Efficient sparse matrix-vector multiplication on parallel processors
A method of multiplication of a sparse matrix and a vector to obtain a new vector and a system for implementing the method are claimed. Embodiments of the method are intended to optimize the performance of sparse matrix-vector multiplication in highly parallel processors, such as GPUs. The sparse matrix is stored in compressed sparse row (CSR) format.
1. A method of multiplication of a sparse matrix and a vector to obtain a new vector, the sparse matrix being stored in compressed sparse row (CSR) format, the method to be executed on a parallel processor, the method comprising:
partitioning, by the parallel processor, the matrix into blocks of consecutive rows; and
for each of said blocks having more than a minimum number of rows:
determining a number of non-zero matrix elements in the block;
executing a first process for sparse-matrix vector multiplication on rows of the block if a number of non-zero matrix elements in the block is less than or equal to a maximum; and
executing a second process for sparse-matrix vector multiplication, distinct from the first process, if the number of non-zero matrix elements is greater than the maximum.
2. The method of claim 1 , wherein the determining a number of non-zero matrix elements in the block, and the executing of the first process or the executing of the second process are performed in parallel by more than one workgroup, each workgroup performing on a different set of blocks.
3. The method of claim 1 , further comprising executing the second process on a block having a number of rows that is less than or equal to the minimum number of rows.
4. The method of claim 1 , wherein executing the first process comprises:
streaming non-zero elements in each block to contiguous locations in a local memory;
multiplying each non-zero element in each block with a corresponding element of the vector; and
adding results of the multiplying from each row of each block to obtain corresponding elements of the new vector.
5. The method of claim 4 , wherein the streaming comprises using consecutive threads in a wavefront.
6. The method of claim 4 , wherein the maximum is determined by a capacity of the local memory.
7. The method of claim 4 , wherein the multiplying and adding are performed in parallel for all rows in each block.
8. The method of claim 4 , wherein the adding for each row is performed by more than one thread in a wavefront.
9. The method of claim 1 , wherein the second process comprises a CSR-vector process.
10. The method of claim 1 , further comprising using the second process to determine an element of the new vector corresponding to a row in the block if said row is the only row in said block and the number of non-zero elements in said row exceeds the maximum.
11. The method of claim 1 , wherein the partitioning of the matrix comprises deriving a rows block buffer, the rows block buffer indicating a number of rows in each block.
12. The method of claim 11 , wherein the determining a number of non-zero matrix elements in the block comprises:
determining a start row and a stop row for each block from the rows block buffer;
determining two values in a row delimiter buffer corresponding to the start row and to the stop row; and
subtracting said two values to determine the number of non-zero elements in each block.
13. The method of claim 1 , wherein the multiplication of a sparse matrix and a vector are used in operation of a stored application, results of said operation being stored in a memory.
14. The method of claim 1 , wherein the multiplication of a sparse matrix and a vector are used in operation of a stored application, results of said operation being visually displayed on a display device.
15. A system configured to multiply a sparse matrix and a vector to obtain a new vector, the system comprising:
a parallel processor;
a storage configured to exchange information with the processor and store the vector and the sparse matrix, the sparse matrix being stored in compressed sparse row (CSR) format; and
a local memory configured to exchange information with the processor;
wherein the parallel processor is configured to implement a method of multiplication of the sparse matrix and the vector; the method comprising:
partitioning the matrix into blocks of consecutive rows; and
for each of said blocks having more than a minimum number of rows:
determining a number of non-zero matrix elements in the block;
executing a first process for sparse-matrix vector multiplication on rows of the block if a number of non-zero matrix elements in the block is less than or equal to a maximum; and
executing a second process for sparse-matrix vector multiplication, distinct from the first process, if the number of non-zero matrix elements is greater than the maximum.
16. The system of claim 15 , wherein the processor is configured to perform the determining a number of non-zero matrix elements in the block, and the executing of the first process or the executing of the second process in parallel in more than one workgroup, each workgroup performing on a different set of blocks.
17. The system of claim 15 , wherein the processor is further configured to execute the second process on a block having a number of rows that is less than or equal to the minimum number of rows.
18. The system of claim 15 , wherein the processor is configured to execute the first process by:
streaming non-zero elements in each block to contiguous locations in the local memory;
multiplying each non-zero element in each block with a corresponding element of the vector; and
adding results of the multiplying from each row of each block to obtain corresponding elements of the new vector.
19. The system of claim 18 , wherein the processor is configured to stream non-zero elements in each block to contiguous locations in the local memory by using consecutive threads in a wavefront.
20. The system of claim 18 , wherein the processor is configured to perform the multiplying and the adding in parallel for all rows in each block.
21. The system of claim 18 , wherein the processor is configured to perform the adding for each row in more than one thread in a wavefront.
22. The system of claim 15 , wherein a capacity of the local memory determines the maximum.
23. The system of claim 15 , wherein the local memory is integrated with the processor.
24. The system of claim 15 , wherein the second process comprises a CSR-vector process.
25. The system of claim 15 , wherein the processor is configured to use the second process to determine an element of the new vector corresponding to a row in the block if said row is the only row in said block and the number of non-zero elements in said row exceeds the maximum.
26. The system of claim 15 wherein the processor is configured to store the new vector in the storage.
27. The system of claim 15 , wherein the processor is configured to perform the partitioning of the matrix by deriving a rows block buffer, the rows block buffer indicating a number of rows in each block.
28. The system of claim 27 , wherein the processor is configured to determine a number of rows in each block by:
determining a start row and a stop row for each block from the rows block buffer;
determining two values in a row delimiter buffer corresponding to the start row and to the stop row; and
subtracting said two values to determine the number of non-zero elements in each block.
29. The system of claim 15 , wherein the processor is configured to:
operate an application stored in the storage, wherein the multiplication of the sparse matrix and the vector are used in the application; and
store results of said operating of the application.
30. The system of claim 15 , further comprising a display device, wherein the processor is configured to:
operate an application stored in the storage, wherein the multiplication of the sparse matrix and the vector are used in the application; and
display results of said operating of the application on the display device.