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<H2><A NAME="SECTION0004108000000000000000">SLA_IMXV - Apply 3D Reverse Rotation</A>
<A NAME="xref_SLA_IMXV"> </A><A NAME="SLA_IMXV"> </A>
</H2>
<DL>
<DT><STRONG>ACTION:</STRONG>
<DD>Multiply a 3-vector by the inverse of a rotation
matrix (single precision).
<P> <DT><STRONG>CALL:</STRONG>
<DD><TT>CALL sla_IMXV (RM, VA, VB)</TT>
<P> </DL>
<P> <DL>
<DT><STRONG>GIVEN:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>RM</EM></TD>
<TH ALIGN="LEFT"><B>R(3,3)</B></TH>
<TD ALIGN="LEFT" NOWRAP>rotation matrix</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>VA</EM></TD>
<TD ALIGN="LEFT"><B>R(3)</B></TD>
<TD ALIGN="LEFT" NOWRAP>vector to be rotated</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>RETURNED:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>VB</EM></TD>
<TH ALIGN="LEFT"><B>R(3)</B></TH>
<TD ALIGN="LEFT" NOWRAP>result vector</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>NOTES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>This routine performs the operation:
<BLOCKQUOTE><B>b</B> = <B>M</B><IMG WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
SRC="img70.gif"
ALT="$^{T}\cdot$"><B>a</B>
</BLOCKQUOTE>
where <B>a</B> and <B>b</B> are the 3-vectors VA and VB
respectively, and <B>M</B> is the <IMG WIDTH="39" HEIGHT="25" ALIGN="MIDDLE" BORDER="0"
SRC="img18.gif"
ALT="$3\times3$"> matrix RM.
<DT>2.
<DD>The main function of this routine is apply an inverse
rotation; under these circumstances, <IMG WIDTH="20" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
SRC="img122.gif"
ALT="${\bf M}$"> is
<I>orthogonal</I>, with its inverse the same as its transpose.
<DT>3.
<DD>To comply with the ANSI Fortran 77 standard, VA and VB 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.
</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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