* rename JacobiRotation => PlanarRotation

* move the makeJacobi and make_givens_* to PlanarRotation
* rename applyJacobi* => apply*

8 files changed, 193 insertions, 167 deletions

diff --git a/Eigen/src/Core/MathFunctions.h b/Eigen/src/Core/MathFunctions.h
index 1570f01e0..40edf4a3c 100644
--- a/Eigen/src/Core/MathFunctions.h
+++ b/Eigen/src/Core/MathFunctions.h
@@ -116,6 +116,7 @@ inline float ei_imag(float)    { return 0.f; }
 inline float ei_conj(float x)  { return x; }
 inline float ei_abs(float x)   { return std::abs(x); }
 inline float ei_abs2(float x)  { return x*x; }
+inline float ei_norm1(float x) { return ei_abs(x); }
 inline float ei_sqrt(float x)  { return std::sqrt(x); }
 inline float ei_exp(float x)   { return std::exp(x); }
 inline float ei_log(float x)   { return std::log(x); }
@@ -164,6 +165,7 @@ inline double ei_imag(double)    { return 0.; }
 inline double ei_conj(double x)  { return x; }
 inline double ei_abs(double x)   { return std::abs(x); }
 inline double ei_abs2(double x)  { return x*x; }
+inline double ei_norm1(double x) { return ei_abs(x); }
 inline double ei_sqrt(double x)  { return std::sqrt(x); }
 inline double ei_exp(double x)   { return std::exp(x); }
 inline double ei_log(double x)   { return std::log(x); }
@@ -212,6 +214,7 @@ inline float& ei_imag_ref(std::complex<float>& x) { return reinterpret_cast<floa
 inline std::complex<float> ei_conj(const std::complex<float>& x) { return std::conj(x); }
 inline float ei_abs(const std::complex<float>& x) { return std::abs(x); }
 inline float ei_abs2(const std::complex<float>& x) { return std::norm(x); }
+inline float ei_norm1(const std::complex<float> &x) { return(ei_abs(x.real()) + ei_abs(x.imag())); }
 inline std::complex<float> ei_exp(std::complex<float> x)  { return std::exp(x); }
 inline std::complex<float> ei_sin(std::complex<float> x)  { return std::sin(x); }
 inline std::complex<float> ei_cos(std::complex<float> x)  { return std::cos(x); }
@@ -248,6 +251,7 @@ inline double& ei_imag_ref(std::complex<double>& x) { return reinterpret_cast<do
 inline std::complex<double> ei_conj(const std::complex<double>& x) { return std::conj(x); }
 inline double ei_abs(const std::complex<double>& x) { return std::abs(x); }
 inline double ei_abs2(const std::complex<double>& x) { return std::norm(x); }
+inline double ei_norm1(const std::complex<double> &x) { return(ei_abs(x.real()) + ei_abs(x.imag())); }
 inline std::complex<double> ei_exp(std::complex<double> x)  { return std::exp(x); }
 inline std::complex<double> ei_sin(std::complex<double> x)  { return std::sin(x); }
 inline std::complex<double> ei_cos(std::complex<double> x)  { return std::cos(x); }
diff --git a/Eigen/src/Core/MatrixBase.h b/Eigen/src/Core/MatrixBase.h
index c2945ab46..9ac964168 100644
--- a/Eigen/src/Core/MatrixBase.h
+++ b/Eigen/src/Core/MatrixBase.h
@@ -803,11 +803,10 @@ template<typename Derived> class MatrixBase
 
 ///////// Jacobi module /////////
 
-    template<typename JacobiScalar>
-    void applyJacobiOnTheLeft(int p, int q, const JacobiRotation<JacobiScalar>& j);
-    template<typename JacobiScalar>
-    void applyJacobiOnTheRight(int p, int q, const JacobiRotation<JacobiScalar>& j);
-    bool makeJacobi(int p, int q, JacobiRotation<Scalar> *j) const;
+    template<typename OtherScalar>
+    void applyOnTheLeft(int p, int q, const PlanarRotation<OtherScalar>& j);
+    template<typename OtherScalar>
+    void applyOnTheRight(int p, int q, const PlanarRotation<OtherScalar>& j);
 
     #ifdef EIGEN_MATRIXBASE_PLUGIN
     #include EIGEN_MATRIXBASE_PLUGIN
diff --git a/Eigen/src/Core/util/ForwardDeclarations.h b/Eigen/src/Core/util/ForwardDeclarations.h
index 18d3af7c5..c5f27d80b 100644
--- a/Eigen/src/Core/util/ForwardDeclarations.h
+++ b/Eigen/src/Core/util/ForwardDeclarations.h
@@ -123,7 +123,7 @@ template<typename MatrixType> class SVD;
 template<typename MatrixType, unsigned int Options = 0> class JacobiSVD;
 template<typename MatrixType, int UpLo = LowerTriangular> class LLT;
 template<typename MatrixType> class LDLT;
-template<typename Scalar>     class JacobiRotation;
+template<typename Scalar>     class PlanarRotation;
 
 // Geometry module:
 template<typename Derived, int _Dim> class RotationBase;
diff --git a/Eigen/src/Jacobi/Jacobi.h b/Eigen/src/Jacobi/Jacobi.h
index 24fb7e782..c38d4583f 100644
--- a/Eigen/src/Jacobi/Jacobi.h
+++ b/Eigen/src/Jacobi/Jacobi.h
@@ -27,97 +27,72 @@
 #define EIGEN_JACOBI_H
 
 /** \ingroup Jacobi
-  * \class JacobiRotation
+  * \class PlanarRotation
   * \brief Represents a rotation in the plane from a cosine-sine pair.
   *
-  * This class represents a Jacobi rotation which is also known as a Givens rotation.
+  * This class represents a Jacobi or Givens rotation.
   * This is a 2D clock-wise rotation in the plane \c J of angle \f$ \theta \f$ defined by
   * its cosine \c c and sine \c s as follow:
   * \f$ J = \left ( \begin{array}{cc} c & \overline s \\ -s  & \overline c \end{array} \right ) \f$
   *
-  * \sa MatrixBase::makeJacobi(), MatrixBase::applyJacobiOnTheLeft(), MatrixBase::applyJacobiOnTheRight()
+  * \sa MatrixBase::makeJacobi(), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
   */
-template<typename Scalar> class JacobiRotation
+template<typename Scalar> class PlanarRotation
 {
   public:
+    typedef typename NumTraits<Scalar>::Real RealScalar;
+
     /** Default constructor without any initialization. */
-    JacobiRotation() {}
+    PlanarRotation() {}
 
-    /** Construct a Jacobi rotation from a cosine-sine pair (\a c, \c s). */
-    JacobiRotation(const Scalar& c, const Scalar& s) : m_c(c), m_s(s) {}
+    /** Construct a planar rotation from a cosine-sine pair (\a c, \c s). */
+    PlanarRotation(const Scalar& c, const Scalar& s) : m_c(c), m_s(s) {}
 
     Scalar& c() { return m_c; }
     Scalar c() const { return m_c; }
     Scalar& s() { return m_s; }
     Scalar s() const { return m_s; }
 
-    /** Concatenates two Jacobi rotation */
-    JacobiRotation operator*(const JacobiRotation& other)
+    /** Concatenates two planar rotation */
+    PlanarRotation operator*(const PlanarRotation& other)
     {
-      return JacobiRotation(m_c * other.m_c - ei_conj(m_s) * other.m_s,
+      return PlanarRotation(m_c * other.m_c - ei_conj(m_s) * other.m_s,
                             ei_conj(m_c * ei_conj(other.m_s) + ei_conj(m_s) * ei_conj(other.m_c)));
     }
 
     /** Returns the transposed transformation */
-    JacobiRotation transpose() const { return JacobiRotation(m_c, -ei_conj(m_s)); }
+    PlanarRotation transpose() const { return PlanarRotation(m_c, -ei_conj(m_s)); }
 
     /** Returns the adjoint transformation */
-    JacobiRotation adjoint()   const { return JacobiRotation(ei_conj(m_c), -m_s); }
+    PlanarRotation adjoint() const { return PlanarRotation(ei_conj(m_c), -m_s); }
 
-  protected:
-    Scalar m_c, m_s;
-};
+    template<typename Derived>
+    bool makeJacobi(const MatrixBase<Derived>&, int p, int q);
+    bool makeJacobi(RealScalar x, Scalar y, RealScalar z);
 
-/** Applies the clock wise 2D rotation \a j to the set of 2D vectors of cordinates \a x and \a y:
-  * \f$ \left ( \begin{array}{cc} x \\ y \end{array} \right )  =  J \left ( \begin{array}{cc} x \\ y \end{array} \right ) \f$
-  *
-  * \sa MatrixBase::applyJacobiOnTheLeft(), MatrixBase::applyJacobiOnTheRight()
-  */
-template<typename VectorX, typename VectorY, typename JacobiScalar>
-void ei_apply_rotation_in_the_plane(VectorX& _x, VectorY& _y, const JacobiRotation<JacobiScalar>& j);
+    void makeGivens(const Scalar& p, const Scalar& q, Scalar* z=0);
 
-/** Applies the rotation in the plane \a j to the rows \a p and \a q of \c *this, i.e., it computes B = J * B,
-  * with \f$ B = \left ( \begin{array}{cc} \text{*this.row}(p) \\ \text{*this.row}(q) \end{array} \right ) \f$.
-  *
-  * \sa class JacobiRotation, MatrixBase::applyJacobiOnTheRight(), ei_apply_rotation_in_the_plane()
-  */
-template<typename Derived>
-template<typename JacobiScalar>
-inline void MatrixBase<Derived>::applyJacobiOnTheLeft(int p, int q, const JacobiRotation<JacobiScalar>& j)
-{
-  RowXpr x(row(p));
-  RowXpr y(row(q));
-  ei_apply_rotation_in_the_plane(x, y, j);
-}
+  protected:
+    void makeGivens(const Scalar& p, const Scalar& q, Scalar* z, ei_meta_true);
+    void makeGivens(const Scalar& p, const Scalar& q, Scalar* z, ei_meta_false);
 
-/** Applies the rotation in the plane \a j to the columns \a p and \a q of \c *this, i.e., it computes B = B * J
-  * with \f$ B = \left ( \begin{array}{cc} \text{*this.col}(p) & \text{*this.col}(q) \end{array} \right ) \f$.
-  *
-  * \sa class JacobiRotation, MatrixBase::applyJacobiOnTheLeft(), ei_apply_rotation_in_the_plane()
-  */
-template<typename Derived>
-template<typename JacobiScalar>
-inline void MatrixBase<Derived>::applyJacobiOnTheRight(int p, int q, const JacobiRotation<JacobiScalar>& j)
-{
-  ColXpr x(col(p));
-  ColXpr y(col(q));
-  ei_apply_rotation_in_the_plane(x, y, j.transpose());
-}
+    Scalar m_c, m_s;
+};
 
-/** Computes the Jacobi rotation \a J such that applying \a J on both the right and left sides of the 2x2 matrix
+/** Makes \c *this as a Jacobi rotation \a J such that applying \a J on both the right and left sides of the 2x2 matrix
   * \f$ B = \left ( \begin{array}{cc} x & y \\ * & z \end{array} \right )\f$ yields
   * a diagonal matrix \f$ A = J^* B J \f$
   *
-  * \sa MatrixBase::makeJacobi(), MatrixBase::applyJacobiOnTheLeft(), MatrixBase::applyJacobiOnTheRight()
+  * \sa MatrixBase::makeJacobi(), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
   */
 template<typename Scalar>
-bool ei_makeJacobi(typename NumTraits<Scalar>::Real x, Scalar y, typename NumTraits<Scalar>::Real z, JacobiRotation<Scalar> *j)
+bool PlanarRotation<Scalar>::makeJacobi(RealScalar x, Scalar y, RealScalar z)
 {
   typedef typename NumTraits<Scalar>::Real RealScalar;
   if(y == Scalar(0))
   {
-    j->c() = Scalar(1);
-    j->s() = Scalar(0);
+    m_c = Scalar(1);
+    m_s = Scalar(0);
     return false;
   }
   else
@@ -135,26 +110,132 @@ bool ei_makeJacobi(typename NumTraits<Scalar>::Real x, Scalar y, typename NumTra
     }
     RealScalar sign_t = t > 0 ? 1 : -1;
     RealScalar n = RealScalar(1) / ei_sqrt(ei_abs2(t)+1);
-    j->s() = - sign_t * (ei_conj(y) / ei_abs(y)) * ei_abs(t) * n;
-    j->c() = n;
+    m_s = - sign_t * (ei_conj(y) / ei_abs(y)) * ei_abs(t) * n;
+    m_c = n;
     return true;
   }
 }
 
-/** Computes the Jacobi rotation \a J such that applying \a J on both the right and left sides of the 2x2 matrix
+/** Makes \c *this as a Jacobi rotation \c J such that applying \a J on both the right and left sides of the 2x2 matrix
   * \f$ B = \left ( \begin{array}{cc} \text{this}_{pp} & \text{this}_{pq} \\ * & \text{this}_{qq} \end{array} \right )\f$ yields
   * a diagonal matrix \f$ A = J^* B J \f$
   *
-  * \sa MatrixBase::ei_make_jacobi(), MatrixBase::applyJacobiOnTheLeft(), MatrixBase::applyJacobiOnTheRight()
+  * \sa PlanarRotation::makeJacobi(RealScalar, Scalar, RealScalar), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
   */
+template<typename Scalar>
 template<typename Derived>
-inline bool MatrixBase<Derived>::makeJacobi(int p, int q, JacobiRotation<Scalar> *j) const
+inline bool PlanarRotation<Scalar>::makeJacobi(const MatrixBase<Derived>& m, int p, int q)
+{
+  return makeJacobi(ei_real(m.coeff(p,p)), m.coeff(p,q), ei_real(m.coeff(q,q)));
+}
+
+/** Makes \c *this as a Givens rotation \c G such that applying \f$ G^* \f$ to the left of the vector
+  * \f$ V = \left ( \begin{array}{c} p \\ q \end{array} \right )\f$ yields:
+  * \f$ G^* V = \left ( \begin{array}{c} z \\ 0 \end{array} \right )\f$.
+  *
+  * The value of \a z is returned if \a z is not null (the default is null).
+  * Also note that G is built such that the cosine is always real.
+  *
+  * \sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
+  */
+template<typename Scalar>
+void PlanarRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* z)
 {
-  return ei_makeJacobi(ei_real(coeff(p,p)), coeff(p,q), ei_real(coeff(q,q)), j);
+  makeGivens(p, q, z, typename ei_meta_if<NumTraits<Scalar>::IsComplex, ei_meta_true, ei_meta_false>::ret());
 }
 
-template<typename VectorX, typename VectorY, typename JacobiScalar>
-void /*EIGEN_DONT_INLINE*/ ei_apply_rotation_in_the_plane(VectorX& _x, VectorY& _y, const JacobiRotation<JacobiScalar>& j)
+
+// specialization for complexes
+template<typename Scalar>
+void PlanarRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* z, ei_meta_true)
+{
+  RealScalar scale, absx, absxy;
+  if(q==Scalar(0))
+  {
+    // return identity
+    m_c = Scalar(1);
+    m_s = Scalar(0);
+    if(z) *z = p;
+  }
+  else
+  {
+    scale = ei_norm1(p);
+    absx = scale * ei_sqrt(ei_abs2(p/scale));
+    scale = ei_abs(scale) + ei_norm1(q);
+    absxy = scale * ei_sqrt((absx/scale)*(absx/scale) + ei_abs2(q/scale));
+    m_c = Scalar(absx / absxy);
+    Scalar np = p/absx;
+    m_s = -ei_conj(np) * q / absxy;
+    if(z) *z = np * absxy;
+  }
+}
+
+// specialization for reals
+template<typename Scalar>
+void PlanarRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* z, ei_meta_false)
+{
+  // from Golub's "Matrix Computations", algorithm 5.1.3
+  if(q==0)
+  {
+    m_c = 1; m_s = 0;
+  }
+  else if(ei_abs(q)>ei_abs(p))
+  {
+    Scalar t = -p/q;
+    m_s = Scalar(1)/ei_sqrt(1+t*t);
+    m_c = m_s * t;
+  }
+  else
+  {
+    Scalar t = -q/p;
+    m_c = Scalar(1)/ei_sqrt(1+t*t);
+    m_s = m_c * t;
+  }
+}
+
+/****************************************************************************************
+*   Implementation of MatrixBase methods
+/***************************************************************************************/
+
+/** Applies the clock wise 2D rotation \a j to the set of 2D vectors of cordinates \a x and \a y:
+  * \f$ \left ( \begin{array}{cc} x \\ y \end{array} \right )  =  J \left ( \begin{array}{cc} x \\ y \end{array} \right ) \f$
+  *
+  * \sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
+  */
+template<typename VectorX, typename VectorY, typename OtherScalar>
+void ei_apply_rotation_in_the_plane(VectorX& _x, VectorY& _y, const PlanarRotation<OtherScalar>& j);
+
+/** Applies the rotation in the plane \a j to the rows \a p and \a q of \c *this, i.e., it computes B = J * B,
+  * with \f$ B = \left ( \begin{array}{cc} \text{*this.row}(p) \\ \text{*this.row}(q) \end{array} \right ) \f$.
+  *
+  * \sa class PlanarRotation, MatrixBase::applyOnTheRight(), ei_apply_rotation_in_the_plane()
+  */
+template<typename Derived>
+template<typename OtherScalar>
+inline void MatrixBase<Derived>::applyOnTheLeft(int p, int q, const PlanarRotation<OtherScalar>& j)
+{
+  RowXpr x(row(p));
+  RowXpr y(row(q));
+  ei_apply_rotation_in_the_plane(x, y, j);
+}
+
+/** Applies the rotation in the plane \a j to the columns \a p and \a q of \c *this, i.e., it computes B = B * J
+  * with \f$ B = \left ( \begin{array}{cc} \text{*this.col}(p) & \text{*this.col}(q) \end{array} \right ) \f$.
+  *
+  * \sa class PlanarRotation, MatrixBase::applyOnTheLeft(), ei_apply_rotation_in_the_plane()
+  */
+template<typename Derived>
+template<typename OtherScalar>
+inline void MatrixBase<Derived>::applyOnTheRight(int p, int q, const PlanarRotation<OtherScalar>& j)
+{
+  ColXpr x(col(p));
+  ColXpr y(col(q));
+  ei_apply_rotation_in_the_plane(x, y, j.transpose());
+}
+
+
+template<typename VectorX, typename VectorY, typename OtherScalar>
+void /*EIGEN_DONT_INLINE*/ ei_apply_rotation_in_the_plane(VectorX& _x, VectorY& _y, const PlanarRotation<OtherScalar>& j)
 {
   typedef typename VectorX::Scalar Scalar;
   ei_assert(_x.size() == _y.size());
diff --git a/Eigen/src/QR/ComplexSchur.h b/Eigen/src/QR/ComplexSchur.h
index a0b954d49..153826811 100644
--- a/Eigen/src/QR/ComplexSchur.h
+++ b/Eigen/src/QR/ComplexSchur.h
@@ -80,34 +80,6 @@ template<typename _MatrixType> class ComplexSchur
     bool m_isInitialized;
 };
 
-// computes the plane rotation G such that G' x |p| = | c  s' |' |p| = |z|
-//                                              |q|   |-s  c' |  |q|   |0|
-// and returns z if requested. Note that the returned c is real.
-template<typename T> void ei_make_givens(const std::complex<T>& p, const std::complex<T>& q,
-                                           JacobiRotation<std::complex<T> >& rot, std::complex<T>* z=0)
-{
-  typedef std::complex<T> Complex;
-  T scale, absx, absxy;
-  if(p==Complex(0))
-  {
-    // return identity
-    rot.c() = Complex(1,0);
-    rot.s() = Complex(0,0);
-    if(z) *z = p;
-  }
-  else
-  {
-    scale = cnorm1(p);
-    absx = scale * ei_sqrt(ei_abs2(p/scale));
-    scale = ei_abs(scale) + cnorm1(q);
-    absxy = scale * ei_sqrt((absx/scale)*(absx/scale) + ei_abs2(q/scale));
-    rot.c() = Complex(absx / absxy);
-    Complex np = p/absx;
-    rot.s() = -ei_conj(np) * q / absxy;
-    if(z) *z = np * absxy;
-  }
-}
-
 template<typename MatrixType>
 void ComplexSchur<MatrixType>::compute(const MatrixType& matrix)
 {
@@ -133,8 +105,8 @@ void ComplexSchur<MatrixType>::compute(const MatrixType& matrix)
     //locate the range in which to iterate
     while(iu > 0)
     {
-      d = cnorm1(m_matT.coeffRef(iu,iu)) + cnorm1(m_matT.coeffRef(iu-1,iu-1));
-      sd = cnorm1(m_matT.coeffRef(iu,iu-1));
+      d = ei_norm1(m_matT.coeffRef(iu,iu)) + ei_norm1(m_matT.coeffRef(iu-1,iu-1));
+      sd = ei_norm1(m_matT.coeffRef(iu,iu-1));
 
       if(sd >= eps * d) break; // FIXME : precision criterion ??
 
@@ -156,8 +128,8 @@ void ComplexSchur<MatrixType>::compute(const MatrixType& matrix)
     while( il > 0 )
     {
       // check if the current 2x2 block on the diagonal is upper triangular
-      d = cnorm1(m_matT.coeffRef(il,il)) + cnorm1(m_matT.coeffRef(il-1,il-1));
-      sd = cnorm1(m_matT.coeffRef(il,il-1));
+      d = ei_norm1(m_matT.coeffRef(il,il)) + ei_norm1(m_matT.coeffRef(il-1,il-1));
+      sd = ei_norm1(m_matT.coeffRef(il,il-1));
 
       if(sd < eps * d) break; // FIXME : precision criterion ??
 
@@ -179,32 +151,32 @@ void ComplexSchur<MatrixType>::compute(const MatrixType& matrix)
     r1 = (b+disc)/RealScalar(2);
     r2 = (b-disc)/RealScalar(2);
 
-    if(cnorm1(r1) > cnorm1(r2))
+    if(ei_norm1(r1) > ei_norm1(r2))
       r2 = c/r1;
     else
       r1 = c/r2;
 
-    if(cnorm1(r1-t.coeff(1,1)) < cnorm1(r2-t.coeff(1,1)))
+    if(ei_norm1(r1-t.coeff(1,1)) < ei_norm1(r2-t.coeff(1,1)))
       kappa = sf * r1;
     else
       kappa = sf * r2;
 
     // perform the QR step using Givens rotations
-    JacobiRotation<Complex> rot;
-    ei_make_givens(m_matT.coeff(il,il) - kappa, m_matT.coeff(il+1,il), rot);
+    PlanarRotation<Complex> rot;
+    rot.makeGivens(m_matT.coeff(il,il) - kappa, m_matT.coeff(il+1,il));
 
     for(int i=il ; i<iu ; i++)
     {
-      m_matT.block(0,i,n,n-i).applyJacobiOnTheLeft(i, i+1, rot.adjoint());
-      m_matT.block(0,0,std::min(i+2,iu)+1,n).applyJacobiOnTheRight(i, i+1, rot);
-      m_matU.applyJacobiOnTheRight(i, i+1, rot);
+      m_matT.block(0,i,n,n-i).applyOnTheLeft(i, i+1, rot.adjoint());
+      m_matT.block(0,0,std::min(i+2,iu)+1,n).applyOnTheRight(i, i+1, rot);
+      m_matU.applyOnTheRight(i, i+1, rot);
 
       if(i != iu-1)
       {
         int i1 = i+1;
         int i2 = i+2;
 
-        ei_make_givens(m_matT.coeffRef(i1,i), m_matT.coeffRef(i2,i), rot, &m_matT.coeffRef(i1,i));
+        rot.makeGivens(m_matT.coeffRef(i1,i), m_matT.coeffRef(i2,i), &m_matT.coeffRef(i1,i));
         m_matT.coeffRef(i2,i) = Complex(0);
       }
     }
@@ -223,13 +195,6 @@ void ComplexSchur<MatrixType>::compute(const MatrixType& matrix)
   m_isInitialized = true;
 }
 
-// norm1 of complex numbers
-template<typename T>
-T cnorm1(const std::complex<T> &Z)
-{
-  return(ei_abs(Z.real()) + ei_abs(Z.imag()));
-}
-
 /**
   * Computes the principal value of the square root of the complex \a z.
   */
diff --git a/Eigen/src/QR/SelfAdjointEigenSolver.h b/Eigen/src/QR/SelfAdjointEigenSolver.h
index dd1736e28..580b042f6 100644
--- a/Eigen/src/QR/SelfAdjointEigenSolver.h
+++ b/Eigen/src/QR/SelfAdjointEigenSolver.h
@@ -135,28 +135,6 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
 
 #ifndef EIGEN_HIDE_HEAVY_CODE
 
-// from Golub's "Matrix Computations", algorithm 5.1.3
-template<typename Scalar>
-static void ei_givens_rotation(Scalar a, Scalar b, Scalar& c, Scalar& s)
-{
-  if (b==0)
-  {
-    c = 1; s = 0;
-  }
-  else if (ei_abs(b)>ei_abs(a))
-  {
-    Scalar t = -a/b;
-    s = Scalar(1)/ei_sqrt(1+t*t);
-    c = s * t;
-  }
-  else
-  {
-    Scalar t = -b/a;
-    c = Scalar(1)/ei_sqrt(1+t*t);
-    s = c * t;
-  }
-}
-
 /** \internal
   *
   * \qr_module
@@ -353,34 +331,33 @@ static void ei_tridiagonal_qr_step(RealScalar* diag, RealScalar* subdiag, int st
 
   for (int k = start; k < end; ++k)
   {
-    RealScalar c, s;
-    ei_givens_rotation(x, z, c, s);
+    PlanarRotation<RealScalar> rot;
+    rot.makeGivens(x, z);
 
     // do T = G' T G
-    RealScalar sdk = s * diag[k] + c * subdiag[k];
-    RealScalar dkp1 = s * subdiag[k] + c * diag[k+1];
+    RealScalar sdk = rot.s() * diag[k] + rot.c() * subdiag[k];
+    RealScalar dkp1 = rot.s() * subdiag[k] + rot.c() * diag[k+1];
 
-    diag[k] = c * (c * diag[k] - s * subdiag[k]) - s * (c * subdiag[k] - s * diag[k+1]);
-    diag[k+1] = s * sdk + c * dkp1;
-    subdiag[k] = c * sdk - s * dkp1;
+    diag[k] = rot.c() * (rot.c() * diag[k] - rot.s() * subdiag[k]) - rot.s() * (rot.c() * subdiag[k] - rot.s() * diag[k+1]);
+    diag[k+1] = rot.s() * sdk + rot.c() * dkp1;
+    subdiag[k] = rot.c() * sdk - rot.s() * dkp1;
 
     if (k > start)
-      subdiag[k - 1] = c * subdiag[k-1] - s * z;
+      subdiag[k - 1] = rot.c() * subdiag[k-1] - rot.s() * z;
 
     x = subdiag[k];
 
     if (k < end - 1)
     {
-      z = -s * subdiag[k+1];
-      subdiag[k + 1] = c * subdiag[k+1];
+      z = -rot.s() * subdiag[k+1];
+      subdiag[k + 1] = rot.c() * subdiag[k+1];
     }
 
     // apply the givens rotation to the unit matrix Q = Q * G
-    // G only modifies the two columns k and k+1
     if (matrixQ)
     {
       Map<Matrix<Scalar,Dynamic,Dynamic> > q(matrixQ,n,n);
-      q.applyJacobiOnTheRight(k,k+1,JacobiRotation<RealScalar>(c,s));
+      q.applyOnTheRight(k,k+1,rot);
     }
   }
 }
diff --git a/Eigen/src/SVD/JacobiSVD.h b/Eigen/src/SVD/JacobiSVD.h
index 654f8981a..ca359832b 100644
--- a/Eigen/src/SVD/JacobiSVD.h
+++ b/Eigen/src/SVD/JacobiSVD.h
@@ -125,7 +125,7 @@ struct ei_svd_precondition_2x2_block_to_be_real<MatrixType, Options, true>
   static void run(MatrixType& work_matrix, JacobiSVD<MatrixType, Options>& svd, int p, int q)
   {
     Scalar z;
-    JacobiRotation<Scalar> rot;
+    PlanarRotation<Scalar> rot;
     RealScalar n = ei_sqrt(ei_abs2(work_matrix.coeff(p,p)) + ei_abs2(work_matrix.coeff(q,p)));
     if(n==0)
     {
@@ -140,8 +140,8 @@ struct ei_svd_precondition_2x2_block_to_be_real<MatrixType, Options, true>
     {
       rot.c() = ei_conj(work_matrix.coeff(p,p)) / n;
       rot.s() = work_matrix.coeff(q,p) / n;
-      work_matrix.applyJacobiOnTheLeft(p,q,rot);
-      if(ComputeU) svd.m_matrixU.applyJacobiOnTheRight(p,q,rot.adjoint());
+      work_matrix.applyOnTheLeft(p,q,rot);
+      if(ComputeU) svd.m_matrixU.applyOnTheRight(p,q,rot.adjoint());
       if(work_matrix.coeff(p,q) != Scalar(0))
       {
         Scalar z = ei_abs(work_matrix.coeff(p,q)) / work_matrix.coeff(p,q);
@@ -160,13 +160,13 @@ struct ei_svd_precondition_2x2_block_to_be_real<MatrixType, Options, true>
 
 template<typename MatrixType, typename RealScalar>
 void ei_real_2x2_jacobi_svd(const MatrixType& matrix, int p, int q,
-                            JacobiRotation<RealScalar> *j_left,
-                            JacobiRotation<RealScalar> *j_right)
+                            PlanarRotation<RealScalar> *j_left,
+                            PlanarRotation<RealScalar> *j_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));
-  JacobiRotation<RealScalar> rot1;
+  PlanarRotation<RealScalar> rot1;
   RealScalar t = m.coeff(0,0) + m.coeff(1,1);
   RealScalar d = m.coeff(1,0) - m.coeff(0,1);
   if(t == RealScalar(0))
@@ -180,8 +180,8 @@ void ei_real_2x2_jacobi_svd(const MatrixType& matrix, int p, int q,
     rot1.c() = RealScalar(1) / ei_sqrt(1 + ei_abs2(u));
     rot1.s() = rot1.c() * u;
   }
-  m.applyJacobiOnTheLeft(0,1,rot1);
-  m.makeJacobi(0,1,j_right);
+  m.applyOnTheLeft(0,1,rot1);
+  j_right->makeJacobi(m,0,1);
   *j_left  = rot1 * j_right->transpose();
 }
 
@@ -214,7 +214,7 @@ JacobiSVD<MatrixType, Options>& JacobiSVD<MatrixType, Options>::compute(const Ma
     if(ComputeU)
       for(int i = 0; i < rows; i++)
         m_matrixU.coeffRef(qr.colsPermutation().coeff(i),i) = Scalar(1);
-    
+
   }
   else
   {
@@ -232,14 +232,14 @@ sweep_again:
       {
         ei_svd_precondition_2x2_block_to_be_real<MatrixType, Options>::run(work_matrix, *this, p, q);
 
-        JacobiRotation<RealScalar> j_left, j_right;
+        PlanarRotation<RealScalar> j_left, j_right;
         ei_real_2x2_jacobi_svd(work_matrix, p, q, &j_left, &j_right);
 
-        work_matrix.applyJacobiOnTheLeft(p,q,j_left);
-        if(ComputeU) m_matrixU.applyJacobiOnTheRight(p,q,j_left.transpose());
+        work_matrix.applyOnTheLeft(p,q,j_left);
+        if(ComputeU) m_matrixU.applyOnTheRight(p,q,j_left.transpose());
 
-        work_matrix.applyJacobiOnTheRight(p,q,j_right);
-        if(ComputeV) m_matrixV.applyJacobiOnTheRight(p,q,j_right);
+        work_matrix.applyOnTheRight(p,q,j_right);
+        if(ComputeV) m_matrixV.applyOnTheRight(p,q,j_right);
       }
     }
   }
diff --git a/Eigen/src/SVD/SVD.h b/Eigen/src/SVD/SVD.h
index 095e18b3e..da01cf396 100644
--- a/Eigen/src/SVD/SVD.h
+++ b/Eigen/src/SVD/SVD.h
@@ -309,7 +309,7 @@ SVD<MatrixType>& SVD<MatrixType>::compute(const MatrixType& matrix)
           h = Scalar(1.0)/h;
           c = g*h;
           s = -f*h;
-          V.applyJacobiOnTheRight(i,nm,JacobiRotation<Scalar>(c,s));
+          V.applyOnTheRight(i,nm,PlanarRotation<Scalar>(c,s));
         }
       }
       z = W[k];
@@ -342,7 +342,7 @@ SVD<MatrixType>& SVD<MatrixType>::compute(const MatrixType& matrix)
         y = W[i];
         h = s*g;
         g = c*g;
-        
+
         z = pythag(f,h);
         rv1[j] = z;
         c = f/z;
@@ -351,8 +351,8 @@ SVD<MatrixType>& SVD<MatrixType>::compute(const MatrixType& matrix)
         g = g*c - x*s;
         h = y*s;
         y *= c;
-        V.applyJacobiOnTheRight(i,j,JacobiRotation<Scalar>(c,s));
-        
+        V.applyOnTheRight(i,j,PlanarRotation<Scalar>(c,s));
+
         z = pythag(f,h);
         W[j] = z;
         // Rotation can be arbitrary if z = 0.
@@ -364,7 +364,7 @@ SVD<MatrixType>& SVD<MatrixType>::compute(const MatrixType& matrix)
         }
         f = c*g + s*y;
         x = c*y - s*g;
-        A.applyJacobiOnTheRight(i,j,JacobiRotation<Scalar>(c,s));
+        A.applyOnTheRight(i,j,PlanarRotation<Scalar>(c,s));
       }
       rv1[l] = 0.0;
       rv1[k] = f;