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/**
* @file frankwolfe_test.cpp
* @author Chenzhe Diao
* @author Marcus Edel
*
* Test file for Frank-Wolfe type optimizer.
*
* ensmallen is free software; you may redistribute it and/or modify it under
* the terms of the 3-clause BSD license. You should have received a copy of
* the 3-clause BSD license along with ensmallen. If not, see
* http://www.opensource.org/licenses/BSD-3-Clause for more information.
*/
#if defined(ENS_USE_COOT)
#include <armadillo>
#include <bandicoot>
#endif
#include <ensmallen.hpp>
#include "catch.hpp"
#include "test_function_tools.hpp"
#include "test_types.hpp"
using namespace arma;
using namespace ens;
using namespace ens::test;
/**
* Simple test of Orthogonal Matching Pursuit algorithm.
*/
TEMPLATE_TEST_CASE("FrankWolfe_OMP", "[FrankWolfe]", arma::mat)
{
typedef typename TestType::elem_type ElemType;
const int k = 5;
TestType B1 = arma::eye<TestType>(3, 3);
TestType B2 = 0.1 * arma::randn<TestType>(3, k);
// The dictionary is input as columns of A.
TestType A = join_horiz(B1, B2);
// Vector to be sparsely approximated.
arma::Col<ElemType> b = {1.0, 1.0, 0.0};
FuncSq f(A, b);
ConstrLpBallSolver linearConstrSolver(1);
UpdateSpan updateRule;
OMP s(linearConstrSolver, updateRule);
TestType coordinates = zeros<TestType>(k + 3, 1);
ElemType result = s.Optimize(f, coordinates);
const double margin = Tolerances<TestType>::Coord;
REQUIRE(result == Approx(0.0).margin(margin));
REQUIRE(coordinates(0) - 1 == Approx(0.0).margin(margin));
REQUIRE(coordinates(1) - 1 == Approx(0.0).margin(margin));
REQUIRE(coordinates(2) == Approx(0.0).margin(margin));
for (int ii = 0; ii < k; ++ii)
{
REQUIRE(coordinates[ii + 3] == Approx(0.0).margin(margin));
}
}
/**
* Simple test of Orthogonal Matching Pursuit with regularization.
*/
TEMPLATE_TEST_CASE("FrankWolfe_RegularizedOMP", "[FrankWolfe]", arma::mat)
{
typedef typename TestType::elem_type ElemType;
const int k = 10;
TestType B1 = 0.1 * arma::eye<TestType>(k, k);
TestType B2 = 100 * arma::randn<TestType>(k, k);
// The dictionary is input as columns of A.
TestType A = join_horiz(B1, B2);
// Vector to be sparsely approximated.
arma::Col<ElemType> b(k, arma::fill::zeros);
b(0) = 1;
b(1) = 1;
arma::Col<ElemType> lambda(A.n_cols);
for (size_t ii = 0; ii < A.n_cols; ii++)
lambda(ii) = norm(A.col(ii), 2);
FuncSq f(A, b);
ConstrLpBallSolver linearConstrSolver(1, lambda);
UpdateSpan updateRule;
OMP s(linearConstrSolver, updateRule);
TestType coordinates = zeros<TestType>(2 * k, 1);
ElemType result = s.Optimize(f, coordinates);
REQUIRE(result == Approx(0.0).margin(Tolerances<TestType>::Coord));
}
/**
* Simple test of Orthogonal Matching Pursuit with support prune.
*/
TEMPLATE_TEST_CASE("FrankWolfe_PruneSupportOMP", "[FrankWolfe]", arma::mat)
{
typedef typename TestType::elem_type ElemType;
// The dictionary is input as columns of A.
const int k = 3;
TestType B1 = { { 1.0, 0.0, 1.0 },
{ 0.0, 1.0, 1.0 },
{ 0.0, 0.0, 1.0 } };
TestType B2 = arma::randu<TestType>(k, k);
// The dictionary is input as columns of A.
TestType A = join_horiz(B1, B2);
// Vector to be sparsely approximated.
arma::Col<ElemType> b = { 1.0, 1.0, 0.0 };
FuncSq f(A, b);
ConstrLpBallSolver linearConstrSolver(1);
UpdateSpan updateRule(true);
OMP s(linearConstrSolver, updateRule);
TestType coordinates = zeros<TestType>(k + 3, 1);
ElemType result = s.Optimize(f, coordinates);
REQUIRE(result == Approx(0.0).margin(Tolerances<TestType>::Coord));
}
/**
* Simple test of sparse soluton in atom domain with atom norm constraint.
*/
TEMPLATE_TEST_CASE("FrankWolfe_AtomNormConstraint", "[FrankWolfe]",
arma::mat)
{
typedef typename TestType::elem_type ElemType;
const int k = 5;
TestType B1 = arma::eye<TestType>(3, 3);
TestType B2 = 0.1 * arma::randn<TestType>(3, k);
// The dictionary is input as columns of A.
TestType A = join_horiz(B1, B2);
// Vector to be sparsely approximated.
arma::Col<ElemType> b = { 1.0, 1.0, 0.0 };
FuncSq f(A, b);
ConstrLpBallSolver linearConstrSolver(1);
UpdateFullCorrection updateRule(2, 0.2);
FrankWolfe<ConstrLpBallSolver, UpdateFullCorrection>
s(linearConstrSolver, updateRule);
TestType coordinates = zeros<TestType>(k + 3, 1);
ElemType result = s.Optimize(f, coordinates);
REQUIRE(result == Approx(0.0).margin(Tolerances<TestType>::Coord));
}
/**
* A very simple test of classic Frank-Wolfe algorithm.
* The constrained domain used is unit lp ball.
*/
TEMPLATE_TEST_CASE("FrankWolfe_Classic", "[FrankWolfe]", arma::mat)
{
typedef typename TestType::elem_type ElemType;
TestFuncFW<TestType> f;
double p = 2; // Constraint set is unit lp ball.
ConstrLpBallSolver linearConstrSolver(p);
UpdateClassic updateRule;
FrankWolfe<ConstrLpBallSolver, UpdateClassic>
s(linearConstrSolver, updateRule);
TestType coordinates = arma::randu<TestType>(3, 1);
ElemType result = s.Optimize(f, coordinates);
REQUIRE(result == Approx(0.0).margin(Tolerances<TestType>::Obj));
const double coordTol = Tolerances<TestType>::Coord;
REQUIRE(coordinates(0) - 0.1 == Approx(0.0).margin(coordTol));
REQUIRE(coordinates(1) - 0.2 == Approx(0.0).margin(coordTol));
REQUIRE(coordinates(2) - 0.3 == Approx(0.0).margin(coordTol));
}
/**
* Exactly the same problem with ClassicFW.
* The update step performs a line search now.
* It converges much faster.
*/
TEMPLATE_TEST_CASE("FrankWolfe_LineSearch", "[FrankWolfe]",
ENS_FULLPREC_TEST_TYPES)
{
typedef typename TestType::elem_type ElemType;
typedef typename ForwardType<TestType>::brow RowType;
TestFuncFW<TestType> f;
double p = 2; // Constraint set is unit lp ball.
ConstrLpBallSolverType<RowType> linearConstrSolver(p);
UpdateLineSearch updateRule;
FrankWolfe<decltype(linearConstrSolver), UpdateLineSearch>
s(linearConstrSolver, updateRule);
TestType coordinates = randu<TestType>(3);
ElemType result = s.Optimize(f, coordinates);
REQUIRE(result == Approx(0.0).margin(Tolerances<TestType>::Obj));
const double coordTol = Tolerances<TestType>::Coord;
REQUIRE(coordinates(0) - 0.1 == Approx(0.0).margin(coordTol));
REQUIRE(coordinates(1) - 0.2 == Approx(0.0).margin(coordTol));
REQUIRE(coordinates(2) - 0.3 == Approx(0.0).margin(coordTol));
}
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