diff --git a/Eigen/Cholesky b/Eigen/Cholesky
index a318ceb79..2c686f175 100644
--- a/Eigen/Cholesky
+++ b/Eigen/Cholesky
@@ -32,11 +32,7 @@
 #include "src/Cholesky/LLT.h"
 #include "src/Cholesky/LDLT.h"
 #ifdef EIGEN_USE_LAPACKE
-#ifdef EIGEN_USE_MKL
-#include "mkl_lapacke.h"
-#else
-#include "src/misc/lapacke.h"
-#endif
+#include "src/misc/lapacke_helpers.h"
 #include "src/Cholesky/LLT_LAPACKE.h"
 #endif
 
diff --git a/Eigen/LU b/Eigen/LU
index 1236ceb04..b7f9a8a9d 100644
--- a/Eigen/LU
+++ b/Eigen/LU
@@ -28,11 +28,7 @@
 #include "src/LU/FullPivLU.h"
 #include "src/LU/PartialPivLU.h"
 #ifdef EIGEN_USE_LAPACKE
-#ifdef EIGEN_USE_MKL
-#include "mkl_lapacke.h"
-#else
-#include "src/misc/lapacke.h"
-#endif
+#include "src/misc/lapacke_helpers.h"
 #include "src/LU/PartialPivLU_LAPACKE.h"
 #endif
 #include "src/LU/Determinant.h"
diff --git a/Eigen/QR b/Eigen/QR
index 8465b62ce..1f6c22e0d 100644
--- a/Eigen/QR
+++ b/Eigen/QR
@@ -36,11 +36,7 @@
 #include "src/QR/ColPivHouseholderQR.h"
 #include "src/QR/CompleteOrthogonalDecomposition.h"
 #ifdef EIGEN_USE_LAPACKE
-#ifdef EIGEN_USE_MKL
-#include "mkl_lapacke.h"
-#else
-#include "src/misc/lapacke.h"
-#endif
+#include "src/misc/lapacke_helpers.h"
 #include "src/QR/HouseholderQR_LAPACKE.h"
 #include "src/QR/ColPivHouseholderQR_LAPACKE.h"
 #endif
diff --git a/Eigen/src/Cholesky/LLT_LAPACKE.h b/Eigen/src/Cholesky/LLT_LAPACKE.h
index bde9bcdd5..62bc679d4 100644
--- a/Eigen/src/Cholesky/LLT_LAPACKE.h
+++ b/Eigen/src/Cholesky/LLT_LAPACKE.h
@@ -39,44 +39,12 @@ namespace Eigen {
 
 namespace internal {
 
-namespace lapacke_llt_helpers {
-
-  // -------------------------------------------------------------------------------------------------------------------
-  //        Translation from Eigen to Lapacke types
-  // -------------------------------------------------------------------------------------------------------------------
-
-  // For complex numbers, the types in Eigen and Lapacke are different, but layout compatible.
-  template<typename Scalar> struct translate_type;
-  template<> struct translate_type<float> { using type = float; };
-  template<> struct translate_type<double> { using type = double; };
-  template<> struct translate_type<dcomplex> { using type = lapack_complex_double; };
-  template<> struct translate_type<scomplex> { using type = lapack_complex_float; };
-
-  // -------------------------------------------------------------------------------------------------------------------
-  //        Dispatch for potrf handling double, float, complex double, complex float types
-  // -------------------------------------------------------------------------------------------------------------------
-
-  inline lapack_int potrf(lapack_int matrix_order, char uplo, lapack_int size, double* a, lapack_int lda) {
-    return LAPACKE_dpotrf( matrix_order, uplo, size, a, lda );
-  }
-
-  inline lapack_int potrf(lapack_int matrix_order, char uplo, lapack_int size, float* a, lapack_int lda) {
-    return LAPACKE_spotrf( matrix_order, uplo, size, a, lda );
-  }
-
-  inline lapack_int potrf(lapack_int matrix_order, char uplo, lapack_int size, lapack_complex_double* a, lapack_int lda) {
-    return LAPACKE_zpotrf( matrix_order, uplo, size, a, lda );
-  }
-
-  inline lapack_int potrf(lapack_int matrix_order, char uplo, lapack_int size, lapack_complex_float* a, lapack_int lda) {
-    return LAPACKE_cpotrf( matrix_order, uplo, size, a, lda );
-  }
-
+namespace lapacke_helpers {
   // -------------------------------------------------------------------------------------------------------------------
   //        Dispatch for rank update handling upper and lower parts
   // -------------------------------------------------------------------------------------------------------------------
 
-  template<unsigned Mode>
+  template<UpLoType Mode>
   struct rank_update {};
 
   template<>
@@ -100,9 +68,8 @@ namespace lapacke_llt_helpers {
   //        Generic lapacke llt implementation that hands of to the dispatches
   // -------------------------------------------------------------------------------------------------------------------
 
-  template<typename Scalar, unsigned Mode>
+  template<typename Scalar, UpLoType Mode>
   struct lapacke_llt {
-    using BlasType = typename translate_type<Scalar>::type;
     template<typename MatrixType>
     static Index blocked(MatrixType& m)
     {
@@ -110,15 +77,13 @@ namespace lapacke_llt_helpers {
       if(m.rows() == 0) {
         return -1;
       }
-
       /* Set up parameters for ?potrf */
-      lapack_int size = convert_index<lapack_int>(m.rows());
-      lapack_int StorageOrder = MatrixType::Flags&RowMajorBit?RowMajor:ColMajor;
-      lapack_int matrix_order = StorageOrder==RowMajor ? LAPACK_ROW_MAJOR : LAPACK_COL_MAJOR;
+      lapack_int size = to_lapack(m.rows());
+      lapack_int matrix_order = lapack_storage_of(m);
       Scalar* a = &(m.coeffRef(0,0));
-      lapack_int lda = convert_index<lapack_int>(m.outerStride());
+      lapack_int lda = to_lapack(m.outerStride());
 
-      lapack_int info = potrf( matrix_order, Mode == Lower ? 'L' : 'U', size, (BlasType*)a, lda );
+      lapack_int info = potrf(matrix_order, translate_mode<Mode>, size, to_lapack(a), lda );
       info = (info==0) ? -1 : info>0 ? info-1 : size;
       return info;
     }
@@ -130,7 +95,7 @@ namespace lapacke_llt_helpers {
     }
   };
 }
-// end namespace lapacke_llt_helpers
+// end namespace lapacke_helpers
 
 /*
  * Here, we just put the generic implementation from lapacke_llt into a full specialization of the llt_inplace
@@ -139,13 +104,13 @@ namespace lapacke_llt_helpers {
  */
 
 #define EIGEN_LAPACKE_LLT(EIGTYPE) \
-template<> struct llt_inplace<EIGTYPE, Lower> : public lapacke_llt_helpers::lapacke_llt<EIGTYPE, Lower> {}; \
-template<> struct llt_inplace<EIGTYPE, Upper> : public lapacke_llt_helpers::lapacke_llt<EIGTYPE, Upper> {};
+template<> struct llt_inplace<EIGTYPE, Lower> : public lapacke_helpers::lapacke_llt<EIGTYPE, Lower> {}; \
+template<> struct llt_inplace<EIGTYPE, Upper> : public lapacke_helpers::lapacke_llt<EIGTYPE, Upper> {};
 
 EIGEN_LAPACKE_LLT(double)
 EIGEN_LAPACKE_LLT(float)
-EIGEN_LAPACKE_LLT(dcomplex)
-EIGEN_LAPACKE_LLT(scomplex)
+EIGEN_LAPACKE_LLT(std::complex<double>)
+EIGEN_LAPACKE_LLT(std::complex<float>)
 
 #undef EIGEN_LAPACKE_LLT
 
diff --git a/Eigen/src/LU/PartialPivLU_LAPACKE.h b/Eigen/src/LU/PartialPivLU_LAPACKE.h
index 2f244f6b4..b63644239 100644
--- a/Eigen/src/LU/PartialPivLU_LAPACKE.h
+++ b/Eigen/src/LU/PartialPivLU_LAPACKE.h
@@ -39,44 +39,55 @@ namespace Eigen {
 
 namespace internal {
 
-/** \internal Specialization for the data types supported by LAPACKe */
+namespace lapacke_helpers {
+// -------------------------------------------------------------------------------------------------------------------
+//        Generic lapacke partial lu implementation that converts arguments and dispatches to the function above
+// -------------------------------------------------------------------------------------------------------------------
 
-#define EIGEN_LAPACKE_LU_PARTPIV(EIGTYPE, LAPACKE_TYPE, LAPACKE_PREFIX) \
-template<int StorageOrder> \
-struct partial_lu_impl<EIGTYPE, StorageOrder, lapack_int> \
-{ \
-  /* \internal performs the LU decomposition in-place of the matrix represented */ \
-  static lapack_int blocked_lu(Index rows, Index cols, EIGTYPE* lu_data, Index luStride, lapack_int* row_transpositions, lapack_int& nb_transpositions, lapack_int maxBlockSize=256) \
-  { \
-    EIGEN_UNUSED_VARIABLE(maxBlockSize);\
-    lapack_int matrix_order, first_zero_pivot; \
-    lapack_int m, n, lda, *ipiv, info; \
-    EIGTYPE* a; \
-/* Set up parameters for ?getrf */ \
-    matrix_order = StorageOrder==RowMajor ? LAPACK_ROW_MAJOR : LAPACK_COL_MAJOR; \
-    lda = convert_index<lapack_int>(luStride); \
-    a = lu_data; \
-    ipiv = row_transpositions; \
-    m = convert_index<lapack_int>(rows); \
-    n = convert_index<lapack_int>(cols); \
-    nb_transpositions = 0; \
-\
-    info = LAPACKE_##LAPACKE_PREFIX##getrf( matrix_order, m, n, (LAPACKE_TYPE*)a, lda, ipiv ); \
-\
-    for(int i=0;i<m;i++) { ipiv[i]--; if (ipiv[i]!=i) nb_transpositions++; } \
-\
-    eigen_assert(info >= 0); \
-/* something should be done with nb_transpositions */ \
-\
-    first_zero_pivot = info; \
-    return first_zero_pivot; \
-  } \
+template<typename Scalar, int StorageOrder>
+struct lapacke_partial_lu {
+  /** \internal performs the LU decomposition in-place of the matrix represented */
+  static lapack_int blocked_lu(Index rows, Index cols, Scalar* lu_data, Index luStride, lapack_int* row_transpositions,
+  lapack_int& nb_transpositions, lapack_int maxBlockSize=256)
+  {
+    EIGEN_UNUSED_VARIABLE(maxBlockSize);
+    // Set up parameters for getrf
+    lapack_int matrix_order = StorageOrder==RowMajor ? LAPACK_ROW_MAJOR : LAPACK_COL_MAJOR;
+    lapack_int lda = to_lapack(luStride);
+    Scalar* a = lu_data;
+    lapack_int* ipiv = row_transpositions;
+    lapack_int m = to_lapack(rows);
+    lapack_int n = to_lapack(cols);
+    nb_transpositions = 0;
+
+    lapack_int info = getrf(matrix_order, m, n, to_lapack(a), lda, ipiv );
+    eigen_assert(info >= 0);
+
+    for(int i=0; i<m; i++) {
+      ipiv[i]--;
+      if (ipiv[i] != i) nb_transpositions++;
+    }
+    lapack_int first_zero_pivot = info;
+    return first_zero_pivot;
+  }
 };
+} // end namespace lapacke_helpers
 
-EIGEN_LAPACKE_LU_PARTPIV(double, double, d)
-EIGEN_LAPACKE_LU_PARTPIV(float, float, s)
-EIGEN_LAPACKE_LU_PARTPIV(dcomplex, lapack_complex_double, z)
-EIGEN_LAPACKE_LU_PARTPIV(scomplex, lapack_complex_float,  c)
+/*
+ * Here, we just put the generic implementation from lapacke_partial_lu into a partial specialization of the partial_lu_impl
+ * type. This specialization is more specialized than the generic implementations that Eigen implements, so if the
+ * Scalar type matches they will be chosen.
+ */
+#define EIGEN_LAPACKE_PARTIAL_LU(EIGTYPE) \
+template<int StorageOrder>                \
+struct partial_lu_impl<EIGTYPE, StorageOrder, lapack_int, Dynamic> : public lapacke_helpers::lapacke_partial_lu<EIGTYPE, StorageOrder> {};
+
+EIGEN_LAPACKE_PARTIAL_LU(double)
+EIGEN_LAPACKE_PARTIAL_LU(float)
+EIGEN_LAPACKE_PARTIAL_LU(std::complex<double>)
+EIGEN_LAPACKE_PARTIAL_LU(std::complex<float>)
+
+#undef EIGEN_LAPACKE_PARTIAL_LU
 
 } // end namespace internal
 
diff --git a/Eigen/src/QR/HouseholderQR_LAPACKE.h b/Eigen/src/QR/HouseholderQR_LAPACKE.h
index ef6776002..57c2f6ab3 100644
--- a/Eigen/src/QR/HouseholderQR_LAPACKE.h
+++ b/Eigen/src/QR/HouseholderQR_LAPACKE.h
@@ -40,28 +40,35 @@ namespace Eigen {
 
 namespace internal {
 
-/** \internal Specialization for the data types supported by LAPACKe */
+namespace lapacke_helpers {
 
-#define EIGEN_LAPACKE_QR_NOPIV(EIGTYPE, LAPACKE_TYPE, LAPACKE_PREFIX) \
-template<typename MatrixQR, typename HCoeffs> \
-struct householder_qr_inplace_blocked<MatrixQR, HCoeffs, EIGTYPE, true> \
-{ \
-  static void run(MatrixQR& mat, HCoeffs& hCoeffs, Index = 32, \
-      typename MatrixQR::Scalar* = 0) \
-  { \
-    lapack_int m = (lapack_int) mat.rows(); \
-    lapack_int n = (lapack_int) mat.cols(); \
-    lapack_int lda = (lapack_int) mat.outerStride(); \
-    lapack_int matrix_order = (MatrixQR::IsRowMajor) ? LAPACK_ROW_MAJOR : LAPACK_COL_MAJOR; \
-    LAPACKE_##LAPACKE_PREFIX##geqrf( matrix_order, m, n, (LAPACKE_TYPE*)mat.data(), lda, (LAPACKE_TYPE*)hCoeffs.data()); \
-    hCoeffs.adjointInPlace(); \
-  } \
+template<typename MatrixQR, typename HCoeffs>
+struct lapacke_hqr
+{
+  static void run(MatrixQR& mat, HCoeffs& hCoeffs, Index = 32, typename MatrixQR::Scalar* = 0)
+  {
+    lapack_int m = to_lapack(mat.rows());
+    lapack_int n = to_lapack(mat.cols());
+    lapack_int lda = to_lapack(mat.outerStride());
+    lapack_int matrix_order = lapack_storage_of(mat);
+    geqrf(matrix_order, m, n, to_lapack(mat.data()), lda, to_lapack(hCoeffs.data()));
+    hCoeffs.adjointInPlace();
+  }
 };
 
-EIGEN_LAPACKE_QR_NOPIV(double, double, d)
-EIGEN_LAPACKE_QR_NOPIV(float, float, s)
-EIGEN_LAPACKE_QR_NOPIV(dcomplex, lapack_complex_double, z)
-EIGEN_LAPACKE_QR_NOPIV(scomplex, lapack_complex_float, c)
+}
+
+/** \internal Specialization for the data types supported by LAPACKe */
+#define EIGEN_LAPACKE_HH_QR(EIGTYPE) \
+template<typename MatrixQR, typename HCoeffs> \
+struct householder_qr_inplace_blocked<MatrixQR, HCoeffs, EIGTYPE, true> : public lapacke_helpers::lapacke_hqr<MatrixQR, HCoeffs> {};
+
+EIGEN_LAPACKE_HH_QR(double)
+EIGEN_LAPACKE_HH_QR(float)
+EIGEN_LAPACKE_HH_QR(std::complex<double>)
+EIGEN_LAPACKE_HH_QR(std::complex<float>)
+
+#undef EIGEN_LAPACKE_HH_QR
 
 } // end namespace internal
 
diff --git a/Eigen/src/misc/lapacke_helpers.h b/Eigen/src/misc/lapacke_helpers.h
new file mode 100644
index 000000000..6fff863f8
--- /dev/null
+++ b/Eigen/src/misc/lapacke_helpers.h
@@ -0,0 +1,159 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2021 Erik Schultheis <erik.schultheis@aalto.fi>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_LAPACKE_HELPERS_H
+#define EIGEN_LAPACKE_HELPERS_H
+
+#include "./InternalHeaderCheck.h"
+
+#ifdef EIGEN_USE_MKL
+#include "mkl_lapacke.h"
+#else
+#include "lapacke.h"
+#endif
+
+namespace Eigen {
+namespace internal {
+/**
+ * \internal
+ * \brief Implementation details and helper functions for the lapacke glue code.
+ */
+namespace lapacke_helpers {
+
+// ---------------------------------------------------------------------------------------------------------------------
+//                  Translation from Eigen to Lapacke for types and constants
+// ---------------------------------------------------------------------------------------------------------------------
+
+// For complex numbers, the types in Eigen and Lapacke are different, but layout compatible.
+template<typename Scalar>
+struct translate_type_imp;
+template<>
+struct translate_type_imp<float> {
+    using type = float;
+};
+template<>
+struct translate_type_imp<double> {
+    using type = double;
+};
+template<>
+struct translate_type_imp<std::complex<double>> {
+    using type = lapack_complex_double;
+};
+template<>
+struct translate_type_imp<std::complex<float>> {
+    using type = lapack_complex_float;
+};
+
+/// Given an Eigen types, this is defined to be the corresponding, layout-compatible lapack type
+template<typename Scalar>
+using translated_type = typename translate_type_imp<Scalar>::type;
+
+/// These functions convert their arguments from Eigen to Lapack types
+/// This function performs conversion for any of the translations defined above.
+template<typename Source, typename Target=translated_type<Source>>
+auto to_lapack(Source value) { return static_cast<Target>(value); }
+
+/// This function performs conversions for pointer types corresponding to the translations abovce.
+/// This is valid because the translations are between layout-compatible types.
+template<typename Source, typename Target=translated_type<Source>>
+auto to_lapack(Source *value) { return reinterpret_cast<Target*>(value); }
+
+/// This function converts the Eigen Index to a lapack index, with possible range checks
+/// \sa internal::convert_index
+lapack_int to_lapack(Index index) {
+  return convert_index<lapack_int>(index);
+}
+
+/// translates storage order of the given Eigen object to the corresponding lapack constant
+template<typename Derived>
+EIGEN_CONSTEXPR lapack_int lapack_storage_of(const EigenBase<Derived> &) {
+  return Derived::IsRowMajor ? LAPACK_ROW_MAJOR : LAPACK_COL_MAJOR;
+}
+
+/// translate UpLo type to the corresponding letter code
+template<UpLoType mode> char translate_mode;
+template<> EIGEN_CONSTEXPR const char translate_mode<Lower> = 'L';
+template<> EIGEN_CONSTEXPR const char translate_mode<Upper> = 'U';
+
+
+// ---------------------------------------------------------------------------------------------------------------------
+//              Automatic generation of low-level wrappers
+// ---------------------------------------------------------------------------------------------------------------------
+
+/*!
+ * \internal
+ * \brief Helper type to facilitate the wrapping of raw LAPACKE functions for different types into a single, overloaded C++ function.
+ * This is achieved in combination with \r EIGEN_MAKE_LAPACKE_WRAPPER
+ * \details This implementation works by providing an overloaded call function that just forwards its arguments to the
+ * underlying lapack function. Each of these overloads is enabled only if the call is actually well formed.
+ * Because these lapack functions take pointers to the underlying scalar type as arguments, even though the actual Scalars
+ * would be implicitly convertible, the pointers are not and therefore only a single overload can be valid at the same time.
+ * Thus, despite all functions taking fully generic `Args&&... args` as arguments, there is never any ambiguity.
+ */
+template<typename DoubleFn, typename SingleFn, typename DoubleCpxFn, typename SingleCpxFn>
+struct WrappingHelper {
+  // The naming of double, single, double complex and single complex is purely for readability
+  // and doesn't actually affect the workings of this class. In principle, the arguments can
+  // be supplied in any permuted order.
+  DoubleFn double_; SingleFn single_; DoubleCpxFn double_cpx_; SingleCpxFn single_cpx_;
+
+  template<typename... Args>
+  auto call(Args&&... args) -> decltype(double_(std::forward<Args>(args)...)) {
+    return double_(std::forward<Args>(args)...);
+  }
+
+  template<typename... Args>
+  auto call(Args&&... args) -> decltype(single_(std::forward<Args>(args)...)){
+    return single_(std::forward<Args>(args)...);
+  }
+
+  template<typename... Args>
+  auto call(Args&&... args) -> decltype(double_cpx_(std::forward<Args>(args)...)){
+    return double_cpx_(std::forward<Args>(args)...);
+  }
+
+  template<typename... Args>
+  auto call(Args&&... args) -> decltype(single_cpx_(std::forward<Args>(args)...)){
+    return single_cpx_(std::forward<Args>(args)...);
+  }
+};
+
+/** \internal Helper function that generates a `WrappingHelper` object with the given function pointers and
+ * invokes its `call` method, thus selecting one of the overloads.
+ * \sa EIGEN_MAKE_LAPACKE_WRAPPER
+ */
+template<typename DoubleFn, typename SingleFn, typename DoubleCpxFn, typename SingleCpxFn, typename... Args>
+auto call_wrapper(DoubleFn df, SingleFn sf, DoubleCpxFn dcf, SingleCpxFn scf, Args&&... args) {
+  WrappingHelper<DoubleFn, SingleFn, DoubleCpxFn, SingleCpxFn> helper{df, sf, dcf, scf};
+  return helper.call(std::forward<Args>(args)...);
+}
+
+/**
+ * \internal
+ * Generates a new function `Function` that dispatches to the corresponding LAPACKE_? prefixed functions.
+ * \sa WrappingHelper
+ */
+#define EIGEN_MAKE_LAPACKE_WRAPPER(FUNCTION) \
+template<typename... Args> \
+auto FUNCTION(Args&&... args) { return call_wrapper(LAPACKE_d##FUNCTION, LAPACKE_s##FUNCTION, LAPACKE_z##FUNCTION, LAPACKE_c##FUNCTION, std::forward<Args>(args)...); }
+
+// Now with this macro and the helper wrappers, we can generate the dispatch for all the lapacke functions that are
+// used in Eigen.
+// We define these here instead of in the files where they are used because this allows us to #undef the macro again
+// right here
+EIGEN_MAKE_LAPACKE_WRAPPER(potrf)
+EIGEN_MAKE_LAPACKE_WRAPPER(getrf)
+EIGEN_MAKE_LAPACKE_WRAPPER(geqrf)
+
+#undef EIGEN_MAKE_LAPACKE_WRAPPER
+}
+}
+}
+
+#endif // EIGEN_LAPACKE_HELPERS_H
\ No newline at end of file