Fix typos.

Change-Id: I61296f42354eab797c55c1435ca46b3475b767e9

include/ceres/internal/autodiff.h

@@ -57,7 +57,7 @@
 //                [ * ]
 //
 // Similar to the 2-parameter example for f described in jet.h, computing the
-// jacobian dy/dx is done by substutiting a suitable jet object for x and all
+// jacobian dy/dx is done by substituting a suitable jet object for x and all
 // intermediate steps of the computation of F. Since x is has 4 dimensions, use
 // a Jet<double, 4>.
 //
@@ -151,7 +151,7 @@
 namespace ceres {
 namespace internal {
 
-// Extends src by a 1st order pertubation for every dimension and puts it in
+// Extends src by a 1st order perturbation for every dimension and puts it in
 // dst. The size of src is N. Since this is also used for perturbations in
 // blocked arrays, offset is used to shift which part of the jet the
 // perturbation occurs. This is used to set up the extended x augmented by an

include/ceres/internal/disable_warnings.h

@@ -35,7 +35,7 @@
 
 #ifdef _MSC_VER
 #pragma warning( push )
-// Disable the warning C4251 which is trigerred by stl classes in
+// Disable the warning C4251 which is triggered by stl classes in
 // Ceres' public interface. To quote MSDN: "C4251 can be ignored "
 // "if you are deriving from a type in the Standard C++ Library"
 #pragma warning( disable : 4251 )

include/ceres/internal/fixed_array.h

@@ -90,7 +90,7 @@ class FixedArray {
   // REQUIRES: n >= 0
   // Creates an array object that can store "n" elements.
   //
-  // FixedArray<T> will not zero-initialiaze POD (simple) types like int,
+  // FixedArray<T> will not zero-initialize POD (simple) types like int,
   // double, bool, etc.
   // Non-POD types will be default-initialized just like regular vectors or
   // arrays.
@@ -131,7 +131,7 @@ class FixedArray {
 
  private:
   // Container to hold elements of type T.  This is necessary to handle
-  // the case where T is a a (C-style) array.  The size of InnerContainer
+  // the case where T is a (C-style) array.  The size of InnerContainer
   // and T must be the same, otherwise callers' assumptions about use
   // of this code will be broken.
   struct InnerContainer {

include/ceres/local_parameterization.h

@@ -60,7 +60,7 @@ namespace ceres {
 // optimize over two dimensional vector delta in the tangent space at
 // that point and then "move" to the point x + delta, where the move
 // operation involves projecting back onto the sphere. Doing so
-// removes a redundent dimension from the optimization, making it
+// removes a redundant dimension from the optimization, making it
 // numerically more robust and efficient.
 //
 // More generally we can define a function

include/ceres/types.h

@@ -146,7 +146,7 @@ enum SparseLinearAlgebraLibraryType {
   // minimum degree ordering.
   SUITE_SPARSE,
 
-  // A lightweight replacment for SuiteSparse, which does not require
+  // A lightweight replacement for SuiteSparse, which does not require
   // a LAPACK/BLAS implementation. Consequently, its performance is
   // also a bit lower than SuiteSparse.
   CX_SPARSE,
@@ -201,7 +201,7 @@ enum LineSearchDirectionType {
   // symmetric matrix but only N conditions are specified by the Secant
   // equation. The requirement that the Hessian approximation be positive
   // definite imposes another N additional constraints, but that still leaves
-  // remaining degrees-of-freedom.  (L)BFGS methods uniquely deteremine the
+  // remaining degrees-of-freedom.  (L)BFGS methods uniquely determine the
   // approximate Hessian by imposing the additional constraints that the
   // approximation at the next iteration must be the 'closest' to the current
   // approximation (the nature of how this proximity is measured is actually
@@ -249,7 +249,7 @@ enum LineSearchDirectionType {
   BFGS,
 };
 
-// Nonliner conjugate gradient methods are a generalization of the
+// Nonlinear conjugate gradient methods are a generalization of the
 // method of Conjugate Gradients for linear systems. The
 // generalization can be carried out in a number of different ways
 // leading to number of different rules for computing the search

internal/ceres/array_utils.h

@@ -68,7 +68,7 @@ void AppendArrayToString(const int size, const double* x, std::string* result);
 
 // This routine takes an array of integer values, sorts and uniques
 // them and then maps each value in the array to its position in the
-// sorted+uniqued array. By doing this, if there are are k unique
+// sorted+uniqued array. By doing this, if there are k unique
 // values in the array, each value is replaced by an integer in the
 // range [0, k-1], while preserving their relative order.
 //

internal/ceres/autodiff_cost_function_benchmark.cc

@@ -56,7 +56,7 @@ struct Rat43CostFunctor {
 };
 
 // Simple implementation of autodiff using Jets directly instead of
-// going through the machineary of AutoDiffCostFunction, which does
+// going through the machinery of AutoDiffCostFunction, which does
 // the same thing, but much more generically.
 class Rat43Automatic : public ceres::SizedCostFunction<1, 4> {
  public: