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
189
190
191
192
193
194
195
196
197
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML3.2 EN">
<HTML>
<HEAD>
<META NAME="GENERATOR" CONTENT="DOCTEXT">
<TITLE>MatCreateMPIAIJ</TITLE>
</HEAD>
<BODY BGCOLOR="FFFFFF">
<A NAME="MatCreateMPIAIJ"><H1>MatCreateMPIAIJ</H1></A>
Creates a sparse parallel matrix in AIJ format (the default parallel PETSc format). For good matrix assembly performance the user should preallocate the matrix storage by setting the parameters d_nz (or d_nnz) and o_nz (or o_nnz). By setting these parameters accurately, performance can be increased by more than a factor of 50.
<H3><FONT COLOR="#CC3333">Synopsis</FONT></H3>
<PRE>
int MatCreateMPIAIJ(MPI_Comm comm,int m,int n,int M,int N,int d_nz,const int d_nnz[],int o_nz,const int o_nnz[],Mat *A)
</PRE>
Collective on <A HREF="../Sys/MPI_Comm.html#MPI_Comm">MPI_Comm</A>
<P>
<H3><FONT COLOR="#CC3333">Input Parameters</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B><A HREF="../Sys/comm.html#comm">comm</A> </B></TD><TD>- MPI communicator
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>m </B></TD><TD>- number of local rows (or <A HREF="../Sys/PETSC_DECIDE.html#PETSC_DECIDE">PETSC_DECIDE</A> to have calculated if M is given)
This value should be the same as the local <A HREF="../Sys/size.html#size">size</A> used in creating the
y vector for the matrix-vector product y = Ax.
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>n </B></TD><TD>- This value should be the same as the local <A HREF="../Sys/size.html#size">size</A> used in creating the
x vector for the matrix-vector product y = Ax. (or <A HREF="../Sys/PETSC_DECIDE.html#PETSC_DECIDE">PETSC_DECIDE</A> to have
calculated if N is given) For square matrices n is almost always m.
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>M </B></TD><TD>- number of global rows (or <A HREF="../Sys/PETSC_DETERMINE.html#PETSC_DETERMINE">PETSC_DETERMINE</A> to have calculated if m is given)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>N </B></TD><TD>- number of global columns (or <A HREF="../Sys/PETSC_DETERMINE.html#PETSC_DETERMINE">PETSC_DETERMINE</A> to have calculated if n is given)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>d_nz </B></TD><TD>- number of nonzeros per row in DIAGONAL portion of local submatrix
(same value is used for all local rows)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>d_nnz </B></TD><TD>- array containing the number of nonzeros in the various rows of the
DIAGONAL portion of the local submatrix (possibly different for each row)
or <A HREF="../Sys/PETSC_NULL.html#PETSC_NULL">PETSC_NULL</A>, if d_nz is used to specify the nonzero structure.
The <A HREF="../Sys/size.html#size">size</A> of this array is equal to the number of local rows, i.e 'm'.
You must leave room for the diagonal entry even if it is zero.
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>o_nz </B></TD><TD>- number of nonzeros per row in the OFF-DIAGONAL portion of local
submatrix (same value is used for all local rows).
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>o_nnz </B></TD><TD>- array containing the number of nonzeros in the various rows of the
OFF-DIAGONAL portion of the local submatrix (possibly different for
each row) or <A HREF="../Sys/PETSC_NULL.html#PETSC_NULL">PETSC_NULL</A>, if o_nz is used to specify the nonzero
structure. The <A HREF="../Sys/size.html#size">size</A> of this array is equal to the number
of local rows, i.e 'm'.
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#CC3333">Output Parameter</FONT></H3>
<DT><B>A </B> -the matrix
<br>
<P>
<H3><FONT COLOR="#CC3333">Notes</FONT></H3>
m,n,M,N parameters specify the <A HREF="../Sys/size.html#size">size</A> of the matrix, and its partitioning across
processors, while d_nz,d_nnz,o_nz,o_nnz parameters specify the approximate
storage requirements for this matrix.
<P>
If <A HREF="../Sys/PETSC_DECIDE.html#PETSC_DECIDE">PETSC_DECIDE</A> or <A HREF="../Sys/PETSC_DETERMINE.html#PETSC_DETERMINE">PETSC_DETERMINE</A> is used for a particular argument on one
processor than it must be used on all processors that share the object for
that argument.
<P>
The AIJ format (also called the Yale sparse matrix format or
compressed row storage), is fully compatible with standard Fortran 77
storage. That is, the stored row and column indices can begin at
either one (as in Fortran) or zero. See the users manual for details.
<P>
The user MUST specify either the local or global matrix dimensions
(possibly both).
<P>
The parallel matrix is partitioned such that the first m0 rows belong to
process 0, the next m1 rows belong to process 1, the next m2 rows belong
to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
<P>
The DIAGONAL portion of the local submatrix of a processor can be defined
as the submatrix which is obtained by extraction the part corresponding
to the rows r1-r2 and columns r1-r2 of the global matrix, where r1 is the
first row that belongs to the processor, and r2 is the last row belonging
to the this processor. This is a square mxm matrix. The remaining portion
of the local submatrix (mxN) constitute the OFF-DIAGONAL portion.
<P>
If o_nnz, d_nnz are specified, then o_nz, and d_nz are ignored.
<P>
When calling this routine with a single process communicator, a matrix of
type SEQAIJ is returned. If a matrix of type MPIAIJ is desired for this
<H3><FONT COLOR="#CC3333">type of communicator, use the construction mechanism</FONT></H3>
<A HREF="../Mat/MatCreate.html#MatCreate">MatCreate</A>(...,&A); <A HREF="../Mat/MatSetType.html#MatSetType">MatSetType</A>(A,MPIAIJ); <A HREF="../Mat/MatMPIAIJSetPreallocation.html#MatMPIAIJSetPreallocation">MatMPIAIJSetPreallocation</A>(A,...);
<P>
By default, this format uses inodes (identical nodes) when possible.
We search for consecutive rows with the same nonzero structure, thereby
reusing matrix information to achieve increased efficiency.
<P>
<H3><FONT COLOR="#CC3333">Options Database Keys</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-mat_aij_no_inode </B></TD><TD>- Do not use inodes
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-mat_aij_inode_limit <limit> </B></TD><TD>- Sets inode limit (max limit=5)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-mat_aij_oneindex </B></TD><TD>- Internally use indexing starting at 1
rather than 0. Note that when calling <A HREF="../Mat/MatSetValues.html#MatSetValues">MatSetValues</A>(),
the user still MUST index entries starting at 0!
</TD></TR></TABLE>
<P>
<P>
<H3><FONT COLOR="#CC3333">Example usage</FONT></H3>
<P>
Consider the following 8x8 matrix with 34 non-zero values, that is
assembled across 3 processors. Lets assume that proc0 owns 3 rows,
proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
<H3><FONT COLOR="#CC3333">as follows</FONT></H3>
<P>
<PRE>
1 2 0 | 0 3 0 | 0 4
Proc0 0 5 6 | 7 0 0 | 8 0
9 0 10 | 11 0 0 | 12 0
-------------------------------------
13 0 14 | 15 16 17 | 0 0
Proc1 0 18 0 | 19 20 21 | 0 0
0 0 0 | 22 23 0 | 24 0
-------------------------------------
Proc2 25 26 27 | 0 0 28 | 29 0
30 0 0 | 31 32 33 | 0 34
</PRE>
<P>
<H3><FONT COLOR="#CC3333">This can be represented as a collection of submatrices as</FONT></H3>
<P>
<PRE>
A B C
D E F
G H I
</PRE>
<P>
Where the submatrices A,B,C are owned by proc0, D,E,F are
owned by proc1, G,H,I are owned by proc2.
<P>
The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
The 'M','N' parameters are 8,8, and have the same values on all procs.
<P>
The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
part as SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ
matrix, ans [DF] as another SeqAIJ matrix.
<P>
When d_nz, o_nz parameters are specified, d_nz storage elements are
allocated for every row of the local diagonal submatrix, and o_nz
storage locations are allocated for every row of the OFF-DIAGONAL submat.
One way to choose d_nz and o_nz is to use the max nonzerors per local
rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
<H3><FONT COLOR="#CC3333">In this case, the values of d_nz,o_nz are</FONT></H3>
<PRE>
proc0 : dnz = 2, o_nz = 2
proc1 : dnz = 3, o_nz = 2
proc2 : dnz = 1, o_nz = 4
</PRE>
We are allocating m*(d_nz+o_nz) storage locations for every proc. This
translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
for proc3. i.e we are using 12+15+10=37 storage locations to store
34 values.
<P>
When d_nnz, o_nnz parameters are specified, the storage is specified
for every row, coresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
<H3><FONT COLOR="#CC3333">In the above case the values for d_nnz,o_nnz are</FONT></H3>
<PRE>
proc0: d_nnz = [2,2,2] and o_nnz = [2,2,2]
proc1: d_nnz = [3,3,2] and o_nnz = [2,1,1]
proc2: d_nnz = [1,1] and o_nnz = [4,4]
</PRE>
Here the space allocated is sum of all the above values i.e 34, and
hence pre-allocation is perfect.
<P>
<P>
<H3><FONT COLOR="#CC3333">Keywords</FONT></H3>
matrix, aij, compressed row, sparse, parallel
<BR>
<P>
<H3><FONT COLOR="#CC3333">See Also</FONT></H3>
<A HREF="../Mat/MatCreate.html#MatCreate">MatCreate</A>(), <A HREF="../Mat/MatCreateSeqAIJ.html#MatCreateSeqAIJ">MatCreateSeqAIJ</A>(), <A HREF="../Mat/MatSetValues.html#MatSetValues">MatSetValues</A>()
<BR><P><B><P><B><FONT COLOR="#CC3333">Level:</FONT></B>intermediate
<BR><FONT COLOR="#CC3333">Location:</FONT></B><A HREF="../../../src/mat/impls/aij/mpi/mpiaij.c.html#MatCreateMPIAIJ">src/mat/impls/aij/mpi/mpiaij.c</A>
<BR><A HREF="./index.html">Index of all Mat routines</A>
<BR><A HREF="../../index.html">Table of Contents for all manual pages</A>
<BR><A HREF="../singleindex.html">Index of all manual pages</A>
<P><H3><FONT COLOR="#CC3333">Examples</FONT></H3>
<A HREF="../../../src/ksp/examples/tutorials/ex2.c.html">src/ksp/examples/tutorials/ex2.c.html</A><BR>
<A HREF="../../../src/ksp/examples/tutorials/ex23.c.html">src/ksp/examples/tutorials/ex23.c.html</A><BR>
<A HREF="../../../src/ksp/examples/tutorials/ex14f.F.html">src/ksp/examples/tutorials/ex14f.F.html</A><BR>
<A HREF="../../../src/snes/examples/tutorials/ex5s.c.html">src/snes/examples/tutorials/ex5s.c.html</A><BR>
</BODY></HTML>
|
