Fig. 2: Benchmark on throughput, memory consumption and correctness for each macromolecular structure in the benchmark dataset.

For all methods, the first 64 eigenpairs were calculated. Methods tested includes 2 ProDy methods (i.e., “ProDy-LAPACK-FullDense” and “ProDy-ARPACK-FullSparse”) and 5 INCHING methods (i.e., “INCHING-TRLM-HalfSparse“, “INCHING-CTRLM-HalfSparse“, “INCHING-JDM-HalfSparse“, “INCHING-IRLM-HalfSparse“, “INCHING-ARPACK-FullSparse“). Text in the name describe the eigensolver (e.g., ARPACK, LAPACK, JDM, TRLM, CTRLM, IRLM), the access of the Hessian matrix (e.g., “Full” means that the whole Hessian matrix is accessed and stored; “Half” means that only the lower triangle of the Hessian matrix is accessed and stored.), and the storage format of the Hessian matrix (e.g., “Dense” means a 2-D array is stored in double precision; “Sparse” means a Compressed Sparse Row (CSR) format is stored in double precision). “TRLM”, “CTRLM”, “JDM”, “IRLM” are our implementation of the Thick Restart Lanczos Method (TRLM), Chebyshev-filtered Thick Restart Lanczos Method (CTRLM), Jacobi-Davidson Method (JDM) and Implicitly Restarted Lanczos Method (IRLM). a Benchmark on overall run time including Hessian realization and subsequent diagonalization. The run time is wall-clock time to complete all the calculation. b Benchmark on peak memory consumption. Note that for “ProDy-LAPACK-FullDense”, we were not able to proceed once there are more than 29 thousand atoms due to memory overflow. Note that for “ProDy-ARPACK-FullSparse”, we were not able to proceed once there are more than 305 thousand atoms as it takes more than 48 h to converge. Also note that “INCHING-TRLM-HalfSparse“, “INCHING-CTRLM-HalfSparse“ and “INCHING-JDM-HalfSparse“ share very similar peak memory requirement. c Benchmark on residual error \({\left|\left|{{{{{\boldsymbol{r}}}}}}\right|\right|}_{2}\), defined as the 2-norm of residual vector \({{{{{\bf{r}}}}}}\) The error bar presented is the 95% confidence interval (n = 64) calculated from the residual error of all the eigenvalues of a macromolecular structure in the benchmark dataset. Note that for “ProDy-LAPACK-FullDense”, the second macromolecular structure (PDBID: 1A8L) were not able to converge within \({10}^{-10}\) likely due to severe fill-ins. All programs were stopped if run time exceeds 48 h. All INCHING programs were stopped if number of restarts exceeded 15000 rounds. Source data are provided as a Source Data file.