## 5 Results and Analysis
### SURAA: Comparative Performance against High npr Variance  
Figure 10 illustrates the relationship between the obtained throughput for the seven schemes, SURAA, CSR5, CSR, HYB, WPK2, SELL-P, and WPK1, with respect to the variance of the non-zero elements of all the 26 matrices in our dataset. The symbols indicate the actual GFLOP/s obtained and the straight lines indicate the smoothened GFLOP/s. We observe that SURAA provides better throughput with the increase in the variance of nonzero elements per row. On extrapolating the GFLOP/s, we observe that larger variations in nonzero elements per row will achieve higher GFLOP/s for SURAA compared to the next best CSR5, CSR, and HYB (note the upward slope for these schemes); and this behavior is highly desirable because higher variations usually decrease SpMV performance. We also observe that larger variations decrease the performance of the WPK2, WPK1, and SELL-P techniques.  
Similarly, Figure 11 depicts the speedup of SURAA against CSR5, HYB, SELL-P, WPK1, WPK2, and CSR, with respect to the variance of the nonzero elements per row for all the 26 matrices in the benchmark suite. As in Figure 10, the symbols indicate the actual SURAA speedups obtained and the straight lines indicates the smoothed speedups. Note that the \(npr\) variance and the speedups are plotted in log10. We observe in the figure that the speedup of SURAA over SELL-P, WPK1, CSR, HYB, WPK2, and CSR5 is increasing with the increase in the variance of the number of non-zeros per row. As seen and discussed before, this indicates an excellent behavior for a sparse matrix computation tool. The rate of increase in speedup of SURAA against SELL-P, WPK1 and CSR is relatively high compared to the rest of the schemes and this has made the plots for HYB, WPK2, and CSR5 appear as  
Figure 9: SURAA: Effective bandwidth comparison with the state of the art commercial (cuSPARSE) and open source (CUSP, MAGMA) tools: CSR, HYB, CSR-5, SELL-P, WPK1, and WPK2 for (**a**) the 13 matrices from the benchmark set that provided lowest bandwidths and (**b**) the 13 matrices that provided the highest bandwidth for SURAA.  
straight lines. To allow a closer look at the SURAA performance, Figure 12 depicts the same graphs as in Figure 11 but excludes the SELL-P, WPK1, and CSR data. The speedup scale now does not use log10. It can now be observed that the SURAA speedup against CSR5 and HYB show an increase for an increasing \(npr\) variance though the rate is lower than the other SpMV computation schemes. The highest rate of increase of SURAA speedup is over the HYB scheme followed by WPK2 and CSR5.  
Figure 13 illustrates the GFLOP/s performance of BSR, SELL-P, WPK1, WPK2, CSR, HYB, CSR5, and SURAA, respectively, against the \(npr\) variance and the total number of nonzero elements, \(nnz\).  
Note the colour legend in the figure depicting colours ranging from blue to green, yellow, orange and red, representing GFLOP/s in increasing order from near zero (SELL-P) to maximum 36.70 (SURAA). More yellow/orange/red means higher throughput. Blue and green colours represent lower throughput.  
BSR provides a low performance for the majority of the cases as shown by the blue shades that cover majority of the figure. The highest GFLOP/s results attained by BSR are 12.95 and 12.75, for the matrices _nemeth23_ and _TSOPF_RS_b2383_, which have a block structure.  
SELL-P shows a performance in the range of 10 to 26.8 GFLOP/s for smaller \(nnz\) values and \(npr\) variance varying from low to medium. However, a higher \(npr\) variance results in poor performance with GFLOP/s in the range of 0 to 5. We had discussed this earlier while evaluating SELL-P individual  
Figure 11: SURAA speedup against \(npr\) variance for the 26 benchmark matrices (compared for CSR5, WPK1, WPK2, HYB, SELL-P, and CSR).  
Figure 10: Throughput against \(npr\) variance for the benchmark suite comprising 26 matrices (compared schemes: CSR5, WPK1, WPK2, HYB, SELL-P, CSR, and SURAA).