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psb_ovrl -- Overlap Update

These subroutines applies an overlap operator to the input vector:


\begin{displaymath}x \leftarrow Q x \end{displaymath}

where:
$x$
is the global dense submatrix $x$
$Q$
is the overlap operator; it is the composition of two operators $ P_a$ and $ P^{T}$.


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


call psb_ovrl(x, desc_a, info)
call psb_ovrl(x, desc_a, info, update=update_type, work=work)

Type:
Synchronous.
On Entry
x
global dense matrix $x$.
Scope: local
Type: required
Intent: inout.
Specified as: a rank one or two array or an object of type vdatapsb_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 descdatapsb_desc_type.
update
Update operator.
update = psb_none_
Do nothing;
update = psb_add_
Sum overlap entries, i.e. apply $P^T$;
update = psb_avg_
Average overlap entries, i.e. apply $P_aP^T$;
Scope: global
Intent: in.
Default: $update\_type = psb\_avg\_ $
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 $x$.

On Return
x
global dense result matrix $x$.
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 $ P^{T}$ performs the reduction sum of overlap elements; it is a ``prolongation'' operator $P^T$ that replicates overlap elements, accounting for the physical replication of data;
  3. The operator $ P_a$ 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.
\includegraphics[scale=0.65]{figures/try8x8_ov.eps} \rotatebox{-90}{\includegraphics[scale=0.65]{figures/try8x8_ov}}
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 $x$ 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


next up previous contents
Next: psb_gather Gather Up: Communication routines Previous: psb_halo Halo   Contents