merge with default branch

3 files changed, 298 insertions, 151 deletions

diff --git a/Eigen/src/SVD/JacobiSVD.h b/Eigen/src/SVD/JacobiSVD.h
index d1b63b607..3d778516a 100644
--- a/Eigen/src/SVD/JacobiSVD.h
+++ b/Eigen/src/SVD/JacobiSVD.h
@@ -2,6 +2,7 @@
 // for linear algebra.
 //
 // Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2013-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
 //
 // 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
@@ -442,6 +443,12 @@ void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
   *j_left  = rot1 * j_right->transpose();
 }
 
+template<typename _MatrixType, int QRPreconditioner> 
+struct traits<JacobiSVD<_MatrixType,QRPreconditioner> >
+{
+  typedef _MatrixType MatrixType;
+};
+
 } // end namespace internal
 
 /** \ingroup SVD_Module
@@ -498,7 +505,9 @@ void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
   * \sa MatrixBase::jacobiSvd()
   */
 template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
+ : public SVDBase<JacobiSVD<_MatrixType,QRPreconditioner> >
 {
+    typedef SVDBase<JacobiSVD> Base;
   public:
 
     typedef _MatrixType MatrixType;
@@ -515,13 +524,10 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
       MatrixOptions = MatrixType::Options
     };
 
-    typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime,
-                   MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime>
-            MatrixUType;
-    typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime,
-                   MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime>
-            MatrixVType;
-    typedef typename internal::plain_diag_type<MatrixType, RealScalar>::type SingularValuesType;
+    typedef typename Base::MatrixUType MatrixUType;
+    typedef typename Base::MatrixVType MatrixVType;
+    typedef typename Base::SingularValuesType SingularValuesType;
+    
     typedef typename internal::plain_row_type<MatrixType>::type RowType;
     typedef typename internal::plain_col_type<MatrixType>::type ColType;
     typedef Matrix<Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime,
@@ -534,11 +540,6 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
       * perform decompositions via JacobiSVD::compute(const MatrixType&).
       */
     JacobiSVD()
-      : m_isInitialized(false),
-        m_isAllocated(false),
-        m_usePrescribedThreshold(false),
-        m_computationOptions(0),
-        m_rows(-1), m_cols(-1), m_diagSize(0)
     {}
 
 
@@ -549,11 +550,6 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
       * \sa JacobiSVD()
       */
     JacobiSVD(Index rows, Index cols, unsigned int computationOptions = 0)
-      : m_isInitialized(false),
-        m_isAllocated(false),
-        m_usePrescribedThreshold(false),
-        m_computationOptions(0),
-        m_rows(-1), m_cols(-1)
     {
       allocate(rows, cols, computationOptions);
     }
@@ -569,11 +565,6 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
      * available with the (non-default) FullPivHouseholderQR preconditioner.
      */
     JacobiSVD(const MatrixType& matrix, unsigned int computationOptions = 0)
-      : m_isInitialized(false),
-        m_isAllocated(false),
-        m_usePrescribedThreshold(false),
-        m_computationOptions(0),
-        m_rows(-1), m_cols(-1)
     {
       compute(matrix, computationOptions);
     }
@@ -601,54 +592,6 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
       return compute(matrix, m_computationOptions);
     }
 
-    /** \returns the \a U matrix.
-     *
-     * For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
-     * the U matrix is n-by-n if you asked for #ComputeFullU, and is n-by-m if you asked for #ComputeThinU.
-     *
-     * The \a m first columns of \a U are the left singular vectors of the matrix being decomposed.
-     *
-     * This method asserts that you asked for \a U to be computed.
-     */
-    const MatrixUType& matrixU() const
-    {
-      eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
-      eigen_assert(computeU() && "This JacobiSVD decomposition didn't compute U. Did you ask for it?");
-      return m_matrixU;
-    }
-
-    /** \returns the \a V matrix.
-     *
-     * For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
-     * the V matrix is p-by-p if you asked for #ComputeFullV, and is p-by-m if you asked for ComputeThinV.
-     *
-     * The \a m first columns of \a V are the right singular vectors of the matrix being decomposed.
-     *
-     * This method asserts that you asked for \a V to be computed.
-     */
-    const MatrixVType& matrixV() const
-    {
-      eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
-      eigen_assert(computeV() && "This JacobiSVD decomposition didn't compute V. Did you ask for it?");
-      return m_matrixV;
-    }
-
-    /** \returns the vector of singular values.
-     *
-     * For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p, the
-     * returned vector has size \a m.  Singular values are always sorted in decreasing order.
-     */
-    const SingularValuesType& singularValues() const
-    {
-      eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
-      return m_singularValues;
-    }
-
-    /** \returns true if \a U (full or thin) is asked for in this SVD decomposition */
-    inline bool computeU() const { return m_computeFullU || m_computeThinU; }
-    /** \returns true if \a V (full or thin) is asked for in this SVD decomposition */
-    inline bool computeV() const { return m_computeFullV || m_computeThinV; }
-
     /** \returns a (least squares) solution of \f$ A x = b \f$ using the current SVD decomposition of A.
       *
       * \param b the right-hand-side of the equation to solve.
@@ -677,80 +620,13 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
       return internal::solve_retval<JacobiSVD, Rhs>(*this, b.derived());
     }
 #endif
-
-    /** \returns the number of singular values that are not exactly 0 */
-    Index nonzeroSingularValues() const
-    {
-      eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
-      return m_nonzeroSingularValues;
-    }
-    
-    /** \returns the rank of the matrix of which \c *this is the SVD.
-      *
-      * \note This method has to determine which singular values should be considered nonzero.
-      *       For that, it uses the threshold value that you can control by calling
-      *       setThreshold(const RealScalar&).
-      */
-    inline Index rank() const
-    {
-      using std::abs;
-      eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
-      if(m_singularValues.size()==0) return 0;
-      RealScalar premultiplied_threshold = m_singularValues.coeff(0) * threshold();
-      Index i = m_nonzeroSingularValues-1;
-      while(i>=0 && m_singularValues.coeff(i) < premultiplied_threshold) --i;
-      return i+1;
-    }
     
-    /** Allows to prescribe a threshold to be used by certain methods, such as rank() and solve(),
-      * which need to determine when singular values are to be considered nonzero.
-      * This is not used for the SVD decomposition itself.
-      *
-      * When it needs to get the threshold value, Eigen calls threshold().
-      * The default is \c NumTraits<Scalar>::epsilon()
-      *
-      * \param threshold The new value to use as the threshold.
-      *
-      * A singular value will be considered nonzero if its value is strictly greater than
-      *  \f$ \vert singular value \vert \leqslant threshold \times \vert max singular value \vert \f$.
-      *
-      * If you want to come back to the default behavior, call setThreshold(Default_t)
-      */
-    JacobiSVD& setThreshold(const RealScalar& threshold)
-    {
-      m_usePrescribedThreshold = true;
-      m_prescribedThreshold = threshold;
-      return *this;
-    }
-
-    /** Allows to come back to the default behavior, letting Eigen use its default formula for
-      * determining the threshold.
-      *
-      * You should pass the special object Eigen::Default as parameter here.
-      * \code svd.setThreshold(Eigen::Default); \endcode
-      *
-      * See the documentation of setThreshold(const RealScalar&).
-      */
-    JacobiSVD& setThreshold(Default_t)
-    {
-      m_usePrescribedThreshold = false;
-      return *this;
-    }
+    using Base::computeU;
+    using Base::computeV;
+    using Base::rows;
+    using Base::cols;
+    using Base::rank;
 
-    /** Returns the threshold that will be used by certain methods such as rank().
-      *
-      * See the documentation of setThreshold(const RealScalar&).
-      */
-    RealScalar threshold() const
-    {
-      eigen_assert(m_isInitialized || m_usePrescribedThreshold);
-      return m_usePrescribedThreshold ? m_prescribedThreshold
-                                      : (std::max<Index>)(1,m_diagSize)*NumTraits<Scalar>::epsilon();
-    }
-
-    inline Index rows() const { return m_rows; }
-    inline Index cols() const { return m_cols; }
-    
     #ifndef EIGEN_PARSED_BY_DOXYGEN
     template<typename RhsType, typename DstType>
     EIGEN_DEVICE_FUNC
@@ -761,16 +637,23 @@ template<typename _MatrixType, int QRPreconditioner> class JacobiSVD
     void allocate(Index rows, Index cols, unsigned int computationOptions);
 
   protected:
-    MatrixUType m_matrixU;
-    MatrixVType m_matrixV;
-    SingularValuesType m_singularValues;
+    using Base::m_matrixU;
+    using Base::m_matrixV;
+    using Base::m_singularValues;
+    using Base::m_isInitialized;
+    using Base::m_isAllocated;
+    using Base::m_usePrescribedThreshold;
+    using Base::m_computeFullU;
+    using Base::m_computeThinU;
+    using Base::m_computeFullV;
+    using Base::m_computeThinV;
+    using Base::m_computationOptions;
+    using Base::m_nonzeroSingularValues;
+    using Base::m_rows;
+    using Base::m_cols;
+    using Base::m_diagSize;
+    using Base::m_prescribedThreshold;
     WorkMatrixType m_workMatrix;
-    bool m_isInitialized, m_isAllocated, m_usePrescribedThreshold;
-    bool m_computeFullU, m_computeThinU;
-    bool m_computeFullV, m_computeThinV;
-    unsigned int m_computationOptions;
-    Index m_nonzeroSingularValues, m_rows, m_cols, m_diagSize;
-    RealScalar m_prescribedThreshold;
 
     template<typename __MatrixType, int _QRPreconditioner, bool _IsComplex>
     friend struct internal::svd_precondition_2x2_block_to_be_real;
diff --git a/Eigen/src/SVD/SVDBase.h b/Eigen/src/SVD/SVDBase.h
new file mode 100644
index 000000000..61b01fb8a
--- /dev/null
+++ b/Eigen/src/SVD/SVDBase.h
@@ -0,0 +1,263 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com>
+// Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr>
+// Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr>
+// Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr>
+//
+// 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_SVDBASE_H
+#define EIGEN_SVDBASE_H
+
+namespace Eigen {
+/** \ingroup SVD_Module
+ *
+ *
+ * \class SVDBase
+ *
+ * \brief Base class of SVD algorithms
+ *
+ * \tparam Derived the type of the actual SVD decomposition
+ *
+ * SVD decomposition consists in decomposing any n-by-p matrix \a A as a product
+ *   \f[ A = U S V^* \f]
+ * where \a U is a n-by-n unitary, \a V is a p-by-p unitary, and \a S is a n-by-p real positive matrix which is zero outside of its main diagonal;
+ * the diagonal entries of S are known as the \em singular \em values of \a A and the columns of \a U and \a V are known as the left
+ * and right \em singular \em vectors of \a A respectively.
+ *
+ * Singular values are always sorted in decreasing order.
+ *
+ * 
+ * You can ask for only \em thin \a U or \a V to be computed, meaning the following. In case of a rectangular n-by-p matrix, letting \a m be the
+ * smaller value among \a n and \a p, there are only \a m singular vectors; the remaining columns of \a U and \a V do not correspond to actual
+ * singular vectors. Asking for \em thin \a U or \a V means asking for only their \a m first columns to be formed. So \a U is then a n-by-m matrix,
+ * and \a V is then a p-by-m matrix. Notice that thin \a U and \a V are all you need for (least squares) solving.
+ *  
+ * If the input matrix has inf or nan coefficients, the result of the computation is undefined, but the computation is guaranteed to
+ * terminate in finite (and reasonable) time.
+ * \sa MatrixBase::genericSvd()
+ */
+template<typename Derived>
+class SVDBase
+{
+
+public:
+  typedef typename internal::traits<Derived>::MatrixType MatrixType;
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+  typedef typename MatrixType::Index Index;
+  enum {
+    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+    ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+    DiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime),
+    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+    MaxDiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(MaxRowsAtCompileTime,MaxColsAtCompileTime),
+    MatrixOptions = MatrixType::Options
+  };
+
+  typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime> MatrixUType;
+  typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime, MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime> MatrixVType;
+  typedef typename internal::plain_diag_type<MatrixType, RealScalar>::type SingularValuesType;
+  
+  Derived& derived() { return *static_cast<Derived*>(this); }
+  const Derived& derived() const { return *static_cast<const Derived*>(this); }
+
+  /** \returns the \a U matrix.
+   *
+   * For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
+   * the U matrix is n-by-n if you asked for #ComputeFullU, and is n-by-m if you asked for #ComputeThinU.
+   *
+   * The \a m first columns of \a U are the left singular vectors of the matrix being decomposed.
+   *
+   * This method asserts that you asked for \a U to be computed.
+   */
+  const MatrixUType& matrixU() const
+  {
+    eigen_assert(m_isInitialized && "SVD is not initialized.");
+    eigen_assert(computeU() && "This SVD decomposition didn't compute U. Did you ask for it?");
+    return m_matrixU;
+  }
+
+  /** \returns the \a V matrix.
+   *
+   * For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
+   * the V matrix is p-by-p if you asked for #ComputeFullV, and is p-by-m if you asked for ComputeThinV.
+   *
+   * The \a m first columns of \a V are the right singular vectors of the matrix being decomposed.
+   *
+   * This method asserts that you asked for \a V to be computed.
+   */
+  const MatrixVType& matrixV() const
+  {
+    eigen_assert(m_isInitialized && "SVD is not initialized.");
+    eigen_assert(computeV() && "This SVD decomposition didn't compute V. Did you ask for it?");
+    return m_matrixV;
+  }
+
+  /** \returns the vector of singular values.
+   *
+   * For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p, the
+   * returned vector has size \a m.  Singular values are always sorted in decreasing order.
+   */
+  const SingularValuesType& singularValues() const
+  {
+    eigen_assert(m_isInitialized && "SVD is not initialized.");
+    return m_singularValues;
+  }
+
+  /** \returns the number of singular values that are not exactly 0 */
+  Index nonzeroSingularValues() const
+  {
+    eigen_assert(m_isInitialized && "SVD is not initialized.");
+    return m_nonzeroSingularValues;
+  }
+  
+  /** \returns the rank of the matrix of which \c *this is the SVD.
+    *
+    * \note This method has to determine which singular values should be considered nonzero.
+    *       For that, it uses the threshold value that you can control by calling
+    *       setThreshold(const RealScalar&).
+    */
+  inline Index rank() const
+  {
+    using std::abs;
+    eigen_assert(m_isInitialized && "JacobiSVD is not initialized.");
+    if(m_singularValues.size()==0) return 0;
+    RealScalar premultiplied_threshold = m_singularValues.coeff(0) * threshold();
+    Index i = m_nonzeroSingularValues-1;
+    while(i>=0 && m_singularValues.coeff(i) < premultiplied_threshold) --i;
+    return i+1;
+  }
+  
+  /** Allows to prescribe a threshold to be used by certain methods, such as rank() and solve(),
+    * which need to determine when singular values are to be considered nonzero.
+    * This is not used for the SVD decomposition itself.
+    *
+    * When it needs to get the threshold value, Eigen calls threshold().
+    * The default is \c NumTraits<Scalar>::epsilon()
+    *
+    * \param threshold The new value to use as the threshold.
+    *
+    * A singular value will be considered nonzero if its value is strictly greater than
+    *  \f$ \vert singular value \vert \leqslant threshold \times \vert max singular value \vert \f$.
+    *
+    * If you want to come back to the default behavior, call setThreshold(Default_t)
+    */
+  Derived& setThreshold(const RealScalar& threshold)
+  {
+    m_usePrescribedThreshold = true;
+    m_prescribedThreshold = threshold;
+    return derived();
+  }
+
+  /** Allows to come back to the default behavior, letting Eigen use its default formula for
+    * determining the threshold.
+    *
+    * You should pass the special object Eigen::Default as parameter here.
+    * \code svd.setThreshold(Eigen::Default); \endcode
+    *
+    * See the documentation of setThreshold(const RealScalar&).
+    */
+  Derived& setThreshold(Default_t)
+  {
+    m_usePrescribedThreshold = false;
+    return derived();
+  }
+
+  /** Returns the threshold that will be used by certain methods such as rank().
+    *
+    * See the documentation of setThreshold(const RealScalar&).
+    */
+  RealScalar threshold() const
+  {
+    eigen_assert(m_isInitialized || m_usePrescribedThreshold);
+    return m_usePrescribedThreshold ? m_prescribedThreshold
+                                    : (std::max<Index>)(1,m_diagSize)*NumTraits<Scalar>::epsilon();
+  }
+
+  /** \returns true if \a U (full or thin) is asked for in this SVD decomposition */
+  inline bool computeU() const { return m_computeFullU || m_computeThinU; }
+  /** \returns true if \a V (full or thin) is asked for in this SVD decomposition */
+  inline bool computeV() const { return m_computeFullV || m_computeThinV; }
+
+  inline Index rows() const { return m_rows; }
+  inline Index cols() const { return m_cols; }
+
+protected:
+  // return true if already allocated
+  bool allocate(Index rows, Index cols, unsigned int computationOptions) ;
+
+  MatrixUType m_matrixU;
+  MatrixVType m_matrixV;
+  SingularValuesType m_singularValues;
+  bool m_isInitialized, m_isAllocated, m_usePrescribedThreshold;
+  bool m_computeFullU, m_computeThinU;
+  bool m_computeFullV, m_computeThinV;
+  unsigned int m_computationOptions;
+  Index m_nonzeroSingularValues, m_rows, m_cols, m_diagSize;
+  RealScalar m_prescribedThreshold;
+
+  /** \brief Default Constructor.
+   *
+   * Default constructor of SVDBase
+   */
+  SVDBase()
+    : m_isInitialized(false),
+      m_isAllocated(false),
+      m_usePrescribedThreshold(false),
+      m_computationOptions(0),
+      m_rows(-1), m_cols(-1), m_diagSize(0)
+  {}
+
+
+};
+
+
+template<typename MatrixType>
+bool SVDBase<MatrixType>::allocate(Index rows, Index cols, unsigned int computationOptions)
+{
+  eigen_assert(rows >= 0 && cols >= 0);
+
+  if (m_isAllocated &&
+      rows == m_rows &&
+      cols == m_cols &&
+      computationOptions == m_computationOptions)
+  {
+    return true;
+  }
+
+  m_rows = rows;
+  m_cols = cols;
+  m_isInitialized = false;
+  m_isAllocated = true;
+  m_computationOptions = computationOptions;
+  m_computeFullU = (computationOptions & ComputeFullU) != 0;
+  m_computeThinU = (computationOptions & ComputeThinU) != 0;
+  m_computeFullV = (computationOptions & ComputeFullV) != 0;
+  m_computeThinV = (computationOptions & ComputeThinV) != 0;
+  eigen_assert(!(m_computeFullU && m_computeThinU) && "SVDBase: you can't ask for both full and thin U");
+  eigen_assert(!(m_computeFullV && m_computeThinV) && "SVDBase: you can't ask for both full and thin V");
+  eigen_assert(EIGEN_IMPLIES(m_computeThinU || m_computeThinV, MatrixType::ColsAtCompileTime==Dynamic) &&
+	       "SVDBase: thin U and V are only available when your matrix has a dynamic number of columns.");
+
+  m_diagSize = (std::min)(m_rows, m_cols);
+  m_singularValues.resize(m_diagSize);
+  if(RowsAtCompileTime==Dynamic)
+    m_matrixU.resize(m_rows, m_computeFullU ? m_rows : m_computeThinU ? m_diagSize : 0);
+  if(ColsAtCompileTime==Dynamic)
+    m_matrixV.resize(m_cols, m_computeFullV ? m_cols : m_computeThinV ? m_diagSize : 0);
+
+  return false;
+}
+
+}// end namespace
+
+#endif // EIGEN_SVDBASE_H
diff --git a/Eigen/src/SVD/UpperBidiagonalization.h b/Eigen/src/SVD/UpperBidiagonalization.h
index 40067682c..225b19e3c 100644
--- a/Eigen/src/SVD/UpperBidiagonalization.h
+++ b/Eigen/src/SVD/UpperBidiagonalization.h
@@ -2,6 +2,7 @@
 // for linear algebra.
 //
 // Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2013-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
 //
 // 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