|
|
/* Copyright (c) 2011, Intel Corporation. All rights reserved. Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr>
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 name of Intel Corporation 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 OWNER 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.
******************************************************************************** * Content : Documentation on the use of Intel MKL through Eigen *********************************************************************************/
namespace StormEigen {
/** \page TopicUsingIntelMKL Using Intel® Math Kernel Library from Eigen
\section TopicUsingIntelMKL_Intro Eigen and Intel® Math Kernel Library (Intel® MKL)
Since Eigen version 3.1 and later, users can benefit from built-in Intel MKL optimizations with an installed copy of Intel MKL 10.3 (or later).<a href="http://eigen.tuxfamily.org/Counter/redirect_to_mkl.php"> Intel MKL </a> provides highly optimized multi-threaded mathematical routines for x86-compatible architectures.Intel MKL is available on Linux, Mac and Windows for both Intel64 and IA32 architectures.
\noteIntel® MKL is a proprietary software and it is the responsibility of users to buy or register for community (free) Intel MKL licenses for their products. Moreover, the license of the user product has to allow linking to proprietary software that excludes any unmodified versions of the GPL.
Using Intel MKL through Eigen is easy:-# define the \c STORMEIGEN_USE_MKL_ALL macro before including any Eigen's header-# link your program to MKL libraries (see the <a href="http://software.intel.com/en-us/articles/intel-mkl-link-line-advisor/">MKL linking advisor</a>)-# on a 64bits system, you must use the LP64 interface (not the ILP64 one)
When doing so, a number of Eigen's algorithms are silently substituted with calls to Intel MKL routines.These substitutions apply only for \b Dynamic \b or \b large enough objects with one of the following four standard scalar types: \c float, \c double, \c complex<float>, and \c complex<double>.Operations on other scalar types or mixing reals and complexes will continue to use the built-in algorithms.
In addition you can coarsely select choose which parts will be substituted by defining one or multiple of the following macros:
<table class="manual"><tr><td>\c STORMEIGEN_USE_BLAS </td><td>Enables the use of external BLAS level 2 and 3 routines (currently works with Intel MKL only)</td></tr><tr class="alt"><td>\c STORMEIGEN_USE_LAPACKE </td><td>Enables the use of external Lapack routines via the <a href="http://www.netlib.org/lapack/lapacke.html">Intel Lapacke</a> C interface to Lapack (currently works with Intel MKL only)</td></tr><tr><td>\c STORMEIGEN_USE_LAPACKE_STRICT </td><td>Same as \c STORMEIGEN_USE_LAPACKE but algorithm of lower robustness are disabled. This currently concerns only JacobiSVD which otherwise would be replaced by \c gesvd that is less robust than Jacobi rotations.</td></tr><tr class="alt"><td>\c STORMEIGEN_USE_MKL_VML </td><td>Enables the use of Intel VML (vector operations)</td></tr><tr><td>\c STORMEIGEN_USE_MKL_ALL </td><td>Defines \c STORMEIGEN_USE_BLAS, \c STORMEIGEN_USE_LAPACKE, and \c STORMEIGEN_USE_MKL_VML </td></tr></table>
Finally, the PARDISO sparse solver shipped with Intel MKL can be used through the \ref PardisoLU, \ref PardisoLLT and \ref PardisoLDLT classes of the \ref PardisoSupport_Module.
\section TopicUsingIntelMKL_SupportedFeatures List of supported features
The breadth of Eigen functionality covered by Intel MKL is listed in the table below.<table class="manual"><tr><th>Functional domain</th><th>Code example</th><th>MKL routines</th></tr><tr><td>Matrix-matrix operations \n \c STORMEIGEN_USE_BLAS </td><td>\codem1*m2.transpose();m1.selfadjointView<Lower>()*m2;m1*m2.triangularView<Upper>();m1.selfadjointView<Lower>().rankUpdate(m2,1.0);\endcode</td><td>\code?gemm?symm/?hemm?trmmdsyrk/ssyrk\endcode</td></tr><tr class="alt"><td>Matrix-vector operations \n \c STORMEIGEN_USE_BLAS </td><td>\codem1.adjoint()*b;m1.selfadjointView<Lower>()*b;m1.triangularView<Upper>()*b;\endcode</td><td>\code?gemv?symv/?hemv?trmv\endcode</td></tr><tr><td>LU decomposition \n \c STORMEIGEN_USE_LAPACKE \n \c STORMEIGEN_USE_LAPACKE_STRICT </td><td>\codev1 = m1.lu().solve(v2);\endcode</td><td>\code?getrf\endcode</td></tr><tr class="alt"><td>Cholesky decomposition \n \c STORMEIGEN_USE_LAPACKE \n \c STORMEIGEN_USE_LAPACKE_STRICT </td><td>\codev1 = m2.selfadjointView<Upper>().llt().solve(v2);\endcode</td><td>\code?potrf\endcode</td></tr><tr><td>QR decomposition \n \c STORMEIGEN_USE_LAPACKE \n \c STORMEIGEN_USE_LAPACKE_STRICT </td><td>\codem1.householderQr();m1.colPivHouseholderQr();\endcode</td><td>\code?geqrf?geqp3\endcode</td></tr><tr class="alt"><td>Singular value decomposition \n \c STORMEIGEN_USE_LAPACKE </td><td>\codeJacobiSVD<MatrixXd> svd;svd.compute(m1, ComputeThinV);\endcode</td><td>\code?gesvd\endcode</td></tr><tr><td>Eigen-value decompositions \n \c STORMEIGEN_USE_LAPACKE \n \c STORMEIGEN_USE_LAPACKE_STRICT </td><td>\codeEigenSolver<MatrixXd> es(m1);ComplexEigenSolver<MatrixXcd> ces(m1);SelfAdjointEigenSolver<MatrixXd> saes(m1+m1.transpose());GeneralizedSelfAdjointEigenSolver<MatrixXd> gsaes(m1+m1.transpose(),m2+m2.transpose());\endcode</td><td>\code?gees?gees?syev/?heev?syev/?heev,?potrf\endcode</td></tr><tr class="alt"><td>Schur decomposition \n \c STORMEIGEN_USE_LAPACKE \n \c STORMEIGEN_USE_LAPACKE_STRICT </td><td>\codeRealSchur<MatrixXd> schurR(m1);ComplexSchur<MatrixXcd> schurC(m1);\endcode</td><td>\code?gees\endcode</td></tr><tr><td>Vector Math \n \c STORMEIGEN_USE_MKL_VML </td><td>\codev2=v1.array().sin();v2=v1.array().asin();v2=v1.array().cos();v2=v1.array().acos();v2=v1.array().tan();v2=v1.array().exp();v2=v1.array().log();v2=v1.array().sqrt();v2=v1.array().square();v2=v1.array().pow(1.5);\endcode</td><td>\codev?Sinv?Asinv?Cosv?Acosv?Tanv?Expv?Lnv?Sqrtv?Sqrv?Powx\endcode</td></tr></table>In the examples, m1 and m2 are dense matrices and v1 and v2 are dense vectors.
\section TopicUsingIntelMKL_Links Links- Intel MKL can be purchased and downloaded <a href="http://eigen.tuxfamily.org/Counter/redirect_to_mkl.php">here</a>.- Intel MKL is also bundled with <a href="http://software.intel.com/en-us/articles/intel-composer-xe/">Intel Composer XE</a>.
*/
}
|
