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gtsam/gtsam/linear/HessianFactor.cpp

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/* ----------------------------------------------------------------------------
* GTSAM Copyright 2010, Georgia Tech Research Corporation,
* Atlanta, Georgia 30332-0415
* All Rights Reserved
* Authors: Frank Dellaert, et al. (see THANKS for the full author list)
* See LICENSE for the license information
* -------------------------------------------------------------------------- */
/**
* @file HessianFactor.cpp
* @author Richard Roberts
* @date Dec 8, 2010
*/
#include <gtsam/linear/HessianFactor.h>
#include <gtsam/linear/GaussianConditional.h>
#include <gtsam/linear/GaussianFactor.h>
#include <gtsam/linear/GaussianFactorGraph.h>
#include <gtsam/linear/JacobianFactor.h>
#include <gtsam/linear/linearExceptions.h>
#include <gtsam/base/cholesky.h>
#include <gtsam/base/debug.h>
#include <gtsam/base/FastMap.h>
#include <gtsam/base/Matrix.h>
#include <gtsam/base/ThreadsafeException.h>
#include <gtsam/base/timing.h>
#include <boost/format.hpp>
#include <boost/tuple/tuple.hpp>
#include <boost/range/adaptor/transformed.hpp>
#include <boost/range/adaptor/map.hpp>
#include <boost/range/algorithm/copy.hpp>
#include <sstream>
#include <limits>
using namespace std;
namespace br {
using namespace boost::range;
using namespace boost::adaptors;
}
namespace gtsam {
// Typedefs used in constructors below.
using Dims = std::vector<Eigen::Index>;
/* ************************************************************************* */
void HessianFactor::Allocate(const Scatter& scatter) {
gttic(HessianFactor_Allocate);
// Allocate with dimensions for each variable plus 1 at the end for the information vector
const size_t n = scatter.size();
keys_.resize(n);
FastVector<DenseIndex> dims(n + 1);
DenseIndex slot = 0;
for(const SlotEntry& slotentry: scatter) {
keys_[slot] = slotentry.key;
dims[slot] = slotentry.dimension;
++slot;
}
dims.back() = 1;
info_ = SymmetricBlockMatrix(dims);
}
/* ************************************************************************* */
HessianFactor::HessianFactor(const Scatter& scatter) {
Allocate(scatter);
}
/* ************************************************************************* */
HessianFactor::HessianFactor() :
info_(Dims{1}) {
assert(info_.rows() == 1);
constantTerm() = 0.0;
}
/* ************************************************************************* */
HessianFactor::HessianFactor(Key j, const Matrix& G, const Vector& g, double f)
: GaussianFactor(KeyVector{j}), info_(Dims{G.cols(), 1}) {
if (G.rows() != G.cols() || G.rows() != g.size())
throw invalid_argument(
"Attempting to construct HessianFactor with inconsistent matrix and/or vector dimensions");
info_.setDiagonalBlock(0, G);
linearTerm() = g;
constantTerm() = f;
}
/* ************************************************************************* */
// error is 0.5*(x-mu)'*inv(Sigma)*(x-mu) = 0.5*(x'*G*x - 2*x'*G*mu + mu'*G*mu)
// where G = inv(Sigma), g = G*mu, f = mu'*G*mu = mu'*g
HessianFactor::HessianFactor(Key j, const Vector& mu, const Matrix& Sigma)
: GaussianFactor(KeyVector{j}), info_(Dims{Sigma.cols(), 1}) {
if (Sigma.rows() != Sigma.cols() || Sigma.rows() != mu.size())
throw invalid_argument(
"Attempting to construct HessianFactor with inconsistent matrix and/or vector dimensions");
info_.setDiagonalBlock(0, Sigma.inverse()); // G
linearTerm() = info_.diagonalBlock(0) * mu; // g
constantTerm() = mu.dot(linearTerm().col(0)); // f
}
/* ************************************************************************* */
HessianFactor::HessianFactor(Key j1, Key j2, const Matrix& G11,
const Matrix& G12, const Vector& g1, const Matrix& G22, const Vector& g2,
double f) :
GaussianFactor(KeyVector{j1,j2}), info_(
Dims{G11.cols(),G22.cols(),1}) {
info_.setDiagonalBlock(0, G11);
info_.setOffDiagonalBlock(0, 1, G12);
info_.setDiagonalBlock(1, G22);
linearTerm() << g1, g2;
constantTerm() = f;
}
/* ************************************************************************* */
HessianFactor::HessianFactor(Key j1, Key j2, Key j3, const Matrix& G11,
const Matrix& G12, const Matrix& G13, const Vector& g1, const Matrix& G22,
const Matrix& G23, const Vector& g2, const Matrix& G33, const Vector& g3,
double f) :
GaussianFactor(KeyVector{j1,j2,j3}), info_(
Dims{G11.cols(),G22.cols(),G33.cols(),1}) {
if (G11.rows() != G11.cols() || G11.rows() != G12.rows()
|| G11.rows() != G13.rows() || G11.rows() != g1.size()
|| G22.cols() != G12.cols() || G33.cols() != G13.cols()
|| G22.cols() != g2.size() || G33.cols() != g3.size())
throw invalid_argument(
"Inconsistent matrix and/or vector dimensions in HessianFactor constructor");
info_.setDiagonalBlock(0, G11);
info_.setOffDiagonalBlock(0, 1, G12);
info_.setOffDiagonalBlock(0, 2, G13);
info_.setDiagonalBlock(1, G22);
info_.setOffDiagonalBlock(1, 2, G23);
info_.setDiagonalBlock(2, G33);
linearTerm() << g1, g2, g3;
constantTerm() = f;
}
/* ************************************************************************* */
namespace {
DenseIndex _getSizeHF(const Vector& m) {
return m.size();
}
}
/* ************************************************************************* */
HessianFactor::HessianFactor(const KeyVector& js,
const std::vector<Matrix>& Gs, const std::vector<Vector>& gs, double f) :
GaussianFactor(js), info_(gs | br::transformed(&_getSizeHF), true) {
// Get the number of variables
size_t variable_count = js.size();
// Verify the provided number of entries in the vectors are consistent
if (gs.size() != variable_count
|| Gs.size() != (variable_count * (variable_count + 1)) / 2)
throw invalid_argument(
"Inconsistent number of entries between js, Gs, and gs in HessianFactor constructor.\nThe number of keys provided \
in js must match the number of linear vector pieces in gs. The number of upper-diagonal blocks in Gs must be n*(n+1)/2");
// Verify the dimensions of each provided matrix are consistent
// Note: equations for calculating the indices derived from the "sum of an arithmetic sequence" formula
for (size_t i = 0; i < variable_count; ++i) {
DenseIndex block_size = gs[i].size();
// Check rows
for (size_t j = 0; j < variable_count - i; ++j) {
size_t index = i * (2 * variable_count - i + 1) / 2 + j;
if (Gs[index].rows() != block_size) {
throw invalid_argument(
"Inconsistent matrix and/or vector dimensions in HessianFactor constructor");
}
}
// Check cols
for (size_t j = 0; j <= i; ++j) {
size_t index = j * (2 * variable_count - j + 1) / 2 + (i - j);
if (Gs[index].cols() != block_size) {
throw invalid_argument(
"Inconsistent matrix and/or vector dimensions in HessianFactor constructor");
}
}
}
// Fill in the blocks
size_t index = 0;
for (size_t i = 0; i < variable_count; ++i) {
for (size_t j = i; j < variable_count; ++j) {
if (i == j) {
info_.setDiagonalBlock(i, Gs[index]);
} else {
info_.setOffDiagonalBlock(i, j, Gs[index]);
}
index++;
}
info_.setOffDiagonalBlock(i, variable_count, gs[i]);
}
constantTerm() = f;
}
/* ************************************************************************* */
namespace {
void _FromJacobianHelper(const JacobianFactor& jf, SymmetricBlockMatrix& info) {
gttic(HessianFactor_fromJacobian);
const SharedDiagonal& jfModel = jf.get_model();
auto A = jf.matrixObject().full();
if (jfModel) {
if (jf.get_model()->isConstrained())
throw invalid_argument(
"Cannot construct HessianFactor from JacobianFactor with constrained noise model");
auto D = (jfModel->invsigmas().array() * jfModel->invsigmas().array()).matrix().asDiagonal();
info.setFullMatrix(A.transpose() * D * A);
} else {
info.setFullMatrix(A.transpose() * A);
}
}
}
/* ************************************************************************* */
HessianFactor::HessianFactor(const JacobianFactor& jf) :
GaussianFactor(jf), info_(
SymmetricBlockMatrix::LikeActiveViewOf(jf.matrixObject())) {
_FromJacobianHelper(jf, info_);
}
/* ************************************************************************* */
HessianFactor::HessianFactor(const GaussianFactor& gf) :
GaussianFactor(gf) {
// Copy the matrix data depending on what type of factor we're copying from
if (const JacobianFactor* jf = dynamic_cast<const JacobianFactor*>(&gf)) {
info_ = SymmetricBlockMatrix::LikeActiveViewOf(jf->matrixObject());
_FromJacobianHelper(*jf, info_);
} else if (const HessianFactor* hf = dynamic_cast<const HessianFactor*>(&gf)) {
info_ = hf->info_;
} else {
throw std::invalid_argument(
"In HessianFactor(const GaussianFactor& gf), gf is neither a JacobianFactor nor a HessianFactor");
}
}
/* ************************************************************************* */
HessianFactor::HessianFactor(const GaussianFactorGraph& factors,
const Scatter& scatter) {
gttic(HessianFactor_MergeConstructor);
Allocate(scatter);
// Form A' * A
gttic(update);
info_.setZero();
for(const auto& factor: factors)
if (factor)
factor->updateHessian(keys_, &info_);
gttoc(update);
}
/* ************************************************************************* */
void HessianFactor::print(const std::string& s,
const KeyFormatter& formatter) const {
cout << s << "\n";
cout << " keys: ";
for (const_iterator key = begin(); key != end(); ++key)
cout << formatter(*key) << "(" << getDim(key) << ") ";
cout << "\n";
gtsam::print(Matrix(info_.selfadjointView()),
"Augmented information matrix: ");
}
/* ************************************************************************* */
bool HessianFactor::equals(const GaussianFactor& lf, double tol) const {
const HessianFactor* rhs = dynamic_cast<const HessianFactor*>(&lf);
if (!rhs || !Factor::equals(lf, tol))
return false;
return equal_with_abs_tol(augmentedInformation(), rhs->augmentedInformation(),
tol);
}
/* ************************************************************************* */
Matrix HessianFactor::augmentedInformation() const {
return info_.selfadjointView();
}
/* ************************************************************************* */
Eigen::SelfAdjointView<SymmetricBlockMatrix::constBlock, Eigen::Upper>
HessianFactor::informationView() const {
return info_.selfadjointView(0, size());
}
/* ************************************************************************* */
Matrix HessianFactor::information() const {
return informationView();
}
/* ************************************************************************* */
void HessianFactor::hessianDiagonalAdd(VectorValues &d) const {
for (DenseIndex j = 0; j < (DenseIndex)size(); ++j) {
auto result = d.emplace(keys_[j], info_.diagonal(j));
if(!result.second) {
// if emplace fails, it returns an iterator to the existing element, which we add to:
result.first->second += info_.diagonal(j);
}
}
}
/* ************************************************************************* */
// Raw memory access version should be called in Regular Factors only currently
void HessianFactor::hessianDiagonal(double* d) const {
throw std::runtime_error(
"HessianFactor::hessianDiagonal raw memory access is allowed for Regular Factors only");
}
/* ************************************************************************* */
map<Key, Matrix> HessianFactor::hessianBlockDiagonal() const {
map<Key, Matrix> blocks;
// Loop over all variables
for (DenseIndex j = 0; j < (DenseIndex) size(); ++j) {
// Get the diagonal block, and insert it
blocks.emplace(keys_[j], info_.diagonalBlock(j));
}
return blocks;
}
/* ************************************************************************* */
Matrix HessianFactor::augmentedJacobian() const {
return JacobianFactor(*this).augmentedJacobian();
}
/* ************************************************************************* */
std::pair<Matrix, Vector> HessianFactor::jacobian() const {
return JacobianFactor(*this).jacobian();
}
/* ************************************************************************* */
double HessianFactor::error(const VectorValues& c) const {
// error 0.5*(f - 2*x'*g + x'*G*x)
const double f = constantTerm();
if (empty()) {
return 0.5 * f;
}
double xtg = 0, xGx = 0;
// extract the relevant subset of the VectorValues
// NOTE may not be as efficient
const Vector x = c.vector(keys());
xtg = x.dot(linearTerm().col(0));
auto AtA = informationView();
xGx = x.transpose() * AtA * x;
return 0.5 * (f - 2.0 * xtg + xGx);
}
/* ************************************************************************* */
void HessianFactor::updateHessian(const KeyVector& infoKeys,
SymmetricBlockMatrix* info) const {
gttic(updateHessian_HessianFactor);
assert(info);
// Apply updates to the upper triangle
DenseIndex nrVariablesInThisFactor = size(), nrBlocksInInfo = info->nBlocks() - 1;
vector<DenseIndex> slots(nrVariablesInThisFactor + 1);
// Loop over this factor's blocks with indices (i,j)
// For every block (i,j), we determine the block (I,J) in info.
for (DenseIndex j = 0; j <= nrVariablesInThisFactor; ++j) {
const bool rhs = (j == nrVariablesInThisFactor);
const DenseIndex J = rhs ? nrBlocksInInfo : Slot(infoKeys, keys_[j]);
slots[j] = J;
for (DenseIndex i = 0; i <= j; ++i) {
const DenseIndex I = slots[i]; // because i<=j, slots[i] is valid.
if (i == j) {
assert(I == J);
info->updateDiagonalBlock(I, info_.diagonalBlock(i));
} else {
assert(i < j);
assert(I != J);
info->updateOffDiagonalBlock(I, J, info_.aboveDiagonalBlock(i, j));
}
}
}
}
/* ************************************************************************* */
GaussianFactor::shared_ptr HessianFactor::negate() const {
shared_ptr result = std::make_shared<This>(*this);
// Negate the information matrix of the result
result->info_.negate();
return result;
}
/* ************************************************************************* */
void HessianFactor::multiplyHessianAdd(double alpha, const VectorValues& x,
VectorValues& yvalues) const {
// Create a vector of temporary y values, corresponding to rows i
vector<Vector> y;
y.reserve(size());
for (const_iterator it = begin(); it != end(); it++)
y.push_back(Vector::Zero(getDim(it)));
// Accessing the VectorValues one by one is expensive
// So we will loop over columns to access x only once per column
// And fill the above temporary y values, to be added into yvalues after
for (DenseIndex j = 0; j < (DenseIndex) size(); ++j) {
// xj is the input vector
Vector xj = x.at(keys_[j]);
DenseIndex i = 0;
for (; i < j; ++i)
y[i] += info_.aboveDiagonalBlock(i, j) * xj;
// blocks on the diagonal are only half
y[i] += info_.diagonalBlock(j) * xj;
// for below diagonal, we take transpose block from upper triangular part
for (i = j + 1; i < (DenseIndex) size(); ++i)
y[i] += info_.aboveDiagonalBlock(j, i).transpose() * xj;
}
// copy to yvalues
for (DenseIndex i = 0; i < (DenseIndex) size(); ++i) {
bool didNotExist;
VectorValues::iterator it;
boost::tie(it, didNotExist) = yvalues.tryInsert(keys_[i], Vector());
if (didNotExist)
it->second = alpha * y[i]; // init
else
it->second += alpha * y[i]; // add
}
}
/* ************************************************************************* */
VectorValues HessianFactor::gradientAtZero() const {
VectorValues g;
size_t n = size();
for (size_t j = 0; j < n; ++j)
g.emplace(keys_[j], -info_.aboveDiagonalBlock(j, n));
return g;
}
/* ************************************************************************* */
// Raw memory access version should be called in Regular Factors only currently
void HessianFactor::gradientAtZero(double* d) const {
throw std::runtime_error(
"HessianFactor::gradientAtZero raw memory access is allowed for Regular Factors only");
}
/* ************************************************************************* */
Vector HessianFactor::gradient(Key key, const VectorValues& x) const {
const Factor::const_iterator it_i = find(key);
const DenseIndex I = std::distance(begin(), it_i);
// Sum over G_ij*xj for all xj connecting to xi
Vector b = Vector::Zero(x.at(key).size());
for (Factor::const_iterator it_j = begin(); it_j != end(); ++it_j) {
const DenseIndex J = std::distance(begin(), it_j);
// Obtain Gij from the Hessian factor
// Hessian factor only stores an upper triangular matrix, so be careful when i>j
const Matrix Gij = info_.block(I, J);
// Accumulate Gij*xj to gradf
b += Gij * x.at(*it_j);
}
// Subtract the linear term gi
b += -linearTerm(it_i);
return b;
}
/* ************************************************************************* */
std::shared_ptr<GaussianConditional> HessianFactor::eliminateCholesky(const Ordering& keys) {
gttic(HessianFactor_eliminateCholesky);
GaussianConditional::shared_ptr conditional;
try {
// Do dense elimination
size_t nFrontals = keys.size();
assert(nFrontals <= size());
info_.choleskyPartial(nFrontals);
// TODO(frank): pre-allocate GaussianConditional and write into it
const VerticalBlockMatrix Ab = info_.split(nFrontals);
conditional = std::make_shared<GaussianConditional>(keys_, nFrontals, Ab);
// Erase the eliminated keys in this factor
keys_.erase(begin(), begin() + nFrontals);
} catch (const CholeskyFailed&) {
#ifndef NDEBUG
cout << "Partial Cholesky on HessianFactor failed." << endl;
keys.print("Frontal keys ");
print("HessianFactor:");
#endif
throw IndeterminantLinearSystemException(keys.front());
}
// Return result
return conditional;
}
/* ************************************************************************* */
VectorValues HessianFactor::solve() {
gttic(HessianFactor_solve);
// Do Cholesky Factorization
const size_t n = size();
assert(size_t(info_.nBlocks()) == n + 1);
info_.choleskyPartial(n);
auto R = info_.triangularView(0, n);
auto eta = linearTerm();
// Solve
const Vector solution = R.solve(eta);
// Parse into VectorValues
VectorValues delta;
std::size_t offset = 0;
for (DenseIndex j = 0; j < (DenseIndex)n; ++j) {
const DenseIndex dim = info_.getDim(j);
delta.emplace(keys_[j], solution.segment(offset, dim));
offset += dim;
}
return delta;
}
/* ************************************************************************* */
std::pair<std::shared_ptr<GaussianConditional>, std::shared_ptr<HessianFactor> >
EliminateCholesky(const GaussianFactorGraph& factors, const Ordering& keys) {
gttic(EliminateCholesky);
// Build joint factor
HessianFactor::shared_ptr jointFactor;
try {
Scatter scatter(factors, keys);
jointFactor = std::make_shared<HessianFactor>(factors, scatter);
} catch (std::invalid_argument&) {
throw InvalidDenseElimination(
"EliminateCholesky was called with a request to eliminate variables that are not\n"
"involved in the provided factors.");
}
// Do dense elimination
auto conditional = jointFactor->eliminateCholesky(keys);
// Return result
return make_pair(conditional, jointFactor);
}
/* ************************************************************************* */
std::pair<std::shared_ptr<GaussianConditional>,
std::shared_ptr<GaussianFactor> > EliminatePreferCholesky(
const GaussianFactorGraph& factors, const Ordering& keys) {
gttic(EliminatePreferCholesky);
// If any JacobianFactors have constrained noise models, we have to convert
// all factors to JacobianFactors. Otherwise, we can convert all factors
// to HessianFactors. This is because QR can handle constrained noise
// models but Cholesky cannot.
if (hasConstraints(factors))
return EliminateQR(factors, keys);
else
return EliminateCholesky(factors, keys);
}
} // gtsam
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