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196 lines
8.4 KiB
TeX
196 lines
8.4 KiB
TeX
\section{Data Structures}
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\label{sec:datastruct}
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%\ifthenelse{\boolean{mtc}}{\minitoc}{}
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In this chapter are illustrated data structures used for definition of
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routines interfaces. This include data structure for sparse matrix,
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communication descriptor and preconditioner. These data structures are used for
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calling PSBLAS routines in Fortran~90 language and will be used to next
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chapters containing these callings. Their definitions are included in
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the modules \verb|psb_spmat_type|, \verb|psb_descriptor_type| and \verb|psb_prec_type|.
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\subsection{Sparse Matrix data structure}
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\label{sec:spmat}
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Contains all information about local portion of the sparse matrix and
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its storage mode. Many of this fields are set in fully-transparent
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mode by PSBLAS-TOOLS routines when inserting a new sparse matrix, user
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must set only fields which describe matrix storage mode (see
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\S~\ref{psb_spall}). \\
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Fields contained in Sparse matrix structures are:
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\begin{description}
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\item[{\bf aspk}] Contains values of the local distributed sparse
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matrix.\\
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Specified as: a pointer to an array of rank one of type corresponding
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to matrix entries type .
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\item[{\bf ia1}] Holds integer information on distributed sparse
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matrix. Actual information will depend on data format used.\\
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Specified as: a pointer to an integer array of rank one.
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\item[{\bf ia2}] Holds integer information on distributed sparse
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matrix. Actual information will depend on data format used.\\
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Specified as: a pointer to an integer array of rank one.
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\item[{\bf infoa}] 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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Specified as: integer array of length 10.
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\item[{\bf fida}] Defines the format of the distributed sparse matrix.\\
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Specified as: a string of length 5
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\item[{\bf descra}] Describe the characteristic of the distributed sparse matrix.\\
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Specified as: array of character of length 9.
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\item[{\bf pl}] 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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Specified as: pointer to integer array of dimension equal to number of local row (matrix\_data[psb\_n\_row\_\hbox{]})
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\item[{\bf pr}] 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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Specified as: pointer to integer array of dimension equal to number of
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local row (matrix\_data[psb\_n\_col\_\hbox{]})
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\item[{\bf m}] 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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\item[{\bf k}] 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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\end{description}
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Values assumed by this fields are compatible with ref. 1 (see \S~\ref{chap:appendix}).\\
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FORTRAN95 interface for distributed sparse matrices containing double precision
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real entries is defined as follows:
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\begin{verbatim}
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type d_spmat
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integer :: m, k
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character*5 :: fida
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character*1 :: descra(9)
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integer :: infoa(10)
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real(kind(1.d0)), pointer :: aspk(:)
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integer, pointer :: ia1(:), ia2(:)
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integer, pointer :: pl(:), pr(:)
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end type d_spmat
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\end{verbatim}
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The following two cases are used in the data insertion routines:
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\begin{description}
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\item[fida=``CSR''] Compressed storage rows. In this case the
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following should hold:
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\begin{enumerate}
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\item \verb|ia2(i)| contains the index of the first element of row
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\verb|i|; the last element of the sparse matrix is thus stored at
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index $ia2(m+1)-1$. It should contain \verb|m+1| entries in
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nondecreasing order (strictly increasing, if there are no empty rows).
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\item \verb|ia1(j)| contains the column index and \verb|aspk(j)|
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contains the corresponding coefficient value, for all $ia2(1) \le j
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\le ia2(m+1)-1$.
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\end{enumerate}
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\item[fida=``COO''] Coordinate storage. In this case the following
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should hold:
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\begin{enumerate}
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\item \verb|infoa(1)| contains the number of nonzero elements in the
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matrix;
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\item For all $1 \le j \le infoa(1)$, the coefficient, row index and
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column index are stored into \verb|apsk(j)|, \verb|ia1(j)| and
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\verb|ia2(j)| respectively.
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\end{enumerate}
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\end{description}
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\subsubsection{Sparse Matrix storage formats}
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\subsection{Descriptor data structure}
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\label{sec:desc}
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All the general matrix informations and elements to be
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exchanged among processes are stored within a data structure of the type $psb_desc_type$.
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Every structure of this type is associated to a sparse matrix, it
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contains data about general matrix informations and elements to be
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exchanged among processes. \\
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It is not necessary for the user to
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know the internal structure of $psb_desc_type$, it is set in
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fully-transparent mode by PSBLAS-TOOLS routines when inserting a new
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sparse matrix, however the definition of the descriptor is the
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following.
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\begin{description}
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\item[{\bf matrix\_data}] includes general information about matrix and
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BLACS grid. More precisely:
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\begin{description}
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\item[matrix\_data[psb\_dec\_type\_\hbox{]}] Identifies the decomposition type
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(global); the actual values are internally defined, so they should
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never be accessed directly.
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\item[matrix\_data[psb\_ctxt\_\hbox{]}] Communication context as returned by the
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BLACS (global).
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\item[matrix\_data[psb\_m\_\hbox{]}] Total number of equations (global).
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\item[matrix\_data[psb\_n\_\hbox{]}] Total number of variables (global).
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\item[matrix\_data[psb\_n\_row\_\hbox{]}] Number of grid variables owned by the
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current process (local); equivalent to the number of local rows in the
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sparse coefficient matrix.
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\item[matrix\_data[psb\_n\_col\_\hbox{]}] Total number of grid variables read by the
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current process (local); equivalent to the number of local columns in
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the sparse coefficient matrix. They include the halo.
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\end{description}
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Specified as: a pointer to integer array of dimension 10.
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\item[{\bf halo\_index}] A list of the halo and boundary elements for
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the current process to be exchanged with other processes; for each
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processes with which it is necessary to communicate:
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\begin{enumerate}
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\item Process identifier;
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\item Number of points to be received;
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\item Indices of points to be received;
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\item Number of points to be sent;
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\item Indices of points to be sent;
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\end{enumerate}
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The list may contain an arbitrary number of groups; its end is marked
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by a -1.\\
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Specified as: a pointer to an integer array of rank one.
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\item [{\bf ovrlap\_index}] A list of the overlap elements for the
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current process, organized in groups like the previous vector:
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\begin{enumerate}
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\item Process identifier;
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\item Number of points to be received;
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\item Indices of points to be received;
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\item Number of points to be sent;
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\item Indices of points to be sent;
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\end{enumerate}
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The list may contain an arbitrary number of groups; its end is marked
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by a -1.\\
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Specified as: a pointer to an integer array of rank one.
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\item [{\bf ovrlap\_index}] For all overlap points belonging to th
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ecurrent process:
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\begin{enumerate}
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\item Overlap point index;
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\item Number of processes sharing that overlap points;
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\end{enumerate}
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The list may contain an arbitrary number of groups; its end is marked
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by a -1.\\
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Specified as: a pointer to an integer array of rank one.
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\item[{\bf loc\_to\_glob}] each element $i$ of this array contains
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global identifier of the local variable $i$.\\
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Specified as: a pointer to an integer array of rank one.
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\item[{\bf glob\_to\_loc}] if global variable $i$ is read by current
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process then element $i$ contains local index correpondent to global variable $i$;
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else element $i$ contains -1 (NULL) value.\\
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Specified as: a pointer to an integer array of rank one.
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\end{description}
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FORTRAN90 interface for $decomp\_data$ structures is therefore defined
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as follows:
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\begin{verbatim}
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type decomp_data_type
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integer, pointer :: matrix_data(:)
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integer, pointer :: halo_index(:)
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integer, pointer :: ovrlap_elem(:)
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integer, pointer :: ovrlap_index(:)
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integer, pointer :: loc_to_glob(:)
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integer, pointer :: glob_to_loc (:)
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end type decomp_data_type
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\end{verbatim}
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\subsection{Preconditioner data structure}
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\label{sec:prec}
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\hypertarget{precdata}{ciao finocchio}
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\subsection{Building and assembling data structures}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: "userguide"
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%%% End:
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