Added logDensity and evaluate to Gaussian conditional and Bayes net

gtsam/linear/GaussianBayesNet.cpp

@@ -224,5 +224,19 @@ namespace gtsam {
   }
 
   /* ************************************************************************* */
+  double GaussianBayesNet::logDensity(const VectorValues& x) const {
+    double sum = 0.0;
+    for (const auto& conditional : *this) {
+      if (conditional) sum += conditional->logDensity(x);
+    }
+    return sum;
+  }
+
+  /* ************************************************************************* */
+  double GaussianBayesNet::evaluate(const VectorValues& x) const {
+    return exp(logDensity(x));
+  }
+
+  /* ************************************************************************* */
 
 } // namespace gtsam

gtsam/linear/GaussianBayesNet.h

@@ -88,6 +88,20 @@ namespace gtsam {
     /// @name Standard Interface
     /// @{
 
+    /**
+     * Calculate log-density for given values `x`:
+     *   -0.5*(error + n*log(2*pi) + log det(Sigma))
+     * where x is the vector of values, and Sigma is the covariance matrix.
+     */
+    double logDensity(const VectorValues& x) const;
+
+    /**
+     * Calculate probability density for given values `x`:
+     *   exp(-0.5*error(x)) / sqrt((2*pi)^n*det(Sigma))
+     * where x is the vector of values, and Sigma is the covariance matrix.
+     */
+    double evaluate(const VectorValues& x) const;
+
     /// Solve the GaussianBayesNet, i.e. return \f$ x = R^{-1}*d \f$, by
     /// back-substitution
     VectorValues optimize() const;

gtsam/linear/GaussianConditional.cpp

@@ -169,6 +169,20 @@ double GaussianConditional::logDeterminant() const {
   return logDet;
 }
 
+  /* ************************************************************************* */
+double GaussianConditional::logDensity(const VectorValues& x) const {
+  constexpr double log2pi = 1.8378770664093454835606594728112;
+  size_t n = d().size();
+  // log det(Sigma)) = - 2 * logDeterminant()
+  double sum = error(x) + n * log2pi - 2 * logDeterminant();
+  return -0.5 * sum;
+}
+
+/* ************************************************************************* */
+double GaussianConditional::evaluate(const VectorValues& x) const {
+  return exp(logDensity(x));
+}
+
   /* ************************************************************************* */
   VectorValues GaussianConditional::solve(const VectorValues& x) const {
     // Concatenate all vector values that correspond to parent variables

gtsam/linear/GaussianConditional.h

@@ -121,6 +121,20 @@ namespace gtsam {
     /// @name Standard Interface
     /// @{
 
+    /**
+     * Calculate log-density for given values `x`:
+     *   -0.5*(error + n*log(2*pi) + log det(Sigma))
+     * where x is the vector of values, and Sigma is the covariance matrix.
+     */
+    double logDensity(const VectorValues& x) const;
+
+    /**
+     * Calculate probability density for given values `x`:
+     *   exp(-0.5*error(x)) / sqrt((2*pi)^n*det(Sigma))
+     * where x is the vector of values, and Sigma is the covariance matrix.
+     */
+    double evaluate(const VectorValues& x) const;
+
     /** Return a view of the upper-triangular R block of the conditional */
     constABlock R() const { return Ab_.range(0, nrFrontals()); }
 
@@ -134,9 +148,7 @@ namespace gtsam {
     const constBVector d() const { return BaseFactor::getb(); }
 
     /**
-     * @brief Compute the log determinant of the Gaussian conditional.
+     * @brief Compute the log determinant of the R matrix.
-     * The determinant is computed using the R matrix, which is upper
-     * triangular.
      * For numerical stability, the determinant is computed in log
      * form, so it is a summation rather than a multiplication.
      *
@@ -145,8 +157,7 @@ namespace gtsam {
     double logDeterminant() const;
 
     /**
-     * @brief Compute the determinant of the conditional from the
+     * @brief Compute the determinant of the R matrix.
-     * upper-triangular R matrix.
      *
      * The determinant is computed in log form (hence summation) for numerical
      * stability and then exponentiated.

gtsam/linear/tests/testGaussianBayesNet.cpp

@@ -68,39 +68,6 @@ TEST( GaussianBayesNet, Matrix )
 }
 
 /* ************************************************************************* */
-/**
- * Calculate log-density for given values `x`:
- *   -0.5*(error + n*log(2*pi) + log det(Sigma))
- * where x is the vector of values, and Sigma is the covariance matrix.
- */
-double logDensity(const GaussianConditional::shared_ptr& gc,
-                  const VectorValues& x) {
-  constexpr double log2pi = 1.8378770664093454835606594728112;
-  size_t n = gc->d().size();
-  // log det(Sigma)) = - 2 * gc->logDeterminant()
-  double sum = gc->error(x) + n * log2pi - 2 * gc->logDeterminant();
-  return -0.5 * sum;
-}
-
-/**
- * Calculate probability density for given values `x`:
- *   exp(-0.5*error(x)) / sqrt((2*pi)^n*det(Sigma))
- * where x is the vector of values, and Sigma is the covariance matrix.
- */
-double evaluate(const GaussianConditional::shared_ptr& gc,
-                const VectorValues& x) {
-  return exp(logDensity(gc, x));
-}
-
-/** Calculate probability for given values `x` */
-double evaluate(const GaussianBayesNet& gbn, const VectorValues& x) {
-  double density = 1.0;
-  for (const auto& conditional : gbn) {
-    if (conditional) density *= evaluate(conditional, x);
-  }
-  return density;
-}
-
 // Check that the evaluate function matches direct calculation with R.
 TEST(GaussianBayesNet, Evaluate1) {
   // Let's evaluate at the mean
@@ -115,7 +82,7 @@ TEST(GaussianBayesNet, Evaluate1) {
   // the normalization constant 1.0/sqrt((2*pi*Sigma).det()).
   // The covariance matrix inv(Sigma) = R'*R, so the determinant is
   const double expected = sqrt((invSigma / (2 * M_PI)).determinant());
-  const double actual = evaluate(smallBayesNet, mean);
+  const double actual = smallBayesNet.evaluate(mean);
   EXPECT_DOUBLES_EQUAL(expected, actual, 1e-9);
 }
 
@@ -126,7 +93,7 @@ TEST(GaussianBayesNet, Evaluate2) {
   const Matrix R = noisyBayesNet.matrix().first;
   const Matrix invSigma = R.transpose() * R;
   const double expected = sqrt((invSigma / (2 * M_PI)).determinant());
-  const double actual = evaluate(noisyBayesNet, mean);
+  const double actual = noisyBayesNet.evaluate(mean);
   EXPECT_DOUBLES_EQUAL(expected, actual, 1e-9);
 }
 

gtsam/linear/tests/testGaussianConditional.cpp

@@ -130,6 +130,44 @@ TEST( GaussianConditional, equals )
   EXPECT( expected.equals(actual) );
 }
 
+namespace density {
+static const Key key = 77;
+static const auto unitPrior =
+                      GaussianConditional(key, Vector1::Constant(5), I_1x1),
+                  widerPrior =
+                      GaussianConditional(key, Vector1::Constant(5), I_1x1,
+                                          noiseModel::Isotropic::Sigma(1, 3.0));
+}  // namespace density
+
+/* ************************************************************************* */
+// Check that the evaluate function matches direct calculation with R.
+TEST(GaussianConditional, Evaluate1) {
+  // Let's evaluate at the mean
+  const VectorValues mean = density::unitPrior.solve(VectorValues());
+
+  // We get the Hessian matrix, which has noise model applied!
+  const Matrix invSigma = density::unitPrior.information();
+
+  // A Gaussian density ~ exp (-0.5*(Rx-d)'*(Rx-d))
+  // which at the mean is 1.0! So, the only thing we need to calculate is
+  // the normalization constant 1.0/sqrt((2*pi*Sigma).det()).
+  // The covariance matrix inv(Sigma) = R'*R, so the determinant is
+  const double expected = sqrt((invSigma / (2 * M_PI)).determinant());
+  const double actual = density::unitPrior.evaluate(mean);
+  EXPECT_DOUBLES_EQUAL(expected, actual, 1e-9);
+}
+
+// Check the evaluate with non-unit noise.
+TEST(GaussianConditional, Evaluate2) {
+  // See comments in test above.
+  const VectorValues mean = density::widerPrior.solve(VectorValues());
+  const Matrix R = density::widerPrior.R();
+  const Matrix invSigma = density::widerPrior.information();
+  const double expected = sqrt((invSigma / (2 * M_PI)).determinant());
+  const double actual = density::widerPrior.evaluate(mean);
+  EXPECT_DOUBLES_EQUAL(expected, actual, 1e-9);
+}
+
 /* ************************************************************************* */
 TEST( GaussianConditional, solve )
 {