iterative-solver

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Overview

Implements iterative solvers for linear and non-linear problems and distributed arrays for HPC. The solvers are specialised to work with specific data types, but are also templated on the container allowing for easy integration into existing software.

List of key features:

• Implements iterative solvers for eigenvalue problem, linear equations, optimisation (L-BFGS) and non-linear equations (DIIS)
• Novel algorithms including P-space and D-space (see paper)
• Structured to allow easy addition of new solvers or modification of the current ones without changes to the user's code
• Templated on container for easy integration into existing programs
  • User defined containers can be used without modification with the help of array handler abstraction
• Specialised for double and complex value types, so that all heavy numerical operations are only compiled once
• Provides distributed arrays in memory and on disk for HPC
• Contains Fortran and C wrappers

Installation

CMake is used to build the library and it can integrate easily with other CMake builds.

include(FetchContent)
FetchContent_Declare(
        iterative-solver
        GIT_REPOSITORY https://github.com/molpro/iterative-solver.git
        GIT_TAG ${COMMIT_HASH_OR_TAG_VALUE})
FetchContent_MakeAvailable(iterative-solver)
target_link_libraries(${YOUR_LIBRARY_NAME} PUBLIC molpro::iterative-solver)

Usage

Interfaces

There is a hierarchy of abstract classes defined in molpro/linalg/itsolv/IterativeSolver.h with IterativeSolver defining the interface for common functionality and LinearEigensystem, LinearEquations, Optimize and NonLinearEquations defining functions that are specific to each type of solver. They are provided to reduce header bloat in user's code.

Each type of solver has at least one implementation class, e.g. LinearEigensystemDavidson in molpro/linalg/itsolv/LinearEigensystemDavidson.h, which implements the full interface. The library is designed to make it easy to add new iterative solvers, so there might be more than one implementation.

Example

The simplest way to use the library is to call solve() and pass a function for getting the action of the matrix on parameter set. Here is an example of using LinearEigensystem with Davidson preconditioner,

#include <molpro/linalg/itsolv/LinearEigensystem.h>
// ...
using molpro::linalg::itsolv::LinearEigensystem;
using R = std::vector<double>;
using Q = std::vector<double>;
LinearEigensystemDavdison<R, Q> solver{};
auto [x, g] = get_initial_parameters_and_action();
solver.set_preconditioner_davidson(get_diagonal_matrix_elements());
solver.solve(x, g, user_specified_action_function);
if (!solver.converged()){
    // deal with the unconverged case
}

More advanced users can copy and modify the code in solve() to tailor it for their own use, see implementation in molpro/linalg/itsolv/IterativeSolverTemplate.h.

Containers and array handlers

In many programs there are special containers for storing the vectors and operating on them. This might be for efficiency reasons, e.g. exploiting symmetry of the problem, or for collecting metadata, e.g. memory usage and operation count. In either case, The code is templated on container types to ease adaptation.

To avoid the code-bloat of header only libraries all of the numerically intensive work is specialised for double and std::complex<double> types. This makes recompilation of IterativeSolver with different container types very fast.

There are 3 types of containers:

• R — working set container
  • fast access to elements
  • used sparingly to preserve memory
• Q — slow container
  • slow access to elements
  • used for most of the subspace
  • usually on disk where there is lots of storage space
• P — sparse container
  • light-weight sparse container (e.g. std::map<size_t, double>)

IterativeSolver does not modify containers directly instead using ArrayHandler for all array related operations. This allows for only modest restrictions on containers:

• must have a move constructor

• must have conforming element type (currently double and std::complex<double>, but this can be easily extended)

ArrayHandler is an abstract class used by IterativeSolver to perform copy and linear algebra operations (dot, axpy). iterative-solver provides implementations for Iterable containers (e.g. std::vector), distributed containers (e.g. molpro::linalg::array::DistrArray), and mapped containers (e.g. std::map). However, some users might need/want to provide their own implementations.

Citing

Any publications resulting from this work should cite relevant papers in CITE.txt

List of Contributors

Peter Knowles

Marat Sibaev

Iakov Polyak

Rob Welch