gtsam/cpp/testNonlinearConstraint.cpp

/**
 * @file testNonlinearConstraint.cpp
 * @brief Tests for nonlinear constraints handled via SQP
 * @author Alex Cunningham
 */

#include <boost/bind.hpp>
#include <CppUnitLite/TestHarness.h>
#include <VectorConfig.h>
#include <NonlinearConstraint.h>
#include <NonlinearConstraint-inl.h>

using namespace std;
using namespace gtsam;

/* ************************************************************************* */
// unary functions with scalar variables
/* ************************************************************************* */
namespace test1 {
/** p = 1, gradG(x) = 2x */
Matrix grad_g(const VectorConfig& config, const list<string>& keys) {
	double x = config[keys.front()](0);
	return Matrix_(1,1, 2*x);
}

/** p = 1, g(x) = x^2-5 = 0 */
Vector g_func(const VectorConfig& config, const list<string>& keys) {
	double x = config[keys.front()](0);
	return Vector_(1, x*x-5);
}
} // \namespace test1

/* ************************************************************************* */
TEST( NonlinearConstraint1, unary_scalar_construction ) {
	// construct a constraint on x
	// the lagrange multipliers will be expected on L_x1
	// and there is only one multiplier
	size_t p = 1;
	NonlinearConstraint1<VectorConfig> c1("x", *test1::grad_g, *test1::g_func, p, "L_x1");

	// get a configuration to use for finding the error
	VectorConfig config;
	config.insert("x", Vector_(1, 1.0));

	// calculate the error
	Vector actual = c1.error_vector(config);
	Vector expected = Vector_(1.0, -4.0);
	CHECK(assert_equal(actual, expected, 1e-5));
}

/* ************************************************************************* */
TEST( NonlinearConstraint1, unary_scalar_linearize ) {
	size_t p = 1;
	NonlinearConstraint1<VectorConfig> c1("x", *test1::grad_g, *test1::g_func, p, "L_x1");

	// get a configuration to use for linearization
	VectorConfig realconfig;
	realconfig.insert("x", Vector_(1, 1.0));

	// get a configuration of Lagrange multipliers
	VectorConfig lagrangeConfig;
	lagrangeConfig.insert("L_x1", Vector_(1, 3.0));

	// linearize the system
	GaussianFactor::shared_ptr actFactor, actConstraint;
	boost::tie(actFactor, actConstraint) = c1.linearize(realconfig, lagrangeConfig);

	// verify
	GaussianFactor expFactor("x", Matrix_(1,1, 6.0), "L_x1", eye(1), zero(1), 1.0);
	GaussianFactor expConstraint("x", Matrix_(1,1, 2.0), Vector_(1, 4.0), 0.0);
	CHECK(assert_equal(*actFactor, expFactor));
	CHECK(assert_equal(*actConstraint, expConstraint));
}

/* ************************************************************************* */
TEST( NonlinearConstraint1, unary_scalar_equal ) {
	NonlinearConstraint1<VectorConfig>
		c1("x", *test1::grad_g, *test1::g_func, 1, "L_x1", true),
		c2("x", *test1::grad_g, *test1::g_func, 1, "L_x1"),
		c3("x", *test1::grad_g, *test1::g_func, 2, "L_x1"),
		c4("y", *test1::grad_g, *test1::g_func, 1, "L_x1");

	CHECK(assert_equal(c1, c2));
	CHECK(assert_equal(c2, c1));
	CHECK(!c1.equals(c3));
	CHECK(!c1.equals(c4));
}

/* ************************************************************************* */
// binary functions with scalar variables
/* ************************************************************************* */
namespace test2 {
/** gradient for x, gradG(x,y) in x: 2x*/
Matrix grad_g1(const VectorConfig& config, const list<string>& keys) {
	double x = config[keys.front()](0);
	return Matrix_(1,1, 2.0*x);
}

/** gradient for y, gradG(x,y) in y: -1 */
Matrix grad_g2(const VectorConfig& config, const list<string>& keys) {
	double x = config[keys.back()](0);
	return Matrix_(1,1, -1.0);
}

/** p = 1, g(x) = x^2-5 -y = 0 */
Vector g_func(const VectorConfig& config, const list<string>& keys) {
	double x = config[keys.front()](0);
	double y = config[keys.back()](0);
	return Vector_(1, x*x-5.0-y);
}
} // \namespace test2

/* ************************************************************************* */
TEST( NonlinearConstraint2, binary_scalar_construction ) {
	// construct a constraint on x and y
	// the lagrange multipliers will be expected on L_xy
	// and there is only one multiplier
	size_t p = 1;
	NonlinearConstraint2<VectorConfig> c1(
			"x", *test2::grad_g1,
			"y", *test2::grad_g2,
			*test2::g_func, p, "L_xy");

	// get a configuration to use for finding the error
	VectorConfig config;
	config.insert("x", Vector_(1, 1.0));
	config.insert("y", Vector_(1, 2.0));

	// calculate the error
	Vector actual = c1.error_vector(config);
	Vector expected = Vector_(1.0, -6.0);
	CHECK(assert_equal(actual, expected, 1e-5));
}

/* ************************************************************************* */
TEST( NonlinearConstraint2, binary_scalar_linearize ) {
	// create a constraint
	size_t p = 1;
	NonlinearConstraint2<VectorConfig> c1(
			"x", *test2::grad_g1,
			"y", *test2::grad_g2,
			*test2::g_func, p, "L_xy");

	// get a configuration to use for finding the error
	VectorConfig realconfig;
	realconfig.insert("x", Vector_(1, 1.0));
	realconfig.insert("y", Vector_(1, 2.0));

	// get a configuration of Lagrange multipliers
	VectorConfig lagrangeConfig;
	lagrangeConfig.insert("L_xy", Vector_(1, 3.0));

	// linearize the system
	GaussianFactor::shared_ptr actFactor, actConstraint;
	boost::tie(actFactor, actConstraint) = c1.linearize(realconfig, lagrangeConfig);

	// verify
	GaussianFactor expFactor("x", Matrix_(1,1, 6.0),
							 "y", Matrix_(1,1, -3.0),
							 "L_xy", eye(1), zero(1), 1.0);
	GaussianFactor expConstraint("x", Matrix_(1,1, 2.0),
								 "y", Matrix_(1,1, -1.0),
								 Vector_(1, 6.0), 0.0);
	CHECK(assert_equal(*actFactor, expFactor));
	CHECK(assert_equal(*actConstraint, expConstraint));
}

/* ************************************************************************* */
TEST( NonlinearConstraint2, binary_scalar_equal ) {
	NonlinearConstraint2<VectorConfig>
		c1("x", *test2::grad_g1, "y", *test2::grad_g2,*test2::g_func, 1, "L_xy"),
		c2("x", *test2::grad_g1, "y", *test2::grad_g2,*test2::g_func, 1, "L_xy"),
		c3("y", *test2::grad_g1, "x", *test2::grad_g2,*test2::g_func, 1, "L_xy"),
		c4("x", *test2::grad_g1, "z", *test2::grad_g2,*test2::g_func, 3, "L_xy");

	CHECK(assert_equal(c1, c2));
	CHECK(assert_equal(c2, c1));
	CHECK(!c1.equals(c3));
	CHECK(!c1.equals(c4));
}

/* ************************************************************************* */
// Inequality tests
/* ************************************************************************* */
namespace inequality_unary {
/** p = 1, gradG(x) = 2*x */
Matrix grad_g(const VectorConfig& config, const list<string>& keys) {
	double x = config[keys.front()](0);
	return Matrix_(1,1, 2*x);
}

/** p = 1, g(x) x^2 - 5 > 0 */
Vector g_func(const VectorConfig& config, const list<string>& keys) {
	double x = config[keys.front()](0);
	double g = x*x-5;
	return Vector_(1, g); // return the actual cost
}
} // \namespace test1

/* ************************************************************************* */
TEST( NonlinearConstraint1, unary_inequality ) {
	size_t p = 1;
	NonlinearConstraint1<VectorConfig> c1("x", *inequality_unary::grad_g,
										  *inequality_unary::g_func, p, "L_x1",
										  false); // inequality constraint

	// get configurations to use for evaluation
	VectorConfig config1, config2;
	config1.insert("x", Vector_(1, 10.0)); // should be inactive
	config2.insert("x", Vector_(1, 1.0)); // should have nonzero error

	// check error
	CHECK(!c1.active(config1));
	Vector actError2 = c1.error_vector(config2);
	CHECK(assert_equal(actError2, Vector_(1, -4.0, 1e-9)));
	CHECK(c1.active(config2));
}

/* ************************************************************************* */
TEST( NonlinearConstraint1, unary_inequality_linearize ) {
	size_t p = 1;
	NonlinearConstraint1<VectorConfig> c1("x", *inequality_unary::grad_g,
										  *inequality_unary::g_func, p, "L_x",
										  false); // inequality constraint

	// get configurations to use for linearization
	VectorConfig config1, config2;
	config1.insert("x", Vector_(1, 10.0)); // should have zero error
	config2.insert("x", Vector_(1, 1.0)); // should have nonzero error

	// get a configuration of Lagrange multipliers
	VectorConfig lagrangeConfig;
	lagrangeConfig.insert("L_x", Vector_(1, 3.0));

	// linearize for inactive constraint
	GaussianFactor::shared_ptr actFactor1, actConstraint1;
	boost::tie(actFactor1, actConstraint1) = c1.linearize(config1, lagrangeConfig);

	// check if the factor is active
	CHECK(!c1.active(config1));

	// linearize for active constraint
	GaussianFactor::shared_ptr actFactor2, actConstraint2;
	boost::tie(actFactor2, actConstraint2) = c1.linearize(config2, lagrangeConfig);
	CHECK(c1.active(config2));

	// verify
	GaussianFactor expFactor("x", Matrix_(1,1, 6.0), "L_x", eye(1), zero(1), 1.0);
	GaussianFactor expConstraint("x", Matrix_(1,1, 2.0), Vector_(1, 4.0), 0.0);
	CHECK(assert_equal(*actFactor2, expFactor));
	CHECK(assert_equal(*actConstraint2, expConstraint));
}

/* ************************************************************************* */
// Binding arbitrary functions
/* ************************************************************************* */
namespace unary_binding_functions {
/** p = 1, gradG(x) = 2*x */
Matrix grad_g(double coeff, const VectorConfig& config, const list<string>& keys) {
	double x = config[keys.front()](0);
	return Matrix_(1,1, coeff*x);
}

/** p = 1, g(x) x^2 - r > 0 */
Vector g_func(double r, const VectorConfig& config, const list<string>& keys) {
	double x = config[keys.front()](0);
	double g = x*x-r;
	return Vector_(1, g); // return the actual cost
}
} // \namespace unary_binding_functions

/* ************************************************************************* */
TEST( NonlinearConstraint1, unary_binding ) {
	size_t p = 1;
	double coeff = 2;
	double radius = 5;
	NonlinearConstraint1<VectorConfig> c1("x",
										  boost::bind(unary_binding_functions::grad_g, coeff, _1, _2),
										  boost::bind(unary_binding_functions::g_func, radius, _1, _2),
										  p, "L_x1",
										  false); // inequality constraint

	// get configurations to use for evaluation
	VectorConfig config1, config2;
	config1.insert("x", Vector_(1, 10.0)); // should have zero error
	config2.insert("x", Vector_(1, 1.0)); // should have nonzero error

	// check error
	CHECK(!c1.active(config1));
	Vector actError2 = c1.error_vector(config2);
	CHECK(assert_equal(actError2, Vector_(1, -4.0, 1e-9)));
	CHECK(c1.active(config2));
}

namespace binary_binding_functions {
/** gradient for x, gradG(x,y) in x: 2x*/
Matrix grad_g1(double c, const VectorConfig& config, const list<string>& keys) {
	double x = config[keys.front()](0);
	return Matrix_(1,1, c*x);
}

/** gradient for y, gradG(x,y) in y: -1 */
Matrix grad_g2(double c, const VectorConfig& config, const list<string>& keys) {
	double x = config[keys.back()](0);
	return Matrix_(1,1, -1.0*c);
}

/** p = 1, g(x) = x^2-5 -y = 0 */
Vector g_func(double r, const VectorConfig& config, const list<string>& keys) {
	double x = config[keys.front()](0);
	double y = config[keys.back()](0);
	return Vector_(1, x*x-r-y);
}
} // \namespace test2

/* ************************************************************************* */
TEST( NonlinearConstraint2, binary_binding ) {
	// construct a constraint on x and y
	// the lagrange multipliers will be expected on L_xy
	// and there is only one multiplier
	size_t p = 1;
	double a = 2.0;
	double b = 1.0;
	double r = 5.0;
	NonlinearConstraint2<VectorConfig> c1(
			"x", boost::bind(binary_binding_functions::grad_g1, a, _1, _2),
			"y", boost::bind(binary_binding_functions::grad_g2, b, _1, _2),
			boost::bind(binary_binding_functions::g_func, r, _1, _2), p, "L_xy");

	// get a configuration to use for finding the error
	VectorConfig config;
	config.insert("x", Vector_(1, 1.0));
	config.insert("y", Vector_(1, 2.0));

	// calculate the error
	Vector actual = c1.error_vector(config);
	Vector expected = Vector_(1.0, -6.0);
	CHECK(assert_equal(actual, expected, 1e-5));
}

/* ************************************************************************* */
int main() { TestResult tr; return TestRegistry::runAllTests(tr); }
/* ************************************************************************* */