tex2html2136" HREF="node131.html">The Quasi-Newton Method.</A> <LI><A NAME="tex2html2137" HREF="node132.html">The Corrected Gauss-Newton No Derivatives.</A> </UL> <LI><A NAME="tex2html2138" HREF="node133.html">Function Specification</A> <LI><A NAME="tex2html2139" HREF="node134.html">External Functions</A> <LI><A NAME="tex2html2140" HREF="node135.html">The Fitting Process.</A> <LI><A NAME="tex2html2141" HREF="node136.html">Outputs</A> <LI><A NAME="tex2html2142" HREF="node137.html">Tutorial</A> <LI><A NAME="tex2html2143" HREF="node138.html">Command Summary</A> <LI><A NAME="tex2html2144" HREF="node139.html">Basic Functions</A> <UL> <LI><A NAME="tex2html2145" HREF="node140.html">Polynomials (1D and 2D)</A> <LI><A NAME="tex2html2146" HREF="node141.html">Logarithmic and Exponential Function</A> <LI><A NAME="tex2html2147" HREF="node142.html">Trigonometric Functions</A> <LI><A NAME="tex2html2148" HREF="node143.html">Sinc and Sinc Square</A> <LI><A NAME="tex2html2149" HREF="node144.html">Distributions</A> </UL> <LI><A NAME="tex2html2150" HREF="node145.html">References</A> </UL> <!--End of Table of Child-Links--> <HR> <!--Navigation Panel--> <A NAME="tex2html2131" HREF="node128.html"> <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="icons.gif/next_motif.gif"></A> <A NAME="tex2html2127" HREF="vol1.html"> <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="icons.gif/up_motif.gif"></A> <A NAME="tex2html2121" HREF="node126.html"> <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="icons.gif/previous_motif.gif"></A> <A NAME="tex2html2129" HREF="node1.html"> <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="icons.gif/contents_motif.gif"></A> <A NAME="tex2html2130" HREF="node216.html"> <IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index" SRC="icons.gif/index_motif.gif"></A> <BR> <B> Next:</B> <A NAME="tex2html2132" HREF="node128.html">Outline of the Available</A> <B> Up:</B> <A NAME="tex2html2128" HREF="vol1.html">No Title</A> <B> Previous:</B> <A NAME="tex2html2122" HREF="node126.html">Bibliography</A> <!--End of Navigation Panel--> <ADDRESS> <I>Petra Nass</I> <BR><I>1999-06-09</I> </ADDRESS> </BODY> </HTML>
