Fix few typos and alter a NULL to nullptr.

Fix typos in docs/source/features.rst and examples/helloworld.cc. Alter a NULL to nullptr in include/ceres/autodiff_cost_function.h

Change-Id: Ibcf00b6ef665ad6be9af14b3add2dd4f3852e7e6

docs/source/features.rst

@@ -44,7 +44,7 @@ Why?
     solvers - dense QR and dense Cholesky factorization (using
     `Eigen`_ or `LAPACK`_) for dense problems, sparse Cholesky
     factorization (`SuiteSparse`_, `CXSparse`_ or `Eigen`_) for large
-    sparse problems custom Schur complement based dense, sparse, and
+    sparse problems, custom Schur complement based dense, sparse, and
     iterative linear solvers for `bundle adjustment`_ problems.
 
   - **Line Search Solvers** - When the problem size is so large that
@@ -63,7 +63,7 @@ Why?
 
 * **Covariance estimation** - Evaluate the sensitivity/uncertainty of
   the solution by evaluating all or part of the covariance
-  matrix. Ceres is one of the few solvers that allows you to to do
+  matrix. Ceres is one of the few solvers that allows you to do
   this analysis at scale.
 
 * **Community** Since its release as an open source software, Ceres

examples/helloworld.cc

@@ -39,15 +39,16 @@
 using ceres::AutoDiffCostFunction;
 using ceres::CostFunction;
 using ceres::Problem;
-using ceres::Solver;
 using ceres::Solve;
+using ceres::Solver;
 
 // A templated cost functor that implements the residual r = 10 -
 // x. The method operator() is templated so that we can then use an
 // automatic differentiation wrapper around it to generate its
 // derivatives.
 struct CostFunctor {
-  template <typename T> bool operator()(const T* const x, T* residual) const {
+  template <typename T>
+  bool operator()(const T* const x, T* residual) const {
     residual[0] = 10.0 - x[0];
     return true;
   }
@@ -68,7 +69,7 @@ int main(int argc, char** argv) {
   // auto-differentiation to obtain the derivative (jacobian).
   CostFunction* cost_function =
       new AutoDiffCostFunction<CostFunctor, 1, 1>(new CostFunctor);
-  problem.AddResidualBlock(cost_function, NULL, &x);
+  problem.AddResidualBlock(cost_function, nullptr, &x);
 
   // Run the solver!
   Solver::Options options;

include/ceres/autodiff_cost_function.h

@@ -54,7 +54,7 @@
 // for a series of measurements, where there is an instance of the cost function
 // for each measurement k.
 //
-// The actual cost added to the total problem is e^2, or (k - x'k)^2; however,
+// The actual cost added to the total problem is e^2, or (k - x'y)^2; however,
 // the squaring is implicitly done by the optimization framework.
 //
 // To write an auto-differentiable cost function for the above model, first