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 |