diff --git a/include/ceres/covariance.h b/include/ceres/covariance.h
index dd87868..930f96c 100644
--- a/include/ceres/covariance.h
+++ b/include/ceres/covariance.h
@@ -420,16 +420,16 @@
   //
   // Compute must be called before calling GetCovarianceMatrix and all
   // parameter_blocks must have been present in the vector
-  // parameters_blocks when Compute was called. Otherwise
+  // parameter_blocks when Compute was called. Otherwise
   // GetCovarianceMatrix returns false.
   //
   // covariance_matrix must point to a memory location that can store
-  // the size of the covariance matrix. The size of the covariance
-  // matrix corresponds the sum of the sizes of the individual
-  // parameter blocks. The covariance matrix will be a row-major
-  // matrix.
-  bool GetCovarianceMatrix(const std::vector<const double*>& parameter_blocks,
-                           double* covariance_matrix);
+  // the size of the covariance matrix. The covariance matrix will be
+  // a square matrix whose row and column count is equal to the sum of
+  // the sizes of the individual parameter blocks. The covariance
+  // matrix will be a row-major matrix.
+  bool GetCovarianceMatrix(const std::vector<const double *> &parameter_blocks,
+                           double *covariance_matrix);
 
   // Return the covariance matrix corresponding to parameter_blocks
   // in the tangent space if a local parameterization is associated
@@ -442,10 +442,10 @@
   // GetCovarianceMatrix returns false.
   //
   // covariance_matrix must point to a memory location that can store
-  // the size of the covariance matrix. The size of the covariance
-  // matrix corresponds the sum of the sizes of the individual
-  // parameter blocks. The covariance matrix will be a row-major
-  // matrix.
+  // the size of the covariance matrix. The covariance matrix will be
+  // a square matrix whose row and column count is equal to the sum of
+  // the sizes of the tangent spaces of the individual parameter
+  // blocks. The covariance matrix will be a row-major matrix.
   bool GetCovarianceMatrixInTangentSpace(
       const std::vector<const double*>& parameter_blocks,
       double* covariance_matrix);
diff --git a/internal/ceres/covariance_impl.cc b/internal/ceres/covariance_impl.cc
index 198a13e..cfa5ffc 100644
--- a/internal/ceres/covariance_impl.cc
+++ b/internal/ceres/covariance_impl.cc
@@ -93,18 +93,19 @@
 
 template <typename T> void CheckForDuplicates(vector<T> blocks) {
   sort(blocks.begin(), blocks.end());
-  typename vector<T>::iterator it = std::adjacent_find(blocks.begin(), blocks
-      .end());
+  typename vector<T>::iterator it =
+      std::adjacent_find(blocks.begin(), blocks.end());
   if (it != blocks.end()) {
     // In case there are duplicates, we search for their location.
     map<T, vector<int> > blocks_map;
-    for (int i=0; i < blocks.size(); ++i) {
+    for (int i = 0; i < blocks.size(); ++i) {
       blocks_map[blocks[i]].push_back(i);
     }
+
     std::ostringstream duplicates;
     while (it != blocks.end()) {
       duplicates << "(";
-      for (int i=0; i < blocks_map[*it].size()-1; ++i) {
+      for (int i = 0; i < blocks_map[*it].size() - 1; ++i) {
         duplicates << blocks_map[*it][i] << ", ";
       }
       duplicates << blocks_map[*it].back() << ")";
@@ -113,9 +114,9 @@
         duplicates << " and ";
       }
     }
-    CHECK(false) << "Covariance::Compute called with duplicate blocks at "
-                 << "indices "
-                 << duplicates.str();
+
+    LOG(FATAL) << "Covariance::Compute called with duplicate blocks at "
+               << "indices " << duplicates.str();
   }
 }
 
@@ -134,20 +135,15 @@
 bool CovarianceImpl::Compute(const vector<const double*>& parameter_blocks,
                              ProblemImpl* problem) {
   CheckForDuplicates<const double*>(parameter_blocks);
-  vector<pair<const double*, const double*> > covariance_blocks;
+  CovarianceBlocks covariance_blocks;
   for (int i = 0; i < parameter_blocks.size(); ++i) {
     for (int j = i; j < parameter_blocks.size(); ++j) {
       covariance_blocks.push_back(make_pair(parameter_blocks[i],
                                             parameter_blocks[j]));
     }
   }
-  problem_ = problem;
-  parameter_block_to_row_index_.clear();
-  covariance_matrix_.reset(NULL);
-  is_valid_ = (ComputeCovarianceSparsity(covariance_blocks, problem) &&
-      ComputeCovarianceValues());
-  is_computed_ = true;
-  return is_valid_;
+
+  return Compute(covariance_blocks, problem);
 }
 
 bool CovarianceImpl::GetCovarianceBlockInTangentOrAmbientSpace(
@@ -319,8 +315,8 @@
   cum_parameter_size.resize(parameters.size() + 1);
   cum_parameter_size[0] = 0;
   for (int i = 0; i < parameters.size(); ++i) {
-    ParameterBlock* block = FindOrDie(parameter_map,
-                                      const_cast<double*>(parameters[i]));
+    ParameterBlock* block =
+        FindOrDie(parameter_map, const_cast<double*>(parameters[i]));
     if (lift_covariance_to_ambient_space) {
       parameter_sizes.push_back(block->Size());
     } else {
@@ -329,19 +325,19 @@
   }
   std::partial_sum(parameter_sizes.begin(), parameter_sizes.end(),
                    cum_parameter_size.begin() + 1);
-  const int max_covariance_block_size = *std::max_element(
-      parameter_sizes.begin(),
-      parameter_sizes.end());
+  const int max_covariance_block_size =
+      *std::max_element(parameter_sizes.begin(), parameter_sizes.end());
   const int covariance_size = cum_parameter_size.back();
 
   // Assemble the blocks in the covariance matrix.
   MatrixRef covariance(covariance_matrix, covariance_size, covariance_size);
   const int num_threads = options_.num_threads;
-  scoped_array<double> workspace(new double[num_threads *
-      max_covariance_block_size * max_covariance_block_size]);
+  scoped_array<double> workspace(
+      new double[num_threads * max_covariance_block_size *
+                 max_covariance_block_size]);
 
   bool success = true;
-#pragma omp parallel for num_threads (num_threads) schedule(dynamic) collapse(2)
+#pragma omp parallel for num_threads(num_threads) schedule(dynamic) collapse(2)
   for (int i = 0; i < parameters.size(); ++i) {
     for (int j = 0; j < parameters.size(); ++j) {
       // The second loop can't start from j = i for compatibility with OpenMP
@@ -356,21 +352,24 @@
 #else
         int thread_id = 0;
 #endif
-        double* covariance_block = workspace.get() + thread_id *
-            max_covariance_block_size * max_covariance_block_size;
+        double* covariance_block =
+            workspace.get() +
+            thread_id * max_covariance_block_size * max_covariance_block_size;
         if (!GetCovarianceBlockInTangentOrAmbientSpace(
-            parameters[i],
-            parameters[j],
-            lift_covariance_to_ambient_space,
-            covariance_block)) {
+                parameters[i], parameters[j], lift_covariance_to_ambient_space,
+                covariance_block)) {
           success = false;
         }
-        covariance.block(covariance_row_idx, covariance_col_idx, size_i,
-                         size_j) = MatrixRef(covariance_block, size_i, size_j);
+
+        covariance.block(covariance_row_idx, covariance_col_idx,
+                         size_i, size_j) =
+            MatrixRef(covariance_block, size_i, size_j);
+
         if (i != j) {
-          covariance.block(covariance_col_idx, covariance_row_idx, size_j,
-                           size_i) = MatrixRef(covariance_block, size_i,
-                                               size_j).transpose();
+          covariance.block(covariance_col_idx, covariance_row_idx,
+                           size_j, size_i) =
+              MatrixRef(covariance_block, size_i, size_j).transpose();
+
         }
       }
     }