Trilinos/Tpetra: Templated Linear Algebra Services Package.

Development

Introduction

Tpetra is an attempt at applying generic algorithm techniques to the serial and parallel linear algebra libraries of Epetra. It is hoped that Tpetra will complement Epetra by providing an alternative foundation for future Trilinos solvers. The lessons learned and discoveries made while creating Tpetra are also being applied to improving their Epetra cousins.

Tpetra provides the same functionality as Epetra: the fundamental construction routines and services functions that are required for serial and parallel linear algebra libraries. Unlike Epetra, Tpetra makes extensive use of templates and the Standard Template Library (STL). This provides numerous benefits, including the ability to template the Ordinal and Scalar fields on any well-defined types, and automatic resource allocation.

Overview of Tpetra.

Templated Types in Tpetra

All classes in Tpetra utilize templates, which allows the user to specify any type they want.

1. PacketType: The most generic type. A PacketType is any built-in type, struct, or class that can be communicated between nodes. Generally this is the same as the ScalarType.

2. OrdinalType: The next-most generic type. An OrdinalType is primarily used for ordering, such as labeling the indices in a matrix or vector. This is typically int or long int.

3. ScalarType: The least generic type. A ScalarType is the data structure used for storing values. This is typically double, float, complex<double> or complex<float>.

The flexibility of Tpetra comes from the fact that the above-mentioned examples are not the only possibilities. As long as they implement a few basic operations and traits, any class can be used as a PacketType, OrdinalType, or ScalarType. You could, for example, use radians as an OrdinalType, or use 3x3 matrices as a ScalarType.

More information can be found in the documentation for Tpetra::PacketTraits, Teuchos::OrdinalTraits, and Teuchos::ScalarTraits.

Tpetra Classes

Tpetra contains a number of classes. They can be categorized as follows:

• Primary parallel user classes. These are typically the most important classes for most users.
  1. Communication classes: Tpetra::Platform, Tpetra::Comm, and Tpetra::Distributor - Platform contains specific information about the parallel machine we are using. Comm provides collective operations, and Distributor provides point-to-point communication. Currently only supports serial operation, but an MPI version is in development.

  2. Mapping classes: Tpetra::ElementSpace, Tpetra::BlockElementSpace and Tpetra::VectorSpace - Contain information used to distribute vectors, matrices and other objects.

  3. Vector class: Tpetra::Vector - Provides vector services such as scaling, norms, and dot products. Is also used in conjunction with Tpetra::CisMatrix for matrix-vector computations.

  4. Sparse matrix class: Tpetra::CisMatrix - Compressed Index Space Matrix. Can be either row-oriented or column-oriented.

  5. Import/Export classes: Tpetra::Import and Tpetra::Export - Constructed from two ElementSpace objects. Allows efficient transfer of objects built using one mapping to a new object with a new mapping. Supports local and global permutations, overlapping Schwarz operations and many other data movement algorithms.

• Utility classes.
  1. Distributed directory class: Tpetra::Directory - Allows construction of a distributed directory. Once constructed, a directory allows one to access randomly distributed objects in an efficient, scalable manner. This class is intended for support of general ElementSpace and BlockElementSpace objects, but is useful in other settings as well.

  2. Traits class: Tpetra::PacketTraits - Much like Teuchos's ScalarTraits and OrdinalTraits. It provides information needed to transfer data on a parallel machine, such as the amount of memory needed to represent a variable of a given type.

Trilinos and Tpetra

Tpetra can be used as a stand-alone package. However, in the future it will also provides the foundation for Trilinos. Trilinos is a collection of solver packages, such as AztecOO and TSF. But as Tpetra is not yet completed, it is suggested that for the time being, Epetra be used in conjunction with other Trilinos packages instead.

---