/* ************************************************************************* */
TEST(GaussianFactorGraph, multiplyHessianAdd2) {
GaussianFactorGraph gfg = createGaussianFactorGraphWithHessianFactor();
// brute force
Matrix AtA;
Vector eta;
boost::tie(AtA, eta) = gfg.hessian();
Vector X(6);
X << 1, 2, 3, 4, 5, 6;
Vector Y(6);
Y << -450, -450, 300, 400, 2950, 3450;
EXPECT(assert_equal(Y, AtA * X));
VectorValues x = map_list_of<Key, Vector>(0, Vector2(1, 2))(1, Vector2(3, 4))(2, Vector2(5, 6));
VectorValues expected;
expected.insert(0, Vector2(-450, -450));
expected.insert(1, Vector2(300, 400));
expected.insert(2, Vector2(2950, 3450));
VectorValues actual;
gfg.multiplyHessianAdd(1.0, x, actual);
EXPECT(assert_equal(expected, actual));
// now, do it with non-zero y
gfg.multiplyHessianAdd(1.0, x, actual);
EXPECT(assert_equal(2 * expected, actual));
}
TEST(LPInitSolver, infinite_loop_multi_var) {
LP initchecker;
Key X = symbol('X', 1);
Key Y = symbol('Y', 1);
Key Z = symbol('Z', 1);
initchecker.cost = LinearCost(Z, kOne); // min alpha
initchecker.inequalities.push_back(
LinearInequality(X, -2.0 * kOne, Y, -1.0 * kOne, Z, -1.0 * kOne, -2,
1)); //-2x-y-alpha <= -2
initchecker.inequalities.push_back(
LinearInequality(X, -1.0 * kOne, Y, 2.0 * kOne, Z, -1.0 * kOne, 6,
2)); // -x+2y-alpha <= 6
initchecker.inequalities.push_back(LinearInequality(
X, -1.0 * kOne, Z, -1.0 * kOne, 0, 3)); // -x - alpha <= 0
initchecker.inequalities.push_back(LinearInequality(
X, 1.0 * kOne, Z, -1.0 * kOne, 20, 4)); // x - alpha <= 20
initchecker.inequalities.push_back(LinearInequality(
Y, -1.0 * kOne, Z, -1.0 * kOne, 0, 5)); // -y - alpha <= 0
LPSolver solver(initchecker);
VectorValues starter;
starter.insert(X, kZero);
starter.insert(Y, kZero);
starter.insert(Z, Vector::Constant(1, 2.0));
VectorValues results, duals;
boost::tie(results, duals) = solver.optimize(starter);
VectorValues expected;
expected.insert(X, Vector::Constant(1, 13.5));
expected.insert(Y, Vector::Constant(1, 6.5));
expected.insert(Z, Vector::Constant(1, -6.5));
CHECK(assert_equal(results, expected, 1e-7));
}
/* ************************************************************************* */
TEST(VectorValues, resizeLike) {
// insert, with out-of-order indices
VectorValues original;
original.insert(0, Vector_(1, 1.0));
original.insert(1, Vector_(2, 2.0, 3.0));
original.insert(5, Vector_(2, 6.0, 7.0));
original.insert(2, Vector_(2, 4.0, 5.0));
VectorValues actual(10, 3);
actual.resizeLike(original);
// Check dimensions
LONGS_EQUAL(6, actual.size());
LONGS_EQUAL(7, actual.dim());
LONGS_EQUAL(1, actual.dim(0));
LONGS_EQUAL(2, actual.dim(1));
LONGS_EQUAL(2, actual.dim(2));
LONGS_EQUAL(2, actual.dim(5));
// Logic
EXPECT(actual.exists(0));
EXPECT(actual.exists(1));
EXPECT(actual.exists(2));
EXPECT(!actual.exists(3));
EXPECT(!actual.exists(4));
EXPECT(actual.exists(5));
EXPECT(!actual.exists(6));
// Check exceptions
CHECK_EXCEPTION(actual.insert(1, Vector()), invalid_argument);
}
/* ************************************************************************* */
TEST(GaussianFactorGraph, gradientAtZero) {
GaussianFactorGraph gfg = createGaussianFactorGraphWithHessianFactor();
VectorValues expected;
VectorValues actual = gfg.gradientAtZero();
expected.insert(0, Vector2(-25, 17.5));
expected.insert(1, Vector2(5, -13.5));
expected.insert(2, Vector2(29, 4));
EXPECT(assert_equal(expected, actual));
}
/* ************************************************************************* */
TEST(GaussianFactorGraph, matrices) {
// Create factor graph:
// x1 x2 x3 x4 x5 b
// 1 2 3 0 0 4
// 5 6 7 0 0 8
// 9 10 0 11 12 13
// 0 0 0 14 15 16
Matrix A00 = (Matrix(2, 3) << 1, 2, 3, 5, 6, 7).finished();
Matrix A10 = (Matrix(2, 3) << 9, 10, 0, 0, 0, 0).finished();
Matrix A11 = (Matrix(2, 2) << 11, 12, 14, 15).finished();
GaussianFactorGraph gfg;
SharedDiagonal model = noiseModel::Unit::Create(2);
gfg.add(0, A00, Vector2(4., 8.), model);
gfg.add(0, A10, 1, A11, Vector2(13., 16.), model);
Matrix Ab(4, 6);
Ab << 1, 2, 3, 0, 0, 4, 5, 6, 7, 0, 0, 8, 9, 10, 0, 11, 12, 13, 0, 0, 0, 14, 15, 16;
// augmented versions
EXPECT(assert_equal(Ab, gfg.augmentedJacobian()));
EXPECT(assert_equal(Ab.transpose() * Ab, gfg.augmentedHessian()));
// jacobian
Matrix A = Ab.leftCols(Ab.cols() - 1);
Vector b = Ab.col(Ab.cols() - 1);
Matrix actualA;
Vector actualb;
boost::tie(actualA, actualb) = gfg.jacobian();
EXPECT(assert_equal(A, actualA));
EXPECT(assert_equal(b, actualb));
// hessian
Matrix L = A.transpose() * A;
Vector eta = A.transpose() * b;
Matrix actualL;
Vector actualeta;
boost::tie(actualL, actualeta) = gfg.hessian();
EXPECT(assert_equal(L, actualL));
EXPECT(assert_equal(eta, actualeta));
// hessianBlockDiagonal
VectorValues expectLdiagonal; // Make explicit that diagonal is sum-squares of columns
expectLdiagonal.insert(0, Vector3(1 + 25 + 81, 4 + 36 + 100, 9 + 49));
expectLdiagonal.insert(1, Vector2(121 + 196, 144 + 225));
EXPECT(assert_equal(expectLdiagonal, gfg.hessianDiagonal()));
// hessianBlockDiagonal
map<Key, Matrix> actualBD = gfg.hessianBlockDiagonal();
LONGS_EQUAL(2, actualBD.size());
EXPECT(assert_equal(A00.transpose() * A00 + A10.transpose() * A10, actualBD[0]));
EXPECT(assert_equal(A11.transpose() * A11, actualBD[1]));
}
/* ************************************************************************* */
TEST(GaussianFactorGraph, hessianDiagonal) {
GaussianFactorGraph gfg = createGaussianFactorGraphWithHessianFactor();
VectorValues expected;
Matrix infoMatrix = gfg.hessian().first;
Vector d = infoMatrix.diagonal();
VectorValues actual = gfg.hessianDiagonal();
expected.insert(0, d.segment<2>(0));
expected.insert(1, d.segment<2>(2));
expected.insert(2, d.segment<2>(4));
EXPECT(assert_equal(expected, actual));
}
/* ************************************************************************* */
TEST(GaussianFactorGraph, transposeMultiplication) {
GaussianFactorGraph A = createSimpleGaussianFactorGraph();
Errors e;
e += Vector2(0.0, 0.0), Vector2(15.0, 0.0), Vector2(0.0, -5.0), Vector2(-7.5, -5.0);
VectorValues expected;
expected.insert(1, Vector2(-37.5, -50.0));
expected.insert(2, Vector2(-150.0, 25.0));
expected.insert(0, Vector2(187.5, 25.0));
VectorValues actual = A.transposeMultiply(e);
EXPECT(assert_equal(expected, actual));
}
/* ************************************************************************* */
VectorValues GaussianConditional::solveOtherRHS(
const VectorValues& parents, const VectorValues& rhs) const
{
// Concatenate all vector values that correspond to parent variables
Vector xS = parents.vector(FastVector<Key>(beginParents(), endParents()));
// Instead of updating getb(), update the right-hand-side from the given rhs
const Vector rhsR = rhs.vector(FastVector<Key>(beginFrontals(), endFrontals()));
xS = rhsR - get_S() * xS;
// Solve Matrix
Vector soln = get_R().triangularView<Eigen::Upper>().solve(xS);
// Scale by sigmas
if(model_)
soln.array() *= model_->sigmas().array();
// Insert solution into a VectorValues
VectorValues result;
DenseIndex vectorPosition = 0;
for(const_iterator frontal = beginFrontals(); frontal != endFrontals(); ++frontal) {
result.insert(*frontal, soln.segment(vectorPosition, getDim(frontal)));
vectorPosition += getDim(frontal);
}
return result;
}
VectorValues KeyInfo::x0() const {
VectorValues result;
BOOST_FOREACH ( const KeyInfo::value_type &item, *this ) {
result.insert(item.first, Vector::Zero(item.second.dim()));
}
return result;
}
/* ************************************************************************* */
VectorValues GaussianConditional::solve(const VectorValues& x) const
{
// Concatenate all vector values that correspond to parent variables
const Vector xS = x.vector(FastVector<Key>(beginParents(), endParents()));
// Update right-hand-side
const Vector rhs = get_d() - get_S() * xS;
// Solve matrix
const Vector solution = get_R().triangularView<Eigen::Upper>().solve(rhs);
// Check for indeterminant solution
if (solution.hasNaN()) {
throw IndeterminantLinearSystemException(keys().front());
}
// Insert solution into a VectorValues
VectorValues result;
DenseIndex vectorPosition = 0;
for (const_iterator frontal = beginFrontals(); frontal != endFrontals(); ++frontal) {
result.insert(*frontal, solution.segment(vectorPosition, getDim(frontal)));
vectorPosition += getDim(frontal);
}
return result;
}
/* ************************************************************************* */
TEST( ISAM, iSAM_smoother )
{
Ordering ordering;
for (int t = 1; t <= 7; t++) ordering += X(t);
// Create smoother with 7 nodes
GaussianFactorGraph smoother = createSmoother(7);
// run iSAM for every factor
GaussianISAM actual;
for(boost::shared_ptr<GaussianFactor> factor: smoother) {
GaussianFactorGraph factorGraph;
factorGraph.push_back(factor);
actual.update(factorGraph);
}
// Create expected Bayes Tree by solving smoother with "natural" ordering
GaussianBayesTree expected = *smoother.eliminateMultifrontal(ordering);
// Verify sigmas in the bayes tree
for(const GaussianBayesTree::sharedClique& clique: expected.nodes() | br::map_values) {
GaussianConditional::shared_ptr conditional = clique->conditional();
EXPECT(!conditional->get_model());
}
// Check whether BayesTree is correct
EXPECT(assert_equal(GaussianFactorGraph(expected).augmentedHessian(), GaussianFactorGraph(actual).augmentedHessian()));
// obtain solution
VectorValues e; // expected solution
for (int t = 1; t <= 7; t++) e.insert(X(t), Vector::Zero(2));
VectorValues optimized = actual.optimize(); // actual solution
EXPECT(assert_equal(e, optimized));
}
/* ************************************************************************* */
TEST(HessianFactor, CombineAndEliminate2) {
Matrix A01 = I_3x3;
Vector3 b0(1.5, 1.5, 1.5);
Vector3 s0(1.6, 1.6, 1.6);
Matrix A10 = 2.0 * I_3x3;
Matrix A11 = -2.0 * I_3x3;
Vector3 b1(2.5, 2.5, 2.5);
Vector3 s1(2.6, 2.6, 2.6);
Matrix A21 = 3.0 * I_3x3;
Vector3 b2(3.5, 3.5, 3.5);
Vector3 s2(3.6, 3.6, 3.6);
GaussianFactorGraph gfg;
gfg.add(1, A01, b0, noiseModel::Diagonal::Sigmas(s0, true));
gfg.add(0, A10, 1, A11, b1, noiseModel::Diagonal::Sigmas(s1, true));
gfg.add(1, A21, b2, noiseModel::Diagonal::Sigmas(s2, true));
Matrix93 A0, A1;
A0 << A10, Z_3x3, Z_3x3;
A1 << A11, A01, A21;
Vector9 b, sigmas;
b << b1, b0, b2;
sigmas << s1, s0, s2;
// create a full, uneliminated version of the factor
JacobianFactor jacobian(0, A0, 1, A1, b,
noiseModel::Diagonal::Sigmas(sigmas, true));
// Make sure combining works
HessianFactor hessian(gfg);
EXPECT(assert_equal(HessianFactor(jacobian), hessian, 1e-6));
EXPECT(
assert_equal(jacobian.augmentedInformation(),
hessian.augmentedInformation(), 1e-9));
// perform elimination on jacobian
Ordering ordering = list_of(0);
GaussianConditional::shared_ptr expectedConditional;
JacobianFactor::shared_ptr expectedFactor;
boost::tie(expectedConditional, expectedFactor) = //
jacobian.eliminate(ordering);
// Eliminate
GaussianConditional::shared_ptr actualConditional;
HessianFactor::shared_ptr actualHessian;
boost::tie(actualConditional, actualHessian) = //
EliminateCholesky(gfg, ordering);
EXPECT(assert_equal(*expectedConditional, *actualConditional, 1e-6));
VectorValues v;
v.insert(1, Vector3(1, 2, 3));
EXPECT_DOUBLES_EQUAL(expectedFactor->error(v), actualHessian->error(v), 1e-9);
EXPECT(
assert_equal(expectedFactor->augmentedInformation(),
actualHessian->augmentedInformation(), 1e-9));
EXPECT(assert_equal(HessianFactor(*expectedFactor), *actualHessian, 1e-6));
}
/* ************************************************************************* */
TEST(LPSolver, LinearCost) {
LinearCost cost(1, Vector3(2., 4., 6.));
VectorValues x;
x.insert(1, Vector3(1., 3., 5.));
double error = cost.error(x);
double expectedError = 44.0;
DOUBLES_EQUAL(expectedError, error, 1e-100);
}
/* ************************************************************************* */
TEST(GaussianFactorGraph, multiplyHessianAdd) {
GaussianFactorGraph gfg = createSimpleGaussianFactorGraph();
VectorValues x = map_list_of<Key, Vector>(0, Vector2(1, 2))(1, Vector2(3, 4))(2, Vector2(5, 6));
VectorValues expected;
expected.insert(0, Vector2(-450, -450));
expected.insert(1, Vector2(0, 0));
expected.insert(2, Vector2(950, 1050));
VectorValues actual;
gfg.multiplyHessianAdd(1.0, x, actual);
EXPECT(assert_equal(expected, actual));
// now, do it with non-zero y
gfg.multiplyHessianAdd(1.0, x, actual);
EXPECT(assert_equal(2 * expected, actual));
}
/* ************************************************************************* */
TEST(LPSolver, simpleTest1) {
LP lp = simpleLP1();
LPSolver lpSolver(lp);
VectorValues init;
init.insert(1, Vector::Zero(2));
VectorValues x1 =
lpSolver.buildWorkingGraph(InequalityFactorGraph(), init).optimize();
VectorValues expected_x1;
expected_x1.insert(1, Vector::Ones(2));
CHECK(assert_equal(expected_x1, x1, 1e-10));
VectorValues result, duals;
boost::tie(result, duals) = lpSolver.optimize(init);
VectorValues expectedResult;
expectedResult.insert(1, Vector2(8. / 3., 2. / 3.));
CHECK(assert_equal(expectedResult, result, 1e-10));
}
/* ************************************************************************* */
TEST(VectorValues, assignment) {
VectorValues actual;
{
// insert, with out-of-order indices
VectorValues original;
original.insert(0, Vector_(1, 1.0));
original.insert(1, Vector_(2, 2.0, 3.0));
original.insert(5, Vector_(2, 6.0, 7.0));
original.insert(2, Vector_(2, 4.0, 5.0));
actual = original;
}
// Check dimensions
LONGS_EQUAL(6, actual.size());
LONGS_EQUAL(7, actual.dim());
LONGS_EQUAL(1, actual.dim(0));
LONGS_EQUAL(2, actual.dim(1));
LONGS_EQUAL(2, actual.dim(2));
LONGS_EQUAL(2, actual.dim(5));
// Logic
EXPECT(actual.exists(0));
EXPECT(actual.exists(1));
EXPECT(actual.exists(2));
EXPECT(!actual.exists(3));
EXPECT(!actual.exists(4));
EXPECT(actual.exists(5));
EXPECT(!actual.exists(6));
// Check values
EXPECT(assert_equal(Vector_(1, 1.0), actual[0]));
EXPECT(assert_equal(Vector_(2, 2.0, 3.0), actual[1]));
EXPECT(assert_equal(Vector_(2, 4.0, 5.0), actual[2]));
EXPECT(assert_equal(Vector_(2, 6.0, 7.0), actual[5]));
EXPECT(assert_equal(Vector_(7, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0), actual.vector()));
// Check exceptions
CHECK_EXCEPTION(actual.insert(1, Vector()), invalid_argument);
}
/* ************************************************************************* */
VectorValues Values::localCoordinates(const Values& cp) const {
if(this->size() != cp.size())
throw DynamicValuesMismatched();
VectorValues result;
for(const_iterator it1=this->begin(), it2=cp.begin(); it1!=this->end(); ++it1, ++it2) {
if(it1->key != it2->key)
throw DynamicValuesMismatched(); // If keys do not match
// Will throw a dynamic_cast exception if types do not match
// NOTE: this is separate from localCoordinates(cp, ordering, result) due to at() vs. insert
result.insert(it1->key, it1->value.localCoordinates_(it2->value));
}
return result;
}
TEST(LPInitSolver, infinite_loop_single_var) {
LP initchecker;
initchecker.cost = LinearCost(1, Vector3(0, 0, 1)); // min alpha
initchecker.inequalities.push_back(
LinearInequality(1, Vector3(-2, -1, -1), -2, 1)); //-2x-y-alpha <= -2
initchecker.inequalities.push_back(
LinearInequality(1, Vector3(-1, 2, -1), 6, 2)); // -x+2y-alpha <= 6
initchecker.inequalities.push_back(
LinearInequality(1, Vector3(-1, 0, -1), 0, 3)); // -x - alpha <= 0
initchecker.inequalities.push_back(
LinearInequality(1, Vector3(1, 0, -1), 20, 4)); // x - alpha <= 20
initchecker.inequalities.push_back(
LinearInequality(1, Vector3(0, -1, -1), 0, 5)); // -y - alpha <= 0
LPSolver solver(initchecker);
VectorValues starter;
starter.insert(1, Vector3(0, 0, 2));
VectorValues results, duals;
boost::tie(results, duals) = solver.optimize(starter);
VectorValues expected;
expected.insert(1, Vector3(13.5, 6.5, -6.5));
CHECK(assert_equal(results, expected, 1e-7));
}
/* ************************************************************************* */
TEST(VectorValues, append) {
// insert
VectorValues actual;
actual.insert(0, Vector_(1, 1.0));
actual.insert(1, Vector_(2, 2.0, 3.0));
actual.insert(2, Vector_(2, 4.0, 5.0));
// append
vector<size_t> dims(2);
dims[0] = 3;
dims[1] = 5;
actual.append(dims);
// Check dimensions
LONGS_EQUAL(5, actual.size());
LONGS_EQUAL(13, actual.dim());
LONGS_EQUAL(1, actual.dim(0));
LONGS_EQUAL(2, actual.dim(1));
LONGS_EQUAL(2, actual.dim(2));
LONGS_EQUAL(3, actual.dim(3));
LONGS_EQUAL(5, actual.dim(4));
// Logic
EXPECT(actual.exists(0));
EXPECT(actual.exists(1));
EXPECT(actual.exists(2));
EXPECT(actual.exists(3));
EXPECT(actual.exists(4));
EXPECT(!actual.exists(5));
// Check values
EXPECT(assert_equal(Vector_(1, 1.0), actual[0]));
EXPECT(assert_equal(Vector_(2, 2.0, 3.0), actual[1]));
EXPECT(assert_equal(Vector_(2, 4.0, 5.0), actual[2]));
// Check exceptions
CHECK_EXCEPTION(actual.insert(3, Vector()), invalid_argument);
}
/* ************************************************************************* */
TEST(HessianFactor, hessianDiagonal)
{
Matrix G11 = (Matrix(1, 1) << 1);
Matrix G12 = (Matrix(1, 2) << 0, 0);
Matrix G22 = (Matrix(2, 2) << 1, 0, 0, 1);
Vector g1 = (Vector(1) << -7);
Vector g2 = (Vector(2) << -8, -9);
double f = 194;
HessianFactor factor(0, 1, G11, G12, g1, G22, g2, f);
// hessianDiagonal
VectorValues expected;
expected.insert(0, (Vector(1) << 1));
expected.insert(1, (Vector(2) << 1,1));
EXPECT(assert_equal(expected, factor.hessianDiagonal()));
// hessianBlockDiagonal
map<Key,Matrix> actualBD = factor.hessianBlockDiagonal();
LONGS_EQUAL(2,actualBD.size());
EXPECT(assert_equal(G11,actualBD[0]));
EXPECT(assert_equal(G22,actualBD[1]));
}
/* ************************************************************************* */
TEST (Serialization, linear_factors) {
VectorValues values;
values.insert(0, (Vector(1) << 1.0));
values.insert(1, (Vector(2) << 2.0,3.0));
values.insert(2, (Vector(2) << 4.0,5.0));
EXPECT(equalsObj<VectorValues>(values));
EXPECT(equalsXML<VectorValues>(values));
EXPECT(equalsBinary<VectorValues>(values));
Key i1 = 4, i2 = 7;
Matrix A1 = eye(3), A2 = -1.0 * eye(3);
Vector b = ones(3);
SharedDiagonal model = noiseModel::Diagonal::Sigmas((Vector(3) << 1.0, 2.0, 3.0));
JacobianFactor jacobianfactor(i1, A1, i2, A2, b, model);
EXPECT(equalsObj(jacobianfactor));
EXPECT(equalsXML(jacobianfactor));
EXPECT(equalsBinary(jacobianfactor));
HessianFactor hessianfactor(jacobianfactor);
EXPECT(equalsObj(hessianfactor));
EXPECT(equalsXML(hessianfactor));
EXPECT(equalsBinary(hessianfactor));
}
/* ************************************************************************* */
TEST(HessianFactor, CombineAndEliminate1) {
Matrix3 A01 = 3.0 * I_3x3;
Vector3 b0(1, 0, 0);
Matrix3 A21 = 4.0 * I_3x3;
Vector3 b2 = Vector3::Zero();
GaussianFactorGraph gfg;
gfg.add(1, A01, b0);
gfg.add(1, A21, b2);
Matrix63 A1;
A1 << A01, A21;
Vector6 b;
b << b0, b2;
// create a full, uneliminated version of the factor
JacobianFactor jacobian(1, A1, b);
// Make sure combining works
HessianFactor hessian(gfg);
VectorValues v;
v.insert(1, Vector3(1, 0, 0));
EXPECT_DOUBLES_EQUAL(jacobian.error(v), hessian.error(v), 1e-9);
EXPECT(assert_equal(HessianFactor(jacobian), hessian, 1e-6));
EXPECT(assert_equal(25.0 * I_3x3, hessian.information(), 1e-9));
EXPECT(
assert_equal(jacobian.augmentedInformation(),
hessian.augmentedInformation(), 1e-9));
// perform elimination on jacobian
Ordering ordering = list_of(1);
GaussianConditional::shared_ptr expectedConditional;
JacobianFactor::shared_ptr expectedFactor;
boost::tie(expectedConditional, expectedFactor) = //
jacobian.eliminate(ordering);
// Eliminate
GaussianConditional::shared_ptr actualConditional;
HessianFactor::shared_ptr actualHessian;
boost::tie(actualConditional, actualHessian) = //
EliminateCholesky(gfg, ordering);
EXPECT(assert_equal(*expectedConditional, *actualConditional, 1e-6));
EXPECT_DOUBLES_EQUAL(expectedFactor->error(v), actualHessian->error(v), 1e-9);
EXPECT(
assert_equal(expectedFactor->augmentedInformation(),
actualHessian->augmentedInformation(), 1e-9));
EXPECT(assert_equal(HessianFactor(*expectedFactor), *actualHessian, 1e-6));
}
/* ************************************************************************* */
TEST(VectorValues, permute) {
VectorValues original;
original.insert(0, Vector_(1, 1.0));
original.insert(1, Vector_(2, 2.0, 3.0));
original.insert(2, Vector_(2, 4.0, 5.0));
original.insert(3, Vector_(2, 6.0, 7.0));
VectorValues expected;
expected.insert(0, Vector_(2, 4.0, 5.0)); // from 2
expected.insert(1, Vector_(1, 1.0)); // from 0
expected.insert(2, Vector_(2, 6.0, 7.0)); // from 3
expected.insert(3, Vector_(2, 2.0, 3.0)); // from 1
Permutation permutation(4);
permutation[0] = 2;
permutation[1] = 0;
permutation[2] = 3;
permutation[3] = 1;
VectorValues actual = original.permute(permutation);
EXPECT(assert_equal(expected, actual));
}
/* ************************************************************************* */
TEST(RegularHessianFactor, Constructors)
{
// First construct a regular JacobianFactor
// 0.5*|x0 + x1 + x3 - [1;2]|^2 = 0.5*|A*x-b|^2, with A=[I I I]
Matrix A1 = I_2x2, A2 = I_2x2, A3 = I_2x2;
Vector2 b(1,2);
vector<pair<Key, Matrix> > terms;
terms += make_pair(0, A1), make_pair(1, A2), make_pair(3, A3);
RegularJacobianFactor<2> jf(terms, b);
// Test conversion from JacobianFactor
RegularHessianFactor<2> factor(jf);
// 0.5*|A*x-b|^2 = 0.5*(Ax-b)'*(Ax-b) = 0.5*x'*A'A*x - x'*A'b + 0.5*b'*b
// Compare with comment in HessianFactor: E(x) = 0.5 x^T G x - x^T g + 0.5 f
// Hence G = I6, g A'*b = [b;b;b], and f = b'*b = 1+4 = 5
Matrix G11 = I_2x2;
Matrix G12 = I_2x2;
Matrix G13 = I_2x2;
Matrix G22 = I_2x2;
Matrix G23 = I_2x2;
Matrix G33 = I_2x2;
Vector2 g1 = b, g2 = b, g3 = b;
double f = 5;
// Test ternary constructor
RegularHessianFactor<2> factor2(0, 1, 3, G11, G12, G13, g1, G22, G23, g2, G33, g3, f);
EXPECT(assert_equal(factor,factor2));
// Test n-way constructor
vector<Key> keys; keys += 0, 1, 3;
vector<Matrix> Gs; Gs += G11, G12, G13, G22, G23, G33;
vector<Vector> gs; gs += g1, g2, g3;
RegularHessianFactor<2> factor3(keys, Gs, gs, f);
EXPECT(assert_equal(factor, factor3));
// Test constructor from Gaussian Factor Graph
GaussianFactorGraph gfg;
gfg += jf;
RegularHessianFactor<2> factor4(gfg);
EXPECT(assert_equal(factor, factor4));
GaussianFactorGraph gfg2;
gfg2 += factor;
RegularHessianFactor<2> factor5(gfg);
EXPECT(assert_equal(factor, factor5));
// Test constructor from Information matrix
Matrix info = factor.augmentedInformation();
vector<size_t> dims; dims += 2, 2, 2;
SymmetricBlockMatrix sym(dims, info, true);
RegularHessianFactor<2> factor6(keys, sym);
EXPECT(assert_equal(factor, factor6));
// multiplyHessianAdd:
{
// brute force
Matrix AtA = factor.information();
HessianFactor::const_iterator i1 = factor.begin();
HessianFactor::const_iterator i2 = i1 + 1;
Vector X(6); X << 1,2,3,4,5,6;
Vector Y(6); Y << 9, 12, 9, 12, 9, 12;
EXPECT(assert_equal(Y,AtA*X));
VectorValues x = map_list_of<Key, Vector>
(0, Vector2(1,2))
(1, Vector2(3,4))
(3, Vector2(5,6));
VectorValues expected;
expected.insert(0, Y.segment<2>(0));
expected.insert(1, Y.segment<2>(2));
expected.insert(3, Y.segment<2>(4));
// VectorValues version
double alpha = 1.0;
VectorValues actualVV;
actualVV.insert(0, Vector2::Zero());
actualVV.insert(1, Vector2::Zero());
actualVV.insert(3, Vector2::Zero());
factor.multiplyHessianAdd(alpha, x, actualVV);
EXPECT(assert_equal(expected, actualVV));
// RAW ACCESS
Vector expected_y(8); expected_y << 9, 12, 9, 12, 0, 0, 9, 12;
Vector fast_y = Vector8::Zero();
double xvalues[8] = {1,2,3,4,0,0,5,6};
factor.multiplyHessianAdd(alpha, xvalues, fast_y.data());
EXPECT(assert_equal(expected_y, fast_y));
// now, do it with non-zero y
factor.multiplyHessianAdd(alpha, xvalues, fast_y.data());
EXPECT(assert_equal(2*expected_y, fast_y));
// check some expressions
EXPECT(assert_equal(G12,factor.info(i1,i2).knownOffDiagonal()));
EXPECT(assert_equal(G22,factor.info(i2,i2).selfadjointView()));
EXPECT(assert_equal((Matrix)G12.transpose(),factor.info(i2,i1).knownOffDiagonal()));
}
}
/* ************************************************************************* */
VectorValues Values::zeroVectors() const {
VectorValues result;
BOOST_FOREACH(const ConstKeyValuePair& key_value, *this)
result.insert(key_value.key, Vector::Zero(key_value.value.dim()));
return result;
}