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<H2><A NAME="SECTION0004110000000000000000">SLA_INVF - Invert Linear Model</A>
<A NAME="xref_SLA_INVF"> </A><A NAME="SLA_INVF"> </A>
</H2>
<DL>
<DT><STRONG>ACTION:</STRONG>
<DD>Invert a linear model of the type produced by the
sla_FITXY routine.
<P> <DT><STRONG>CALL:</STRONG>
<DD><TT>CALL sla_INVF (FWDS,BKWDS,J)</TT>
<P> </DL>
<P> <DL>
<DT><STRONG>GIVEN:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>FWDS</EM></TD>
<TH ALIGN="LEFT"><B>D(6)</B></TH>
<TD ALIGN="LEFT" NOWRAP>model coefficients</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>RETURNED:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>BKWDS</EM></TD>
<TH ALIGN="LEFT"><B>D(6)</B></TH>
<TD ALIGN="LEFT" NOWRAP>inverse model</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>J</EM></TD>
<TD ALIGN="LEFT"><B>I</B></TD>
<TD ALIGN="LEFT" NOWRAP>status: 0 = OK, -1 = no inverse</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>NOTES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>The models relate 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 FWDS <I>a</I>,<I>b</I>,<I>c</I>,<I>d</I>,<I>e</I> & <I>f</I>,
where two sets of coordinates [<I>x<SUB>1</SUB></I>,<I>y<SUB>1</SUB></I>] and
<IMG WIDTH="53" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img56.gif"
ALT="$[x_{2},y_{2}\,]$"> are related thus:
<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 present routine generates a new set of coefficients
<I>p</I>,<I>q</I>,<I>r</I>,<I>s</I>,<I>t</I> & <I>u</I> (the array BKWDS) such that:
<BLOCKQUOTE><I>x<SUB>1</SUB></I> = <I>p</I> + <I>qx<SUB>2</SUB></I> + <I>ry<SUB>2</SUB></I> <BR>
<I>y<SUB>1</SUB></I> = <I>s</I> + <I>tx<SUB>2</SUB></I> + <I>uy<SUB>2</SUB></I></BLOCKQUOTE>
<DT>2.
<DD>Two successive calls to this routine will deliver a set
of coefficients equal to the starting values.
<DT>3.
<DD>To comply with the ANSI Fortran 77 standard, FWDS and BKWDS must
<B>not</B> be the same array. The routine is, in fact, coded
so as to work properly on the VAX and many other systems even
if this rule is violated, something that is <B>not</B>, however,
recommended.
<DT>4.
<DD>See also sla_FITXY, sla_PXY, 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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