Add BDCSVD_LAPACKE binding
diff --git a/Eigen/SVD b/Eigen/SVD
index 3451794..8241c73 100644
--- a/Eigen/SVD
+++ b/Eigen/SVD
@@ -36,14 +36,17 @@
 #include "src/SVD/SVDBase.h"
 #include "src/SVD/JacobiSVD.h"
 #include "src/SVD/BDCSVD.h"
-#if defined(EIGEN_USE_LAPACKE) && !defined(EIGEN_USE_LAPACKE_STRICT)
+#ifdef EIGEN_USE_LAPACKE
 #ifdef EIGEN_USE_MKL
 #include "mkl_lapacke.h"
 #else
 #include "src/misc/lapacke.h"
 #endif
+#ifndef EIGEN_USE_LAPACKE_STRICT
 #include "src/SVD/JacobiSVD_LAPACKE.h"
 #endif
+#include "src/SVD/BDCSVD_LAPACKE.h"
+#endif
 
 #include "src/Core/util/ReenableStupidWarnings.h"
 
diff --git a/Eigen/src/SVD/BDCSVD.h b/Eigen/src/SVD/BDCSVD.h
index 1b10c0e..a69fdca 100644
--- a/Eigen/src/SVD/BDCSVD.h
+++ b/Eigen/src/SVD/BDCSVD.h
@@ -236,7 +236,6 @@
   }
 
 private:
-  void allocate(Index rows, Index cols, unsigned int computationOptions);
   BDCSVD& compute_impl(const MatrixType& matrix, unsigned int computationOptions);
   void divide(Index firstCol, Index lastCol, Index firstRowW, Index firstColW, Index shift);
   void computeSVDofM(Index firstCol, Index n, MatrixXr& U, VectorType& singVals, MatrixXr& V);
@@ -254,6 +253,7 @@
   void computeBaseCase(SVDType& svd, Index n, Index firstCol, Index firstRowW, Index firstColW, Index shift);
 
  protected:
+  void allocate(Index rows, Index cols, unsigned int computationOptions);
   MatrixXr m_naiveU, m_naiveV;
   MatrixXr m_computed;
   Index m_nRec;
diff --git a/Eigen/src/SVD/BDCSVD_LAPACKE.h b/Eigen/src/SVD/BDCSVD_LAPACKE.h
new file mode 100644
index 0000000..d4cc173
--- /dev/null
+++ b/Eigen/src/SVD/BDCSVD_LAPACKE.h
@@ -0,0 +1,163 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2022 Melven Roehrig-Zoellner <Melven.Roehrig-Zoellner@DLR.de>
+// Copyright (c) 2011, Intel Corporation. All rights reserved.
+//
+// This file is based on the JacobiSVD_LAPACKE.h originally from Intel -
+// see license notice below:
+/*
+ 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 : Eigen bindings to LAPACKe
+ *    Singular Value Decomposition - SVD (divide and conquer variant)
+ ********************************************************************************
+*/
+#ifndef EIGEN_BDCSVD_LAPACKE_H
+#define EIGEN_BDCSVD_LAPACKE_H
+
+namespace Eigen {
+
+namespace internal {
+
+namespace lapacke_helpers {
+
+/** \internal Specialization for the data types supported by LAPACKe */
+
+// defining a derived class to allow access to protected members
+template <typename MatrixType_, int Options>
+class BDCSVD_LAPACKE : public BDCSVD<MatrixType_, Options> {
+  typedef BDCSVD<MatrixType_, Options> SVD;
+  typedef typename SVD::MatrixType MatrixType;
+  typedef typename SVD::Scalar Scalar;
+  typedef typename SVD::RealScalar RealScalar;
+
+public:
+  // construct this by moving from a parent object
+  BDCSVD_LAPACKE(SVD&& svd) : SVD(std::move(svd)) {}
+
+  void compute_impl_lapacke(const MatrixType& matrix, unsigned int computationOptions) {
+
+    SVD::allocate(matrix.rows(), matrix.cols(), computationOptions);
+
+    SVD::m_nonzeroSingularValues = SVD::m_diagSize;
+
+    // prepare arguments to ?gesdd
+    const lapack_int matrix_order = lapack_storage_of(matrix);
+    const char jobz  = (SVD::m_computeFullU || SVD::m_computeFullV) ? 'A' : (SVD::m_computeThinU || SVD::m_computeThinV) ? 'S' : 'N';
+    const lapack_int u_cols = (jobz == 'A') ? to_lapack(SVD::m_rows) : (jobz == 'S') ? to_lapack(SVD::m_diagSize) : 1;
+    const lapack_int vt_rows = (jobz == 'A') ? to_lapack(SVD::m_cols) : (jobz == 'S') ? to_lapack(SVD::m_diagSize) : 1;
+    lapack_int ldu, ldvt;
+    Scalar *u, *vt, dummy;
+    MatrixType localU;
+    if (SVD::computeU() && !(SVD::m_computeThinU && SVD::m_computeFullV) ) {
+      ldu  = to_lapack(SVD::m_matrixU.outerStride());
+      u    = SVD::m_matrixU.data();
+    } else if (SVD::computeV()) {
+      localU.resize(SVD::m_rows, u_cols);
+      ldu  = to_lapack(localU.outerStride());
+      u    = localU.data();
+    } else { ldu=1; u=&dummy; }
+    MatrixType localV;
+    if (SVD::computeU() || SVD::computeV()) {
+      localV.resize(vt_rows, SVD::m_cols);
+      ldvt  = to_lapack(localV.outerStride());
+      vt   = localV.data();
+    } else { ldvt=1; vt=&dummy; }
+    MatrixType temp; temp = matrix;
+
+    // actual call to ?gesdd
+    lapack_int info = gesdd( matrix_order, jobz, to_lapack(SVD::m_rows), to_lapack(SVD::m_cols),
+                             to_lapack(temp.data()), to_lapack(temp.outerStride()), (RealScalar*)SVD::m_singularValues.data(),
+                             to_lapack(u), ldu, to_lapack(vt), ldvt);
+
+    // Check the result of the LAPACK call
+    if (info < 0 || !SVD::m_singularValues.allFinite()) {
+      // this includes info == -4 => NaN entry in A
+      SVD::m_info = InvalidInput;
+    } else if (info > 0 ) {
+      SVD::m_info = NoConvergence;
+    } else {
+      SVD::m_info = Success;
+      if (SVD::m_computeThinU && SVD::m_computeFullV) {
+        SVD::m_matrixU = localU.leftCols(SVD::m_matrixU.cols());
+      }
+      if (SVD::computeV()) {
+        SVD::m_matrixV = localV.adjoint().leftCols(SVD::m_matrixV.cols());
+      }
+    }
+    SVD::m_isInitialized = true;
+  }
+};
+
+template<typename MatrixType_, int Options>
+BDCSVD<MatrixType_, Options>& BDCSVD_wrapper(BDCSVD<MatrixType_, Options>& svd, const MatrixType_& matrix, int computationOptions)
+{
+  // we need to move to the wrapper type and back
+  BDCSVD_LAPACKE<MatrixType_, Options> tmpSvd(std::move(svd));
+  tmpSvd.compute_impl_lapacke(matrix, computationOptions);
+  svd = std::move(tmpSvd);
+  return svd;
+}
+
+} // end namespace lapacke_helpers
+
+} // end namespace internal
+
+#define EIGEN_LAPACKE_SDD(EIGTYPE, EIGCOLROW, OPTIONS) \
+template<> inline \
+BDCSVD<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>, OPTIONS>& \
+BDCSVD<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>, OPTIONS>::compute_impl(const Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>& matrix, unsigned int computationOptions) {\
+  return internal::lapacke_helpers::BDCSVD_wrapper(*this, matrix, computationOptions); \
+}
+
+#define EIGEN_LAPACK_SDD_OPTIONS(OPTIONS) \
+  EIGEN_LAPACKE_SDD(double,   ColMajor, OPTIONS) \
+  EIGEN_LAPACKE_SDD(float,    ColMajor, OPTIONS) \
+  EIGEN_LAPACKE_SDD(dcomplex, ColMajor, OPTIONS) \
+  EIGEN_LAPACKE_SDD(scomplex, ColMajor, OPTIONS) \
+\
+  EIGEN_LAPACKE_SDD(double,   RowMajor, OPTIONS) \
+  EIGEN_LAPACKE_SDD(float,    RowMajor, OPTIONS) \
+  EIGEN_LAPACKE_SDD(dcomplex, RowMajor, OPTIONS) \
+  EIGEN_LAPACKE_SDD(scomplex, RowMajor, OPTIONS)
+
+EIGEN_LAPACK_SDD_OPTIONS(0)
+EIGEN_LAPACK_SDD_OPTIONS(ComputeThinU)
+EIGEN_LAPACK_SDD_OPTIONS(ComputeThinV)
+EIGEN_LAPACK_SDD_OPTIONS(ComputeFullU)
+EIGEN_LAPACK_SDD_OPTIONS(ComputeFullV)
+EIGEN_LAPACK_SDD_OPTIONS(ComputeThinU | ComputeThinV)
+EIGEN_LAPACK_SDD_OPTIONS(ComputeFullU | ComputeFullV)
+EIGEN_LAPACK_SDD_OPTIONS(ComputeThinU | ComputeFullV)
+EIGEN_LAPACK_SDD_OPTIONS(ComputeFullU | ComputeThinV)
+
+#undef EIGEN_LAPACK_SDD_OPTIONS
+
+#undef EIGEN_LAPACKE_SDD
+
+} // end namespace Eigen
+
+#endif // EIGEN_BDCSVD_LAPACKE_H
diff --git a/Eigen/src/SVD/JacobiSVD_LAPACKE.h b/Eigen/src/SVD/JacobiSVD_LAPACKE.h
index c5717e9..93244cd 100644
--- a/Eigen/src/SVD/JacobiSVD_LAPACKE.h
+++ b/Eigen/src/SVD/JacobiSVD_LAPACKE.h
@@ -72,8 +72,16 @@
   } else { ldvt=1; vt=&dummy; }\
   Matrix<LAPACKE_RTYPE, Dynamic, Dynamic> superb; superb.resize(m_diagSize, 1); \
   MatrixType m_temp; m_temp = matrix; \
-  LAPACKE_##LAPACKE_PREFIX##gesvd( matrix_order, jobu, jobvt, internal::convert_index<lapack_int>(m_rows), internal::convert_index<lapack_int>(m_cols), (LAPACKE_TYPE*)m_temp.data(), lda, (LAPACKE_RTYPE*)m_singularValues.data(), u, ldu, vt, ldvt, superb.data()); \
-  if (computeV()) m_matrixV = localV.adjoint(); \
+  lapack_int info = LAPACKE_##LAPACKE_PREFIX##gesvd( matrix_order, jobu, jobvt, internal::convert_index<lapack_int>(m_rows), internal::convert_index<lapack_int>(m_cols), (LAPACKE_TYPE*)m_temp.data(), lda, (LAPACKE_RTYPE*)m_singularValues.data(), u, ldu, vt, ldvt, superb.data()); \
+  /* Check the result of the LAPACK call */ \
+  if (info < 0 || !m_singularValues.allFinite()) { \
+    m_info = InvalidInput; \
+  } else if (info > 0 ) { \
+    m_info = NoConvergence; \
+  } else { \
+    m_info = Success; \
+    if (computeV()) m_matrixV = localV.adjoint(); \
+  } \
  /* for(int i=0;i<m_diagSize;i++) if (m_singularValues.coeffRef(i) < precision) { m_nonzeroSingularValues--; m_singularValues.coeffRef(i)=RealScalar(0);}*/ \
   m_isInitialized = true; \
   return *this; \
diff --git a/Eigen/src/misc/lapacke_helpers.h b/Eigen/src/misc/lapacke_helpers.h
index e5d7ca0..b6ad6e8 100644
--- a/Eigen/src/misc/lapacke_helpers.h
+++ b/Eigen/src/misc/lapacke_helpers.h
@@ -150,6 +150,7 @@
 EIGEN_MAKE_LAPACKE_WRAPPER(potrf)
 EIGEN_MAKE_LAPACKE_WRAPPER(getrf)
 EIGEN_MAKE_LAPACKE_WRAPPER(geqrf)
+EIGEN_MAKE_LAPACKE_WRAPPER(gesdd)
 
 #undef EIGEN_MAKE_LAPACKE_WRAPPER
 }
diff --git a/doc/UsingBlasLapackBackends.dox b/doc/UsingBlasLapackBackends.dox
index 4572820..c700d85 100644
--- a/doc/UsingBlasLapackBackends.dox
+++ b/doc/UsingBlasLapackBackends.dox
@@ -106,6 +106,12 @@
 \endcode</td><td>\code
 ?gesvd
 \endcode</td></tr>
+<tr class="alt"><td>Singular value decomposition \n \c EIGEN_USE_LAPACKE \n \c EIGEN_USE_LAPACKE_STRICT </td><td>\code
+BDCSVD<MatrixXd> svd;
+svd.compute(m1);
+\endcode</td><td>\code
+?gesdd
+\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);