1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN">
<!--Converted with LaTeX2HTML 97.1 (release) (July 13th, 1997)
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 Lippman, Marek Rouchal, Martin Wilck and others -->
<HTML>
<HEAD>
<TITLE>SLA_PXY - Apply Linear Model</TITLE>
<META NAME="description" CONTENT="SLA_PXY - Apply Linear Model">
<META NAME="keywords" CONTENT="sun67">
<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="sun67.css">
<LINK REL="next" HREF="node160.html">
<LINK REL="previous" HREF="node158.html">
<LINK REL="up" HREF="node13.html">
<LINK REL="next" HREF="node160.html">
</HEAD>
<BODY >
<BR> <HR>
<A NAME="tex2html2016" HREF="node160.html">
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next_motif.gif"></A>
<A NAME="tex2html2014" HREF="node13.html">
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up_motif.gif"></A>
<A NAME="tex2html2008" HREF="node158.html">
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="previous_motif.gif"></A> <A HREF="sun67.html#stardoccontents"><IMG ALIGN="BOTTOM" BORDER="0"
SRC="contents_motif.gif"></A>
<BR>
<B> Next:</B> <A NAME="tex2html2017" HREF="node160.html">SLA_RANDOM - Random Number</A>
<BR>
<B>Up:</B> <A NAME="tex2html2015" HREF="node13.html">SUBPROGRAM SPECIFICATIONS</A>
<BR>
<B> Previous:</B> <A NAME="tex2html2009" HREF="node158.html">SLA_PVOBS - Observatory Position & Velocity</A>
<BR> <HR> <P>
<P><!--End of Navigation Panel-->
<H2><A NAME="SECTION0004146000000000000000">SLA_PXY - Apply Linear Model</A>
<A NAME="xref_SLA_PXY"> </A><A NAME="SLA_PXY"> </A>
</H2>
<DL>
<DT><STRONG>ACTION:</STRONG>
<DD>Given arrays of <I>expected</I> and <I>measured</I>
<IMG WIDTH="42" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img20.gif"
ALT="$[\,x,y\,]$"> coordinates, and a
linear model relating them (as produced by sla_FITXY), compute
the array of <I>predicted</I> coordinates and the RMS residuals.
<P> <DT><STRONG>CALL:</STRONG>
<DD><TT>CALL sla_PXY (NP,XYE,XYM,COEFFS,XYP,XRMS,YRMS,RRMS)</TT>
<P> </DL>
<P> <DL>
<DT><STRONG>GIVEN:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>NP</EM></TD>
<TH ALIGN="LEFT"><B>I</B></TH>
<TD ALIGN="LEFT" NOWRAP>number of samples</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>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>COEFFS</EM></TD>
<TD ALIGN="LEFT"><B>D(6)</B></TD>
<TD ALIGN="LEFT" NOWRAP>coefficients of model (see below)</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>RETURNED:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>XYP</EM></TD>
<TH ALIGN="LEFT"><B>D(2,NP)</B></TH>
<TD ALIGN="LEFT" NOWRAP>predicted <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>XRMS</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>RMS in X</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>YRMS</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>RMS in Y</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>RRMS</EM></TD>
<TD ALIGN="LEFT"><B>D </B></TD>
<TD ALIGN="LEFT" NOWRAP>total RMS (vector sum of XRMS and YRMS)</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>NOTES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>The model is supplied 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>predicted</I> coordinates
<IMG WIDTH="53" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
SRC="img144.gif"
ALT="$[x_{p},y_{p}\,]$"> as follows:
<BLOCKQUOTE><I>x</I><SUB><I>p</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>p</I></SUB> = <I>d</I> + <I>ex</I><SUB><I>m</I></SUB> + <I>fy</I><SUB><I>m</I></SUB></BLOCKQUOTE>
<DT>2.
<DD>The residuals are (<I>x</I><SUB><I>p</I></SUB>-<I>x</I><SUB><I>e</I></SUB>) and (<I>y</I><SUB><I>p</I></SUB>-<I>y</I><SUB><I>e</I></SUB>).
<DT>3.
<DD>If NP is less than or equal to zero, no coordinates are
transformed, and the RMS residuals are all zero.
<DT>4.
<DD>See also sla_FITXY, sla_INVF, sla_XY2XY, sla_DCMPF
</DL></DL>
<BR> <HR>
<A NAME="tex2html2016" HREF="node160.html">
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next_motif.gif"></A>
<A NAME="tex2html2014" HREF="node13.html">
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up_motif.gif"></A>
<A NAME="tex2html2008" HREF="node158.html">
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="previous_motif.gif"></A> <A HREF="sun67.html#stardoccontents"><IMG ALIGN="BOTTOM" BORDER="0"
SRC="contents_motif.gif"></A>
<BR>
<B> Next:</B> <A NAME="tex2html2017" HREF="node160.html">SLA_RANDOM - Random Number</A>
<BR>
<B>Up:</B> <A NAME="tex2html2015" HREF="node13.html">SUBPROGRAM SPECIFICATIONS</A>
<BR>
<B> Previous:</B> <A NAME="tex2html2009" HREF="node158.html">SLA_PVOBS - Observatory Position & Velocity</A>
<BR> <HR> <P>
<P><!--End of Navigation Panel-->
<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>
</ADDRESS>
</BODY>
</HTML>
|
