Sphinx docs check (#34)

* Documentation tweaks.

Mostly minor typos and grammar fixes.

In the installation instructions, removed a duplication f2py entry.

* One more tiny typo in docs.

* Remove mention of Jupyter notebook.

As the notebook is auto-included in the documentation immediately after.

* In multigrid docs, complete intro to link to numerical_exercises notes

Author: IanHawke

docs/source/compressible_basics.rst

@@ -7,7 +7,7 @@ The equations of compressible hydrodynamics take the form:
 
    \frac{\partial \rho}{\partial t} + \nabla \cdot (\rho U) &= 0 \\
    \frac{\partial (\rho U)}{\partial t} + \nabla \cdot (\rho U U) + \nabla p &= \rho g \\
-   \frac{\partial (\rho E)}{\partial t} + \nabla \cdot [(\rho E + p ) U] &= \rho U \cdot g 
+   \frac{\partial (\rho E)}{\partial t} + \nabla \cdot [(\rho E + p ) U] &= \rho U \cdot g
 
 with :math:`\rho E = \rho e + \frac{1}{2} \rho |U|^2` and :math:`p = p(\rho, e)`.
 
@@ -26,7 +26,7 @@ pyro has several compressible solvers:
 
 The implementations here have flattening at shocks, artificial
 viscosity, a simple gamma-law equation of state, and (in some cases) a
-choice Riemann solvers. Optional constant gravity in the vertical
+choice of Riemann solvers. Optional constant gravity in the vertical
 direction is allowed.
 
 The main parameters that affect this solver are:
@@ -164,7 +164,7 @@ quad
 
 The quad problem sets up different states in four regions of the
 domain and watches the complex interfaces that develop as shocks
-interact. This problem has appear in several places (and a `detailed
+interact. This problem has appeared in several places (and a `detailed
 investigation
 <http://planets.utsc.utoronto.ca/~pawel/Riemann.hydro.html>`_ is
 online by Pawel Artymowicz). It is run as:
@@ -250,7 +250,7 @@ Extensions
   sedov explosion instead of the cylindrical explosion.
 
 * Swap the piecewise linear reconstruction for piecewise parabolic
-  (PPM). The notes and Miller and Colella paper provide a good basis
+  (PPM). The notes and the Miller and Colella paper provide a good basis
   for this.  Research the Roe Riemann solver and implement it in pyro.
 
 

docs/source/design.rst

@@ -94,7 +94,7 @@ Fortran
 -------
 
 Fortran is used to speed up some critical portions of the code, and in
-often cases, provides more clarity than trying to write optimized
+many cases, provides more clarity than trying to write optimized
 python code using array operations in numpy. The Fortran code
 seemlessly integrates into python using f2py.
 
@@ -165,5 +165,3 @@ inheritance is used, so many of these methods come from the base
 * ``write_extras``: any solver-specific writing
 
 Each problem setup needs only provide an ``init_data()`` function that fills the data in the patch object.
-
-

docs/source/incompressible_basics.rst

@@ -4,7 +4,7 @@ Incompressible hydrodynamics solver
 pyro's incompressible solver solves:
 
 .. math::
-  
+
    \frac{\partial U}{\partial t} + U \cdot \nabla U + \nabla p &= 0 \\
    \nabla \cdot U &= 0
 
@@ -43,7 +43,7 @@ we are using an approximate projection.
 convergence
 ^^^^^^^^^^^
 
-The convergence test initialize a simple velocity field on a periodic
+The convergence test initializes a simple velocity field on a periodic
 unit square with known analytic solution. By evolving at a variety of
 resolutions and comparing to the analytic solution, we can measure the
 convergence rate of the algorithm. The particular set of initial
@@ -105,4 +105,3 @@ hydrodynamics code <http://amrex-astro.github.io/MAESTRO/>`_. Maestro
 can do variable-density incompressible, anelastic, and low Mach number
 stratified flows in stellar (and terrestrial) environments in close
 hydrostatic equilibrium.
-

docs/source/installation.rst

@@ -13,7 +13,6 @@ The following python packages are required:
 
 * ``numpy``
 * ``matplotlib``
-* ``f2py``
 * ``f2py`` (part of NumPy)
 * ``pytest`` (for unit tests)
 

docs/source/intro.rst

@@ -8,9 +8,9 @@ hydrodynamics solvers.  It is designed to provide a tutorial for
 students in computational astrophysics (and hydrodynamics in
 general). We introduce simple implementations of some popular methods
 used in the field, with the code written to be easily
-understandable. All simulations use a single grid (no domain decomposition)
+understandable. All simulations use a single grid (no domain decomposition).
 
-.. note:: 
+.. note::
 
    pyro is not meant for demanding scientific simulations—given the
    choice between performance and clarity, clarity is taken.
@@ -37,7 +37,7 @@ Runtime visualization shows the evolution as the equations are solved.
 In the pages that follow, the following format is adopted:
 
 * PDF notes provide the basic theory behind the methods.  References
-  are cited to provide more detail. 
+  are cited to provide more detail.
 
 * An overview of the use of the applicable modules from pyro provided.
 

docs/source/mesh_basics.rst

@@ -55,7 +55,7 @@ There are several main objects in the patch class that we interact with:
   class that subclasses the NumPy ndarray and makes the data in the
   array know about the details of the grid it is defined on. In
   particular, it knows which cells are valid and which are the ghost
-  cells, and it has methods to do the ai+1,j operations that are
+  cells, and it has methods to do the :math:`a_{i+1,j}` operations that are
   common in difference methods.
 
 * :func:`integration.RKIntegrator <mesh.integration.RKIntegrator>`:
@@ -110,6 +110,3 @@ The actual filling of the boundary conditions is done by the ``fill_BC()``
 method. The script ``bc_demo.py`` tests the various types of boundary
 conditions by initializing a small grid with sequential data, filling
 the BCs, and printing out the results.
-
-
-

docs/source/multigrid_basics.rst

@@ -4,7 +4,7 @@ Multigrid solvers
 pyro solves elliptic problems (like Laplace's equation or Poisson's
 equation) through multigrid. This accelerates the convergence of
 simple relaxation by moving the solution down and up through a series
-of grids. Chapter 
+of grids. Chapter 9 of the `pdf notes<http://bender.astro.sunysb.edu/hydro_by_example/CompHydroTutorial.pdf>`_ gives an introduction to solving elliptic equations, including multigrid.
 
 There are three solvers:
 
@@ -17,10 +17,10 @@ There are three solvers:
 * The class :func:`general_MG.GeneralMG2d <multigrid.general_MG.GeneralMG2d>` solves a general elliptic
   equation of the form :math:`\alpha \phi + \nabla \cdot ( \beta
   \nabla \phi) + \gamma \cdot \nabla \phi = f`.  This class inherits
-  the core functionality from ``MG.CellCenterMG2d``. 
+  the core functionality from ``MG.CellCenterMG2d``.
 
   This solver is the only one to support inhomogeneous boundary
-  conditions.  
+  conditions.
 
 We simply use V-cycles in our implementation, and restrict ourselves
 to square grids with zoning a power of 2.
@@ -40,12 +40,12 @@ A basic multigrid test is run as:
 
 The ``mg_test_simple.py`` script solves a Poisson equation with a
 known analytic solution. This particular example comes from the text
-`A Multigrid Tutorial, 2nd Ed.`. The example is:
+`A Multigrid Tutorial, 2nd Ed.`, by Briggs. The example is:
 
 .. math::
 
    u_{xx} + u_{yy} = -2 \left [(1-6x^2)y^2(1-y^2) + (1-6y^2)x^2(1-x^2)\right ]
- 
+
 on :math:`[0,1] \times [0,1]` with :math:`u = 0` on the boundary.
 
 The solution to this is shown below.
@@ -113,10 +113,6 @@ results are shown below:
 
 Left is the original u velocity, middle is the modified field after adding the gradient of the scalar, and right is the recovered field.
 
-Jupyter Notebook
-----------------
-
-A jupyter notebook showing how to use the basic solver can be found here: multigrid-examples.ipynb
 
 Exercises
 ---------

docs/source/output.rst

@@ -17,7 +17,7 @@ Several simply utilities exist to operate on output files
 
     ./compare.py shear_128_0216.pyro incompressible/tests/shear_128_0216.pyro
 
-  Differences on the order of machine precision are may arise because
+  Differences on the order of machine precision may arise because
   of optimizations and compiler differences across platforms. Students
   should familiarize themselves with the details of how computers
   store numbers (floating point). An excellent read is `What every

docs/source/problems.rst

@@ -2,7 +2,7 @@ Adding a problem
 ================
 
 The easiest way to add a problem is to copy an existing problem setup
-in the solver you wish to use (in its problems/ sub-directory. Three
+in the solver you wish to use (in its problems/ sub-directory). Three
 different files will need to be copied (created):
 
 * ``problem.py``: this is the main initialization routine. The
@@ -25,4 +25,3 @@ different files will need to be copied (created):
   problem is defined, you need to add the problem name to the
   ``__all__`` list in the ``__init__.py`` file in the ``problems/``
   sub-directory. This lets python know about the problem.
-

docs/source/running.rst

@@ -16,7 +16,7 @@ For example, to run the Sedov problem with the compressible solver we would do:
 This knows to look for ``inputs.sedov`` in ``compressible/problems/``
 (alternately, you can specify the full path for the inputs file).
 
-To run the smooth Gaussin advection problem with the advection solver, we would do:
+To run the smooth Gaussian advection problem with the advection solver, we would do:
 
 .. code-block:: none
 
@@ -50,7 +50,7 @@ parameters are stored in three places:
 * the ``pyro/_defaults`` file
 * the solver's ``_defaults`` file
 * problem's ``_defaults`` file (named ``_problem-name.defaults`` in the
-  solver's ``problem/`` sub-directory). 
+  solver's ``problem/`` sub-directory).
 
 These three files are parsed at runtime to define the list of valid
 parameters. The inputs file is read next and used to override the
@@ -135,5 +135,3 @@ All solvers use the following parameters:
 +---------------------+---------------------------------------------------------------------------------------------------------+
 |``ny``               | the number zones in the y-direction                                                                     |
 +---------------------+---------------------------------------------------------------------------------------------------------+
-
-