Introduction
•Sparse storage formats are of great
importance if we are dealing with large
data mostly consisting of zeros
•Sparse storage formats are techniques
for storing and processing matrix data
efficiently
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Sparse Matrix Storage Formats: Implementation and Performance Analysis, Slides of Applications of Computer Sciences
The importance of sparse storage formats for large data sets consisting mainly of zeros. The project aims to extend the existing sparselib++ library with more storage formats and efficient matrix-vector multiplication routines for both sequential and parallel processing. The document also covers various sparse storage techniques, their working, and their performance analysis.
Typology: Slides
2011/2012
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Introduction
- Sparse storage formats are of great
importance if we are dealing with large
data mostly consisting of zeros
- Sparse storage formats are techniques
for storing and processing matrix data
efficiently
Project Aim
- The existing library for sparse matrices (SparseLib++) consists of only three sparse storage techniques and routines for their matrix-vector multiplication. The aim of doing this project is to implement a sparse library that will have more storage formats and matrix-vector multiplication in both sequential and parallel
- For performance evaluation I apply different test matrices on these storage techniques, taken from matrix market
Cont…
- Depending on the organization of data first we will convert the network data from dense to some storage format that suits it best
- Now to resolve different issues like allocating network resources we will have to apply different operations on that data
- The conversion to sparse format will make these operations efficient in a reduced storage space.
Cont…
- If there are some more users to be
added in to the existing network, then
it becomes a growing matrix size
problem called expanding matrices,
that can be easily resolved in sparse
environment
- If the network is yet to be initialized, it
falls into the category of dynamic
matrices.
Cont…
- Diagonal storage format
- Jagged diagonal storage format
- Transpose jagged Diagonal storage format
- Java sparse array
- Skyline (symmetric)
- The block entry storage formats that I have implemented are:
- Block Coordinate storage format
- Block Compressed Row format
- Block compressed Column format
Cont…
- Apart from these techniques that are
included in the study are:
- Primary storage format
- Modified Compressed Row
- Modified Compressed Column
- Ellpack-itpack storage format
- Bi-jagged diagonal storage format
- Block Ellpack storage format
- Block diagonal storage format
Analysis
- There are two factors that influence
the performance and storage size of
sparse matrices. They are:
- Number of Non-zeros
- The number of non zeros has the same effect on all the storage formats. It is obvious that if there are more nonzeros in the matrix it will consume more storage size and processing time.
Cont…
- Those storage techniques that have a direct access to values like COO will be more affected in storage size as compared to processing time. While other techniques like CSR and CSC that access values indirectly using pointers will be more affected in processing time as compared to storage size
Type of matrices and the appropriate techniques
- If the nonzeros are distributed in few dense rows then CSR technique is advised
Cont…
- If the nonzeros are concentrated into few dense columns the CSC is advised
Cont…
- If the nonzeros are randomly spread
and there are no patterns to exploit
then we can use JDS or TJDS
Cont…
- If the matrix is symmetric then we can store only one half of the matrix data
- If we require high efficiency at the cost of storage size we can use skyline technique that embed zeros to the matrix data at their locations
- If the matrix size is to large to handle efficiently then we have to use block entry storage formats instead of point entry
- Java sparse array is recently devised technique and has proved very efficient using OO approach
Cont…
- CSR-vector
Multiplication
Cont…
- CSC-vector
Multiplication