yifan-bao / sinv

Implementations of several selected inversion algorithms

SINV : Selected Inversion Library

Implementations of several shared and distributed memory selected-inversion algorithms. These algorithms performs efficient inversion on block tridiagonal matrices.

Solvers: $A \cdot X = B$:

RGF (Recursive Green's Function)

@reference: https://doi.org/10.1063/1.1432117
Serial, non-pivoting, block-tridiagonal matrix selected inversion algorithm.

RGF 2-sided

@reference: https://doi.org/10.1007/s10825-013-0458-7
2-processes parallel version of RGF.

BCR-Serial (Block Cyclic Reduction)

@reference: https://doi.org/10.1016/j.jcp.2009.03.035
@reference: https://doi.org/10.1017/CBO9780511812583
Serial, non-pivoting, block tri-diagonal matrix selected inversion algorithm.

BCR-Parallel (Block Cyclic Reduction)

@reference: https://doi.org/10.1017/CBO9780511812583
Multi-processes version of BCR-Serial.

PSR (Parallel Schur reduction)

@reference: https://doi.org/10.1016/j.jcp.2009.03.035
Multi-processes, Schur-complement reduction based, block-tridiagonal matrix selected inversion algorithm.

PDIV/PairWise (P-Divisions)

@reference: https://doi.org/10.1063/1.2748621
@reference: https://doi.org/10.1063/1.3624612
@reference: https://doi.org/10.1007/978-3-319-78024-5_55

pdiv_localmap:

Specific implementation of PDIV/PairWise algorithm that leave the partitions on the processes and perform the update steps locally. Final results are scattered on the processes.