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<H2><A NAME="SECTION000437000000000000000">SLA_DCMPF - Interpret Linear Fit</A>
<A NAME="xref_SLA_DCMPF"> </A><A NAME="SLA_DCMPF"> </A>
</H2>
<DL>
<DT><STRONG>ACTION:</STRONG>
<DD>Decompose an <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img20.gif"
ALT="$[\,x,y\,]$"> linear fit into its constituent parameters:
zero points, scales, nonperpendicularity and orientation.
<P> <DT><STRONG>CALL:</STRONG>
<DD><TT>CALL sla_DCMPF (COEFFS,XZ,YZ,XS,YS,PERP,ORIENT)</TT>
<P> </DL>
<P> <DL>
<DT><STRONG>GIVEN:</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>transformation coefficients (see note)</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>RETURNED:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>XZ</EM></TD>
<TH ALIGN="LEFT"><B>D</B></TH>
<TH ALIGN="LEFT" NOWRAP><I>x</I> zero point</TH>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>YZ</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP><I>y</I> zero point</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>XS</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP><I>x</I> scale</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>YS</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP><I>y</I> scale</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>PERP</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>nonperpendicularity (radians)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>ORIENT</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>orientation (radians)</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>NOTES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>The model relates two sets of <IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img20.gif"
ALT="$[\,x,y\,]$"> coordinates as follows.
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 coordinates <IMG WIDTH="53" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img55.gif"
ALT="$[x_{1},y_{1}\,]$"> into coordinates
<IMG WIDTH="53" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img56.gif"
ALT="$[x_{2},y_{2}\,]$"> as follows:
<BLOCKQUOTE><I>x<SUB>2</SUB></I> = <I>a</I> + <I>bx<SUB>1</SUB></I> + <I>cy<SUB>1</SUB></I> <BR>
<I>y<SUB>2</SUB></I> = <I>d</I> + <I>ex<SUB>1</SUB></I> + <I>fy<SUB>1</SUB></I></BLOCKQUOTE>
The sla_DCMPF routine decomposes this transformation
into four steps:
<DL COMPACT>
<DT>(a)
<DD>Zero points:
<BLOCKQUOTE><IMG WIDTH="96" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img57.gif"
ALT="$x' = x_{1} + {\rm XZ}$"> <BR>
<IMG WIDTH="94" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img58.gif"
ALT="$y' = y_{1} + {\rm YZ}$"></BLOCKQUOTE>
<DT>(b)
<DD>Scales:
<BLOCKQUOTE><IMG WIDTH="76" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
SRC="img59.gif"
ALT="$x'' = x' {\rm XS}$"> <BR>
<IMG WIDTH="74" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img60.gif"
ALT="$y'' = y' {\rm YS}$"></BLOCKQUOTE>
<DT>(c)
<DD>Nonperpendicularity:
<BLOCKQUOTE><IMG WIDTH="287" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img61.gif"
ALT="$x''' = + x'' \cos {\rm PERP}/2 + y'' \sin {\rm PERP}/2$"> <BR>
<IMG WIDTH="286" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img62.gif"
ALT="$y''' = + x'' \sin {\rm PERP}/2 + y'' \cos {\rm PERP}/2$"></BLOCKQUOTE>
<DT>(d)
<DD>Orientation:
<BLOCKQUOTE><IMG WIDTH="298" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img63.gif"
ALT="$x_{2} = + x''' \cos {\rm ORIENT} +
y''' \sin {\rm ORIENT}$"> <BR>
<IMG WIDTH="297" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img64.gif"
ALT="$y_{2} = - x''' \sin {\rm ORIENT} +
y''' \cos {\rm ORIENT}$"></BLOCKQUOTE></DL>
<DT>2.
<DD>See also sla_FITXY, sla_PXY, sla_INVF, sla_XY2XY.
</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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