85 lines
2.2 KiB
C++
85 lines
2.2 KiB
C++
/**
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* @file proximal_test.cpp
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* @author Chenzhe Diao
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* @author Marcus Edel
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* @author Conrad Sanderson
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*
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* ensmallen is free software; you may redistribute it and/or modify it under
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* the terms of the 3-clause BSD license. You should have received a copy of
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* the 3-clause BSD license along with ensmallen. If not, see
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* http://www.opensource.org/licenses/BSD-3-Clause for more information.
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*/
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#include <ensmallen.hpp>
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#include "catch.hpp"
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using namespace arma;
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using namespace ens;
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using namespace ens::test;
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/**
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* Approximate vector using a vector with l1 norm small than or equal to tau.
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*/
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TEST_CASE("ProjectToL1", "[ProximalTest]")
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{
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int D = 100; // Dimension of the problem.
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// Norm of L1 ball.
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double tau1 = 1.5;
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double tau2 = 0.5;
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// Vector to be projected, with unit l1 norm.
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vec v = randu<vec>(D);
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v = normalise(v, 1);
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// v is inside the l1 ball, so the projection will not change v.
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vec v1 = v;
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Proximal::ProjectToL1Ball(v1, tau1);
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REQUIRE(norm(v - v1, 2) == Approx(0.0).margin(1e-10));
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// v is outside the l1 ball, so the projection should find the closest.
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vec v2 = v;
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Proximal::ProjectToL1Ball(v2, tau2);
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double distance = norm(v2 - v, 2);
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for (size_t i = 1; i < 1000; i++)
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{
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// Randomly generate a vector on the surface of the l1 ball with norm tau2.
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vec vSurface = randu<vec>(D);
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vSurface = tau2 * normalise(vSurface, 1);
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double distanceNew = norm(vSurface - v, 2);
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REQUIRE(distanceNew >= distance);
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}
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}
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/**
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* Approximate a vector with a tau-sparse vector.
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*/
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TEST_CASE("ProjectToL0", "[ProximalTest]")
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{
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int D = 100; // Dimension of the problem.
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int tau = 25; // Sparsity requirement.
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// Vector to be projected.
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vec v = randn<vec>(D);
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vec v0 = v;
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Proximal::ProjectToL0Ball(v0, tau);
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double distance = norm(v0 - v, 2);
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for (size_t i = 1; i < 1000; i++)
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{
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// Randomly find a subset of the support of v, generate a tau-sparse
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// vector by restricting v to this support.
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uvec indices = linspace<uvec>(0, D - 1, D);
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indices = shuffle(indices);
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indices = indices.head(tau);
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vec vNew = zeros<vec>(D);
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vNew.elem(indices) = v.elem(indices);
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double distanceNew = norm(v - vNew, 2);
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REQUIRE(distanceNew >= distance);
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}
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}
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