compute logNormalizers and pass to GaussianMixtureFactor

gtsam/hybrid/GaussianMixture.cpp

@@ -200,24 +200,27 @@ std::shared_ptr<GaussianMixtureFactor> GaussianMixture::likelihood(
   const GaussianMixtureFactor::Factors likelihoods(
       conditionals_, [&](const GaussianConditional::shared_ptr &conditional) {
         const auto likelihood_m = conditional->likelihood(given);
-        const double Cgm_Kgcm =
-            logConstant_ - conditional->logNormalizationConstant();
-        if (Cgm_Kgcm == 0.0) {
-          return likelihood_m;
-        } else {
-          // Add a constant factor to the likelihood in case the noise models
-          // are not all equal.
-          GaussianFactorGraph gfg;
-          gfg.push_back(likelihood_m);
-          Vector c(1);
-          c << std::sqrt(2.0 * Cgm_Kgcm);
-          auto constantFactor = std::make_shared<JacobianFactor>(c);
-          gfg.push_back(constantFactor);
-          return std::make_shared<JacobianFactor>(gfg);
-        }
+        return likelihood_m;
       });
+
+  // First compute all the sqrt(|2 pi Sigma|) terms
+  auto computeLogNormalizers = [](const GaussianFactor::shared_ptr &gf) {
+    auto jf = std::dynamic_pointer_cast<JacobianFactor>(gf);
+    // If we have, say, a Hessian factor, then no need to do anything
+    if (!jf) return 0.0;
+
+    auto model = jf->get_model();
+    // If there is no noise model, there is nothing to do.
+    if (!model) {
+      return 0.0;
+    }
+    return ComputeLogNormalizer(model);
+  };
+
+  AlgebraicDecisionTree<Key> log_normalizers =
+      DecisionTree<Key, double>(likelihoods, computeLogNormalizers);
   return std::make_shared<GaussianMixtureFactor>(
-      continuousParentKeys, discreteParentKeys, likelihoods);
+      continuousParentKeys, discreteParentKeys, likelihoods, log_normalizers);
 }
 
 /* ************************************************************************* */

gtsam/hybrid/GaussianMixtureFactor.cpp

@@ -28,11 +28,55 @@
 
 namespace gtsam {
 
+/**
+ * @brief Helper function to augment the [A|b] matrices in the factor components
+ * with the normalizer values.
+ * This is done by storing the normalizer value in
+ * the `b` vector as an additional row.
+ *
+ * @param factors DecisionTree of GaussianFactor shared pointers.
+ * @param logNormalizers Tree of log-normalizers corresponding to each
+ * Gaussian factor in factors.
+ * @return GaussianMixtureFactor::Factors
+ */
+GaussianMixtureFactor::Factors augment(
+    const GaussianMixtureFactor::Factors &factors,
+    const AlgebraicDecisionTree<Key> &logNormalizers) {
+  // Find the minimum value so we can "proselytize" to positive values.
+  // Done because we can't have sqrt of negative numbers.
+  double min_log_normalizer = logNormalizers.min();
+  AlgebraicDecisionTree<Key> log_normalizers = logNormalizers.apply(
+      [&min_log_normalizer](double n) { return n - min_log_normalizer; });
+
+  // Finally, update the [A|b] matrices.
+  auto update = [&log_normalizers](
+                    const Assignment<Key> &assignment,
+                    const GaussianMixtureFactor::sharedFactor &gf) {
+    auto jf = std::dynamic_pointer_cast<JacobianFactor>(gf);
+    if (!jf) return gf;
+    // If the log_normalizer is 0, do nothing
+    if (log_normalizers(assignment) == 0.0) return gf;
+
+    GaussianFactorGraph gfg;
+    gfg.push_back(jf);
+
+    Vector c(1);
+    c << std::sqrt(log_normalizers(assignment));
+    auto constantFactor = std::make_shared<JacobianFactor>(c);
+
+    gfg.push_back(constantFactor);
+    return std::dynamic_pointer_cast<GaussianFactor>(
+        std::make_shared<JacobianFactor>(gfg));
+  };
+  return factors.apply(update);
+}
+
 /* *******************************************************************************/
-GaussianMixtureFactor::GaussianMixtureFactor(const KeyVector &continuousKeys,
-                                             const DiscreteKeys &discreteKeys,
-                                             const Factors &factors)
-    : Base(continuousKeys, discreteKeys), factors_(factors) {}
+GaussianMixtureFactor::GaussianMixtureFactor(
+    const KeyVector &continuousKeys, const DiscreteKeys &discreteKeys,
+    const Factors &factors, const AlgebraicDecisionTree<Key> &logNormalizers)
+    : Base(continuousKeys, discreteKeys),
+      factors_(augment(factors, logNormalizers)) {}
 
 /* *******************************************************************************/
 bool GaussianMixtureFactor::equals(const HybridFactor &lf, double tol) const {
@@ -120,4 +164,20 @@ double GaussianMixtureFactor::error(const HybridValues &values) const {
   return gf->error(values.continuous());
 }
 
+/* *******************************************************************************/
+double ComputeLogNormalizer(
+    const noiseModel::Gaussian::shared_ptr &noise_model) {
+  // Since noise models are Gaussian, we can get the logDeterminant using
+  // the same trick as in GaussianConditional
+  double logDetR = noise_model->R()
+                       .diagonal()
+                       .unaryExpr([](double x) { return log(x); })
+                       .sum();
+  double logDeterminantSigma = -2.0 * logDetR;
+
+  size_t n = noise_model->dim();
+  constexpr double log2pi = 1.8378770664093454835606594728112;
+  return n * log2pi + logDeterminantSigma;
+}
+
 }  // namespace gtsam

gtsam/hybrid/GaussianMixtureFactor.h

@@ -82,10 +82,14 @@ class GTSAM_EXPORT GaussianMixtureFactor : public HybridFactor {
    * their cardinalities.
    * @param factors The decision tree of Gaussian factors stored as the mixture
    * density.
+   * @param logNormalizers Tree of log-normalizers corresponding to each
+   * Gaussian factor in factors.
    */
   GaussianMixtureFactor(const KeyVector &continuousKeys,
                         const DiscreteKeys &discreteKeys,
-                        const Factors &factors);
+                        const Factors &factors,
+                        const AlgebraicDecisionTree<Key> &logNormalizers =
+                            AlgebraicDecisionTree<Key>(0.0));
 
   /**
    * @brief Construct a new GaussianMixtureFactor object using a vector of
@@ -94,12 +98,16 @@ class GTSAM_EXPORT GaussianMixtureFactor : public HybridFactor {
    * @param continuousKeys Vector of keys for continuous factors.
    * @param discreteKeys Vector of discrete keys.
    * @param factors Vector of gaussian factor shared pointers.
+   * @param logNormalizers Tree of log-normalizers corresponding to each
+   * Gaussian factor in factors.
    */
   GaussianMixtureFactor(const KeyVector &continuousKeys,
                         const DiscreteKeys &discreteKeys,
-                        const std::vector<sharedFactor> &factors)
+                        const std::vector<sharedFactor> &factors,
+                        const AlgebraicDecisionTree<Key> &logNormalizers =
+                            AlgebraicDecisionTree<Key>(0.0))
       : GaussianMixtureFactor(continuousKeys, discreteKeys,
-                              Factors(discreteKeys, factors)) {}
+                              Factors(discreteKeys, factors), logNormalizers) {}
 
   /// @}
   /// @name Testable