Merge pull request #1041 from borglab/release/4.2a3

.github/workflows/build-linux.yml

@@ -15,7 +15,7 @@ jobs:
       BOOST_VERSION: 1.67.0
 
     strategy:
-      fail-fast: false
+      fail-fast: true
       matrix:
         # Github Actions requires a single row to be added to the build matrix.
         # See https://help.github.com/en/articles/workflow-syntax-for-github-actions.

CMakeLists.txt

@@ -11,7 +11,7 @@ endif()
 set (GTSAM_VERSION_MAJOR 4)
 set (GTSAM_VERSION_MINOR 2)
 set (GTSAM_VERSION_PATCH 0)
-set (GTSAM_PRERELEASE_VERSION "a2")
+set (GTSAM_PRERELEASE_VERSION "a3")
 math (EXPR GTSAM_VERSION_NUMERIC "10000 * ${GTSAM_VERSION_MAJOR} + 100 * ${GTSAM_VERSION_MINOR} + ${GTSAM_VERSION_PATCH}")
 
 if (${GTSAM_VERSION_PATCH} EQUAL 0)

gtsam/discrete/DecisionTreeFactor.h

@@ -57,7 +57,7 @@ namespace gtsam {
     /** Default constructor for I/O */
     DecisionTreeFactor();
 
-    /** Constructor from Indices, Ordering, and AlgebraicDecisionDiagram */
+    /** Constructor from DiscreteKeys and AlgebraicDecisionTree */
     DecisionTreeFactor(const DiscreteKeys& keys, const ADT& potentials);
 
     /** Constructor from doubles */
@@ -139,14 +139,14 @@ namespace gtsam {
     /**
      * Apply binary operator (*this) "op" f
      * @param f the second argument for op
-     * @param op a binary operator that operates on AlgebraicDecisionDiagram potentials
+     * @param op a binary operator that operates on AlgebraicDecisionTree
      */
     DecisionTreeFactor apply(const DecisionTreeFactor& f, ADT::Binary op) const;
 
     /**
      * Combine frontal variables using binary operator "op"
      * @param nrFrontals nr. of frontal to combine variables in this factor
-     * @param op a binary operator that operates on AlgebraicDecisionDiagram potentials
+     * @param op a binary operator that operates on AlgebraicDecisionTree
      * @return shared pointer to newly created DecisionTreeFactor
      */
     shared_ptr combine(size_t nrFrontals, ADT::Binary op) const;
@@ -154,7 +154,7 @@ namespace gtsam {
     /**
      * Combine frontal variables in an Ordering using binary operator "op"
      * @param nrFrontals nr. of frontal to combine variables in this factor
-     * @param op a binary operator that operates on AlgebraicDecisionDiagram potentials
+     * @param op a binary operator that operates on AlgebraicDecisionTree
      * @return shared pointer to newly created DecisionTreeFactor
      */
     shared_ptr combine(const Ordering& keys, ADT::Binary op) const;

gtsam/discrete/DiscreteBayesNet.h

@@ -19,7 +19,7 @@
 #pragma once
 
 #include <gtsam/discrete/DiscreteConditional.h>
-#include <gtsam/discrete/DiscretePrior.h>
+#include <gtsam/discrete/DiscreteDistribution.h>
 #include <gtsam/inference/BayesNet.h>
 #include <gtsam/inference/FactorGraph.h>
 
@@ -79,9 +79,9 @@ namespace gtsam {
     // Add inherited versions of add.
     using Base::add;
 
-    /** Add a DiscretePrior using a table or a string */
+    /** Add a DiscreteDistribution using a table or a string */
     void add(const DiscreteKey& key, const std::string& spec) {
-      emplace_shared<DiscretePrior>(key, spec);
+      emplace_shared<DiscreteDistribution>(key, spec);
     }
 
     /** Add a DiscreteCondtional */

gtsam/discrete/DiscreteConditional.cpp

@@ -30,6 +30,7 @@
 #include <string>
 #include <vector>
 #include <utility>
+#include <set>
 
 using namespace std;
 using std::stringstream;
@@ -38,38 +39,97 @@ using std::pair;
 namespace gtsam {
 
 // Instantiate base class
-template class GTSAM_EXPORT Conditional<DecisionTreeFactor, DiscreteConditional> ;
+template class GTSAM_EXPORT
+    Conditional<DecisionTreeFactor, DiscreteConditional>;
 
-/* ******************************************************************************** */
+/* ************************************************************************** */
 DiscreteConditional::DiscreteConditional(const size_t nrFrontals,
-    const DecisionTreeFactor& f) :
+                                         const DecisionTreeFactor& f)
-    BaseFactor(f / (*f.sum(nrFrontals))), BaseConditional(nrFrontals) {
+    : BaseFactor(f / (*f.sum(nrFrontals))), BaseConditional(nrFrontals) {}
-}
 
-/* ******************************************************************************** */
+/* ************************************************************************** */
-DiscreteConditional::DiscreteConditional(const DecisionTreeFactor& joint,
+DiscreteConditional::DiscreteConditional(size_t nrFrontals,
-    const DecisionTreeFactor& marginal) :
+                                         const DiscreteKeys& keys,
-    BaseFactor(
+                                         const ADT& potentials)
-        ISDEBUG("DiscreteConditional::COUNT") ? joint : joint / marginal), BaseConditional(
+    : BaseFactor(keys, potentials), BaseConditional(nrFrontals) {}
-            joint.size()-marginal.size()) {
-  if (ISDEBUG("DiscreteConditional::DiscreteConditional"))
-    cout << (firstFrontalKey()) << endl; //TODO Print all keys
-}
 
-/* ******************************************************************************** */
+/* ************************************************************************** */
 DiscreteConditional::DiscreteConditional(const DecisionTreeFactor& joint,
-    const DecisionTreeFactor& marginal, const Ordering& orderedKeys) :
+                                         const DecisionTreeFactor& marginal)
-    DiscreteConditional(joint, marginal) {
+    : BaseFactor(joint / marginal),
+      BaseConditional(joint.size() - marginal.size()) {}
+
+/* ************************************************************************** */
+DiscreteConditional::DiscreteConditional(const DecisionTreeFactor& joint,
+                                         const DecisionTreeFactor& marginal,
+                                         const Ordering& orderedKeys)
+    : DiscreteConditional(joint, marginal) {
   keys_.clear();
   keys_.insert(keys_.end(), orderedKeys.begin(), orderedKeys.end());
 }
 
-/* ******************************************************************************** */
+/* ************************************************************************** */
 DiscreteConditional::DiscreteConditional(const Signature& signature)
     : BaseFactor(signature.discreteKeys(), signature.cpt()),
       BaseConditional(1) {}
 
-/* ******************************************************************************** */
+/* ************************************************************************** */
+DiscreteConditional DiscreteConditional::operator*(
+    const DiscreteConditional& other) const {
+  // Take union of frontal keys
+  std::set<Key> newFrontals;
+  for (auto&& key : this->frontals()) newFrontals.insert(key);
+  for (auto&& key : other.frontals()) newFrontals.insert(key);
+
+  // Check if frontals overlapped
+  if (nrFrontals() + other.nrFrontals() > newFrontals.size())
+    throw std::invalid_argument(
+        "DiscreteConditional::operator* called with overlapping frontal keys.");
+
+  // Now, add cardinalities.
+  DiscreteKeys discreteKeys;
+  for (auto&& key : frontals())
+    discreteKeys.emplace_back(key, cardinality(key));
+  for (auto&& key : other.frontals())
+    discreteKeys.emplace_back(key, other.cardinality(key));
+
+  // Sort
+  std::sort(discreteKeys.begin(), discreteKeys.end());
+
+  // Add parents to set, to make them unique
+  std::set<DiscreteKey> parents;
+  for (auto&& key : this->parents())
+    if (!newFrontals.count(key)) parents.emplace(key, cardinality(key));
+  for (auto&& key : other.parents())
+    if (!newFrontals.count(key)) parents.emplace(key, other.cardinality(key));
+
+  // Finally, add parents to keys, in order
+  for (auto&& dk : parents) discreteKeys.push_back(dk);
+
+  ADT product = ADT::apply(other, ADT::Ring::mul);
+  return DiscreteConditional(newFrontals.size(), discreteKeys, product);
+}
+
+/* ************************************************************************** */
+DiscreteConditional DiscreteConditional::marginal(Key key) const {
+  if (nrParents() > 0)
+    throw std::invalid_argument(
+        "DiscreteConditional::marginal: single argument version only valid for "
+        "fully specified joint distributions (i.e., no parents).");
+
+  // Calculate the keys as the frontal keys without the given key.
+  DiscreteKeys discreteKeys{{key, cardinality(key)}};
+
+  // Calculate sum
+  ADT adt(*this);
+  for (auto&& k : frontals())
+    if (k != key) adt = adt.sum(k, cardinality(k));
+
+  // Return new factor
+  return DiscreteConditional(1, discreteKeys, adt);
+}
+
+/* ************************************************************************** */
 void DiscreteConditional::print(const string& s,
                                 const KeyFormatter& formatter) const {
   cout << s << " P( ";
@@ -82,7 +142,7 @@ void DiscreteConditional::print(const string& s,
       cout << formatter(*it) << " ";
     }
   }
-  cout << ")";
+  cout << "):\n";
   ADT::print("");
   cout << endl;
 }

gtsam/discrete/DiscreteConditional.h

@@ -49,14 +49,21 @@ class GTSAM_EXPORT DiscreteConditional
   /// @name Standard Constructors
   /// @{
 
-  /** default constructor needed for serialization */
+  /// Default constructor needed for serialization.
   DiscreteConditional() {}
 
-  /** constructor from factor */
+  /// Construct from factor, taking the first `nFrontals` keys as frontals.
   DiscreteConditional(size_t nFrontals, const DecisionTreeFactor& f);
 
+  /**
+   * Construct from DiscreteKeys and AlgebraicDecisionTree, taking the first
+   * `nFrontals` keys as frontals, in the order given.
+   */
+  DiscreteConditional(size_t nFrontals, const DiscreteKeys& keys,
+                      const ADT& potentials);
+
   /** Construct from signature */
-  DiscreteConditional(const Signature& signature);
+  explicit DiscreteConditional(const Signature& signature);
 
   /**
    * Construct from key, parents, and a Signature::Table specifying the
@@ -82,31 +89,45 @@ class GTSAM_EXPORT DiscreteConditional
                       const std::string& spec)
       : DiscreteConditional(Signature(key, parents, spec)) {}
 
-  /// No-parent specialization; can also use DiscretePrior.
+  /// No-parent specialization; can also use DiscreteDistribution.
   DiscreteConditional(const DiscreteKey& key, const std::string& spec)
       : DiscreteConditional(Signature(key, {}, spec)) {}
 
-  /** construct P(X|Y)=P(X,Y)/P(Y) from P(X,Y) and P(Y) */
+  /** 
+   * @brief construct P(X|Y) = f(X,Y)/f(Y) from f(X,Y) and f(Y)
+   * Assumes but *does not check* that f(Y)=sum_X f(X,Y). 
+   */
   DiscreteConditional(const DecisionTreeFactor& joint,
                       const DecisionTreeFactor& marginal);
 
-  /** construct P(X|Y)=P(X,Y)/P(Y) from P(X,Y) and P(Y) */
+  /** 
+   * @brief construct P(X|Y) = f(X,Y)/f(Y) from f(X,Y) and f(Y)
+   * Assumes but *does not check* that f(Y)=sum_X f(X,Y).
+   * Makes sure the keys are ordered as given. Does not check orderedKeys.
+   */
   DiscreteConditional(const DecisionTreeFactor& joint,
                       const DecisionTreeFactor& marginal,
                       const Ordering& orderedKeys);
 
   /**
-   * Combine several conditional into a single one.
+   * @brief Combine two conditionals, yielding a new conditional with the union
-   * The conditionals must be given in increasing order, meaning that the
+   * of the frontal keys, ordered by gtsam::Key.
-   * parents of any conditional may not include a conditional coming before it.
+   *
-   * @param firstConditional Iterator to the first conditional to combine, must
+   * The two conditionals must make a valid Bayes net fragment, i.e.,
-   * dereference to a shared_ptr<DiscreteConditional>.
+   * the frontal variables cannot overlap, and must be acyclic:
-   * @param lastConditional Iterator to after the last conditional to combine,
+   * Example of correct use:
-   * must dereference to a shared_ptr<DiscreteConditional>.
+   *   P(A,B) = P(A|B) * P(B)
-   * */
+   *   P(A,B|C) = P(A|B) * P(B|C)
-  template <typename ITERATOR>
+   *   P(A,B,C) = P(A,B|C) * P(C)
-  static shared_ptr Combine(ITERATOR firstConditional,
+   * Example of incorrect use:
-                            ITERATOR lastConditional);
+   *   P(A|B) * P(A|C) = ?
+   *   P(A|B) * P(B|A) = ?
+   * We check for overlapping frontals, but do *not* check for cyclic.
+   */
+  DiscreteConditional operator*(const DiscreteConditional& other) const;
+
+  /** Calculate marginal on given key, no parent case. */
+  DiscreteConditional marginal(Key key) const;
 
   /// @}
   /// @name Testable
@@ -136,11 +157,6 @@ class GTSAM_EXPORT DiscreteConditional
     return ADT::operator()(values);
   }
 
-  /** Convert to a factor */
-  DecisionTreeFactor::shared_ptr toFactor() const {
-    return DecisionTreeFactor::shared_ptr(new DecisionTreeFactor(*this));
-  }
-
   /** Restrict to given parent values, returns DecisionTreeFactor */
   DecisionTreeFactor::shared_ptr choose(
       const DiscreteValues& parentsValues) const;
@@ -208,23 +224,4 @@ class GTSAM_EXPORT DiscreteConditional
 template <>
 struct traits<DiscreteConditional> : public Testable<DiscreteConditional> {};
 
-/* ************************************************************************* */
-template <typename ITERATOR>
-DiscreteConditional::shared_ptr DiscreteConditional::Combine(
-    ITERATOR firstConditional, ITERATOR lastConditional) {
-  // TODO:  check for being a clique
-
-  // multiply all the potentials of the given conditionals
-  size_t nrFrontals = 0;
-  DecisionTreeFactor product;
-  for (ITERATOR it = firstConditional; it != lastConditional;
-       ++it, ++nrFrontals) {
-    DiscreteConditional::shared_ptr c = *it;
-    DecisionTreeFactor::shared_ptr factor = c->toFactor();
-    product = (*factor) * product;
-  }
-  // and then create a new multi-frontal conditional
-  return boost::make_shared<DiscreteConditional>(nrFrontals, product);
-}
-
 }  // namespace gtsam

gtsam/discrete/DiscreteDistribution.cpp

@@ -10,21 +10,23 @@
  * -------------------------------------------------------------------------- */
 
 /**
- *  @file DiscretePrior.cpp
+ *  @file DiscreteDistribution.cpp
  *  @date December 2021
  *  @author Frank Dellaert
  */
 
-#include <gtsam/discrete/DiscretePrior.h>
+#include <gtsam/discrete/DiscreteDistribution.h>
+
+#include <vector>
 
 namespace gtsam {
 
-void DiscretePrior::print(const std::string& s,
+void DiscreteDistribution::print(const std::string& s,
                                  const KeyFormatter& formatter) const {
   Base::print(s, formatter);
 }
 
-double DiscretePrior::operator()(size_t value) const {
+double DiscreteDistribution::operator()(size_t value) const {
   if (nrFrontals() != 1)
     throw std::invalid_argument(
         "Single value operator can only be invoked on single-variable "
@@ -34,10 +36,10 @@ double DiscretePrior::operator()(size_t value) const {
   return Base::operator()(values);
 }
 
-std::vector<double> DiscretePrior::pmf() const {
+std::vector<double> DiscreteDistribution::pmf() const {
   if (nrFrontals() != 1)
     throw std::invalid_argument(
-        "DiscretePrior::pmf only defined for single-variable priors");
+        "DiscreteDistribution::pmf only defined for single-variable priors");
   const size_t nrValues = cardinalities_.at(keys_[0]);
   std::vector<double> array;
   array.reserve(nrValues);

gtsam/discrete/DiscreteDistribution.h

@@ -10,7 +10,7 @@
  * -------------------------------------------------------------------------- */
 
 /**
- *  @file DiscretePrior.h
+ *  @file DiscreteDistribution.h
  *  @date December 2021
  *  @author Frank Dellaert
  */
@@ -20,6 +20,7 @@
 #include <gtsam/discrete/DiscreteConditional.h>
 
 #include <string>
+#include <vector>
 
 namespace gtsam {
 
@@ -27,7 +28,7 @@ namespace gtsam {
  * A prior probability on a set of discrete variables.
  * Derives from DiscreteConditional
  */
-class GTSAM_EXPORT DiscretePrior : public DiscreteConditional {
+class GTSAM_EXPORT DiscreteDistribution : public DiscreteConditional {
  public:
   using Base = DiscreteConditional;
 
@@ -35,35 +36,36 @@ class GTSAM_EXPORT DiscretePrior : public DiscreteConditional {
   /// @{
 
   /// Default constructor needed for serialization.
-  DiscretePrior() {}
+  DiscreteDistribution() {}
 
   /// Constructor from factor.
-  DiscretePrior(const DecisionTreeFactor& f) : Base(f.size(), f) {}
+  explicit DiscreteDistribution(const DecisionTreeFactor& f)
+      : Base(f.size(), f) {}
 
   /**
    * Construct from a Signature.
    *
-   * Example: DiscretePrior P(D % "3/2");
+   * Example: DiscreteDistribution P(D % "3/2");
    */
-  DiscretePrior(const Signature& s) : Base(s) {}
+  explicit DiscreteDistribution(const Signature& s) : Base(s) {}
 
   /**
-   * Construct from key and a Signature::Table specifying the
+   * Construct from key and a vector of floats specifying the probability mass
-   * conditional probability table (CPT).
+   * function (PMF).
    *
-   * Example: DiscretePrior P(D, table);
+   * Example: DiscreteDistribution P(D, {0.4, 0.6});
    */
-  DiscretePrior(const DiscreteKey& key, const Signature::Table& table)
+  DiscreteDistribution(const DiscreteKey& key, const std::vector<double>& spec)
-      : Base(Signature(key, {}, table)) {}
+      : DiscreteDistribution(Signature(key, {}, Signature::Table{spec})) {}
 
   /**
-   * Construct from key and a string specifying the conditional
+   * Construct from key and a string specifying the probability mass function
-   * probability table (CPT).
+   * (PMF).
    *
-   * Example: DiscretePrior P(D, "9/1 2/8 3/7 1/9");
+   * Example: DiscreteDistribution P(D, "9/1 2/8 3/7 1/9");
    */
-  DiscretePrior(const DiscreteKey& key, const std::string& spec)
+  DiscreteDistribution(const DiscreteKey& key, const std::string& spec)
-      : DiscretePrior(Signature(key, {}, spec)) {}
+      : DiscreteDistribution(Signature(key, {}, spec)) {}
 
   /// @}
   /// @name Testable
@@ -102,10 +104,10 @@ class GTSAM_EXPORT DiscretePrior : public DiscreteConditional {
 
   /// @}
 };
-// DiscretePrior
+// DiscreteDistribution
 
 // traits
 template <>
-struct traits<DiscretePrior> : public Testable<DiscretePrior> {};
+struct traits<DiscreteDistribution> : public Testable<DiscreteDistribution> {};
 
 }  // namespace gtsam

gtsam/discrete/discrete.i

@@ -58,6 +58,15 @@ virtual class DecisionTreeFactor : gtsam::DiscreteFactor {
              const gtsam::KeyFormatter& keyFormatter =
                  gtsam::DefaultKeyFormatter) const;
   bool equals(const gtsam::DecisionTreeFactor& other, double tol = 1e-9) const;
+
+  double operator()(const gtsam::DiscreteValues& values) const;
+  gtsam::DecisionTreeFactor operator*(const gtsam::DecisionTreeFactor& f) const;
+  size_t cardinality(gtsam::Key j) const;
+  gtsam::DecisionTreeFactor operator/(const gtsam::DecisionTreeFactor& f) const;
+  gtsam::DecisionTreeFactor* sum(size_t nrFrontals) const;
+  gtsam::DecisionTreeFactor* sum(const gtsam::Ordering& keys) const;
+  gtsam::DecisionTreeFactor* max(size_t nrFrontals) const;
+
   string dot(
       const gtsam::KeyFormatter& keyFormatter = gtsam::DefaultKeyFormatter,
       bool showZero = true) const;
@@ -86,14 +95,18 @@ virtual class DiscreteConditional : gtsam::DecisionTreeFactor {
   DiscreteConditional(const gtsam::DecisionTreeFactor& joint,
                       const gtsam::DecisionTreeFactor& marginal,
                       const gtsam::Ordering& orderedKeys);
+  gtsam::DiscreteConditional operator*(
+      const gtsam::DiscreteConditional& other) const;
+  DiscreteConditional marginal(gtsam::Key key) const;
   void print(string s = "Discrete Conditional\n",
              const gtsam::KeyFormatter& keyFormatter =
                  gtsam::DefaultKeyFormatter) const;
   bool equals(const gtsam::DiscreteConditional& other, double tol = 1e-9) const;
+  size_t nrFrontals() const;
+  size_t nrParents() const;
   void printSignature(
       string s = "Discrete Conditional: ",
       const gtsam::KeyFormatter& formatter = gtsam::DefaultKeyFormatter) const;
-  gtsam::DecisionTreeFactor* toFactor() const;
   gtsam::DecisionTreeFactor* choose(
       const gtsam::DiscreteValues& parentsValues) const;
   gtsam::DecisionTreeFactor* likelihood(
@@ -115,11 +128,12 @@ virtual class DiscreteConditional : gtsam::DecisionTreeFactor {
               std::map<gtsam::Key, std::vector<std::string>> names) const;
 };
 
-#include <gtsam/discrete/DiscretePrior.h>
+#include <gtsam/discrete/DiscreteDistribution.h>
-virtual class DiscretePrior : gtsam::DiscreteConditional {
+virtual class DiscreteDistribution : gtsam::DiscreteConditional {
-  DiscretePrior();
+  DiscreteDistribution();
-  DiscretePrior(const gtsam::DecisionTreeFactor& f);
+  DiscreteDistribution(const gtsam::DecisionTreeFactor& f);
-  DiscretePrior(const gtsam::DiscreteKey& key, string spec);
+  DiscreteDistribution(const gtsam::DiscreteKey& key, string spec);
+  DiscreteDistribution(const gtsam::DiscreteKey& key, std::vector<double> spec);
   void print(string s = "Discrete Prior\n",
              const gtsam::KeyFormatter& keyFormatter =
                  gtsam::DefaultKeyFormatter) const;

gtsam/discrete/tests/testDecisionTreeFactor.cpp

@@ -17,10 +17,12 @@
  *  @author Duy-Nguyen Ta
  */
 
-#include <gtsam/discrete/Signature.h>
-#include <gtsam/discrete/DecisionTreeFactor.h>
-#include <gtsam/base/Testable.h>
 #include <CppUnitLite/TestHarness.h>
+#include <gtsam/base/Testable.h>
+#include <gtsam/discrete/DecisionTreeFactor.h>
+#include <gtsam/discrete/DiscreteDistribution.h>
+#include <gtsam/discrete/Signature.h>
+
 #include <boost/assign/std/map.hpp>
 using namespace boost::assign;
 
@@ -51,17 +53,21 @@ TEST( DecisionTreeFactor, constructors)
 }
 
 /* ************************************************************************* */
-TEST_UNSAFE( DecisionTreeFactor, multiplication)
+TEST(DecisionTreeFactor, multiplication) {
-{
+  DiscreteKey v0(0, 2), v1(1, 2), v2(2, 2);
-  DiscreteKey v0(0,2), v1(1,2), v2(2,2);
 
+  // Multiply with a DiscreteDistribution, i.e., Bayes Law!
+  DiscreteDistribution prior(v1 % "1/3");
   DecisionTreeFactor f1(v0 & v1, "1 2 3 4");
+  DecisionTreeFactor expected(v0 & v1, "0.25 1.5 0.75 3");
+  CHECK(assert_equal(expected, static_cast<DecisionTreeFactor>(prior) * f1));
+  CHECK(assert_equal(expected, f1 * prior));
+
+  // Multiply two factors
   DecisionTreeFactor f2(v1 & v2, "5 6 7 8");
-
-  DecisionTreeFactor expected(v0 & v1 & v2, "5 6 14 16 15 18 28 32");
-
   DecisionTreeFactor actual = f1 * f2;
-  CHECK(assert_equal(expected, actual));
+  DecisionTreeFactor expected2(v0 & v1 & v2, "5 6 14 16 15 18 28 32");
+  CHECK(assert_equal(expected2, actual));
 }
 
 /* ************************************************************************* */

gtsam/discrete/tests/testDiscreteConditional.cpp

@@ -34,20 +34,21 @@ using namespace gtsam;
 TEST(DiscreteConditional, constructors) {
   DiscreteKey X(0, 2), Y(2, 3), Z(1, 2);  // watch ordering !
 
-  DiscreteConditional expected(X | Y = "1/1 2/3 1/4");
+  DiscreteConditional actual(X | Y = "1/1 2/3 1/4");
-  EXPECT_LONGS_EQUAL(0, *(expected.beginFrontals()));
+  EXPECT_LONGS_EQUAL(0, *(actual.beginFrontals()));
-  EXPECT_LONGS_EQUAL(2, *(expected.beginParents()));
+  EXPECT_LONGS_EQUAL(2, *(actual.beginParents()));
-  EXPECT(expected.endParents() == expected.end());
+  EXPECT(actual.endParents() == actual.end());
-  EXPECT(expected.endFrontals() == expected.beginParents());
+  EXPECT(actual.endFrontals() == actual.beginParents());
 
   DecisionTreeFactor f1(X & Y, "0.5 0.4 0.2 0.5 0.6 0.8");
-  DiscreteConditional actual1(1, f1);
+  DiscreteConditional expected1(1, f1);
-  EXPECT(assert_equal(expected, actual1, 1e-9));
+  EXPECT(assert_equal(expected1, actual, 1e-9));
 
   DecisionTreeFactor f2(
       X & Y & Z, "0.2 0.5 0.3 0.6 0.4 0.7 0.25 0.55 0.35 0.65 0.45 0.75");
   DiscreteConditional actual2(1, f2);
-  EXPECT(assert_equal(f2 / *f2.sum(1), *actual2.toFactor(), 1e-9));
+  DecisionTreeFactor expected2 = f2 / *f2.sum(1);
+  EXPECT(assert_equal(expected2, static_cast<DecisionTreeFactor>(actual2)));
 }
 
 /* ************************************************************************* */
@@ -61,6 +62,7 @@ TEST(DiscreteConditional, constructors_alt_interface) {
   r3 += 1.0, 4.0;
   table += r1, r2, r3;
   DiscreteConditional actual1(X, {Y}, table);
+
   DecisionTreeFactor f1(X & Y, "0.5 0.4 0.2 0.5 0.6 0.8");
   DiscreteConditional expected1(1, f1);
   EXPECT(assert_equal(expected1, actual1, 1e-9));
@@ -68,41 +70,141 @@ TEST(DiscreteConditional, constructors_alt_interface) {
   DecisionTreeFactor f2(
       X & Y & Z, "0.2 0.5 0.3 0.6 0.4 0.7 0.25 0.55 0.35 0.65 0.45 0.75");
   DiscreteConditional actual2(1, f2);
-  EXPECT(assert_equal(f2 / *f2.sum(1), *actual2.toFactor(), 1e-9));
+  DecisionTreeFactor expected2 = f2 / *f2.sum(1);
+  EXPECT(assert_equal(expected2, static_cast<DecisionTreeFactor>(actual2)));
 }
 
 /* ************************************************************************* */
 TEST(DiscreteConditional, constructors2) {
-  // Declare keys and ordering
   DiscreteKey C(0, 2), B(1, 2);
-  DecisionTreeFactor actual(C & B, "0.8 0.75 0.2 0.25");
   Signature signature((C | B) = "4/1 3/1");
-  DiscreteConditional expected(signature);
+  DiscreteConditional actual(signature);
-  DecisionTreeFactor::shared_ptr expectedFactor = expected.toFactor();
+
-  EXPECT(assert_equal(*expectedFactor, actual));
+  DecisionTreeFactor expected(C & B, "0.8 0.75 0.2 0.25");
+  EXPECT(assert_equal(expected, static_cast<DecisionTreeFactor>(actual)));
 }
 
 /* ************************************************************************* */
 TEST(DiscreteConditional, constructors3) {
-  // Declare keys and ordering
   DiscreteKey C(0, 2), B(1, 2), A(2, 2);
-  DecisionTreeFactor actual(C & B & A, "0.8 0.5 0.5 0.2 0.2 0.5 0.5 0.8");
   Signature signature((C | B, A) = "4/1 1/1 1/1 1/4");
-  DiscreteConditional expected(signature);
+  DiscreteConditional actual(signature);
-  DecisionTreeFactor::shared_ptr expectedFactor = expected.toFactor();
+
-  EXPECT(assert_equal(*expectedFactor, actual));
+  DecisionTreeFactor expected(C & B & A, "0.8 0.5 0.5 0.2 0.2 0.5 0.5 0.8");
+  EXPECT(assert_equal(expected, static_cast<DecisionTreeFactor>(actual)));
 }
 
 /* ************************************************************************* */
-TEST(DiscreteConditional, Combine) {
+// Check calculation of joint P(A,B)
-  DiscreteKey A(0, 2), B(1, 2);
+TEST(DiscreteConditional, Multiply) {
-  vector<DiscreteConditional::shared_ptr> c;
+  DiscreteKey A(1, 2), B(0, 2);
-  c.push_back(boost::make_shared<DiscreteConditional>(A | B = "1/2 2/1"));
+  DiscreteConditional conditional(A | B = "1/2 2/1");
-  c.push_back(boost::make_shared<DiscreteConditional>(B % "1/2"));
+  DiscreteConditional prior(B % "1/2");
-  DecisionTreeFactor factor(A & B, "0.111111 0.444444 0.222222 0.222222");
+
-  DiscreteConditional expected(2, factor);
+  // The expected factor
-  auto actual = DiscreteConditional::Combine(c.begin(), c.end());
+  DecisionTreeFactor f(A & B, "1 4 2 2");
-  EXPECT(assert_equal(expected, *actual, 1e-5));
+  DiscreteConditional expected(2, f);
+
+  // P(A,B) = P(A|B) * P(B) = P(B) * P(A|B)
+  for (auto&& actual : {prior * conditional, conditional * prior}) {
+    EXPECT_LONGS_EQUAL(2, actual.nrFrontals());
+    KeyVector frontals(actual.beginFrontals(), actual.endFrontals());
+    EXPECT((frontals == KeyVector{0, 1}));
+    for (auto&& it : actual.enumerate()) {
+      const DiscreteValues& v = it.first;
+      EXPECT_DOUBLES_EQUAL(actual(v), conditional(v) * prior(v), 1e-9);
+    }
+    // And for good measure:
+    EXPECT(assert_equal(expected, actual));
+  }
+}
+
+/* ************************************************************************* */
+// Check calculation of conditional joint P(A,B|C)
+TEST(DiscreteConditional, Multiply2) {
+  DiscreteKey A(0, 2), B(1, 2), C(2, 2);
+  DiscreteConditional A_given_B(A | B = "1/3 3/1");
+  DiscreteConditional B_given_C(B | C = "1/3 3/1");
+
+  // P(A,B|C) = P(A|B)P(B|C) = P(B|C)P(A|B)
+  for (auto&& actual : {A_given_B * B_given_C, B_given_C * A_given_B}) {
+    EXPECT_LONGS_EQUAL(2, actual.nrFrontals());
+    EXPECT_LONGS_EQUAL(1, actual.nrParents());
+    KeyVector frontals(actual.beginFrontals(), actual.endFrontals());
+    EXPECT((frontals == KeyVector{0, 1}));
+    for (auto&& it : actual.enumerate()) {
+      const DiscreteValues& v = it.first;
+      EXPECT_DOUBLES_EQUAL(actual(v), A_given_B(v) * B_given_C(v), 1e-9);
+    }
+  }
+}
+
+/* ************************************************************************* */
+// Check calculation of conditional joint P(A,B|C), double check keys
+TEST(DiscreteConditional, Multiply3) {
+  DiscreteKey A(1, 2), B(2, 2), C(0, 2);  // different keys!!!
+  DiscreteConditional A_given_B(A | B = "1/3 3/1");
+  DiscreteConditional B_given_C(B | C = "1/3 3/1");
+
+  // P(A,B|C) = P(A|B)P(B|C) = P(B|C)P(A|B)
+  for (auto&& actual : {A_given_B * B_given_C, B_given_C * A_given_B}) {
+    EXPECT_LONGS_EQUAL(2, actual.nrFrontals());
+    EXPECT_LONGS_EQUAL(1, actual.nrParents());
+    KeyVector frontals(actual.beginFrontals(), actual.endFrontals());
+    EXPECT((frontals == KeyVector{1, 2}));
+    for (auto&& it : actual.enumerate()) {
+      const DiscreteValues& v = it.first;
+      EXPECT_DOUBLES_EQUAL(actual(v), A_given_B(v) * B_given_C(v), 1e-9);
+    }
+  }
+}
+
+/* ************************************************************************* */
+// Check calculation of conditional joint P(A,B,C|D,E) = P(A,B|D) P(C|D,E)
+TEST(DiscreteConditional, Multiply4) {
+  DiscreteKey A(0, 2), B(1, 2), C(2, 2), D(4, 2), E(3, 2);
+  DiscreteConditional A_given_B(A | B = "1/3 3/1");
+  DiscreteConditional B_given_D(B | D = "1/3 3/1");
+  DiscreteConditional AB_given_D = A_given_B * B_given_D;
+  DiscreteConditional C_given_DE((C | D, E) = "4/1 1/1 1/1 1/4");
+
+  // P(A,B,C|D,E) = P(A,B|D) P(C|D,E) = P(C|D,E) P(A,B|D)
+  for (auto&& actual : {AB_given_D * C_given_DE, C_given_DE * AB_given_D}) {
+    EXPECT_LONGS_EQUAL(3, actual.nrFrontals());
+    EXPECT_LONGS_EQUAL(2, actual.nrParents());
+    KeyVector frontals(actual.beginFrontals(), actual.endFrontals());
+    EXPECT((frontals == KeyVector{0, 1, 2}));
+    KeyVector parents(actual.beginParents(), actual.endParents());
+    EXPECT((parents == KeyVector{3, 4}));
+    for (auto&& it : actual.enumerate()) {
+      const DiscreteValues& v = it.first;
+      EXPECT_DOUBLES_EQUAL(actual(v), AB_given_D(v) * C_given_DE(v), 1e-9);
+    }
+  }
+}
+
+/* ************************************************************************* */
+// Check calculation of marginals for joint P(A,B)
+TEST(DiscreteConditional, marginals) {
+  DiscreteKey A(1, 2), B(0, 2);
+  DiscreteConditional conditional(A | B = "1/2 2/1");
+  DiscreteConditional prior(B % "1/2");
+  DiscreteConditional pAB = prior * conditional;
+
+  DiscreteConditional actualA = pAB.marginal(A.first);
+  DiscreteConditional pA(A % "5/4");
+  EXPECT(assert_equal(pA, actualA));
+  EXPECT_LONGS_EQUAL(1, actualA.nrFrontals());
+  EXPECT_LONGS_EQUAL(0, actualA.nrParents());
+  KeyVector frontalsA(actualA.beginFrontals(), actualA.endFrontals());
+  EXPECT((frontalsA == KeyVector{1}));
+
+  DiscreteConditional actualB = pAB.marginal(B.first);
+  EXPECT(assert_equal(prior, actualB));
+  EXPECT_LONGS_EQUAL(1, actualB.nrFrontals());
+  EXPECT_LONGS_EQUAL(0, actualB.nrParents());
+  KeyVector frontalsB(actualB.beginFrontals(), actualB.endFrontals());
+  EXPECT((frontalsB == KeyVector{0}));
 }
 
 /* ************************************************************************* */

gtsam/discrete/tests/testDiscreteDistribution.cpp

@@ -11,47 +11,66 @@
 
 /*
  * @file    testDiscretePrior.cpp
- * @brief   unit tests for DiscretePrior
+ * @brief   unit tests for DiscreteDistribution
  * @author  Frank dellaert
  * @date    December 2021
  */
 
 #include <CppUnitLite/TestHarness.h>
-#include <gtsam/discrete/DiscretePrior.h>
+#include <gtsam/discrete/DiscreteDistribution.h>
 #include <gtsam/discrete/Signature.h>
 
-using namespace std;
 using namespace gtsam;
 
 static const DiscreteKey X(0, 2);
 
 /* ************************************************************************* */
-TEST(DiscretePrior, constructors) {
+TEST(DiscreteDistribution, constructors) {
-  DiscretePrior actual(X % "2/3");
+  DecisionTreeFactor f(X, "0.4 0.6");
+  DiscreteDistribution expected(f);
+
+  DiscreteDistribution actual(X % "2/3");
   EXPECT_LONGS_EQUAL(1, actual.nrFrontals());
   EXPECT_LONGS_EQUAL(0, actual.nrParents());
-  DecisionTreeFactor f(X, "0.4 0.6");
-  DiscretePrior expected(f);
   EXPECT(assert_equal(expected, actual, 1e-9));
+
+  const std::vector<double> pmf{0.4, 0.6};
+  DiscreteDistribution actual2(X, pmf);
+  EXPECT_LONGS_EQUAL(1, actual2.nrFrontals());
+  EXPECT_LONGS_EQUAL(0, actual2.nrParents());
+  EXPECT(assert_equal(expected, actual2, 1e-9));
 }
 
 /* ************************************************************************* */
-TEST(DiscretePrior, operator) {
+TEST(DiscreteDistribution, Multiply) {
-  DiscretePrior prior(X % "2/3");
+  DiscreteKey A(0, 2), B(1, 2);
+  DiscreteConditional conditional(A | B = "1/2 2/1");
+  DiscreteDistribution prior(B, "1/2");
+  DiscreteConditional actual = prior * conditional;  // P(A|B) * P(B)
+
+  EXPECT_LONGS_EQUAL(2, actual.nrFrontals());  // = P(A,B)
+  DecisionTreeFactor factor(A & B, "1 4 2 2");
+  DiscreteConditional expected(2, factor);
+  EXPECT(assert_equal(expected, actual, 1e-5));
+}
+
+/* ************************************************************************* */
+TEST(DiscreteDistribution, operator) {
+  DiscreteDistribution prior(X % "2/3");
   EXPECT_DOUBLES_EQUAL(prior(0), 0.4, 1e-9);
   EXPECT_DOUBLES_EQUAL(prior(1), 0.6, 1e-9);
 }
 
 /* ************************************************************************* */
-TEST(DiscretePrior, pmf) {
+TEST(DiscreteDistribution, pmf) {
-  DiscretePrior prior(X % "2/3");
+  DiscreteDistribution prior(X % "2/3");
-  vector<double> expected {0.4, 0.6};
+  std::vector<double> expected{0.4, 0.6};
   EXPECT(prior.pmf() == expected);
 }
 
 /* ************************************************************************* */
-TEST(DiscretePrior, sample) {
+TEST(DiscreteDistribution, sample) {
-  DiscretePrior prior(X % "2/3");
+  DiscreteDistribution prior(X % "2/3");
   prior.sample();
 }
 

gtsam/linear/GaussianFactorGraph.h

@@ -154,7 +154,8 @@ namespace gtsam {
 
     /** Unnormalized probability. O(n) */
     double probPrime(const VectorValues& c) const {
-      return exp(-0.5 * error(c));
+      // NOTE the 0.5 constant is handled by the factor error.
+      return exp(-error(c));
     }
 
     /**

gtsam/linear/tests/testGaussianFactorGraph.cpp

@@ -426,6 +426,7 @@ TEST(GaussianFactorGraph, hessianDiagonal) {
   EXPECT(assert_equal(expected, actual));
 }
 
+/* ************************************************************************* */
 TEST(GaussianFactorGraph, DenseSolve) {
   GaussianFactorGraph fg = createSimpleGaussianFactorGraph();
   VectorValues expected = fg.optimize();
@@ -433,6 +434,28 @@ TEST(GaussianFactorGraph, DenseSolve) {
   EXPECT(assert_equal(expected, actual));
 }
 
+/* ************************************************************************* */
+TEST(GaussianFactorGraph, ProbPrime) {
+  GaussianFactorGraph gfg;
+  gfg.emplace_shared<JacobianFactor>(1, I_1x1, Z_1x1,
+                                     noiseModel::Isotropic::Sigma(1, 1.0));
+
+  VectorValues values;
+  values.insert(1, I_1x1);
+
+  // We are testing the normal distribution PDF where info matrix Σ = 1,
+  // mean mu = 0  and x = 1.
+  // Therefore factor squared error: y = 0.5 * (Σ*x - mu)^2 =
+  // 0.5 * (1.0 - 0)^2 = 0.5
+  // NOTE the 0.5 constant is a part of the factor error.
+  EXPECT_DOUBLES_EQUAL(0.5, gfg.error(values), 1e-12);
+
+  // The gaussian PDF value is: exp^(-0.5 * (Σ*x - mu)^2) / sqrt(2 * PI)
+  // Ignore the denominator and we get: exp^(-0.5 * (1.0)^2) = exp^(-0.5)
+  double expected = exp(-0.5);
+  EXPECT_DOUBLES_EQUAL(expected, gfg.probPrime(values), 1e-12);
+}
+
 /* ************************************************************************* */
 int main() {
   TestResult tr;

gtsam/nonlinear/NonlinearFactorGraph.cpp

@@ -45,7 +45,8 @@ template class FactorGraph<NonlinearFactor>;
 
 /* ************************************************************************* */
 double NonlinearFactorGraph::probPrime(const Values& values) const {
-  return exp(-0.5 * error(values));
+  // NOTE the 0.5 constant is handled by the factor error.
+  return exp(-error(values));
 }
 
 /* ************************************************************************* */
@@ -54,9 +55,14 @@ void NonlinearFactorGraph::print(const std::string& str, const KeyFormatter& key
   for (size_t i = 0; i < factors_.size(); i++) {
     stringstream ss;
     ss << "Factor " << i << ": ";
-    if (factors_[i] != nullptr) factors_[i]->print(ss.str(), keyFormatter);
+    if (factors_[i] != nullptr) {
-    cout << endl;
+      factors_[i]->print(ss.str(), keyFormatter);
+      cout << "\n";
+    } else {
+      cout << ss.str() << "nullptr\n";
     }
+  }
+  std::cout.flush();
 }
 
 /* ************************************************************************* */
@@ -80,8 +86,9 @@ void NonlinearFactorGraph::printErrors(const Values& values, const std::string&
       factor->print(ss.str(), keyFormatter);
       cout << "error = " << errorValue << "\n";
     }
-    cout << endl; // only one "endl" at end might be faster, \n for each factor
+    cout << "\n";
   }
+  std::cout.flush();
 }
 
 /* ************************************************************************* */

gtsam/nonlinear/NonlinearFactorGraph.h

@@ -90,7 +90,7 @@ namespace gtsam {
     /** Test equality */
     bool equals(const NonlinearFactorGraph& other, double tol = 1e-9) const;
 
-    /** unnormalized error, \f$ 0.5 \sum_i (h_i(X_i)-z)^2/\sigma^2 \f$ in the most common case */
+    /** unnormalized error, \f$ \sum_i 0.5 (h_i(X_i)-z)^2 / \sigma^2 \f$ in the most common case */
     double error(const Values& values) const;
 
     /** Unnormalized probability. O(n) */

gtsam/slam/slam.i

@@ -11,7 +11,7 @@ namespace gtsam {
 // ######
 
 #include <gtsam/slam/BetweenFactor.h>
-template <T = {Vector, gtsam::Point2, gtsam::Point3, gtsam::Rot2, gtsam::SO3,
+template <T = {double, Vector, gtsam::Point2, gtsam::Point3, gtsam::Rot2, gtsam::SO3,
                gtsam::SO4, gtsam::Rot3, gtsam::Pose2, gtsam::Pose3,
                gtsam::imuBias::ConstantBias}>
 virtual class BetweenFactor : gtsam::NoiseModelFactor {

python/gtsam/tests/test_DecisionTreeFactor.py

@@ -13,7 +13,7 @@ Author: Frank Dellaert
 
 import unittest
 
-from gtsam import DecisionTreeFactor, DecisionTreeFactor, DiscreteKeys
+from gtsam import DecisionTreeFactor, DiscreteValues, DiscreteDistribution, Ordering
 from gtsam.utils.test_case import GtsamTestCase
 
 
@@ -21,15 +21,59 @@ class TestDecisionTreeFactor(GtsamTestCase):
     """Tests for DecisionTreeFactors."""
 
     def setUp(self):
-        A = (12, 3)
+        self.A = (12, 3)
-        B = (5, 2)
+        self.B = (5, 2)
-        self.factor = DecisionTreeFactor([A, B], "1 2  3 4  5 6")
+        self.factor = DecisionTreeFactor([self.A, self.B], "1 2  3 4  5 6")
 
     def test_enumerate(self):
         actual = self.factor.enumerate()
         _, values = zip(*actual)
         self.assertEqual(list(values), [1.0, 2.0, 3.0, 4.0, 5.0, 6.0])
 
+    def test_multiplication(self):
+        """Test whether multiplication works with overloading."""
+        v0 = (0, 2)
+        v1 = (1, 2)
+        v2 = (2, 2)
+
+        # Multiply with a DiscreteDistribution, i.e., Bayes Law!
+        prior = DiscreteDistribution(v1, [1, 3])
+        f1 = DecisionTreeFactor([v0, v1], "1 2 3 4")
+        expected = DecisionTreeFactor([v0, v1], "0.25 1.5 0.75 3")
+        self.gtsamAssertEquals(DecisionTreeFactor(prior) * f1, expected)
+        self.gtsamAssertEquals(f1 * prior, expected)
+
+        # Multiply two factors
+        f2 = DecisionTreeFactor([v1, v2], "5 6 7 8")
+        actual = f1 * f2
+        expected2 = DecisionTreeFactor([v0, v1, v2], "5 6 14 16 15 18 28 32")
+        self.gtsamAssertEquals(actual, expected2)
+
+    def test_methods(self):
+        """Test whether we can call methods in python."""
+        # double operator()(const DiscreteValues& values) const;
+        values = DiscreteValues()
+        values[self.A[0]] = 0
+        values[self.B[0]] = 0
+        self.assertIsInstance(self.factor(values), float)
+
+        # size_t cardinality(Key j) const;
+        self.assertIsInstance(self.factor.cardinality(self.A[0]), int)
+
+        # DecisionTreeFactor operator/(const DecisionTreeFactor& f) const;
+        self.assertIsInstance(self.factor / self.factor, DecisionTreeFactor)
+
+        # DecisionTreeFactor* sum(size_t nrFrontals) const;
+        self.assertIsInstance(self.factor.sum(1), DecisionTreeFactor)
+
+        # DecisionTreeFactor* sum(const Ordering& keys) const;
+        ordering = Ordering()
+        ordering.push_back(self.A[0])
+        self.assertIsInstance(self.factor.sum(ordering), DecisionTreeFactor)
+
+        # DecisionTreeFactor* max(size_t nrFrontals) const;
+        self.assertIsInstance(self.factor.max(1), DecisionTreeFactor)
+
     def test_markdown(self):
         """Test whether the _repr_markdown_ method."""
 

python/gtsam/tests/test_DiscreteBayesNet.py

@@ -14,7 +14,7 @@ Author: Frank Dellaert
 import unittest
 
 from gtsam import (DiscreteBayesNet, DiscreteConditional, DiscreteFactorGraph,
-                   DiscreteKeys, DiscretePrior, DiscreteValues, Ordering)
+                   DiscreteKeys, DiscreteDistribution, DiscreteValues, Ordering)
 from gtsam.utils.test_case import GtsamTestCase
 
 
@@ -74,7 +74,7 @@ class TestDiscreteBayesNet(GtsamTestCase):
         for j in range(8):
             ordering.push_back(j)
         chordal = fg.eliminateSequential(ordering)
-        expected2 = DiscretePrior(Bronchitis, "11/9")
+        expected2 = DiscreteDistribution(Bronchitis, "11/9")
         self.gtsamAssertEquals(chordal.at(7), expected2)
 
         # solve

python/gtsam/tests/test_DiscreteConditional.py

@@ -16,6 +16,13 @@ import unittest
 from gtsam import DecisionTreeFactor, DiscreteConditional, DiscreteKeys
 from gtsam.utils.test_case import GtsamTestCase
 
+# Some DiscreteKeys for binary variables:
+A = 0, 2
+B = 1, 2
+C = 2, 2
+D = 4, 2
+E = 3, 2
+
 
 class TestDiscreteConditional(GtsamTestCase):
     """Tests for Discrete Conditionals."""
@@ -36,6 +43,53 @@ class TestDiscreteConditional(GtsamTestCase):
         actual = conditional.sample(2)
         self.assertIsInstance(actual, int)
 
+    def test_multiply(self):
+        """Check calculation of joint P(A,B)"""
+        conditional = DiscreteConditional(A, [B], "1/2 2/1")
+        prior = DiscreteConditional(B, "1/2")
+
+        # P(A,B) = P(A|B) * P(B) = P(B) * P(A|B)
+        for actual in [prior * conditional, conditional * prior]:
+            self.assertEqual(2, actual.nrFrontals())
+            for v, value in actual.enumerate():
+                self.assertAlmostEqual(actual(v), conditional(v) * prior(v))
+
+    def test_multiply2(self):
+        """Check calculation of conditional joint P(A,B|C)"""
+        A_given_B = DiscreteConditional(A, [B], "1/3 3/1")
+        B_given_C = DiscreteConditional(B, [C], "1/3 3/1")
+
+        # P(A,B|C) = P(A|B)P(B|C) = P(B|C)P(A|B)
+        for actual in [A_given_B * B_given_C, B_given_C * A_given_B]:
+            self.assertEqual(2, actual.nrFrontals())
+            self.assertEqual(1, actual.nrParents())
+            for v, value in actual.enumerate():
+                self.assertAlmostEqual(actual(v), A_given_B(v) * B_given_C(v))
+
+    def test_multiply4(self):
+        """Check calculation of joint P(A,B,C|D,E) = P(A,B|D) P(C|D,E)"""
+        A_given_B = DiscreteConditional(A, [B], "1/3 3/1")
+        B_given_D = DiscreteConditional(B, [D], "1/3 3/1")
+        AB_given_D = A_given_B * B_given_D
+        C_given_DE = DiscreteConditional(C, [D,  E], "4/1 1/1 1/1 1/4")
+
+        # P(A,B,C|D,E) = P(A,B|D) P(C|D,E) = P(C|D,E) P(A,B|D)
+        for actual in [AB_given_D * C_given_DE, C_given_DE * AB_given_D]:
+            self.assertEqual(3, actual.nrFrontals())
+            self.assertEqual(2, actual.nrParents())
+            for v, value in actual.enumerate():
+                self.assertAlmostEqual(
+                    actual(v), AB_given_D(v) * C_given_DE(v))
+
+    def test_marginals(self):
+        conditional = DiscreteConditional(A, [B], "1/2 2/1")
+        prior = DiscreteConditional(B, "1/2")
+        pAB = prior * conditional
+        self.gtsamAssertEquals(prior, pAB.marginal(B[0]))
+
+        pA = DiscreteConditional(A, "5/4")
+        self.gtsamAssertEquals(pA, pAB.marginal(A[0]))
+
     def test_markdown(self):
         """Test whether the _repr_markdown_ method."""
 
@@ -48,8 +102,7 @@ class TestDiscreteConditional(GtsamTestCase):
 
         conditional = DiscreteConditional(A, parents,
                                           "0/1 1/3  1/1 3/1  0/1 1/0")
-        expected = \
+        expected = " *P(A|B,C):*\n\n" \
-            " *P(A|B,C):*\n\n" \
             "|*B*|*C*|0|1|\n" \
             "|:-:|:-:|:-:|:-:|\n" \
             "|0|0|0|1|\n" \

python/gtsam/tests/test_DiscreteDistribution.py

@@ -14,7 +14,7 @@ Author: Frank Dellaert
 import unittest
 
 import numpy as np
-from gtsam import DecisionTreeFactor, DiscreteKeys, DiscretePrior
+from gtsam import DecisionTreeFactor, DiscreteKeys, DiscreteDistribution
 from gtsam.utils.test_case import GtsamTestCase
 
 X = 0, 2
@@ -25,32 +25,36 @@ class TestDiscretePrior(GtsamTestCase):
 
     def test_constructor(self):
         """Test various constructors."""
-        actual = DiscretePrior(X, "2/3")
         keys = DiscreteKeys()
         keys.push_back(X)
         f = DecisionTreeFactor(keys, "0.4 0.6")
-        expected = DiscretePrior(f)
+        expected = DiscreteDistribution(f)
+
+        actual = DiscreteDistribution(X, "2/3")
         self.gtsamAssertEquals(actual, expected)
 
+        actual2 = DiscreteDistribution(X, [0.4, 0.6])
+        self.gtsamAssertEquals(actual2, expected)
+
     def test_operator(self):
-        prior = DiscretePrior(X, "2/3")
+        prior = DiscreteDistribution(X, "2/3")
         self.assertAlmostEqual(prior(0), 0.4)
         self.assertAlmostEqual(prior(1), 0.6)
 
     def test_pmf(self):
-        prior = DiscretePrior(X, "2/3")
+        prior = DiscreteDistribution(X, "2/3")
         expected = np.array([0.4, 0.6])
         np.testing.assert_allclose(expected, prior.pmf())
 
     def test_sample(self):
-        prior = DiscretePrior(X, "2/3")
+        prior = DiscreteDistribution(X, "2/3")
         actual = prior.sample()
         self.assertIsInstance(actual, int)
 
     def test_markdown(self):
         """Test the _repr_markdown_ method."""
 
-        prior = DiscretePrior(X, "2/3")
+        prior = DiscreteDistribution(X, "2/3")
         expected = " *P(0):*\n\n" \
             "|0|value|\n" \
             "|:-:|:-:|\n" \

tests/testNonlinearFactorGraph.cpp

@@ -107,6 +107,24 @@ TEST( NonlinearFactorGraph, probPrime )
   DOUBLES_EQUAL(expected,actual,0);
 }
 
+/* ************************************************************************* */
+TEST(NonlinearFactorGraph, ProbPrime2) {
+  NonlinearFactorGraph fg;
+  fg.emplace_shared<PriorFactor<double>>(1, 0.0,
+                                         noiseModel::Isotropic::Sigma(1, 1.0));
+
+  Values values;
+  values.insert(1, 1.0);
+
+  // The prior factor squared error is: 0.5.
+  EXPECT_DOUBLES_EQUAL(0.5, fg.error(values), 1e-12);
+
+  // The probability value is: exp^(-factor_error) / sqrt(2 * PI)
+  // Ignore the denominator and we get: exp^(-factor_error) = exp^(-0.5)
+  double expected = exp(-0.5);
+  EXPECT_DOUBLES_EQUAL(expected, fg.probPrime(values), 1e-12);
+}
+
 /* ************************************************************************* */
 TEST( NonlinearFactorGraph, linearize )
 {