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* rename JacobiRotation => PlanarRotation
* move the makeJacobi and make_givens_* to PlanarRotation * rename applyJacobi* => apply*
This commit is contained in:
Gael Guennebaud
@@ -27,97 +27,72 @@
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#define EIGEN_JACOBI_H
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/** \ingroup Jacobi
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* \class JacobiRotation
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* \class PlanarRotation
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* \brief Represents a rotation in the plane from a cosine-sine pair.
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*
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* This class represents a Jacobi rotation which is also known as a Givens rotation.
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* This class represents a Jacobi or Givens rotation.
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* This is a 2D clock-wise rotation in the plane \c J of angle \f$ \theta \f$ defined by
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* its cosine \c c and sine \c s as follow:
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* \f$ J = \left ( \begin{array}{cc} c & \overline s \\ -s & \overline c \end{array} \right ) \f$
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*
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* \sa MatrixBase::makeJacobi(), MatrixBase::applyJacobiOnTheLeft(), MatrixBase::applyJacobiOnTheRight()
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* \sa MatrixBase::makeJacobi(), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
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*/
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template<typename Scalar> class JacobiRotation
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template<typename Scalar> class PlanarRotation
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{
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public:
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/** Default constructor without any initialization. */
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JacobiRotation() {}
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typedef typename NumTraits<Scalar>::Real RealScalar;
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/** Construct a Jacobi rotation from a cosine-sine pair (\a c, \c s). */
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JacobiRotation(const Scalar& c, const Scalar& s) : m_c(c), m_s(s) {}
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/** Default constructor without any initialization. */
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PlanarRotation() {}
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/** Construct a planar rotation from a cosine-sine pair (\a c, \c s). */
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PlanarRotation(const Scalar& c, const Scalar& s) : m_c(c), m_s(s) {}
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Scalar& c() { return m_c; }
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Scalar c() const { return m_c; }
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Scalar& s() { return m_s; }
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Scalar s() const { return m_s; }
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/** Concatenates two Jacobi rotation */
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JacobiRotation operator*(const JacobiRotation& other)
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/** Concatenates two planar rotation */
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PlanarRotation operator*(const PlanarRotation& other)
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{
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return JacobiRotation(m_c * other.m_c - ei_conj(m_s) * other.m_s,
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return PlanarRotation(m_c * other.m_c - ei_conj(m_s) * other.m_s,
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ei_conj(m_c * ei_conj(other.m_s) + ei_conj(m_s) * ei_conj(other.m_c)));
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}
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/** Returns the transposed transformation */
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JacobiRotation transpose() const { return JacobiRotation(m_c, -ei_conj(m_s)); }
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PlanarRotation transpose() const { return PlanarRotation(m_c, -ei_conj(m_s)); }
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/** Returns the adjoint transformation */
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JacobiRotation adjoint() const { return JacobiRotation(ei_conj(m_c), -m_s); }
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PlanarRotation adjoint() const { return PlanarRotation(ei_conj(m_c), -m_s); }
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template<typename Derived>
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bool makeJacobi(const MatrixBase<Derived>&, int p, int q);
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bool makeJacobi(RealScalar x, Scalar y, RealScalar z);
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void makeGivens(const Scalar& p, const Scalar& q, Scalar* z=0);
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protected:
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void makeGivens(const Scalar& p, const Scalar& q, Scalar* z, ei_meta_true);
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void makeGivens(const Scalar& p, const Scalar& q, Scalar* z, ei_meta_false);
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Scalar m_c, m_s;
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};
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/** Applies the clock wise 2D rotation \a j to the set of 2D vectors of cordinates \a x and \a y:
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* \f$ \left ( \begin{array}{cc} x \\ y \end{array} \right ) = J \left ( \begin{array}{cc} x \\ y \end{array} \right ) \f$
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*
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* \sa MatrixBase::applyJacobiOnTheLeft(), MatrixBase::applyJacobiOnTheRight()
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*/
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template<typename VectorX, typename VectorY, typename JacobiScalar>
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void ei_apply_rotation_in_the_plane(VectorX& _x, VectorY& _y, const JacobiRotation<JacobiScalar>& j);
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/** 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,
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* with \f$ B = \left ( \begin{array}{cc} \text{*this.row}(p) \\ \text{*this.row}(q) \end{array} \right ) \f$.
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*
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* \sa class JacobiRotation, MatrixBase::applyJacobiOnTheRight(), ei_apply_rotation_in_the_plane()
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*/
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template<typename Derived>
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template<typename JacobiScalar>
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inline void MatrixBase<Derived>::applyJacobiOnTheLeft(int p, int q, const JacobiRotation<JacobiScalar>& j)
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{
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RowXpr x(row(p));
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RowXpr y(row(q));
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ei_apply_rotation_in_the_plane(x, y, j);
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}
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/** Applies the rotation in the plane \a j to the columns \a p and \a q of \c *this, i.e., it computes B = B * J
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* with \f$ B = \left ( \begin{array}{cc} \text{*this.col}(p) & \text{*this.col}(q) \end{array} \right ) \f$.
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*
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* \sa class JacobiRotation, MatrixBase::applyJacobiOnTheLeft(), ei_apply_rotation_in_the_plane()
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*/
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template<typename Derived>
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template<typename JacobiScalar>
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inline void MatrixBase<Derived>::applyJacobiOnTheRight(int p, int q, const JacobiRotation<JacobiScalar>& j)
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{
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ColXpr x(col(p));
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ColXpr y(col(q));
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ei_apply_rotation_in_the_plane(x, y, j.transpose());
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}
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/** Computes the Jacobi rotation \a J such that applying \a J on both the right and left sides of the 2x2 matrix
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/** Makes \c *this as a Jacobi rotation \a J such that applying \a J on both the right and left sides of the 2x2 matrix
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* \f$ B = \left ( \begin{array}{cc} x & y \\ * & z \end{array} \right )\f$ yields
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* a diagonal matrix \f$ A = J^* B J \f$
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*
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* \sa MatrixBase::makeJacobi(), MatrixBase::applyJacobiOnTheLeft(), MatrixBase::applyJacobiOnTheRight()
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* \sa MatrixBase::makeJacobi(), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
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*/
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template<typename Scalar>
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bool ei_makeJacobi(typename NumTraits<Scalar>::Real x, Scalar y, typename NumTraits<Scalar>::Real z, JacobiRotation<Scalar> *j)
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bool PlanarRotation<Scalar>::makeJacobi(RealScalar x, Scalar y, RealScalar z)
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{
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typedef typename NumTraits<Scalar>::Real RealScalar;
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if(y == Scalar(0))
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{
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j->c() = Scalar(1);
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j->s() = Scalar(0);
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m_c = Scalar(1);
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m_s = Scalar(0);
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return false;
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}
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else
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@@ -135,26 +110,132 @@ bool ei_makeJacobi(typename NumTraits<Scalar>::Real x, Scalar y, typename NumTra
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}
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RealScalar sign_t = t > 0 ? 1 : -1;
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RealScalar n = RealScalar(1) / ei_sqrt(ei_abs2(t)+1);
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j->s() = - sign_t * (ei_conj(y) / ei_abs(y)) * ei_abs(t) * n;
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j->c() = n;
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m_s = - sign_t * (ei_conj(y) / ei_abs(y)) * ei_abs(t) * n;
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m_c = n;
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return true;
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}
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}
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/** Computes the Jacobi rotation \a J such that applying \a J on both the right and left sides of the 2x2 matrix
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/** 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
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* \f$ B = \left ( \begin{array}{cc} \text{this}_{pp} & \text{this}_{pq} \\ * & \text{this}_{qq} \end{array} \right )\f$ yields
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* a diagonal matrix \f$ A = J^* B J \f$
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*
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* \sa MatrixBase::ei_make_jacobi(), MatrixBase::applyJacobiOnTheLeft(), MatrixBase::applyJacobiOnTheRight()
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* \sa PlanarRotation::makeJacobi(RealScalar, Scalar, RealScalar), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
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*/
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template<typename Scalar>
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template<typename Derived>
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inline bool MatrixBase<Derived>::makeJacobi(int p, int q, JacobiRotation<Scalar> *j) const
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inline bool PlanarRotation<Scalar>::makeJacobi(const MatrixBase<Derived>& m, int p, int q)
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{
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return ei_makeJacobi(ei_real(coeff(p,p)), coeff(p,q), ei_real(coeff(q,q)), j);
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return makeJacobi(ei_real(m.coeff(p,p)), m.coeff(p,q), ei_real(m.coeff(q,q)));
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}
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template<typename VectorX, typename VectorY, typename JacobiScalar>
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void /*EIGEN_DONT_INLINE*/ ei_apply_rotation_in_the_plane(VectorX& _x, VectorY& _y, const JacobiRotation<JacobiScalar>& j)
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/** Makes \c *this as a Givens rotation \c G such that applying \f$ G^* \f$ to the left of the vector
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* \f$ V = \left ( \begin{array}{c} p \\ q \end{array} \right )\f$ yields:
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* \f$ G^* V = \left ( \begin{array}{c} z \\ 0 \end{array} \right )\f$.
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*
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* The value of \a z is returned if \a z is not null (the default is null).
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* Also note that G is built such that the cosine is always real.
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*
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* \sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
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*/
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template<typename Scalar>
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void PlanarRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* z)
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{
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makeGivens(p, q, z, typename ei_meta_if<NumTraits<Scalar>::IsComplex, ei_meta_true, ei_meta_false>::ret());
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}
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// specialization for complexes
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template<typename Scalar>
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void PlanarRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* z, ei_meta_true)
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{
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RealScalar scale, absx, absxy;
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if(q==Scalar(0))
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{
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// return identity
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m_c = Scalar(1);
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m_s = Scalar(0);
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if(z) *z = p;
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}
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else
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{
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scale = ei_norm1(p);
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absx = scale * ei_sqrt(ei_abs2(p/scale));
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scale = ei_abs(scale) + ei_norm1(q);
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absxy = scale * ei_sqrt((absx/scale)*(absx/scale) + ei_abs2(q/scale));
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m_c = Scalar(absx / absxy);
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Scalar np = p/absx;
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m_s = -ei_conj(np) * q / absxy;
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if(z) *z = np * absxy;
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}
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}
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// specialization for reals
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template<typename Scalar>
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void PlanarRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* z, ei_meta_false)
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{
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// from Golub's "Matrix Computations", algorithm 5.1.3
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if(q==0)
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{
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m_c = 1; m_s = 0;
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}
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else if(ei_abs(q)>ei_abs(p))
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{
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Scalar t = -p/q;
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m_s = Scalar(1)/ei_sqrt(1+t*t);
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m_c = m_s * t;
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}
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else
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{
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Scalar t = -q/p;
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m_c = Scalar(1)/ei_sqrt(1+t*t);
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m_s = m_c * t;
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}
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}
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/****************************************************************************************
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* Implementation of MatrixBase methods
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/***************************************************************************************/
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/** Applies the clock wise 2D rotation \a j to the set of 2D vectors of cordinates \a x and \a y:
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* \f$ \left ( \begin{array}{cc} x \\ y \end{array} \right ) = J \left ( \begin{array}{cc} x \\ y \end{array} \right ) \f$
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*
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* \sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
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*/
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template<typename VectorX, typename VectorY, typename OtherScalar>
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void ei_apply_rotation_in_the_plane(VectorX& _x, VectorY& _y, const PlanarRotation<OtherScalar>& j);
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/** 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,
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* with \f$ B = \left ( \begin{array}{cc} \text{*this.row}(p) \\ \text{*this.row}(q) \end{array} \right ) \f$.
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*
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* \sa class PlanarRotation, MatrixBase::applyOnTheRight(), ei_apply_rotation_in_the_plane()
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*/
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template<typename Derived>
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template<typename OtherScalar>
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inline void MatrixBase<Derived>::applyOnTheLeft(int p, int q, const PlanarRotation<OtherScalar>& j)
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{
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RowXpr x(row(p));
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RowXpr y(row(q));
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ei_apply_rotation_in_the_plane(x, y, j);
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}
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/** Applies the rotation in the plane \a j to the columns \a p and \a q of \c *this, i.e., it computes B = B * J
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* with \f$ B = \left ( \begin{array}{cc} \text{*this.col}(p) & \text{*this.col}(q) \end{array} \right ) \f$.
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*
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* \sa class PlanarRotation, MatrixBase::applyOnTheLeft(), ei_apply_rotation_in_the_plane()
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*/
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template<typename Derived>
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template<typename OtherScalar>
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inline void MatrixBase<Derived>::applyOnTheRight(int p, int q, const PlanarRotation<OtherScalar>& j)
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{
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ColXpr x(col(p));
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ColXpr y(col(q));
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ei_apply_rotation_in_the_plane(x, y, j.transpose());
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}
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template<typename VectorX, typename VectorY, typename OtherScalar>
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void /*EIGEN_DONT_INLINE*/ ei_apply_rotation_in_the_plane(VectorX& _x, VectorY& _y, const PlanarRotation<OtherScalar>& j)
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{
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typedef typename VectorX::Scalar Scalar;
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ei_assert(_x.size() == _y.size());
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