  In this paper, we research the run-time sparse matrix data transformation
from Compressed Row Storage (CRS) to Coordinate (COO) storage and an ELL
(ELLPACK/ITPACK) format with OpenMP parallelization for sparse matrix-vector
multiplication (SpMV). We propose an auto-tuning (AT) method by using the
$D_{mat}^i$ - $R_{ell}^i$ graph, which plots the derivation/average for the
number of non-zero elements per row ($D_{mat}^i$) and the ratio, SpMV
speedups/transformation time from the CRS to ELL ($R_{ell}^i$ ). The
experimental results show the ELL format is very effective in the Earth
Simulator 2. The speedup factor of 151 with the ELL-Row inner-parallelized
format is obtained. The transformation overhead is also very small, such as
0.01 to 1.0 SpMV time with the CRS format. In addition, the $D_{mat}^i$ -
$R_{ell}^i$ graph can be modeled for the effectiveness of transformation
according to the $D_{mat}^i$ value.
