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## psb_ovrl -- Overlap Update

These subroutines applies an overlap operator to the input vector:

where:

  is the global dense submatrix
  is the overlap operator; it is the composition of two operators and .

Table 15: Data types
| Subroutine
Short Precision Real | psb_ovrl
Long Precision Real | psb_ovrl
Short Precision Complex | psb_ovrl
Long Precision Complex | psb_ovrl

Type:
  Synchronous.
On Entry
x
  global dense matrix .
  Scope: local
  Type: required
  Intent: inout.
  Specified as: a rank one or two array or an object of type vdata`psb_T_vect_type` containing numbers of type specified in Table 15.
desc_a
  contains data structures for communications.
  Scope: local
  Type: required
  Intent: in.
  Specified as: a structured data of type descdata`psb_desc_type`.
update
  Update operator.
  update = psb_none_
    Do nothing;
  update = psb_add_
    Sum overlap entries, i.e. apply ;
  update = psb_avg_
    Average overlap entries, i.e. apply ;
  Scope: global
  Intent: in.
  Default:
  Scope: global
  Specified as: a integer variable.
work
  the work array.
  Scope: local
  Type: optional
  Intent: inout.
  Specified as: a one dimensional array of the same type of .

On Return
x
  global dense result matrix .
  Scope: local
  Type: required
  Intent: inout.
  Specified as: an array of rank one or two containing numbers of type specified in Table 15.
info
  Error code.
  Scope: local
  Type: required
  Intent: out.
  An integer value; 0 means no error has been detected.

Notes

1. If there is no overlap in the data distribution associated with the descriptor, no operations are performed;
2. The operator performs the reduction sum of overlap elements; it is a ``prolongation'' operator that replicates overlap elements, accounting for the physical replication of data;
3. The operator performs a scaling on the overlap elements by the amount of replication; thus, when combined with the reduction operator, it implements the average of replicated elements over all of their instances.

Figure 8: Sample discretization mesh.

Example of use Consider the discretization mesh depicted in fig. 8, partitioned among two processes as shown by the dashed lines, with an overlap of 1 extra layer with respect to the partition of fig. 7; the data distribution is such that each process will own 40 entries in the index space, with an overlap of 16 entries placed at local indices 25 through 40; the halo will run from local index 41 through local index 48.. If process 0 assigns an initial value of 1 to its entries in the vector, and process 1 assigns a value of 2, then after a call to `psb_ovrl` with `psb_avg_` and a call to `psb_halo_` the contents of the local vectors will be the following (showing a transition among the two subdomains)

Process 0 |  | Process 1
I | GLOB(I) | X(I) |  | I | GLOB(I) | X(I)
1 | 1 | 1.0 |  | 1 | 33 | 1.5
2 | 2 | 1.0 |  | 2 | 34 | 1.5
3 | 3 | 1.0 |  | 3 | 35 | 1.5
4 | 4 | 1.0 |  | 4 | 36 | 1.5
5 | 5 | 1.0 |  | 5 | 37 | 1.5
6 | 6 | 1.0 |  | 6 | 38 | 1.5
7 | 7 | 1.0 |  | 7 | 39 | 1.5
8 | 8 | 1.0 |  | 8 | 40 | 1.5
9 | 9 | 1.0 |  | 9 | 41 | 2.0
10 | 10 | 1.0 |  | 10 | 42 | 2.0
11 | 11 | 1.0 |  | 11 | 43 | 2.0
12 | 12 | 1.0 |  | 12 | 44 | 2.0
13 | 13 | 1.0 |  | 13 | 45 | 2.0
14 | 14 | 1.0 |  | 14 | 46 | 2.0
15 | 15 | 1.0 |  | 15 | 47 | 2.0
16 | 16 | 1.0 |  | 16 | 48 | 2.0
17 | 17 | 1.0 |  | 17 | 49 | 2.0
18 | 18 | 1.0 |  | 18 | 50 | 2.0
19 | 19 | 1.0 |  | 19 | 51 | 2.0
20 | 20 | 1.0 |  | 20 | 52 | 2.0
21 | 21 | 1.0 |  | 21 | 53 | 2.0
22 | 22 | 1.0 |  | 22 | 54 | 2.0
23 | 23 | 1.0 |  | 23 | 55 | 2.0
24 | 24 | 1.0 |  | 24 | 56 | 2.0
25 | 25 | 1.5 |  | 25 | 57 | 2.0
26 | 26 | 1.5 |  | 26 | 58 | 2.0
27 | 27 | 1.5 |  | 27 | 59 | 2.0
28 | 28 | 1.5 |  | 28 | 60 | 2.0
29 | 29 | 1.5 |  | 29 | 61 | 2.0
30 | 30 | 1.5 |  | 30 | 62 | 2.0
31 | 31 | 1.5 |  | 31 | 63 | 2.0
32 | 32 | 1.5 |  | 32 | 64 | 2.0
33 | 33 | 1.5 |  | 33 | 25 | 1.5
34 | 34 | 1.5 |  | 34 | 26 | 1.5
35 | 35 | 1.5 |  | 35 | 27 | 1.5
36 | 36 | 1.5 |  | 36 | 28 | 1.5
37 | 37 | 1.5 |  | 37 | 29 | 1.5
38 | 38 | 1.5 |  | 38 | 30 | 1.5
39 | 39 | 1.5 |  | 39 | 31 | 1.5
40 | 40 | 1.5 |  | 40 | 32 | 1.5
41 | 41 | 2.0 |  | 41 | 17 | 1.0
42 | 42 | 2.0 |  | 42 | 18 | 1.0
43 | 43 | 2.0 |  | 43 | 19 | 1.0
44 | 44 | 2.0 |  | 44 | 20 | 1.0
45 | 45 | 2.0 |  | 45 | 21 | 1.0
46 | 46 | 2.0 |  | 46 | 22 | 1.0
47 | 47 | 2.0 |  | 47 | 23 | 1.0
48 | 48 | 2.0 |  | 48 | 24 | 1.0

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