Eigen
3.3.9

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 IntelĀ® MKL, Apple's Accelerate framework on OSX, OpenBLAS, Netlib LAPACK, etc.
Do not miss this page for further discussions on the specific use of IntelĀ® 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 Lapacke 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 (before including any Eigen's header):
framework
Accelerate
/opt/local/lib/lapack/liblapacke
.dylibEIGEN_USE_BLAS  Enables the use of external BLAS level 2 and 3 routines (compatible with any F77 BLAS interface) 
EIGEN_USE_LAPACKE  Enables the use of external Lapack routines via the Lapacke C interface to Lapack (compatible with any F77 LAPACK interface) 
EIGEN_USE_LAPACKE_STRICT  Same as EIGEN_USE_LAPACKE but algorithms of lower numerical robustness are disabled. This currently concerns only JacobiSVD which otherwise would be replaced by gesvd that is less robust than Jacobi rotations. 
When doing so, a number of Eigen's algorithms are silently substituted with calls to BLAS or LAPACK 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.
The breadth of Eigen functionality that can be substituted is listed in the table below.
Functional domain  Code example  BLAS/LAPACK routines 

Matrixmatrix operations EIGEN_USE_BLAS  ?gemm
?symm/?hemm
?trmm
dsyrk/ssyrk
 
Matrixvector operations EIGEN_USE_BLAS  ?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

Eigenvalue 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

In the examples, m1 and m2 are dense matrices and v1 and v2 are dense vectors.