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<TITLE>SLA_FITXY - Fit Linear Model to Two Sets</TITLE>
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<H2><A NAME="SECTION000490000000000000000"> </A><A NAME="xref_SLA_FITXY"> </A><A NAME="SLA_FITXY"> </A>
<BR>
SLA_FITXY - Fit Linear Model to Two <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img20.gif"
ALT="$[\,x,y\,]$"> Sets
</H2>
<DL>
<DT><STRONG>ACTION:</STRONG>
<DD>Fit a linear model to relate two sets of <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img20.gif"
ALT="$[\,x,y\,]$"> coordinates.
<DT><STRONG>CALL:</STRONG>
<DD><TT>CALL sla_FITXY (ITYPE,NP,XYE,XYM,COEFFS,J)</TT>
<P> </DL>
<P> <DL>
<DT><STRONG>GIVEN:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>ITYPE</EM></TD>
<TH ALIGN="LEFT"><B>I</B></TH>
<TD ALIGN="LEFT" NOWRAP>type of model: 4 or 6 (note 1)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>NP</EM></TD>
<TD ALIGN="LEFT"><B>I</B></TD>
<TD ALIGN="LEFT" NOWRAP>number of samples (note 2)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>XYE</EM></TD>
<TD ALIGN="LEFT"><B>D(2,NP)</B></TD>
<TD ALIGN="LEFT" NOWRAP>expected <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img20.gif"
ALT="$[\,x,y\,]$"> for each sample</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>XYM</EM></TD>
<TD ALIGN="LEFT"><B>D(2,NP)</B></TD>
<TD ALIGN="LEFT" NOWRAP>measured <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img20.gif"
ALT="$[\,x,y\,]$"> for each sample</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>RETURNED:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>COEFFS</EM></TD>
<TH ALIGN="LEFT"><B>D(6)</B></TH>
<TD ALIGN="LEFT" NOWRAP>coefficients of model (note 3)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>J</EM></TD>
<TD ALIGN="LEFT"><B>I</B></TD>
<TD ALIGN="LEFT" NOWRAP>status:</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
<TD ALIGN="LEFT"><B></B></TD>
<TD ALIGN="LEFT" NOWRAP> 0 = OK</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
<TD ALIGN="LEFT"><B></B></TD>
<TD ALIGN="LEFT" NOWRAP> -1 = illegal ITYPE</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
<TD ALIGN="LEFT"><B></B></TD>
<TD ALIGN="LEFT" NOWRAP> -2 = insufficient data</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM></EM></TD>
<TD ALIGN="LEFT"><B></B></TD>
<TD ALIGN="LEFT" NOWRAP> -3 = singular solution</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>NOTES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>ITYPE, which must be either 4 or 6, selects the type of model
fitted. Both allowed ITYPE values produce a model COEFFS which
consists of six coefficients, namely the zero points and, for
each of XE and YE, the coefficient of XM and YM. For ITYPE=6,
all six coefficients are independent, modelling squash and shear
as well as origin, scale, and orientation. However, ITYPE=4
selects the <I>solid body rotation</I> option; the model COEFFS
still consists of the same six coefficients, but now two of
them are used twice (appropriately signed). Origin, scale
and orientation are still modelled, but not squash or shear -
the units of X and Y have to be the same.
<DT>2.
<DD>For NC=4, NP must be at least 2. For NC=6, NP must be at
least 3.
<DT>3.
<DD>The model is returned in the array COEFFS. Naming the
six elements of COEFFS <I>a</I>,<I>b</I>,<I>c</I>,<I>d</I>,<I>e</I> & <I>f</I>,
the model transforms <I>measured</I> coordinates
<IMG WIDTH="63" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img113.gif"
ALT="$[x_{m},y_{m}\,]$"> into <I>expected</I> coordinates
<IMG WIDTH="52" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img114.gif"
ALT="$[x_{e},y_{e}\,]$"> as follows:
<BLOCKQUOTE><I>x</I><SUB><I>e</I></SUB> = <I>a</I> + <I>bx</I><SUB><I>m</I></SUB> + <I>cy</I><SUB><I>m</I></SUB> <BR>
<I>y</I><SUB><I>e</I></SUB> = <I>d</I> + <I>ex</I><SUB><I>m</I></SUB> + <I>fy</I><SUB><I>m</I></SUB></BLOCKQUOTE>
For the <I>solid body rotation</I> option (ITYPE=4), the
magnitudes of <I>b</I> and <I>f</I>, and of <I>c</I> and <I>e</I>, are equal. The
signs of these coefficients depend on whether there is a
sign reversal between [<I>x</I><SUB><I>e</I></SUB>,<I>y</I><SUB><I>e</I></SUB>] and [<I>x</I><SUB><I>m</I></SUB>,<I>y</I><SUB><I>m</I></SUB>];
fits are performed
with and without a sign reversal and the best one chosen.
<DT>4.
<DD>Error status values J=-1 and -2 leave COEFFS unchanged;
if J=-3 COEFFS may have been changed.
<DT>5.
<DD>See also sla_PXY, sla_INVF, sla_XY2XY, sla_DCMPF.
</DL></DL>
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<ADDRESS>
<I>SLALIB --- Positional Astronomy Library<BR>Starlink User Note 67<BR>P. T. Wallace<BR>12 October 1999<BR>E-mail:ptw@star.rl.ac.uk</I>
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