Eigen libary for mbed
Diff: src/Jacobi/Jacobi.h
- Revision:
- 0:13a5d365ba16
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Jacobi/Jacobi.h Thu Oct 13 04:07:23 2016 +0000
@@ -0,0 +1,433 @@
+// 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>&, typename Derived::Index p, typename Derived::Index q);
+ bool makeJacobi(const RealScalar& x, const Scalar& y, const RealScalar& z);
+
+ void makeGivens(const Scalar& p, const Scalar& q, Scalar* z=0);
+
+ protected:
+ void makeGivens(const Scalar& p, const Scalar& q, Scalar* z, internal::true_type);
+ void makeGivens(const Scalar& p, const Scalar& q, Scalar* z, 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;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+ if(y == Scalar(0))
+ {
+ m_c = Scalar(1);
+ m_s = Scalar(0);
+ return false;
+ }
+ else
+ {
+ RealScalar tau = (x-z)/(RealScalar(2)*abs(y));
+ 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, typename Derived::Index p, typename Derived::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 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.
+ *
+ * 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* z)
+{
+ makeGivens(p, q, z, 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
+****************************************************************************************/
+
+/** \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()
+ */
+namespace internal {
+template<typename VectorX, typename VectorY, typename OtherScalar>
+void apply_rotation_in_the_plane(VectorX& _x, VectorY& _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 VectorX, typename VectorY, typename OtherScalar>
+void /*EIGEN_DONT_INLINE*/ apply_rotation_in_the_plane(VectorX& _x, VectorY& _y, const JacobiRotation<OtherScalar>& j)
+{
+ typedef typename VectorX::Index Index;
+ typedef typename VectorX::Scalar Scalar;
+ enum { PacketSize = packet_traits<Scalar>::size };
+ typedef typename packet_traits<Scalar>::type Packet;
+ eigen_assert(_x.size() == _y.size());
+ Index size = _x.size();
+ Index incrx = _x.innerStride();
+ Index incry = _y.innerStride();
+
+ Scalar* EIGEN_RESTRICT x = &_x.coeffRef(0);
+ Scalar* EIGEN_RESTRICT y = &_y.coeffRef(0);
+
+ OtherScalar c = j.c();
+ OtherScalar s = j.s();
+ if (c==OtherScalar(1) && s==OtherScalar(0))
+ return;
+
+ /*** dynamic-size vectorized paths ***/
+
+ if(VectorX::SizeAtCompileTime == Dynamic &&
+ (VectorX::Flags & VectorY::Flags & PacketAccessBit) &&
+ ((incrx==1 && incry==1) || PacketSize == 1))
+ {
+ // both vectors are sequentially stored in memory => vectorization
+ enum { Peeling = 2 };
+
+ Index alignedStart = internal::first_aligned(y, size);
+ Index alignedEnd = alignedStart + ((size-alignedStart)/PacketSize)*PacketSize;
+
+ const Packet pc = pset1<Packet>(c);
+ const Packet ps = pset1<Packet>(s);
+ conj_helper<Packet,Packet,NumTraits<Scalar>::IsComplex,false> pcj;
+
+ 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_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(pmul(pc,xi),pcj.pmul(ps,yi)));
+ pstore(py, psub(pcj.pmul(pc,yi),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(pmul(pc,xi),pcj.pmul(ps,yi)));
+ pstoreu(px+PacketSize, padd(pmul(pc,xi1),pcj.pmul(ps,yi1)));
+ pstore (py, psub(pcj.pmul(pc,yi),pmul(ps,xi)));
+ pstore (py+PacketSize, psub(pcj.pmul(pc,yi1),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(pmul(pc,xi),pcj.pmul(ps,yi)));
+ pstore (y+peelingEnd, psub(pcj.pmul(pc,yi),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(VectorX::SizeAtCompileTime != Dynamic &&
+ (VectorX::Flags & VectorY::Flags & PacketAccessBit) &&
+ (VectorX::Flags & VectorY::Flags & AlignedBit))
+ {
+ const Packet pc = pset1<Packet>(c);
+ const Packet ps = pset1<Packet>(s);
+ conj_helper<Packet,Packet,NumTraits<Scalar>::IsComplex,false> pcj;
+ 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(pmul(pc,xi),pcj.pmul(ps,yi)));
+ pstore(py, psub(pcj.pmul(pc,yi),pmul(ps,xi)));
+ px += PacketSize;
+ py += PacketSize;
+ }
+ }
+
+ /*** non-vectorized path ***/
+ else
+ {
+ 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;
+ }
+ }
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_JACOBI_H
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