Rewrite of the tutorial.
1. Quicker starting point.
2. Better discussion of derivatives.
3. Better hyperlinking to code and class documentation.
4. New robust estimation example.
5. Better naming of example code.
6. Removed dependency on gflags in all the core examples covered
in the tutorial.
Change-Id: Ibf3c7fe946fa2b4d22f8916a9366df267d34ca26
diff --git a/docs/source/modeling.rst b/docs/source/modeling.rst
index d17423a..c816676 100644
--- a/docs/source/modeling.rst
+++ b/docs/source/modeling.rst
@@ -10,26 +10,26 @@
Modeling API
============
-
-Introduction
-------------
-
-Ceres solves robustified non-linear least squares problems of the form
+Recall that Ceres solves robustified non-linear least squares problems
+of the form
.. math:: \frac{1}{2}\sum_{i=1} \rho_i\left(\left\|f_i\left(x_{i_1}, ... ,x_{i_k}\right)\right\|^2\right).
- :label: ceresproblem
+ :label: ceresproblem3
-The term
+The expression
:math:`\rho_i\left(\left\|f_i\left(x_{i_1},...,x_{i_k}\right)\right\|^2\right)`
is known as a ``ResidualBlock``, where :math:`f_i(\cdot)` is a
:class:`CostFunction` that depends on the parameter blocks
-:math:`\left[x_{i_1},... , x_{i_k}\right]` and :math:`\rho_i` is a
-:class:`LossFunction`. In most optimization problems small groups of
-scalars occur together. For example the three components of a
-translation vector and the four components of the quaternion that
-define the pose of a camera. We refer to such a group of small scalars
-as a ``ParameterBlock``. Of course a ``ParameterBlock`` can just have
-a single parameter.
+:math:`\left[x_{i_1},... , x_{i_k}\right]`. In most optimization
+problems small groups of scalars occur together. For example the three
+components of a translation vector and the four components of the
+quaternion that define the pose of a camera. We refer to such a group
+of small scalars as a ``ParameterBlock``. Of course a
+``ParameterBlock`` can just be a single parameter. :math:`\rho_i` is a
+:class:`LossFunction`. A :class:`LossFunction` is a scalar function
+that is used to reduce the influence of outliers on the solution of
+non-linear least squares problems.
+
:class:`CostFunction`
---------------------
@@ -101,7 +101,6 @@
is the case when the a parameter block is marked constant.
-
:class:`SizedCostFunction`
--------------------------
