Fix typos.

Contributed by Ishamis@, IanBoyanZhang@, gkrobner@ & mithunjacob@.

Change-Id: Iab3c19a07a6f3db2486e3557dcb55bfe5de2aee5

docs/source/nnls_modeling.rst

@@ -2343,7 +2343,7 @@ numbers.
 
 .. code::
 
-  const double data[] = {1.0, 2.0, 5.0, 6.0};
+  const double x[] = {1.0, 2.0, 5.0, 6.0};
   Grid1D<double, 1> array(x, 0, 4);
   CubicInterpolator interpolator(array);
   double f, dfdx;

docs/source/nnls_solving.rst

@@ -58,8 +58,8 @@ the step :math:`\Delta x` is controlled, non-linear optimization
 algorithms can be divided into two major categories [NocedalWright]_.
 
 1. **Trust Region** The trust region approach approximates the
-   objective function using using a model function (often a quadratic)
-   over a subset of the search space known as the trust region. If the
+   objective function using a model function (often a quadratic) over
+   a subset of the search space known as the trust region. If the
    model function succeeds in minimizing the true objective function
    the trust region is expanded; conversely, otherwise it is
    contracted and the model optimization problem is solved again.
@@ -1192,7 +1192,7 @@ elimination group [LiSaad]_.
 
 .. member:: double Solver::Options::min_lm_diagonal
 
-   Default: ``1e6``
+   Default: ``1e-6``
 
    The ``LEVENBERG_MARQUARDT`` strategy, uses a diagonal matrix to
    regularize the trust region step. This is the lower bound on

include/ceres/local_parameterization.h

@@ -90,8 +90,8 @@ namespace ceres {
 //
 // An example that occurs commonly in Structure from Motion problems
 // is when camera rotations are parameterized using Quaternion. There,
-// it is useful only make updates orthogonal to that 4-vector defining
-// the quaternion. One way to do this is to let delta be a 3
+// it is useful to only make updates orthogonal to that 4-vector
+// defining the quaternion. One way to do this is to let delta be a 3
 // dimensional vector and define Plus to be
 //
 //   Plus(x, delta) = [cos(|delta|), sin(|delta|) delta / |delta|] * x
@@ -99,7 +99,7 @@ namespace ceres {
 // The multiplication between the two 4-vectors on the RHS is the
 // standard quaternion product.
 //
-// Given g and a point x, optimizing f can now be restated as
+// Given f and a point x, optimizing f can now be restated as
 //
 //     min  f(Plus(x, delta))
 //    delta

internal/ceres/visibility_based_preconditioner.cc

@@ -144,11 +144,11 @@ void VisibilityBasedPreconditioner::ComputeClusterJacobiSparsity(
 }
 
 // Determine the sparsity structure of the CLUSTER_TRIDIAGONAL
-// preconditioner. It clusters cameras using using the scene
-// visibility and then finds the strongly interacting pairs of
-// clusters by constructing another graph with the clusters as
-// vertices and approximating it with a degree-2 maximum spanning
-// forest. The set of edges in this forest are the cluster pairs.
+// preconditioner. It clusters cameras using the scene visibility and
+// then finds the strongly interacting pairs of clusters by
+// constructing another graph with the clusters as vertices and
+// approximating it with a degree-2 maximum spanning forest. The set
+// of edges in this forest are the cluster pairs.
 void VisibilityBasedPreconditioner::ComputeClusterTridiagonalSparsity(
     const CompressedRowBlockStructure& bs) {
   vector<set<int>> visibility;