Split BLAS/LAPACK versus MKL documentation

3 files changed, 140 insertions, 77 deletions

diff --git a/doc/Manual.dox b/doc/Manual.dox
index cd261b410..db73e1199 100644
--- a/doc/Manual.dox
+++ b/doc/Manual.dox
@@ -10,6 +10,7 @@ namespace Eigen {
   - \subpage TopicAssertions
   - \subpage TopicCustomizingEigen
   - \subpage TopicMultiThreading
+  - \subpage TopicUsingBlasLapack
   - \subpage TopicUsingIntelMKL
   - \subpage TopicCUDA
   - \subpage TopicPitfalls
diff --git a/doc/UsingBlasLapackBackends.dox b/doc/UsingBlasLapackBackends.dox
new file mode 100644
index 000000000..a3ffdda57
--- /dev/null
+++ b/doc/UsingBlasLapackBackends.dox
@@ -0,0 +1,126 @@
+/*
+ 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):
+
+<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.
+
+*/
+
+}
diff --git a/doc/UsingIntelMKL.dox b/doc/UsingIntelMKL.dox
index a5c1a20b9..a1a3a18f2 100644
--- a/doc/UsingIntelMKL.dox
+++ b/doc/UsingIntelMKL.dox
@@ -32,12 +32,11 @@
 
 namespace Eigen {
 
-/** \page TopicUsingIntelMKL Using BLAS/LAPACK and Intel® Math Kernel Library from Eigen
+/** \page TopicUsingIntelMKL Using Intel® MKL 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).
-Since %Eigen version 3.3 and later, <strong>any BLAS or LAPACK libraries</strong> can be used as backends.
+Since %Eigen version 3.1 and later, users can benefit from built-in Intel® Math Kernel Library (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.
@@ -45,96 +44,33 @@ Intel MKL is available on Linux, Mac and Windows for both Intel64 and IA32 archi
 \note
 Intel® 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 EIGEN_USE_MKL_ALL macro before including any Eigen's header
+Using Intel MKL through %Eigen is easy:
+-# define the \c EIGEN_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.
+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 choose which parts will be substituted by defining one or multiple of the following macros:
 
 <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, not only Intel MKL)</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_BLAS </td><td>Enables the use of external BLAS level 2 and 3 routines</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</td></tr>
 <tr><td>\c EIGEN_USE_LAPACKE_STRICT </td><td>Same as \c EIGEN_USE_LAPACKE but algorithm of lower 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>
 <tr class="alt"><td>\c EIGEN_USE_MKL_VML </td><td>Enables the use of Intel VML (vector operations)</td></tr>
 <tr><td>\c EIGEN_USE_MKL_ALL </td><td>Defines \c EIGEN_USE_BLAS, \c EIGEN_USE_LAPACKE, and \c EIGEN_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.
-
+Note that the BLAS and LAPACKE backends can be enabled for any F77 compatible BLAS and LAPACK libraries. See this \link TopicUsingBlasLapack page \endlink for the details.
 
-\section TopicUsingIntelMKL_SupportedFeatures List of supported features
+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.
 
-The breadth of Eigen functionality covered by Intel MKL is listed in the table below.
+The following table summarizes the list of functions covered by \c EIGEN_USE_MKL_VML:
 <table class="manual">
-<tr><th>Functional domain</th><th>Code example</th><th>MKL 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>
-<tr><td>Vector Math \n \c EIGEN_USE_MKL_VML </td><td>\code
+<tr><th>Code example</th><th>MKL routines</th></tr>
+<tr><td>\code
 v2=v1.array().sin();
 v2=v1.array().asin();
 v2=v1.array().cos();
@@ -158,7 +94,7 @@ v?Sqr
 v?Powx
 \endcode</td></tr>
 </table>
-In the examples, m1 and m2 are dense matrices and v1 and v2 are dense vectors.
+In the examples, v1 and v2 are dense vectors.
 
 
 \section TopicUsingIntelMKL_Links Links