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Diffstat (limited to 'eigen/Eigen/src/Jacobi/Jacobi.h')
-rw-r--r-- | eigen/Eigen/src/Jacobi/Jacobi.h | 462 |
1 files changed, 0 insertions, 462 deletions
diff --git a/eigen/Eigen/src/Jacobi/Jacobi.h b/eigen/Eigen/src/Jacobi/Jacobi.h deleted file mode 100644 index 1998c63..0000000 --- a/eigen/Eigen/src/Jacobi/Jacobi.h +++ /dev/null @@ -1,462 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com> -// 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: - typedef typename NumTraits<Scalar>::Real RealScalar; - - /** Default constructor without any initialization. */ - JacobiRotation() {} - - /** Construct a planar rotation from a cosine-sine pair (\a c, \c s). */ - JacobiRotation(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 planar rotation */ - JacobiRotation operator*(const JacobiRotation& other) - { - using numext::conj; - return JacobiRotation(m_c * other.m_c - conj(m_s) * other.m_s, - conj(m_c * conj(other.m_s) + conj(m_s) * conj(other.m_c))); - } - - /** Returns the transposed transformation */ - JacobiRotation transpose() const { using numext::conj; return JacobiRotation(m_c, -conj(m_s)); } - - /** Returns the adjoint transformation */ - JacobiRotation adjoint() const { using numext::conj; return JacobiRotation(conj(m_c), -m_s); } - - template<typename Derived> - bool makeJacobi(const MatrixBase<Derived>&, Index p, Index q); - bool makeJacobi(const RealScalar& x, const Scalar& y, const RealScalar& z); - - void makeGivens(const Scalar& p, const Scalar& q, Scalar* r=0); - - protected: - void makeGivens(const Scalar& p, const Scalar& q, Scalar* r, internal::true_type); - void makeGivens(const Scalar& p, const Scalar& q, Scalar* r, internal::false_type); - - Scalar m_c, m_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> -bool JacobiRotation<Scalar>::makeJacobi(const RealScalar& x, const Scalar& y, const RealScalar& z) -{ - using std::sqrt; - using std::abs; - RealScalar deno = RealScalar(2)*abs(y); - if(deno < (std::numeric_limits<RealScalar>::min)()) - { - m_c = Scalar(1); - m_s = Scalar(0); - return false; - } - else - { - RealScalar tau = (x-z)/deno; - RealScalar w = sqrt(numext::abs2(tau) + RealScalar(1)); - RealScalar t; - if(tau>RealScalar(0)) - { - t = RealScalar(1) / (tau + w); - } - else - { - t = RealScalar(1) / (tau - w); - } - RealScalar sign_t = t > RealScalar(0) ? RealScalar(1) : RealScalar(-1); - RealScalar n = RealScalar(1) / sqrt(numext::abs2(t)+RealScalar(1)); - m_s = - sign_t * (numext::conj(y) / abs(y)) * abs(t) * n; - m_c = n; - return true; - } -} - -/** 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> -inline bool 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> -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> -void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* r, internal::true_type) -{ - using std::sqrt; - using std::abs; - using numext::conj; - - if(q==Scalar(0)) - { - m_c = numext::real(p)<0 ? Scalar(-1) : Scalar(1); - m_s = 0; - if(r) *r = m_c * p; - } - else if(p==Scalar(0)) - { - m_c = 0; - m_s = -q/abs(q); - if(r) *r = abs(q); - } - else - { - RealScalar p1 = numext::norm1(p); - RealScalar q1 = numext::norm1(q); - if(p1>=q1) - { - Scalar ps = p / p1; - RealScalar p2 = numext::abs2(ps); - Scalar qs = q / p1; - RealScalar q2 = numext::abs2(qs); - - RealScalar u = sqrt(RealScalar(1) + q2/p2); - if(numext::real(p)<RealScalar(0)) - u = -u; - - m_c = Scalar(1)/u; - m_s = -qs*conj(ps)*(m_c/p2); - if(r) *r = p * u; - } - else - { - Scalar ps = p / q1; - RealScalar p2 = numext::abs2(ps); - Scalar qs = q / q1; - RealScalar q2 = numext::abs2(qs); - - RealScalar u = q1 * sqrt(p2 + q2); - if(numext::real(p)<RealScalar(0)) - u = -u; - - p1 = abs(p); - ps = p/p1; - m_c = p1/u; - m_s = -conj(ps) * (q/u); - if(r) *r = ps * u; - } - } -} - -// specialization for reals -template<typename Scalar> -void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* r, internal::false_type) -{ - using std::sqrt; - using std::abs; - if(q==Scalar(0)) - { - m_c = p<Scalar(0) ? Scalar(-1) : Scalar(1); - m_s = Scalar(0); - if(r) *r = abs(p); - } - else if(p==Scalar(0)) - { - m_c = Scalar(0); - m_s = q<Scalar(0) ? Scalar(1) : Scalar(-1); - if(r) *r = abs(q); - } - else if(abs(p) > abs(q)) - { - Scalar t = q/p; - Scalar u = sqrt(Scalar(1) + numext::abs2(t)); - if(p<Scalar(0)) - u = -u; - m_c = Scalar(1)/u; - m_s = -t * m_c; - if(r) *r = p * u; - } - else - { - Scalar t = p/q; - Scalar u = sqrt(Scalar(1) + numext::abs2(t)); - if(q<Scalar(0)) - u = -u; - m_s = -Scalar(1)/u; - m_c = -t * m_s; - if(r) *r = q * u; - } - -} - -/**************************************************************************************** -* Implementation of MatrixBase methods -****************************************************************************************/ - -namespace internal { -/** \jacobi_module - * 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 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$. - * - * \sa class JacobiRotation, MatrixBase::applyOnTheRight(), internal::apply_rotation_in_the_plane() - */ -template<typename Derived> -template<typename OtherScalar> -inline void MatrixBase<Derived>::applyOnTheLeft(Index p, Index q, const JacobiRotation<OtherScalar>& j) -{ - RowXpr x(this->row(p)); - RowXpr y(this->row(q)); - internal::apply_rotation_in_the_plane(x, y, j); -} - -/** \ingroup Jacobi_Module - * Applies the rotation in the plane \a j to the columns \a p and \a q of \c *this, i.e., it computes B = B * J - * with \f$ 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> -inline void 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 inline void 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 */> -{ - static inline void 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 - }; - typedef typename packet_traits<Scalar>::type Packet; - typedef typename packet_traits<OtherScalar>::type OtherPacket; - - /*** dynamic-size vectorized paths ***/ - if(SizeAtCompileTime == Dynamic && ((incrx==1 && incry==1) || PacketSize == 1)) - { - // both vectors are sequentially stored in memory => vectorization - enum { Peeling = 2 }; - - Index alignedStart = internal::first_default_aligned(y, size); - Index alignedEnd = alignedStart + ((size-alignedStart)/PacketSize)*PacketSize; - - const OtherPacket pc = pset1<OtherPacket>(c); - const OtherPacket ps = pset1<OtherPacket>(s); - conj_helper<OtherPacket,Packet,NumTraits<OtherScalar>::IsComplex,false> pcj; - conj_helper<OtherPacket,Packet,false,false> pm; - - for(Index i=0; i<alignedStart; ++i) - { - Scalar xi = x[i]; - Scalar yi = y[i]; - x[i] = c * xi + numext::conj(s) * yi; - y[i] = -s * xi + numext::conj(c) * yi; - } - - Scalar* EIGEN_RESTRICT px = x + alignedStart; - Scalar* EIGEN_RESTRICT py = y + alignedStart; - - if(internal::first_default_aligned(x, size)==alignedStart) - { - for(Index i=alignedStart; i<alignedEnd; i+=PacketSize) - { - Packet xi = pload<Packet>(px); - 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; - } - } - else - { - Index peelingEnd = alignedStart + ((size-alignedStart)/(Peeling*PacketSize))*(Peeling*PacketSize); - for(Index i=alignedStart; i<peelingEnd; i+=Peeling*PacketSize) - { - Packet xi = ploadu<Packet>(px); - Packet xi1 = ploadu<Packet>(px+PacketSize); - Packet yi = pload <Packet>(py); - Packet yi1 = pload <Packet>(py+PacketSize); - pstoreu(px, padd(pm.pmul(pc,xi),pcj.pmul(ps,yi))); - pstoreu(px+PacketSize, padd(pm.pmul(pc,xi1),pcj.pmul(ps,yi1))); - pstore (py, psub(pcj.pmul(pc,yi),pm.pmul(ps,xi))); - pstore (py+PacketSize, psub(pcj.pmul(pc,yi1),pm.pmul(ps,xi1))); - px += Peeling*PacketSize; - py += Peeling*PacketSize; - } - if(alignedEnd!=peelingEnd) - { - Packet xi = ploadu<Packet>(x+peelingEnd); - Packet yi = pload <Packet>(y+peelingEnd); - pstoreu(x+peelingEnd, padd(pm.pmul(pc,xi),pcj.pmul(ps,yi))); - pstore (y+peelingEnd, psub(pcj.pmul(pc,yi),pm.pmul(ps,xi))); - } - } - - for(Index i=alignedEnd; i<size; ++i) - { - Scalar xi = x[i]; - Scalar yi = y[i]; - x[i] = c * xi + numext::conj(s) * yi; - y[i] = -s * xi + numext::conj(c) * yi; - } - } - - /*** fixed-size vectorized path ***/ - else if(SizeAtCompileTime != Dynamic && MinAlignment>0) // FIXME should be compared to the required alignment - { - const OtherPacket pc = pset1<OtherPacket>(c); - const OtherPacket ps = pset1<OtherPacket>(s); - conj_helper<OtherPacket,Packet,NumTraits<OtherPacket>::IsComplex,false> pcj; - conj_helper<OtherPacket,Packet,false,false> pm; - Scalar* EIGEN_RESTRICT px = x; - Scalar* EIGEN_RESTRICT py = y; - for(Index i=0; i<size; i+=PacketSize) - { - Packet xi = pload<Packet>(px); - 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 |