488 lines
16 KiB
C++
488 lines
16 KiB
C++
/**
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* @file GaussianFactor.cpp
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* @brief Linear Factor....A Gaussian
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* @brief linearFactor
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* @author Christian Potthast
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*/
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#include <boost/foreach.hpp>
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#include <boost/assign/list_inserter.hpp> // for 'insert()'
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#include <boost/assign/std/list.hpp> // for operator += in Ordering
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#include "Matrix.h"
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#include "Ordering.h"
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#include "GaussianConditional.h"
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#include "GaussianFactor.h"
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using namespace std;
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using namespace boost::assign;
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namespace ublas = boost::numeric::ublas;
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using namespace gtsam;
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typedef pair<Symbol,Matrix> NamedMatrix;
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// MACRO to loop. Ugly with pointer, but best I could in short time
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#define FOREACH_PAIR(KEY,VAL,COL) const_iterator it = COL.begin(); \
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const Symbol* KEY = it == COL.end() ? NULL : &(it->first); \
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const Matrix* VAL = it == COL.end() ? NULL : &(it->second); \
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for (; it != COL.end(); it++, KEY=&(it->first), VAL=&(it->second))
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/* ************************************************************************* */
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GaussianFactor::GaussianFactor(const boost::shared_ptr<GaussianConditional>& cg) :
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b_(cg->get_d()) {
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As_.insert(make_pair(cg->key(), cg->get_R()));
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SymbolMap<Matrix>::const_iterator it = cg->parentsBegin();
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for (; it != cg->parentsEnd(); it++) {
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const Symbol& j = it->first;
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const Matrix& Aj = it->second;
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As_.insert(make_pair(j, Aj));
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}
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// set sigmas from precisions
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size_t n = b_.size();
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model_ = noiseModel::Diagonal::Sigmas(cg->get_sigmas());
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}
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/* ************************************************************************* */
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GaussianFactor::GaussianFactor(const vector<shared_ptr> & factors)
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{
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bool verbose = false;
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if (verbose) cout << "GaussianFactor::GaussianFactor (factors)" << endl;
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// Create RHS and sigmas of right size by adding together row counts
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size_t m = 0;
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BOOST_FOREACH(shared_ptr factor, factors) m += factor->numberOfRows();
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b_ = Vector(m);
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Vector sigmas(m);
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size_t pos = 0; // save last position inserted into the new rhs vector
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// iterate over all factors
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BOOST_FOREACH(shared_ptr factor, factors){
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if (verbose) factor->print();
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// number of rows for factor f
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const size_t mf = factor->numberOfRows();
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// copy the rhs vector from factor to b
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const Vector bf = factor->get_b();
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for (size_t i=0; i<mf; i++) b_(pos+i) = bf(i);
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// copy the model_
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for (size_t i=0; i<mf; i++) sigmas(pos+i) = factor->model_->sigma(i);
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// update the matrices
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append_factor(factor,m,pos);
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pos += mf;
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}
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if (verbose) cout << "GaussianFactor::GaussianFactor done" << endl;
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model_ = noiseModel::Diagonal::Sigmas(sigmas);
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}
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/* ************************************************************************* */
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void GaussianFactor::print(const string& s) const {
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cout << s << endl;
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if (empty()) cout << " empty" << endl;
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else {
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FOREACH_PAIR(j,Aj,As_)
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gtsam::print(*Aj, "A["+(string)*j+"]=\n");
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gtsam::print(b_,"b=");
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model_->print("model");
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}
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}
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/* ************************************************************************* */
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size_t GaussianFactor::getDim(const Symbol& key) const {
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const_iterator it = As_.find(key);
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if (it != As_.end())
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return it->second.size2();
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else
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return 0;
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}
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/* ************************************************************************* */
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// Check if two linear factors are equal
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bool GaussianFactor::equals(const Factor<VectorConfig>& f, double tol) const {
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const GaussianFactor* lf = dynamic_cast<const GaussianFactor*>(&f);
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if (lf == NULL) return false;
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if (empty()) return (lf->empty());
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const_iterator it1 = As_.begin(), it2 = lf->As_.begin();
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if(As_.size() != lf->As_.size()) return false;
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for(; it1 != As_.end(); it1++, it2++) {
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const Symbol& j1 = it1->first, j2 = it2->first;
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const Matrix A1 = it1->second, A2 = it2->second;
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if (j1 != j2) return false;
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if (!equal_with_abs_tol(A1,A2,tol))
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return false;
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}
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if( !(::equal_with_abs_tol(b_, (lf->b_),tol)) )
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return false;
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return model_->equals(*(lf->model_),tol);
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}
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/* ************************************************************************* */
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Vector GaussianFactor::unweighted_error(const VectorConfig& c) const {
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Vector e = -b_;
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if (empty()) return e;
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FOREACH_PAIR(j,Aj,As_)
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e += (*Aj * c[*j]);
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return e;
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}
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/* ************************************************************************* */
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Vector GaussianFactor::error_vector(const VectorConfig& c) const {
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if (empty()) return model_->whiten(-b_);
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return model_->whiten(unweighted_error(c));
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}
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/* ************************************************************************* */
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double GaussianFactor::error(const VectorConfig& c) const {
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if (empty()) return 0;
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Vector weighted = error_vector(c); // rtodo: copying vector here?
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return 0.5 * inner_prod(weighted,weighted);
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}
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/* ************************************************************************* */
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list<Symbol> GaussianFactor::keys() const {
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list<Symbol> result;
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typedef pair<Symbol,Matrix> NamedMatrix;
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BOOST_FOREACH(const NamedMatrix& jA, As_)
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result.push_back(jA.first);
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return result;
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}
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/* ************************************************************************* */
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Dimensions GaussianFactor::dimensions() const {
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Dimensions result;
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FOREACH_PAIR(j,Aj,As_)
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result.insert(make_pair(*j,Aj->size2()));
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return result;
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}
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/* ************************************************************************* */
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void GaussianFactor::tally_separator(const Symbol& key, set<Symbol>& separator) const {
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if(involves(key)) {
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FOREACH_PAIR(j,A,As_)
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if(*j != key) separator.insert(*j);
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}
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}
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/* ************************************************************************* */
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Vector GaussianFactor::operator*(const VectorConfig& x) const {
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Vector Ax = zero(b_.size());
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if (empty()) return Ax;
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// Just iterate over all A matrices and multiply in correct config part
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FOREACH_PAIR(j, Aj, As_)
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Ax += (*Aj * x[*j]);
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return model_->whiten(Ax);
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}
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/* ************************************************************************* */
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VectorConfig GaussianFactor::operator^(const Vector& e) const {
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Vector E = model_->whiten(e);
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VectorConfig x;
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// Just iterate over all A matrices and insert Ai^e into VectorConfig
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FOREACH_PAIR(j, Aj, As_)
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x.insert(*j,(*Aj)^E);
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return x;
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}
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/* ************************************************************************* */
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pair<Matrix,Vector> GaussianFactor::matrix(const Ordering& ordering, bool weight) const {
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// rtodo: this is called in eliminate, potential function to optimize?
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// get pointers to the matrices
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vector<const Matrix *> matrices;
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BOOST_FOREACH(const Symbol& j, ordering) {
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const Matrix& Aj = get_A(j);
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matrices.push_back(&Aj);
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}
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// assemble
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Matrix A = collect(matrices);
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Vector b(b_);
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// divide in sigma so error is indeed 0.5*|Ax-b|
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if (weight) model_->WhitenSystem(A,b);
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return make_pair(A, b);
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}
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/* ************************************************************************* */
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Matrix GaussianFactor::matrix_augmented(const Ordering& ordering, bool weight) const {
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// get pointers to the matrices
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vector<const Matrix *> matrices;
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BOOST_FOREACH(const Symbol& j, ordering) {
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const Matrix& Aj = get_A(j);
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matrices.push_back(&Aj);
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}
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// load b into a matrix
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size_t rows = b_.size();
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Matrix B_mat(rows, 1);
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memcpy(B_mat.data().begin(), b_.data().begin(), rows*sizeof(double));
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matrices.push_back(&B_mat);
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// divide in sigma so error is indeed 0.5*|Ax-b|
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Matrix Ab = collect(matrices);
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if (weight) model_->WhitenInPlace(Ab);
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return Ab;
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}
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/* ************************************************************************* */
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boost::tuple<list<int>, list<int>, list<double> >
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GaussianFactor::sparse(const Dimensions& columnIndices) const {
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// declare return values
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list<int> I,J;
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list<double> S;
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// iterate over all matrices in the factor
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FOREACH_PAIR( key, Aj, As_) {
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// find first column index for this key
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int column_start = columnIndices.at(*key);
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for (size_t i = 0; i < Aj->size1(); i++) {
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double sigma_i = model_->sigma(i);
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for (size_t j = 0; j < Aj->size2(); j++)
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if ((*Aj)(i, j) != 0.0) {
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I.push_back(i + 1);
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J.push_back(j + column_start);
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S.push_back((*Aj)(i, j) / sigma_i);
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}
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}
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}
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// return the result
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return boost::tuple<list<int>, list<int>, list<double> >(I,J,S);
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}
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/* ************************************************************************* */
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void GaussianFactor::append_factor(GaussianFactor::shared_ptr f, size_t m, size_t pos) {
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// iterate over all matrices from the factor f
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FOREACH_PAIR( key, A, f->As_) {
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// find the corresponding matrix among As
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iterator mine = As_.find(*key);
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const bool exists = mine != As_.end();
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// find rows and columns
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const size_t n = A->size2();
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// use existing or create new matrix
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if (exists)
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copy(A->data().begin(), A->data().end(), (mine->second).data().begin()+pos*n);
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else {
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Matrix Z = zeros(m, n);
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copy(A->data().begin(), A->data().end(), Z.data().begin()+pos*n);
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insert(*key, Z);
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}
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} // FOREACH
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}
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/* ************************************************************************* */
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/* Note, in place !!!!
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* Do incomplete QR factorization for the first n columns
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* We will do QR on all matrices and on RHS
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* Then take first n rows and make a GaussianConditional,
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* and last rows to make a new joint linear factor on separator
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*/
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/* ************************************************************************* */
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#include <boost/numeric/ublas/triangular.hpp>
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#include <boost/numeric/ublas/io.hpp>
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#include <boost/numeric/ublas/matrix_proxy.hpp>
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pair<GaussianConditional::shared_ptr, GaussianFactor::shared_ptr>
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GaussianFactor::eliminate(const Symbol& key) const
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{
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// if this factor does not involve key, we exit with empty CG and LF
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const_iterator it = As_.find(key);
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if (it==As_.end()) {
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// Conditional Gaussian is just a parent-less node with P(x)=1
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GaussianFactor::shared_ptr lf(new GaussianFactor);
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GaussianConditional::shared_ptr cg(new GaussianConditional(key));
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return make_pair(cg,lf);
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}
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// create an internal ordering that eliminates key first
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Ordering ordering;
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ordering += key;
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BOOST_FOREACH(const Symbol& k, keys())
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if (k != key) ordering += k;
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// extract [A b] from the combined linear factor (ensure that x is leading)
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Matrix Ab = matrix_augmented(ordering,false);
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// Use in-place QR on dense Ab appropriate to NoiseModel
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SharedDiagonal noiseModel = model_->QR(Ab);
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// get dimensions of the eliminated variable
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// TODO: this is another map find that should be avoided !
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size_t n1 = getDim(key), n = Ab.size2() - 1;
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// if m<n1, this factor cannot be eliminated
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size_t maxRank = noiseModel->dim();
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if (maxRank<n1) {
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cout << "Perhaps your factor graph is singular." << endl;
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cout << "Here are the keys involved in the factor now being eliminated:" << endl;
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ordering.print("Keys");
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cout << "The first key, '" << (string)ordering.front() << "', corresponds to the variable being eliminated" << endl;
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throw(domain_error("GaussianFactor::eliminate: fewer constraints than unknowns"));
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}
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// Get alias to augmented RHS d
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ublas::matrix_column<Matrix> d(Ab,n);
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// create base conditional Gaussian
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GaussianConditional::shared_ptr conditional(new GaussianConditional(key,
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sub(d, 0, n1), // form d vector
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sub(Ab, 0, n1, 0, n1), // form R matrix
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sub(noiseModel->sigmas(),0,n1))); // get standard deviations
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// extract the block matrices for parents in both CG and LF
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GaussianFactor::shared_ptr factor(new GaussianFactor);
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size_t j = n1;
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BOOST_FOREACH(Symbol& cur_key, ordering)
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if (cur_key!=key) {
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size_t dim = getDim(cur_key); // TODO avoid find !
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conditional->add(cur_key, sub(Ab, 0, n1, j, j+dim));
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factor->insert(cur_key, sub(Ab, n1, maxRank, j, j+dim));
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j+=dim;
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}
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// Set sigmas
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factor->model_ = noiseModel::Diagonal::Sigmas(sub(noiseModel->sigmas(),n1,maxRank));
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// extract ds vector for the new b
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factor->set_b(sub(d, n1, maxRank));
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return make_pair(conditional, factor);
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}
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/* ************************************************************************* */
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/* Note, in place !!!!
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* Do incomplete QR factorization for the first n columns
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* We will do QR on all matrices and on RHS
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* Then take first n rows and make a GaussianConditional,
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* and last rows to make a new joint linear factor on separator
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*/
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/* ************************************************************************* *
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pair<GaussianConditional::shared_ptr, GaussianFactor::shared_ptr>
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GaussianFactor::eliminate(const Symbol& key) const
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{
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// if this factor does not involve key, we exit with empty CG and LF
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const_iterator it = As_.find(key);
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if (it==As_.end()) {
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// Conditional Gaussian is just a parent-less node with P(x)=1
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GaussianFactor::shared_ptr lf(new GaussianFactor);
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GaussianConditional::shared_ptr cg(new GaussianConditional(key));
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return make_pair(cg,lf);
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}
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// create an internal ordering that eliminates key first
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Ordering ordering;
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ordering += key;
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BOOST_FOREACH(const Symbol& k, keys())
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if (k != key) ordering += k;
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// extract A, b from the combined linear factor (ensure that x is leading)
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// TODO: get Ab as augmented matrix
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// Matrix Ab = matrix_augmented(ordering,false);
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Matrix A; Vector b;
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boost::tie(A, b) = matrix(ordering, false);
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size_t n = A.size2();
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// Do in-place QR to get R, d of the augmented system
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std::list<boost::tuple<Vector, double, double> > solution =
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weighted_eliminate(A, b, model_->sigmas());
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// get dimensions of the eliminated variable
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// TODO: this is another map find that should be avoided !
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size_t n1 = getDim(key);
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// if m<n1, this factor cannot be eliminated
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size_t maxRank = solution.size();
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if (maxRank<n1)
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throw(domain_error("GaussianFactor::eliminate: fewer constraints than unknowns"));
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// unpack the solutions
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Matrix R(maxRank, n);
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Vector r, d(maxRank), newSigmas(maxRank); double di, sigma;
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Matrix::iterator2 Rit = R.begin2();
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size_t i = 0;
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BOOST_FOREACH(boost::tie(r, di, sigma), solution) {
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copy(r.begin(), r.end(), Rit); // copy r vector
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d(i) = di; // copy in rhs
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newSigmas(i) = sigma; // copy in new sigmas
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Rit += n; i += 1;
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}
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// create base conditional Gaussian
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GaussianConditional::shared_ptr conditional(new GaussianConditional(key,
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sub(d, 0, n1), // form d vector
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sub(R, 0, n1, 0, n1), // form R matrix
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sub(newSigmas, 0, n1))); // get standard deviations
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// extract the block matrices for parents in both CG and LF
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GaussianFactor::shared_ptr factor(new GaussianFactor);
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size_t j = n1;
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BOOST_FOREACH(Symbol& cur_key, ordering)
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if (cur_key!=key) {
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size_t dim = getDim(cur_key);
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conditional->add(cur_key, sub(R, 0, n1, j, j+dim));
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factor->insert(cur_key, sub(R, n1, maxRank, j, j+dim));
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j+=dim;
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}
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// Set sigmas
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factor->model_ = noiseModel::Diagonal::Sigmas(sub(newSigmas,n1,maxRank));
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// extract ds vector for the new b
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factor->set_b(sub(d, n1, maxRank));
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return make_pair(conditional, factor);
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}
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/* ************************************************************************* */
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// Creates a factor on step-size, given initial estimate and direction d, e.g.
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// Factor |A1*x+A2*y-b|/sigma -> |A1*(x0+alpha*dx)+A2*(y0+alpha*dy)-b|/sigma
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// -> |(A1*dx+A2*dy)*alpha-(b-A1*x0-A2*y0)|/sigma
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/* ************************************************************************* */
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GaussianFactor::shared_ptr GaussianFactor::alphaFactor(const Symbol& key, const VectorConfig& x,
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const VectorConfig& d) const {
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// Calculate A matrix
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size_t m = b_.size();
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Vector A = zero(m);
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FOREACH_PAIR(j, Aj, As_)
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A += *Aj * d[*j];
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// calculate the value of the factor for RHS
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Vector b = - unweighted_error(x);
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// construct factor
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shared_ptr factor(new GaussianFactor(key,Matrix_(A),b,model_));
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return factor;
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}
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/* ************************************************************************* */
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namespace gtsam {
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string symbol(char c, int index) {
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stringstream ss;
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ss << c << index;
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return ss.str();
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}
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}
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/* ************************************************************************* */
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