mv the Skyline module to unsupported/

8 files changed, 2168 insertions, 0 deletions

diff --git a/unsupported/Eigen/Skyline b/unsupported/Eigen/Skyline
new file mode 100644
index 000000000..5bcb87c76
--- /dev/null
+++ b/unsupported/Eigen/Skyline
@@ -0,0 +1,34 @@
+#ifndef EIGEN_SKYLINE_MODULE_H
+#define EIGEN_SKYLINE_MODULE_H
+
+
+#include "Eigen/Core"
+
+#include "Eigen/src/Core/util/DisableMSVCWarnings.h"
+
+#include <map>
+#include <cstdlib>
+#include <cstring>
+#include <algorithm>
+
+namespace Eigen {
+
+    /** \defgroup Skyline_Module Skyline module
+     *
+     * \nonstableyet
+     *
+     *
+     */
+
+#include "src/Skyline/SkylineUtil.h"
+#include "src/Skyline/SkylineMatrixBase.h"
+#include "src/Skyline/SkylineStorage.h"
+#include "src/Skyline/SkylineMatrix.h"
+#include "src/Skyline/SkylineInplaceLU.h"
+#include "src/Skyline/SkylineProduct.h"
+
+} // namespace Eigen
+
+#include "Eigen/src/Core/util/EnableMSVCWarnings.h"
+
+#endif // EIGEN_SKYLINE_MODULE_H
diff --git a/unsupported/Eigen/src/CMakeLists.txt b/unsupported/Eigen/src/CMakeLists.txt
index 3a688afd8..195808c59 100644
--- a/unsupported/Eigen/src/CMakeLists.txt
+++ b/unsupported/Eigen/src/CMakeLists.txt
@@ -2,3 +2,6 @@ ADD_SUBDIRECTORY(IterativeSolvers)
 ADD_SUBDIRECTORY(BVH)
 ADD_SUBDIRECTORY(AutoDiff)
 ADD_SUBDIRECTORY(MoreVectorization)
+ADD_SUBDIRECTORY(FFT)
+ADD_SUBDIRECTORY(Skyline)
+ADD_SUBDIRECTORY(MatrixFunctions)
diff --git a/unsupported/Eigen/src/Skyline/SkylineInplaceLU.h b/unsupported/Eigen/src/Skyline/SkylineInplaceLU.h
new file mode 100644
index 000000000..feed564c5
--- /dev/null
+++ b/unsupported/Eigen/src/Skyline/SkylineInplaceLU.h
@@ -0,0 +1,361 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Guillaume Saupin <guillaume.saupin@cea.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_SKYLINEINPLACELU_H
+#define EIGEN_SKYLINEINPLACELU_H
+
+/** \ingroup Skyline_Module
+ *
+ * \class SkylineInplaceLU
+ *
+ * \brief Inplace LU decomposition of a skyline matrix and associated features
+ *
+ * \param MatrixType the type of the matrix of which we are computing the LU factorization
+ *
+ */
+template<typename MatrixType>
+class SkylineInplaceLU {
+protected:
+    typedef typename MatrixType::Scalar Scalar;
+    typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+
+public:
+
+    /** Creates a LU object and compute the respective factorization of \a matrix using
+     * flags \a flags. */
+    SkylineInplaceLU(MatrixType& matrix, int flags = 0)
+    : /*m_matrix(matrix.rows(), matrix.cols()),*/ m_flags(flags), m_status(0), m_lu(matrix) {
+        m_precision = RealScalar(0.1) * Eigen::precision<RealScalar > ();
+        m_lu.IsRowMajor ? computeRowMajor() : compute();
+    }
+
+    /** Sets the relative threshold value used to prune zero coefficients during the decomposition.
+     *
+     * Setting a value greater than zero speeds up computation, and yields to an imcomplete
+     * factorization with fewer non zero coefficients. Such approximate factors are especially
+     * useful to initialize an iterative solver.
+     *
+     * Note that the exact meaning of this parameter might depends on the actual
+     * backend. Moreover, not all backends support this feature.
+     *
+     * \sa precision() */
+    void setPrecision(RealScalar v) {
+        m_precision = v;
+    }
+
+    /** \returns the current precision.
+     *
+     * \sa setPrecision() */
+    RealScalar precision() const {
+        return m_precision;
+    }
+
+    /** Sets the flags. Possible values are:
+     *  - CompleteFactorization
+     *  - IncompleteFactorization
+     *  - MemoryEfficient
+     *  - one of the ordering methods
+     *  - etc...
+     *
+     * \sa flags() */
+    void setFlags(int f) {
+        m_flags = f;
+    }
+
+    /** \returns the current flags */
+    int flags() const {
+        return m_flags;
+    }
+
+    void setOrderingMethod(int m) {
+        m_flags = m;
+    }
+
+    int orderingMethod() const {
+        return m_flags;
+    }
+
+    /** Computes/re-computes the LU factorization */
+    void compute();
+    void computeRowMajor();
+
+    /** \returns the lower triangular matrix L */
+    //inline const MatrixType& matrixL() const { return m_matrixL; }
+
+    /** \returns the upper triangular matrix U */
+    //inline const MatrixType& matrixU() const { return m_matrixU; }
+
+    template<typename BDerived, typename XDerived>
+    bool solve(const MatrixBase<BDerived> &b, MatrixBase<XDerived>* x,
+            const int transposed = 0) const;
+
+    /** \returns true if the factorization succeeded */
+    inline bool succeeded(void) const {
+        return m_succeeded;
+    }
+
+protected:
+    RealScalar m_precision;
+    int m_flags;
+    mutable int m_status;
+    bool m_succeeded;
+    MatrixType& m_lu;
+};
+
+/** Computes / recomputes the in place LU decomposition of the SkylineInplaceLU.
+ * using the default algorithm.
+ */
+template<typename MatrixType>
+//template<typename _Scalar>
+void SkylineInplaceLU<MatrixType>::compute() {
+    const size_t rows = m_lu.rows();
+    const size_t cols = m_lu.cols();
+
+    ei_assert(rows == cols && "We do not (yet) support rectangular LU.");
+    ei_assert(!m_lu.IsRowMajor && "LU decomposition does not work with rowMajor Storage");
+
+    for (unsigned int row = 0; row < rows; row++) {
+        const double pivot = m_lu.coeffDiag(row);
+
+        //Lower matrix Columns update
+        const unsigned int& col = row;
+        for (typename MatrixType::InnerLowerIterator lIt(m_lu, col); lIt; ++lIt) {
+            lIt.valueRef() /= pivot;
+        }
+
+        //Upper matrix update -> contiguous memory access
+        typename MatrixType::InnerLowerIterator lIt(m_lu, col);
+        for (unsigned int rrow = row + 1; rrow < m_lu.rows(); rrow++) {
+            typename MatrixType::InnerUpperIterator uItPivot(m_lu, row);
+            typename MatrixType::InnerUpperIterator uIt(m_lu, rrow);
+            const double coef = lIt.value();
+
+            uItPivot += (rrow - row - 1);
+
+            //update upper part  -> contiguous memory access
+            for (++uItPivot; uIt && uItPivot;) {
+                uIt.valueRef() -= uItPivot.value() * coef;
+
+                ++uIt;
+                ++uItPivot;
+            }
+            ++lIt;
+        }
+
+        //Upper matrix update -> non contiguous memory access
+        typename MatrixType::InnerLowerIterator lIt3(m_lu, col);
+        for (unsigned int rrow = row + 1; rrow < m_lu.rows(); rrow++) {
+            typename MatrixType::InnerUpperIterator uItPivot(m_lu, row);
+            const double coef = lIt3.value();
+
+            //update lower part ->  non contiguous memory access
+            for (unsigned int i = 0; i < rrow - row - 1; i++) {
+                m_lu.coeffRefLower(rrow, row + i + 1) -= uItPivot.value() * coef;
+                ++uItPivot;
+            }
+            ++lIt3;
+        }
+        //update diag -> contiguous
+        typename MatrixType::InnerLowerIterator lIt2(m_lu, col);
+        for (unsigned int rrow = row + 1; rrow < m_lu.rows(); rrow++) {
+
+            typename MatrixType::InnerUpperIterator uItPivot(m_lu, row);
+            typename MatrixType::InnerUpperIterator uIt(m_lu, rrow);
+            const double coef = lIt2.value();
+
+            uItPivot += (rrow - row - 1);
+            m_lu.coeffRefDiag(rrow) -= uItPivot.value() * coef;
+            ++lIt2;
+        }
+    }
+}
+
+template<typename MatrixType>
+void SkylineInplaceLU<MatrixType>::computeRowMajor() {
+    const size_t rows = m_lu.rows();
+    const size_t cols = m_lu.cols();
+
+    ei_assert(rows == cols && "We do not (yet) support rectangular LU.");
+    ei_assert(m_lu.IsRowMajor && "You're trying to apply rowMajor decomposition on a ColMajor matrix !");
+
+    for (unsigned int row = 0; row < rows; row++) {
+        typename MatrixType::InnerLowerIterator llIt(m_lu, row);
+
+
+        for (unsigned int col = llIt.col(); col < row; col++) {
+            if (m_lu.coeffExistLower(row, col)) {
+                const double diag = m_lu.coeffDiag(col);
+
+                typename MatrixType::InnerLowerIterator lIt(m_lu, row);
+                typename MatrixType::InnerUpperIterator uIt(m_lu, col);
+
+
+                const int offset = lIt.col() - uIt.row();
+
+
+                int stop = offset > 0 ? col - lIt.col() : col - uIt.row();
+
+                //#define VECTORIZE
+#ifdef VECTORIZE
+                Map<VectorXd > rowVal(lIt.valuePtr() + (offset > 0 ? 0 : -offset), stop);
+                Map<VectorXd > colVal(uIt.valuePtr() + (offset > 0 ? offset : 0), stop);
+
+
+                Scalar newCoeff = m_lu.coeffLower(row, col) - rowVal.dot(colVal);
+#else
+                if (offset > 0) //Skip zero value of lIt
+                    uIt += offset;
+                else //Skip zero values of uIt
+                    lIt += -offset;
+                Scalar newCoeff = m_lu.coeffLower(row, col);
+
+                for (int k = 0; k < stop; ++k) {
+                    const Scalar tmp = newCoeff;
+                    newCoeff = tmp - lIt.value() * uIt.value();
+                    ++lIt;
+                    ++uIt;
+                }
+#endif
+
+                m_lu.coeffRefLower(row, col) = newCoeff / diag;
+            }
+        }
+
+        //Upper matrix update
+        const int col = row;
+        typename MatrixType::InnerUpperIterator uuIt(m_lu, col);
+        for (unsigned int rrow = uuIt.row(); rrow < col; rrow++) {
+
+            typename MatrixType::InnerLowerIterator lIt(m_lu, rrow);
+            typename MatrixType::InnerUpperIterator uIt(m_lu, col);
+            const int offset = lIt.col() - uIt.row();
+
+            int stop = offset > 0 ? rrow - lIt.col() : rrow - uIt.row();
+
+#ifdef VECTORIZE
+            Map<VectorXd > rowVal(lIt.valuePtr() + (offset > 0 ? 0 : -offset), stop);
+            Map<VectorXd > colVal(uIt.valuePtr() + (offset > 0 ? offset : 0), stop);
+
+            Scalar newCoeff = m_lu.coeffUpper(rrow, col) - rowVal.dot(colVal);
+#else
+            if (offset > 0) //Skip zero value of lIt
+                uIt += offset;
+            else //Skip zero values of uIt
+                lIt += -offset;
+            Scalar newCoeff = m_lu.coeffUpper(rrow, col);
+            for (int k = 0; k < stop; ++k) {
+                const Scalar tmp = newCoeff;
+                newCoeff = tmp - lIt.value() * uIt.value();
+
+                ++lIt;
+                ++uIt;
+            }
+#endif
+            m_lu.coeffRefUpper(rrow, col) = newCoeff;
+        }
+
+
+        //Diag matrix update
+        typename MatrixType::InnerLowerIterator lIt(m_lu, row);
+        typename MatrixType::InnerUpperIterator uIt(m_lu, row);
+
+        const int offset = lIt.col() - uIt.row();
+
+
+        int stop = offset > 0 ? lIt.size() : uIt.size();
+#ifdef VECTORIZE
+        Map<VectorXd > rowVal(lIt.valuePtr() + (offset > 0 ? 0 : -offset), stop);
+        Map<VectorXd > colVal(uIt.valuePtr() + (offset > 0 ? offset : 0), stop);
+        Scalar newCoeff = m_lu.coeffDiag(row) - rowVal.dot(colVal);
+#else
+        if (offset > 0) //Skip zero value of lIt
+            uIt += offset;
+        else //Skip zero values of uIt
+            lIt += -offset;
+        Scalar newCoeff = m_lu.coeffDiag(row);
+        for (unsigned int k = 0; k < stop; ++k) {
+            const Scalar tmp = newCoeff;
+            newCoeff = tmp - lIt.value() * uIt.value();
+            ++lIt;
+            ++uIt;
+        }
+#endif
+        m_lu.coeffRefDiag(row) = newCoeff;
+    }
+}
+
+/** Computes *x = U^-1 L^-1 b
+ *
+ * If \a transpose is set to SvTranspose or SvAdjoint, the solution
+ * of the transposed/adjoint system is computed instead.
+ *
+ * Not all backends implement the solution of the transposed or
+ * adjoint system.
+ */
+template<typename MatrixType>
+template<typename BDerived, typename XDerived>
+bool SkylineInplaceLU<MatrixType>::solve(const MatrixBase<BDerived> &b, MatrixBase<XDerived>* x, const int transposed) const {
+    const size_t rows = m_lu.rows();
+    const size_t cols = m_lu.cols();
+
+
+    for (int row = 0; row < rows; row++) {
+        x->coeffRef(row) = b.coeff(row);
+        Scalar newVal = x->coeff(row);
+        typename MatrixType::InnerLowerIterator lIt(m_lu, row);
+
+        unsigned int col = lIt.col();
+        while (lIt.col() < row) {
+
+            newVal -= x->coeff(col++) * lIt.value();
+            ++lIt;
+        }
+
+        x->coeffRef(row) = newVal;
+    }
+
+
+    for (int col = rows - 1; col > 0; col--) {
+        x->coeffRef(col) = x->coeff(col) / m_lu.coeffDiag(col);
+
+        const Scalar x_col = x->coeff(col);
+
+        typename MatrixType::InnerUpperIterator uIt(m_lu, col);
+        uIt += uIt.size()-1;
+
+
+        while (uIt) {
+            x->coeffRef(uIt.row()) -= x_col * uIt.value();
+            //TODO : introduce --operator
+            uIt += -1;
+        }
+
+
+    }
+    x->coeffRef(0) = x->coeff(0) / m_lu.coeffDiag(0);
+
+    return true;
+}
+
+#endif // EIGEN_SKYLINELU_H
diff --git a/unsupported/Eigen/src/Skyline/SkylineMatrix.h b/unsupported/Eigen/src/Skyline/SkylineMatrix.h
new file mode 100644
index 000000000..5d47d970f
--- /dev/null
+++ b/unsupported/Eigen/src/Skyline/SkylineMatrix.h
@@ -0,0 +1,870 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Guillaume Saupin <guillaume.saupin@cea.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_SKYLINEMATRIX_H
+#define EIGEN_SKYLINEMATRIX_H
+
+#include "SkylineStorage.h"
+#include "SkylineMatrixBase.h"
+
+/** \ingroup Skyline_Module
+ *
+ * \class SkylineMatrix
+ *
+ * \brief The main skyline matrix class
+ *
+ * This class implements a skyline matrix using the very uncommon storage
+ * scheme.
+ *
+ * \param _Scalar the scalar type, i.e. the type of the coefficients
+ * \param _Options Union of bit flags controlling the storage scheme. Currently the only possibility
+ *                 is RowMajor. The default is 0 which means column-major.
+ *
+ *
+ */
+template<typename _Scalar, int _Options>
+struct ei_traits<SkylineMatrix<_Scalar, _Options> > {
+    typedef _Scalar Scalar;
+
+    enum {
+        RowsAtCompileTime = Dynamic,
+        ColsAtCompileTime = Dynamic,
+        MaxRowsAtCompileTime = Dynamic,
+        MaxColsAtCompileTime = Dynamic,
+        Flags = SkylineBit | _Options,
+        CoeffReadCost = NumTraits<Scalar>::ReadCost,
+    };
+};
+
+template<typename _Scalar, int _Options>
+class SkylineMatrix
+: public SkylineMatrixBase<SkylineMatrix<_Scalar, _Options> > {
+public:
+    EIGEN_SKYLINE_GENERIC_PUBLIC_INTERFACE(SkylineMatrix)
+    EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATOR(SkylineMatrix, +=)
+    EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATOR(SkylineMatrix, -=)
+
+    using Base::IsRowMajor;
+
+protected:
+
+    typedef SkylineMatrix<Scalar, (Flags&~RowMajorBit) | (IsRowMajor ? RowMajorBit : 0) > TransposedSkylineMatrix;
+
+    int m_outerSize;
+    int m_innerSize;
+
+public:
+    int* m_colStartIndex;
+    int* m_rowStartIndex;
+    SkylineStorage<Scalar> m_data;
+
+public:
+
+    inline int rows() const {
+        return IsRowMajor ? m_outerSize : m_innerSize;
+    }
+
+    inline int cols() const {
+        return IsRowMajor ? m_innerSize : m_outerSize;
+    }
+
+    inline int innerSize() const {
+        return m_innerSize;
+    }
+
+    inline int outerSize() const {
+        return m_outerSize;
+    }
+
+    inline int upperNonZeros() const {
+        return m_data.upperSize();
+    }
+
+    inline int lowerNonZeros() const {
+        return m_data.lowerSize();
+    }
+
+    inline int upperNonZeros(int j) const {
+        return m_colStartIndex[j + 1] - m_colStartIndex[j];
+    }
+
+    inline int lowerNonZeros(int j) const {
+        return m_rowStartIndex[j + 1] - m_rowStartIndex[j];
+    }
+
+    inline const Scalar* _diagPtr() const {
+        return &m_data.diag(0);
+    }
+
+    inline Scalar* _diagPtr() {
+        return &m_data.diag(0);
+    }
+
+    inline const Scalar* _upperPtr() const {
+        return &m_data.upper(0);
+    }
+
+    inline Scalar* _upperPtr() {
+        return &m_data.upper(0);
+    }
+
+    inline const Scalar* _lowerPtr() const {
+        return &m_data.lower(0);
+    }
+
+    inline Scalar* _lowerPtr() {
+        return &m_data.lower(0);
+    }
+
+    inline const int* _upperProfilePtr() const {
+        return &m_data.upperProfile(0);
+    }
+
+    inline int* _upperProfilePtr() {
+        return &m_data.upperProfile(0);
+    }
+
+    inline const int* _lowerProfilePtr() const {
+        return &m_data.lowerProfile(0);
+    }
+
+    inline int* _lowerProfilePtr() {
+        return &m_data.lowerProfile(0);
+    }
+
+    inline Scalar coeff(int row, int col) const {
+        const int outer = IsRowMajor ? row : col;
+        const int inner = IsRowMajor ? col : row;
+
+        ei_assert(outer < outerSize());
+        ei_assert(inner < innerSize());
+
+        if (outer == inner)
+            return this->m_data.diag(outer);
+
+        if (IsRowMajor) {
+            if (inner > outer) //upper matrix
+            {
+                const int minOuterIndex = inner - m_data.upperProfile(inner);
+                if (outer >= minOuterIndex)
+                    return this->m_data.upper(m_colStartIndex[inner] + outer - (inner - m_data.upperProfile(inner)));
+                else
+                    return Scalar(0);
+            }
+            if (inner < outer) //lower matrix
+            {
+                const int minInnerIndex = outer - m_data.lowerProfile(outer);
+                if (inner >= minInnerIndex)
+                    return this->m_data.lower(m_rowStartIndex[outer] + inner - (outer - m_data.lowerProfile(outer)));
+                else
+                    return Scalar(0);
+            }
+            return m_data.upper(m_colStartIndex[inner] + outer - inner);
+        } else {
+            if (outer > inner) //upper matrix
+            {
+                const int maxOuterIndex = inner + m_data.upperProfile(inner);
+                if (outer <= maxOuterIndex)
+                    return this->m_data.upper(m_colStartIndex[inner] + (outer - inner));
+                else
+                    return Scalar(0);
+            }
+            if (outer < inner) //lower matrix
+            {
+                const int maxInnerIndex = outer + m_data.lowerProfile(outer);
+
+                if (inner <= maxInnerIndex)
+                    return this->m_data.lower(m_rowStartIndex[outer] + (inner - outer));
+                else
+                    return Scalar(0);
+            }
+        }
+    }
+
+    inline Scalar& coeffRef(int row, int col) {
+        const int outer = IsRowMajor ? row : col;
+        const int inner = IsRowMajor ? col : row;
+
+        ei_assert(outer < outerSize());
+        ei_assert(inner < innerSize());
+
+        if (outer == inner)
+            return this->m_data.diag(outer);
+
+        if (IsRowMajor) {
+            if (col > row) //upper matrix
+            {
+                const int minOuterIndex = inner - m_data.upperProfile(inner);
+                ei_assert(outer >= minOuterIndex && "you try to acces a coeff that do not exist in the storage");
+                return this->m_data.upper(m_colStartIndex[inner] + outer - (inner - m_data.upperProfile(inner)));
+            }
+            if (col < row) //lower matrix
+            {
+                const int minInnerIndex = outer - m_data.lowerProfile(outer);
+                ei_assert(inner >= minInnerIndex && "you try to acces a coeff that do not exist in the storage");
+                return this->m_data.lower(m_rowStartIndex[outer] + inner - (outer - m_data.lowerProfile(outer)));
+            }
+        } else {
+            if (outer > inner) //upper matrix
+            {
+                const int maxOuterIndex = inner + m_data.upperProfile(inner);
+                ei_assert(outer <= maxOuterIndex && "you try to acces a coeff that do not exist in the storage");
+                return this->m_data.upper(m_colStartIndex[inner] + (outer - inner));
+            }
+            if (outer < inner) //lower matrix
+            {
+                const int maxInnerIndex = outer + m_data.lowerProfile(outer);
+                ei_assert(inner <= maxInnerIndex && "you try to acces a coeff that do not exist in the storage");
+                return this->m_data.lower(m_rowStartIndex[outer] + (inner - outer));
+            }
+        }
+    }
+
+    inline Scalar coeffDiag(int idx) const {
+        ei_assert(idx < outerSize());
+        ei_assert(idx < innerSize());
+        return this->m_data.diag(idx);
+    }
+
+    inline Scalar coeffLower(int row, int col) const {
+        const int outer = IsRowMajor ? row : col;
+        const int inner = IsRowMajor ? col : row;
+
+        ei_assert(outer < outerSize());
+        ei_assert(inner < innerSize());
+        ei_assert(inner != outer);
+
+        if (IsRowMajor) {
+            const int minInnerIndex = outer - m_data.lowerProfile(outer);
+            if (inner >= minInnerIndex)
+                return this->m_data.lower(m_rowStartIndex[outer] + inner - (outer - m_data.lowerProfile(outer)));
+            else
+                return Scalar(0);
+
+        } else {
+            const int maxInnerIndex = outer + m_data.lowerProfile(outer);
+            if (inner <= maxInnerIndex)
+                return this->m_data.lower(m_rowStartIndex[outer] + (inner - outer));
+            else
+                return Scalar(0);
+        }
+    }
+
+    inline Scalar coeffUpper(int row, int col) const {
+        const int outer = IsRowMajor ? row : col;
+        const int inner = IsRowMajor ? col : row;
+
+        ei_assert(outer < outerSize());
+        ei_assert(inner < innerSize());
+        ei_assert(inner != outer);
+
+        if (IsRowMajor) {
+            const int minOuterIndex = inner - m_data.upperProfile(inner);
+            if (outer >= minOuterIndex)
+                return this->m_data.upper(m_colStartIndex[inner] + outer - (inner - m_data.upperProfile(inner)));
+            else
+                return Scalar(0);
+        } else {
+            const int maxOuterIndex = inner + m_data.upperProfile(inner);
+            if (outer <= maxOuterIndex)
+                return this->m_data.upper(m_colStartIndex[inner] + (outer - inner));
+            else
+                return Scalar(0);
+        }
+    }
+
+    inline Scalar& coeffRefDiag(int idx) {
+        ei_assert(idx < outerSize());
+        ei_assert(idx < innerSize());
+        return this->m_data.diag(idx);
+    }
+
+    inline Scalar& coeffRefLower(int row, int col) {
+        const int outer = IsRowMajor ? row : col;
+        const int inner = IsRowMajor ? col : row;
+
+        ei_assert(outer < outerSize());
+        ei_assert(inner < innerSize());
+        ei_assert(inner != outer);
+
+        if (IsRowMajor) {
+            const int minInnerIndex = outer - m_data.lowerProfile(outer);
+            ei_assert(inner >= minInnerIndex && "you try to acces a coeff that do not exist in the storage");
+            return this->m_data.lower(m_rowStartIndex[outer] + inner - (outer - m_data.lowerProfile(outer)));
+        } else {
+            const int maxInnerIndex = outer + m_data.lowerProfile(outer);
+            ei_assert(inner <= maxInnerIndex && "you try to acces a coeff that do not exist in the storage");
+            return this->m_data.lower(m_rowStartIndex[outer] + (inner - outer));
+        }
+    }
+
+    inline bool coeffExistLower(int row, int col) {
+        const int outer = IsRowMajor ? row : col;
+        const int inner = IsRowMajor ? col : row;
+
+        ei_assert(outer < outerSize());
+        ei_assert(inner < innerSize());
+        ei_assert(inner != outer);
+
+        if (IsRowMajor) {
+            const int minInnerIndex = outer - m_data.lowerProfile(outer);
+            return inner >= minInnerIndex;
+        } else {
+            const int maxInnerIndex = outer + m_data.lowerProfile(outer);
+            return inner <= maxInnerIndex;
+        }
+    }
+
+    inline Scalar& coeffRefUpper(int row, int col) {
+        const int outer = IsRowMajor ? row : col;
+        const int inner = IsRowMajor ? col : row;
+
+        ei_assert(outer < outerSize());
+        ei_assert(inner < innerSize());
+        ei_assert(inner != outer);
+
+        if (IsRowMajor) {
+            const int minOuterIndex = inner - m_data.upperProfile(inner);
+            ei_assert(outer >= minOuterIndex && "you try to acces a coeff that do not exist in the storage");
+            return this->m_data.upper(m_colStartIndex[inner] + outer - (inner - m_data.upperProfile(inner)));
+        } else {
+            const int maxOuterIndex = inner + m_data.upperProfile(inner);
+            ei_assert(outer <= maxOuterIndex && "you try to acces a coeff that do not exist in the storage");
+            return this->m_data.upper(m_colStartIndex[inner] + (outer - inner));
+        }
+    }
+
+    inline bool coeffExistUpper(int row, int col) {
+        const int outer = IsRowMajor ? row : col;
+        const int inner = IsRowMajor ? col : row;
+
+        ei_assert(outer < outerSize());
+        ei_assert(inner < innerSize());
+        ei_assert(inner != outer);
+
+        if (IsRowMajor) {
+            const int minOuterIndex = inner - m_data.upperProfile(inner);
+            return outer >= minOuterIndex;
+        } else {
+            const int maxOuterIndex = inner + m_data.upperProfile(inner);
+            return outer <= maxOuterIndex;
+        }
+    }
+
+
+protected:
+
+public:
+    class InnerUpperIterator;
+    class InnerLowerIterator;
+
+    class OuterUpperIterator;
+    class OuterLowerIterator;
+
+    /** Removes all non zeros */
+    inline void setZero() {
+        m_data.clear();
+        memset(m_colStartIndex, 0, (m_outerSize + 1) * sizeof (int));
+        memset(m_rowStartIndex, 0, (m_outerSize + 1) * sizeof (int));
+    }
+
+    /** \returns the number of non zero coefficients */
+    inline int nonZeros() const {
+        return m_data.diagSize() + m_data.upperSize() + m_data.lowerSize();
+    }
+
+    /** Preallocates \a reserveSize non zeros */
+    inline void reserve(int reserveSize, int reserveUpperSize, int reserveLowerSize) {
+        m_data.reserve(reserveSize, reserveUpperSize, reserveLowerSize);
+    }
+
+    /** \returns a reference to a novel non zero coefficient with coordinates \a row x \a col.
+
+     *
+     * \warning This function can be extremely slow if the non zero coefficients
+     * are not inserted in a coherent order.
+     *
+     * After an insertion session, you should call the finalize() function.
+     */
+    EIGEN_DONT_INLINE Scalar & insert(int row, int col) {
+        const int outer = IsRowMajor ? row : col;
+        const int inner = IsRowMajor ? col : row;
+
+        ei_assert(outer < outerSize());
+        ei_assert(inner < innerSize());
+
+        if (outer == inner)
+            return m_data.diag(col);
+
+        if (IsRowMajor) {
+            if (outer < inner) //upper matrix
+            {
+                int minOuterIndex = 0;
+                minOuterIndex = inner - m_data.upperProfile(inner);
+
+                if (outer < minOuterIndex) //The value does not yet exist
+                {
+                    const int previousProfile = m_data.upperProfile(inner);
+
+                    m_data.upperProfile(inner) = inner - outer;
+
+
+                    const int bandIncrement = m_data.upperProfile(inner) - previousProfile;
+                    //shift data stored after this new one
+                    const int stop = m_colStartIndex[cols()];
+                    const int start = m_colStartIndex[inner];
+
+
+                    for (int innerIdx = stop; innerIdx >= start; innerIdx--) {
+                        m_data.upper(innerIdx + bandIncrement) = m_data.upper(innerIdx);
+                    }
+
+                    for (int innerIdx = cols(); innerIdx > inner; innerIdx--) {
+                        m_colStartIndex[innerIdx] += bandIncrement;
+                    }
+
+                    //zeros new data
+                    memset(this->_upperPtr() + start, 0, (bandIncrement - 1) * sizeof (Scalar));
+
+                    return m_data.upper(m_colStartIndex[inner]);
+                } else {
+                    return m_data.upper(m_colStartIndex[inner] + outer - (inner - m_data.upperProfile(inner)));
+                }
+            }
+
+            if (outer > inner) //lower matrix
+            {
+                const int minInnerIndex = outer - m_data.lowerProfile(outer);
+                if (inner < minInnerIndex) //The value does not yet exist
+                {
+                    const int previousProfile = m_data.lowerProfile(outer);
+                    m_data.lowerProfile(outer) = outer - inner;
+
+                    const int bandIncrement = m_data.lowerProfile(outer) - previousProfile;
+                    //shift data stored after this new one
+                    const int stop = m_rowStartIndex[rows()];
+                    const int start = m_rowStartIndex[outer];
+
+
+                    for (int innerIdx = stop; innerIdx >= start; innerIdx--) {
+                        m_data.lower(innerIdx + bandIncrement) = m_data.lower(innerIdx);
+                    }
+
+                    for (int innerIdx = rows(); innerIdx > outer; innerIdx--) {
+                        m_rowStartIndex[innerIdx] += bandIncrement;
+                    }
+
+                    //zeros new data
+                    memset(this->_lowerPtr() + start, 0, (bandIncrement - 1) * sizeof (Scalar));
+                    return m_data.lower(m_rowStartIndex[outer]);
+                } else {
+                    return m_data.lower(m_rowStartIndex[outer] + inner - (outer - m_data.lowerProfile(outer)));
+                }
+            }
+        } else {
+            if (outer > inner) //upper matrix
+            {
+                const int maxOuterIndex = inner + m_data.upperProfile(inner);
+                if (outer > maxOuterIndex) //The value does not yet exist
+                {
+                    const int previousProfile = m_data.upperProfile(inner);
+                    m_data.upperProfile(inner) = outer - inner;
+
+                    const int bandIncrement = m_data.upperProfile(inner) - previousProfile;
+                    //shift data stored after this new one
+                    const int stop = m_rowStartIndex[rows()];
+                    const int start = m_rowStartIndex[inner + 1];
+
+                    for (int innerIdx = stop; innerIdx >= start; innerIdx--) {
+                        m_data.upper(innerIdx + bandIncrement) = m_data.upper(innerIdx);
+                    }
+
+                    for (int innerIdx = inner + 1; innerIdx < outerSize() + 1; innerIdx++) {
+                        m_rowStartIndex[innerIdx] += bandIncrement;
+                    }
+                    memset(this->_upperPtr() + m_rowStartIndex[inner] + previousProfile + 1, 0, (bandIncrement - 1) * sizeof (Scalar));
+                    return m_data.upper(m_rowStartIndex[inner] + m_data.upperProfile(inner));
+                } else {
+                    return m_data.upper(m_rowStartIndex[inner] + (outer - inner));
+                }
+            }
+
+            if (outer < inner) //lower matrix
+            {
+                const int maxInnerIndex = outer + m_data.lowerProfile(outer);
+                if (inner > maxInnerIndex) //The value does not yet exist
+                {
+                    const int previousProfile = m_data.lowerProfile(outer);
+                    m_data.lowerProfile(outer) = inner - outer;
+
+                    const int bandIncrement = m_data.lowerProfile(outer) - previousProfile;
+                    //shift data stored after this new one
+                    const int stop = m_colStartIndex[cols()];
+                    const int start = m_colStartIndex[outer + 1];
+
+                    for (int innerIdx = stop; innerIdx >= start; innerIdx--) {
+                        m_data.lower(innerIdx + bandIncrement) = m_data.lower(innerIdx);
+                    }
+
+                    for (int innerIdx = outer + 1; innerIdx < outerSize() + 1; innerIdx++) {
+                        m_colStartIndex[innerIdx] += bandIncrement;
+                    }
+                    memset(this->_lowerPtr() + m_colStartIndex[outer] + previousProfile + 1, 0, (bandIncrement - 1) * sizeof (Scalar));
+                    return m_data.lower(m_colStartIndex[outer] + m_data.lowerProfile(outer));
+                } else {
+                    return m_data.lower(m_colStartIndex[outer] + (inner - outer));
+                }
+            }
+        }
+    }
+
+    /** Must be called after inserting a set of non zero entries.
+     */
+    inline void finalize() {
+        if (IsRowMajor) {
+            if (rows() > cols())
+                m_data.resize(cols(), cols(), rows(), m_colStartIndex[cols()] + 1, m_rowStartIndex[rows()] + 1);
+            else
+                m_data.resize(rows(), cols(), rows(), m_colStartIndex[cols()] + 1, m_rowStartIndex[rows()] + 1);
+
+            //            ei_assert(rows() == cols() && "memory reorganisatrion only works with suare matrix");
+            //
+            //            Scalar* newArray = new Scalar[m_colStartIndex[cols()] + 1 + m_rowStartIndex[rows()] + 1];
+            //            unsigned int dataIdx = 0;
+            //            for (unsigned int row = 0; row < rows(); row++) {
+            //
+            //                const unsigned int nbLowerElts = m_rowStartIndex[row + 1] - m_rowStartIndex[row];
+            //                //                std::cout << "nbLowerElts" << nbLowerElts << std::endl;
+            //                memcpy(newArray + dataIdx, m_data.m_lower + m_rowStartIndex[row], nbLowerElts * sizeof (Scalar));
+            //                m_rowStartIndex[row] = dataIdx;
+            //                dataIdx += nbLowerElts;
+            //
+            //                const unsigned int nbUpperElts = m_colStartIndex[row + 1] - m_colStartIndex[row];
+            //                memcpy(newArray + dataIdx, m_data.m_upper + m_colStartIndex[row], nbUpperElts * sizeof (Scalar));
+            //                m_colStartIndex[row] = dataIdx;
+            //                dataIdx += nbUpperElts;
+            //
+            //
+            //            }
+            //            //todo : don't access m_data profile directly : add an accessor from SkylineMatrix
+            //            m_rowStartIndex[rows()] = m_rowStartIndex[rows()-1] + m_data.lowerProfile(rows()-1);
+            //            m_colStartIndex[cols()] = m_colStartIndex[cols()-1] + m_data.upperProfile(cols()-1);
+            //
+            //            delete[] m_data.m_lower;
+            //            delete[] m_data.m_upper;
+            //
+            //            m_data.m_lower = newArray;
+            //            m_data.m_upper = newArray;
+        } else {
+            if (rows() > cols())
+                m_data.resize(cols(), rows(), cols(), m_rowStartIndex[cols()] + 1, m_colStartIndex[cols()] + 1);
+            else
+                m_data.resize(rows(), rows(), cols(), m_rowStartIndex[rows()] + 1, m_colStartIndex[rows()] + 1);
+        }
+    }
+
+    inline void squeeze() {
+        finalize();
+        m_data.squeeze();
+    }
+
+    void prune(Scalar reference, RealScalar epsilon = precision<RealScalar > ()) {
+        //TODO
+    }
+
+    /** Resizes the matrix to a \a rows x \a cols matrix and initializes it to zero
+     * \sa resizeNonZeros(int), reserve(), setZero()
+     */
+    void resize(size_t rows, size_t cols) {
+        const int diagSize = rows > cols ? cols : rows;
+        m_innerSize = IsRowMajor ? cols : rows;
+
+        ei_assert(rows == cols && "Skyline matrix must be square matrix");
+
+        if (diagSize % 2) { // diagSize is odd
+            const int k = (diagSize - 1) / 2;
+
+            m_data.resize(diagSize, IsRowMajor ? cols : rows, IsRowMajor ? rows : cols,
+                    2 * k * k + k + 1,
+                    2 * k * k + k + 1);
+
+        } else // diagSize is even
+        {
+            const int k = diagSize / 2;
+            m_data.resize(diagSize, IsRowMajor ? cols : rows, IsRowMajor ? rows : cols,
+                    2 * k * k - k + 1,
+                    2 * k * k - k + 1);
+        }
+
+        if (m_colStartIndex && m_rowStartIndex) {
+            delete[] m_colStartIndex;
+            delete[] m_rowStartIndex;
+        }
+        m_colStartIndex = new int [cols + 1];
+        m_rowStartIndex = new int [rows + 1];
+        m_outerSize = diagSize;
+
+        m_data.reset();
+        m_data.clear();
+
+        m_outerSize = diagSize;
+        memset(m_colStartIndex, 0, (cols + 1) * sizeof (int));
+        memset(m_rowStartIndex, 0, (rows + 1) * sizeof (int));
+    }
+
+    void resizeNonZeros(int size) {
+        m_data.resize(size);
+    }
+
+    inline SkylineMatrix()
+    : m_outerSize(-1), m_innerSize(0), m_colStartIndex(0), m_rowStartIndex(0) {
+        resize(0, 0);
+    }
+
+    inline SkylineMatrix(size_t rows, size_t cols)
+    : m_outerSize(0), m_innerSize(0), m_colStartIndex(0), m_rowStartIndex(0) {
+        resize(rows, cols);
+    }
+
+    template<typename OtherDerived>
+    inline SkylineMatrix(const SkylineMatrixBase<OtherDerived>& other)
+    : m_outerSize(0), m_innerSize(0), m_colStartIndex(0), m_rowStartIndex(0) {
+        *this = other.derived();
+    }
+
+    inline SkylineMatrix(const SkylineMatrix & other)
+    : Base(), m_outerSize(0), m_innerSize(0), m_colStartIndex(0), m_rowStartIndex(0) {
+        *this = other.derived();
+    }
+
+    inline void swap(SkylineMatrix & other) {
+        //EIGEN_DBG_SKYLINE(std::cout << "SkylineMatrix:: swap\n");
+        std::swap(m_colStartIndex, other.m_colStartIndex);
+        std::swap(m_rowStartIndex, other.m_rowStartIndex);
+        std::swap(m_innerSize, other.m_innerSize);
+        std::swap(m_outerSize, other.m_outerSize);
+        m_data.swap(other.m_data);
+    }
+
+    inline SkylineMatrix & operator=(const SkylineMatrix & other) {
+        std::cout << "SkylineMatrix& operator=(const SkylineMatrix& other)\n";
+        if (other.isRValue()) {
+            swap(other.const_cast_derived());
+        } else {
+            resize(other.rows(), other.cols());
+            memcpy(m_colStartIndex, other.m_colStartIndex, (m_outerSize + 1) * sizeof (int));
+            memcpy(m_rowStartIndex, other.m_rowStartIndex, (m_outerSize + 1) * sizeof (int));
+            m_data = other.m_data;
+        }
+        return *this;
+    }
+
+    template<typename OtherDerived>
+            inline SkylineMatrix & operator=(const SkylineMatrixBase<OtherDerived>& other) {
+        const bool needToTranspose = (Flags & RowMajorBit) != (OtherDerived::Flags & RowMajorBit);
+        if (needToTranspose) {
+            //         TODO
+            //            return *this;
+        } else {
+            // there is no special optimization
+            return SkylineMatrixBase<SkylineMatrix>::operator=(other.derived());
+        }
+    }
+
+    friend std::ostream & operator <<(std::ostream & s, const SkylineMatrix & m) {
+
+        EIGEN_DBG_SKYLINE(
+        std::cout << "upper elements : " << std::endl;
+        for (unsigned int i = 0; i < m.m_data.upperSize(); i++)
+            std::cout << m.m_data.upper(i) << "\t";
+        std::cout << std::endl;
+        std::cout << "upper profile : " << std::endl;
+        for (unsigned int i = 0; i < m.m_data.upperProfileSize(); i++)
+            std::cout << m.m_data.upperProfile(i) << "\t";
+        std::cout << std::endl;
+        std::cout << "lower startIdx : " << std::endl;
+        for (unsigned int i = 0; i < m.m_data.upperProfileSize(); i++)
+            std::cout << (IsRowMajor ? m.m_colStartIndex[i] : m.m_rowStartIndex[i]) << "\t";
+        std::cout << std::endl;
+
+
+        std::cout << "lower elements : " << std::endl;
+        for (unsigned int i = 0; i < m.m_data.lowerSize(); i++)
+            std::cout << m.m_data.lower(i) << "\t";
+        std::cout << std::endl;
+        std::cout << "lower profile : " << std::endl;
+        for (unsigned int i = 0; i < m.m_data.lowerProfileSize(); i++)
+            std::cout << m.m_data.lowerProfile(i) << "\t";
+        std::cout << std::endl;
+        std::cout << "lower startIdx : " << std::endl;
+        for (unsigned int i = 0; i < m.m_data.lowerProfileSize(); i++)
+            std::cout << (IsRowMajor ? m.m_rowStartIndex[i] : m.m_colStartIndex[i]) << "\t";
+        std::cout << std::endl;
+        );
+        for (unsigned int rowIdx = 0; rowIdx < m.rows(); rowIdx++) {
+            for (unsigned int colIdx = 0; colIdx < m.cols(); colIdx++) {
+                s << m.coeff(rowIdx, colIdx) << "\t";
+            }
+            s << std::endl;
+        }
+        return s;
+    }
+
+    /** Destructor */
+    inline ~SkylineMatrix() {
+        delete[] m_colStartIndex;
+        delete[] m_rowStartIndex;
+    }
+
+    /** Overloaded for performance */
+    Scalar sum() const;
+};
+
+template<typename Scalar, int _Options>
+class SkylineMatrix<Scalar, _Options>::InnerUpperIterator {
+public:
+
+    InnerUpperIterator(const SkylineMatrix& mat, int outer)
+    : m_matrix(mat), m_outer(outer),
+    m_id(_Options == RowMajor ? mat.m_colStartIndex[outer] : mat.m_rowStartIndex[outer] + 1),
+    m_start(m_id),
+    m_end(_Options == RowMajor ? mat.m_colStartIndex[outer + 1] : mat.m_rowStartIndex[outer + 1] + 1) {
+    }
+
+    inline InnerUpperIterator & operator++() {
+        m_id++;
+        return *this;
+    }
+
+    inline InnerUpperIterator & operator+=(unsigned int shift) {
+        m_id += shift;
+        return *this;
+    }
+
+    inline Scalar value() const {
+        return m_matrix.m_data.upper(m_id);
+    }
+
+    inline Scalar* valuePtr() {
+        return const_cast<Scalar*> (&(m_matrix.m_data.upper(m_id)));
+    }
+
+    inline Scalar& valueRef() {
+        return const_cast<Scalar&> (m_matrix.m_data.upper(m_id));
+    }
+
+    inline int index() const {
+        return IsRowMajor ? m_outer - m_matrix.m_data.upperProfile(m_outer) + (m_id - m_start) :
+                m_outer + (m_id - m_start) + 1;
+    }
+
+    inline int row() const {
+        return IsRowMajor ? index() : m_outer;
+    }
+
+    inline int col() const {
+        return IsRowMajor ? m_outer : index();
+    }
+
+    inline size_t size() const {
+        return m_matrix.m_data.upperProfile(m_outer);
+    }
+
+    inline operator bool() const {
+        return (m_id < m_end) && (m_id >= m_start);
+    }
+
+protected:
+    const SkylineMatrix& m_matrix;
+    const int m_outer;
+    int m_id;
+    const int m_start;
+    const int m_end;
+};
+
+template<typename Scalar, int _Options>
+class SkylineMatrix<Scalar, _Options>::InnerLowerIterator {
+public:
+
+    InnerLowerIterator(const SkylineMatrix& mat, int outer)
+    : m_matrix(mat),
+    m_outer(outer),
+    m_id(_Options == RowMajor ? mat.m_rowStartIndex[outer] : mat.m_colStartIndex[outer] + 1),
+    m_start(m_id),
+    m_end(_Options == RowMajor ? mat.m_rowStartIndex[outer + 1] : mat.m_colStartIndex[outer + 1] + 1) {
+    }
+
+    inline InnerLowerIterator & operator++() {
+        m_id++;
+        return *this;
+    }
+
+    inline InnerLowerIterator & operator+=(unsigned int shift) {
+        m_id += shift;
+        return *this;
+    }
+
+    inline Scalar value() const {
+        return m_matrix.m_data.lower(m_id);
+    }
+
+    inline Scalar* valuePtr() {
+        return const_cast<Scalar*> (&(m_matrix.m_data.lower(m_id)));
+    }
+
+    inline Scalar& valueRef() {
+        return const_cast<Scalar&> (m_matrix.m_data.lower(m_id));
+    }
+
+    inline int index() const {
+        return IsRowMajor ? m_outer - m_matrix.m_data.lowerProfile(m_outer) + (m_id - m_start) :
+                m_outer + (m_id - m_start) + 1;
+        ;
+    }
+
+    inline int row() const {
+        return IsRowMajor ? m_outer : index();
+    }
+
+    inline int col() const {
+        return IsRowMajor ? index() : m_outer;
+    }
+
+    inline size_t size() const {
+        return m_matrix.m_data.lowerProfile(m_outer);
+    }
+
+    inline operator bool() const {
+        return (m_id < m_end) && (m_id >= m_start);
+    }
+
+protected:
+    const SkylineMatrix& m_matrix;
+    const int m_outer;
+    int m_id;
+    const int m_start;
+    const int m_end;
+};
+
+#endif // EIGEN_SkylineMatrix_H
diff --git a/unsupported/Eigen/src/Skyline/SkylineMatrixBase.h b/unsupported/Eigen/src/Skyline/SkylineMatrixBase.h
new file mode 100644
index 000000000..b90a6f9e9
--- /dev/null
+++ b/unsupported/Eigen/src/Skyline/SkylineMatrixBase.h
@@ -0,0 +1,221 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Guillaume Saupin <guillaume.saupin@cea.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_SKYLINEMATRIXBASE_H
+#define EIGEN_SKYLINEMATRIXBASE_H
+
+#include "SkylineUtil.h"
+
+/** \ingroup Skyline_Module
+ *
+ * \class SkylineMatrixBase
+ *
+ * \brief Base class of any skyline matrices or skyline expressions
+ *
+ * \param Derived
+ *
+ */
+template<typename Derived> class SkylineMatrixBase : public AnyMatrixBase<Derived> {
+public:
+
+    typedef typename ei_traits<Derived>::Scalar Scalar;
+
+    enum {
+        RowsAtCompileTime = ei_traits<Derived>::RowsAtCompileTime,
+        /**< The number of rows at compile-time. This is just a copy of the value provided
+         * by the \a Derived type. If a value is not known at compile-time,
+         * it is set to the \a Dynamic constant.
+         * \sa MatrixBase::rows(), MatrixBase::cols(), ColsAtCompileTime, SizeAtCompileTime */
+
+        ColsAtCompileTime = ei_traits<Derived>::ColsAtCompileTime,
+        /**< The number of columns at compile-time. This is just a copy of the value provided
+         * by the \a Derived type. If a value is not known at compile-time,
+         * it is set to the \a Dynamic constant.
+         * \sa MatrixBase::rows(), MatrixBase::cols(), RowsAtCompileTime, SizeAtCompileTime */
+
+
+        SizeAtCompileTime = (ei_size_at_compile_time<ei_traits<Derived>::RowsAtCompileTime,
+        ei_traits<Derived>::ColsAtCompileTime>::ret),
+        /**< This is equal to the number of coefficients, i.e. the number of
+         * rows times the number of columns, or to \a Dynamic if this is not
+         * known at compile-time. \sa RowsAtCompileTime, ColsAtCompileTime */
+
+        MaxRowsAtCompileTime = RowsAtCompileTime,
+        MaxColsAtCompileTime = ColsAtCompileTime,
+
+        MaxSizeAtCompileTime = (ei_size_at_compile_time<MaxRowsAtCompileTime,
+        MaxColsAtCompileTime>::ret),
+
+        IsVectorAtCompileTime = RowsAtCompileTime == 1 || ColsAtCompileTime == 1,
+        /**< This is set to true if either the number of rows or the number of
+         * columns is known at compile-time to be equal to 1. Indeed, in that case,
+         * we are dealing with a column-vector (if there is only one column) or with
+         * a row-vector (if there is only one row). */
+
+        Flags = ei_traits<Derived>::Flags,
+        /**< This stores expression \ref flags flags which may or may not be inherited by new expressions
+         * constructed from this one. See the \ref flags "list of flags".
+         */
+
+        CoeffReadCost = ei_traits<Derived>::CoeffReadCost,
+        /**< This is a rough measure of how expensive it is to read one coefficient from
+         * this expression.
+         */
+
+        IsRowMajor = Flags & RowMajorBit ? 1 : 0
+    };
+
+#ifndef EIGEN_PARSED_BY_DOXYGEN
+    /** This is the "real scalar" type; if the \a Scalar type is already real numbers
+     * (e.g. int, float or double) then \a RealScalar is just the same as \a Scalar. If
+     * \a Scalar is \a std::complex<T> then RealScalar is \a T.
+     *
+     * \sa class NumTraits
+     */
+    typedef typename NumTraits<Scalar>::Real RealScalar;
+
+    /** type of the equivalent square matrix */
+    typedef Matrix<Scalar, EIGEN_ENUM_MAX(RowsAtCompileTime, ColsAtCompileTime),
+    EIGEN_ENUM_MAX(RowsAtCompileTime, ColsAtCompileTime) > SquareMatrixType;
+
+    inline const Derived& derived() const {
+        return *static_cast<const Derived*> (this);
+    }
+
+    inline Derived& derived() {
+        return *static_cast<Derived*> (this);
+    }
+
+    inline Derived& const_cast_derived() const {
+        return *static_cast<Derived*> (const_cast<SkylineMatrixBase*> (this));
+    }
+#endif // not EIGEN_PARSED_BY_DOXYGEN
+
+    /** \returns the number of rows. \sa cols(), RowsAtCompileTime */
+    inline int rows() const {
+        return derived().rows();
+    }
+
+    /** \returns the number of columns. \sa rows(), ColsAtCompileTime*/
+    inline int cols() const {
+        return derived().cols();
+    }
+
+    /** \returns the number of coefficients, which is \a rows()*cols().
+     * \sa rows(), cols(), SizeAtCompileTime. */
+    inline int size() const {
+        return rows() * cols();
+    }
+
+    /** \returns the number of nonzero coefficients which is in practice the number
+     * of stored coefficients. */
+    inline int nonZeros() const {
+        return derived().nonZeros();
+    }
+
+    /** \returns the size of the storage major dimension,
+     * i.e., the number of columns for a columns major matrix, and the number of rows otherwise */
+    int outerSize() const {
+        return (int(Flags) & RowMajorBit) ? this->rows() : this->cols();
+    }
+
+    /** \returns the size of the inner dimension according to the storage order,
+     * i.e., the number of rows for a columns major matrix, and the number of cols otherwise */
+    int innerSize() const {
+        return (int(Flags) & RowMajorBit) ? this->cols() : this->rows();
+    }
+
+    bool isRValue() const {
+        return m_isRValue;
+    }
+
+    Derived& markAsRValue() {
+        m_isRValue = true;
+        return derived();
+    }
+
+    SkylineMatrixBase() : m_isRValue(false) {
+        /* TODO check flags */
+    }
+
+    inline Derived & operator=(const Derived& other) {
+        this->operator=<Derived > (other);
+        return derived();
+    }
+
+    template<typename OtherDerived>
+    inline void assignGeneric(const OtherDerived& other) {
+        derived().resize(other.rows(), other.cols());
+        for (unsigned int row = 0; row < rows(); row++)
+            for (unsigned int col = 0; col < cols(); col++) {
+                if (other.coeff(row, col) != Scalar(0))
+                    derived().insert(row, col) = other.coeff(row, col);
+            }
+        derived().finalize();
+    }
+
+    template<typename OtherDerived>
+            inline Derived & operator=(const SkylineMatrixBase<OtherDerived>& other) {
+        //TODO
+    }
+
+    template<typename Lhs, typename Rhs>
+            inline Derived & operator=(const SkylineProduct<Lhs, Rhs, SkylineTimeSkylineProduct>& product);
+
+    friend std::ostream & operator <<(std::ostream & s, const SkylineMatrixBase& m) {
+        s << m.derived();
+        return s;
+    }
+
+    template<typename OtherDerived>
+    const typename SkylineProductReturnType<Derived, OtherDerived>::Type
+    operator*(const MatrixBase<OtherDerived> &other) const;
+
+    /** \internal use operator= */
+    template<typename DenseDerived>
+    void evalTo(MatrixBase<DenseDerived>& dst) const {
+        dst.setZero();
+        for (unsigned int i = 0; i < rows(); i++)
+            for (unsigned int j = 0; j < rows(); j++)
+                dst(i, j) = derived().coeff(i, j);
+    }
+
+    Matrix<Scalar, RowsAtCompileTime, ColsAtCompileTime> toDense() const {
+        return derived();
+    }
+
+    /** \returns the matrix or vector obtained by evaluating this expression.
+     *
+     * Notice that in the case of a plain matrix or vector (not an expression) this function just returns
+     * a const reference, in order to avoid a useless copy.
+     */
+    EIGEN_STRONG_INLINE const typename ei_eval<Derived, IsSkyline>::type eval() const {
+        return typename ei_eval<Derived>::type(derived());
+    }
+
+protected:
+    bool m_isRValue;
+};
+
+#endif // EIGEN_SkylineMatrixBase_H
diff --git a/unsupported/Eigen/src/Skyline/SkylineProduct.h b/unsupported/Eigen/src/Skyline/SkylineProduct.h
new file mode 100644
index 000000000..85ccacac8
--- /dev/null
+++ b/unsupported/Eigen/src/Skyline/SkylineProduct.h
@@ -0,0 +1,314 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Guillaume Saupin <guillaume.saupin@cea.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_SKYLINEPRODUCT_H
+#define EIGEN_SKYLINEPRODUCT_H
+
+template<typename Lhs, typename Rhs> struct ei_skyline_product_mode {
+
+    enum {
+        value = (Rhs::Flags & Lhs::Flags & SkylineBit) == SkylineBit
+        ? SkylineTimeSkylineProduct
+        : (Lhs::Flags & SkylineBit) == SkylineBit
+        ? SkylineTimeDenseProduct
+        : DenseTimeSkylineProduct
+    };
+};
+
+template<typename Lhs, typename Rhs, int ProductMode>
+struct SkylineProductReturnType {
+    typedef const typename ei_nested<Lhs, Rhs::RowsAtCompileTime>::type LhsNested;
+    typedef const typename ei_nested<Rhs, Lhs::RowsAtCompileTime>::type RhsNested;
+
+    typedef SkylineProduct<LhsNested, RhsNested, ProductMode> Type;
+};
+
+template<typename LhsNested, typename RhsNested, int ProductMode>
+struct ei_traits<SkylineProduct<LhsNested, RhsNested, ProductMode> > {
+    // clean the nested types:
+    typedef typename ei_cleantype<LhsNested>::type _LhsNested;
+    typedef typename ei_cleantype<RhsNested>::type _RhsNested;
+    typedef typename _LhsNested::Scalar Scalar;
+
+    enum {
+        LhsCoeffReadCost = _LhsNested::CoeffReadCost,
+        RhsCoeffReadCost = _RhsNested::CoeffReadCost,
+        LhsFlags = _LhsNested::Flags,
+        RhsFlags = _RhsNested::Flags,
+
+        RowsAtCompileTime = _LhsNested::RowsAtCompileTime,
+        ColsAtCompileTime = _RhsNested::ColsAtCompileTime,
+        InnerSize = EIGEN_ENUM_MIN(_LhsNested::ColsAtCompileTime, _RhsNested::RowsAtCompileTime),
+
+        MaxRowsAtCompileTime = _LhsNested::MaxRowsAtCompileTime,
+        MaxColsAtCompileTime = _RhsNested::MaxColsAtCompileTime,
+
+        EvalToRowMajor = (RhsFlags & LhsFlags & RowMajorBit),
+        ResultIsSkyline = ProductMode == SkylineTimeSkylineProduct,
+
+        RemovedBits = ~((EvalToRowMajor ? 0 : RowMajorBit) | (ResultIsSkyline ? 0 : SkylineBit)),
+
+        Flags = (int(LhsFlags | RhsFlags) & HereditaryBits & RemovedBits)
+        | EvalBeforeAssigningBit
+        | EvalBeforeNestingBit,
+
+        CoeffReadCost = Dynamic
+    };
+
+    typedef typename ei_meta_if<ResultIsSkyline,
+            SkylineMatrixBase<SkylineProduct<LhsNested, RhsNested, ProductMode> >,
+            MatrixBase<SkylineProduct<LhsNested, RhsNested, ProductMode> > >::ret Base;
+};
+
+template<typename LhsNested, typename RhsNested, int ProductMode>
+class SkylineProduct : ei_no_assignment_operator,
+public ei_traits<SkylineProduct<LhsNested, RhsNested, ProductMode> >::Base {
+public:
+
+    EIGEN_GENERIC_PUBLIC_INTERFACE(SkylineProduct)
+
+private:
+
+    typedef typename ei_traits<SkylineProduct>::_LhsNested _LhsNested;
+    typedef typename ei_traits<SkylineProduct>::_RhsNested _RhsNested;
+
+public:
+
+    template<typename Lhs, typename Rhs>
+    EIGEN_STRONG_INLINE SkylineProduct(const Lhs& lhs, const Rhs& rhs)
+    : m_lhs(lhs), m_rhs(rhs) {
+        ei_assert(lhs.cols() == rhs.rows());
+
+        enum {
+            ProductIsValid = _LhsNested::ColsAtCompileTime == Dynamic
+            || _RhsNested::RowsAtCompileTime == Dynamic
+            || int(_LhsNested::ColsAtCompileTime) == int(_RhsNested::RowsAtCompileTime),
+            AreVectors = _LhsNested::IsVectorAtCompileTime && _RhsNested::IsVectorAtCompileTime,
+            SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(_LhsNested, _RhsNested)
+        };
+        // note to the lost user:
+        //    * for a dot product use: v1.dot(v2)
+        //    * for a coeff-wise product use: v1.cwise()*v2
+        EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
+                INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
+                EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
+                INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
+                EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
+    }
+
+    EIGEN_STRONG_INLINE int rows() const {
+        return m_lhs.rows();
+    }
+
+    EIGEN_STRONG_INLINE int cols() const {
+        return m_rhs.cols();
+    }
+
+    EIGEN_STRONG_INLINE const _LhsNested& lhs() const {
+        return m_lhs;
+    }
+
+    EIGEN_STRONG_INLINE const _RhsNested& rhs() const {
+        return m_rhs;
+    }
+
+protected:
+    LhsNested m_lhs;
+    RhsNested m_rhs;
+};
+
+// dense = skyline * dense
+// Note that here we force no inlining and separate the setZero() because GCC messes up otherwise
+
+template<typename Lhs, typename Rhs, typename Dest>
+EIGEN_DONT_INLINE void ei_skyline_row_major_time_dense_product(const Lhs& lhs, const Rhs& rhs, Dest& dst) {
+    typedef typename ei_cleantype<Lhs>::type _Lhs;
+    typedef typename ei_cleantype<Rhs>::type _Rhs;
+    typedef typename ei_traits<Lhs>::Scalar Scalar;
+
+    enum {
+        LhsIsRowMajor = (_Lhs::Flags & RowMajorBit) == RowMajorBit,
+        LhsIsSelfAdjoint = (_Lhs::Flags & SelfAdjointBit) == SelfAdjointBit,
+        ProcessFirstHalf = LhsIsSelfAdjoint
+        && (((_Lhs::Flags & (UpperTriangularBit | LowerTriangularBit)) == 0)
+        || ((_Lhs::Flags & UpperTriangularBit) && !LhsIsRowMajor)
+        || ((_Lhs::Flags & LowerTriangularBit) && LhsIsRowMajor)),
+        ProcessSecondHalf = LhsIsSelfAdjoint && (!ProcessFirstHalf)
+    };
+
+    //Use matrix diagonal part <- Improvement : use inner iterator on dense matrix.
+    for (unsigned int col = 0; col < rhs.cols(); col++) {
+        for (unsigned int row = 0; row < lhs.rows(); row++) {
+            dst(row, col) = lhs.coeffDiag(row) * rhs(row, col);
+        }
+    }
+    //Use matrix lower triangular part
+    for (unsigned int row = 0; row < lhs.rows(); row++) {
+        typename _Lhs::InnerLowerIterator lIt(lhs, row);
+        const int stop = lIt.col() + lIt.size();
+        for (unsigned int col = 0; col < rhs.cols(); col++) {
+
+            unsigned int k = lIt.col();
+            Scalar tmp = 0;
+            while (k < stop) {
+                tmp +=
+                        lIt.value() *
+                        rhs(k++, col);
+                ++lIt;
+            }
+            dst(row, col) += tmp;
+            lIt += -lIt.size();
+        }
+
+    }
+
+    //Use matrix upper triangular part
+    for (unsigned int lhscol = 0; lhscol < lhs.cols(); lhscol++) {
+        typename _Lhs::InnerUpperIterator uIt(lhs, lhscol);
+        const int stop = uIt.size() + uIt.row();
+        for (unsigned int rhscol = 0; rhscol < rhs.cols(); rhscol++) {
+
+
+            const Scalar rhsCoeff = rhs.coeff(lhscol, rhscol);
+            unsigned int k = uIt.row();
+            while (k < stop) {
+                dst(k++, rhscol) +=
+                        uIt.value() *
+                        rhsCoeff;
+                ++uIt;
+            }
+            uIt += -uIt.size();
+        }
+    }
+
+}
+
+template<typename Lhs, typename Rhs, typename Dest>
+EIGEN_DONT_INLINE void ei_skyline_col_major_time_dense_product(const Lhs& lhs, const Rhs& rhs, Dest& dst) {
+    typedef typename ei_cleantype<Lhs>::type _Lhs;
+    typedef typename ei_cleantype<Rhs>::type _Rhs;
+    typedef typename ei_traits<Lhs>::Scalar Scalar;
+
+    enum {
+        LhsIsRowMajor = (_Lhs::Flags & RowMajorBit) == RowMajorBit,
+        LhsIsSelfAdjoint = (_Lhs::Flags & SelfAdjointBit) == SelfAdjointBit,
+        ProcessFirstHalf = LhsIsSelfAdjoint
+        && (((_Lhs::Flags & (UpperTriangularBit | LowerTriangularBit)) == 0)
+        || ((_Lhs::Flags & UpperTriangularBit) && !LhsIsRowMajor)
+        || ((_Lhs::Flags & LowerTriangularBit) && LhsIsRowMajor)),
+        ProcessSecondHalf = LhsIsSelfAdjoint && (!ProcessFirstHalf)
+    };
+
+    //Use matrix diagonal part <- Improvement : use inner iterator on dense matrix.
+    for (unsigned int col = 0; col < rhs.cols(); col++) {
+        for (unsigned int row = 0; row < lhs.rows(); row++) {
+            dst(row, col) = lhs.coeffDiag(row) * rhs(row, col);
+        }
+    }
+
+    //Use matrix upper triangular part
+    for (unsigned int row = 0; row < lhs.rows(); row++) {
+        typename _Lhs::InnerUpperIterator uIt(lhs, row);
+        const int stop = uIt.col() + uIt.size();
+        for (unsigned int col = 0; col < rhs.cols(); col++) {
+
+            unsigned int k = uIt.col();
+            Scalar tmp = 0;
+            while (k < stop) {
+                tmp +=
+                        uIt.value() *
+                        rhs(k++, col);
+                ++uIt;
+            }
+
+
+            dst(row, col) += tmp;
+            uIt += -uIt.size();
+        }
+    }
+
+    //Use matrix lower triangular part
+    for (unsigned int lhscol = 0; lhscol < lhs.cols(); lhscol++) {
+        typename _Lhs::InnerLowerIterator lIt(lhs, lhscol);
+        const int stop = lIt.size() + lIt.row();
+        for (unsigned int rhscol = 0; rhscol < rhs.cols(); rhscol++) {
+
+            const Scalar rhsCoeff = rhs.coeff(lhscol, rhscol);
+            unsigned int k = lIt.row();
+            while (k < stop) {
+                dst(k++, rhscol) +=
+                        lIt.value() *
+                        rhsCoeff;
+                ++lIt;
+            }
+            lIt += -lIt.size();
+        }
+    }
+
+}
+
+template<typename Lhs, typename Rhs, typename ResultType,
+        int LhsStorageOrder = ei_traits<Lhs>::Flags&RowMajorBit>
+        struct ei_skyline_product_selector;
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct ei_skyline_product_selector<Lhs, Rhs, ResultType, RowMajor> {
+    typedef typename ei_traits<typename ei_cleantype<Lhs>::type>::Scalar Scalar;
+
+    static void run(const Lhs& lhs, const Rhs& rhs, ResultType & res) {
+        ei_skyline_row_major_time_dense_product<Lhs, Rhs, ResultType > (lhs, rhs, res);
+    }
+};
+
+template<typename Lhs, typename Rhs, typename ResultType>
+struct ei_skyline_product_selector<Lhs, Rhs, ResultType, ColMajor> {
+    typedef typename ei_traits<typename ei_cleantype<Lhs>::type>::Scalar Scalar;
+
+    static void run(const Lhs& lhs, const Rhs& rhs, ResultType & res) {
+        ei_skyline_col_major_time_dense_product<Lhs, Rhs, ResultType > (lhs, rhs, res);
+    }
+};
+
+template<typename Derived>
+template<typename Lhs, typename Rhs >
+Derived & MatrixBase<Derived>::lazyAssign(const SkylineProduct<Lhs, Rhs, SkylineTimeDenseProduct>& product) {
+    typedef typename ei_cleantype<Lhs>::type _Lhs;
+    ei_skyline_product_selector<typename ei_cleantype<Lhs>::type,
+            typename ei_cleantype<Rhs>::type,
+            Derived>::run(product.lhs(), product.rhs(), derived());
+
+    return derived();
+}
+
+// skyline * dense
+
+template<typename Derived>
+template<typename OtherDerived >
+EIGEN_STRONG_INLINE const typename SkylineProductReturnType<Derived, OtherDerived>::Type
+SkylineMatrixBase<Derived>::operator*(const MatrixBase<OtherDerived> &other) const {
+
+    return typename SkylineProductReturnType<Derived, OtherDerived>::Type(derived(), other.derived());
+}
+
+#endif // EIGEN_SKYLINEPRODUCT_H
diff --git a/unsupported/Eigen/src/Skyline/SkylineStorage.h b/unsupported/Eigen/src/Skyline/SkylineStorage.h
new file mode 100644
index 000000000..f725da0bf
--- /dev/null
+++ b/unsupported/Eigen/src/Skyline/SkylineStorage.h
@@ -0,0 +1,269 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Guillaume Saupin <guillaume.saupin@cea.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_SKYLINE_STORAGE_H
+#define EIGEN_SKYLINE_STORAGE_H
+
+/** Stores a skyline set of values in three structures :
+ * The diagonal elements
+ * The upper elements
+ * The lower elements
+ *
+ */
+template<typename Scalar>
+class SkylineStorage {
+    typedef typename NumTraits<Scalar>::Real RealScalar;
+public:
+
+    SkylineStorage()
+    : m_diag(0),
+    m_lower(0),
+    m_upper(0),
+    m_lowerProfile(0),
+    m_upperProfile(0),
+    m_diagSize(0),
+    m_upperSize(0),
+    m_lowerSize(0),
+    m_upperProfileSize(0),
+    m_lowerProfileSize(0),
+    m_allocatedSize(0) {
+    }
+
+    SkylineStorage(const SkylineStorage& other)
+    : m_diag(0),
+    m_lower(0),
+    m_upper(0),
+    m_lowerProfile(0),
+    m_upperProfile(0),
+    m_diagSize(0),
+    m_upperSize(0),
+    m_lowerSize(0),
+    m_upperProfileSize(0),
+    m_lowerProfileSize(0),
+    m_allocatedSize(0) {
+        *this = other;
+    }
+
+    SkylineStorage & operator=(const SkylineStorage& other) {
+        resize(other.diagSize(), other.m_upperProfileSize, other.m_lowerProfileSize, other.upperSize(), other.lowerSize());
+        memcpy(m_diag, other.m_diag, m_diagSize * sizeof (Scalar));
+        memcpy(m_upper, other.m_upper, other.upperSize() * sizeof (Scalar));
+        memcpy(m_lower, other.m_lower, other.lowerSize() * sizeof (Scalar));
+        memcpy(m_upperProfile, other.m_upperProfile, m_upperProfileSize * sizeof (int));
+        memcpy(m_lowerProfile, other.m_lowerProfile, m_lowerProfileSize * sizeof (int));
+        return *this;
+    }
+
+    void swap(SkylineStorage& other) {
+        std::swap(m_diag, other.m_diag);
+        std::swap(m_upper, other.m_upper);
+        std::swap(m_lower, other.m_lower);
+        std::swap(m_upperProfile, other.m_upperProfile);
+        std::swap(m_lowerProfile, other.m_lowerProfile);
+        std::swap(m_diagSize, other.m_diagSize);
+        std::swap(m_upperSize, other.m_upperSize);
+        std::swap(m_lowerSize, other.m_lowerSize);
+        std::swap(m_allocatedSize, other.m_allocatedSize);
+    }
+
+    ~SkylineStorage() {
+        delete[] m_diag;
+        delete[] m_upper;
+        if (m_upper != m_lower)
+            delete[] m_lower;
+        delete[] m_upperProfile;
+        delete[] m_lowerProfile;
+    }
+
+    void reserve(size_t size, size_t upperProfileSize, size_t lowerProfileSize, size_t upperSize, size_t lowerSize) {
+        int newAllocatedSize = size + upperSize + lowerSize;
+        if (newAllocatedSize > m_allocatedSize)
+            reallocate(size, upperProfileSize, lowerProfileSize, upperSize, lowerSize);
+    }
+
+    void squeeze() {
+        if (m_allocatedSize > m_diagSize + m_upperSize + m_lowerSize)
+            reallocate(m_diagSize, m_upperProfileSize, m_lowerProfileSize, m_upperSize, m_lowerSize);
+    }
+
+    void resize(size_t diagSize, size_t upperProfileSize, size_t lowerProfileSize, size_t upperSize, size_t lowerSize, float reserveSizeFactor = 0) {
+        if (m_allocatedSize < diagSize + upperSize + lowerSize)
+            reallocate(diagSize, upperProfileSize, lowerProfileSize, upperSize + size_t(reserveSizeFactor * upperSize), lowerSize + size_t(reserveSizeFactor * lowerSize));
+        m_diagSize = diagSize;
+        m_upperSize = upperSize;
+        m_lowerSize = lowerSize;
+        m_upperProfileSize = upperProfileSize;
+        m_lowerProfileSize = lowerProfileSize;
+    }
+
+    inline size_t diagSize() const {
+        return m_diagSize;
+    }
+
+    inline size_t upperSize() const {
+        return m_upperSize;
+    }
+
+    inline size_t lowerSize() const {
+        return m_lowerSize;
+    }
+
+    inline size_t upperProfileSize() const {
+        return m_upperProfileSize;
+    }
+
+    inline size_t lowerProfileSize() const {
+        return m_lowerProfileSize;
+    }
+
+    inline size_t allocatedSize() const {
+        return m_allocatedSize;
+    }
+
+    inline void clear() {
+        m_diagSize = 0;
+    }
+
+    inline Scalar& diag(size_t i) {
+        return m_diag[i];
+    }
+
+    inline const Scalar& diag(size_t i) const {
+        return m_diag[i];
+    }
+
+    inline Scalar& upper(size_t i) {
+        return m_upper[i];
+    }
+
+    inline const Scalar& upper(size_t i) const {
+        return m_upper[i];
+    }
+
+    inline Scalar& lower(size_t i) {
+        return m_lower[i];
+    }
+
+    inline const Scalar& lower(size_t i) const {
+        return m_lower[i];
+    }
+
+    inline int& upperProfile(size_t i) {
+        return m_upperProfile[i];
+    }
+
+    inline const int& upperProfile(size_t i) const {
+        return m_upperProfile[i];
+    }
+
+    inline int& lowerProfile(size_t i) {
+        return m_lowerProfile[i];
+    }
+
+    inline const int& lowerProfile(size_t i) const {
+        return m_lowerProfile[i];
+    }
+
+    static SkylineStorage Map(int* upperProfile, int* lowerProfile, Scalar* diag, Scalar* upper, Scalar* lower, size_t size, size_t upperSize, size_t lowerSize) {
+        SkylineStorage res;
+        res.m_upperProfile = upperProfile;
+        res.m_lowerProfile = lowerProfile;
+        res.m_diag = diag;
+        res.m_upper = upper;
+        res.m_lower = lower;
+        res.m_allocatedSize = res.m_diagSize = size;
+        res.m_upperSize = upperSize;
+        res.m_lowerSize = lowerSize;
+        return res;
+    }
+
+    inline void reset() {
+        memset(m_diag, 0, m_diagSize * sizeof (Scalar));
+        memset(m_upper, 0, m_upperSize * sizeof (Scalar));
+        memset(m_lower, 0, m_lowerSize * sizeof (Scalar));
+        memset(m_upperProfile, 0, m_diagSize * sizeof (int));
+        memset(m_lowerProfile, 0, m_diagSize * sizeof (int));
+    }
+
+    void prune(Scalar reference, RealScalar epsilon = precision<RealScalar>()) {
+        //TODO
+    }
+
+protected:
+
+    inline void reallocate(size_t diagSize, size_t upperProfileSize, size_t lowerProfileSize, size_t upperSize, size_t lowerSize) {
+
+        Scalar* diag = new Scalar[diagSize];
+        Scalar* upper = new Scalar[upperSize];
+        Scalar* lower = new Scalar[lowerSize];
+        int* upperProfile = new int[upperProfileSize];
+        int* lowerProfile = new int[lowerProfileSize];
+
+        size_t copyDiagSize = std::min(diagSize, m_diagSize);
+        size_t copyUpperSize = std::min(upperSize, m_upperSize);
+        size_t copyLowerSize = std::min(lowerSize, m_lowerSize);
+        size_t copyUpperProfileSize = std::min(upperProfileSize, m_upperProfileSize);
+        size_t copyLowerProfileSize = std::min(lowerProfileSize, m_lowerProfileSize);
+
+        // copy
+        memcpy(diag, m_diag, copyDiagSize * sizeof (Scalar));
+        memcpy(upper, m_upper, copyUpperSize * sizeof (Scalar));
+        memcpy(lower, m_lower, copyLowerSize * sizeof (Scalar));
+        memcpy(upperProfile, m_upperProfile, copyUpperProfileSize * sizeof (int));
+        memcpy(lowerProfile, m_lowerProfile, copyLowerProfileSize * sizeof (int));
+
+
+
+        // delete old stuff
+        delete[] m_diag;
+        delete[] m_upper;
+        delete[] m_lower;
+        delete[] m_upperProfile;
+        delete[] m_lowerProfile;
+        m_diag = diag;
+        m_upper = upper;
+        m_lower = lower;
+        m_upperProfile = upperProfile;
+        m_lowerProfile = lowerProfile;
+        m_allocatedSize = diagSize + upperSize + lowerSize;
+        m_upperSize = upperSize;
+        m_lowerSize = lowerSize;
+    }
+
+public:
+    Scalar* m_diag;
+    Scalar* m_upper;
+    Scalar* m_lower;
+    int* m_upperProfile;
+    int* m_lowerProfile;
+    size_t m_diagSize;
+    size_t m_upperSize;
+    size_t m_lowerSize;
+    size_t m_upperProfileSize;
+    size_t m_lowerProfileSize;
+    size_t m_allocatedSize;
+
+};
+
+#endif // EIGEN_COMPRESSED_STORAGE_H
diff --git a/unsupported/Eigen/src/Skyline/SkylineUtil.h b/unsupported/Eigen/src/Skyline/SkylineUtil.h
new file mode 100644
index 000000000..71563adfb
--- /dev/null
+++ b/unsupported/Eigen/src/Skyline/SkylineUtil.h
@@ -0,0 +1,96 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Guillaume Saupin <guillaume.saupin@cea.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_SKYLINEUTIL_H
+#define EIGEN_SKYLINEUTIL_H
+
+#ifdef NDEBUG
+#define EIGEN_DBG_SKYLINE(X)
+#else
+#define EIGEN_DBG_SKYLINE(X) X
+#endif
+
+const unsigned int SkylineBit = 0x1200;
+template<typename Lhs, typename Rhs, int ProductMode> class SkylineProduct;
+enum AdditionalProductEvaluationMode {SkylineTimeDenseProduct, SkylineTimeSkylineProduct, DenseTimeSkylineProduct};
+enum {IsSkyline = SkylineBit};
+
+
+#define EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATOR(Derived, Op) \
+template<typename OtherDerived> \
+EIGEN_STRONG_INLINE Derived& operator Op(const Eigen::SkylineMatrixBase<OtherDerived>& other) \
+{ \
+  return Base::operator Op(other.derived()); \
+} \
+EIGEN_STRONG_INLINE Derived& operator Op(const Derived& other) \
+{ \
+  return Base::operator Op(other); \
+}
+
+#define EIGEN_SKYLINE_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(Derived, Op) \
+template<typename Other> \
+EIGEN_STRONG_INLINE Derived& operator Op(const Other& scalar) \
+{ \
+  return Base::operator Op(scalar); \
+}
+
+#define EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATORS(Derived) \
+EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATOR(Derived, =) \
+EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATOR(Derived, +=) \
+EIGEN_SKYLINE_INHERIT_ASSIGNMENT_OPERATOR(Derived, -=) \
+EIGEN_SKYLINE_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(Derived, *=) \
+EIGEN_SKYLINE_INHERIT_SCALAR_ASSIGNMENT_OPERATOR(Derived, /=)
+
+#define _EIGEN_SKYLINE_GENERIC_PUBLIC_INTERFACE(Derived, BaseClass) \
+typedef BaseClass Base; \
+typedef typename Eigen::ei_traits<Derived>::Scalar Scalar; \
+typedef typename Eigen::NumTraits<Scalar>::Real RealScalar; \
+enum {  Flags = Eigen::ei_traits<Derived>::Flags, };
+
+#define EIGEN_SKYLINE_GENERIC_PUBLIC_INTERFACE(Derived) \
+_EIGEN_SKYLINE_GENERIC_PUBLIC_INTERFACE(Derived, Eigen::SkylineMatrixBase<Derived>)
+
+template<typename Derived> class SkylineMatrixBase;
+template<typename _Scalar, int _Flags = 0> class SkylineMatrix;
+template<typename _Scalar, int _Flags = 0> class DynamicSkylineMatrix;
+template<typename _Scalar, int _Flags = 0> class SkylineVector;
+template<typename _Scalar, int _Flags = 0> class MappedSkylineMatrix;
+
+template<typename Lhs, typename Rhs> struct ei_skyline_product_mode;
+template<typename Lhs, typename Rhs, int ProductMode = ei_skyline_product_mode<Lhs,Rhs>::value> struct SkylineProductReturnType;
+
+
+template<typename T> class ei_eval<T,IsSkyline>
+{
+    typedef typename ei_traits<T>::Scalar _Scalar;
+    enum {
+          _Flags = ei_traits<T>::Flags
+    };
+
+  public:
+    typedef SkylineMatrix<_Scalar, _Flags> type;
+};
+
+
+#endif // EIGEN_SKYLINEUTIL_H