/* 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;
}
bool KinematicsMetrics::getManipulability(const robot_state::RobotState &state,
const robot_model::JointModelGroup *joint_model_group,
double &manipulability,
bool translation) const
{
// state.getJacobian() only works for chain groups.
if(!joint_model_group->isChain())
{
return false;
}
// Get joint limits penalty
double penalty = getJointLimitsPenalty(state, joint_model_group);
if (translation)
{
Eigen::MatrixXd jacobian = state.getJacobian(joint_model_group);
Eigen::JacobiSVD<Eigen::MatrixXd> svdsolver(jacobian.topLeftCorner(3,jacobian.cols()));
Eigen::MatrixXd singular_values = svdsolver.singularValues();
for (int i = 0; i < singular_values.rows(); ++i)
logDebug("moveit.kin_metrics: Singular value: %d %f",i,singular_values(i,0));
manipulability = penalty * singular_values.minCoeff()/singular_values.maxCoeff();
}
else
{
Eigen::MatrixXd jacobian = state.getJacobian(joint_model_group);
Eigen::JacobiSVD<Eigen::MatrixXd> svdsolver(jacobian);
Eigen::MatrixXd singular_values = svdsolver.singularValues();
for(int i=0; i < singular_values.rows(); ++i)
logDebug("moveit.kin_metrics: Singular value: %d %f",i,singular_values(i,0));
manipulability = penalty * singular_values.minCoeff()/singular_values.maxCoeff();
}
return true;
}
bool KinematicsMetrics::getManipulabilityIndex(const robot_state::RobotState &state,
const robot_model::JointModelGroup *joint_model_group,
double &manipulability_index,
bool translation) const
{
// state.getJacobian() only works for chain groups.
if(!joint_model_group->isChain())
{
return false;
}
Eigen::MatrixXd jacobian = state.getJacobian(joint_model_group);
// Get joint limits penalty
double penalty = getJointLimitsPenalty(state, joint_model_group);
if (translation)
{
Eigen::MatrixXd jacobian_2 = jacobian.topLeftCorner(3,jacobian.cols());
Eigen::MatrixXd matrix = jacobian_2*jacobian_2.transpose();
// Get manipulability index
manipulability_index = penalty * sqrt(matrix.determinant());
}
else
{
Eigen::MatrixXd matrix = jacobian*jacobian.transpose();
// Get manipulability index
manipulability_index = penalty * sqrt(matrix.determinant());
}
return true;
}
int main(int argc, char* argv[]) {
shared_ptr<lcm::LCM> lcm(new lcm::LCM);
if (!lcm->good()) return 1;
auto quad = std::make_shared<Quadrotor>();
const int num_states = getNumStates(*quad);
const int num_positions = num_states / 2;
const int num_inputs = getNumInputs(*quad);
Eigen::MatrixXd Q = Eigen::MatrixXd::Identity(num_states, num_states);
Q.topLeftCorner(num_positions, num_positions) =
10.0 * Eigen::MatrixXd::Identity(num_positions, num_positions);
Eigen::MatrixXd R = 0.1 * Eigen::MatrixXd::Identity(num_inputs, num_inputs);
QuadrotorState<double> xG;
xG.z = 1;
QuadrotorInput<double> uG;
uG.w1 = quad->m * quad->g * 0.25;
uG.w2 = uG.w1;
uG.w3 = uG.w1;
uG.w4 = uG.w1;
auto c = MakeTimeInvariantLqrSystem(*quad, xG, uG, Q, R);
auto v = std::make_shared<BotVisualizer<QuadrotorState> >(
lcm, GetDrakePath() + "/examples/Quadrotor/quadrotor.urdf",
drake::multibody::joints::kRollPitchYaw);
auto sys = cascade(feedback(quad, c), v);
SimulationOptions options;
options.realtime_factor = 1.0;
options.initial_step_size = 0.005;
if (commandLineOptionExists(argv, argv + argc, "--non-realtime")) {
options.warn_real_time_violation = true;
}
for (int i = 0; i < 5; i++) {
Eigen::Matrix<double, 12, 1> x0 = toEigen(xG);
x0 += toEigen(getRandomVector<QuadrotorState>());
simulate(*sys, 0, 10, x0, options);
}
// todo: change this back to runLCM instead of just simulate
}
/* static */ bool ocraWbiConversions::wbiToOcraCoMJacobian(const Eigen::MatrixXd &jac, Eigen::Matrix<double,3,Eigen::Dynamic> &J)
{
if(DIM_T != jac.rows() || jac.cols() != J.cols())
{
std::cout<<"ERROR: Input and output matrices dimensions should be the same" <<std::endl;
return false;
}
Eigen::MatrixXd jac3;
Eigen::Matrix3d jac1,jac2;
jac3.resize(3,jac.cols()-6);
jac1 = jac.topLeftCorner(3,3);
jac2 = jac.block<3,3>(0,3);
jac3 = jac.topRightCorner(3,jac.cols()-6);
J.topLeftCorner(3,3) = jac2;
J.block<3,3>(0,3) = jac1;
J.topRightCorner(3,jac.cols()-6) = jac3;
return true;
}
void MagCal::calcMagComp()
{
/*
* Inspired by
* http://davidegironi.blogspot.it/2013/01/magnetometer-calibration-helper-01-for.html#.UriTqkMjulM
*
* Ellipsoid fit from:
* http://www.mathworks.com/matlabcentral/fileexchange/24693-ellipsoid-fit
*
* To use Eigen to convert matlab code, have a look at Eigen/AsciiQuickReference.txt
*/
if (mMagSamples.size() < 9) {
QMessageBox::warning(this, "Magnetometer compensation",
"Too few points.");
return;
}
int samples = mMagSamples.size();
Eigen::VectorXd ex(samples);
Eigen::VectorXd ey(samples);
Eigen::VectorXd ez(samples);
for (int i = 0;i < samples;i++) {
ex(i) = mMagSamples.at(i).at(0);
ey(i) = mMagSamples.at(i).at(1);
ez(i) = mMagSamples.at(i).at(2);
}
Eigen::MatrixXd eD(samples, 9);
for (int i = 0;i < samples;i++) {
eD(i, 0) = ex(i) * ex(i);
eD(i, 1) = ey(i) * ey(i);
eD(i, 2) = ez(i) * ez(i);
eD(i, 3) = 2.0 * ex(i) * ey(i);
eD(i, 4) = 2.0 * ex(i) * ez(i);
eD(i, 5) = 2.0 * ey(i) * ez(i);
eD(i, 6) = 2.0 * ex(i);
eD(i, 7) = 2.0 * ey(i);
eD(i, 8) = 2.0 * ez(i);
}
Eigen::MatrixXd etmp1 = eD.transpose() * eD;
Eigen::MatrixXd etmp2 = eD.transpose() * Eigen::MatrixXd::Ones(samples, 1);
Eigen::VectorXd eV = etmp1.lu().solve(etmp2);
Eigen::MatrixXd eA(4, 4);
eA(0,0)=eV(0); eA(0,1)=eV(3); eA(0,2)=eV(4); eA(0,3)=eV(6);
eA(1,0)=eV(3); eA(1,1)=eV(1); eA(1,2)=eV(5); eA(1,3)=eV(7);
eA(2,0)=eV(4); eA(2,1)=eV(5); eA(2,2)=eV(2); eA(2,3)=eV(8);
eA(3,0)=eV(6); eA(3,1)=eV(7); eA(3,2)=eV(8); eA(3,3)=-1.0;
Eigen::MatrixXd eCenter = -eA.topLeftCorner(3, 3).lu().solve(eV.segment(6, 3));
Eigen::MatrixXd eT = Eigen::MatrixXd::Identity(4, 4);
eT(3, 0) = eCenter(0);
eT(3, 1) = eCenter(1);
eT(3, 2) = eCenter(2);
Eigen::MatrixXd eR = eT * eA * eT.transpose();
Eigen::SelfAdjointEigenSolver<Eigen::Matrix3d> eEv(eR.topLeftCorner(3, 3) * (-1.0 / eR(3, 3)));
Eigen::MatrixXd eVecs = eEv.eigenvectors();
Eigen::MatrixXd eVals = eEv.eigenvalues();
Eigen::MatrixXd eRadii(3, 1);
eRadii(0) = sqrt(1.0 / eVals(0));
eRadii(1) = sqrt(1.0 / eVals(1));
eRadii(2) = sqrt(1.0 / eVals(2));
Eigen::MatrixXd eScale = eRadii.asDiagonal().inverse() * eRadii.minCoeff();
Eigen::MatrixXd eComp = eVecs * eScale * eVecs.transpose();
mMagComp.resize(9);
mMagComp[0] = eComp(0, 0);
mMagComp[1] = eComp(0, 1);
mMagComp[2] = eComp(0, 2);
mMagComp[3] = eComp(1, 0);
mMagComp[4] = eComp(1, 1);
mMagComp[5] = eComp(1, 2);
mMagComp[6] = eComp(2, 0);
mMagComp[7] = eComp(2, 1);
mMagComp[8] = eComp(2, 2);
mMagCompCenter.resize(3);
mMagCompCenter[0] = eCenter(0, 0);
mMagCompCenter[1] = eCenter(1, 0);
mMagCompCenter[2] = eCenter(2, 0);
QVector<double> magX, magY, magZ;
for (int i = 0;i < mMagSamples.size();i++) {
double mx = mMagSamples.at(i).at(0);
double my = mMagSamples.at(i).at(1);
double mz = mMagSamples.at(i).at(2);
mx -= mMagCompCenter.at(0);
my -= mMagCompCenter.at(1);
mz -= mMagCompCenter.at(2);
magX.append(mx * mMagComp.at(0) + my * mMagComp.at(1) + mz * mMagComp.at(2));
magY.append(mx * mMagComp.at(3) + my * mMagComp.at(4) + mz * mMagComp.at(5));
magZ.append(mx * mMagComp.at(6) + my * mMagComp.at(7) + mz * mMagComp.at(8));
}
ui->magSampXyPlot->graph(1)->setData(magX, magY);
ui->magSampXzPlot->graph(1)->setData(magX, magZ);
ui->magSampYzPlot->graph(1)->setData(magY, magZ);
updateMagPlots();
}
static void gradCov(omxFitFunction *oo, FitContext *fc)
{
const double Scale = Global->llScale;
omxExpectation *expectation = oo->expectation;
BA81FitState *state = (BA81FitState*) oo->argStruct;
BA81Expect *estate = (BA81Expect*) expectation->argStruct;
if (estate->verbose >= 1) mxLog("%s: cross product approximation", oo->name());
estate->grp.ba81OutcomeProb(estate->itemParam->data, FALSE);
const int numThreads = Global->numThreads;
const int numUnique = estate->getNumUnique();
ba81NormalQuad &quad = estate->getQuad();
const int numSpecific = quad.numSpecific;
const int maxDims = quad.maxDims;
const int pDims = numSpecific? maxDims-1 : maxDims;
const int maxAbilities = quad.maxAbilities;
Eigen::MatrixXd icovMat(pDims, pDims);
if (maxAbilities) {
Eigen::VectorXd mean;
Eigen::MatrixXd srcMat;
estate->getLatentDistribution(fc, mean, srcMat);
icovMat = srcMat.topLeftCorner(pDims, pDims);
Matrix tmp(icovMat.data(), pDims, pDims);
int info = InvertSymmetricPosDef(tmp, 'U');
if (info) {
omxRaiseErrorf("%s: latent covariance matrix is not positive definite", oo->name());
return;
}
icovMat.triangularView<Eigen::Lower>() = icovMat.transpose().triangularView<Eigen::Lower>();
}
std::vector<int> &rowMap = estate->grp.rowMap;
double *rowWeight = estate->grp.rowWeight;
std::vector<bool> &rowSkip = estate->grp.rowSkip;
const int totalQuadPoints = quad.totalQuadPoints;
omxMatrix *itemParam = estate->itemParam;
omxBuffer<double> patternLik(numUnique);
const int priDerivCoef = pDims + triangleLoc1(pDims);
const int numLatents = maxAbilities + triangleLoc1(maxAbilities);
const int thrDerivSize = itemParam->cols * state->itemDerivPadSize;
const int totalOutcomes = estate->totalOutcomes();
const int numItems = state->freeItemParams? estate->numItems() : 0;
const size_t numParam = fc->varGroup->vars.size();
std::vector<double> thrGrad(numThreads * numParam);
std::vector<double> thrMeat(numThreads * numParam * numParam);
const double *wherePrep = quad.wherePrep.data();
if (numSpecific == 0) {
omxBuffer<double> thrLxk(totalQuadPoints * numThreads);
omxBuffer<double> derivCoef(totalQuadPoints * priDerivCoef);
if (state->freeLatents) {
#pragma omp parallel for num_threads(numThreads)
for (int qx=0; qx < totalQuadPoints; qx++) {
const double *where = wherePrep + qx * maxDims;
calcDerivCoef(fc, state, estate, icovMat.data(), where,
derivCoef.data() + qx * priDerivCoef);
}
}
#pragma omp parallel for num_threads(numThreads)
for (int px=0; px < numUnique; px++) {
if (rowSkip[px]) continue;
int thrId = omx_absolute_thread_num();
double *lxk = thrLxk.data() + thrId * totalQuadPoints;
omxBuffer<double> expected(totalOutcomes); // can use maxOutcomes instead TODO
std::vector<double> deriv0(thrDerivSize);
std::vector<double> latentGrad(numLatents);
std::vector<double> patGrad(numParam);
double *grad = thrGrad.data() + thrId * numParam;
double *meat = thrMeat.data() + thrId * numParam * numParam;
estate->grp.ba81LikelihoodSlow2(px, lxk);
// If patternLik is already valid, maybe could avoid this loop TODO
double patternLik1 = 0;
for (int qx=0; qx < totalQuadPoints; qx++) {
patternLik1 += lxk[qx];
}
patternLik[px] = patternLik1;
// if (!validPatternLik(state, patternLik1)) complain, TODO
for (int qx=0; qx < totalQuadPoints; qx++) {
double tmp = lxk[qx];
mapLatentDeriv(state, estate, tmp, derivCoef.data() + qx * priDerivCoef,
latentGrad.data());
for (int ix=0; ix < numItems; ++ix) {
int pick = estate->grp.dataColumns[ix][rowMap[px]];
if (pick == NA_INTEGER) continue;
OMXZERO(expected.data(), estate->itemOutcomes(ix));
expected[pick-1] = tmp;
const double *spec = estate->itemSpec(ix);
double *iparam = omxMatrixColumn(itemParam, ix);
const int id = spec[RPF_ISpecID];
double *myDeriv = deriv0.data() + ix * state->itemDerivPadSize;
(*Glibrpf_model[id].dLL1)(spec, iparam, wherePrep + qx * maxDims,
expected.data(), myDeriv);
}
}
gradCov_finish_1pat(1 / patternLik1, rowWeight[px], numItems, numLatents, numParam,
state, estate, itemParam, deriv0, latentGrad, Scale, patGrad, grad, meat);
}
} else {
const int totalPrimaryPoints = quad.totalPrimaryPoints;
const int specificPoints = quad.quadGridSize;
omxBuffer<double> thrLxk(totalQuadPoints * numSpecific * numThreads);
omxBuffer<double> thrEi(totalPrimaryPoints * numThreads);
omxBuffer<double> thrEis(totalPrimaryPoints * numSpecific * numThreads);
const int derivPerPoint = priDerivCoef + 2 * numSpecific;
omxBuffer<double> derivCoef(totalQuadPoints * derivPerPoint);
if (state->freeLatents) {
#pragma omp parallel for num_threads(numThreads)
for (int qx=0; qx < totalQuadPoints; qx++) {
const double *where = wherePrep + qx * maxDims;
calcDerivCoef(fc, state, estate, icovMat.data(), where,
derivCoef.data() + qx * derivPerPoint);
for (int Sgroup=0; Sgroup < numSpecific; ++Sgroup) {
calcDerivCoef1(fc, state, estate, where, Sgroup,
derivCoef.data() + qx * derivPerPoint + priDerivCoef + 2 * Sgroup);
}
}
}
#pragma omp parallel for num_threads(numThreads)
for (int px=0; px < numUnique; px++) {
if (rowSkip[px]) continue;
int thrId = omx_absolute_thread_num();
double *lxk = thrLxk.data() + totalQuadPoints * numSpecific * thrId;
double *Ei = thrEi.data() + totalPrimaryPoints * thrId;
double *Eis = thrEis.data() + totalPrimaryPoints * numSpecific * thrId;
omxBuffer<double> expected(totalOutcomes); // can use maxOutcomes instead TODO
std::vector<double> deriv0(thrDerivSize);
std::vector<double> latentGrad(numLatents);
std::vector<double> patGrad(numParam);
double *grad = thrGrad.data() + thrId * numParam;
double *meat = thrMeat.data() + thrId * numParam * numParam;
estate->grp.cai2010EiEis(px, lxk, Eis, Ei);
for (int qx=0, qloc = 0; qx < totalPrimaryPoints; qx++) {
for (int sgroup=0; sgroup < numSpecific; ++sgroup) {
Eis[qloc] = Ei[qx] / Eis[qloc];
++qloc;
}
}
for (int qloc=0, eisloc=0, qx=0; eisloc < totalPrimaryPoints * numSpecific; eisloc += numSpecific) {
for (int sx=0; sx < specificPoints; sx++) {
mapLatentDeriv(state, estate, Eis[eisloc] * lxk[qloc],
derivCoef.data() + qx * derivPerPoint,
latentGrad.data());
for (int Sgroup=0; Sgroup < numSpecific; Sgroup++) {
double lxk1 = lxk[qloc];
double Eis1 = Eis[eisloc + Sgroup];
double tmp = Eis1 * lxk1;
mapLatentDerivS(state, estate, Sgroup, tmp,
derivCoef.data() + qx * derivPerPoint + priDerivCoef + 2 * Sgroup,
latentGrad.data());
for (int ix=0; ix < numItems; ++ix) {
if (estate->grp.Sgroup[ix] != Sgroup) continue;
int pick = estate->grp.dataColumns[ix][rowMap[px]];
if (pick == NA_INTEGER) continue;
OMXZERO(expected.data(), estate->itemOutcomes(ix));
expected[pick-1] = tmp;
const double *spec = estate->itemSpec(ix);
double *iparam = omxMatrixColumn(itemParam, ix);
const int id = spec[RPF_ISpecID];
const int dims = spec[RPF_ISpecDims];
double *myDeriv = deriv0.data() + ix * state->itemDerivPadSize;
const double *where = wherePrep + qx * maxDims;
Eigen::VectorXd ptheta(dims);
for (int dx=0; dx < dims; dx++) {
ptheta[dx] = where[std::min(dx, maxDims-1)];
}
(*Glibrpf_model[id].dLL1)(spec, iparam, ptheta.data(),
expected.data(), myDeriv);
}
++qloc;
}
++qx;
}
}
// If patternLik is already valid, maybe could avoid this loop TODO
double patternLik1 = 0;
for (int qx=0; qx < totalPrimaryPoints; ++qx) {
patternLik1 += Ei[qx];
}
patternLik[px] = patternLik1;
gradCov_finish_1pat(1 / patternLik1, rowWeight[px], numItems, numLatents, numParam,
state, estate, itemParam, deriv0, latentGrad, Scale, patGrad, grad, meat);
}
}
for (int tx=1; tx < numThreads; ++tx) {
double *th = thrGrad.data() + tx * numParam;
for (size_t en=0; en < numParam; ++en) {
thrGrad[en] += th[en];
}
}
for (int tx=1; tx < numThreads; ++tx) {
double *th = thrMeat.data() + tx * numParam * numParam;
for (size_t en=0; en < numParam * numParam; ++en) {
thrMeat[en] += th[en];
}
}
for (size_t d1=0; d1 < numParam; ++d1) {
fc->grad(d1) += thrGrad[d1];
}
if (fc->infoB) {
for (size_t d1=0; d1 < numParam; ++d1) {
for (size_t d2=0; d2 < numParam; ++d2) {
int cell = d1 * numParam + d2;
fc->infoB[cell] += thrMeat[cell];
}
}
}
}
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();
}
}