/* static */ bool ocraWbiConversions::wbiToOcraSegJacobian(const Eigen::MatrixXd &jac, Eigen::MatrixXd &J)
{
int dof = DIM_T + DIM_R;
if(dof != jac.rows() || dof != J.rows()||jac.cols() != J.cols())
{
std::cout<<"ERROR: Input and output matrices dimensions should be the same" <<std::endl;
return false;
}
// FOR FULL n+6 Jacobian ONLY
Eigen::MatrixXd jac5,jac6;
Eigen::Matrix3d jac1,jac2,jac3,jac4;
jac5.resize(3,jac.cols()-6);
jac6.resize(3,jac.cols()-6);
jac1 = jac.topLeftCorner(3,3);
jac2 = jac.block<3,3>(0,3);
jac3 = jac.bottomLeftCorner(3,3);
jac4 = jac.block<3,3>(3,3);
jac5 = jac.topRightCorner(3,jac.cols()-6);
jac6 = jac.bottomRightCorner(3,jac.cols()-6);
J.topLeftCorner(3,3) = jac4;
J.block<3,3>(0,3) = jac3;
J.bottomLeftCorner(3,3) = jac2;
J.block<3,3>(3,3) = jac1;
J.topRightCorner(3,jac.cols()-6) = jac6;
J.bottomRightCorner(3,jac.cols()-6) = jac5;
return true;
}
TEST(SparseMatrixFunctionTests, testSchurComplement1)
{
try {
using namespace aslam::backend;
typedef sparse_block_matrix::SparseBlockMatrix<Eigen::MatrixXd> SparseBlockMatrix;
// Create the sparse Hessian. Two dense blocks. Three sparse.
int structure[5] = {2, 2, 3, 3, 3};
std::partial_sum(structure, structure + 5, structure);
int marginalizedStartingBlock = 2;
int marginalizedStartingIndex = structure[ marginalizedStartingBlock - 1 ];
double lambda = 1;
SparseBlockMatrix H(structure, structure, 5, 5, true);
Eigen::VectorXd e(H.rows());
e.setRandom();
Eigen::VectorXd b(H.rowBaseOfBlock(marginalizedStartingBlock));
b.setZero();
boost::shared_ptr<SparseBlockMatrix> A(H.slice(0, marginalizedStartingBlock, 0, marginalizedStartingBlock, true));
ASSERT_EQ(marginalizedStartingBlock, A->bRows());
ASSERT_EQ(marginalizedStartingBlock, A->bCols());
A->clear(false);
std::vector<Eigen::MatrixXd> invVi;
invVi.resize(H.bRows() - marginalizedStartingBlock);
// Fill in H.
*H.block(0, 0, true) = sm::eigen::randomCovariance<2>() * 100;
*H.block(1, 1, true) = sm::eigen::randomCovariance<2>() * 100;
*H.block(2, 2, true) = sm::eigen::randomCovariance<3>() * 100;
*H.block(3, 3, true) = sm::eigen::randomCovariance<3>() * 100;
*H.block(4, 4, true) = sm::eigen::randomCovariance<3>() * 100;
// Start with two off diagonals.
H.block(0, 4, true)->setRandom();
H.block(0, 4, true)->array() *= 100;
H.block(1, 4, true)->setRandom();
H.block(1, 4, true)->array() *= 100;
//std::cout << "H:\n" << H << std::endl;
applySchurComplement(H,
e,
lambda,
marginalizedStartingBlock,
true,
*A,
invVi,
b);
Eigen::MatrixXd Hd = H.toDense();
Eigen::MatrixXd U = Hd.topLeftCorner(marginalizedStartingIndex, marginalizedStartingIndex);
Eigen::MatrixXd V = Hd.bottomRightCorner(H.rows() - marginalizedStartingIndex, H.rows() - marginalizedStartingIndex);
Eigen::MatrixXd W = Hd.topRightCorner(marginalizedStartingIndex, H.rows() - marginalizedStartingIndex);
V.diagonal().array() += lambda;
Eigen::MatrixXd AA = U - W * V.inverse() * W.transpose();
AA.diagonal().array() += lambda;
Eigen::VectorXd epsSparse = e.tail(e.size() - marginalizedStartingIndex);
Eigen::VectorXd epsDense = e.head(marginalizedStartingIndex);
Eigen::VectorXd bb = epsDense - W * V.inverse() * epsSparse;
{
SCOPED_TRACE("");
Eigen::MatrixXd Asa = A->toDense().selfadjointView<Eigen::Upper>();
sm::eigen::assertNear(Asa, AA, 1e-12, SM_SOURCE_FILE_POS, "Testing the lhs schur complement");
}
{
SCOPED_TRACE("");
sm::eigen::assertNear(b, bb, 1e-12, SM_SOURCE_FILE_POS, "Testing the rhs schur complement");
}
// Let's try it again to make sure stuff gets initialized correctly.
applySchurComplement(H,
e,
lambda,
marginalizedStartingBlock,
true,
*A,
invVi,
b);
{
SCOPED_TRACE("");
Eigen::MatrixXd Asa = A->toDense().selfadjointView<Eigen::Upper>();
sm::eigen::assertNear(Asa, AA, 1e-12, SM_SOURCE_FILE_POS, "Testing the lhs schur complement");
}
{
SCOPED_TRACE("");
sm::eigen::assertNear(b, bb, 1e-12, SM_SOURCE_FILE_POS, "Testing the rhs schur complement");
}
// Now we check the update function.
Eigen::VectorXd dx(marginalizedStartingIndex);
dx.setRandom();
Eigen::VectorXd denseDs = V.inverse() * (epsSparse - W.transpose() * dx);
for (int i = 0; i < H.bRows() - marginalizedStartingBlock; ++i) {
Eigen::VectorXd outDsi;
buildDsi(i, H, e, marginalizedStartingBlock, invVi[i], dx, outDsi);
Eigen::VectorXd dsi = denseDs.segment(H.rowBaseOfBlock(i + marginalizedStartingBlock) - marginalizedStartingIndex, H.rowsOfBlock(i + marginalizedStartingBlock));
sm::eigen::assertNear(outDsi, dsi, 1e-12, SM_SOURCE_FILE_POS, "Checking the update step calculation");
}
} catch (const std::exception& e) {
FAIL() << "Exception: " << e.what();
}
}