DSS Distributed Symmetric Matrix
Storage
The distributed assembled matrix input format can be
used by the Parallel Direct Sparse Solver for Clusters Interface.
In this format, the symmetric input matrix
A
is divided
into sequential row subsets, or domains. Each domain belongs to an MPI process.
Neighboring domains can overlap. For such intersection between two domains, the
element values of the full matrix can be obtained by summing the respective
elements of both domains.
As in the centralized format, the distributed format
uses three arrays to describe the input data, but the
values
,
columns
, and
rowIndex
arrays
on each processor only describe the domain belonging to that particular
processor and not the entire matrix.
For example, consider a symmetric matrix
A
:
This array could be distributed between two domains
corresponding to two MPI processes, with the first containing rows 1 through 3,
and the second containing rows 3 through 5.
For the symmetric input matrix, it is not necessary
to store the values from the lower triangle.
one-based indexing | |||||||
values | =
| (6
| -1
| -3
| 5
| 3
| 2)
|
columns | =
| (1
| 2
| 4
| 2
| 3
| 5)
|
rowIndex | =
| (1
| 4
| 5
| 7)
| ||
zero-based indexing | |||||||
values | =
| (6
| -1
| -3
| 5
| 3
| 2)
|
columns | =
| (0
| 1
| 3
| 1
| 2
| 4)
|
rowIndex | =
| (0
| 3
| 4
| 6)
|
one-based indexing | ||||||
values | =
| (8
| 5
| 2
| 10
| 5)
|
columns | =
| (3
| 4
| 5
| 4
| 5)
|
rowIndex | =
| (1
| 4
| 5
| 6)
| |
zero-based indexing | ||||||
values | =
| (8
| 5
| 2
| 10
| 5)
|
columns | =
| (2
| 3
| 4
| 3
| 4)
|
rowIndex | =
| (0
| 3
| 4
| 5)
|
The third row of matrix
A
is common
between domain 1 and domain 2. The values of row 3 of matrix
A
are the sums of
the respective elements of row 3 of matrix
A
Domain1
and row 1 of matrix
A
Domain2
.
Storage Format Restrictions
The storage format for the sparse solver must conform
to two important restrictions:
- the non-zero values in a given row must be placed into thevaluesarray in the order in which they occur in the row (from left to right);
- no diagonal element can be omitted from thevaluesarray for any symmetric or structurally symmetric matrix.
The second restriction implies that if symmetric or
structurally symmetric matrices have zero diagonal elements, then they must be
explicitly represented in the
values
array.
Product and Performance Information
|
|---|
Performance varies by use, configuration and other factors. Learn more at
www.Intel.com/PerformanceIndex.
Notice revision #20201201
|