Resolvent4py

resolvent4py is a parallel Python toolbox to perform analysis, model reduction and control of high-dimensional linear systems. It relies on mpi4py for multi-processing parallelism, and it leverages the functionalities and data structures provided by petsc4py and slepc4py. The goal of this project is to provide users with a friendly python-like experience, while also leveraging the high-performance and parallel-computing capabilities of the PETSc and SLEPc libraries. The core of the package is an abstract class, called LinearOperator, which serves as a blueprint for user-defined child classes that can be used to define any linear operator. resolvent4py currently ships with 5 linear operator subclasses:

• MatrixLinearOperator
• LowRankLinearOperator
• LowRankUpdatedLinearOperator
• ProjectionLinearOperator
• ProductLinearOperator

Once a linear operator is instantiated, resolvent4py currently allows for several analyses, including:

• Right and left eigendecomposition using Arnoldi iteration (with shift and invert)
• (Randomized) singular value decomposition (SVD)
• Resolvent analysis via randomized SVD (algebraic and with time stepping)
• Harmonic resolvent analysis via algebraic randomized SVD
• Balanced truncation for time-invariant linear systems using frequential Gramians

Additional functionalities (found in resolvent4py/utils) and available to the user through the resolvent4py namespace are:

• Support for parallel I/O through petsc4py
• Support for MPI communications using mpi4py
• Support for manipulation of PETSc matrices/vector and SLEPc BVs

Documentation

Click here.

Dependencies

• Python>=3.10
• numpy
• scipy
• matplotlib
• mpi4py
• petsc4py >= 3.20 (must be installed from source, see below)
• slepc4py >= 3.20 (must be installed from source, see below)

Installation instructions

Installing PETSc, SLEPc, petsc4py and slepc4py

Note
If you have an existing parallel build of PETSc and SLEPc and their 4py counterparts configured with complex scalars (i.e., --with-scalar-type=complex) and with MUMPS (i.e., --download-mumps) you can skip this subsection and go directly to "Installing resolvent4py and building the documentation".

All the dependencies above can be installed straightforwardly with pip, except for petsc4py and slepc4py whose installation is easier if PETSc and SLEPc are built from source.

• We recommend creating a clean Python environment.
• Download PETSc. Any version >= 3.20.0 should work. (The latest version that we tested is 3.23.3.)
• Configure PETSc using the command below,

  ./configure PETSC_ARCH=resolvent4py_arch --download-fblaslapack 
  --download-mumps --download-scalapack --download-parmetis 
  --download-metis --download-ptscotch --with-scalar-type=complex 
  --with-debugging=0 COPTFLAGS=-O3 CXXOPTFLAGS=-O3 FOPTFLAGS=-O3
  

  If some of the libraries above (e.g., scalapack, metis, etc.) are already available to the user, then see the PETSc configuration guidelines for details on how to link against them.
• Follow the PETSc instructions (provided during the configuration step) to build the library. Then make sure to export the environment variables PETSC_DIR and PETSC_ARCH.
• Install SLEPc. Any version >= 3.20.0 should work. (The latest version that we tested was 3.23.1.)
• Install mpi4py, petsc4py and slepc4py

  pip install mpi4py petsc4py==petsc-version slepc4py==slepc-version
  

• Ensure that the installation was successful by running

  python -c "from mpi4py import MPI"
  python -c "from petsc4py import PETSc"
  python -c "from slepc4py import SLEPc"
  

Installing resolvent4py

• Install resolvent4py with

      pip install resolvent4py
  

• Alternatively, clone the repository into the local directory resolvent4py, navigate to it and run

      pip install resolvent4py