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original version by: Nikos Drakos, CBLU, University of Leeds
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* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
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<TITLE>Sparse Matrix data structure</TITLE>
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HREF="node1.html">Contents</A></B>
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<!--End of Navigation Panel-->
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<H2><A NAME="SECTION00042000000000000000"></A>
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<A NAME="sec:spmat"></A>
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<BR>
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Sparse Matrix data structure
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</H2>
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The spdata<TT>psb_spmat_type</TT> data structure
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contains all information about local portion of the sparse matrix and
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its storage mode. Most of these fields are set by the tools
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routines when inserting a new sparse matrix; the user needs only
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choose, if he/she so whishes, a specific matrix storage mode.
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<BR><DL>
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<DT><STRONG><B>aspk</B></STRONG></DT>
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<DD>Contains values of the local distributed sparse
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matrix.
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<BR>
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Specified as: an allocatable array of rank one of type corresponding
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to matrix entries type.
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</DD>
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<DT><STRONG><B>ia1</B></STRONG></DT>
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<DD>Holds integer information on distributed sparse
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matrix. Actual information will depend on data format used.
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<BR>
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Specified as: an allocatable integer array of rank one.
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</DD>
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<DT><STRONG><B>ia2</B></STRONG></DT>
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<DD>Holds integer information on distributed sparse
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matrix. Actual information will depend on data format used.
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<BR>
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Specified as: an allocatable integer array of rank one.
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</DD>
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<DT><STRONG><B>infoa</B></STRONG></DT>
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<DD>On entry can hold auxiliary information on distributed sparse
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matrix. Actual information will depend on data format used.
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<BR>
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Specified as: an integer array of length <code>psb_ifasize_</code>.
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</DD>
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<DT><STRONG><B>fida</B></STRONG></DT>
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<DD>Defines the format of the distributed sparse matrix.
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<BR>
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Specified as: a string of length 5
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</DD>
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<DT><STRONG><B>descra</B></STRONG></DT>
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<DD>Describe the characteristic of the distributed sparse matrix.
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<BR>
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Specified as: array of character of length 9.
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</DD>
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<DT><STRONG><B>pl</B></STRONG></DT>
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<DD>Specifies the local row permutation of distributed sparse
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matrix. If pl(1) is equal to 0, then there isn't row permutation.
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<BR>
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Specified as: an allocatable integer array of dimension equal to number of local row (matrix_data[psb_n_row_])
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</DD>
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<DT><STRONG><B>pr</B></STRONG></DT>
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<DD>Specifies the local column permutation of distributed sparse
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matrix. If PR(1) is equal to 0, then there isn't columnm permutation.
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<BR>
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Specified as: an allocatable integer array of dimension equal to number of
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local row (matrix_data[psb_n_col_])
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</DD>
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<DT><STRONG><B>m</B></STRONG></DT>
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<DD>Number of rows; if row indices are stored explicitly,
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as in Coordinate Storage, should be greater than or equal to the
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maximum row index actually present in the sparse matrix.
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Specified as: integer variable.
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</DD>
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<DT><STRONG><B>k</B></STRONG></DT>
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<DD>Number of columns; if column indices are stored explicitly,
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as in Coordinate Storage or Compressed Sparse Rows, should be greater
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than or equal to the maximum column index actually present in the sparse matrix.
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Specified as: integer variable.
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</DD>
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</DL>
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The Fortran 95 interface for distributed sparse matrices containing
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double precision real entries is defined as shown in
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figure <A HREF="#fig:spmattype">4</A>. The definitions for single precision and
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complex data are identical except for the <code>real</code> declaration and
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for the kind type parameter.
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<DIV ALIGN="CENTER"><A NAME="fig:spmattype"></A><A NAME="622"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 4:</STRONG>
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The PSBLAS defined data type that
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contains a sparse matrix.</CAPTION>
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<TR><TD>
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<BR>
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<DIV ALIGN="CENTER">
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<!-- MATH
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$\fbox{\TheSbox}$
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-->
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<IMG
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WIDTH="536" HEIGHT="218" ALIGN="MIDDLE" BORDER="0"
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SRC="img19.png"
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ALT="\fbox{\TheSbox}">
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</DIV></TD></TR>
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</TABLE>
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</DIV>
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<P>
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The following two cases are among the most commonly used:
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<DL>
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<DT><STRONG>fida=``CSR''</STRONG></DT>
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<DD>Compressed storage by rows. In this case the
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following should hold:
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<OL>
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<LI><code>ia2(i)</code> contains the index of the first element of row
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<code>i</code>; the last element of the sparse matrix is thus stored at
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index <IMG
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WIDTH="107" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img21.png"
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ALT="$ia2(m+1)-1$">. It should contain <code>m+1</code> entries in
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nondecreasing order (strictly increasing, if there are no empty rows).
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</LI>
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<LI><code>ia1(j)</code> contains the column index and <code>aspk(j)</code>
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contains the corresponding coefficient value, for all <!-- MATH
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$ia2(1) \le j
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\le ia2(m+1)-1$
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-->
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<IMG
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WIDTH="199" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img22.png"
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ALT="$ia2(1) \le j
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\le ia2(m+1)-1$">.
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</LI>
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</OL>
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</DD>
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<DT><STRONG>fida=``COO''</STRONG></DT>
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<DD>Coordinate storage. In this case the following
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should hold:
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<OL>
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<LI><code>infoa(1)</code> contains the number of nonzero elements in the
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matrix;
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</LI>
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<LI>For all <!-- MATH
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$1 \le j \le infoa(1)$
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-->
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<IMG
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WIDTH="123" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
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SRC="img23.png"
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ALT="$1 \le j \le infoa(1)$">, the coefficient, row index and
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column index are stored into <code>apsk(j)</code>, <code>ia1(j)</code> and
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<code>ia2(j)</code> respectively.
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</LI>
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</OL>
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</DD>
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</DL>
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A sparse matrix has an associated state, which can take the following
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values:
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<DL>
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<DT><STRONG>Build:</STRONG></DT>
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<DD>State entered after the first allocation, and before the
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first assembly; in this state it is possible to add nonzero entries.
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</DD>
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<DT><STRONG>Assembled:</STRONG></DT>
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<DD>State entered after the assembly; computations using
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the sparse matrix, such as matrix-vector products, are only possible
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in this state;
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</DD>
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<DT><STRONG>Update:</STRONG></DT>
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<DD>State entered after a reinitalization; this is used to
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handle applications in which the same sparsity pattern is used
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multiple times with different coefficients. In this state it is only
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possible to enter coefficients for already existing nonzero entries.
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</DD>
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</DL>
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<BR><HR>
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<!--Table of Child-Links-->
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<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
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<LI><A NAME="tex2html307"
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