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-/*
- Copyright (c) 2011, Intel Corporation. All rights reserved.
- Copyright (C) 2011-2016 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 BLAS/LAPACK libraries through Eigen
- ********************************************************************************
-*/
-
-namespace Eigen {
-
-/** \page TopicUsingBlasLapack Using BLAS/LAPACK from %Eigen
-
-
-Since %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.
-For 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.
-
-Do not miss this \link TopicUsingIntelMKL page \endlink for further discussions on the specific use of Intel® MKL (also includes VML, PARDISO, etc.)
-
-In order to use an external BLAS and/or LAPACK library, you must link you own application to the respective libraries and their dependencies.
-For 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):
-
-\note For Mac users, in order to use the lapack version shipped with the Accelerate framework, you also need the lapacke library.
-Using <a href="https://www.macports.org/">MacPorts</a>, this is as easy as:
-\code
-sudo port install lapack
-\endcode
-and then use the following link flags: \c -framework \c Accelerate \c /opt/local/lib/lapack/liblapacke.dylib
-
-<table class="manual">
-<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>
-<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>
-<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>
-</table>
-
-When doing so, a number of %Eigen's algorithms are silently substituted with calls to BLAS or LAPACK 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.
-
-The breadth of %Eigen functionality that can be substituted is listed in the table below.
-<table class="manual">
-<tr><th>Functional domain</th><th>Code example</th><th>BLAS/LAPACK routines</th></tr>
-<tr><td>Matrix-matrix operations \n \c EIGEN_USE_BLAS </td><td>\code
-m1*m2.transpose();
-m1.selfadjointView<Lower>()*m2;
-m1*m2.triangularView<Upper>();
-m1.selfadjointView<Lower>().rankUpdate(m2,1.0);
-\endcode</td><td>\code
-?gemm
-?symm/?hemm
-?trmm
-dsyrk/ssyrk
-\endcode</td></tr>
-<tr class="alt"><td>Matrix-vector operations \n \c EIGEN_USE_BLAS </td><td>\code
-m1.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 EIGEN_USE_LAPACKE \n \c EIGEN_USE_LAPACKE_STRICT </td><td>\code
-v1 = m1.lu().solve(v2);
-\endcode</td><td>\code
-?getrf
-\endcode</td></tr>
-<tr class="alt"><td>Cholesky decomposition \n \c EIGEN_USE_LAPACKE \n \c EIGEN_USE_LAPACKE_STRICT </td><td>\code
-v1 = m2.selfadjointView<Upper>().llt().solve(v2);
-\endcode</td><td>\code
-?potrf
-\endcode</td></tr>
-<tr><td>QR decomposition \n \c EIGEN_USE_LAPACKE \n \c EIGEN_USE_LAPACKE_STRICT </td><td>\code
-m1.householderQr();
-m1.colPivHouseholderQr();
-\endcode</td><td>\code
-?geqrf
-?geqp3
-\endcode</td></tr>
-<tr class="alt"><td>Singular value decomposition \n \c EIGEN_USE_LAPACKE </td><td>\code
-JacobiSVD<MatrixXd> svd;
-svd.compute(m1, ComputeThinV);
-\endcode</td><td>\code
-?gesvd
-\endcode</td></tr>
-<tr><td>Eigen-value decompositions \n \c EIGEN_USE_LAPACKE \n \c EIGEN_USE_LAPACKE_STRICT </td><td>\code
-EigenSolver<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 EIGEN_USE_LAPACKE \n \c EIGEN_USE_LAPACKE_STRICT </td><td>\code
-RealSchur<MatrixXd> schurR(m1);
-ComplexSchur<MatrixXcd> schurC(m1);
-\endcode</td><td>\code
-?gees
-\endcode</td></tr>
-</table>
-In the examples, m1 and m2 are dense matrices and v1 and v2 are dense vectors.
-
-*/
-
-}