add Eigen as a dependency
This commit is contained in:
Sven Czarnian
462
external/include/eigen3/Eigen/src/Jacobi/Jacobi.h
vendored
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462
external/include/eigen3/Eigen/src/Jacobi/Jacobi.h
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
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// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#ifndef EIGEN_JACOBI_H
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#define EIGEN_JACOBI_H
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namespace Eigen {
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/** \ingroup Jacobi_Module
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* \jacobi_module
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* \class JacobiRotation
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* \brief Rotation given by a cosine-sine pair.
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*
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* This class represents a Jacobi or Givens rotation.
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* This is a 2D 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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* You can apply the respective counter-clockwise rotation to a column vector \c v by
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* applying its adjoint on the left: \f$ v = J^* v \f$ that translates to the following Eigen code:
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* \code
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* v.applyOnTheLeft(J.adjoint());
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* \endcode
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*
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* \sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
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*/
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template<typename Scalar> class JacobiRotation
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{
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public:
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typedef typename NumTraits<Scalar>::Real RealScalar;
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/** Default constructor without any initialization. */
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JacobiRotation() {}
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/** Construct a planar 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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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 planar rotation */
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JacobiRotation operator*(const JacobiRotation& other)
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{
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using numext::conj;
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return JacobiRotation(m_c * other.m_c - conj(m_s) * other.m_s,
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conj(m_c * conj(other.m_s) + conj(m_s) * conj(other.m_c)));
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}
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/** Returns the transposed transformation */
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JacobiRotation transpose() const { using numext::conj; return JacobiRotation(m_c, -conj(m_s)); }
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/** Returns the adjoint transformation */
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JacobiRotation adjoint() const { using numext::conj; return JacobiRotation(conj(m_c), -m_s); }
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template<typename Derived>
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bool makeJacobi(const MatrixBase<Derived>&, Index p, Index q);
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bool makeJacobi(const RealScalar& x, const Scalar& y, const RealScalar& z);
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void makeGivens(const Scalar& p, const Scalar& q, Scalar* r=0);
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protected:
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void makeGivens(const Scalar& p, const Scalar& q, Scalar* r, internal::true_type);
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void makeGivens(const Scalar& p, const Scalar& q, Scalar* r, internal::false_type);
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Scalar m_c, m_s;
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};
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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 selfadjoint 2x2 matrix
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* \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$
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*
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* \sa MatrixBase::makeJacobi(const MatrixBase<Derived>&, Index, Index), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
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*/
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template<typename Scalar>
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bool JacobiRotation<Scalar>::makeJacobi(const RealScalar& x, const Scalar& y, const RealScalar& z)
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{
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using std::sqrt;
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using std::abs;
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RealScalar deno = RealScalar(2)*abs(y);
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if(deno < (std::numeric_limits<RealScalar>::min)())
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{
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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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{
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RealScalar tau = (x-z)/deno;
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RealScalar w = sqrt(numext::abs2(tau) + RealScalar(1));
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RealScalar t;
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if(tau>RealScalar(0))
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{
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t = RealScalar(1) / (tau + w);
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}
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else
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{
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t = RealScalar(1) / (tau - w);
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}
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RealScalar sign_t = t > RealScalar(0) ? RealScalar(1) : RealScalar(-1);
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RealScalar n = RealScalar(1) / sqrt(numext::abs2(t)+RealScalar(1));
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m_s = - sign_t * (numext::conj(y) / abs(y)) * 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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/** 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
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* \f$ B = \left ( \begin{array}{cc} \text{this}_{pp} & \text{this}_{pq} \\ (\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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* Example: \include Jacobi_makeJacobi.cpp
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* Output: \verbinclude Jacobi_makeJacobi.out
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*
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* \sa JacobiRotation::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 JacobiRotation<Scalar>::makeJacobi(const MatrixBase<Derived>& m, Index p, Index q)
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{
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return makeJacobi(numext::real(m.coeff(p,p)), m.coeff(p,q), numext::real(m.coeff(q,q)));
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}
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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} r \\ 0 \end{array} \right )\f$.
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*
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* The value of \a r is returned if \a r 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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* Example: \include Jacobi_makeGivens.cpp
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* Output: \verbinclude Jacobi_makeGivens.out
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*
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* This function implements the continuous Givens rotation generation algorithm
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* found in Anderson (2000), Discontinuous Plane Rotations and the Symmetric Eigenvalue Problem.
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* LAPACK Working Note 150, University of Tennessee, UT-CS-00-454, December 4, 2000.
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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 JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* r)
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{
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makeGivens(p, q, r, typename internal::conditional<NumTraits<Scalar>::IsComplex, internal::true_type, internal::false_type>::type());
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}
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// specialization for complexes
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template<typename Scalar>
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void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* r, internal::true_type)
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{
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using std::sqrt;
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using std::abs;
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using numext::conj;
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if(q==Scalar(0))
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{
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m_c = numext::real(p)<0 ? Scalar(-1) : Scalar(1);
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m_s = 0;
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if(r) *r = m_c * p;
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}
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else if(p==Scalar(0))
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{
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m_c = 0;
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m_s = -q/abs(q);
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if(r) *r = abs(q);
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}
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else
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{
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RealScalar p1 = numext::norm1(p);
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RealScalar q1 = numext::norm1(q);
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if(p1>=q1)
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{
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Scalar ps = p / p1;
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RealScalar p2 = numext::abs2(ps);
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Scalar qs = q / p1;
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RealScalar q2 = numext::abs2(qs);
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RealScalar u = sqrt(RealScalar(1) + q2/p2);
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if(numext::real(p)<RealScalar(0))
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u = -u;
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m_c = Scalar(1)/u;
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m_s = -qs*conj(ps)*(m_c/p2);
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if(r) *r = p * u;
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}
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else
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{
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Scalar ps = p / q1;
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RealScalar p2 = numext::abs2(ps);
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Scalar qs = q / q1;
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RealScalar q2 = numext::abs2(qs);
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RealScalar u = q1 * sqrt(p2 + q2);
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if(numext::real(p)<RealScalar(0))
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u = -u;
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p1 = abs(p);
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ps = p/p1;
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m_c = p1/u;
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m_s = -conj(ps) * (q/u);
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if(r) *r = ps * u;
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}
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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 JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* r, internal::false_type)
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{
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using std::sqrt;
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using std::abs;
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if(q==Scalar(0))
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{
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m_c = p<Scalar(0) ? Scalar(-1) : Scalar(1);
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m_s = Scalar(0);
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if(r) *r = abs(p);
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}
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else if(p==Scalar(0))
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{
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m_c = Scalar(0);
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m_s = q<Scalar(0) ? Scalar(1) : Scalar(-1);
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if(r) *r = abs(q);
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}
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else if(abs(p) > abs(q))
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{
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Scalar t = q/p;
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Scalar u = sqrt(Scalar(1) + numext::abs2(t));
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if(p<Scalar(0))
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u = -u;
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m_c = Scalar(1)/u;
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m_s = -t * m_c;
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if(r) *r = p * u;
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}
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else
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{
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Scalar t = p/q;
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Scalar u = sqrt(Scalar(1) + numext::abs2(t));
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if(q<Scalar(0))
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u = -u;
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m_s = -Scalar(1)/u;
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m_c = -t * m_s;
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if(r) *r = q * u;
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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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namespace internal {
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/** \jacobi_module
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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 apply_rotation_in_the_plane(DenseBase<VectorX>& xpr_x, DenseBase<VectorY>& xpr_y, const JacobiRotation<OtherScalar>& j);
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}
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/** \jacobi_module
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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$.
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*
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* \sa class JacobiRotation, MatrixBase::applyOnTheRight(), internal::apply_rotation_in_the_plane()
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*/
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template<typename Derived>
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template<typename OtherScalar>
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inline void MatrixBase<Derived>::applyOnTheLeft(Index p, Index q, const JacobiRotation<OtherScalar>& j)
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{
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RowXpr x(this->row(p));
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RowXpr y(this->row(q));
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internal::apply_rotation_in_the_plane(x, y, j);
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}
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/** \ingroup Jacobi_Module
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* Applies the rotation in the plane \a j to the columns \a p and \a q of \c *this, i.e., it computes B = B * J
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* with \f$ 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::applyOnTheLeft(), internal::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(Index p, Index q, const JacobiRotation<OtherScalar>& j)
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{
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ColXpr x(this->col(p));
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ColXpr y(this->col(q));
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internal::apply_rotation_in_the_plane(x, y, j.transpose());
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}
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namespace internal {
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template<typename Scalar, typename OtherScalar,
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int SizeAtCompileTime, int MinAlignment, bool Vectorizable>
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struct apply_rotation_in_the_plane_selector
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{
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static inline void run(Scalar *x, Index incrx, Scalar *y, Index incry, Index size, OtherScalar c, OtherScalar s)
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{
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for(Index i=0; i<size; ++i)
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{
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Scalar xi = *x;
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Scalar yi = *y;
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*x = c * xi + numext::conj(s) * yi;
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*y = -s * xi + numext::conj(c) * yi;
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x += incrx;
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y += incry;
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}
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}
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};
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template<typename Scalar, typename OtherScalar,
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int SizeAtCompileTime, int MinAlignment>
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struct apply_rotation_in_the_plane_selector<Scalar,OtherScalar,SizeAtCompileTime,MinAlignment,true /* vectorizable */>
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{
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static inline void run(Scalar *x, Index incrx, Scalar *y, Index incry, Index size, OtherScalar c, OtherScalar s)
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{
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enum {
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PacketSize = packet_traits<Scalar>::size,
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OtherPacketSize = packet_traits<OtherScalar>::size
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};
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typedef typename packet_traits<Scalar>::type Packet;
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typedef typename packet_traits<OtherScalar>::type OtherPacket;
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/*** dynamic-size vectorized paths ***/
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if(SizeAtCompileTime == Dynamic && ((incrx==1 && incry==1) || PacketSize == 1))
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{
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// both vectors are sequentially stored in memory => vectorization
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enum { Peeling = 2 };
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Index alignedStart = internal::first_default_aligned(y, size);
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Index alignedEnd = alignedStart + ((size-alignedStart)/PacketSize)*PacketSize;
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const OtherPacket pc = pset1<OtherPacket>(c);
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const OtherPacket ps = pset1<OtherPacket>(s);
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conj_helper<OtherPacket,Packet,NumTraits<OtherScalar>::IsComplex,false> pcj;
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conj_helper<OtherPacket,Packet,false,false> pm;
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for(Index i=0; i<alignedStart; ++i)
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{
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Scalar xi = x[i];
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Scalar yi = y[i];
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x[i] = c * xi + numext::conj(s) * yi;
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y[i] = -s * xi + numext::conj(c) * yi;
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}
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Scalar* EIGEN_RESTRICT px = x + alignedStart;
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Scalar* EIGEN_RESTRICT py = y + alignedStart;
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if(internal::first_default_aligned(x, size)==alignedStart)
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{
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for(Index i=alignedStart; i<alignedEnd; i+=PacketSize)
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{
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Packet xi = pload<Packet>(px);
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Packet yi = pload<Packet>(py);
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pstore(px, padd(pm.pmul(pc,xi),pcj.pmul(ps,yi)));
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pstore(py, psub(pcj.pmul(pc,yi),pm.pmul(ps,xi)));
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px += PacketSize;
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py += PacketSize;
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}
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}
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else
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{
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Index peelingEnd = alignedStart + ((size-alignedStart)/(Peeling*PacketSize))*(Peeling*PacketSize);
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for(Index i=alignedStart; i<peelingEnd; i+=Peeling*PacketSize)
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{
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Packet xi = ploadu<Packet>(px);
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Packet xi1 = ploadu<Packet>(px+PacketSize);
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Packet yi = pload <Packet>(py);
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Packet yi1 = pload <Packet>(py+PacketSize);
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pstoreu(px, padd(pm.pmul(pc,xi),pcj.pmul(ps,yi)));
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pstoreu(px+PacketSize, padd(pm.pmul(pc,xi1),pcj.pmul(ps,yi1)));
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pstore (py, psub(pcj.pmul(pc,yi),pm.pmul(ps,xi)));
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pstore (py+PacketSize, psub(pcj.pmul(pc,yi1),pm.pmul(ps,xi1)));
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px += Peeling*PacketSize;
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py += Peeling*PacketSize;
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}
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if(alignedEnd!=peelingEnd)
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{
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Packet xi = ploadu<Packet>(x+peelingEnd);
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Packet yi = pload <Packet>(y+peelingEnd);
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pstoreu(x+peelingEnd, padd(pm.pmul(pc,xi),pcj.pmul(ps,yi)));
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pstore (y+peelingEnd, psub(pcj.pmul(pc,yi),pm.pmul(ps,xi)));
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}
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}
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for(Index i=alignedEnd; i<size; ++i)
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{
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Scalar xi = x[i];
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Scalar yi = y[i];
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x[i] = c * xi + numext::conj(s) * yi;
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y[i] = -s * xi + numext::conj(c) * yi;
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}
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}
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/*** fixed-size vectorized path ***/
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else if(SizeAtCompileTime != Dynamic && MinAlignment>0) // FIXME should be compared to the required alignment
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{
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const OtherPacket pc = pset1<OtherPacket>(c);
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const OtherPacket ps = pset1<OtherPacket>(s);
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conj_helper<OtherPacket,Packet,NumTraits<OtherPacket>::IsComplex,false> pcj;
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conj_helper<OtherPacket,Packet,false,false> pm;
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Scalar* EIGEN_RESTRICT px = x;
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Scalar* EIGEN_RESTRICT py = y;
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for(Index i=0; i<size; i+=PacketSize)
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{
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Packet xi = pload<Packet>(px);
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Packet yi = pload<Packet>(py);
|
||||
pstore(px, padd(pm.pmul(pc,xi),pcj.pmul(ps,yi)));
|
||||
pstore(py, psub(pcj.pmul(pc,yi),pm.pmul(ps,xi)));
|
||||
px += PacketSize;
|
||||
py += PacketSize;
|
||||
}
|
||||
}
|
||||
|
||||
/*** non-vectorized path ***/
|
||||
else
|
||||
{
|
||||
apply_rotation_in_the_plane_selector<Scalar,OtherScalar,SizeAtCompileTime,MinAlignment,false>::run(x,incrx,y,incry,size,c,s);
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
template<typename VectorX, typename VectorY, typename OtherScalar>
|
||||
void /*EIGEN_DONT_INLINE*/ apply_rotation_in_the_plane(DenseBase<VectorX>& xpr_x, DenseBase<VectorY>& xpr_y, const JacobiRotation<OtherScalar>& j)
|
||||
{
|
||||
typedef typename VectorX::Scalar Scalar;
|
||||
const bool Vectorizable = (VectorX::Flags & VectorY::Flags & PacketAccessBit)
|
||||
&& (int(packet_traits<Scalar>::size) == int(packet_traits<OtherScalar>::size));
|
||||
|
||||
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;
|
||||
|
||||
apply_rotation_in_the_plane_selector<
|
||||
Scalar,OtherScalar,
|
||||
VectorX::SizeAtCompileTime,
|
||||
EIGEN_PLAIN_ENUM_MIN(evaluator<VectorX>::Alignment, evaluator<VectorY>::Alignment),
|
||||
Vectorizable>::run(x,incrx,y,incry,size,c,s);
|
||||
}
|
||||
|
||||
} // end namespace internal
|
||||
|
||||
} // end namespace Eigen
|
||||
|
||||
#endif // EIGEN_JACOBI_H
|
||||
Reference in New Issue
Block a user