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authorStanislaw Halik <sthalik@misaki.pl>2019-03-03 21:09:10 +0100
committerStanislaw Halik <sthalik@misaki.pl>2019-03-03 21:10:13 +0100
commitf0238cfb6997c4acfc2bd200de7295f3fa36968f (patch)
treeb215183760e4f615b9c1dabc1f116383b72a1b55 /eigen/unsupported/Eigen/src/NonLinearOptimization
parent543edd372a5193d04b3de9f23c176ab439e51b31 (diff)
don't index Eigen
Diffstat (limited to 'eigen/unsupported/Eigen/src/NonLinearOptimization')
-rw-r--r--eigen/unsupported/Eigen/src/NonLinearOptimization/HybridNonLinearSolver.h601
-rw-r--r--eigen/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h657
-rw-r--r--eigen/unsupported/Eigen/src/NonLinearOptimization/chkder.h66
-rw-r--r--eigen/unsupported/Eigen/src/NonLinearOptimization/covar.h70
-rw-r--r--eigen/unsupported/Eigen/src/NonLinearOptimization/dogleg.h107
-rw-r--r--eigen/unsupported/Eigen/src/NonLinearOptimization/fdjac1.h79
-rw-r--r--eigen/unsupported/Eigen/src/NonLinearOptimization/lmpar.h298
-rw-r--r--eigen/unsupported/Eigen/src/NonLinearOptimization/qrsolv.h91
-rw-r--r--eigen/unsupported/Eigen/src/NonLinearOptimization/r1mpyq.h30
-rw-r--r--eigen/unsupported/Eigen/src/NonLinearOptimization/r1updt.h99
-rw-r--r--eigen/unsupported/Eigen/src/NonLinearOptimization/rwupdt.h49
11 files changed, 0 insertions, 2147 deletions
diff --git a/eigen/unsupported/Eigen/src/NonLinearOptimization/HybridNonLinearSolver.h b/eigen/unsupported/Eigen/src/NonLinearOptimization/HybridNonLinearSolver.h
deleted file mode 100644
index 8fe3ed8..0000000
--- a/eigen/unsupported/Eigen/src/NonLinearOptimization/HybridNonLinearSolver.h
+++ /dev/null
@@ -1,601 +0,0 @@
-// -*- coding: utf-8
-// vim: set fileencoding=utf-8
-
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
-//
-// 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_HYBRIDNONLINEARSOLVER_H
-#define EIGEN_HYBRIDNONLINEARSOLVER_H
-
-namespace Eigen {
-
-namespace HybridNonLinearSolverSpace {
- enum Status {
- Running = -1,
- ImproperInputParameters = 0,
- RelativeErrorTooSmall = 1,
- TooManyFunctionEvaluation = 2,
- TolTooSmall = 3,
- NotMakingProgressJacobian = 4,
- NotMakingProgressIterations = 5,
- UserAsked = 6
- };
-}
-
-/**
- * \ingroup NonLinearOptimization_Module
- * \brief Finds a zero of a system of n
- * nonlinear functions in n variables by a modification of the Powell
- * hybrid method ("dogleg").
- *
- * The user must provide a subroutine which calculates the
- * functions. The Jacobian is either provided by the user, or approximated
- * using a forward-difference method.
- *
- */
-template<typename FunctorType, typename Scalar=double>
-class HybridNonLinearSolver
-{
-public:
- typedef DenseIndex Index;
-
- HybridNonLinearSolver(FunctorType &_functor)
- : functor(_functor) { nfev=njev=iter = 0; fnorm= 0.; useExternalScaling=false;}
-
- struct Parameters {
- Parameters()
- : factor(Scalar(100.))
- , maxfev(1000)
- , xtol(std::sqrt(NumTraits<Scalar>::epsilon()))
- , nb_of_subdiagonals(-1)
- , nb_of_superdiagonals(-1)
- , epsfcn(Scalar(0.)) {}
- Scalar factor;
- Index maxfev; // maximum number of function evaluation
- Scalar xtol;
- Index nb_of_subdiagonals;
- Index nb_of_superdiagonals;
- Scalar epsfcn;
- };
- typedef Matrix< Scalar, Dynamic, 1 > FVectorType;
- typedef Matrix< Scalar, Dynamic, Dynamic > JacobianType;
- /* TODO: if eigen provides a triangular storage, use it here */
- typedef Matrix< Scalar, Dynamic, Dynamic > UpperTriangularType;
-
- HybridNonLinearSolverSpace::Status hybrj1(
- FVectorType &x,
- const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())
- );
-
- HybridNonLinearSolverSpace::Status solveInit(FVectorType &x);
- HybridNonLinearSolverSpace::Status solveOneStep(FVectorType &x);
- HybridNonLinearSolverSpace::Status solve(FVectorType &x);
-
- HybridNonLinearSolverSpace::Status hybrd1(
- FVectorType &x,
- const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())
- );
-
- HybridNonLinearSolverSpace::Status solveNumericalDiffInit(FVectorType &x);
- HybridNonLinearSolverSpace::Status solveNumericalDiffOneStep(FVectorType &x);
- HybridNonLinearSolverSpace::Status solveNumericalDiff(FVectorType &x);
-
- void resetParameters(void) { parameters = Parameters(); }
- Parameters parameters;
- FVectorType fvec, qtf, diag;
- JacobianType fjac;
- UpperTriangularType R;
- Index nfev;
- Index njev;
- Index iter;
- Scalar fnorm;
- bool useExternalScaling;
-private:
- FunctorType &functor;
- Index n;
- Scalar sum;
- bool sing;
- Scalar temp;
- Scalar delta;
- bool jeval;
- Index ncsuc;
- Scalar ratio;
- Scalar pnorm, xnorm, fnorm1;
- Index nslow1, nslow2;
- Index ncfail;
- Scalar actred, prered;
- FVectorType wa1, wa2, wa3, wa4;
-
- HybridNonLinearSolver& operator=(const HybridNonLinearSolver&);
-};
-
-
-
-template<typename FunctorType, typename Scalar>
-HybridNonLinearSolverSpace::Status
-HybridNonLinearSolver<FunctorType,Scalar>::hybrj1(
- FVectorType &x,
- const Scalar tol
- )
-{
- n = x.size();
-
- /* check the input parameters for errors. */
- if (n <= 0 || tol < 0.)
- return HybridNonLinearSolverSpace::ImproperInputParameters;
-
- resetParameters();
- parameters.maxfev = 100*(n+1);
- parameters.xtol = tol;
- diag.setConstant(n, 1.);
- useExternalScaling = true;
- return solve(x);
-}
-
-template<typename FunctorType, typename Scalar>
-HybridNonLinearSolverSpace::Status
-HybridNonLinearSolver<FunctorType,Scalar>::solveInit(FVectorType &x)
-{
- n = x.size();
-
- wa1.resize(n); wa2.resize(n); wa3.resize(n); wa4.resize(n);
- fvec.resize(n);
- qtf.resize(n);
- fjac.resize(n, n);
- if (!useExternalScaling)
- diag.resize(n);
- eigen_assert( (!useExternalScaling || diag.size()==n) && "When useExternalScaling is set, the caller must provide a valid 'diag'");
-
- /* Function Body */
- nfev = 0;
- njev = 0;
-
- /* check the input parameters for errors. */
- if (n <= 0 || parameters.xtol < 0. || parameters.maxfev <= 0 || parameters.factor <= 0. )
- return HybridNonLinearSolverSpace::ImproperInputParameters;
- if (useExternalScaling)
- for (Index j = 0; j < n; ++j)
- if (diag[j] <= 0.)
- return HybridNonLinearSolverSpace::ImproperInputParameters;
-
- /* evaluate the function at the starting point */
- /* and calculate its norm. */
- nfev = 1;
- if ( functor(x, fvec) < 0)
- return HybridNonLinearSolverSpace::UserAsked;
- fnorm = fvec.stableNorm();
-
- /* initialize iteration counter and monitors. */
- iter = 1;
- ncsuc = 0;
- ncfail = 0;
- nslow1 = 0;
- nslow2 = 0;
-
- return HybridNonLinearSolverSpace::Running;
-}
-
-template<typename FunctorType, typename Scalar>
-HybridNonLinearSolverSpace::Status
-HybridNonLinearSolver<FunctorType,Scalar>::solveOneStep(FVectorType &x)
-{
- using std::abs;
-
- eigen_assert(x.size()==n); // check the caller is not cheating us
-
- Index j;
- std::vector<JacobiRotation<Scalar> > v_givens(n), w_givens(n);
-
- jeval = true;
-
- /* calculate the jacobian matrix. */
- if ( functor.df(x, fjac) < 0)
- return HybridNonLinearSolverSpace::UserAsked;
- ++njev;
-
- wa2 = fjac.colwise().blueNorm();
-
- /* on the first iteration and if external scaling is not used, scale according */
- /* to the norms of the columns of the initial jacobian. */
- if (iter == 1) {
- if (!useExternalScaling)
- for (j = 0; j < n; ++j)
- diag[j] = (wa2[j]==0.) ? 1. : wa2[j];
-
- /* on the first iteration, calculate the norm of the scaled x */
- /* and initialize the step bound delta. */
- xnorm = diag.cwiseProduct(x).stableNorm();
- delta = parameters.factor * xnorm;
- if (delta == 0.)
- delta = parameters.factor;
- }
-
- /* compute the qr factorization of the jacobian. */
- HouseholderQR<JacobianType> qrfac(fjac); // no pivoting:
-
- /* copy the triangular factor of the qr factorization into r. */
- R = qrfac.matrixQR();
-
- /* accumulate the orthogonal factor in fjac. */
- fjac = qrfac.householderQ();
-
- /* form (q transpose)*fvec and store in qtf. */
- qtf = fjac.transpose() * fvec;
-
- /* rescale if necessary. */
- if (!useExternalScaling)
- diag = diag.cwiseMax(wa2);
-
- while (true) {
- /* determine the direction p. */
- internal::dogleg<Scalar>(R, diag, qtf, delta, wa1);
-
- /* store the direction p and x + p. calculate the norm of p. */
- wa1 = -wa1;
- wa2 = x + wa1;
- pnorm = diag.cwiseProduct(wa1).stableNorm();
-
- /* on the first iteration, adjust the initial step bound. */
- if (iter == 1)
- delta = (std::min)(delta,pnorm);
-
- /* evaluate the function at x + p and calculate its norm. */
- if ( functor(wa2, wa4) < 0)
- return HybridNonLinearSolverSpace::UserAsked;
- ++nfev;
- fnorm1 = wa4.stableNorm();
-
- /* compute the scaled actual reduction. */
- actred = -1.;
- if (fnorm1 < fnorm) /* Computing 2nd power */
- actred = 1. - numext::abs2(fnorm1 / fnorm);
-
- /* compute the scaled predicted reduction. */
- wa3 = R.template triangularView<Upper>()*wa1 + qtf;
- temp = wa3.stableNorm();
- prered = 0.;
- if (temp < fnorm) /* Computing 2nd power */
- prered = 1. - numext::abs2(temp / fnorm);
-
- /* compute the ratio of the actual to the predicted reduction. */
- ratio = 0.;
- if (prered > 0.)
- ratio = actred / prered;
-
- /* update the step bound. */
- if (ratio < Scalar(.1)) {
- ncsuc = 0;
- ++ncfail;
- delta = Scalar(.5) * delta;
- } else {
- ncfail = 0;
- ++ncsuc;
- if (ratio >= Scalar(.5) || ncsuc > 1)
- delta = (std::max)(delta, pnorm / Scalar(.5));
- if (abs(ratio - 1.) <= Scalar(.1)) {
- delta = pnorm / Scalar(.5);
- }
- }
-
- /* test for successful iteration. */
- if (ratio >= Scalar(1e-4)) {
- /* successful iteration. update x, fvec, and their norms. */
- x = wa2;
- wa2 = diag.cwiseProduct(x);
- fvec = wa4;
- xnorm = wa2.stableNorm();
- fnorm = fnorm1;
- ++iter;
- }
-
- /* determine the progress of the iteration. */
- ++nslow1;
- if (actred >= Scalar(.001))
- nslow1 = 0;
- if (jeval)
- ++nslow2;
- if (actred >= Scalar(.1))
- nslow2 = 0;
-
- /* test for convergence. */
- if (delta <= parameters.xtol * xnorm || fnorm == 0.)
- return HybridNonLinearSolverSpace::RelativeErrorTooSmall;
-
- /* tests for termination and stringent tolerances. */
- if (nfev >= parameters.maxfev)
- return HybridNonLinearSolverSpace::TooManyFunctionEvaluation;
- if (Scalar(.1) * (std::max)(Scalar(.1) * delta, pnorm) <= NumTraits<Scalar>::epsilon() * xnorm)
- return HybridNonLinearSolverSpace::TolTooSmall;
- if (nslow2 == 5)
- return HybridNonLinearSolverSpace::NotMakingProgressJacobian;
- if (nslow1 == 10)
- return HybridNonLinearSolverSpace::NotMakingProgressIterations;
-
- /* criterion for recalculating jacobian. */
- if (ncfail == 2)
- break; // leave inner loop and go for the next outer loop iteration
-
- /* calculate the rank one modification to the jacobian */
- /* and update qtf if necessary. */
- wa1 = diag.cwiseProduct( diag.cwiseProduct(wa1)/pnorm );
- wa2 = fjac.transpose() * wa4;
- if (ratio >= Scalar(1e-4))
- qtf = wa2;
- wa2 = (wa2-wa3)/pnorm;
-
- /* compute the qr factorization of the updated jacobian. */
- internal::r1updt<Scalar>(R, wa1, v_givens, w_givens, wa2, wa3, &sing);
- internal::r1mpyq<Scalar>(n, n, fjac.data(), v_givens, w_givens);
- internal::r1mpyq<Scalar>(1, n, qtf.data(), v_givens, w_givens);
-
- jeval = false;
- }
- return HybridNonLinearSolverSpace::Running;
-}
-
-template<typename FunctorType, typename Scalar>
-HybridNonLinearSolverSpace::Status
-HybridNonLinearSolver<FunctorType,Scalar>::solve(FVectorType &x)
-{
- HybridNonLinearSolverSpace::Status status = solveInit(x);
- if (status==HybridNonLinearSolverSpace::ImproperInputParameters)
- return status;
- while (status==HybridNonLinearSolverSpace::Running)
- status = solveOneStep(x);
- return status;
-}
-
-
-
-template<typename FunctorType, typename Scalar>
-HybridNonLinearSolverSpace::Status
-HybridNonLinearSolver<FunctorType,Scalar>::hybrd1(
- FVectorType &x,
- const Scalar tol
- )
-{
- n = x.size();
-
- /* check the input parameters for errors. */
- if (n <= 0 || tol < 0.)
- return HybridNonLinearSolverSpace::ImproperInputParameters;
-
- resetParameters();
- parameters.maxfev = 200*(n+1);
- parameters.xtol = tol;
-
- diag.setConstant(n, 1.);
- useExternalScaling = true;
- return solveNumericalDiff(x);
-}
-
-template<typename FunctorType, typename Scalar>
-HybridNonLinearSolverSpace::Status
-HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffInit(FVectorType &x)
-{
- n = x.size();
-
- if (parameters.nb_of_subdiagonals<0) parameters.nb_of_subdiagonals= n-1;
- if (parameters.nb_of_superdiagonals<0) parameters.nb_of_superdiagonals= n-1;
-
- wa1.resize(n); wa2.resize(n); wa3.resize(n); wa4.resize(n);
- qtf.resize(n);
- fjac.resize(n, n);
- fvec.resize(n);
- if (!useExternalScaling)
- diag.resize(n);
- eigen_assert( (!useExternalScaling || diag.size()==n) && "When useExternalScaling is set, the caller must provide a valid 'diag'");
-
- /* Function Body */
- nfev = 0;
- njev = 0;
-
- /* check the input parameters for errors. */
- if (n <= 0 || parameters.xtol < 0. || parameters.maxfev <= 0 || parameters.nb_of_subdiagonals< 0 || parameters.nb_of_superdiagonals< 0 || parameters.factor <= 0. )
- return HybridNonLinearSolverSpace::ImproperInputParameters;
- if (useExternalScaling)
- for (Index j = 0; j < n; ++j)
- if (diag[j] <= 0.)
- return HybridNonLinearSolverSpace::ImproperInputParameters;
-
- /* evaluate the function at the starting point */
- /* and calculate its norm. */
- nfev = 1;
- if ( functor(x, fvec) < 0)
- return HybridNonLinearSolverSpace::UserAsked;
- fnorm = fvec.stableNorm();
-
- /* initialize iteration counter and monitors. */
- iter = 1;
- ncsuc = 0;
- ncfail = 0;
- nslow1 = 0;
- nslow2 = 0;
-
- return HybridNonLinearSolverSpace::Running;
-}
-
-template<typename FunctorType, typename Scalar>
-HybridNonLinearSolverSpace::Status
-HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffOneStep(FVectorType &x)
-{
- using std::sqrt;
- using std::abs;
-
- assert(x.size()==n); // check the caller is not cheating us
-
- Index j;
- std::vector<JacobiRotation<Scalar> > v_givens(n), w_givens(n);
-
- jeval = true;
- if (parameters.nb_of_subdiagonals<0) parameters.nb_of_subdiagonals= n-1;
- if (parameters.nb_of_superdiagonals<0) parameters.nb_of_superdiagonals= n-1;
-
- /* calculate the jacobian matrix. */
- if (internal::fdjac1(functor, x, fvec, fjac, parameters.nb_of_subdiagonals, parameters.nb_of_superdiagonals, parameters.epsfcn) <0)
- return HybridNonLinearSolverSpace::UserAsked;
- nfev += (std::min)(parameters.nb_of_subdiagonals+parameters.nb_of_superdiagonals+ 1, n);
-
- wa2 = fjac.colwise().blueNorm();
-
- /* on the first iteration and if external scaling is not used, scale according */
- /* to the norms of the columns of the initial jacobian. */
- if (iter == 1) {
- if (!useExternalScaling)
- for (j = 0; j < n; ++j)
- diag[j] = (wa2[j]==0.) ? 1. : wa2[j];
-
- /* on the first iteration, calculate the norm of the scaled x */
- /* and initialize the step bound delta. */
- xnorm = diag.cwiseProduct(x).stableNorm();
- delta = parameters.factor * xnorm;
- if (delta == 0.)
- delta = parameters.factor;
- }
-
- /* compute the qr factorization of the jacobian. */
- HouseholderQR<JacobianType> qrfac(fjac); // no pivoting:
-
- /* copy the triangular factor of the qr factorization into r. */
- R = qrfac.matrixQR();
-
- /* accumulate the orthogonal factor in fjac. */
- fjac = qrfac.householderQ();
-
- /* form (q transpose)*fvec and store in qtf. */
- qtf = fjac.transpose() * fvec;
-
- /* rescale if necessary. */
- if (!useExternalScaling)
- diag = diag.cwiseMax(wa2);
-
- while (true) {
- /* determine the direction p. */
- internal::dogleg<Scalar>(R, diag, qtf, delta, wa1);
-
- /* store the direction p and x + p. calculate the norm of p. */
- wa1 = -wa1;
- wa2 = x + wa1;
- pnorm = diag.cwiseProduct(wa1).stableNorm();
-
- /* on the first iteration, adjust the initial step bound. */
- if (iter == 1)
- delta = (std::min)(delta,pnorm);
-
- /* evaluate the function at x + p and calculate its norm. */
- if ( functor(wa2, wa4) < 0)
- return HybridNonLinearSolverSpace::UserAsked;
- ++nfev;
- fnorm1 = wa4.stableNorm();
-
- /* compute the scaled actual reduction. */
- actred = -1.;
- if (fnorm1 < fnorm) /* Computing 2nd power */
- actred = 1. - numext::abs2(fnorm1 / fnorm);
-
- /* compute the scaled predicted reduction. */
- wa3 = R.template triangularView<Upper>()*wa1 + qtf;
- temp = wa3.stableNorm();
- prered = 0.;
- if (temp < fnorm) /* Computing 2nd power */
- prered = 1. - numext::abs2(temp / fnorm);
-
- /* compute the ratio of the actual to the predicted reduction. */
- ratio = 0.;
- if (prered > 0.)
- ratio = actred / prered;
-
- /* update the step bound. */
- if (ratio < Scalar(.1)) {
- ncsuc = 0;
- ++ncfail;
- delta = Scalar(.5) * delta;
- } else {
- ncfail = 0;
- ++ncsuc;
- if (ratio >= Scalar(.5) || ncsuc > 1)
- delta = (std::max)(delta, pnorm / Scalar(.5));
- if (abs(ratio - 1.) <= Scalar(.1)) {
- delta = pnorm / Scalar(.5);
- }
- }
-
- /* test for successful iteration. */
- if (ratio >= Scalar(1e-4)) {
- /* successful iteration. update x, fvec, and their norms. */
- x = wa2;
- wa2 = diag.cwiseProduct(x);
- fvec = wa4;
- xnorm = wa2.stableNorm();
- fnorm = fnorm1;
- ++iter;
- }
-
- /* determine the progress of the iteration. */
- ++nslow1;
- if (actred >= Scalar(.001))
- nslow1 = 0;
- if (jeval)
- ++nslow2;
- if (actred >= Scalar(.1))
- nslow2 = 0;
-
- /* test for convergence. */
- if (delta <= parameters.xtol * xnorm || fnorm == 0.)
- return HybridNonLinearSolverSpace::RelativeErrorTooSmall;
-
- /* tests for termination and stringent tolerances. */
- if (nfev >= parameters.maxfev)
- return HybridNonLinearSolverSpace::TooManyFunctionEvaluation;
- if (Scalar(.1) * (std::max)(Scalar(.1) * delta, pnorm) <= NumTraits<Scalar>::epsilon() * xnorm)
- return HybridNonLinearSolverSpace::TolTooSmall;
- if (nslow2 == 5)
- return HybridNonLinearSolverSpace::NotMakingProgressJacobian;
- if (nslow1 == 10)
- return HybridNonLinearSolverSpace::NotMakingProgressIterations;
-
- /* criterion for recalculating jacobian. */
- if (ncfail == 2)
- break; // leave inner loop and go for the next outer loop iteration
-
- /* calculate the rank one modification to the jacobian */
- /* and update qtf if necessary. */
- wa1 = diag.cwiseProduct( diag.cwiseProduct(wa1)/pnorm );
- wa2 = fjac.transpose() * wa4;
- if (ratio >= Scalar(1e-4))
- qtf = wa2;
- wa2 = (wa2-wa3)/pnorm;
-
- /* compute the qr factorization of the updated jacobian. */
- internal::r1updt<Scalar>(R, wa1, v_givens, w_givens, wa2, wa3, &sing);
- internal::r1mpyq<Scalar>(n, n, fjac.data(), v_givens, w_givens);
- internal::r1mpyq<Scalar>(1, n, qtf.data(), v_givens, w_givens);
-
- jeval = false;
- }
- return HybridNonLinearSolverSpace::Running;
-}
-
-template<typename FunctorType, typename Scalar>
-HybridNonLinearSolverSpace::Status
-HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiff(FVectorType &x)
-{
- HybridNonLinearSolverSpace::Status status = solveNumericalDiffInit(x);
- if (status==HybridNonLinearSolverSpace::ImproperInputParameters)
- return status;
- while (status==HybridNonLinearSolverSpace::Running)
- status = solveNumericalDiffOneStep(x);
- return status;
-}
-
-} // end namespace Eigen
-
-#endif // EIGEN_HYBRIDNONLINEARSOLVER_H
-
-//vim: ai ts=4 sts=4 et sw=4
diff --git a/eigen/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h b/eigen/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h
deleted file mode 100644
index fe3b79c..0000000
--- a/eigen/unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h
+++ /dev/null
@@ -1,657 +0,0 @@
-// -*- coding: utf-8
-// vim: set fileencoding=utf-8
-
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
-//
-// 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_LEVENBERGMARQUARDT__H
-#define EIGEN_LEVENBERGMARQUARDT__H
-
-namespace Eigen {
-
-namespace LevenbergMarquardtSpace {
- enum Status {
- NotStarted = -2,
- Running = -1,
- ImproperInputParameters = 0,
- RelativeReductionTooSmall = 1,
- RelativeErrorTooSmall = 2,
- RelativeErrorAndReductionTooSmall = 3,
- CosinusTooSmall = 4,
- TooManyFunctionEvaluation = 5,
- FtolTooSmall = 6,
- XtolTooSmall = 7,
- GtolTooSmall = 8,
- UserAsked = 9
- };
-}
-
-
-
-/**
- * \ingroup NonLinearOptimization_Module
- * \brief Performs non linear optimization over a non-linear function,
- * using a variant of the Levenberg Marquardt algorithm.
- *
- * Check wikipedia for more information.
- * http://en.wikipedia.org/wiki/Levenberg%E2%80%93Marquardt_algorithm
- */
-template<typename FunctorType, typename Scalar=double>
-class LevenbergMarquardt
-{
- static Scalar sqrt_epsilon()
- {
- using std::sqrt;
- return sqrt(NumTraits<Scalar>::epsilon());
- }
-
-public:
- LevenbergMarquardt(FunctorType &_functor)
- : functor(_functor) { nfev = njev = iter = 0; fnorm = gnorm = 0.; useExternalScaling=false; }
-
- typedef DenseIndex Index;
-
- struct Parameters {
- Parameters()
- : factor(Scalar(100.))
- , maxfev(400)
- , ftol(sqrt_epsilon())
- , xtol(sqrt_epsilon())
- , gtol(Scalar(0.))
- , epsfcn(Scalar(0.)) {}
- Scalar factor;
- Index maxfev; // maximum number of function evaluation
- Scalar ftol;
- Scalar xtol;
- Scalar gtol;
- Scalar epsfcn;
- };
-
- typedef Matrix< Scalar, Dynamic, 1 > FVectorType;
- typedef Matrix< Scalar, Dynamic, Dynamic > JacobianType;
-
- LevenbergMarquardtSpace::Status lmder1(
- FVectorType &x,
- const Scalar tol = sqrt_epsilon()
- );
-
- LevenbergMarquardtSpace::Status minimize(FVectorType &x);
- LevenbergMarquardtSpace::Status minimizeInit(FVectorType &x);
- LevenbergMarquardtSpace::Status minimizeOneStep(FVectorType &x);
-
- static LevenbergMarquardtSpace::Status lmdif1(
- FunctorType &functor,
- FVectorType &x,
- Index *nfev,
- const Scalar tol = sqrt_epsilon()
- );
-
- LevenbergMarquardtSpace::Status lmstr1(
- FVectorType &x,
- const Scalar tol = sqrt_epsilon()
- );
-
- LevenbergMarquardtSpace::Status minimizeOptimumStorage(FVectorType &x);
- LevenbergMarquardtSpace::Status minimizeOptimumStorageInit(FVectorType &x);
- LevenbergMarquardtSpace::Status minimizeOptimumStorageOneStep(FVectorType &x);
-
- void resetParameters(void) { parameters = Parameters(); }
-
- Parameters parameters;
- FVectorType fvec, qtf, diag;
- JacobianType fjac;
- PermutationMatrix<Dynamic,Dynamic> permutation;
- Index nfev;
- Index njev;
- Index iter;
- Scalar fnorm, gnorm;
- bool useExternalScaling;
-
- Scalar lm_param(void) { return par; }
-private:
-
- FunctorType &functor;
- Index n;
- Index m;
- FVectorType wa1, wa2, wa3, wa4;
-
- Scalar par, sum;
- Scalar temp, temp1, temp2;
- Scalar delta;
- Scalar ratio;
- Scalar pnorm, xnorm, fnorm1, actred, dirder, prered;
-
- LevenbergMarquardt& operator=(const LevenbergMarquardt&);
-};
-
-template<typename FunctorType, typename Scalar>
-LevenbergMarquardtSpace::Status
-LevenbergMarquardt<FunctorType,Scalar>::lmder1(
- FVectorType &x,
- const Scalar tol
- )
-{
- n = x.size();
- m = functor.values();
-
- /* check the input parameters for errors. */
- if (n <= 0 || m < n || tol < 0.)
- return LevenbergMarquardtSpace::ImproperInputParameters;
-
- resetParameters();
- parameters.ftol = tol;
- parameters.xtol = tol;
- parameters.maxfev = 100*(n+1);
-
- return minimize(x);
-}
-
-
-template<typename FunctorType, typename Scalar>
-LevenbergMarquardtSpace::Status
-LevenbergMarquardt<FunctorType,Scalar>::minimize(FVectorType &x)
-{
- LevenbergMarquardtSpace::Status status = minimizeInit(x);
- if (status==LevenbergMarquardtSpace::ImproperInputParameters)
- return status;
- do {
- status = minimizeOneStep(x);
- } while (status==LevenbergMarquardtSpace::Running);
- return status;
-}
-
-template<typename FunctorType, typename Scalar>
-LevenbergMarquardtSpace::Status
-LevenbergMarquardt<FunctorType,Scalar>::minimizeInit(FVectorType &x)
-{
- n = x.size();
- m = functor.values();
-
- wa1.resize(n); wa2.resize(n); wa3.resize(n);
- wa4.resize(m);
- fvec.resize(m);
- fjac.resize(m, n);
- if (!useExternalScaling)
- diag.resize(n);
- eigen_assert( (!useExternalScaling || diag.size()==n) && "When useExternalScaling is set, the caller must provide a valid 'diag'");
- qtf.resize(n);
-
- /* Function Body */
- nfev = 0;
- njev = 0;
-
- /* check the input parameters for errors. */
- if (n <= 0 || m < n || parameters.ftol < 0. || parameters.xtol < 0. || parameters.gtol < 0. || parameters.maxfev <= 0 || parameters.factor <= 0.)
- return LevenbergMarquardtSpace::ImproperInputParameters;
-
- if (useExternalScaling)
- for (Index j = 0; j < n; ++j)
- if (diag[j] <= 0.)
- return LevenbergMarquardtSpace::ImproperInputParameters;
-
- /* evaluate the function at the starting point */
- /* and calculate its norm. */
- nfev = 1;
- if ( functor(x, fvec) < 0)
- return LevenbergMarquardtSpace::UserAsked;
- fnorm = fvec.stableNorm();
-
- /* initialize levenberg-marquardt parameter and iteration counter. */
- par = 0.;
- iter = 1;
-
- return LevenbergMarquardtSpace::NotStarted;
-}
-
-template<typename FunctorType, typename Scalar>
-LevenbergMarquardtSpace::Status
-LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType &x)
-{
- using std::abs;
- using std::sqrt;
-
- eigen_assert(x.size()==n); // check the caller is not cheating us
-
- /* calculate the jacobian matrix. */
- Index df_ret = functor.df(x, fjac);
- if (df_ret<0)
- return LevenbergMarquardtSpace::UserAsked;
- if (df_ret>0)
- // numerical diff, we evaluated the function df_ret times
- nfev += df_ret;
- else njev++;
-
- /* compute the qr factorization of the jacobian. */
- wa2 = fjac.colwise().blueNorm();
- ColPivHouseholderQR<JacobianType> qrfac(fjac);
- fjac = qrfac.matrixQR();
- permutation = qrfac.colsPermutation();
-
- /* on the first iteration and if external scaling is not used, scale according */
- /* to the norms of the columns of the initial jacobian. */
- if (iter == 1) {
- if (!useExternalScaling)
- for (Index j = 0; j < n; ++j)
- diag[j] = (wa2[j]==0.)? 1. : wa2[j];
-
- /* on the first iteration, calculate the norm of the scaled x */
- /* and initialize the step bound delta. */
- xnorm = diag.cwiseProduct(x).stableNorm();
- delta = parameters.factor * xnorm;
- if (delta == 0.)
- delta = parameters.factor;
- }
-
- /* form (q transpose)*fvec and store the first n components in */
- /* qtf. */
- wa4 = fvec;
- wa4.applyOnTheLeft(qrfac.householderQ().adjoint());
- qtf = wa4.head(n);
-
- /* compute the norm of the scaled gradient. */
- gnorm = 0.;
- if (fnorm != 0.)
- for (Index j = 0; j < n; ++j)
- if (wa2[permutation.indices()[j]] != 0.)
- gnorm = (std::max)(gnorm, abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]]));
-
- /* test for convergence of the gradient norm. */
- if (gnorm <= parameters.gtol)
- return LevenbergMarquardtSpace::CosinusTooSmall;
-
- /* rescale if necessary. */
- if (!useExternalScaling)
- diag = diag.cwiseMax(wa2);
-
- do {
-
- /* determine the levenberg-marquardt parameter. */
- internal::lmpar2<Scalar>(qrfac, diag, qtf, delta, par, wa1);
-
- /* store the direction p and x + p. calculate the norm of p. */
- wa1 = -wa1;
- wa2 = x + wa1;
- pnorm = diag.cwiseProduct(wa1).stableNorm();
-
- /* on the first iteration, adjust the initial step bound. */
- if (iter == 1)
- delta = (std::min)(delta,pnorm);
-
- /* evaluate the function at x + p and calculate its norm. */
- if ( functor(wa2, wa4) < 0)
- return LevenbergMarquardtSpace::UserAsked;
- ++nfev;
- fnorm1 = wa4.stableNorm();
-
- /* compute the scaled actual reduction. */
- actred = -1.;
- if (Scalar(.1) * fnorm1 < fnorm)
- actred = 1. - numext::abs2(fnorm1 / fnorm);
-
- /* compute the scaled predicted reduction and */
- /* the scaled directional derivative. */
- wa3 = fjac.template triangularView<Upper>() * (qrfac.colsPermutation().inverse() *wa1);
- temp1 = numext::abs2(wa3.stableNorm() / fnorm);
- temp2 = numext::abs2(sqrt(par) * pnorm / fnorm);
- prered = temp1 + temp2 / Scalar(.5);
- dirder = -(temp1 + temp2);
-
- /* compute the ratio of the actual to the predicted */
- /* reduction. */
- ratio = 0.;
- if (prered != 0.)
- ratio = actred / prered;
-
- /* update the step bound. */
- if (ratio <= Scalar(.25)) {
- if (actred >= 0.)
- temp = Scalar(.5);
- if (actred < 0.)
- temp = Scalar(.5) * dirder / (dirder + Scalar(.5) * actred);
- if (Scalar(.1) * fnorm1 >= fnorm || temp < Scalar(.1))
- temp = Scalar(.1);
- /* Computing MIN */
- delta = temp * (std::min)(delta, pnorm / Scalar(.1));
- par /= temp;
- } else if (!(par != 0. && ratio < Scalar(.75))) {
- delta = pnorm / Scalar(.5);
- par = Scalar(.5) * par;
- }
-
- /* test for successful iteration. */
- if (ratio >= Scalar(1e-4)) {
- /* successful iteration. update x, fvec, and their norms. */
- x = wa2;
- wa2 = diag.cwiseProduct(x);
- fvec = wa4;
- xnorm = wa2.stableNorm();
- fnorm = fnorm1;
- ++iter;
- }
-
- /* tests for convergence. */
- if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)
- return LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall;
- if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)
- return LevenbergMarquardtSpace::RelativeReductionTooSmall;
- if (delta <= parameters.xtol * xnorm)
- return LevenbergMarquardtSpace::RelativeErrorTooSmall;
-
- /* tests for termination and stringent tolerances. */
- if (nfev >= parameters.maxfev)
- return LevenbergMarquardtSpace::TooManyFunctionEvaluation;
- if (abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)
- return LevenbergMarquardtSpace::FtolTooSmall;
- if (delta <= NumTraits<Scalar>::epsilon() * xnorm)
- return LevenbergMarquardtSpace::XtolTooSmall;
- if (gnorm <= NumTraits<Scalar>::epsilon())
- return LevenbergMarquardtSpace::GtolTooSmall;
-
- } while (ratio < Scalar(1e-4));
-
- return LevenbergMarquardtSpace::Running;
-}
-
-template<typename FunctorType, typename Scalar>
-LevenbergMarquardtSpace::Status
-LevenbergMarquardt<FunctorType,Scalar>::lmstr1(
- FVectorType &x,
- const Scalar tol
- )
-{
- n = x.size();
- m = functor.values();
-
- /* check the input parameters for errors. */
- if (n <= 0 || m < n || tol < 0.)
- return LevenbergMarquardtSpace::ImproperInputParameters;
-
- resetParameters();
- parameters.ftol = tol;
- parameters.xtol = tol;
- parameters.maxfev = 100*(n+1);
-
- return minimizeOptimumStorage(x);
-}
-
-template<typename FunctorType, typename Scalar>
-LevenbergMarquardtSpace::Status
-LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageInit(FVectorType &x)
-{
- n = x.size();
- m = functor.values();
-
- wa1.resize(n); wa2.resize(n); wa3.resize(n);
- wa4.resize(m);
- fvec.resize(m);
- // Only R is stored in fjac. Q is only used to compute 'qtf', which is
- // Q.transpose()*rhs. qtf will be updated using givens rotation,
- // instead of storing them in Q.
- // The purpose it to only use a nxn matrix, instead of mxn here, so
- // that we can handle cases where m>>n :
- fjac.resize(n, n);
- if (!useExternalScaling)
- diag.resize(n);
- eigen_assert( (!useExternalScaling || diag.size()==n) && "When useExternalScaling is set, the caller must provide a valid 'diag'");
- qtf.resize(n);
-
- /* Function Body */
- nfev = 0;
- njev = 0;
-
- /* check the input parameters for errors. */
- if (n <= 0 || m < n || parameters.ftol < 0. || parameters.xtol < 0. || parameters.gtol < 0. || parameters.maxfev <= 0 || parameters.factor <= 0.)
- return LevenbergMarquardtSpace::ImproperInputParameters;
-
- if (useExternalScaling)
- for (Index j = 0; j < n; ++j)
- if (diag[j] <= 0.)
- return LevenbergMarquardtSpace::ImproperInputParameters;
-
- /* evaluate the function at the starting point */
- /* and calculate its norm. */
- nfev = 1;
- if ( functor(x, fvec) < 0)
- return LevenbergMarquardtSpace::UserAsked;
- fnorm = fvec.stableNorm();
-
- /* initialize levenberg-marquardt parameter and iteration counter. */
- par = 0.;
- iter = 1;
-
- return LevenbergMarquardtSpace::NotStarted;
-}
-
-
-template<typename FunctorType, typename Scalar>
-LevenbergMarquardtSpace::Status
-LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorType &x)
-{
- using std::abs;
- using std::sqrt;
-
- eigen_assert(x.size()==n); // check the caller is not cheating us
-
- Index i, j;
- bool sing;
-
- /* compute the qr factorization of the jacobian matrix */
- /* calculated one row at a time, while simultaneously */
- /* forming (q transpose)*fvec and storing the first */
- /* n components in qtf. */
- qtf.fill(0.);
- fjac.fill(0.);
- Index rownb = 2;
- for (i = 0; i < m; ++i) {
- if (functor.df(x, wa3, rownb) < 0) return LevenbergMarquardtSpace::UserAsked;
- internal::rwupdt<Scalar>(fjac, wa3, qtf, fvec[i]);
- ++rownb;
- }
- ++njev;
-
- /* if the jacobian is rank deficient, call qrfac to */
- /* reorder its columns and update the components of qtf. */
- sing = false;
- for (j = 0; j < n; ++j) {
- if (fjac(j,j) == 0.)
- sing = true;
- wa2[j] = fjac.col(j).head(j).stableNorm();
- }
- permutation.setIdentity(n);
- if (sing) {
- wa2 = fjac.colwise().blueNorm();
- // TODO We have no unit test covering this code path, do not modify
- // until it is carefully tested
- ColPivHouseholderQR<JacobianType> qrfac(fjac);
- fjac = qrfac.matrixQR();
- wa1 = fjac.diagonal();
- fjac.diagonal() = qrfac.hCoeffs();
- permutation = qrfac.colsPermutation();
- // TODO : avoid this:
- for(Index ii=0; ii< fjac.cols(); ii++) fjac.col(ii).segment(ii+1, fjac.rows()-ii-1) *= fjac(ii,ii); // rescale vectors
-
- for (j = 0; j < n; ++j) {
- if (fjac(j,j) != 0.) {
- sum = 0.;
- for (i = j; i < n; ++i)
- sum += fjac(i,j) * qtf[i];
- temp = -sum / fjac(j,j);
- for (i = j; i < n; ++i)
- qtf[i] += fjac(i,j) * temp;
- }
- fjac(j,j) = wa1[j];
- }
- }
-
- /* on the first iteration and if external scaling is not used, scale according */
- /* to the norms of the columns of the initial jacobian. */
- if (iter == 1) {
- if (!useExternalScaling)
- for (j = 0; j < n; ++j)
- diag[j] = (wa2[j]==0.)? 1. : wa2[j];
-
- /* on the first iteration, calculate the norm of the scaled x */
- /* and initialize the step bound delta. */
- xnorm = diag.cwiseProduct(x).stableNorm();
- delta = parameters.factor * xnorm;
- if (delta == 0.)
- delta = parameters.factor;
- }
-
- /* compute the norm of the scaled gradient. */
- gnorm = 0.;
- if (fnorm != 0.)
- for (j = 0; j < n; ++j)
- if (wa2[permutation.indices()[j]] != 0.)
- gnorm = (std::max)(gnorm, abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]]));
-
- /* test for convergence of the gradient norm. */
- if (gnorm <= parameters.gtol)
- return LevenbergMarquardtSpace::CosinusTooSmall;
-
- /* rescale if necessary. */
- if (!useExternalScaling)
- diag = diag.cwiseMax(wa2);
-
- do {
-
- /* determine the levenberg-marquardt parameter. */
- internal::lmpar<Scalar>(fjac, permutation.indices(), diag, qtf, delta, par, wa1);
-
- /* store the direction p and x + p. calculate the norm of p. */
- wa1 = -wa1;
- wa2 = x + wa1;
- pnorm = diag.cwiseProduct(wa1).stableNorm();
-
- /* on the first iteration, adjust the initial step bound. */
- if (iter == 1)
- delta = (std::min)(delta,pnorm);
-
- /* evaluate the function at x + p and calculate its norm. */
- if ( functor(wa2, wa4) < 0)
- return LevenbergMarquardtSpace::UserAsked;
- ++nfev;
- fnorm1 = wa4.stableNorm();
-
- /* compute the scaled actual reduction. */
- actred = -1.;
- if (Scalar(.1) * fnorm1 < fnorm)
- actred = 1. - numext::abs2(fnorm1 / fnorm);
-
- /* compute the scaled predicted reduction and */
- /* the scaled directional derivative. */
- wa3 = fjac.topLeftCorner(n,n).template triangularView<Upper>() * (permutation.inverse() * wa1);
- temp1 = numext::abs2(wa3.stableNorm() / fnorm);
- temp2 = numext::abs2(sqrt(par) * pnorm / fnorm);
- prered = temp1 + temp2 / Scalar(.5);
- dirder = -(temp1 + temp2);
-
- /* compute the ratio of the actual to the predicted */
- /* reduction. */
- ratio = 0.;
- if (prered != 0.)
- ratio = actred / prered;
-
- /* update the step bound. */
- if (ratio <= Scalar(.25)) {
- if (actred >= 0.)
- temp = Scalar(.5);
- if (actred < 0.)
- temp = Scalar(.5) * dirder / (dirder + Scalar(.5) * actred);
- if (Scalar(.1) * fnorm1 >= fnorm || temp < Scalar(.1))
- temp = Scalar(.1);
- /* Computing MIN */
- delta = temp * (std::min)(delta, pnorm / Scalar(.1));
- par /= temp;
- } else if (!(par != 0. && ratio < Scalar(.75))) {
- delta = pnorm / Scalar(.5);
- par = Scalar(.5) * par;
- }
-
- /* test for successful iteration. */
- if (ratio >= Scalar(1e-4)) {
- /* successful iteration. update x, fvec, and their norms. */
- x = wa2;
- wa2 = diag.cwiseProduct(x);
- fvec = wa4;
- xnorm = wa2.stableNorm();
- fnorm = fnorm1;
- ++iter;
- }
-
- /* tests for convergence. */
- if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)
- return LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall;
- if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)
- return LevenbergMarquardtSpace::RelativeReductionTooSmall;
- if (delta <= parameters.xtol * xnorm)
- return LevenbergMarquardtSpace::RelativeErrorTooSmall;
-
- /* tests for termination and stringent tolerances. */
- if (nfev >= parameters.maxfev)
- return LevenbergMarquardtSpace::TooManyFunctionEvaluation;
- if (abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)
- return LevenbergMarquardtSpace::FtolTooSmall;
- if (delta <= NumTraits<Scalar>::epsilon() * xnorm)
- return LevenbergMarquardtSpace::XtolTooSmall;
- if (gnorm <= NumTraits<Scalar>::epsilon())
- return LevenbergMarquardtSpace::GtolTooSmall;
-
- } while (ratio < Scalar(1e-4));
-
- return LevenbergMarquardtSpace::Running;
-}
-
-template<typename FunctorType, typename Scalar>
-LevenbergMarquardtSpace::Status
-LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorage(FVectorType &x)
-{
- LevenbergMarquardtSpace::Status status = minimizeOptimumStorageInit(x);
- if (status==LevenbergMarquardtSpace::ImproperInputParameters)
- return status;
- do {
- status = minimizeOptimumStorageOneStep(x);
- } while (status==LevenbergMarquardtSpace::Running);
- return status;
-}
-
-template<typename FunctorType, typename Scalar>
-LevenbergMarquardtSpace::Status
-LevenbergMarquardt<FunctorType,Scalar>::lmdif1(
- FunctorType &functor,
- FVectorType &x,
- Index *nfev,
- const Scalar tol
- )
-{
- Index n = x.size();
- Index m = functor.values();
-
- /* check the input parameters for errors. */
- if (n <= 0 || m < n || tol < 0.)
- return LevenbergMarquardtSpace::ImproperInputParameters;
-
- NumericalDiff<FunctorType> numDiff(functor);
- // embedded LevenbergMarquardt
- LevenbergMarquardt<NumericalDiff<FunctorType>, Scalar > lm(numDiff);
- lm.parameters.ftol = tol;
- lm.parameters.xtol = tol;
- lm.parameters.maxfev = 200*(n+1);
-
- LevenbergMarquardtSpace::Status info = LevenbergMarquardtSpace::Status(lm.minimize(x));
- if (nfev)
- * nfev = lm.nfev;
- return info;
-}
-
-} // end namespace Eigen
-
-#endif // EIGEN_LEVENBERGMARQUARDT__H
-
-//vim: ai ts=4 sts=4 et sw=4
diff --git a/eigen/unsupported/Eigen/src/NonLinearOptimization/chkder.h b/eigen/unsupported/Eigen/src/NonLinearOptimization/chkder.h
deleted file mode 100644
index db8ff7d..0000000
--- a/eigen/unsupported/Eigen/src/NonLinearOptimization/chkder.h
+++ /dev/null
@@ -1,66 +0,0 @@
-#define chkder_log10e 0.43429448190325182765
-#define chkder_factor 100.
-
-namespace Eigen {
-
-namespace internal {
-
-template<typename Scalar>
-void chkder(
- const Matrix< Scalar, Dynamic, 1 > &x,
- const Matrix< Scalar, Dynamic, 1 > &fvec,
- const Matrix< Scalar, Dynamic, Dynamic > &fjac,
- Matrix< Scalar, Dynamic, 1 > &xp,
- const Matrix< Scalar, Dynamic, 1 > &fvecp,
- int mode,
- Matrix< Scalar, Dynamic, 1 > &err
- )
-{
- using std::sqrt;
- using std::abs;
- using std::log;
-
- typedef DenseIndex Index;
-
- const Scalar eps = sqrt(NumTraits<Scalar>::epsilon());
- const Scalar epsf = chkder_factor * NumTraits<Scalar>::epsilon();
- const Scalar epslog = chkder_log10e * log(eps);
- Scalar temp;
-
- const Index m = fvec.size(), n = x.size();
-
- if (mode != 2) {
- /* mode = 1. */
- xp.resize(n);
- for (Index j = 0; j < n; ++j) {
- temp = eps * abs(x[j]);
- if (temp == 0.)
- temp = eps;
- xp[j] = x[j] + temp;
- }
- }
- else {
- /* mode = 2. */
- err.setZero(m);
- for (Index j = 0; j < n; ++j) {
- temp = abs(x[j]);
- if (temp == 0.)
- temp = 1.;
- err += temp * fjac.col(j);
- }
- for (Index i = 0; i < m; ++i) {
- temp = 1.;
- if (fvec[i] != 0. && fvecp[i] != 0. && abs(fvecp[i] - fvec[i]) >= epsf * abs(fvec[i]))
- temp = eps * abs((fvecp[i] - fvec[i]) / eps - err[i]) / (abs(fvec[i]) + abs(fvecp[i]));
- err[i] = 1.;
- if (temp > NumTraits<Scalar>::epsilon() && temp < eps)
- err[i] = (chkder_log10e * log(temp) - epslog) / epslog;
- if (temp >= eps)
- err[i] = 0.;
- }
- }
-}
-
-} // end namespace internal
-
-} // end namespace Eigen
diff --git a/eigen/unsupported/Eigen/src/NonLinearOptimization/covar.h b/eigen/unsupported/Eigen/src/NonLinearOptimization/covar.h
deleted file mode 100644
index 68260d1..0000000
--- a/eigen/unsupported/Eigen/src/NonLinearOptimization/covar.h
+++ /dev/null
@@ -1,70 +0,0 @@
-namespace Eigen {
-
-namespace internal {
-
-template <typename Scalar>
-void covar(
- Matrix< Scalar, Dynamic, Dynamic > &r,
- const VectorXi &ipvt,
- Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon()) )
-{
- using std::abs;
- typedef DenseIndex Index;
-
- /* Local variables */
- Index i, j, k, l, ii, jj;
- bool sing;
- Scalar temp;
-
- /* Function Body */
- const Index n = r.cols();
- const Scalar tolr = tol * abs(r(0,0));
- Matrix< Scalar, Dynamic, 1 > wa(n);
- eigen_assert(ipvt.size()==n);
-
- /* form the inverse of r in the full upper triangle of r. */
- l = -1;
- for (k = 0; k < n; ++k)
- if (abs(r(k,k)) > tolr) {
- r(k,k) = 1. / r(k,k);
- for (j = 0; j <= k-1; ++j) {
- temp = r(k,k) * r(j,k);
- r(j,k) = 0.;
- r.col(k).head(j+1) -= r.col(j).head(j+1) * temp;
- }
- l = k;
- }
-
- /* form the full upper triangle of the inverse of (r transpose)*r */
- /* in the full upper triangle of r. */
- for (k = 0; k <= l; ++k) {
- for (j = 0; j <= k-1; ++j)
- r.col(j).head(j+1) += r.col(k).head(j+1) * r(j,k);
- r.col(k).head(k+1) *= r(k,k);
- }
-
- /* form the full lower triangle of the covariance matrix */
- /* in the strict lower triangle of r and in wa. */
- for (j = 0; j < n; ++j) {
- jj = ipvt[j];
- sing = j > l;
- for (i = 0; i <= j; ++i) {
- if (sing)
- r(i,j) = 0.;
- ii = ipvt[i];
- if (ii > jj)
- r(ii,jj) = r(i,j);
- if (ii < jj)
- r(jj,ii) = r(i,j);
- }
- wa[jj] = r(j,j);
- }
-
- /* symmetrize the covariance matrix in r. */
- r.topLeftCorner(n,n).template triangularView<StrictlyUpper>() = r.topLeftCorner(n,n).transpose();
- r.diagonal() = wa;
-}
-
-} // end namespace internal
-
-} // end namespace Eigen
diff --git a/eigen/unsupported/Eigen/src/NonLinearOptimization/dogleg.h b/eigen/unsupported/Eigen/src/NonLinearOptimization/dogleg.h
deleted file mode 100644
index 80c5d27..0000000
--- a/eigen/unsupported/Eigen/src/NonLinearOptimization/dogleg.h
+++ /dev/null
@@ -1,107 +0,0 @@
-namespace Eigen {
-
-namespace internal {
-
-template <typename Scalar>
-void dogleg(
- const Matrix< Scalar, Dynamic, Dynamic > &qrfac,
- const Matrix< Scalar, Dynamic, 1 > &diag,
- const Matrix< Scalar, Dynamic, 1 > &qtb,
- Scalar delta,
- Matrix< Scalar, Dynamic, 1 > &x)
-{
- using std::abs;
- using std::sqrt;
-
- typedef DenseIndex Index;
-
- /* Local variables */
- Index i, j;
- Scalar sum, temp, alpha, bnorm;
- Scalar gnorm, qnorm;
- Scalar sgnorm;
-
- /* Function Body */
- const Scalar epsmch = NumTraits<Scalar>::epsilon();
- const Index n = qrfac.cols();
- eigen_assert(n==qtb.size());
- eigen_assert(n==x.size());
- eigen_assert(n==diag.size());
- Matrix< Scalar, Dynamic, 1 > wa1(n), wa2(n);
-
- /* first, calculate the gauss-newton direction. */
- for (j = n-1; j >=0; --j) {
- temp = qrfac(j,j);
- if (temp == 0.) {
- temp = epsmch * qrfac.col(j).head(j+1).maxCoeff();
- if (temp == 0.)
- temp = epsmch;
- }
- if (j==n-1)
- x[j] = qtb[j] / temp;
- else
- x[j] = (qtb[j] - qrfac.row(j).tail(n-j-1).dot(x.tail(n-j-1))) / temp;
- }
-
- /* test whether the gauss-newton direction is acceptable. */
- qnorm = diag.cwiseProduct(x).stableNorm();
- if (qnorm <= delta)
- return;
-
- // TODO : this path is not tested by Eigen unit tests
-
- /* the gauss-newton direction is not acceptable. */
- /* next, calculate the scaled gradient direction. */
-
- wa1.fill(0.);
- for (j = 0; j < n; ++j) {
- wa1.tail(n-j) += qrfac.row(j).tail(n-j) * qtb[j];
- wa1[j] /= diag[j];
- }
-
- /* calculate the norm of the scaled gradient and test for */
- /* the special case in which the scaled gradient is zero. */
- gnorm = wa1.stableNorm();
- sgnorm = 0.;
- alpha = delta / qnorm;
- if (gnorm == 0.)
- goto algo_end;
-
- /* calculate the point along the scaled gradient */
- /* at which the quadratic is minimized. */
- wa1.array() /= (diag*gnorm).array();
- // TODO : once unit tests cover this part,:
- // wa2 = qrfac.template triangularView<Upper>() * wa1;
- for (j = 0; j < n; ++j) {
- sum = 0.;
- for (i = j; i < n; ++i) {
- sum += qrfac(j,i) * wa1[i];
- }
- wa2[j] = sum;
- }
- temp = wa2.stableNorm();
- sgnorm = gnorm / temp / temp;
-
- /* test whether the scaled gradient direction is acceptable. */
- alpha = 0.;
- if (sgnorm >= delta)
- goto algo_end;
-
- /* the scaled gradient direction is not acceptable. */
- /* finally, calculate the point along the dogleg */
- /* at which the quadratic is minimized. */
- bnorm = qtb.stableNorm();
- temp = bnorm / gnorm * (bnorm / qnorm) * (sgnorm / delta);
- temp = temp - delta / qnorm * numext::abs2(sgnorm / delta) + sqrt(numext::abs2(temp - delta / qnorm) + (1.-numext::abs2(delta / qnorm)) * (1.-numext::abs2(sgnorm / delta)));
- alpha = delta / qnorm * (1. - numext::abs2(sgnorm / delta)) / temp;
-algo_end:
-
- /* form appropriate convex combination of the gauss-newton */
- /* direction and the scaled gradient direction. */
- temp = (1.-alpha) * (std::min)(sgnorm,delta);
- x = temp * wa1 + alpha * x;
-}
-
-} // end namespace internal
-
-} // end namespace Eigen
diff --git a/eigen/unsupported/Eigen/src/NonLinearOptimization/fdjac1.h b/eigen/unsupported/Eigen/src/NonLinearOptimization/fdjac1.h
deleted file mode 100644
index bb7cf26..0000000
--- a/eigen/unsupported/Eigen/src/NonLinearOptimization/fdjac1.h
+++ /dev/null
@@ -1,79 +0,0 @@
-namespace Eigen {
-
-namespace internal {
-
-template<typename FunctorType, typename Scalar>
-DenseIndex fdjac1(
- const FunctorType &Functor,
- Matrix< Scalar, Dynamic, 1 > &x,
- Matrix< Scalar, Dynamic, 1 > &fvec,
- Matrix< Scalar, Dynamic, Dynamic > &fjac,
- DenseIndex ml, DenseIndex mu,
- Scalar epsfcn)
-{
- using std::sqrt;
- using std::abs;
-
- typedef DenseIndex Index;
-
- /* Local variables */
- Scalar h;
- Index j, k;
- Scalar eps, temp;
- Index msum;
- int iflag;
- Index start, length;
-
- /* Function Body */
- const Scalar epsmch = NumTraits<Scalar>::epsilon();
- const Index n = x.size();
- eigen_assert(fvec.size()==n);
- Matrix< Scalar, Dynamic, 1 > wa1(n);
- Matrix< Scalar, Dynamic, 1 > wa2(n);
-
- eps = sqrt((std::max)(epsfcn,epsmch));
- msum = ml + mu + 1;
- if (msum >= n) {
- /* computation of dense approximate jacobian. */
- for (j = 0; j < n; ++j) {
- temp = x[j];
- h = eps * abs(temp);
- if (h == 0.)
- h = eps;
- x[j] = temp + h;
- iflag = Functor(x, wa1);
- if (iflag < 0)
- return iflag;
- x[j] = temp;
- fjac.col(j) = (wa1-fvec)/h;
- }
-
- }else {
- /* computation of banded approximate jacobian. */
- for (k = 0; k < msum; ++k) {
- for (j = k; (msum<0) ? (j>n): (j<n); j += msum) {
- wa2[j] = x[j];
- h = eps * abs(wa2[j]);
- if (h == 0.) h = eps;
- x[j] = wa2[j] + h;
- }
- iflag = Functor(x, wa1);
- if (iflag < 0)
- return iflag;
- for (j = k; (msum<0) ? (j>n): (j<n); j += msum) {
- x[j] = wa2[j];
- h = eps * abs(wa2[j]);
- if (h == 0.) h = eps;
- fjac.col(j).setZero();
- start = std::max<Index>(0,j-mu);
- length = (std::min)(n-1, j+ml) - start + 1;
- fjac.col(j).segment(start, length) = ( wa1.segment(start, length)-fvec.segment(start, length))/h;
- }
- }
- }
- return 0;
-}
-
-} // end namespace internal
-
-} // end namespace Eigen
diff --git a/eigen/unsupported/Eigen/src/NonLinearOptimization/lmpar.h b/eigen/unsupported/Eigen/src/NonLinearOptimization/lmpar.h
deleted file mode 100644
index 4c17d4c..0000000
--- a/eigen/unsupported/Eigen/src/NonLinearOptimization/lmpar.h
+++ /dev/null
@@ -1,298 +0,0 @@
-namespace Eigen {
-
-namespace internal {
-
-template <typename Scalar>
-void lmpar(
- Matrix< Scalar, Dynamic, Dynamic > &r,
- const VectorXi &ipvt,
- const Matrix< Scalar, Dynamic, 1 > &diag,
- const Matrix< Scalar, Dynamic, 1 > &qtb,
- Scalar delta,
- Scalar &par,
- Matrix< Scalar, Dynamic, 1 > &x)
-{
- using std::abs;
- using std::sqrt;
- typedef DenseIndex Index;
-
- /* Local variables */
- Index i, j, l;
- Scalar fp;
- Scalar parc, parl;
- Index iter;
- Scalar temp, paru;
- Scalar gnorm;
- Scalar dxnorm;
-
-
- /* Function Body */
- const Scalar dwarf = (std::numeric_limits<Scalar>::min)();
- const Index n = r.cols();
- eigen_assert(n==diag.size());
- eigen_assert(n==qtb.size());
- eigen_assert(n==x.size());
-
- Matrix< Scalar, Dynamic, 1 > wa1, wa2;
-
- /* compute and store in x the gauss-newton direction. if the */
- /* jacobian is rank-deficient, obtain a least squares solution. */
- Index nsing = n-1;
- wa1 = qtb;
- for (j = 0; j < n; ++j) {
- if (r(j,j) == 0. && nsing == n-1)
- nsing = j - 1;
- if (nsing < n-1)
- wa1[j] = 0.;
- }
- for (j = nsing; j>=0; --j) {
- wa1[j] /= r(j,j);
- temp = wa1[j];
- for (i = 0; i < j ; ++i)
- wa1[i] -= r(i,j) * temp;
- }
-
- for (j = 0; j < n; ++j)
- x[ipvt[j]] = wa1[j];
-
- /* initialize the iteration counter. */
- /* evaluate the function at the origin, and test */
- /* for acceptance of the gauss-newton direction. */
- iter = 0;
- wa2 = diag.cwiseProduct(x);
- dxnorm = wa2.blueNorm();
- fp = dxnorm - delta;
- if (fp <= Scalar(0.1) * delta) {
- par = 0;
- return;
- }
-
- /* if the jacobian is not rank deficient, the newton */
- /* step provides a lower bound, parl, for the zero of */
- /* the function. otherwise set this bound to zero. */
- parl = 0.;
- if (nsing >= n-1) {
- for (j = 0; j < n; ++j) {
- l = ipvt[j];
- wa1[j] = diag[l] * (wa2[l] / dxnorm);
- }
- // it's actually a triangularView.solveInplace(), though in a weird
- // way:
- for (j = 0; j < n; ++j) {
- Scalar sum = 0.;
- for (i = 0; i < j; ++i)
- sum += r(i,j) * wa1[i];
- wa1[j] = (wa1[j] - sum) / r(j,j);
- }
- temp = wa1.blueNorm();
- parl = fp / delta / temp / temp;
- }
-
- /* calculate an upper bound, paru, for the zero of the function. */
- for (j = 0; j < n; ++j)
- wa1[j] = r.col(j).head(j+1).dot(qtb.head(j+1)) / diag[ipvt[j]];
-
- gnorm = wa1.stableNorm();
- paru = gnorm / delta;
- if (paru == 0.)
- paru = dwarf / (std::min)(delta,Scalar(0.1));
-
- /* if the input par lies outside of the interval (parl,paru), */
- /* set par to the closer endpoint. */
- par = (std::max)(par,parl);
- par = (std::min)(par,paru);
- if (par == 0.)
- par = gnorm / dxnorm;
-
- /* beginning of an iteration. */
- while (true) {
- ++iter;
-
- /* evaluate the function at the current value of par. */
- if (par == 0.)
- par = (std::max)(dwarf,Scalar(.001) * paru); /* Computing MAX */
- wa1 = sqrt(par)* diag;
-
- Matrix< Scalar, Dynamic, 1 > sdiag(n);
- qrsolv<Scalar>(r, ipvt, wa1, qtb, x, sdiag);
-
- wa2 = diag.cwiseProduct(x);
- dxnorm = wa2.blueNorm();
- temp = fp;
- fp = dxnorm - delta;
-
- /* if the function is small enough, accept the current value */
- /* of par. also test for the exceptional cases where parl */
- /* is zero or the number of iterations has reached 10. */
- if (abs(fp) <= Scalar(0.1) * delta || (parl == 0. && fp <= temp && temp < 0.) || iter == 10)
- break;
-
- /* compute the newton correction. */
- for (j = 0; j < n; ++j) {
- l = ipvt[j];
- wa1[j] = diag[l] * (wa2[l] / dxnorm);
- }
- for (j = 0; j < n; ++j) {
- wa1[j] /= sdiag[j];
- temp = wa1[j];
- for (i = j+1; i < n; ++i)
- wa1[i] -= r(i,j) * temp;
- }
- temp = wa1.blueNorm();
- parc = fp / delta / temp / temp;
-
- /* depending on the sign of the function, update parl or paru. */
- if (fp > 0.)
- parl = (std::max)(parl,par);
- if (fp < 0.)
- paru = (std::min)(paru,par);
-
- /* compute an improved estimate for par. */
- /* Computing MAX */
- par = (std::max)(parl,par+parc);
-
- /* end of an iteration. */
- }
-
- /* termination. */
- if (iter == 0)
- par = 0.;
- return;
-}
-
-template <typename Scalar>
-void lmpar2(
- const ColPivHouseholderQR<Matrix< Scalar, Dynamic, Dynamic> > &qr,
- const Matrix< Scalar, Dynamic, 1 > &diag,
- const Matrix< Scalar, Dynamic, 1 > &qtb,
- Scalar delta,
- Scalar &par,
- Matrix< Scalar, Dynamic, 1 > &x)
-
-{
- using std::sqrt;
- using std::abs;
- typedef DenseIndex Index;
-
- /* Local variables */
- Index j;
- Scalar fp;
- Scalar parc, parl;
- Index iter;
- Scalar temp, paru;
- Scalar gnorm;
- Scalar dxnorm;
-
-
- /* Function Body */
- const Scalar dwarf = (std::numeric_limits<Scalar>::min)();
- const Index n = qr.matrixQR().cols();
- eigen_assert(n==diag.size());
- eigen_assert(n==qtb.size());
-
- Matrix< Scalar, Dynamic, 1 > wa1, wa2;
-
- /* compute and store in x the gauss-newton direction. if the */
- /* jacobian is rank-deficient, obtain a least squares solution. */
-
-// const Index rank = qr.nonzeroPivots(); // exactly double(0.)
- const Index rank = qr.rank(); // use a threshold
- wa1 = qtb;
- wa1.tail(n-rank).setZero();
- qr.matrixQR().topLeftCorner(rank, rank).template triangularView<Upper>().solveInPlace(wa1.head(rank));
-
- x = qr.colsPermutation()*wa1;
-
- /* initialize the iteration counter. */
- /* evaluate the function at the origin, and test */
- /* for acceptance of the gauss-newton direction. */
- iter = 0;
- wa2 = diag.cwiseProduct(x);
- dxnorm = wa2.blueNorm();
- fp = dxnorm - delta;
- if (fp <= Scalar(0.1) * delta) {
- par = 0;
- return;
- }
-
- /* if the jacobian is not rank deficient, the newton */
- /* step provides a lower bound, parl, for the zero of */
- /* the function. otherwise set this bound to zero. */
- parl = 0.;
- if (rank==n) {
- wa1 = qr.colsPermutation().inverse() * diag.cwiseProduct(wa2)/dxnorm;
- qr.matrixQR().topLeftCorner(n, n).transpose().template triangularView<Lower>().solveInPlace(wa1);
- temp = wa1.blueNorm();
- parl = fp / delta / temp / temp;
- }
-
- /* calculate an upper bound, paru, for the zero of the function. */
- for (j = 0; j < n; ++j)
- wa1[j] = qr.matrixQR().col(j).head(j+1).dot(qtb.head(j+1)) / diag[qr.colsPermutation().indices()(j)];
-
- gnorm = wa1.stableNorm();
- paru = gnorm / delta;
- if (paru == 0.)
- paru = dwarf / (std::min)(delta,Scalar(0.1));
-
- /* if the input par lies outside of the interval (parl,paru), */
- /* set par to the closer endpoint. */
- par = (std::max)(par,parl);
- par = (std::min)(par,paru);
- if (par == 0.)
- par = gnorm / dxnorm;
-
- /* beginning of an iteration. */
- Matrix< Scalar, Dynamic, Dynamic > s = qr.matrixQR();
- while (true) {
- ++iter;
-
- /* evaluate the function at the current value of par. */
- if (par == 0.)
- par = (std::max)(dwarf,Scalar(.001) * paru); /* Computing MAX */
- wa1 = sqrt(par)* diag;
-
- Matrix< Scalar, Dynamic, 1 > sdiag(n);
- qrsolv<Scalar>(s, qr.colsPermutation().indices(), wa1, qtb, x, sdiag);
-
- wa2 = diag.cwiseProduct(x);
- dxnorm = wa2.blueNorm();
- temp = fp;
- fp = dxnorm - delta;
-
- /* if the function is small enough, accept the current value */
- /* of par. also test for the exceptional cases where parl */
- /* is zero or the number of iterations has reached 10. */
- if (abs(fp) <= Scalar(0.1) * delta || (parl == 0. && fp <= temp && temp < 0.) || iter == 10)
- break;
-
- /* compute the newton correction. */
- wa1 = qr.colsPermutation().inverse() * diag.cwiseProduct(wa2/dxnorm);
- // we could almost use this here, but the diagonal is outside qr, in sdiag[]
- // qr.matrixQR().topLeftCorner(n, n).transpose().template triangularView<Lower>().solveInPlace(wa1);
- for (j = 0; j < n; ++j) {
- wa1[j] /= sdiag[j];
- temp = wa1[j];
- for (Index i = j+1; i < n; ++i)
- wa1[i] -= s(i,j) * temp;
- }
- temp = wa1.blueNorm();
- parc = fp / delta / temp / temp;
-
- /* depending on the sign of the function, update parl or paru. */
- if (fp > 0.)
- parl = (std::max)(parl,par);
- if (fp < 0.)
- paru = (std::min)(paru,par);
-
- /* compute an improved estimate for par. */
- par = (std::max)(parl,par+parc);
- }
- if (iter == 0)
- par = 0.;
- return;
-}
-
-} // end namespace internal
-
-} // end namespace Eigen
diff --git a/eigen/unsupported/Eigen/src/NonLinearOptimization/qrsolv.h b/eigen/unsupported/Eigen/src/NonLinearOptimization/qrsolv.h
deleted file mode 100644
index feafd62..0000000
--- a/eigen/unsupported/Eigen/src/NonLinearOptimization/qrsolv.h
+++ /dev/null
@@ -1,91 +0,0 @@
-namespace Eigen {
-
-namespace internal {
-
-// TODO : once qrsolv2 is removed, use ColPivHouseholderQR or PermutationMatrix instead of ipvt
-template <typename Scalar>
-void qrsolv(
- Matrix< Scalar, Dynamic, Dynamic > &s,
- // TODO : use a PermutationMatrix once lmpar is no more:
- const VectorXi &ipvt,
- const Matrix< Scalar, Dynamic, 1 > &diag,
- const Matrix< Scalar, Dynamic, 1 > &qtb,
- Matrix< Scalar, Dynamic, 1 > &x,
- Matrix< Scalar, Dynamic, 1 > &sdiag)
-
-{
- typedef DenseIndex Index;
-
- /* Local variables */
- Index i, j, k, l;
- Scalar temp;
- Index n = s.cols();
- Matrix< Scalar, Dynamic, 1 > wa(n);
- JacobiRotation<Scalar> givens;
-
- /* Function Body */
- // the following will only change the lower triangular part of s, including
- // the diagonal, though the diagonal is restored afterward
-
- /* copy r and (q transpose)*b to preserve input and initialize s. */
- /* in particular, save the diagonal elements of r in x. */
- x = s.diagonal();
- wa = qtb;
-
- s.topLeftCorner(n,n).template triangularView<StrictlyLower>() = s.topLeftCorner(n,n).transpose();
-
- /* eliminate the diagonal matrix d using a givens rotation. */
- for (j = 0; j < n; ++j) {
-
- /* prepare the row of d to be eliminated, locating the */
- /* diagonal element using p from the qr factorization. */
- l = ipvt[j];
- if (diag[l] == 0.)
- break;
- sdiag.tail(n-j).setZero();
- sdiag[j] = diag[l];
-
- /* the transformations to eliminate the row of d */
- /* modify only a single element of (q transpose)*b */
- /* beyond the first n, which is initially zero. */
- Scalar qtbpj = 0.;
- for (k = j; k < n; ++k) {
- /* determine a givens rotation which eliminates the */
- /* appropriate element in the current row of d. */
- givens.makeGivens(-s(k,k), sdiag[k]);
-
- /* compute the modified diagonal element of r and */
- /* the modified element of ((q transpose)*b,0). */
- s(k,k) = givens.c() * s(k,k) + givens.s() * sdiag[k];
- temp = givens.c() * wa[k] + givens.s() * qtbpj;
- qtbpj = -givens.s() * wa[k] + givens.c() * qtbpj;
- wa[k] = temp;
-
- /* accumulate the tranformation in the row of s. */
- for (i = k+1; i<n; ++i) {
- temp = givens.c() * s(i,k) + givens.s() * sdiag[i];
- sdiag[i] = -givens.s() * s(i,k) + givens.c() * sdiag[i];
- s(i,k) = temp;
- }
- }
- }
-
- /* solve the triangular system for z. if the system is */
- /* singular, then obtain a least squares solution. */
- Index nsing;
- for(nsing=0; nsing<n && sdiag[nsing]!=0; nsing++) {}
-
- wa.tail(n-nsing).setZero();
- s.topLeftCorner(nsing, nsing).transpose().template triangularView<Upper>().solveInPlace(wa.head(nsing));
-
- // restore
- sdiag = s.diagonal();
- s.diagonal() = x;
-
- /* permute the components of z back to components of x. */
- for (j = 0; j < n; ++j) x[ipvt[j]] = wa[j];
-}
-
-} // end namespace internal
-
-} // end namespace Eigen
diff --git a/eigen/unsupported/Eigen/src/NonLinearOptimization/r1mpyq.h b/eigen/unsupported/Eigen/src/NonLinearOptimization/r1mpyq.h
deleted file mode 100644
index 36ff700..0000000
--- a/eigen/unsupported/Eigen/src/NonLinearOptimization/r1mpyq.h
+++ /dev/null
@@ -1,30 +0,0 @@
-namespace Eigen {
-
-namespace internal {
-
-// TODO : move this to GivensQR once there's such a thing in Eigen
-
-template <typename Scalar>
-void r1mpyq(DenseIndex m, DenseIndex n, Scalar *a, const std::vector<JacobiRotation<Scalar> > &v_givens, const std::vector<JacobiRotation<Scalar> > &w_givens)
-{
- typedef DenseIndex Index;
-
- /* apply the first set of givens rotations to a. */
- for (Index j = n-2; j>=0; --j)
- for (Index i = 0; i<m; ++i) {
- Scalar temp = v_givens[j].c() * a[i+m*j] - v_givens[j].s() * a[i+m*(n-1)];
- a[i+m*(n-1)] = v_givens[j].s() * a[i+m*j] + v_givens[j].c() * a[i+m*(n-1)];
- a[i+m*j] = temp;
- }
- /* apply the second set of givens rotations to a. */
- for (Index j = 0; j<n-1; ++j)
- for (Index i = 0; i<m; ++i) {
- Scalar temp = w_givens[j].c() * a[i+m*j] + w_givens[j].s() * a[i+m*(n-1)];
- a[i+m*(n-1)] = -w_givens[j].s() * a[i+m*j] + w_givens[j].c() * a[i+m*(n-1)];
- a[i+m*j] = temp;
- }
-}
-
-} // end namespace internal
-
-} // end namespace Eigen
diff --git a/eigen/unsupported/Eigen/src/NonLinearOptimization/r1updt.h b/eigen/unsupported/Eigen/src/NonLinearOptimization/r1updt.h
deleted file mode 100644
index f287660..0000000
--- a/eigen/unsupported/Eigen/src/NonLinearOptimization/r1updt.h
+++ /dev/null
@@ -1,99 +0,0 @@
-namespace Eigen {
-
-namespace internal {
-
-template <typename Scalar>
-void r1updt(
- Matrix< Scalar, Dynamic, Dynamic > &s,
- const Matrix< Scalar, Dynamic, 1> &u,
- std::vector<JacobiRotation<Scalar> > &v_givens,
- std::vector<JacobiRotation<Scalar> > &w_givens,
- Matrix< Scalar, Dynamic, 1> &v,
- Matrix< Scalar, Dynamic, 1> &w,
- bool *sing)
-{
- typedef DenseIndex Index;
- const JacobiRotation<Scalar> IdentityRotation = JacobiRotation<Scalar>(1,0);
-
- /* Local variables */
- const Index m = s.rows();
- const Index n = s.cols();
- Index i, j=1;
- Scalar temp;
- JacobiRotation<Scalar> givens;
-
- // r1updt had a broader usecase, but we dont use it here. And, more
- // importantly, we can not test it.
- eigen_assert(m==n);
- eigen_assert(u.size()==m);
- eigen_assert(v.size()==n);
- eigen_assert(w.size()==n);
-
- /* move the nontrivial part of the last column of s into w. */
- w[n-1] = s(n-1,n-1);
-
- /* rotate the vector v into a multiple of the n-th unit vector */
- /* in such a way that a spike is introduced into w. */
- for (j=n-2; j>=0; --j) {
- w[j] = 0.;
- if (v[j] != 0.) {
- /* determine a givens rotation which eliminates the */
- /* j-th element of v. */
- givens.makeGivens(-v[n-1], v[j]);
-
- /* apply the transformation to v and store the information */
- /* necessary to recover the givens rotation. */
- v[n-1] = givens.s() * v[j] + givens.c() * v[n-1];
- v_givens[j] = givens;
-
- /* apply the transformation to s and extend the spike in w. */
- for (i = j; i < m; ++i) {
- temp = givens.c() * s(j,i) - givens.s() * w[i];
- w[i] = givens.s() * s(j,i) + givens.c() * w[i];
- s(j,i) = temp;
- }
- } else
- v_givens[j] = IdentityRotation;
- }
-
- /* add the spike from the rank 1 update to w. */
- w += v[n-1] * u;
-
- /* eliminate the spike. */
- *sing = false;
- for (j = 0; j < n-1; ++j) {
- if (w[j] != 0.) {
- /* determine a givens rotation which eliminates the */
- /* j-th element of the spike. */
- givens.makeGivens(-s(j,j), w[j]);
-
- /* apply the transformation to s and reduce the spike in w. */
- for (i = j; i < m; ++i) {
- temp = givens.c() * s(j,i) + givens.s() * w[i];
- w[i] = -givens.s() * s(j,i) + givens.c() * w[i];
- s(j,i) = temp;
- }
-
- /* store the information necessary to recover the */
- /* givens rotation. */
- w_givens[j] = givens;
- } else
- v_givens[j] = IdentityRotation;
-
- /* test for zero diagonal elements in the output s. */
- if (s(j,j) == 0.) {
- *sing = true;
- }
- }
- /* move w back into the last column of the output s. */
- s(n-1,n-1) = w[n-1];
-
- if (s(j,j) == 0.) {
- *sing = true;
- }
- return;
-}
-
-} // end namespace internal
-
-} // end namespace Eigen
diff --git a/eigen/unsupported/Eigen/src/NonLinearOptimization/rwupdt.h b/eigen/unsupported/Eigen/src/NonLinearOptimization/rwupdt.h
deleted file mode 100644
index 6ebf856..0000000
--- a/eigen/unsupported/Eigen/src/NonLinearOptimization/rwupdt.h
+++ /dev/null
@@ -1,49 +0,0 @@
-namespace Eigen {
-
-namespace internal {
-
-template <typename Scalar>
-void rwupdt(
- Matrix< Scalar, Dynamic, Dynamic > &r,
- const Matrix< Scalar, Dynamic, 1> &w,
- Matrix< Scalar, Dynamic, 1> &b,
- Scalar alpha)
-{
- typedef DenseIndex Index;
-
- const Index n = r.cols();
- eigen_assert(r.rows()>=n);
- std::vector<JacobiRotation<Scalar> > givens(n);
-
- /* Local variables */
- Scalar temp, rowj;
-
- /* Function Body */
- for (Index j = 0; j < n; ++j) {
- rowj = w[j];
-
- /* apply the previous transformations to */
- /* r(i,j), i=0,1,...,j-1, and to w(j). */
- for (Index i = 0; i < j; ++i) {
- temp = givens[i].c() * r(i,j) + givens[i].s() * rowj;
- rowj = -givens[i].s() * r(i,j) + givens[i].c() * rowj;
- r(i,j) = temp;
- }
-
- /* determine a givens rotation which eliminates w(j). */
- givens[j].makeGivens(-r(j,j), rowj);
-
- if (rowj == 0.)
- continue; // givens[j] is identity
-
- /* apply the current transformation to r(j,j), b(j), and alpha. */
- r(j,j) = givens[j].c() * r(j,j) + givens[j].s() * rowj;
- temp = givens[j].c() * b[j] + givens[j].s() * alpha;
- alpha = -givens[j].s() * b[j] + givens[j].c() * alpha;
- b[j] = temp;
- }
-}
-
-} // end namespace internal
-
-} // end namespace Eigen