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<H2><A NAME="SECTION00042000000000000000"></A>
<A NAME="sec:spmat"></A>
<BR>
Sparse Matrix data structure
</H2>
The spdata<TT>psb_spmat_type</TT> data structure
contains all information about local portion of the sparse matrix and   
its storage mode. Most  of these fields are set  by the tools
routines when inserting a new sparse matrix; the user needs only
choose, if he/she so whishes, a specific matrix storage mode. 
<BR><DL>
<DT><STRONG><B>aspk</B></STRONG></DT>
<DD>Contains values of the local distributed sparse
matrix.
<BR>
Specified as: an allocatable array of rank one of type corresponding
to matrix entries type.
</DD>
<DT><STRONG><B>ia1</B></STRONG></DT>
<DD>Holds integer information on distributed sparse
matrix. Actual information will depend on data format used.
<BR>
Specified as: an allocatable  integer array of rank one.
</DD>
<DT><STRONG><B>ia2</B></STRONG></DT>
<DD>Holds integer information on distributed sparse
matrix. Actual information will depend on data format used.
<BR>
Specified as: an allocatable  integer array of rank one.
</DD>
<DT><STRONG><B>infoa</B></STRONG></DT>
<DD>On entry can hold auxiliary information on distributed sparse
matrix.  Actual information will depend on data format used.
<BR>
Specified as: an integer array of length <code>psb_ifasize_</code>.
</DD>
<DT><STRONG><B>fida</B></STRONG></DT>
<DD>Defines the format of the distributed sparse matrix.
<BR>
Specified as: a string of length 5
</DD>
<DT><STRONG><B>descra</B></STRONG></DT>
<DD>Describe the characteristic of the distributed sparse matrix.
<BR>
Specified as: array of character of length 9.
</DD>
<DT><STRONG><B>pl</B></STRONG></DT>
<DD>Specifies the local row permutation of distributed sparse
matrix. If pl(1) is equal to 0, then there isn't row permutation.
<BR>
Specified as: an allocatable integer array of dimension equal to number of local row (matrix_data[psb_n_row_])
</DD>
<DT><STRONG><B>pr</B></STRONG></DT>
<DD>Specifies the local column permutation of distributed sparse
matrix. If PR(1) is equal to 0, then there isn't columnm permutation.
<BR>
Specified as: an allocatable integer array of dimension equal to number of
local row (matrix_data[psb_n_col_])
</DD>
<DT><STRONG><B>m</B></STRONG></DT>
<DD>Number of rows; if row indices are stored explicitly,
as in Coordinate Storage, should be greater than or equal to the
maximum row index actually present in the sparse matrix.
Specified as: integer variable.
</DD>
<DT><STRONG><B>k</B></STRONG></DT>
<DD>Number of columns; if column indices are stored explicitly,
as in Coordinate Storage or Compressed Sparse Rows, should be greater
than or equal to the maximum column  index actually present in the sparse matrix.
Specified as: integer variable.
</DD>
</DL>
The Fortran&nbsp;95 interface for distributed sparse matrices containing
double precision real entries is defined as shown in
figure&nbsp;<A HREF="#fig:spmattype">4</A>. The definitions for single precision and
complex data are identical except for the <code>real</code> declaration and
for the kind type parameter.

<DIV ALIGN="CENTER"><A NAME="fig:spmattype"></A><A NAME="620"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 4:</STRONG>
    The PSBLAS defined data type that
    contains a sparse matrix.</CAPTION>
<TR><TD>
<BR>
   
  <DIV ALIGN="CENTER">
<!-- MATH
 $\fbox{\TheSbox}$
 -->
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<P>
The following two cases are among the most commonly used: 
<DL>
<DT><STRONG>fida=``CSR''</STRONG></DT>
<DD>Compressed storage by rows. In this case the
following should hold: 

<OL>
<LI><code>ia2(i)</code> contains the index of the first element of row
<code>i</code>; the last element of the sparse matrix is thus stored at
index <IMG
 WIDTH="107" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="img19.png"
 ALT="$ia2(m+1)-1$">. It should contain <code>m+1</code> entries in
nondecreasing order (strictly increasing, if there are no empty rows).
</LI>
<LI><code>ia1(j)</code> contains the column index and <code>aspk(j)</code>
contains the corresponding coefficient value, for all <!-- MATH
 $ia2(1) \le j
\le ia2(m+1)-1$
 -->
<IMG
 WIDTH="199" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="img20.png"
 ALT="$ia2(1) \le j
\le ia2(m+1)-1$">.
</LI>
</OL>
</DD>
<DT><STRONG>fida=``COO''</STRONG></DT>
<DD>Coordinate storage. In this case the following
should hold: 

<OL>
<LI><code>infoa(1)</code> contains the number of nonzero elements in the
matrix; 
</LI>
<LI>For all <!-- MATH
 $1 \le j \le infoa(1)$
 -->
<IMG
 WIDTH="123" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="img21.png"
 ALT="$1 \le j \le infoa(1)$">, the coefficient, row index and
column index are stored into <code>apsk(j)</code>, <code>ia1(j)</code> and
<code>ia2(j)</code> respectively. 
</LI>
</OL>
</DD>
</DL>
A sparse matrix has an associated state, which can take the following
values:
<DL>
<DT><STRONG>Build:</STRONG></DT>
<DD>State entered after the first allocation, and before the
  first assembly; in this state it is possible to add nonzero entries.
</DD>
<DT><STRONG>Assembled:</STRONG></DT>
<DD>State entered after the assembly; computations using
  the sparse matrix, such as matrix-vector products, are only possible
  in this state;
</DD>
<DT><STRONG>Update:</STRONG></DT>
<DD>State entered after a reinitalization; this is used to
  handle applications in which the same sparsity pattern is used
  multiple times with different coefficients. In this state it is only
  possible to enter coefficients for already existing nonzero entries.
</DD>
</DL>
<BR><HR>
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