Eigen
3.3.8

Since Eigen version 3.1 and later, users can benefit from builtin Intel® Math Kernel Library (MKL) optimizations with an installed copy of Intel MKL 10.3 (or later).
Intel MKL provides highly optimized multithreaded mathematical routines for x86compatible architectures. Intel MKL is available on Linux, Mac and Windows for both Intel64 and IA32 architectures.
Using Intel MKL through Eigen is easy:
EIGEN_USE_MKL_ALL
macro before including any Eigen's headerWhen doing so, a number of Eigen's algorithms are silently substituted with calls to Intel MKL routines. These substitutions apply only for Dynamic or large enough objects with one of the following four standard scalar types: float
, double
, complex<float>
, and complex<double>
. Operations on other scalar types or mixing reals and complexes will continue to use the builtin algorithms.
In addition you can choose which parts will be substituted by defining one or multiple of the following macros:
EIGEN_USE_BLAS  Enables the use of external BLAS level 2 and 3 routines 
EIGEN_USE_LAPACKE  Enables the use of external Lapack routines via the Lapacke C interface to Lapack 
EIGEN_USE_LAPACKE_STRICT  Same as EIGEN_USE_LAPACKE but algorithm of lower robustness are disabled. This currently concerns only JacobiSVD which otherwise would be replaced by gesvd that is less robust than Jacobi rotations. 
EIGEN_USE_MKL_VML  Enables the use of Intel VML (vector operations) 
EIGEN_USE_MKL_ALL  Defines EIGEN_USE_BLAS , EIGEN_USE_LAPACKE , and EIGEN_USE_MKL_VML 
The options can be combined with MKL_DIRECT_CALL to enable MKL direct call feature. This may help to increase performance of some MKL BLAS (?GEMM, ?GEMV, ?TRSM, ?AXPY and ?DOT) and LAPACK (LU, Cholesky and QR) routines for very small matrices. To make it work properly, the macro EIGEN_USE_MKL
must also be defined in the case none of the other EIGEN_USE_MKL_*
macros has been defined.
Note that the BLAS and LAPACKE backends can be enabled for any F77 compatible BLAS and LAPACK libraries. See this page for the details.
Finally, the PARDISO sparse solver shipped with Intel MKL can be used through the PardisoLU, PardisoLLT and PardisoLDLT classes of the PardisoSupport module.
The following table summarizes the list of functions covered by EIGEN_USE_MKL_VML:
Code example  MKL routines 

v2=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);
 v?Sin
v?Asin
v?Cos
v?Acos
v?Tan
v?Exp
v?Ln
v?Sqrt
v?Sqr
v?Powx

In the examples, v1 and v2 are dense vectors.