Memory Efficiency Benchmarking

CSR vs Dense Storage Comparison

Dimensions: 128 * 1M

• Allocated a uniformly distributed ndarray for sparse and dense of shape (128, 1M) and compared peak memory consumption

Density(%)	Peak Memory Consumption (Sparse)	Peak Memory Consumption (Dense)	Ratio of Memory Consumption
0.01	29	1456	50.20689655
0.02	32	1456	45.5
0.04	34	1456	42.82352941
0.08	40	1456	36.4
0.16	53	1456	27.47169811
0.32	78	1456	18.66666667
0.64	130	1456	11.2
1.28	232	1456	6.275862069
2.56	437	1456	3.33180778
5.12	846	1456	1.721040189
10.24	1626	1456	0.895448954

RSP vs Dense Storage Comparison

• Allocated a uniformly distributed ndarray for rsp and dense of shape (1M, 256) and compared peak memory consumption
• NOTE: for rsp density doesn't mean number of nnzs / total elements in the matrix. the density is approximately equal to the number of non zero rows from the total number of rows (This is because rand_ndarray tries to generate a single dimension array with shape (shape[0]) with random values between 0 and 1 and selects only those indexes from array with values less than density. This array is used as the indices array and the rest are set to zeros. Thus it is approximately equal to the number of non zero rows/total rows)

Density(%)	Peak Memory Consumption (Sparse)	Peak Memory Consumption (Dense)	Ratio of Memory Consumption
0.01	52	1456	28
0.02	52	1456	28
0.04	52	1456	28
0.08	54	1456	26.96296296
0.16	56	1456	26
0.32	61	1456	23.86885246
0.64	70	1456	20.8
1.28	88	1456	16.54545455
2.56	126	1456	11.55555556
5.12	202	1456	7.207920792
10.24	351	1456	4.148148148
20.48	654	1456	2.226299694
40.96	1222	1456	1.191489362
81.92	2399	1456	0.60691955

dot(csr, rsp) vs dot(csr, dense) Peak Memory consumption Comparison

• rhs_density is the same as lhs_density
• lhs_shape = (128, 1000000) , rhs_shape = (1000000, 256)

Density(%)	Peak Memory Consumption (Sparse)	Peak Memory Consumption (Dense)	Ratio of Memory Consumption
0.01	52	1575	30.28846154
0.02	52	1575	30.28846154
0.04	54	1575	29.16666667
0.08	57	1575	27.63157895
0.16	65	1575	24.23076923
0.32	87	1575	18.10344828
0.64	132	1575	11.93181818
1.28	221	1575	7.126696833
2.56	400	1575	3.9375
5.12	758	1575	2.077836412
10.24	1480	1575	1.064189189

dot(csr, rsp) vs dot(dense, dense) Peak Memory consumption Comparison

• rhs_density is the same as lhs_density
• lhs_shape = (128, 1000000) , rhs_shape = (1000000, 256)

Density(%)	Peak Memory Consumption (Sparse)	Peak Memory Consumption (Dense)	Ratio of Memory Consumption
0.01	52	3380	65
0.02	52	3380	65
0.04	54	3380	62.59259259
0.08	57	3380	59.29824561
0.16	65	3380	52
0.32	87	3380	38.85057471
0.64	132	3380	25.60606061
1.28	221	3380	15.29411765
2.56	400	3380	8.45
5.12	758	3380	4.459102902
10.24	1480	3380	2.283783784