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Using Intel® Math Kernel Library from Eigen

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). Intel MKL 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.

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:

  1. define the EIGEN_USE_MKL_ALL macro before including any Eigen's header
  2. link your program to MKL libraries (see the MKL linking advisor)
  3. 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 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 built-in algorithms.

In addition you can coarsely select 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 (currently works with Intel MKL only)
EIGEN_USE_LAPACKE Enables the use of external Lapack routines via the Intel Lapacke C interface to Lapack (currently works with Intel MKL only)
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

Finally, the PARDISO sparse solver shipped with Intel MKL can be used through the PardisoLU, PardisoLLT and PardisoLDLT classes of the PardisoSupport module.

List of supported features

The breadth of Eigen functionality covered by Intel MKL is listed in the table below.

Functional domainCode exampleMKL routines
Matrix-matrix operations
EIGEN_USE_BLAS
m1*m2.transpose();
m1.selfadjointView<Lower>()*m2;
m1*m2.triangularView<Upper>();
m1.selfadjointView<Lower>().rankUpdate(m2,1.0);
?gemm
?symm/?hemm
?trmm
dsyrk/ssyrk
Matrix-vector operations
EIGEN_USE_BLAS
m1.adjoint()*b;
m1.selfadjointView<Lower>()*b;
m1.triangularView<Upper>()*b;
?gemv
?symv/?hemv
?trmv
LU decomposition
EIGEN_USE_LAPACKE
EIGEN_USE_LAPACKE_STRICT
v1 = m1.lu().solve(v2);
?getrf
Cholesky decomposition
EIGEN_USE_LAPACKE
EIGEN_USE_LAPACKE_STRICT
v1 = m2.selfadjointView<Upper>().llt().solve(v2);
?potrf
QR decomposition
EIGEN_USE_LAPACKE
EIGEN_USE_LAPACKE_STRICT
m1.householderQr();
m1.colPivHouseholderQr();
?geqrf
?geqp3
Singular value decomposition
EIGEN_USE_LAPACKE
JacobiSVD<MatrixXd> svd;
svd.compute(m1, ComputeThinV);
?gesvd
Eigen-value decompositions
EIGEN_USE_LAPACKE
EIGEN_USE_LAPACKE_STRICT
EigenSolver<MatrixXd> es(m1);
ComplexEigenSolver<MatrixXcd> ces(m1);
SelfAdjointEigenSolver<MatrixXd> saes(m1+m1.transpose());
GeneralizedSelfAdjointEigenSolver<MatrixXd>
gsaes(m1+m1.transpose(),m2+m2.transpose());
?gees
?gees
?syev/?heev
?syev/?heev,
?potrf
Schur decomposition
EIGEN_USE_LAPACKE
EIGEN_USE_LAPACKE_STRICT
RealSchur<MatrixXd> schurR(m1);
ComplexSchur<MatrixXcd> schurC(m1);
?gees
Vector Math
EIGEN_USE_MKL_VML
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, m1 and m2 are dense matrices and v1 and v2 are dense vectors.

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