Final report on the Sherman-Morrison-Woodbury kernels, implemented in QMCkl

This work has been executed in the context of the TREX-CoE. To that end we aim to address the
following goals. To
  - solve a numerical problem that exists in the Sherman-Morrison method, as implemented and
    used extensively in the QMC=Chem software package,
  - extend and generalise this method to include higher-rank cases (Woodbury matrix identity),
  - implement these methods and optimise them to run efficiently on high performance computing
    (HPC) architectures.

QMC=Chem is used as a test case to address the numerical problems in its implementation of
the Sherman-Morrison method. However, it is often used in other Quantum Monte Carlo (QMC)
applications as well. Indeed, the method itself is more general and can be employed in many
other application domains. Because of this, these algorithms have been made available to the
public in the form of computational kernels inside the Quantum Monte Carlo kernel
library (QMCkl).
      
Finally, we include performance- and numerical benchmarks to demonstrate that the numerical
issues that have been identified in QMC=Chem have been resolved and the stated objectives
have been met.

Read the report: 'SMWB_report.pdf'