Descriptor data structure

All the general matrix informations and elements to be exchanged among processes are stored within a data structure of the type descdatapsb_desc_type. Every structure of this type is associated to a sparse matrix, it contains data about general matrix informations and elements to be exchanged among processes.

It is not necessary for the user to know the internal structure of psb_desc_type, it is set in a transparent mode by the tools routines of Sec. 6, and its fields may be accessed if necessary via the routines of sec. 3.4; nevertheless we include a description for the curious reader:

matrix_data

includes general information about matrix and process grid, such as the communication context, the size of the global matrix, the size of the portion of matrix stored on the current process, and so on. Specified as: an allocatable integer array of dimension psb_mdata_size_.

halo_index

A list of the halo and boundary elements for the current process to be exchanged with other processes; for each processes with which it is necessary to communicate:

1. Process identifier;
2. Number of points to be received;
3. Indices of points to be received;
4. Number of points to be sent;
5. Indices of points to be sent;

The list may contain an arbitrary number of groups; its end is marked by a -1.
Specified as: an allocatable integer array of rank one.

ext_index

A list of element indices to be exchanged to implement the mapping between a base descriptor and a descriptor with overlap.

ovrlap_index

A list of the overlap elements for the current process, organized in groups like the previous vector:

1. Process identifier;
2. Number of points to be received;
3. Indices of points to be received;
4. Number of points to be sent;
5. Indices of points to be sent;

The list may contain an arbitrary number of groups; its end is marked by a -1.
Specified as: an allocatable integer array of rank one.

ovr_mst_idx

A list to retrieve the value of each overlap element from the respective master process.
Specified as: an allocatable integer array of rank one.

ovrlap_elem

For all overlap points belonging to th ecurrent process:

1. Overlap point index;
2. Number of processes sharing that overlap points;
3. Index of a ``master'' process:

Specified as: an allocatable integer array of rank two.

loc_to_glob

each element $i$ of this array contains global identifier of the local variable $i$.
Specified as: an allocatable integer array of rank one.

glob_to_loc, glb_lc, hashv

Contain a mapping from global to local indices.

The Fortran 95 definition for psb_desc_type structures is as follows:

Figure 3: The PSBLAS defined data type that contains the communication descriptor.

A communication descriptor associated with a sparse matrix has a state, which can take the following values:

Build:

State entered after the first allocation, and before the first assembly; in this state it is possible to add communication requirements among different processes.

Assembled:

State entered after the assembly; computations using the associated sparse matrix, such as matrix-vector products, are only possible in this state.

The global to local index mapping may be stored in two different formats: the first is simpler but more expensive, as it requires on each process an amount of memory proportional to the global size of the index space; the second is more complex, but only requires memory proportional to the local index space size. The choice is made at the time of the initialization according to a threshold; this threshold may be queried and set using the functions in sec. 3.4.