1/* 2 Copyright (c) 2011, Intel Corporation. All rights reserved. 3 Copyright (C) 2011-2016 Gael Guennebaud <gael.guennebaud@inria.fr> 4 5 Redistribution and use in source and binary forms, with or without modification, 6 are permitted provided that the following conditions are met: 7 8 * Redistributions of source code must retain the above copyright notice, this 9 list of conditions and the following disclaimer. 10 * Redistributions in binary form must reproduce the above copyright notice, 11 this list of conditions and the following disclaimer in the documentation 12 and/or other materials provided with the distribution. 13 * Neither the name of Intel Corporation nor the names of its contributors may 14 be used to endorse or promote products derived from this software without 15 specific prior written permission. 16 17 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND 18 ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED 19 WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE 20 DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR 21 ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES 22 (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 23 LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON 24 ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 25 (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 26 SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 27 28 ******************************************************************************** 29 * Content : Documentation on the use of BLAS/LAPACK libraries through Eigen 30 ******************************************************************************** 31*/ 32 33namespace Eigen { 34 35/** \page TopicUsingBlasLapack Using BLAS/LAPACK from %Eigen 36 37 38Since %Eigen version 3.3 and later, any F77 compatible BLAS or LAPACK libraries can be used as backends for dense matrix products and dense matrix decompositions. 39For instance, one can use <a href="http://eigen.tuxfamily.org/Counter/redirect_to_mkl.php">Intel® MKL</a>, Apple's Accelerate framework on OSX, <a href="http://www.openblas.net/">OpenBLAS</a>, <a href="http://www.netlib.org/lapack">Netlib LAPACK</a>, etc. 40 41Do not miss this \link TopicUsingIntelMKL page \endlink for further discussions on the specific use of Intel® MKL (also includes VML, PARDISO, etc.) 42 43In order to use an external BLAS and/or LAPACK library, you must link you own application to the respective libraries and their dependencies. 44For LAPACK, you must also link to the standard <a href="http://www.netlib.org/lapack/lapacke.html">Lapacke</a> library, which is used as a convenient think layer between %Eigen's C++ code and LAPACK F77 interface. Then you must activate their usage by defining one or multiple of the following macros (\b before including any %Eigen's header): 45 46\note For Mac users, in order to use the lapack version shipped with the Accelerate framework, you also need the lapacke library. 47Using <a href="https://www.macports.org/">MacPorts</a>, this is as easy as: 48\code 49sudo port install lapack 50\endcode 51and then use the following link flags: \c -framework \c Accelerate \c /opt/local/lib/lapack/liblapacke.dylib 52 53<table class="manual"> 54<tr><td>\c EIGEN_USE_BLAS </td><td>Enables the use of external BLAS level 2 and 3 routines (compatible with any F77 BLAS interface)</td></tr> 55<tr class="alt"><td>\c EIGEN_USE_LAPACKE </td><td>Enables the use of external Lapack routines via the <a href="http://www.netlib.org/lapack/lapacke.html">Lapacke</a> C interface to Lapack (compatible with any F77 LAPACK interface)</td></tr> 56<tr><td>\c EIGEN_USE_LAPACKE_STRICT </td><td>Same as \c EIGEN_USE_LAPACKE but algorithms of lower numerical robustness are disabled. \n This currently concerns only JacobiSVD which otherwise would be replaced by \c gesvd that is less robust than Jacobi rotations.</td></tr> 57</table> 58 59When doing so, a number of %Eigen's algorithms are silently substituted with calls to BLAS or LAPACK routines. 60These 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>. 61Operations on other scalar types or mixing reals and complexes will continue to use the built-in algorithms. 62 63The breadth of %Eigen functionality that can be substituted is listed in the table below. 64<table class="manual"> 65<tr><th>Functional domain</th><th>Code example</th><th>BLAS/LAPACK routines</th></tr> 66<tr><td>Matrix-matrix operations \n \c EIGEN_USE_BLAS </td><td>\code 67m1*m2.transpose(); 68m1.selfadjointView<Lower>()*m2; 69m1*m2.triangularView<Upper>(); 70m1.selfadjointView<Lower>().rankUpdate(m2,1.0); 71\endcode</td><td>\code 72?gemm 73?symm/?hemm 74?trmm 75dsyrk/ssyrk 76\endcode</td></tr> 77<tr class="alt"><td>Matrix-vector operations \n \c EIGEN_USE_BLAS </td><td>\code 78m1.adjoint()*b; 79m1.selfadjointView<Lower>()*b; 80m1.triangularView<Upper>()*b; 81\endcode</td><td>\code 82?gemv 83?symv/?hemv 84?trmv 85\endcode</td></tr> 86<tr><td>LU decomposition \n \c EIGEN_USE_LAPACKE \n \c EIGEN_USE_LAPACKE_STRICT </td><td>\code 87v1 = m1.lu().solve(v2); 88\endcode</td><td>\code 89?getrf 90\endcode</td></tr> 91<tr class="alt"><td>Cholesky decomposition \n \c EIGEN_USE_LAPACKE \n \c EIGEN_USE_LAPACKE_STRICT </td><td>\code 92v1 = m2.selfadjointView<Upper>().llt().solve(v2); 93\endcode</td><td>\code 94?potrf 95\endcode</td></tr> 96<tr><td>QR decomposition \n \c EIGEN_USE_LAPACKE \n \c EIGEN_USE_LAPACKE_STRICT </td><td>\code 97m1.householderQr(); 98m1.colPivHouseholderQr(); 99\endcode</td><td>\code 100?geqrf 101?geqp3 102\endcode</td></tr> 103<tr class="alt"><td>Singular value decomposition \n \c EIGEN_USE_LAPACKE </td><td>\code 104JacobiSVD<MatrixXd> svd; 105svd.compute(m1, ComputeThinV); 106\endcode</td><td>\code 107?gesvd 108\endcode</td></tr> 109<tr><td>Eigen-value decompositions \n \c EIGEN_USE_LAPACKE \n \c EIGEN_USE_LAPACKE_STRICT </td><td>\code 110EigenSolver<MatrixXd> es(m1); 111ComplexEigenSolver<MatrixXcd> ces(m1); 112SelfAdjointEigenSolver<MatrixXd> saes(m1+m1.transpose()); 113GeneralizedSelfAdjointEigenSolver<MatrixXd> 114 gsaes(m1+m1.transpose(),m2+m2.transpose()); 115\endcode</td><td>\code 116?gees 117?gees 118?syev/?heev 119?syev/?heev, 120?potrf 121\endcode</td></tr> 122<tr class="alt"><td>Schur decomposition \n \c EIGEN_USE_LAPACKE \n \c EIGEN_USE_LAPACKE_STRICT </td><td>\code 123RealSchur<MatrixXd> schurR(m1); 124ComplexSchur<MatrixXcd> schurC(m1); 125\endcode</td><td>\code 126?gees 127\endcode</td></tr> 128</table> 129In the examples, m1 and m2 are dense matrices and v1 and v2 are dense vectors. 130 131*/ 132 133} 134