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gtsam/cpp/GaussianFactor.cpp

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/**
* @file GaussianFactor.cpp
* @brief Linear Factor....A Gaussian
* @brief linearFactor
* @author Christian Potthast
*/
#include <boost/foreach.hpp>
#include <boost/assign/list_inserter.hpp> // for 'insert()'
#include <boost/assign/std/list.hpp> // for operator += in Ordering
#include "Matrix.h"
#include "Ordering.h"
#include "GaussianConditional.h"
#include "GaussianFactor.h"
using namespace std;
using namespace boost::assign;
namespace ublas = boost::numeric::ublas;
using namespace gtsam;
typedef pair<Symbol,Matrix> NamedMatrix;
// MACRO to loop. Ugly with pointer, but best I could in short time
#define FOREACH_PAIR(KEY,VAL,COL) const_iterator it = COL.begin(); \
const Symbol* KEY = it == COL.end() ? NULL : &(it->first); \
const Matrix* VAL = it == COL.end() ? NULL : &(it->second); \
for (; it != COL.end(); it++, KEY=&(it->first), VAL=&(it->second))
/* ************************************************************************* */
GaussianFactor::GaussianFactor(const boost::shared_ptr<GaussianConditional>& cg) :
b_(cg->get_d()) {
As_.insert(make_pair(cg->key(), cg->get_R()));
SymbolMap<Matrix>::const_iterator it = cg->parentsBegin();
for (; it != cg->parentsEnd(); it++) {
const Symbol& j = it->first;
const Matrix& Aj = it->second;
As_.insert(make_pair(j, Aj));
}
// set sigmas from precisions
size_t n = b_.size();
model_ = noiseModel::Diagonal::Sigmas(cg->get_sigmas());
}
/* ************************************************************************* */
GaussianFactor::GaussianFactor(const vector<shared_ptr> & factors)
{
bool verbose = false;
if (verbose) cout << "GaussianFactor::GaussianFactor (factors)" << endl;
// Create RHS and sigmas of right size by adding together row counts
size_t m = 0;
BOOST_FOREACH(shared_ptr factor, factors) m += factor->numberOfRows();
b_ = Vector(m);
Vector sigmas(m);
size_t pos = 0; // save last position inserted into the new rhs vector
// iterate over all factors
bool constrained = false;
BOOST_FOREACH(shared_ptr factor, factors){
if (verbose) factor->print();
// number of rows for factor f
const size_t mf = factor->numberOfRows();
// copy the rhs vector from factor to b
const Vector bf = factor->get_b();
for (size_t i=0; i<mf; i++) b_(pos+i) = bf(i);
// copy the model_
for (size_t i=0; i<mf; i++) sigmas(pos+i) = factor->model_->sigma(i);
// update the matrices
append_factor(factor,m,pos);
// check if there are constraints
if (verbose) factor->model_->print("Checking for zeros");
if (!constrained && factor->model_->isConstrained()) {
constrained = true;
if (verbose) cout << "Found a constraint!" << endl;
}
pos += mf;
}
if (verbose) cout << "GaussianFactor::GaussianFactor done" << endl;
if (constrained) {
model_ = noiseModel::Constrained::MixedSigmas(sigmas);
if (verbose) model_->print("Just created Constraint ^");
} else {
model_ = noiseModel::Diagonal::Sigmas(sigmas);
if (verbose) model_->print("Just created Diagonal");
}
}
/* ************************************************************************* */
void GaussianFactor::print(const string& s) const {
cout << s << endl;
if (empty()) cout << " empty" << endl;
else {
FOREACH_PAIR(j,Aj,As_)
gtsam::print(*Aj, "A["+(string)*j+"]=\n");
gtsam::print(b_,"b=");
model_->print("model");
}
}
/* ************************************************************************* */
size_t GaussianFactor::getDim(const Symbol& key) const {
const_iterator it = As_.find(key);
if (it != As_.end())
return it->second.size2();
else
return 0;
}
/* ************************************************************************* */
// Check if two linear factors are equal
bool GaussianFactor::equals(const Factor<VectorConfig>& f, double tol) const {
const GaussianFactor* lf = dynamic_cast<const GaussianFactor*>(&f);
if (lf == NULL) return false;
if (empty()) return (lf->empty());
const_iterator it1 = As_.begin(), it2 = lf->As_.begin();
if(As_.size() != lf->As_.size()) return false;
for(; it1 != As_.end(); it1++, it2++) {
const Symbol& j1 = it1->first, j2 = it2->first;
const Matrix A1 = it1->second, A2 = it2->second;
if (j1 != j2) return false;
if (!equal_with_abs_tol(A1,A2,tol))
return false;
}
if( !(::equal_with_abs_tol(b_, (lf->b_),tol)) )
return false;
return model_->equals(*(lf->model_),tol);
}
/* ************************************************************************* */
Vector GaussianFactor::unweighted_error(const VectorConfig& c) const {
Vector e = -b_;
if (empty()) return e;
FOREACH_PAIR(j,Aj,As_)
e += (*Aj * c[*j]);
return e;
}
/* ************************************************************************* */
Vector GaussianFactor::error_vector(const VectorConfig& c) const {
if (empty()) return model_->whiten(-b_);
return model_->whiten(unweighted_error(c));
}
/* ************************************************************************* */
double GaussianFactor::error(const VectorConfig& c) const {
if (empty()) return 0;
Vector weighted = error_vector(c); // rtodo: copying vector here?
return 0.5 * inner_prod(weighted,weighted);
}
/* ************************************************************************* */
list<Symbol> GaussianFactor::keys() const {
list<Symbol> result;
typedef pair<Symbol,Matrix> NamedMatrix;
BOOST_FOREACH(const NamedMatrix& jA, As_)
result.push_back(jA.first);
return result;
}
/* ************************************************************************* */
Dimensions GaussianFactor::dimensions() const {
Dimensions result;
FOREACH_PAIR(j,Aj,As_) result.insert(make_pair(*j,Aj->size2()));
return result;
}
/* ************************************************************************* */
void GaussianFactor::tally_separator(const Symbol& key, set<Symbol>& separator) const {
if(involves(key)) {
FOREACH_PAIR(j,A,As_)
if(*j != key) separator.insert(*j);
}
}
/* ************************************************************************* */
Vector GaussianFactor::operator*(const VectorConfig& x) const {
Vector Ax = zero(b_.size());
if (empty()) return Ax;
// Just iterate over all A matrices and multiply in correct config part
FOREACH_PAIR(j, Aj, As_)
Ax += (*Aj * x[*j]);
return model_->whiten(Ax);
}
/* ************************************************************************* */
VectorConfig GaussianFactor::operator^(const Vector& e) const {
Vector E = model_->whiten(e);
VectorConfig x;
// Just iterate over all A matrices and insert Ai^e into VectorConfig
FOREACH_PAIR(j, Aj, As_)
x.insert(*j,(*Aj)^E);
return x;
}
/* ************************************************************************* */
void GaussianFactor::transposeMultiplyAdd(double alpha, const Vector& e,
VectorConfig& x) const {
Vector E = alpha * model_->whiten(e);
// Just iterate over all A matrices and insert Ai^e into VectorConfig
FOREACH_PAIR(j, Aj, As_)
{
Vector& Xj = x.getReference(*j);
gtsam::transposeMultiplyAdd(1.0, *Aj, E, Xj);
}
}
/* ************************************************************************* */
pair<Matrix,Vector> GaussianFactor::matrix(const Ordering& ordering, bool weight) const {
// rtodo: this is called in eliminate, potential function to optimize?
// get pointers to the matrices
vector<const Matrix *> matrices;
BOOST_FOREACH(const Symbol& j, ordering) {
const Matrix& Aj = get_A(j);
matrices.push_back(&Aj);
}
// assemble
Matrix A = collect(matrices);
Vector b(b_);
// divide in sigma so error is indeed 0.5*|Ax-b|
if (weight) model_->WhitenSystem(A,b);
return make_pair(A, b);
}
/* ************************************************************************* */
Matrix GaussianFactor::matrix_augmented(const Ordering& ordering, bool weight) const {
// get pointers to the matrices
vector<const Matrix *> matrices;
BOOST_FOREACH(const Symbol& j, ordering) {
const Matrix& Aj = get_A(j);
matrices.push_back(&Aj);
}
// load b into a matrix
size_t rows = b_.size();
Matrix B_mat(rows, 1);
memcpy(B_mat.data().begin(), b_.data().begin(), rows*sizeof(double));
matrices.push_back(&B_mat);
// divide in sigma so error is indeed 0.5*|Ax-b|
Matrix Ab = collect(matrices);
if (weight) model_->WhitenInPlace(Ab);
return Ab;
}
/* ************************************************************************* */
std::pair<Matrix, SharedDiagonal> GaussianFactor::combineFactorsAndCreateMatrix(
const vector<GaussianFactor::shared_ptr>& factors,
const Ordering& order, const Dimensions& dimensions) {
// find the size of Ab
size_t m = 0, n = 1;
// number of rows
BOOST_FOREACH(GaussianFactor::shared_ptr factor, factors) {
m += factor->numberOfRows();
}
// find the number of columns
BOOST_FOREACH(const Symbol& key, order) {
n += dimensions.at(key);
}
// Allocate the new matrix
Matrix Ab = zeros(m,n);
// Allocate a sigmas vector to make into a full noisemodel
Vector sigmas = ones(m);
// copy data over
size_t cur_m = 0;
bool constrained = false;
bool unit = true;
BOOST_FOREACH(GaussianFactor::shared_ptr factor, factors) {
// loop through ordering
size_t cur_n = 0;
BOOST_FOREACH(const Symbol& key, order) {
// copy over matrix if it exists
if (factor->involves(key)) {
insertSub(Ab, factor->get_A(key), cur_m, cur_n);
}
// move onto next element
cur_n += dimensions.at(key);
}
// copy over the RHS
insertColumn(Ab, factor->get_b(), cur_m, n-1);
// check if the model is unit already
if (!boost::shared_dynamic_cast<noiseModel::Unit>(factor->get_model())) {
unit = false;
const Vector& subsigmas = factor->get_model()->sigmas();
subInsert(sigmas, subsigmas, cur_m);
// check for constraint
if (boost::shared_dynamic_cast<noiseModel::Constrained>(factor->get_model()))
constrained = true;
}
// move to next row
cur_m += factor->numberOfRows();
}
// combine the noisemodels
SharedDiagonal model;
if (unit) {
model = noiseModel::Unit::Create(m);
} else if (constrained) {
model = noiseModel::Constrained::MixedSigmas(sigmas);
} else {
model = noiseModel::Diagonal::Sigmas(sigmas);
}
return make_pair(Ab, model);
}
/* ************************************************************************* */
boost::tuple<list<int>, list<int>, list<double> >
GaussianFactor::sparse(const Dimensions& columnIndices) const {
// declare return values
list<int> I,J;
list<double> S;
// iterate over all matrices in the factor
FOREACH_PAIR( key, Aj, As_) {
// find first column index for this key
int column_start = columnIndices.at(*key);
for (size_t i = 0; i < Aj->size1(); i++) {
double sigma_i = model_->sigma(i);
for (size_t j = 0; j < Aj->size2(); j++)
if ((*Aj)(i, j) != 0.0) {
I.push_back(i + 1);
J.push_back(j + column_start);
S.push_back((*Aj)(i, j) / sigma_i);
}
}
}
// return the result
return boost::tuple<list<int>, list<int>, list<double> >(I,J,S);
}
/* ************************************************************************* */
void GaussianFactor::append_factor(GaussianFactor::shared_ptr f, size_t m, size_t pos) {
// iterate over all matrices from the factor f
FOREACH_PAIR( key, A, f->As_) {
// find the corresponding matrix among As
iterator mine = As_.find(*key);
const bool exists = mine != As_.end();
// find rows and columns
const size_t n = A->size2();
// use existing or create new matrix
if (exists)
copy(A->data().begin(), A->data().end(), (mine->second).data().begin()+pos*n);
else {
Matrix Z = zeros(m, n);
copy(A->data().begin(), A->data().end(), Z.data().begin()+pos*n);
insert(*key, Z);
}
} // FOREACH
}
/* ************************************************************************* */
/* Note, in place !!!!
* Do incomplete QR factorization for the first n columns
* We will do QR on all matrices and on RHS
* Then take first n rows and make a GaussianConditional,
* and last rows to make a new joint linear factor on separator
*/
/* ************************************************************************* */
#include <boost/numeric/ublas/triangular.hpp>
#include <boost/numeric/ublas/io.hpp>
#include <boost/numeric/ublas/matrix_proxy.hpp>
pair<GaussianConditional::shared_ptr, GaussianFactor::shared_ptr>
GaussianFactor::eliminateMatrix(Matrix& Ab, SharedDiagonal model,
const Ordering& ordering,
const Dimensions& dimensions) {
bool verbose = false;
Symbol key = ordering.front();
// Use in-place QR on dense Ab appropriate to NoiseModel
if (verbose) model->print("Before QR");
SharedDiagonal noiseModel = model->QR(Ab);
if (verbose) model->print("After QR");
// get dimensions of the eliminated variable
// TODO: this is another map find that should be avoided !
size_t n1 = dimensions.at(key), n = Ab.size2() - 1;
// if m<n1, this factor cannot be eliminated
size_t maxRank = noiseModel->dim();
if (maxRank<n1) {
cout << "Perhaps your factor graph is singular." << endl;
cout << "Here are the keys involved in the factor now being eliminated:" << endl;
ordering.print("Keys");
cout << "The first key, '" << (string)ordering.front() << "', corresponds to the variable being eliminated" << endl;
throw(domain_error("GaussianFactor::eliminate: fewer constraints than unknowns"));
}
// Get alias to augmented RHS d
ublas::matrix_column<Matrix> d(Ab,n);
// create base conditional Gaussian
GaussianConditional::shared_ptr conditional(new GaussianConditional(key,
sub(d, 0, n1), // form d vector
sub(Ab, 0, n1, 0, n1), // form R matrix
sub(noiseModel->sigmas(),0,n1))); // get standard deviations
// extract the block matrices for parents in both CG and LF
GaussianFactor::shared_ptr factor(new GaussianFactor);
size_t j = n1;
BOOST_FOREACH(const Symbol& cur_key, ordering)
if (cur_key!=key) {
size_t dim = dimensions.at(cur_key); // TODO avoid find !
conditional->add(cur_key, sub(Ab, 0, n1, j, j+dim));
factor->insert(cur_key, sub(Ab, n1, maxRank, j, j+dim)); // TODO: handle zeros properly
j+=dim;
}
// Set sigmas
// set the right model here
if (noiseModel->isConstrained())
factor->model_ = noiseModel::Constrained::MixedSigmas(sub(noiseModel->sigmas(),n1,maxRank));
else
factor->model_ = noiseModel::Diagonal::Sigmas(sub(noiseModel->sigmas(),n1,maxRank));
// extract ds vector for the new b
factor->set_b(sub(d, n1, maxRank));
return make_pair(conditional, factor);
}
pair<GaussianConditional::shared_ptr, GaussianFactor::shared_ptr>
GaussianFactor::eliminate(const Symbol& key) const
{
bool verbose = false;
// if this factor does not involve key, we exit with empty CG and LF
const_iterator it = As_.find(key);
if (it==As_.end()) {
// Conditional Gaussian is just a parent-less node with P(x)=1
GaussianFactor::shared_ptr lf(new GaussianFactor);
GaussianConditional::shared_ptr cg(new GaussianConditional(key));
return make_pair(cg,lf);
}
// create an internal ordering that eliminates key first
Ordering ordering;
ordering += key;
BOOST_FOREACH(const Symbol& k, keys())
if (k != key) ordering += k;
// extract [A b] from the combined linear factor (ensure that x is leading)
Matrix Ab = matrix_augmented(ordering,false);
// TODO: this is where to split
return eliminateMatrix(Ab, model_, ordering, dimensions());
}
/* ************************************************************************* */
// Creates a factor on step-size, given initial estimate and direction d, e.g.
// Factor |A1*x+A2*y-b|/sigma -> |A1*(x0+alpha*dx)+A2*(y0+alpha*dy)-b|/sigma
// -> |(A1*dx+A2*dy)*alpha-(b-A1*x0-A2*y0)|/sigma
/* ************************************************************************* */
GaussianFactor::shared_ptr GaussianFactor::alphaFactor(const Symbol& key, const VectorConfig& x,
const VectorConfig& d) const {
// Calculate A matrix
size_t m = b_.size();
Vector A = zero(m);
FOREACH_PAIR(j, Aj, As_)
A += *Aj * d[*j];
// calculate the value of the factor for RHS
Vector b = - unweighted_error(x);
// construct factor
shared_ptr factor(new GaussianFactor(key,Matrix_(A),b,model_));
return factor;
}
/* ************************************************************************* */
namespace gtsam {
string symbol(char c, int index) {
stringstream ss;
ss << c << index;
return ss.str();
}
}
/* ************************************************************************* */
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