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
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
|
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML 2.0//EN">
<!--Converted with LaTeX2HTML 96.1-h (September 30, 1996) by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds -->
<HTML>
<HEAD>
<TITLE>Submatrix Argument Descriptions</TITLE>
<META NAME="description" CONTENT="Submatrix Argument Descriptions">
<META NAME="keywords" CONTENT="slug">
<META NAME="resource-type" CONTENT="document">
<META NAME="distribution" CONTENT="global">
<LINK REL=STYLESHEET HREF="slug.css">
</HEAD>
<BODY LANG="EN" >
<A NAME="tex2html3170" HREF="node80.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="http://www.netlib.org/utk/icons/next_motif.gif"></A> <A NAME="tex2html3168" HREF="node74.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="http://www.netlib.org/utk/icons/up_motif.gif"></A> <A NAME="tex2html3162" HREF="node78.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="http://www.netlib.org/utk/icons/previous_motif.gif"></A> <A NAME="tex2html3172" HREF="node1.html"><IMG WIDTH=65 HEIGHT=24 ALIGN=BOTTOM ALT="contents" SRC="http://www.netlib.org/utk/icons/contents_motif.gif"></A> <A NAME="tex2html3173" HREF="node190.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="http://www.netlib.org/utk/icons/index_motif.gif"></A> <BR>
<B> Next:</B> <A NAME="tex2html3171" HREF="node80.html">Matrix and Vector Storage </A>
<B>Up:</B> <A NAME="tex2html3169" HREF="node74.html">In-core Dense Matrices</A>
<B> Previous:</B> <A NAME="tex2html3163" HREF="node78.html">Example</A>
<BR> <P>
<H2><A NAME="SECTION04435000000000000000">Submatrix Argument Descriptions</A></H2>
<A NAME="subsecargdesc"> </A>
<A NAME="2591"> </A>
<P>
As previously mentioned, the ScaLAPACK
routines that solve dense linear systems
and eigenvalue problems assume that all
global arrays are distributed in a one-
or two-dimensional block cyclic fashion.
<A NAME="2592"> </A>
<A NAME="2593"> </A><A NAME="2594"> </A>
<A NAME="2595"> </A><A NAME="2596"> </A>
<A NAME="2597"> </A>
After a global vector or matrix
has been block-cyclicly distributed
over a process grid, the user may
choose to perform an operation on
a portion of the global matrix.
This subset of the global matrix
is referred to as a ``submatrix''
and is referenced through the use
of six arguments in the calling
sequence: the number of rows of
the submatrix <TT>M</TT>, the number
of columns of the submatrix <TT>N</TT>,
the local array <TT>A</TT> containing
the global array, the row index
<TT>IA</TT>, the column index <TT>JA</TT>
and the array descriptor of the
global array <TT>DESCA</TT>. This
argument convention allows
for a global view of the
matrix operands and the
global addressing of
distributed matrices as
illustrated in figure <A HREF="node79.html#figview">4.7</A>.
This scheme allows the complete
specification of the submatrix
<TT>A(IA:IA+M-1,JA:JA+N-1)</TT>
on which to be operated.
<P><A NAME="2608"> </A><A NAME="figview"> </A><IMG WIDTH=227 HEIGHT=111 ALIGN=BOTTOM ALT="figure2606" SRC="img307.gif"><BR>
<STRONG>Figure 4.7:</STRONG> Global view of the matrix operands<BR>
<P>
<P>
The description of a global dense subarray
consists of <TT>(M, N, A, IA, JA, DESCA)</TT>
<UL>
<LI> the number of rows and columns <TT>M</TT> and <TT>N</TT>
of the global subarray,
<LI> a pointer to the local array containing the entire global array
(<TT>A</TT>, for example),
<LI> the row and column indices, <TT>(IA, JA)</TT>, in the global array, and
<LI> the array descriptor, <TT>DESCA</TT>, for the global array.
</UL>
<P>
The names of the row and column indices
for the global array have the form
I<array_name><A NAME="2619"> </A> and
J<array_name><A NAME="2620"> </A>,
respectively. The array descriptor
has a name of the form DESC<array_name><A NAME="2621"> </A>.
<A NAME="2622"> </A><A NAME="2623"> </A>
The length of the array descriptor is
specified by DLEN_ and varies according
to the descriptor type DTYPE_.
<P>
Included in the leading comments of
each subroutine (immediately preceding
the Argument section), is a brief note
describing the
<B>array descriptor</B><A NAME="2625"> </A><A NAME="2626"> </A><A NAME="2627"> </A>
and some commonly used expressions in
calculating workspace.
<P>
The style of the argument<A NAME="2628"> </A>
descriptions for dense matrices
is illustrated by the following
example. As previously mentioned,
the notations x_ used in the entries
of the array descriptor denote the
attributes of a global array. For
readability of the code, we have
associated symbolic names for the
descriptor entries. For example,
M_ denotes the number of rows and
M_A specifically denotes the number
of rows in global matrix A. Complete
details can be found in section <A HREF="node77.html#secdesc1">4.3.3</A>.
<P>
<UL>
<DT>M
<DD> (global input) INTEGER <BR>
The number of rows of the matrix A(IA:IA+M-1,JA:JA+N-1) on
which to be operated. M <IMG WIDTH=11 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline14966" SRC="img308.gif"> 0 and IA+M-1 <IMG WIDTH=11 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline14970" SRC="img309.gif"> M_A.
<DT>N
<DD> (global input) INTEGER <BR>
The number of columns of the matrix A(IA:IA+M-1,JA:JA+N-1) on
which to be operated. N <IMG WIDTH=11 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline14966" SRC="img308.gif"> 0 and JA+N-1 <IMG WIDTH=11 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline14970" SRC="img309.gif"> N_A.
<DT>NRHS
<DD> (global input) INTEGER <BR>
The number of right hand side vectors, i.e. the number of columns
of the matrix B(IB:IB+N-1,JB:JB+NRHS-1). NRHS <IMG WIDTH=11 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline14966" SRC="img308.gif"> 0.
<DT>A
<DD> (local input/local output) REAL pointer into the local
memory to an array of local dimension (LLD_A, LOC<IMG WIDTH=6 HEIGHT=7 ALIGN=MIDDLE ALT="tex2html_wrap_inline12114" SRC="img16.gif">(JA+N-1))
<DT>IA
<DD> (global input) INTEGER <BR>
The row index in the global array A indicating the first
row of A(IA:IA+M-1,JA:JA+N-1).
<DT>JA
<DD> (global input) INTEGER <BR>
The column index in the global array A indicating the
first column of A(IA:IA+M-1,JA:JA+N-1).
<DT>DESCA
<DD> (global and local input) INTEGER array of dimension DLEN_ <BR>
The array descriptor for the global matrix A.
<DT>B
<DD> (local input/local output) REAL pointer into the local
memory to an array of local dimension (LLD_B, LOC<IMG WIDTH=6 HEIGHT=7 ALIGN=MIDDLE ALT="tex2html_wrap_inline12114" SRC="img16.gif">(JB+NRHS-1)).
<DT>IB
<DD> (global input) INTEGER <BR>
The row index in the global array B indicating the first
row of B(IB:IB+N-1,JB:JB+NRHS-1).
<DT>JB
<DD> (global input) INTEGER <BR>
The column index in the global array B indicating the first
column of B(IB:IB+N-1,JB:JB+NRHS-1).
<DT>DESCB
<DD> (global and local input) INTEGER array of dimension DLEN_ <BR>
The array descriptor for the global matrix B.
</UL>
<P>
The description of each argument gives
<P>
<UL>
<LI> A classification of the argument as (local input), (global and
local input), (local input/local output), (global input),
(local output), (global output), (global input/global output),
(local input or local output),<A NAME="tex2html703" HREF="footnode.html#2653"><IMG ALIGN=BOTTOM ALT="gif" SRC="http://www.netlib.org/utk/icons/foot_motif.gif"></A>
(local or global input),<A NAME="tex2html704" HREF="footnode.html#2654"><IMG ALIGN=BOTTOM ALT="gif" SRC="http://www.netlib.org/utk/icons/foot_motif.gif"></A>
(local workspace), or (local workspace/local output).
<LI> The type of the argument;
<LI> For an array, its dimension(s).
<P>
These dimensions are often expressed in terms of
LOC<IMG WIDTH=6 HEIGHT=7 ALIGN=MIDDLE ALT="tex2html_wrap_inline12112" SRC="img15.gif">() and LOC<IMG WIDTH=6 HEIGHT=7 ALIGN=MIDDLE ALT="tex2html_wrap_inline12114" SRC="img16.gif">() calculations. For
further details, please refer to section <A HREF="node76.html#seclocalstorage">4.3.2</A>.
<LI> A specification of the value(s) that must be supplied for the
argument (if it is an input argument), or of the value(s) returned
by the routine (if it is an output argument), or both (if it is an
input/output argument). In the last case, the two parts of the
description are introduced by the phrases ``On entry'' and ``On exit''.
<LI> For a scalar input argument, any constraints that the
supplied values must satisfy (such as N <IMG WIDTH=11 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline14966" SRC="img308.gif"> 0 in the
example above).
<P>
</UL><HR><A NAME="tex2html3170" HREF="node80.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="http://www.netlib.org/utk/icons/next_motif.gif"></A> <A NAME="tex2html3168" HREF="node74.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="http://www.netlib.org/utk/icons/up_motif.gif"></A> <A NAME="tex2html3162" HREF="node78.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="http://www.netlib.org/utk/icons/previous_motif.gif"></A> <A NAME="tex2html3172" HREF="node1.html"><IMG WIDTH=65 HEIGHT=24 ALIGN=BOTTOM ALT="contents" SRC="http://www.netlib.org/utk/icons/contents_motif.gif"></A> <A NAME="tex2html3173" HREF="node190.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="http://www.netlib.org/utk/icons/index_motif.gif"></A> <BR>
<B> Next:</B> <A NAME="tex2html3171" HREF="node80.html">Matrix and Vector Storage </A>
<B>Up:</B> <A NAME="tex2html3169" HREF="node74.html">In-core Dense Matrices</A>
<B> Previous:</B> <A NAME="tex2html3163" HREF="node78.html">Example</A>
<P><ADDRESS>
<I>Susan Blackford <BR>
Tue May 13 09:21:01 EDT 1997</I>
</ADDRESS>
</BODY>
</HTML>
|
