5.2 psb_ovrl — Overlap Update

These subroutines applies an overlap operator to the input vector:

x ← Qx

where:

x
is the global dense submatrix x
Q
is the overlap operator; it is the composition of two operators Pa and PT.




x Subroutine


Short Precision Real psb_ovrl
Long Precision Real psb_ovrl
Short Precision Complexpsb_ovrl
Long Precision Complex psb_ovrl



Table 18: Data types

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 psb_T_vect_type containing numbers of type specified in Table 18.
desc_a
contains data structures for communications.
Scope: local
Type: required
Intent: in.
Specified as: a structured data of type psb_desc_type.
update
Update operator.
update = psb_none_
Do nothing;
update = psb_add_
Sum overlap entries, i.e. apply PT;
update = psb_avg_
Average overlap entries, i.e. apply PaPT;

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 18.
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 PT performs the reduction sum of overlap elements; it is a “prolongation” operator PT that replicates overlap elements, accounting for the physical replication of data;
  3. The operator Pa 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.


PIC


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 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
IGLOB(I)X(I) IGLOB(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 1.010 42 2.0
11 11 1.011 43 2.0
12 12 1.012 44 2.0
13 13 1.013 45 2.0
14 14 1.014 46 2.0
15 15 1.015 47 2.0
16 16 1.016 48 2.0
17 17 1.017 49 2.0
18 18 1.018 50 2.0
19 19 1.019 51 2.0
20 20 1.020 52 2.0
21 21 1.021 53 2.0
22 22 1.022 54 2.0
23 23 1.023 55 2.0
24 24 1.024 56 2.0
25 25 1.525 57 2.0
26 26 1.526 58 2.0
27 27 1.527 59 2.0
28 28 1.528 60 2.0
29 29 1.529 61 2.0
30 30 1.530 62 2.0
31 31 1.531 63 2.0
32 32 1.532 64 2.0
33 33 1.533 25 1.5
34 34 1.534 26 1.5
35 35 1.535 27 1.5
36 36 1.536 28 1.5
37 37 1.537 29 1.5
38 38 1.538 30 1.5
39 39 1.539 31 1.5
40 40 1.540 32 1.5
41 41 2.041 17 1.0
42 42 2.042 18 1.0
43 43 2.043 19 1.0
44 44 2.044 20 1.0
45 45 2.045 21 1.0
46 46 2.046 22 1.0
47 47 2.047 23 1.0
48 48 2.048 24 1.0