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Blaze is an open-source, high-performance C++ math library for dense and sparse arithmetic. With its state-of-the-art Smart Expression Template implementation Blaze combines the elegance and ease of use of a domain-specific language with HPC-grade performance, making it one of the most intuitive and fastest C++ math libraries available.

The Blaze library offers ...

  • ... high performance through the integration of BLAS libraries and manually tuned HPC math kernels
  • ... vectorization by SSE, SSE2, SSE3, SSSE3, SSE4, AVX, AVX2, AVX-512, FMA, and SVML
  • ... parallel execution by OpenMP, HPX, C++11 threads and Boost threads
  • ... the intuitive and easy to use API of a domain specific language
  • ... unified arithmetic with dense and sparse vectors and matrices
  • ... thoroughly tested matrix and vector arithmetic
  • ... completely portable, high quality C++ source code

Get an impression of the clear but powerful syntax of Blaze in the Getting Started tutorial and of the impressive performance in the Benchmarks section.

Download

white20x120.jpg blaze-3.5.jpg white40x120.jpg blaze-docu-3.5.jpg

Older releases of Blaze can be found in the downloads section or in our [release archive](https://bitbucket.org/blaze-lib/blaze/wiki/Release Archive).

Blaze Projects

blaze_tensor: An implementation of 3D tensors for the Blaze library (Stellar Group)

BlazeIterative: A collection of iterative solvers (CG, BiCGSTAB, ...) for the Blaze library (Tyler Olsen)

RcppBlaze: A Blaze port for the R language (ChingChuan Chen)

News

26.2.2019: Today we present the next evolution of the Blaze library, Blaze 3.5. This new release introduces several new, requested features:

#!c++
blaze::UniformVector<int> u( 5UL );          // Creating a 5D uniform vector
blaze::UniformMatrix<double> U( 4UL, 6UL );  // Creating a 4x6 uniform matrix

blaze::ZeroVector<float> z( 4UL );           // Creating a 4D zero vector
blaze::ZeroMatrix<double> Z( 3UL, 7UL );     // Creating a 3x7 zero matrix
  • More flexible element selections, row selections, and column selections:
#!c++
blaze::DynamicVector<double,blaze::rowVector> x{ 1, 2, 3, 4, 5, 6, 7, 8, 9 };
blaze::DynamicMatrix<double,blaze::rowMajor> A( 9UL, 9UL );

// Selecting all even elements of the vector, i.e. selecting (1,3,5,7,9)
auto e = elements( x, []( size_t i ){ return i*2UL; }, 5UL );

// Selecting all odd rows of the matrix, i.e. selecting the rows 1, 3, 5, and 7
auto rs = rows( A, []( size_t i ){ return i*2UL+1UL; }, 4UL );

// Reversing the columns of the matrix, i.e. selecting the columns 8, 7, 6, 5, 4, 3, 2, 1, and 0
auto cs = columns( A, [max=A.columns()-1UL]( size_t i ){ return max-i; }, 9UL );
  • Vector expansion via the expand() function:
#!c++
blaze::DynamicVector<int,columnVector> a{ 1, 2, 3 };
blaze::CompressedVector<int,rowVector> b{ 1, 0, 3, 0, 5 };

// Expand the dense column vector ( 1 2 3 ) into a dense 3x5 column-major matrix
//
//   ( 1 1 1 1 1 )
//   ( 2 2 2 2 2 )
//   ( 3 3 3 3 3 )
//
expand( a, 5 );  // Runtime parameter
expand<5>( a );  // Compile time parameter

// Expand the sparse row vector ( 1 0 3 0 5 ) into a sparse 3x5 row-major matrix
//
//   ( 1 0 3 0 5 )
//   ( 1 0 3 0 5 )
//   ( 1 0 3 0 5 )
//
expand( b, 3 );  // Runtime parameter
expand<3>( b );  // Compile time parameter

With the release of Blaze 3.5 we also officially deprecate the Blazemark, which means that we will eventually remove it in an upcoming release. We hope that you enjoy this new release!

25.11.2018: We are proud to announce a new Blaze project: blaze_tensor provides an implementation of Blaze-style 3D tensors. A big thank you to the Stellar Group!

Wiki: Table of Contents

License

The Blaze library is licensed under the New (Revised) BSD license. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

  • Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
  • Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
  • Neither the names of the Blaze development group nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

Compiler Compatibility

Blaze supports the C++14 standard and is compatible with a wide range of C++ compilers. In fact, Blaze is constantly tested with the GNU compiler collection (version 6.0 through 7.2), the Clang compiler (version 5.0 through 7.0), and Visual C++ 2017 (Win64 only). Other compilers are not explicitly tested, but might work with a high probability.

If you are looking for a C++98 compatible math library you might consider using an older release of Blaze. Until the release 2.6 Blaze was written in C++-98 and constantly tested with the GNU compiler collection (version 4.5 through 5.0), the Intel C++ compiler (12.1, 13.1, 14.0, 15.0), the Clang compiler (version 3.4 through 3.7), and Visual C++ 2010, 2012, 2013, and 2015 (Win64 only).

Publications

  • K. Iglberger, G. Hager, J. Treibig, and U. Rüde: Expression Templates Revisited: A Performance Analysis of Current Methodologies (Download). SIAM Journal on Scientific Computing, 34(2): C42--C69, 2012
  • K. Iglberger, G. Hager, J. Treibig, and U. Rüde: High Performance Smart Expression Template Math Libraries (Download). Proceedings of the 2nd International Workshop on New Algorithms and Programming Models for the Manycore Era (APMM 2012) at HPCS 2012

Contributions

Klaus Iglberger -- Project initiator and main developer

Georg Hager -- Performance analysis and optimization

Christian Godenschwager -- Visual Studio 2010/2012/2013/2015 bug fixes and testing

Tobias Scharpff -- Sparse matrix multiplication algorithms

byzhang -- Bug fixes

Emerson Ferreira -- Bug fixes

Fabien Péan -- CMake support

Denis Demidov -- Export CMake package configuration

Jannik Schürg -- AVX-512 support and cache size detection for macOS in CMake

Marcin Copik -- CMake fixes

Hartmut Kaiser -- HPX backend

Patrick Diehl -- Integration of HPX to the Blazemark and maintainer of the Blaze Fedora package

Mario Emmenlauer -- Blazemark extensions

Jeff Pollock -- CMake extensions

Darcy Beurle -- Integration of Blaze into the Compiler Explorer

Robert Schumacher -- CMake fixes

Jan Rudolph -- CMake fixes

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C++ HPC Math Library

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