fraction_to_the_boundary_rule.hpp

// Copyright (c) Sleipnir contributors
 
#pragma once
 
#include <Eigen/Core>
 
// See docs/algorithms.md#Works_cited for citation definitions
 
namespace slp {
 
template <typename Scalar>
Scalar fraction_to_the_boundary_rule(
    const Eigen::Ref<const Eigen::Vector<Scalar, Eigen::Dynamic>>& x,
    const Eigen::Ref<const Eigen::Vector<Scalar, Eigen::Dynamic>>& p,
    Scalar τ) {
  // α = max(α ∈ (0, 1] : x + αp ≥ (1 − τ)x)
  //
  // where x and τ are positive.
  //
  // x + αp ≥ (1 − τ)x
  // x + αp ≥ x − τx
  // αp ≥ −τx
  //
  // If the inequality is false, p < 0 and α is too big. Find the largest value
  // of α that makes the inequality true.
  //
  // α = −τ/p x
  Scalar α(1);
  for (int i = 0; i < x.rows(); ++i) {
    if (α * p(i) < -τ * x(i)) {
      α = -τ / p(i) * x(i);
    }
  }
 
  return α;
}
 
}  // namespace slp