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add missing copyrights
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Gael Guennebaud
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bench/eig33.cpp
164
bench/eig33.cpp
@ -1,3 +1,56 @@
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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) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
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//
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// Eigen is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 3 of the License, or (at your option) any later version.
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//
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// Alternatively, you can redistribute it and/or
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// modify it under the terms of the GNU General Public License as
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// published by the Free Software Foundation; either version 2 of
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// the License, or (at your option) any later version.
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//
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// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
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// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License and a copy of the GNU General Public License along with
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// Eigen. If not, see <http://www.gnu.org/licenses/>.
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// The computeRoots function included in this is based on materials
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// covered by the following copyright and license:
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//
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// Geometric Tools, LLC
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// Copyright (c) 1998-2010
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// Distributed under the Boost Software License, Version 1.0.
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//
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// Permission is hereby granted, free of charge, to any person or organization
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// obtaining a copy of the software and accompanying documentation covered by
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// this license (the "Software") to use, reproduce, display, distribute,
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// execute, and transmit the Software, and to prepare derivative works of the
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// Software, and to permit third-parties to whom the Software is furnished to
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// do so, all subject to the following:
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//
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// The copyright notices in the Software and this entire statement, including
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// the above license grant, this restriction and the following disclaimer,
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// must be included in all copies of the Software, in whole or in part, and
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// all derivative works of the Software, unless such copies or derivative
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// works are solely in the form of machine-executable object code generated by
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// a source language processor.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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// FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
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// SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
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// FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
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// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
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// DEALINGS IN THE SOFTWARE.
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#include <iostream>
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#include <Eigen/Core>
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#include <Eigen/Eigenvalues>
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@ -8,56 +61,49 @@ using namespace Eigen;
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using namespace std;
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template<typename Matrix, typename Roots>
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inline void computeRoots (const Matrix& rkA, Roots& adRoot)
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inline void computeRoots(const Matrix& m, Roots& roots)
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{
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typedef typename Matrix::Scalar Scalar;
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const Scalar msInv3 = 1.0/3.0;
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const Scalar msRoot3 = ei_sqrt(Scalar(3.0));
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Scalar dA00 = rkA(0,0);
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Scalar dA01 = rkA(0,1);
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Scalar dA02 = rkA(0,2);
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Scalar dA11 = rkA(1,1);
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Scalar dA12 = rkA(1,2);
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Scalar dA22 = rkA(2,2);
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const Scalar s_inv3 = 1.0/3.0;
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const Scalar s_sqrt3 = ei_sqrt(Scalar(3.0));
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// The characteristic equation is x^3 - c2*x^2 + c1*x - c0 = 0. The
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// eigenvalues are the roots to this equation, all guaranteed to be
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// real-valued, because the matrix is symmetric.
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Scalar dC0 = dA00*dA11*dA22 + Scalar(2)*dA01*dA02*dA12 - dA00*dA12*dA12 - dA11*dA02*dA02 - dA22*dA01*dA01;
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Scalar dC1 = dA00*dA11 - dA01*dA01 + dA00*dA22 - dA02*dA02 + dA11*dA22 - dA12*dA12;
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Scalar dC2 = dA00 + dA11 + dA22;
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Scalar c0 = m(0,0)*m(1,1)*m(2,2) + Scalar(2)*m(0,1)*m(0,2)*m(1,2) - m(0,0)*m(1,2)*m(1,2) - m(1,1)*m(0,2)*m(0,2) - m(2,2)*m(0,1)*m(0,1);
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Scalar c1 = m(0,0)*m(1,1) - m(0,1)*m(0,1) + m(0,0)*m(2,2) - m(0,2)*m(0,2) + m(1,1)*m(2,2) - m(1,2)*m(1,2);
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Scalar c2 = m(0,0) + m(1,1) + m(2,2);
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// Construct the parameters used in classifying the roots of the equation
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// and in solving the equation for the roots in closed form.
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Scalar dC2Div3 = dC2*msInv3;
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Scalar dADiv3 = (dC1 - dC2*dC2Div3)*msInv3;
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if (dADiv3 > Scalar(0))
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dADiv3 = Scalar(0);
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Scalar c2_over_3 = c2*s_inv3;
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Scalar a_over_3 = (c1 - c2*c2_over_3)*s_inv3;
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if (a_over_3 > Scalar(0))
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a_over_3 = Scalar(0);
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Scalar dMBDiv2 = Scalar(0.5)*(dC0 + dC2Div3*(Scalar(2)*dC2Div3*dC2Div3 - dC1));
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Scalar half_b = Scalar(0.5)*(c0 + c2_over_3*(Scalar(2)*c2_over_3*c2_over_3 - c1));
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Scalar dQ = dMBDiv2*dMBDiv2 + dADiv3*dADiv3*dADiv3;
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if (dQ > Scalar(0))
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dQ = Scalar(0);
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Scalar q = half_b*half_b + a_over_3*a_over_3*a_over_3;
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if (q > Scalar(0))
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q = Scalar(0);
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// Compute the eigenvalues by solving for the roots of the polynomial.
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Scalar dMagnitude = ei_sqrt(-dADiv3);
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Scalar dAngle = std::atan2(ei_sqrt(-dQ),dMBDiv2)*msInv3;
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Scalar dCos = ei_cos(dAngle);
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Scalar dSin = ei_sin(dAngle);
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adRoot(0) = dC2Div3 + 2.f*dMagnitude*dCos;
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adRoot(1) = dC2Div3 - dMagnitude*(dCos + msRoot3*dSin);
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adRoot(2) = dC2Div3 - dMagnitude*(dCos - msRoot3*dSin);
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Scalar rho = ei_sqrt(-a_over_3);
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Scalar theta = std::atan2(ei_sqrt(-q),half_b)*s_inv3;
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Scalar cos_theta = ei_cos(theta);
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Scalar sin_theta = ei_sin(theta);
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roots(0) = c2_over_3 + Scalar(2)*rho*cos_theta;
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roots(1) = c2_over_3 - rho*(cos_theta + s_sqrt3*sin_theta);
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roots(2) = c2_over_3 - rho*(cos_theta - s_sqrt3*sin_theta);
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// Sort in increasing order.
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if (adRoot(0) >= adRoot(1))
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std::swap(adRoot(0),adRoot(1));
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if (adRoot(1) >= adRoot(2))
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if (roots(0) >= roots(1))
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std::swap(roots(0),roots(1));
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if (roots(1) >= roots(2))
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{
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std::swap(adRoot(1),adRoot(2));
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if (adRoot(0) >= adRoot(1))
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std::swap(adRoot(0),adRoot(1));
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std::swap(roots(1),roots(2));
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if (roots(0) >= roots(1))
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std::swap(roots(0),roots(1));
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}
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}
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@ -65,21 +111,21 @@ template<typename Matrix, typename Vector>
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void eigen33(const Matrix& mat, Matrix& evecs, Vector& evals)
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{
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typedef typename Matrix::Scalar Scalar;
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// Scale the matrix so its entries are in [-1,1]. The scaling is applied
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// only when at least one matrix entry has magnitude larger than 1.
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// Scale the matrix so its entries are in [-1,1]. The scaling is applied
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// only when at least one matrix entry has magnitude larger than 1.
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Scalar scale = mat.cwiseAbs()/*.template triangularView<Lower>()*/.maxCoeff();
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scale = std::max(scale,Scalar(1));
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Matrix scaledMat = mat / scale;
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Scalar scale = mat.cwiseAbs()/*.template triangularView<Lower>()*/.maxCoeff();
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scale = std::max(scale,Scalar(1));
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Matrix scaledMat = mat / scale;
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// Compute the eigenvalues
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// scaledMat.setZero();
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computeRoots(scaledMat,evals);
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// Compute the eigenvalues
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// scaledMat.setZero();
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computeRoots(scaledMat,evals);
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// compute the eigen vectors
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// here we assume 3 differents eigenvalues
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// compute the eigen vectors
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// **here we assume 3 differents eigenvalues**
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// "optimized version" which appears to be slower with gcc!
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// "optimized version" which appears to be slower with gcc!
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// Vector base;
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// Scalar alpha, beta;
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// base << scaledMat(1,0) * scaledMat(2,1),
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@ -93,22 +139,22 @@ void eigen33(const Matrix& mat, Matrix& evecs, Vector& evals)
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// }
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// evecs.col(2) = evecs.col(0).cross(evecs.col(1)).normalized();
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// naive version
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Matrix tmp;
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tmp = scaledMat;
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tmp.diagonal().array() -= evals(0);
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evecs.col(0) = tmp.row(0).cross(tmp.row(1)).normalized();
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// naive version
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Matrix tmp;
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tmp = scaledMat;
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tmp.diagonal().array() -= evals(0);
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evecs.col(0) = tmp.row(0).cross(tmp.row(1)).normalized();
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tmp = scaledMat;
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tmp.diagonal().array() -= evals(1);
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evecs.col(1) = tmp.row(0).cross(tmp.row(1)).normalized();
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tmp = scaledMat;
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tmp.diagonal().array() -= evals(1);
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evecs.col(1) = tmp.row(0).cross(tmp.row(1)).normalized();
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tmp = scaledMat;
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tmp.diagonal().array() -= evals(2);
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evecs.col(2) = tmp.row(0).cross(tmp.row(1)).normalized();
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// Rescale back to the original size.
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evals *= scale;
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tmp = scaledMat;
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tmp.diagonal().array() -= evals(2);
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evecs.col(2) = tmp.row(0).cross(tmp.row(1)).normalized();
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// Rescale back to the original size.
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evals *= scale;
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}
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int main()
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