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
146
147
148
149
150
151
152
|
<!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_DMAT - Solve Simultaneous Equations</TITLE>
<META NAME="description" CONTENT="SLA_DMAT - Solve Simultaneous Equations">
<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="node62.html">
<LINK REL="previous" HREF="node60.html">
<LINK REL="up" HREF="node13.html">
<LINK REL="next" HREF="node62.html">
</HEAD>
<BODY >
<BR> <HR>
<A NAME="tex2html1036" HREF="node62.html">
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next_motif.gif"></A>
<A NAME="tex2html1034" HREF="node13.html">
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up_motif.gif"></A>
<A NAME="tex2html1028" HREF="node60.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="tex2html1037" HREF="node62.html">SLA_DMOON - Approx Moon Pos/Vel</A>
<BR>
<B>Up:</B> <A NAME="tex2html1035" HREF="node13.html">SUBPROGRAM SPECIFICATIONS</A>
<BR>
<B> Previous:</B> <A NAME="tex2html1029" HREF="node60.html">SLA_DM2AV - Rotation Matrix to Axial Vector</A>
<BR> <HR> <P>
<P><!--End of Navigation Panel-->
<H2><A NAME="SECTION000448000000000000000">SLA_DMAT - Solve Simultaneous Equations</A>
<A NAME="xref_SLA_DMAT"> </A><A NAME="SLA_DMAT"> </A>
</H2>
<DL>
<DT><STRONG>ACTION:</STRONG>
<DD>Matrix inversion and solution of simultaneous equations
(double precision).
<P> <DT><STRONG>CALL:</STRONG>
<DD><TT>CALL sla_DMAT (N, A, Y, D, JF, IW)</TT>
<P> </DL>
<P> <DL>
<DT><STRONG>GIVEN:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>N</EM></TD>
<TH ALIGN="LEFT"><B>I</B></TH>
<TD ALIGN="LEFT" NOWRAP>number of unknowns</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>A</EM></TD>
<TD ALIGN="LEFT"><B>D(N,N)</B></TD>
<TD ALIGN="LEFT" NOWRAP>matrix</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>Y</EM></TD>
<TD ALIGN="LEFT"><B>D(N)</B></TD>
<TD ALIGN="LEFT" NOWRAP>vector</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>RETURNED:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>A</EM></TD>
<TH ALIGN="LEFT"><B>D(N,N)</B></TH>
<TD ALIGN="LEFT" NOWRAP>matrix inverse</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>Y</EM></TD>
<TD ALIGN="LEFT"><B>D(N)</B></TD>
<TD ALIGN="LEFT" NOWRAP>solution</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>D</EM></TD>
<TD ALIGN="LEFT"><B>D</B></TD>
<TD ALIGN="LEFT" NOWRAP>determinant</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>JF</EM></TD>
<TD ALIGN="LEFT"><B>I</B></TD>
<TD ALIGN="LEFT" NOWRAP>singularity flag: 0=OK</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>IW</EM></TD>
<TD ALIGN="LEFT"><B>I(N)</B></TD>
<TD ALIGN="LEFT" NOWRAP>workspace</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>NOTES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>For the set of <I>n</I> simultaneous linear equations in <I>n</I> unknowns:
<BLOCKQUOTE><B>A</B><IMG WIDTH="7" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img72.gif"
ALT="$\cdot$"><B>y</B> = <B>x</B>
</BLOCKQUOTE>
where:
<UL>
<LI> <B>A</B> is a non-singular <IMG WIDTH="42" HEIGHT="25" ALIGN="MIDDLE" BORDER="0"
SRC="img73.gif"
ALT="$n \times n$"> matrix,
<LI> <B>y</B> is the vector of <I>n</I> unknowns, and
<LI> <B>x</B> is the known vector,
</UL>
sla_DMAT computes:
<UL>
<LI> the inverse of matrix <B>A</B>,
<LI> the determinant of matrix <B>A</B>, and
<LI> the vector of <I>n</I> unknowns <B>y</B>.
</UL>
Argument N is the order <I>n</I>, A (given) is the matrix <B>A</B>,
Y (given) is the vector <B>x</B> and Y (returned)
is the vector <B>y</B>.
The argument A (returned) is the inverse matrix <B>A</B><SUP>-1</SUP>,
and D is <I>det</I>(<B>A</B>).
<DT>2.
<DD>JF is the singularity flag. If the matrix is non-singular,
JF=0 is returned. If the matrix is singular, JF=-1
and D=0D0 are returned. In the latter case, the contents
of array A on return are undefined.
<DT>3.
<DD>The algorithm is Gaussian elimination with partial pivoting.
This method is very fast; some much slower algorithms can give
better accuracy, but only by a small factor.
<DT>4.
<DD>This routine replaces the obsolete sla_DMATRX.
</DL></DL>
<BR> <HR>
<A NAME="tex2html1036" HREF="node62.html">
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next_motif.gif"></A>
<A NAME="tex2html1034" HREF="node13.html">
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up_motif.gif"></A>
<A NAME="tex2html1028" HREF="node60.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="tex2html1037" HREF="node62.html">SLA_DMOON - Approx Moon Pos/Vel</A>
<BR>
<B>Up:</B> <A NAME="tex2html1035" HREF="node13.html">SUBPROGRAM SPECIFICATIONS</A>
<BR>
<B> Previous:</B> <A NAME="tex2html1029" HREF="node60.html">SLA_DM2AV - Rotation Matrix to Axial Vector</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>
|
