GaussianConditional.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
 
 * -------------------------------------------------------------------------- */
 
#include <gtsam/linear/GaussianConditional.h>
#include <gtsam/linear/Sampler.h>
#include <gtsam/linear/VectorValues.h>
#include <gtsam/linear/linearExceptions.h>
#include <gtsam/hybrid/HybridValues.h>
 
#ifdef __GNUC__
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wunused-variable"
#endif
#ifdef __GNUC__
#pragma GCC diagnostic pop
#endif
 
#include <functional>
#include <list>
#include <string>
#include <cmath>
 
// In Wrappers we have no access to this so have a default ready
static std::mt19937_64 kRandomNumberGenerator(42);
 
using namespace std;
 
namespace gtsam {
 
  /* ************************************************************************* */
  GaussianConditional::GaussianConditional(
    Key key, const Vector& d, const Matrix& R, const SharedDiagonal& sigmas) :
  BaseFactor(key, R, d, sigmas), BaseConditional(1) {}
 
  /* ************************************************************************ */
  GaussianConditional::GaussianConditional(Key key, const Vector& d,
                                           const Matrix& R, Key parent1,
                                           const Matrix& S,
                                           const SharedDiagonal& sigmas)
      : BaseFactor(key, R, parent1, S, d, sigmas), BaseConditional(1) {}
 
  /* ************************************************************************ */
  GaussianConditional::GaussianConditional(Key key, const Vector& d,
                                           const Matrix& R, Key parent1,
                                           const Matrix& S, Key parent2,
                                           const Matrix& T,
                                           const SharedDiagonal& sigmas)
      : BaseFactor(key, R, parent1, S, parent2, T, d, sigmas),
        BaseConditional(1) {}
 
  /* ************************************************************************ */
  GaussianConditional GaussianConditional::FromMeanAndStddev(Key key,
                                                             const Vector& mu,
                                                             double sigma) {
    // |Rx - d| = |x - mu|/sigma
    const Matrix R = Matrix::Identity(mu.size(), mu.size());
    const Vector& d = mu;
    return GaussianConditional(key, d, R,
                               noiseModel::Isotropic::Sigma(mu.size(), sigma));
  }
 
  /* ************************************************************************ */
  GaussianConditional GaussianConditional::FromMeanAndStddev(
      Key key, const Matrix& A, Key parent, const Vector& b, double sigma) {
    // |Rx + Sy - d| = |x-(Ay + b)|/sigma
    const Matrix R = Matrix::Identity(b.size(), b.size());
    const Matrix S = -A;
    const Vector& d = b;
    return GaussianConditional(key, d, R, parent, S,
                               noiseModel::Isotropic::Sigma(b.size(), sigma));
  }
 
  /* ************************************************************************ */
  GaussianConditional GaussianConditional::FromMeanAndStddev(
      Key key, const Matrix& A1, Key parent1, const Matrix& A2, Key parent2,
      const Vector& b, double sigma) {
    // |Rx + Sy + Tz - d| = |x-(A1 y + A2 z + b)|/sigma
    const Matrix R = Matrix::Identity(b.size(), b.size());
    const Matrix S = -A1;
    const Matrix T = -A2;
    const Vector& d = b;
    return GaussianConditional(key, d, R, parent1, S, parent2, T,
                               noiseModel::Isotropic::Sigma(b.size(), sigma));
  }
 
  /* ************************************************************************ */
  void GaussianConditional::print(const string &s, const KeyFormatter& formatter) const {
    cout << (s.empty() ? "" : s + " ") << "p(";
    for (const_iterator it = beginFrontals(); it != endFrontals(); ++it) {
      cout << formatter(*it) << (nrFrontals() > 1 ? " " : "");
    }
 
    if (nrParents()) {
      cout << " |";
      for (const_iterator it = beginParents(); it != endParents(); ++it) {
        cout << " " << formatter(*it);
      }
    }
    cout << ")" << endl;
 
    cout << formatMatrixIndented("  R = ", R()) << endl;
    for (const_iterator it = beginParents() ; it != endParents() ; ++it) {
      cout << formatMatrixIndented("  S[" + formatter(*it) + "] = ", getA(it)) << endl;
    }
    cout << formatMatrixIndented("  d = ", getb(), true) << "\n";
    if (nrParents() == 0) {
      const auto mean = solve({});  // solve for mean.
      mean.print("  mean", formatter);
    }
    cout << "  logNormalizationConstant: " << -negLogConstant() << endl;
    if (model_)
      model_->print("  Noise model: ");
    else
      cout << "  No noise model" << endl;
  }
 
  /* ************************************************************************* */
  bool GaussianConditional::equals(const GaussianFactor& f, double tol) const {
    if (const GaussianConditional* c = dynamic_cast<const GaussianConditional*>(&f)) {
      // check if the size of the parents_ map is the same
      if (parents().size() != c->parents().size())
        return false;
 
      // check if R_ and d_ are linear independent
      for (DenseIndex i = 0; i < Ab_.rows(); i++) {
        list<Vector> rows1, rows2;
        rows1.push_back(Vector(R().row(i)));
        rows2.push_back(Vector(c->R().row(i)));
 
        // check if the matrices are the same
        // iterate over the parents_ map
        for (const_iterator it = beginParents(); it != endParents(); ++it) {
          const_iterator it2 = c->beginParents() + (it - beginParents());
          if (*it != *(it2))
            return false;
          rows1.push_back(row(getA(it), i));
          rows2.push_back(row(c->getA(it2), i));
        }
 
        Vector row1 = concatVectors(rows1);
        Vector row2 = concatVectors(rows2);
        if (!linear_dependent(row1, row2, tol))
          return false;
      }
 
      // check if sigmas are equal
      if ((model_ && !c->model_) || (!model_ && c->model_)
        || (model_ && c->model_ && !model_->equals(*c->model_, tol)))
        return false;
 
      return true;
    } else {
      return false;
    }
  }
 
  /* ************************************************************************* */
  double GaussianConditional::logDeterminant() const {
    if (get_model()) {
      Vector diag = R().diagonal();
      get_model()->whitenInPlace(diag);
      return diag.unaryExpr([](double x) { return log(x); }).sum();
    } else {
      return R().diagonal().unaryExpr([](double x) { return log(x); }).sum();
    }
  }
 
  /* ************************************************************************* */
  //  normalization constant = 1.0 / sqrt((2*pi)^n*det(Sigma))
  //  neg-log = 0.5 * n*log(2*pi) + 0.5 * log det(Sigma)
  double GaussianConditional::negLogConstant() const {
    constexpr double log2pi = 1.8378770664093454835606594728112;
    size_t n = d().size();
    // Sigma = (R'R)^{-1}, det(Sigma) = det((R'R)^{-1}) = det(R'R)^{-1}
    // log det(Sigma) = -log(det(R'R)) = -2*log(det(R))
    // Hence, log det(Sigma)) = -2.0 * logDeterminant()
    // which gives neg-log = 0.5*n*log(2*pi) + 0.5*(-2.0 * logDeterminant())
    //     = 0.5*n*log(2*pi) - (0.5*2.0 * logDeterminant())
    //     = 0.5*n*log(2*pi) - logDeterminant()
    return 0.5 * n * log2pi - logDeterminant();
  }
 
  /* ************************************************************************* */
  //  density = k exp(-error(x))
  //  log = log(k) - error(x)
  double GaussianConditional::logProbability(const VectorValues& x) const {
    return -(negLogConstant() + error(x));
  }
 
  double GaussianConditional::logProbability(const HybridValues& x) const {
    return logProbability(x.continuous());
  }
 
  /* ************************************************************************* */
  double GaussianConditional::evaluate(const VectorValues& x) const {
    return exp(logProbability(x));
  }
 
  double GaussianConditional::evaluate(const HybridValues& x) const {
    return evaluate(x.continuous());
  }
 
  /* ************************************************************************* */
  VectorValues GaussianConditional::solve(const VectorValues& x) const {
    // Concatenate all vector values that correspond to parent variables
    const Vector xS = x.vector(KeyVector(beginParents(), endParents()));
 
    // Update right-hand-side
    const Vector rhs = d() - S() * xS;
 
    // Solve matrix
    const Vector solution = R().triangularView<Eigen::Upper>().solve(rhs);
 
    // Check for indeterminant solution
    if (solution.hasNaN()) {
      throw IndeterminantLinearSystemException(keys().front());
    }
 
    // Insert solution into a VectorValues
    VectorValues result;
    DenseIndex vectorPosition = 0;
    for (const_iterator frontal = beginFrontals(); frontal != endFrontals(); ++frontal) {
      result.emplace(*frontal, solution.segment(vectorPosition, getDim(frontal)));
      vectorPosition += getDim(frontal);
    }
 
    return result;
  }
 
  /* ************************************************************************* */
  VectorValues GaussianConditional::solveOtherRHS(
    const VectorValues& parents, const VectorValues& rhs) const {
    // Concatenate all vector values that correspond to parent variables
    Vector xS = parents.vector(KeyVector(beginParents(), endParents()));
 
    // Instead of updating getb(), update the right-hand-side from the given rhs
    const Vector rhsR = rhs.vector(KeyVector(beginFrontals(), endFrontals()));
    xS = rhsR - S() * xS;
 
    // Solve Matrix
    Vector soln = R().triangularView<Eigen::Upper>().solve(xS);
 
    // Scale by sigmas
    if (model_)
      soln.array() *= model_->sigmas().array();
 
    // Insert solution into a VectorValues
    VectorValues result;
    DenseIndex vectorPosition = 0;
    for (const_iterator frontal = beginFrontals(); frontal != endFrontals(); ++frontal) {
      result.emplace(*frontal, soln.segment(vectorPosition, getDim(frontal)));
      vectorPosition += getDim(frontal);
    }
 
    return result;
  }
 
  /* ************************************************************************* */
  void GaussianConditional::solveTransposeInPlace(VectorValues& gy) const {
    Vector frontalVec = gy.vector(KeyVector(beginFrontals(), endFrontals()));
    frontalVec = R().transpose().triangularView<Eigen::Lower>().solve(frontalVec);
 
    // Check for indeterminate solution
    if (frontalVec.hasNaN()) throw IndeterminantLinearSystemException(this->keys().front());
 
    for (const_iterator it = beginParents(); it!= endParents(); it++)
      gy[*it].noalias() += -1.0 * getA(it).transpose() * frontalVec;
 
    // Scale by sigmas
    if (model_)
      frontalVec.array() *= model_->sigmas().array();
 
    // Write frontal solution into a VectorValues
    DenseIndex vectorPosition = 0;
    for (const_iterator frontal = beginFrontals(); frontal != endFrontals(); ++frontal) {
      gy[*frontal] = frontalVec.segment(vectorPosition, getDim(frontal));
      vectorPosition += getDim(frontal);
    }
  }
 
  /* ************************************************************************ */
  JacobianFactor::shared_ptr GaussianConditional::likelihood(
      const VectorValues& frontalValues) const {
    // Error is |Rx - (d - Sy - Tz - ...)|^2
    // so when we instantiate x (which has to be completely known) we beget:
    // |Sy + Tz + ... - (d - Rx)|^2
    // The noise model just transfers over!
 
    // Get frontalValues as vector
    const Vector x =
        frontalValues.vector(KeyVector(beginFrontals(), endFrontals()));
 
    // Copy the augmented Jacobian matrix:
    auto newAb = Ab_;
 
    // Restrict view to parent blocks
    newAb.firstBlock() += nrFrontals_;
 
    // Update right-hand-side (last column)
    auto last = newAb.matrix().cols() - 1;
    const auto RR = R().triangularView<Eigen::Upper>();
    newAb.matrix().col(last) -= RR * x;
 
    // The keys now do not include the frontal keys:
    KeyVector newKeys;
    newKeys.reserve(nrParents());
    for (auto&& key : parents()) newKeys.push_back(key);
 
    // Hopefully second newAb copy below is optimized out...
    return std::make_shared<JacobianFactor>(newKeys, newAb, model_);
  }
 
  /* **************************************************************************/
  JacobianFactor::shared_ptr GaussianConditional::likelihood(
      const Vector& frontal) const {
    if (nrFrontals() != 1)
      throw std::invalid_argument(
          "GaussianConditional Single value likelihood can only be invoked on "
          "single-variable conditional");
    VectorValues values;
    values.insert(keys_[0], frontal);
    return likelihood(values);
  }
 
  /* ************************************************************************ */
  VectorValues GaussianConditional::sample(const VectorValues& parentsValues,
                                           std::mt19937_64* rng) const {
    if (nrFrontals() != 1) {
      throw std::invalid_argument(
          "GaussianConditional::sample can only be called on single variable "
          "conditionals");
    }
 
    VectorValues solution = solve(parentsValues);
    Key key = firstFrontalKey();
    // The vector of sigma values for sampling.
    // If no model, initialize sigmas to 1, else to model sigmas
    const Vector& sigmas = (!model_) ? Vector::Ones(rows()) : model_->sigmas();
    solution[key] += Sampler::sampleDiagonal(sigmas, rng);
    return solution;
  }
 
  VectorValues GaussianConditional::sample(std::mt19937_64* rng) const {
    if (nrParents() != 0)
      throw std::invalid_argument(
          "sample() can only be invoked on no-parent prior");
    VectorValues values;
    return sample(values);
  }
 
  /* ************************************************************************ */
  VectorValues GaussianConditional::sample() const {
    return sample(&kRandomNumberGenerator);
  }
 
  VectorValues GaussianConditional::sample(const VectorValues& given) const {
    return sample(given, &kRandomNumberGenerator);
  }
 
  /* ************************************************************************ */
 
}  // namespace gtsam