Release Notes

pyMOR 2019.2 (December 16, 2019)

We are proud to announce the release of pyMOR 2019.2! For this release we have worked hard to make implementing new models and reduction algorithms with pyMOR even easier. Further highlights of this release are an extended VectorArray interface with generic support for complex numbers, vastly extended and improved system-theoretic MOR methods, as well as builtin support for model outputs and parameter sensitivities.

Over 700 single commits have entered this release. For a full list of changes see here.

pyMOR 2019.2 contains contributions by Linus Balicki, Dennis Eickhorn and Tim Keil. See here for more details.

Release highlights

Implement new models and reductors more easily

As many users have been struggling with the notion of Discretization in pyMOR and to account for the fact that not every full-order model needs to be a discretized PDE model, we have decided to rename DiscretizationInterface to ModelInterface and all deriving classes accordingly [#568]. Consequently, the variable names m, rom, fom will now be found throughout pyMOR’s code to refer to an arbitrary Model, a reduced-order Model or a full-order Model.

Moreover, following the Zen of Python’s ‘Explicit is better than implicit’ and ‘Simple is better than complex’, we have completely revamped the implementation of Models and reductors to facilitate the implementation of new model types and reduction methods [#592]. In particular, the complicated and error-prone approach of trying to automatically correctly project the Operators of any given Model in GenericRBReductor and GenericPGReductor has been replaced by simple Model-adapted reductors which explicitly state with which bases each Operator shall be projected. As a consequence, we could remove the operators dict and the notion of special_operators in ModelBase, vastly simplifying its implementation and the definition of new Model classes.

Extended VectorArray interface with generic complex number support

The VectorArrayInterface has been extended to allow the creation of non-zero vectors using the ones and full methods [#612]. Vectors with random values can be created using the random method [#618]. All VectorArray implementations shipped with pyMOR support these new interface methods. As an important step to improve the support for system-theoretic MOR methods with external PDE solvers, we have implemented facilities to provide generic support for complex-valued VectorArrays even for PDE solvers that do not support complex vectors natively [#755].

Improved and extended support for system-theoretic MOR methods

To increase compatibility between input-output models in iosys and the InstationaryModel, support for models with parametric operators has been added [#626], which also enables implementation of parametric MOR methods for such models. Furthermore, the state_space attribute was removed in favor of solution_space [#648] to make more explicit the result of the solve method. Further improvements in naming has been renaming attributes n, m, and p to order, input_dim, and output_dim [#578] and the bode method to freq_resp [#729]. Reductors in bt and h2 received numerous improvements ([#656], [#661], [#807]) and variants of one-sided IRKA have been added [#579]. As for Lyapunov equations, a low-rank solver for Riccati equations has been added [#736].

Model outputs and parameter sensitivities

The notion of a Model’s output has been formally added to the ModelInterface [#750]: The output of a Model is defined to be a VectorArray of the model’s output_space VectorSpace and can be computed using the new output method. Alternatively, solve method can now be called with return_output=True to return the output alongside the state space solution.

To compute parameter sensitivities, we have added d_mu methods to OperatorInterface and ParameterFunctionalInterface which return the partial derivative with respect to a given parameter component [#748].

Additional new features

Extended FEniCS bindings

FEniCS support has been improved by adding support for nonlinear Operators including an implementation of restricted to enable fast local evaluation of the operator for efficient empirical interpolation [#819]. Moreover the parallel implementations of amax and dofs have been fixed [#616] and solver_options are now correctly handled in _assemble_lincomb [#812].

Improved greedy algorithms

pyMOR’s greedy algorithms have been refactored into weak_greedy and adaptive_weak_greedy functions that use a common WeakGreedySurrogate to estimate the approximation error and extend the greedy bases. This allows these functions to be used more flexible, e.g. for goal-oriented basis generation, by implementing a new WeakGreedySurrogate [#757].

Numerical linear algebra algorithms

By specifying return_R=True, the gram_schmidt algorithm can now also be used to compute a QR decomposition of a given VectorArray [#577]. Moreover, gram_schmidt can be used as a more accurate (but often more expensive) alternative for computing the pod of a VectorArray. Both, the older method-of-snapshots approach as well as the QR decomposition are now available for computing a truncated SVD of a VectorArray via the newly added svd_va module [#718]. Basic randomized algorithms for approximating the image of a linear Operator are implemented in the randrangefinder module [#665].

Support for low-rank operators

Low-rank Operators and as well as sums of arbitrary Operators with a low-rank Operator can now be represented by LowRankOperator and LowRankUpdatedOperator. For the latter, apply_inverse and apply_inverse_adjoint are implemented via the Sherman-Morrison-Woodbury formula [#743].

Improved string representations of pyMOR objects

Custom __str__ special methods have been implemented for all Model classes shipped with pyMOR [#652]. Moreover, we have added a generic __repr__ implementation to BasicInterface which recursively prints all class attributes corresponding to an __init__ argument (with a non-default value) [#706].

Easier working with immutable objects

A new check in ImmutableMeta enforces all __init__ arguments of an immutable object to be available as object attributes, thus ensuring that with_ works reliably with all immutable objects in pyMOR [#694]. To facilitate the initialization of these attributes in __init__ the __auto_init method has been added to BasicInterface [#732]. Finally, with_ now has a new_type parameter which allows to change the class of the object returned by it [#705].

project and assemble_lincomb are easier to extend

In pyMOR 0.5, we have introduced RuleTables to make central algorithms in pyMOR, like the projection of an Operator via project, easier to trace and extend. For pyMOR 2019.2, we have further simplified project by removing the product argument from the underlying RuleTable [#785]. As the inheritance-based implementation of assemble_lincomb was showing similar complexity issues as the old inheritance-based implementation of projected, we moved all backend-agnostic logic into the RuleTable-based free function assemble_lincomb, leaving the remaining backend code in _assemble_lincomb [#619].

Backward incompatible changes

Dropped Python 3.5 support

As Python 3.6 or newer now ships with the current versions of all major Linux distributions, we have decided to drop support for Python 3.6 in pyMOR 2019.2. This allows us to benefit from new language features, in particular f-strings and class attribute definition order preservation [#553], [#584].

Global RandomState

pyMOR now has a (mutable) global default RandomState. This means that when sample_randomly is called repeatedly without specifying a random_state or seed argument, different Parameter samples will be returned in contrast to the (surprising) previous behavior where the same samples would have been returned. The same RandomState is used by the newly introduced random method of the VectorArrayInterface [#620].

Further API Changes

pyMOR 0.5 (January 17, 2019)

After more than two years of development, we are proud to announce the release of pyMOR 0.5! Highlights of this release are support for Python 3, bindings for the NGSolve finite element library, new linear algebra algorithms, various VectorArray usability improvements, as well as a redesign of pyMOR’s projection algorithms based on RuleTables.

Especially we would like to highlight the addition of various system-theoretic reduction methods such as Balanced Truncation or IRKA. All algorithms are implemented in terms of pyMOR’s Operator and VectorArray interfaces, allowing their application to any model implemented using one of the PDE solver supported by pyMOR. In particular, no import of the system matrices is required.

Over 1,500 single commits have entered this release. For a full list of changes see here.

pyMOR 0.5 contains contributions by Linus Balicki, Julia Brunken and Christoph Lehrenfeld. See here for more details.

Release highlights

Python 3 support

pyMOR is now compatible with Python 3.5 or greater. Since the use of Python 3 is now standard in the scientific computing community and security updates for Python 2 will stop in less than a year (, we decided to no longer support Python 2 and make pyMOR 0.5 a Python 3-only release. Switching to Python 3 also allows us to leverage newer language features such as the @ binary operator for concatenation of Operators, keyword-only arguments or improved support for asynchronous programming.

System-theoretic MOR methods

With 386 commits, [#464] added systems-theoretic methods to pyMOR. Module pymor.discretizations.iosys contains new discretization classes for input-output systems, e.g. LTISystem, SecondOrderSystem and TransferFunction. At present, methods related to these classes mainly focus on continuous-time, non-parametric systems.

Since matrix equation solvers are important tools in many system-theoretic methods, support for Lyapunov, Riccati and Sylvester equations has been added in pymor.algorithms.lyapunov, pymor.algorithms.riccati and pymor.algorithms.sylvester. A generic low-rank ADI (Alternating Direction Implicit) solver for Lyapunov equations is implemented in pymor.algorithms.lradi. Furthermore, bindings to low-rank and dense solvers for Lyapunov and Riccati equations from SciPy, Slycot and Py-M.E.S.S. are provided in pymor.bindings.scipy, pymor.bindings.slycot and pymor.bindings.pymess. A generic Schur decomposition-based solver for sparse-dense Sylvester equations is implemented in pymor.algorithms.sylvester.

Balancing Truncation (BT) and Iterative Rational Krylov Algorithm (IRKA) are implemented in BTReductor and IRKAReductor. LQG and Bounded Real variants of BT are also available (LQGBTReductor, BRBTReductor). Bitangential Hermite interpolation (used in IRKA) is implemented in LTI_BHIReductor. Two-Sided Iteration Algorithm (TSIA), a method related to IRKA, is implemented in TSIAReductor.

Several structure-preserving MOR methods for second-order systems have been implemented. Balancing-based MOR methods are implemented in pymor.reductors.sobt, bitangential Hermite interpolation in SO_BHIReductor and Second-Order Reduced IRKA (SOR-IRKA) in SOR_IRKAReductor.

For more general transfer functions, MOR methods which return LTISystems are also available. Bitangential Hermite interpolation is implemented in TFInterpReductor and Transfer Function IRKA (TF-IRKA) in TF_IRKAReductor.

Usage examples can be found in the heat and string_equation demo scripts.

NGSolve support

We now ship bindings for the NGSolve finite element library. Wrapper classes for VectorArrays and matrix-based Operators can be found in the pymor.bindings.ngsolve module. A usage example can be found in the thermalblock_simple demo script.

New linear algebra algorithms

pyMOR now includes an implementation of the HAPOD algorithm for fast distributed or incremental computation of the Proper Orthogonal Decomposition (pymor.algorithms.hapod). The code allows for arbitrary sub-POD trees, on-the-fly snapshot generation and shared memory parallelization via concurrent.futures. A basic usage example can be found in the hapod demo script.

In addition, the Gram-Schmidt biorthogonalization algorithm has been included in pymor.algorithms.gram_schmidt.

VectorArray improvements

VectorArrays in pyMOR have undergone several usability improvements:

  • The somewhat dubious concept of a subtype has been superseded by the concept of VectorSpaces which act as factories for VectorArrays. In particular, instead of a subtype, VectorSpaces can now hold meaningful attributes (e.g. the dimension) which are required to construct VectorArrays contained in the space. The id attribute allows to differentiate between technically identical but mathematically different spaces [#323].

  • VectorArrays can now be indexed to select a subset of vectors to operate on. In contrast to advanced indexing in NumPy, indexing a VectorArray will always return a view onto the original array data [#299].

  • New methods with clear semantics have been introduced for the conversion of VectorArrays to (to_numpy) and from (from_numpy) NumPy arrays [#446].

  • Inner products between VectorArrays w.r.t. to a given inner product Operator or their norm w.r.t. such an operator can now easily be computed by passing the Operator as the optional product argument to the new inner and norm methods [#407].

  • The components method of VectorArrays has been renamed to the more intuitive name dofs [#414].

  • The l2_norm2 and norm2 have been introduced to compute the squared vector norms [#237].

RuleTable based algorithms

In pyMOR 0.5, projection algorithms are implemented via recursively applied tables of transformation rules. This replaces the previous inheritance-based approach. In particular, the projected method to perform a (Petrov-)Galerkin projection of an arbitrary Operator has been removed and replaced by a free project function. Rule-based algorithms are implemented by deriving from the RuleTable base class [#367], [#408].

This approach has several advantages:

  • Rules can match based on the class of the object, but also on more general conditions, e.g. the name of the Operator or being linear and non-parametric.

  • The entire mathematical algorithm can be specified in a single file even when the definition of the possible classes the algorithm can be applied to is scattered over various files.

  • The precedence of rules is directly apparent from the definition of the RuleTable.

  • Generic rules (e.g. the projection of a linear non-parametric Operator by simply applying the basis) can be easily scheduled to take precedence over more specific rules.

  • Users can implement or modify RuleTables without modification of the classes shipped with pyMOR.

Additional new features

  • Reduction algorithms are now implemented using mutable reductor objects, e.g. GenericRBReductor, which store and extend the reduced bases onto which the model is projected. The only return value of the reductor’s reduce method is now the reduced discretization. Instead of a separate reconstructor, the reductor’s reconstruct method can be used to reconstruct a high-dimensional state-space representation. Additional reduction data (e.g. used to speed up repeated reductions in greedy algorithms) is now managed by the reductor [#375].

  • Linear combinations and concatenations of Operators can now easily be formed using arithmetic operators [#421].

  • The handling of complex numbers in pyMOR is now more consistent. See [#458], [#362], [#447] for details. As a consequence of these changes, the rhs Operator in StationaryDiscretization is now a vector-like Operator instead of a functional.

  • The analytical problems and discretizers of pyMOR’s discretization toolbox have been reorganized and improved. All problems are now implemented as instances of StationaryProblem or InstationaryProblem, which allows an easy exchange of data Functions of a predefined problem with user-defined Functions. Affine decomposition of Functions is now represented by specifying a LincombFunction as the respective data function [#312], [#316], [#318], [#337].

  • The pymor.core.config module allows simple run-time checking of the availability of optional dependencies and their versions [#339].

  • Packaging improvements

    A compiler toolchain is no longer necessary to install pyMOR as we are now distributing binary wheels for releases through the Python Package Index (PyPI). Using the extras_require mechanism the user can select to install either a minimal set:

    pip install pymor

    or almost all, including optional, dependencies:

    pip install pymor[full]

    A docker image containing all of the discretization packages pyMOR has bindings to is available for demonstration and development purposes:

    docker run -it pymor/demo:0.5 pymor-demo -h
    docker run -it pymor/demo:0.5 pymor-demo thermalblock --fenics 2 2 5 5

Backward incompatible changes

  • dim_outer has been removed from the grid interface [#277].

  • All wrapper code for interfacing with external PDE libraries or equation solvers has been moved to the pymor.bindings package. For instance, FenicsMatrixOperator can now be found in the pymor.bindings.fenics module. [#353]

  • The source and range arguments of the constructor of ZeroOperator have been swapped to comply with related function signatures [#415].

  • The identifiers discretization, rb_discretization, ei_discretization have been replaced by d, rd, ei_d throughout pyMOR [#416].

  • The _matrix attribute of NumpyMatrixOperator has been renamed to matrix [#436]. If matrix holds a NumPy array this array is automatically made read-only to prevent accidental modification of the Operator [#462].

  • The BoundaryType class has been removed in favor of simple strings [#305].

  • The complicated and unused mapping of local parameter component names to global names has been removed [#306].

Further notable improvements

pyMOR 0.4 (September 28, 2016)

With the pyMOR 0.4 release we have changed the copyright of pyMOR to

Copyright 2013-2016 pyMOR developers and contributors. All rights reserved.

Moreover, we have added a Contribution guideline to help new users with starting to contribute to pyMOR. Over 800 single commits have entered this release. For a full list of changes see here. pyMOR 0.4 contains contributions by Andreas Buhr, Michael Laier, Falk Meyer, Petar Mlinarić and Michael Schaefer. See here for more details.

Release highlights

FEniCS and deal.II support

pyMOR now includes wrapper classes for integrating PDE solvers written with the dolfin library of the FEniCS project. For a usage example, see pymordemos.thermalblock_simple.discretize_fenics. Experimental support for deal.II can be found in the pymor-deal.II repository of the pyMOR GitHub organization.

Parallelization of pyMOR’s reduction algorithms

We have added a parallelization framework to pyMOR which allows parallel execution of reduction algorithms based on a simple WorkerPool interface [#14]. The greedy [#155] and ei_greedy algorithms [#162] have been refactored to utilize this interface. Two WorkerPool implementations are shipped with pyMOR: IPythonPool utilizes the parallel computing features of IPython, allowing parallel algorithm execution in large heterogeneous clusters of computing nodes. MPIPool can be used to benefit from existing MPI-based parallel HPC computing architectures [#161].

Support classes for MPI distributed external PDE solvers

While pyMOR’s VectorArray, Operator and Discretization interfaces are agnostic to the concrete (parallel) implementation of the corresponding objects in the PDE solver, external solvers are often integrated by creating wrapper classes directly corresponding to the solvers data structures. However, when the solver is executed in an MPI distributed context, these wrapper classes will then only correspond to the rank-local data of a distributed VectorArray or Operator.

To facilitate the integration of MPI parallel solvers, we have added MPI helper classes [#163] in pymor.vectorarrays.mpi, pymor.operators.mpi and pymor.discretizations.mpi that allow an automatic wrapping of existing sequential bindings for MPI distributed use. These wrapper classes are based on a simple event loop provided by, which is used in the interface methods of the wrapper classes to dispatch into MPI distributed execution of the corresponding methods on the underlying MPI distributed objects.

The resulting objects can be used on MPI rank 0 (including interactive Python sessions) without any further changes to pyMOR or the user code. For an example, see pymordemos.thermalblock_simple.discretize_fenics.

New reduction algorithms

  • adaptive_greedy uses adaptive parameter training set refinement according to [HDO11] to prevent overfitting of the reduced model to the training set [#213].

  • reduce_parabolic reduces linear parabolic problems using reduce_generic_rb and assembles an error estimator similar to [GP05], [HO08]. The parabolic_mor demo contains a simple sample application using this reductor [#190].

  • The estimate_image and estimate_image_hierarchical algorithms can be used to find an as small as possible space in which the images of a given list of operators for a given source space are contained for all possible parameters mu. For possible applications, see reduce_residual which now uses estimate_image_hierarchical for Petrov-Galerkin projection of the residual operator [#223].

Copy-on-write semantics for VectorArrays

The copy method of the VectorArray interface is now assumed to have copy-on-write semantics. I.e., the returned VectorArray will contain a reference to the same data as the original array, and the actual data will only be copied when one of the arrays is changed. Both NumpyVectorArray and ListVectorArray have been updated accordingly [#55]. As a main benefit of this approach, immutable objects having a VectorArray as an attribute now can safely create copies of the passed VectorArrays (to ensure the immutability of their state) without having to worry about unnecessarily increased memory consumption.

Improvements to pyMOR’s discretizaion tookit

  • An unstructured triangular Grid is now provided by UnstructuredTriangleGrid. Such a Grid can be obtained using the discretize_gmsh method, which can parse Gmsh output files. Moreover, this method can generate Gmsh input files to create unstructured meshes for an arbitrary PolygonalDomain [#9].

  • Basic support for parabolic problems has been added. The discretize_parabolic_cg and discretize_parabolic_fv methods can be used to build continuous finite element or finite volume Discretizations from a given pymor.analyticalproblems.parabolic.ParabolicProblem. The parabolic demo demonstrates the use of these methods [#189].

  • The pymor.discretizers.disk module contains methods to create stationary and instationary affinely decomposed Discretizations from matrix data files and an .ini file defining the given problem.

  • EllipticProblems can now also contain advection and reaction terms in addition to the diffusion part. discretize_elliptic_cg has been extended accordingly [#211].

  • The continuous Galerkin module has been extended to support Robin boundary conditions [#110].

  • BitmapFunction allows to use grayscale image data as data Functions [#194].

  • For the visualization of time-dependent data, the colorbars can now be rescaled with each new frame [#91].

Caching improvements

  • state id generation is now based on deterministic pickling. In previous version of pyMOR, the state id of immutable objects was computed from the state ids of the parameters passed to the object’s __init__ method. This approach was complicated and error-prone. Instead, we now compute the state id as a hash of a deterministic serialization of the object’s state. While this approach is more robust, it is also slightly more expensive. However, due to the object’s immutability, the state id only has to be computed once, and state ids are now only required for storing results in persistent cache regions (see below). Computing such results will usually be much more expensive than the state id calculation [#106].

  • CacheRegions now have a persistent attribute indicating whether the cache data will be kept between program runs. For persistent cache regions the state id of the object for which the cached method is called has to be computed to obtain a unique persistent id for the given object. For non-persistent regions the object’s uid can be used instead. pymor.core.cache_regions now by default contains 'memory', 'disk' and 'persistent' cache regions [#182], [#121] .

  • defaults can now be marked to not affect state id computation. In previous version of pyMOR, changing any default value caused a change of the state id pyMOR’s defaults dictionary, leading to cache misses. While this in general is desirable, as, for instance, changed linear solver default error tolerances might lead to different solutions for the same Discretization object, it is clear for many I/O related defaults, that these will not affect the outcome of any computation. For these defaults, the defaults decorator now accepts a sid_ignore parameter, to exclude these defaults from state id computation, preventing changes of these defaults causing cache misses [#81].

  • As an alternative to using the @cached decorator, cached_method_call can be used to cache the results of a function call. This is now used in solve to enable parsing of the input parameter before it enters the cache key calculation [#231].

Additional new features

Backward incompatible changes

  • VectorArray implementations have been moved to the pymor.vectorarrays sub-package [#89].

  • The dot method of the VectorArray interface has been split into dot and pairwise_dot [#76].

    The pairwise parameter of dot has been removed, always assuming pairwise == False. The method pairwise_dot corresponds to the pairwise == True case. Similarly the pariwise parameter of the apply2 method of the Operator interface has been removed and a pairwise_apply2 method has been added.

  • almost_equal has been removed from the VectorArray interface [#143].

    As a replacement, the new method pymor.algorithms.basic.almost_equal can be used to compare VectorArrays for almost equality by the norm of their difference.

  • lincomb has been removed from the Operator interface [#83].

    Instead, a LincombOperator should be directly instantiated.

  • Removal of the options parameter of apply_inverse in favor of solver_options attribute [#122].

    The options parameter of OperatorInterface.apply_inverse has been replaced by the solver_options attribute. This attribute controls which fixed (linear) solver options are used when apply_inverse is called. See here for more details.

  • Renaming of reductors for coercive problems [#224].

    pymor.reductors.linear.reduce_stationary_affine_linear and pymor.reductors.stationary.reduce_stationary_coercive have been renamed to pymor.reductors.coercive.reduce_coercive and pymor.reductors.coercive.reduce_coercive_simple. The old names are deprecated and will be removed in pyMOR 0.5.

  • Non-parametric objects have now parameter_type {} instead of None [#84].

  • Sampling methods of ParameterSpaces now return iterables instead of iterators [#108].

  • Caching of solve is now disabled by default [#178].

    Caching of solve must now be explicitly enabled by using pymor.core.cache.CacheableInterface.enable_caching.

  • The default value for extension_algorithm parameter of greedy has been removed [#82].

  • Changes to ei_greedy [#159], [#160].

    The default for the projection parameter has been changed from 'orthogonal' to 'ei' to let the default algorithm agree with literature. In addition a copy parameter with default True has been added. When copy is True, the input data is copied before executing the algorithm, ensuring, that the original VectorArray is left unchanged. When possible, copy should be set to False in order to reduce memory consumption.

  • The copy parameter of pymor.algorithms.gram_schmidt.gram_schmidt now defaults to True [#123].

  • with_ has been moved from BasicInterface to ImmutableInterface [#154].

  • BasicInterface.add_attributes has been removed [#158].

  • Auto-generated names no longer contain the uid [#198].

    The auto-generated name of pyMOR objects no longer contains their uid. Instead, the name is now simply set to the class name.

  • Python fallbacks to Cython functions have been removed [#145].

    In order to use pyMOR’s discretization toolkit, building of the _unstructured, inplace, relations Cython extension modules is now required.

pyMOR 0.3 (March 2, 2015)

  • Introduction of the vector space concept for even simpler integration with external solvers.

  • Addition of a generic Newton algorithm.

  • Support for Jacobian evaluation of empirically interpolated operators.

  • Greatly improved performance of the EI-Greedy algorithm. Addition of the DEIM algorithm.

  • A new algorithm for residual operator projection and a new, numerically stable a posteriori error estimator for stationary coercive problems based on this algorithm. (cf. A. Buhr, C. Engwer, M. Ohlberger, S. Rave, ‘A numerically stable a posteriori error estimator for reduced basis approximations of elliptic equations’, proceedings of WCCM 2014, Barcelona, 2014.)

  • A new, easy to use mechanism for setting and accessing default values.

  • Serialization via the pickle module is now possible for each class in pyMOR. (See the new ‘analyze_pickle’ demo.)

  • Addition of generic iterative linear solvers which can be used in conjunction with any operator satisfying pyMOR’s operator interface. Support for least squares solvers and PyAMG (

  • An improved SQLite-based cache backend.

  • Improvements to the built-in discretizations: support for bilinear finite elements and addition of a finite volume diffusion operator.

  • Test coverage has been raised from 46% to 75%.

Over 500 single commits have entered this release. A full list of all changes can be obtained under the following address:…0.3.0