add ellipsoid walks: Dikin, John and Vaidya walk. #39
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| // Code from https://github.com/rzrsk/vaidya-walk | ||
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There was a problem hiding this comment. You can add Also please add the info and copyright notes as in all the files of the library |
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| // Modified by Apostolos Chalkis, as part of Google Summer of Code 2019 program. | ||
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| #ifndef PWALK_DIKIN_WALKER_HPP_ | ||
| #define PWALK_DIKIN_WALKER_HPP_ | ||
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| #include <Eigen/Dense> | ||
| #include "math_functions.h" | ||
| #include "walker.h" | ||
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| //namespace pwalk { | ||
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| template <typename Dtype> | ||
| class DikinWalker: public Walker<Dtype> { | ||
| public: | ||
| DikinWalker(const Eigen::Matrix<Dtype, Eigen::Dynamic, 1>& initialization, const Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic>& cons_A, const Eigen::Matrix<Dtype, Eigen::Dynamic, 1>& cons_b, const Dtype r) : Walker<Dtype>(initialization, cons_A, cons_b), r_(r){} | ||
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| // getter for radius | ||
| Dtype getRadius() { | ||
| return r_; | ||
| } | ||
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| void proposal(Eigen::Matrix<Dtype, Eigen::Dynamic, 1>& new_sample){ | ||
| Eigen::Matrix<Dtype, Eigen::Dynamic, 1> gaussian_step = Eigen::Matrix<Dtype, Eigen::Dynamic, 1>::Zero(this->nb_dim_); | ||
| sample_gaussian<Dtype>(this->nb_dim_, 0., 1., gaussian_step); | ||
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| // get hessian | ||
| Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic> new_sqrt_inv_hess = Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic>::Zero(this->nb_dim_, this->nb_dim_); | ||
| sqrtInvHessBarrier(this->curr_sample_, new_sqrt_inv_hess); | ||
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| new_sample = this->curr_sample_ + r_ / std::sqrt(Dtype(this->nb_dim_)) * (new_sqrt_inv_hess * gaussian_step); | ||
| } | ||
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| bool acceptRejectReverse(const Eigen::Matrix<Dtype, Eigen::Dynamic, 1>& new_sample){ | ||
| // get hessian on x | ||
| Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic> new_sqrt_inv_hess_x = Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic>::Zero(this->nb_dim_, this->nb_dim_); | ||
| sqrtInvHessBarrier(this->curr_sample_, new_sqrt_inv_hess_x); | ||
| // get hessian on y | ||
| Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic> new_sqrt_inv_hess_y = Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic>::Zero(this->nb_dim_, this->nb_dim_); | ||
| sqrtInvHessBarrier(new_sample, new_sqrt_inv_hess_y); | ||
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| Dtype scale = r_/std::sqrt(Dtype(this->nb_dim_)); | ||
| Dtype p_y_to_x = gaussian_density<Dtype>(this->curr_sample_, new_sample, new_sqrt_inv_hess_y.inverse()/scale); | ||
| Dtype p_x_to_y = gaussian_density<Dtype>(new_sample, this->curr_sample_, new_sqrt_inv_hess_x.inverse()/scale); | ||
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| Dtype ar_ratio = std::min<Dtype>(1., p_y_to_x/p_x_to_y); | ||
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| Dtype random_num = rng_uniform<Dtype>(0., 1.); | ||
| // lazy version of the walk | ||
| if (random_num > ar_ratio) { | ||
| return false; | ||
| } | ||
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| return true; | ||
| } | ||
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| bool doSample(Eigen::Matrix<Dtype, Eigen::Dynamic, 1>& new_sample, const Dtype lazy = Dtype(0.5)){ | ||
| proposal(new_sample); | ||
| this->nb_curr_samples_ += 1; | ||
| // for lazy markov chain | ||
| Dtype random_num = rng_uniform<Dtype>(0., 1.); | ||
| // check balance and check in polytope | ||
| if (random_num < lazy && this->checkInPolytope(new_sample) && acceptRejectReverse(new_sample)){ | ||
| this->curr_sample_ = new_sample; | ||
| return true; | ||
| } else { | ||
| new_sample = this->curr_sample_; | ||
| return false; | ||
| } | ||
| } | ||
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| void sqrtInvHessBarrier(const Eigen::Matrix<Dtype, Eigen::Dynamic, 1>& new_sample, Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic>& new_sqrt_inv_hess){ | ||
| Eigen::Matrix<Dtype, Eigen::Dynamic, 1> inv_slack = (this->cons_b_ - this->cons_A_ * new_sample).cwiseInverse(); | ||
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| Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic> half_hess = inv_slack.asDiagonal()* this->cons_A_; | ||
| Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic> new_hess = half_hess.transpose() * half_hess; | ||
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| // compute eigenvectors and eigenvalues | ||
| Eigen::SelfAdjointEigenSolver<Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic> > es(new_hess); | ||
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| Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic> V = es.eigenvectors(); | ||
| Eigen::Matrix<Dtype, Eigen::Dynamic, 1> Dv = es.eigenvalues(); | ||
| new_sqrt_inv_hess = V * Dv.cwiseInverse().cwiseSqrt().asDiagonal() * V.transpose(); | ||
| } | ||
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| private: | ||
| const Dtype r_; | ||
| }; | ||
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| //} // namespace pwalk | ||
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| #endif // PWALK_DIKIN_WALKER_HPP_ | ||
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,134 @@ | ||
| // Code from https://github.com/rzrsk/vaidya-walk | ||
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| // Modified by Apostolos Chalkis, as part of Google Summer of Code 2019 program. | ||
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| #ifndef PWALK_JOHN_WALKER_HPP_ | ||
| #define PWALK_JOHN_WALKER_HPP_ | ||
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| #include <cmath> | ||
| #include <Eigen/Dense> | ||
| #include "math_functions.h" | ||
| #include "walker.h" | ||
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| //namespace pwalk { | ||
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| template <typename Dtype> | ||
| class JohnWalker: public Walker<Dtype> { | ||
| public: | ||
| JohnWalker(const Eigen::Matrix<Dtype, Eigen::Dynamic, 1>& initialization, const Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic>& cons_A, const Eigen::Matrix<Dtype, Eigen::Dynamic, 1>& cons_b, const Dtype r) : Walker<Dtype>(initialization, cons_A, cons_b), r_(r), alpha_(1. - 1. / std::log2(2.*Dtype(cons_A.rows())/Dtype(cons_A.cols()))), beta_(Dtype(cons_A.cols())/2./Dtype(cons_A.rows())), curr_weight_(Eigen::Matrix<Dtype, Eigen::Dynamic, 1>::Ones(cons_A.rows())){} | ||
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| // getter for radius | ||
| Dtype getRadius() { | ||
| return r_; | ||
| } | ||
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| void proposal(Eigen::Matrix<Dtype, Eigen::Dynamic, 1>& new_sample){ | ||
| Eigen::Matrix<Dtype, Eigen::Dynamic, 1> gaussian_step = Eigen::Matrix<Dtype, Eigen::Dynamic, 1>::Zero(this->nb_dim_); | ||
| sample_gaussian<Dtype>(this->nb_dim_, 0., 1., gaussian_step); | ||
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| // get hessian | ||
| Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic> new_sqrt_inv_hess = Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic>::Zero(this->nb_dim_, this->nb_dim_); | ||
| sqrtInvHessBarrier(this->curr_sample_, new_sqrt_inv_hess); | ||
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| new_sample = this->curr_sample_ + r_ / std::sqrt(Dtype(this->nb_dim_)) * (new_sqrt_inv_hess * gaussian_step); | ||
| } | ||
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| bool acceptRejectReverse(const Eigen::Matrix<Dtype, Eigen::Dynamic, 1>& new_sample){ | ||
| // get hessian on y | ||
| Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic> new_sqrt_inv_hess_y = Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic>::Zero(this->nb_dim_, this->nb_dim_); | ||
| sqrtInvHessBarrier(new_sample, new_sqrt_inv_hess_y); | ||
| // get hessian on x | ||
| Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic> new_sqrt_inv_hess_x = Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic>::Zero(this->nb_dim_, this->nb_dim_); | ||
| sqrtInvHessBarrier(this->curr_sample_, new_sqrt_inv_hess_x); | ||
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| Dtype scale = r_ / std::sqrt(Dtype(this->nb_dim_)); | ||
| Dtype p_y_to_x = gaussian_density<Dtype>(this->curr_sample_, new_sample, new_sqrt_inv_hess_y.inverse()/scale); | ||
| Dtype p_x_to_y = gaussian_density<Dtype>(new_sample, this->curr_sample_, new_sqrt_inv_hess_x.inverse()/scale); | ||
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| Dtype ar_ratio = std::min<Dtype>(1., p_y_to_x/p_x_to_y); | ||
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| Dtype random_num = rng_uniform<Dtype>(0., 1.); | ||
| // lazy version of the walk | ||
| if (random_num > ar_ratio) { | ||
| return false; | ||
| } | ||
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| return true; | ||
| } | ||
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| bool doSample(Eigen::Matrix<Dtype, Eigen::Dynamic, 1>& new_sample, const Dtype lazy = Dtype(0.5)){ | ||
| proposal(new_sample); | ||
| this->nb_curr_samples_ += 1; | ||
| // for lazy markov chain | ||
| Dtype random_num = rng_uniform<Dtype>(0., 1.); | ||
| // check balance and check in polytope | ||
| if (random_num < lazy && this->checkInPolytope(new_sample) && acceptRejectReverse(new_sample)){ | ||
| this->curr_sample_ = new_sample; | ||
| return true; | ||
| } else { | ||
| new_sample = this->curr_sample_; | ||
| return false; | ||
| } | ||
| } | ||
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| void sqrtInvHessBarrier(const Eigen::Matrix<Dtype, Eigen::Dynamic, 1>& new_sample, Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic>& new_sqrt_inv_hess){ | ||
| Eigen::Matrix<Dtype, Eigen::Dynamic, 1> inv_slack = (this->cons_b_ - this->cons_A_ * new_sample).cwiseInverse(); | ||
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| Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic> half_hess = inv_slack.asDiagonal()* this->cons_A_; | ||
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| Eigen::Matrix<Dtype, Eigen::Dynamic, 1> gradient; | ||
| Eigen::Matrix<Dtype, Eigen::Dynamic, 1> score; | ||
| Eigen::Matrix<Dtype, Eigen::Dynamic, 1> weight_half_alpha; | ||
| Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic> weight_half_hess; | ||
| Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic> new_hess; | ||
| Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic> new_hess_inv; | ||
| Eigen::Matrix<Dtype, Eigen::Dynamic, 1> beta_ones = beta_ * Eigen::Matrix<Dtype, Eigen::Dynamic, 1>::Ones(this->nb_cons_); | ||
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| Eigen::Matrix<Dtype, Eigen::Dynamic, 1> next_weight = curr_weight_; | ||
| // compute scores using gradient descent | ||
| do { | ||
| curr_weight_ = next_weight; | ||
| weight_half_alpha = curr_weight_.array().pow(alpha_/2.); | ||
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| weight_half_hess = (weight_half_alpha.cwiseProduct(inv_slack)).asDiagonal() * this->cons_A_ ; | ||
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| new_hess = weight_half_hess.transpose() * weight_half_hess; | ||
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| new_hess_inv = new_hess.inverse(); | ||
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| score = ((weight_half_hess * new_hess_inv).cwiseProduct(weight_half_hess)).rowwise().sum(); | ||
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| // gradient = Eigen::Matrix<Dtype, Eigen::Dynamic, 1>::Ones(this->nb_cons_) - (score + beta_ones).cwiseQuotient(curr_weight_); | ||
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| // curr_weight_ = (curr_weight_ - 0.5 * gradient).cwiseMax(beta_ones); | ||
| next_weight = (0.5*(curr_weight_ + score + beta_ones)).cwiseMax(beta_ones); | ||
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| } while ((next_weight - curr_weight_).template lpNorm<Eigen::Infinity>() > Dtype(0.00001)); | ||
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| // std::cout << "inv_slack" << inv_slack.transpose() << std::endl; | ||
| // std::cout << "score" << score.transpose() << std::endl; | ||
| // std::cout << "curr_weight_ " << curr_weight_.transpose() << std::endl; | ||
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| // compute john hessian | ||
| Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic> john_new_hess = half_hess.transpose() * curr_weight_.asDiagonal() * half_hess; | ||
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| // compute eigenvectors and eigenvalues | ||
| Eigen::SelfAdjointEigenSolver<Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic> > es(john_new_hess); | ||
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| Eigen::Matrix<Dtype, Eigen::Dynamic, Eigen::Dynamic> V = es.eigenvectors(); | ||
| Eigen::Matrix<Dtype, Eigen::Dynamic, 1> Dv = es.eigenvalues(); | ||
| new_sqrt_inv_hess = V * Dv.cwiseInverse().cwiseSqrt().asDiagonal() * V.transpose(); | ||
| } | ||
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| private: | ||
| const Dtype r_; | ||
| const Dtype alpha_; | ||
| const Dtype beta_; | ||
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| Eigen::Matrix<Dtype, Eigen::Dynamic, 1> curr_weight_; | ||
| }; | ||
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| //} // namespace pwalk | ||
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| #endif // PWALK_JOHN_WALKER_HPP_ | ||
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Why having all those
boolvars, one per walk type and not just oneenumthat takes the value related to the walk type, e.g.enum Walk { RDHnR, CDHnR, Ball, Billiard, Vaidya, John, Dikin, ... };