mumps

The mumps solver supports the following input types.

• data type: DSZC
• index type: std::int32_t (32-bit, typically int)

MUMPS supports both 32-bit and 64-bit integer indexing. There are some caveats.

1. If 64-bit integer is enabled via MUMPS_INTSIZE64, all integers are 64-bit, thus MKL and MPI need to use 64-bit integer for indexing as well. This may cause compatibility problems as 1) MPI with 64-bit integer may not be available on various platforms, 2) other libraries may only need linkage to conventional 32-bit version.
2. Even if 64-bit integer is not enabled, MUMPS uses 64-bit integer for nnz, thus as long as the size of the matrix does not exceed 2 billion, the 32-bit integer version is sufficient.

To allow maximum compatibility, MUMPS_INTSIZE64 is not enabled, even if EZP_USE_64BIT_INT is switched on. Thus the underlying mumps library needs to be linked to 32-bit ScaLAPACK and MPI.

Solver Options

There are two ways to configure the solver.

Member Methods

The operator() operator provides access to icntl array. There are explicitly named memeber methods, which give the same functionality.

solver(3) = 1;
solver.icntl_printing_level(1);

When using the explicit methods, it is possible to chain multiple methods together.

solver.icntl_printing_level(1).icntl_iterative_refinement(2);

Verbose String Arguments

The mumps.parser.hpp provides a parsing function. Setting parameters can be done via the following.

#include <ezp/mumps.parser.hpp>

mumps_set("--printing-level 1 --iterative-refinement 2", solver);

All available options are listed as follows.

Usage: mumps [--output-error-message INT] [--output-diagnostic-statistics-warning INT] [--output-global-information INT] [--printing-level INT] [--permutation-and-scaling INT] [--symmetric-permutation INT] [--scaling-strategy INT] [--transpose-matrix INT] [--iterative-refinement INT] [--error-analysis INT] [--ordering-strategy INT] [--root-parallelism INT] [--working-space-percentage-increase INT] [--compression-block-format INT] [--openmp-threads INT] [--distribution-strategy-input INT] [--schur-complement INT] [--distribution-strategy-solution INT] [--out-of-core INT] [--maximum-working-memory INT] [--null-pivot-row-detection INT] [--deficient-and-null-space-basis INT] [--schur-complement-solution INT] [--rhs-block-size INT] [--ordering-computation INT] [--inverse-computation INT] [--forward-elimination INT] [--determinant-computation INT] [--out-of-core-file INT] [--blr INT] [--blr-variant INT] [--blr-compression INT] [--lu-compression-rate INT] [--block-compression-rate INT] [--tree-parallelism INT] [--compact-working-space INT] [--rank-revealing-factorization INT] [--symbolic-factorization INT]

Optional arguments:
  --output-error-message INT                  [1] output stream for error messages. [default: 6]
  --output-diagnostic-statistics-warning INT  [2] output stream for diagnostic printing and statistics local to each MPI process. [default: 0]
  --output-global-information INT             [3] output stream for global information, collected on the host. [default: 6]
  --printing-level INT                        [4] level of printing for error, warning, and diagnostic messages. [default: 2]
  --permutation-and-scaling INT               [6] permutes the matrix to a zero-free diagonal and/or scale the matrix. [default: 7]
  --symmetric-permutation INT                 [7] computes a symmetric permutation (ordering) to determine the pivot order to be used for the factorization in case of sequential analysis. [default: 7]
  --scaling-strategy INT                      [8] describes the scaling strategy. [default: 77]
  --transpose-matrix INT                      [9] computes the solution using A or transpose of A. [default: 1]
  --iterative-refinement INT                  [10] applies the iterative refinement to the computed solution. [default: 0]
  --error-analysis INT                        [11] computes statistics related to an error analysis of the linear system solved. [default: 0]
  --ordering-strategy INT                     [12] defines an ordering strategy for symmetric matrices and is used, in conjunction with ICNTL(6), to add constraints to the ordering algorithm. [default: 0]
  --root-parallelism INT                      [13] controls the parallelism of the root node (enabling or not the use of ScaLAPACK) and also its splitting. [default: 0]
  --working-space-percentage-increase INT     [14] controls the percentage increase in the estimated working space. [default: 30]
  --compression-block-format INT              [15] exploits compression of the input matrix resulting from a block format. [default: 0]
  --openmp-threads INT                        [16] controls the setting of the number of OpenMP threads by MUMPS when the setting of multithreading is not possible outside MUMPS. [default: 0]
  --distribution-strategy-input INT           [18] defines the strategy for the distributed input matrix. [default: 0]
  --schur-complement INT                      [19] computes the Schur complement matrix. [default: 0]
  --distribution-strategy-solution INT        [21] determines the distribution (centralized or distributed) of the solution vectors. [default: 0]
  --out-of-core INT                           [22] controls the in-core/out-of-core (OOC) factorization and solve. [default: 0]
  --maximum-working-memory INT                [23] corresponds to the maximum size of the working memory in MB that MUMPS can allocate per working process. [default: 0]
  --null-pivot-row-detection INT              [24] controls the detection of "null pivot rows". [default: 0]
  --deficient-and-null-space-basis INT        [25] allows the computation of a solution of a deficient matrix and also of a null space basis. [default: 0]
  --schur-complement-solution INT             [26] drives the solution phase if a Schur complement matrix has been computed. [default: 0]
  --rhs-block-size INT                        [27] controls the blocking size for multiple right-hand sides. [default: -32]
  --ordering-computation INT                  [28] determines whether a sequential or parallel computation of the ordering is performed. [default: 0]
  --inverse-computation INT                   [30] computes a user-specified set of entries in the inverse of the original matrix. [default: 0]
  --forward-elimination INT                   [32] performs the forward elimination of the right-hand sides during the factorization. [default: 0]
  --determinant-computation INT               [33] computes the determinant of the input matrix. [default: 0]
  --out-of-core-file INT                      [34] controls the conservation of the OOC files. [default: 0]
  --blr INT                                   [35] controls the activation of the BLR feature. [default: 0]
  --blr-variant INT                           [36] controls the choice of BLR factorization variant. [default: 0]
  --blr-compression INT                       [37] controls the BLR compression of the contribution blocks. [default: 0]
  --lu-compression-rate INT                   [38] estimates compression rate of LU factors. [default: 600]
  --block-compression-rate INT                [39] estimates compression rate of contribution blocks. [default: 500]
  --tree-parallelism INT                      [48] controls multithreading with tree parallelism. [default: 1]
  --compact-working-space INT                 [49] compacts workarray at the end of factorization phase. [default: 0]
  --rank-revealing-factorization INT          [56] detects pseudo-singularities during factorization and factorizes the root node with a rank-revealing method. [default: 0]
  --symbolic-factorization INT                [58] defines options for symbolic factorization. [default: 2]