A Fast 3 x N Matrix Multiply Routine for Calculation of Protein RMSD

The bottleneck for the rapid calculation of the root-mean-square deviation in atomic coordinates (RMSD) between pairs of protein structures for large numbers of conformations is the evaluation of a 3 x N x N x 3 matrix product over conformation pairs. Here we describe two matrix multiply routines specialized for the 3 x N case that are able to significantly outperform (by up to 3X) off-the-shelf high-performance linear algebra libraries for this computation, reaching machine limits on performance. The routines are implemented in C and Python libraries, and are available at https://github.com/simtk/IRMSD.