# Basic Linear Algebra

uBLAS is a C++ template class library that provides BLAS level 1, 2, 3 functionality for dense, packed and sparse matrices. The design and implementation unify mathematical notation via operator overloading and efficient code generation via expression templates.

## Functionality

uBLAS provides templated C++ classes for dense, unit and sparse vectors, dense, identity, triangular, banded, symmetric, hermitian and sparse matrices. Views into vectors and matrices can be constructed via ranges or slices and adaptor classes. The library covers the usual basic linear algebra operations on vectors and matrices: reductions like different norms, addition and subtraction of vectors and matrices and multiplication with a scalar, inner and outer products of vectors, matrix vector and matrix matrix products and triangular solver. The glue between containers, views and expression templated operations is a mostly STL conforming iterator interface.

Known limitations:

- The implementation assumes a linear memory address model.
- Tuning was focussed on dense matrices.

## Documentation

- Overview
  - Overview of Matrix- and Vector-Types
  - Overview of Matrix and Vector Operations
  - Effective uBLAS and further information
- Expression Concepts
  - Scalar Expression
  - Vector Expression
  - Matrix Expression
- Container Concepts
  - Vector
  - Matrix
- Iterator Concepts
  - Indexed Bidirectional Iterator
  - Indexed Random Access Iterator
  - Indexed Bidirectional Column/Row Iterator
  - Indexed Random Access Column/Row Iterator
- Storage
  - Unbounded Array
  - Bounded Array
  - Range
  - Slice
- Sparse Storage
  - Default Standard Map
  - Map Array
- Vector
  - Vector
  - Unit Vector
  - Zero Vector
  - Scalar Vector
- Sparse Vector
  - Sparse Vector
  - Compressed Vector
  - Coordinate Vector
- Vector Proxies
  - Vector Range
  - Vector Slice
- Vector Expressions
  - Vector Expression
  - Vector References
  - Vector Operations
  - Vector Reductions
- Matrix
  - Matrix
  - Identity Matrix
  - Zero Matrix
  - Scalar Matrix
- Triangular Matrix
  - Triangular Matrix
  - Triangular Adaptor
- Symmetric Matrix
  - Symmetric Matrix
  - Symmetric Adaptor
- Hermitian Matrix
  - Hermitian Matrix
  - Hermitian Adaptor
- Banded Matrix
  - Banded Matrix
  - Banded Adaptor
- Sparse Matrix
  - Sparse Matrix
  - Compressed Matrix
  - Coordinate Matrix
- Matrix Proxies
  - Matrix Row
  - Matrix Column
  - Vector Range
  - Vector Slice
  - Matrix Range
  - Matrix Slice
- Matrix Expressions
  - Matrix Expression
  - Matrix References
  - Matrix Operations
  - Matrix Vector Operations
  - Matrix Matrix Operations
- Operations & Functions
  - Special Products
  - BLAS

## Supported Platforms

The original development platform for uBLAS we used MSVC 6.0 with Dinkumware STL. Compilers known to accept the library are:

- MSVC 6.0, 7.0, 7.1
- GCC 2.95.x, 3.0.x, 3.1.x, 3.2.x, 3.3.x, 3.4.x
- ICC 7.0, 7.1 8.0
- Comeau 4.2.x
- MWCW 8.3, 9.3

For possible problems please consult the Boost regression tests.

## Further Information

### Documentation and Discussion

Visit the Effective uBLAS wiki for up to date information and contributions.

There is also an active uBLAS development mailing list where user and development questions are answered.

### uBLAS and Boost Project

uBLAS development takes place on the Boost CVS on Sourceforge. You can view the Boost CVS archive directly. You will find the library here. Documentation and test programs reside here.

Bugs are tracked via a seperate Sourcefourge "http://sourceforge.net/projects/ublas">uBLAS project.

### Project Location and Download

The latest stable release of uBLAS is part of the Boost libraries.

## Authors and Credits

uBLAS initially was written by Joerg Walter and Mathias Koch. We would like to thank all, which supported and contributed to the development of this library: David Abrahams, Ed Brey, Fernando Cacciola, Juan Jose Gomez Cadenas, Beman Dawes, Matt Davies, Bob Fletcher, Kresimir Fresl, Joachim Kessel, Patrick Kowalzick, Toon Knapen, Hendrik Kueck, John Maddock, Jens Maurer, Alexei Novakov, Gary Powell, Joachim Pyras, Peter Schmitteckert, Jeremy Siek, Markus Steffl, Michael Stevens, Benedikt Weber, Martin Weiser, Gunter Winkler, Marc Zimmermann and the members of Boost

## Frequently Asked Questions

Q: I'm running the uBLAS dense vector and matrix benchmarks. Why do I see a significant performance difference between the native C and library implementations?
A: uBLAS distinguishes debug mode (size and type conformance checks enabled, expression templates disabled) and release mode (size and type conformance checks disabled, expression templates enabled). Please check, if the preprocessor symbol `NDEBUG` of `cassert` is defined. `NDEBUG` enables release mode, which in turn uses expression templates.

Q: I've written some uBLAS tests, which try to incorrectly assign different matrix types or overrun vector and matrix dimensions. Why don't I get a compile time or runtime diagnostic?
A: uBLAS distinguishes debug mode (size and type conformance checks enabled, expression templates disabled) and release mode (size and type conformance checks disabled, expression templates enabled). Please check, if the preprocessor symbol `NDEBUG` of `cassert` is defined. `NDEBUG` disables debug mode, which is needed to get size and type conformance checks.

Q: I've written some uBLAS benchmarks to measure the performance of matrix chain multiplications like `prod (A, prod (B, C))` and see a significant performance penalty due to the use of expression templates. How can I disable expression templates?
A: You do not need to disable expression templates. Please try reintroducing temporaries using either `prod (A,` `matrix_type` `(prod (B, C)))` or `prod (A, prod<``matrix_type` `> (B, C))`.

Copyright (©) 2000-2002 Joerg Walter, Mathias Koch
Permission to copy, use, modify, sell and distribute this document is granted provided this copyright notice appears in all copies. This document is provided ``as is'' without express or implied warranty, and with no claim as to its suitability for any purpose.

Last revised: 2004-07-05