* JacobiSVD:

 - support complex numbers
 - big rewrite of the 2x2 kernel, much more robust
* Jacobi:
 - fix weirdness in initial design, e.g. applyJacobiOnTheRight actually did the inverse transformation
 - fully support complex numbers
 - fix logic to decide whether to vectorize
 - remove several clumsy methods

fix for complex numbers

2 files changed, 258 insertions, 169 deletions

diff --git a/Eigen/src/SVD/JacobiSVD.h b/Eigen/src/SVD/JacobiSVD.h
new file mode 100644
index 000000000..e5e7fb6fc
--- /dev/null
+++ b/Eigen/src/SVD/JacobiSVD.h
@@ -0,0 +1,258 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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_JACOBISVD_H
+#define EIGEN_JACOBISVD_H
+
+/** \ingroup SVD_Module
+  * \nonstableyet
+  *
+  * \class JacobiSVD
+  *
+  * \brief Jacobi SVD decomposition of a square matrix
+  *
+  * \param MatrixType the type of the matrix of which we are computing the SVD decomposition
+  * \param ComputeU whether the U matrix should be computed
+  * \param ComputeV whether the V matrix should be computed
+  *
+  * \sa MatrixBase::jacobiSvd()
+  */
+template<typename MatrixType, unsigned int Options> class JacobiSVD
+{
+  private:
+    typedef typename MatrixType::Scalar Scalar;
+    typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
+    enum {
+      ComputeU = 1,
+      ComputeV = 1,
+      RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+      ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+      DiagSizeAtCompileTime = EIGEN_ENUM_MIN(RowsAtCompileTime,ColsAtCompileTime),
+      MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
+      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
+      MaxDiagSizeAtCompileTime = EIGEN_ENUM_MIN(MaxRowsAtCompileTime,MaxColsAtCompileTime),
+      MatrixOptions = MatrixType::Options
+    };
+    
+    typedef Matrix<Scalar, Dynamic, Dynamic, MatrixOptions> DummyMatrixType;
+    typedef typename ei_meta_if<ComputeU,
+                                Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime,
+                                       MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime>,
+                                DummyMatrixType>::ret MatrixUType;
+    typedef typename ei_meta_if<ComputeV,
+                                Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime,
+                                       MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime>,
+                                DummyMatrixType>::ret MatrixVType;
+    typedef Matrix<RealScalar, DiagSizeAtCompileTime, 1,
+                   Options, MaxDiagSizeAtCompileTime, 1> SingularValuesType;
+    typedef Matrix<Scalar, 1, RowsAtCompileTime, MatrixOptions, 1, MaxRowsAtCompileTime> RowType;
+    typedef Matrix<Scalar, RowsAtCompileTime, 1, MatrixOptions, MaxRowsAtCompileTime, 1> ColType;
+
+  public:
+
+    JacobiSVD() : m_isInitialized(false) {}
+
+    JacobiSVD(const MatrixType& matrix) : m_isInitialized(false) 
+    {
+      compute(matrix);
+    }
+    
+    JacobiSVD& compute(const MatrixType& matrix);
+    
+    const MatrixUType& matrixU() const
+    {
+      ei_assert(m_isInitialized && "JacobiSVD is not initialized.");
+      return m_matrixU;
+    }
+
+    const SingularValuesType& singularValues() const
+    {
+      ei_assert(m_isInitialized && "JacobiSVD is not initialized.");
+      return m_singularValues;
+    }
+
+    const MatrixUType& matrixV() const
+    {
+      ei_assert(m_isInitialized && "JacobiSVD is not initialized.");
+      return m_matrixV;
+    }
+
+  protected:
+    MatrixUType m_matrixU;
+    MatrixVType m_matrixV;
+    SingularValuesType m_singularValues;
+    bool m_isInitialized;
+    
+    template<typename _MatrixType, unsigned int _Options, bool _IsComplex>
+    friend struct ei_svd_precondition_2x2_block_to_be_real;
+};
+
+template<typename MatrixType, unsigned int Options, bool IsComplex = NumTraits<typename MatrixType::Scalar>::IsComplex>
+struct ei_svd_precondition_2x2_block_to_be_real
+{
+  static void run(MatrixType&, JacobiSVD<MatrixType, Options>&, int, int) {}
+};
+
+template<typename MatrixType, unsigned int Options>
+struct ei_svd_precondition_2x2_block_to_be_real<MatrixType, Options, true>
+{
+  typedef JacobiSVD<MatrixType, Options> SVD;
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename MatrixType::RealScalar RealScalar;
+  
+  enum { ComputeU = SVD::ComputeU, ComputeV = SVD::ComputeV };
+  static void run(MatrixType& work_matrix, JacobiSVD<MatrixType, Options>& svd, int p, int q)
+  {
+    Scalar c, s, z;
+    RealScalar n = ei_sqrt(ei_abs2(work_matrix.coeff(p,p)) + ei_abs2(work_matrix.coeff(q,p)));
+    if(n==0)
+    {
+      z = ei_abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
+      work_matrix.row(p) *= z;
+      if(ComputeU) svd.m_matrixU.col(p) *= ei_conj(z);
+      z = ei_abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
+      work_matrix.row(q) *= z;
+      if(ComputeU) svd.m_matrixU.col(q) *= ei_conj(z);
+    }
+    else
+    {
+      c = ei_conj(work_matrix.coeff(p,p)) / n;
+      s = work_matrix.coeff(q,p) / n;
+      work_matrix.applyJacobiOnTheLeft(p,q,c,s);
+      if(ComputeU) svd.m_matrixU.applyJacobiOnTheRight(p,q,ei_conj(c),-s);
+      if(work_matrix.coeff(p,q) != Scalar(0))
+      {
+        Scalar z = ei_abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
+        work_matrix.col(q) *= z;
+        if(ComputeV) svd.m_matrixV.col(q) *= z;
+      }
+      if(work_matrix.coeff(q,q) != Scalar(0))
+      {
+        z = ei_abs(work_matrix.coeff(q,q)) / work_matrix.coeff(q,q);
+        work_matrix.row(q) *= z;
+        if(ComputeU) svd.m_matrixU.col(q) *= ei_conj(z);
+      }
+    }
+  }  
+};
+
+template<typename MatrixType, typename RealScalar>
+void ei_real_2x2_jacobi_svd(const MatrixType& matrix, int p, int q,
+                            RealScalar *c_left, RealScalar *s_left,
+                            RealScalar *c_right, RealScalar *s_right)
+{
+  Matrix<RealScalar,2,2> m;
+  m << ei_real(matrix.coeff(p,p)), ei_real(matrix.coeff(p,q)),
+        ei_real(matrix.coeff(q,p)), ei_real(matrix.coeff(q,q));
+  RealScalar c1, s1;
+  RealScalar t = m.coeff(0,0) + m.coeff(1,1);
+  RealScalar d = m.coeff(1,0) - m.coeff(0,1);
+  if(t == RealScalar(0))
+  {
+    c1 = 0;
+    s1 = d > 0 ? 1 : -1;
+  }
+  else
+  {
+    RealScalar u = d / t;
+    c1 = RealScalar(1) / ei_sqrt(1 + ei_abs2(u));
+    s1 = c1 * u;
+  }
+  m.applyJacobiOnTheLeft(0,1,c1,s1);
+  RealScalar c2, s2;
+  m.makeJacobi(0,1,&c2,&s2);
+  *c_left = c1*c2 + s1*s2;
+  *s_left = s1*c2 - c1*s2;
+  *c_right = c2;
+  *s_right = s2;
+}
+
+template<typename MatrixType, unsigned int Options>
+JacobiSVD<MatrixType, Options>& JacobiSVD<MatrixType, Options>::compute(const MatrixType& matrix)
+{
+  MatrixType work_matrix(matrix);
+  int size = matrix.rows();
+  if(ComputeU) m_matrixU = MatrixUType::Identity(size,size);
+  if(ComputeV) m_matrixV = MatrixUType::Identity(size,size);
+  m_singularValues.resize(size);
+  const RealScalar precision = 2 * epsilon<Scalar>();
+
+sweep_again:
+  for(int p = 1; p < size; ++p)
+  {
+    for(int q = 0; q < p; ++q)
+    {
+      if(std::max(ei_abs(work_matrix.coeff(p,q)),ei_abs(work_matrix.coeff(q,p)))
+          > std::max(ei_abs(work_matrix.coeff(p,p)),ei_abs(work_matrix.coeff(q,q)))*precision)
+      {
+        ei_svd_precondition_2x2_block_to_be_real<MatrixType, Options>::run(work_matrix, *this, p, q);
+
+        RealScalar c_left, s_left, c_right, s_right;
+        ei_real_2x2_jacobi_svd(work_matrix, p, q, &c_left, &s_left, &c_right, &s_right);
+        
+        work_matrix.applyJacobiOnTheLeft(p,q,c_left,s_left);
+        if(ComputeU) m_matrixU.applyJacobiOnTheRight(p,q,c_left,-s_left);
+        
+        work_matrix.applyJacobiOnTheRight(p,q,c_right,s_right);
+        if(ComputeV) m_matrixV.applyJacobiOnTheRight(p,q,c_right,s_right);
+      }
+    }
+  }
+  
+  RealScalar biggestOnDiag = work_matrix.diagonal().cwise().abs().maxCoeff();
+  RealScalar maxAllowedOffDiag = biggestOnDiag * precision;
+  for(int p = 0; p < size; ++p)
+  {
+    for(int q = 0; q < p; ++q)
+      if(ei_abs(work_matrix.coeff(p,q)) > maxAllowedOffDiag)
+        goto sweep_again;
+    for(int q = p+1; q < size; ++q)
+      if(ei_abs(work_matrix.coeff(p,q)) > maxAllowedOffDiag)
+        goto sweep_again;
+  }
+  
+  for(int i = 0; i < size; ++i)
+  {
+    RealScalar a = ei_abs(work_matrix.coeff(i,i));
+    m_singularValues.coeffRef(i) = a;
+    if(ComputeU && (a!=RealScalar(0))) m_matrixU.col(i) *= work_matrix.coeff(i,i)/a;
+  }
+
+  for(int i = 0; i < size; i++)
+  {
+    int pos;
+    m_singularValues.end(size-i).maxCoeff(&pos);
+    if(pos)
+    {
+      pos += i;
+      std::swap(m_singularValues.coeffRef(i), m_singularValues.coeffRef(pos));
+      if(ComputeU) m_matrixU.col(pos).swap(m_matrixU.col(i));
+      if(ComputeV) m_matrixV.col(pos).swap(m_matrixV.col(i));
+    }
+  }
+  
+  m_isInitialized = true;
+  return *this;
+}
+#endif // EIGEN_JACOBISVD_H
diff --git a/Eigen/src/SVD/JacobiSquareSVD.h b/Eigen/src/SVD/JacobiSquareSVD.h
deleted file mode 100644
index f21c9edca..000000000
--- a/Eigen/src/SVD/JacobiSquareSVD.h
+++ /dev/null
@@ -1,169 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
-//
-// 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_JACOBISQUARESVD_H
-#define EIGEN_JACOBISQUARESVD_H
-
-/** \ingroup SVD_Module
-  * \nonstableyet
-  *
-  * \class JacobiSquareSVD
-  *
-  * \brief Jacobi SVD decomposition of a square matrix
-  *
-  * \param MatrixType the type of the matrix of which we are computing the SVD decomposition
-  * \param ComputeU whether the U matrix should be computed
-  * \param ComputeV whether the V matrix should be computed
-  *
-  * \sa MatrixBase::jacobiSvd()
-  */
-template<typename MatrixType, bool ComputeU, bool ComputeV> class JacobiSquareSVD
-{
-  private:
-    typedef typename MatrixType::Scalar Scalar;
-    typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
-    enum {
-      RowsAtCompileTime = MatrixType::RowsAtCompileTime,
-      MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
-      Options = MatrixType::Options
-    };
-    
-    typedef Matrix<Scalar, Dynamic, Dynamic, Options> DummyMatrixType;
-    typedef typename ei_meta_if<ComputeU,
-                                Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime,
-                                       Options, MaxRowsAtCompileTime, MaxRowsAtCompileTime>,
-                                DummyMatrixType>::ret MatrixUType;
-    typedef typename Diagonal<MatrixType,0>::PlainMatrixType SingularValuesType;
-    typedef Matrix<Scalar, 1, RowsAtCompileTime, Options, 1, MaxRowsAtCompileTime> RowType;
-    typedef Matrix<Scalar, RowsAtCompileTime, 1, Options, MaxRowsAtCompileTime, 1> ColType;
-
-  public:
-
-    JacobiSquareSVD() : m_isInitialized(false) {}
-
-    JacobiSquareSVD(const MatrixType& matrix) : m_isInitialized(false) 
-    {
-      compute(matrix);
-    }
-    
-    JacobiSquareSVD& compute(const MatrixType& matrix);
-    
-    const MatrixUType& matrixU() const
-    {
-      ei_assert(m_isInitialized && "SVD is not initialized.");
-      return m_matrixU;
-    }
-
-    const SingularValuesType& singularValues() const
-    {
-      ei_assert(m_isInitialized && "SVD is not initialized.");
-      return m_singularValues;
-    }
-
-    const MatrixUType& matrixV() const
-    {
-      ei_assert(m_isInitialized && "SVD is not initialized.");
-      return m_matrixV;
-    }
-
-  protected:
-    MatrixUType m_matrixU;
-    MatrixUType m_matrixV;
-    SingularValuesType m_singularValues;
-    bool m_isInitialized;
-};
-
-template<typename MatrixType, bool ComputeU, bool ComputeV>
-JacobiSquareSVD<MatrixType, ComputeU, ComputeV>& JacobiSquareSVD<MatrixType, ComputeU, ComputeV>::compute(const MatrixType& matrix)
-{
-  MatrixType work_matrix(matrix);
-  int size = matrix.rows();
-  if(ComputeU) m_matrixU = MatrixUType::Identity(size,size);
-  if(ComputeV) m_matrixV = MatrixUType::Identity(size,size);
-  m_singularValues.resize(size);
-  const RealScalar precision = 2 * epsilon<Scalar>();
-
-sweep_again:
-  for(int p = 1; p < size; ++p)
-  {
-    for(int q = 0; q < p; ++q)
-    {
-      Scalar c, s;
-      while(std::max(ei_abs(work_matrix.coeff(p,q)),ei_abs(work_matrix.coeff(q,p)))
-          > std::max(ei_abs(work_matrix.coeff(p,p)),ei_abs(work_matrix.coeff(q,q)))*precision)
-      {  
-        if(work_matrix.makeJacobiForAtA(p,q,&c,&s))
-        {
-          work_matrix.applyJacobiOnTheRight(p,q,c,s);
-          if(ComputeV) m_matrixV.applyJacobiOnTheRight(p,q,c,s);
-        }
-        if(work_matrix.makeJacobiForAAt(p,q,&c,&s))
-        {
-          ei_normalizeJacobi(&c, &s, work_matrix.coeff(p,p), work_matrix.coeff(q,p)),
-          work_matrix.applyJacobiOnTheLeft(p,q,c,s);
-          if(ComputeU) m_matrixU.applyJacobiOnTheRight(p,q,c,s);
-        }
-      }
-    }
-  }
-  
-  RealScalar biggestOnDiag = work_matrix.diagonal().cwise().abs().maxCoeff();
-  RealScalar maxAllowedOffDiag = biggestOnDiag * precision;
-  for(int p = 0; p < size; ++p)
-  {
-    for(int q = 0; q < p; ++q)
-      if(ei_abs(work_matrix.coeff(p,q)) > maxAllowedOffDiag)
-        goto sweep_again;
-    for(int q = p+1; q < size; ++q)
-      if(ei_abs(work_matrix.coeff(p,q)) > maxAllowedOffDiag)
-        goto sweep_again;
-  }
-
-  m_singularValues = work_matrix.diagonal().cwise().abs();
-  RealScalar biggestSingularValue = m_singularValues.maxCoeff();
-
-  for(int i = 0; i < size; ++i)
-  {
-    RealScalar a = ei_abs(work_matrix.coeff(i,i));
-    m_singularValues.coeffRef(i) = a;
-    if(ComputeU && !ei_isMuchSmallerThan(a, biggestSingularValue)) m_matrixU.col(i) *= work_matrix.coeff(i,i)/a;
-  }
-
-  for(int i = 0; i < size; i++)
-  {
-    int pos;
-    m_singularValues.end(size-i).maxCoeff(&pos);
-    if(pos)
-    {
-      pos += i;
-      std::swap(m_singularValues.coeffRef(i), m_singularValues.coeffRef(pos));
-      if(ComputeU) m_matrixU.col(pos).swap(m_matrixU.col(i));
-      if(ComputeV) m_matrixV.col(pos).swap(m_matrixV.col(i));
-    }
-  }
-
-  m_isInitialized = true;
-  return *this;
-}
-#endif // EIGEN_JACOBISQUARESVD_H