// This file is part of Eigen, a lightweight C++ template library // for linear algebra. // // Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com> // Copyright (C) 2009 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 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_JACOBI_H #define EIGEN_JACOBI_H
namespace Eigen {
/** \ingroup Jacobi_Module * \jacobi_module * \class JacobiRotation * \brief Rotation given by a cosine-sine pair. * * This class represents a Jacobi or Givens rotation. * This is a 2D 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$ * * You can apply the respective counter-clockwise rotation to a column vector \c v by * applying its adjoint on the left: \f$ v = J^* v \f$ that translates to the following Eigen code: * \code * v.applyOnTheLeft(J.adjoint()); * \endcode * * \sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
*/ template<typename Scalar> class JacobiRotation
{ public: typedeftypename NumTraits<Scalar>::Real RealScalar;
/** Default constructor without any initialization. */
EIGEN_DEVICE_FUNC
JacobiRotation() {}
/** Construct a planar rotation from a cosine-sine pair (\a c, \c s). */
EIGEN_DEVICE_FUNC
JacobiRotation(const Scalar& c, const Scalar& s) : m_c(c), m_s(s) {}
/** Makes \c *this as a Jacobi rotation \a J such that applying \a J on both the right and left sides of the selfadjoint 2x2 matrix * \f$ B = \left ( \begin{array}{cc} x & y \\ \overline y & z \end{array} \right )\f$ yields a diagonal matrix \f$ A = J^* B J \f$ * * \sa MatrixBase::makeJacobi(const MatrixBase<Derived>&, Index, Index), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
*/ template<typename Scalar>
EIGEN_DEVICE_FUNC bool JacobiRotation<Scalar>::makeJacobi(const RealScalar& x, const Scalar& y, const RealScalar& z)
{ using std::sqrt; using std::abs;
/** Makes \c *this as a Jacobi rotation \c J such that applying \a J on both the right and left sides of the 2x2 selfadjoint matrix * \f$ B = \left ( \begin{array}{cc} \text{this}_{pp} & \text{this}_{pq} \\ (\text{this}_{pq})^* & \text{this}_{qq} \end{array} \right )\f$ yields * a diagonal matrix \f$ A = J^* B J \f$ * * Example: \include Jacobi_makeJacobi.cpp * Output: \verbinclude Jacobi_makeJacobi.out * * \sa JacobiRotation::makeJacobi(RealScalar, Scalar, RealScalar), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
*/ template<typename Scalar> template<typename Derived>
EIGEN_DEVICE_FUNC inlinebool JacobiRotation<Scalar>::makeJacobi(const MatrixBase<Derived>& m, Index p, Index q)
{ return makeJacobi(numext::real(m.coeff(p,p)), m.coeff(p,q), numext::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} r \\ 0 \end{array} \right )\f$. * * The value of \a r is returned if \a r is not null (the default is null). * Also note that G is built such that the cosine is always real. * * Example: \include Jacobi_makeGivens.cpp * Output: \verbinclude Jacobi_makeGivens.out * * This function implements the continuous Givens rotation generation algorithm * found in Anderson (2000), Discontinuous Plane Rotations and the Symmetric Eigenvalue Problem. * LAPACK Working Note 150, University of Tennessee, UT-CS-00-454, December 4, 2000. * * \sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
*/ template<typename Scalar>
EIGEN_DEVICE_FUNC void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* r)
{
makeGivens(p, q, r, typename internal::conditional<NumTraits<Scalar>::IsComplex, internal::true_type, internal::false_type>::type());
}
// specialization for complexes template<typename Scalar>
EIGEN_DEVICE_FUNC void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* r, internal::true_type)
{ using std::sqrt; using std::abs; using numext::conj;
/**************************************************************************************** * Implementation of MatrixBase methods
****************************************************************************************/
namespace internal { /** \jacobi_module * Applies the clock wise 2D rotation \a j to the set of 2D vectors of coordinates \a x and \a y: * \f$ \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>
EIGEN_DEVICE_FUNC void apply_rotation_in_the_plane(DenseBase<VectorX>& xpr_x, DenseBase<VectorY>& xpr_y, const JacobiRotation<OtherScalar>& j);
}
/** \jacobi_module * 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$. * * \sa class JacobiRotation, MatrixBase::applyOnTheRight(), internal::apply_rotation_in_the_plane()
*/ template<typename Derived> template<typename OtherScalar>
EIGEN_DEVICE_FUNC inlinevoid MatrixBase<Derived>::applyOnTheLeft(Index p, Index q, const JacobiRotation<OtherScalar>& j)
{
RowXpr x(this->row(p));
RowXpr y(this->row(q));
internal::apply_rotation_in_the_plane(x, y, j);
}
/** \ingroup Jacobi_Module * Applies the rotation in the plane \a j to the columns \a p and \a q of \c *this, i.e., it computes B = B * J * with \f$ B = \left ( \begin{array}{cc} \text{*this.col}(p) & \text{*this.col}(q) \end{array} \right ) \f$. * * \sa class JacobiRotation, MatrixBase::applyOnTheLeft(), internal::apply_rotation_in_the_plane()
*/ template<typename Derived> template<typename OtherScalar>
EIGEN_DEVICE_FUNC inlinevoid MatrixBase<Derived>::applyOnTheRight(Index p, Index q, const JacobiRotation<OtherScalar>& j)
{
ColXpr x(this->col(p));
ColXpr y(this->col(q));
internal::apply_rotation_in_the_plane(x, y, j.transpose());
}
namespace internal {
template<typename Scalar, typename OtherScalar, int SizeAtCompileTime, int MinAlignment, bool Vectorizable> struct apply_rotation_in_the_plane_selector
{ static EIGEN_DEVICE_FUNC inlinevoid run(Scalar *x, Index incrx, Scalar *y, Index incry, Index size, OtherScalar c, OtherScalar s)
{ for(Index i=0; i<size; ++i)
{
Scalar xi = *x;
Scalar yi = *y;
*x = c * xi + numext::conj(s) * yi;
*y = -s * xi + numext::conj(c) * yi;
x += incrx;
y += incry;
}
}
};
template<typename Scalar, typename OtherScalar, int SizeAtCompileTime, int MinAlignment> struct apply_rotation_in_the_plane_selector<Scalar,OtherScalar,SizeAtCompileTime,MinAlignment,true/* vectorizable */>
{ staticinlinevoid run(Scalar *x, Index incrx, Scalar *y, Index incry, Index size, OtherScalar c, OtherScalar s)
{ enum {
PacketSize = packet_traits<Scalar>::size,
OtherPacketSize = packet_traits<OtherScalar>::size
}; typedeftypename packet_traits<Scalar>::type Packet; typedeftypename packet_traits<OtherScalar>::type OtherPacket;
eigen_assert(xpr_x.size() == xpr_y.size());
Index size = xpr_x.size();
Index incrx = xpr_x.derived().innerStride();
Index incry = xpr_y.derived().innerStride();
Scalar* EIGEN_RESTRICT x = &xpr_x.derived().coeffRef(0);
Scalar* EIGEN_RESTRICT y = &xpr_y.derived().coeffRef(0);
OtherScalar c = j.c();
OtherScalar s = j.s(); if (c==OtherScalar(1) && s==OtherScalar(0)) return;
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