reweighted.cc File Reference

#include <catch2/catch_all.hpp>
#include <random>
#include <Eigen/Dense>
#include "sopt/imaging_padmm.h"
#include "sopt/reweighted.h"

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Classes
struct	DummyAlgorithm
	Minimum set of functions and type aliases needed by reweighting. More...
struct	DummyAlgorithm::DiagnosticAndResult

Functions
	TEST_CASE ("L0-Approximation")

Function Documentation

TEST_CASE()

TEST_CASE

(

"L0-Approximation"

)

Definition at line 59 of file reweighted.cc.

                              {
  auto constexpr N = 6;
  DummyAlgorithm::t_Vector const input = DummyAlgorithm::t_Vector::Random(N);
 
  auto l0algo = algorithm::reweighted(DummyAlgorithm(), DummyAlgorithm::set_weights,
                                      DummyAlgorithm::reweightee);
 
  DummyAlgorithm::called_with_x = 0;
  DummyAlgorithm::called_with_warm = 0;
  DummyAlgorithm::called_reweightee = 0;
  DummyAlgorithm::called_weights = 0;
  DummyAlgorithm::DiagnosticAndResult::x = DummyAlgorithm::t_Vector::Zero(0);
  DummyAlgorithm::weights = DummyAlgorithm::t_Vector::Zero(0);
 
  GIVEN("The maximum number of iteration is zero") {
    l0algo.itermax(0);
    WHEN("The reweighting algorithm is called") {
      auto const result = l0algo(input);
      THEN("The algorithm exited at the first iteration") {
        CHECK(result.niters == 0);
        CHECK(result.good == true);
      }
      THEN("The weights is set to 1") {
        CHECK(result.weights.size() == 1);
        CHECK(std::abs(result.weights(0) - 1) < 1e-12);
      }
      THEN("The inner algorithm was called once") {
        CHECK(DummyAlgorithm::called_with_x == 1);
        CHECK(DummyAlgorithm::called_with_warm == 0);
        CHECK(result.algo.x.array().isApprox(input.array() + 0.1));
      }
    }
  }
 
  GIVEN("The maximum number of iterations is one") {
    l0algo.itermax(1);
    WHEN("The reweighting algorithm is called") {
      auto const result = l0algo(input);
      THEN("The algorithm exited at the second iteration") {
        CHECK(result.niters == 1);
        CHECK(result.good == true);
      }
      THEN("The weights are not one") {
        CHECK(result.weights.size() == input.size());
        // standard deviation of Ψ^T x, with x the output of the first call to the inner algorithm
        Vector<> const PsiT_x = DummyAlgorithm::reweightee({}, input.array() + 0.1);
        auto delta = standard_deviation(PsiT_x);
        CHECK(result.weights.array().isApprox(delta / (delta + PsiT_x.array().abs())));
      }
      THEN("The inner algorithm was called twice") {
        CHECK(DummyAlgorithm::called_with_x == 1);
        CHECK(DummyAlgorithm::called_with_warm == 1);
        CHECK(result.algo.x.array().isApprox(input.array() + 0.2));
      }
    }
  }
}

References DummyAlgorithm::called_reweightee, DummyAlgorithm::called_weights, DummyAlgorithm::called_with_warm, DummyAlgorithm::called_with_x, N, sopt::algorithm::reweighted(), DummyAlgorithm::reweightee(), DummyAlgorithm::set_weights(), sopt::standard_deviation(), DummyAlgorithm::weights, and DummyAlgorithm::DiagnosticAndResult::x.