Reorganize documentation

docs/advanced/cast/chrono.rst

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+Chrono
+======
+
+When including the additional header file :file:`pybind11/chrono.h` conversions
+from C++11 chrono datatypes to python datetime objects are automatically enabled.
+This header also enables conversions of python floats (often from sources such
+as `time.monotonic()`, `time.perf_counter()` and `time.process_time()`) into
+durations.
+
+An overview of clocks in C++11
+------------------------------
+
+A point of confusion when using these conversions is the differences between
+clocks provided in C++11. There are three clock types defined by the C++11
+standard and users can define their own if needed. Each of these clocks have
+different properties and when converting to and from python will give different
+results.
+
+The first clock defined by the standard is ``std::chrono::system_clock``. This
+clock measures the current date and time. However, this clock changes with to
+updates to the operating system time. For example, if your time is synchronised
+with a time server this clock will change. This makes this clock a poor choice
+for timing purposes but good for measuring the wall time.
+
+The second clock defined in the standard is ``std::chrono::steady_clock``.
+This clock ticks at a steady rate and is never adjusted. This makes it excellent
+for timing purposes, however the value in this clock does not correspond to the
+current date and time. Often this clock will be the amount of time your system
+has been on, although it does not have to be. This clock will never be the same
+clock as the system clock as the system clock can change but steady clocks
+cannot.
+
+The third clock defined in the standard is ``std::chrono::high_resolution_clock``.
+This clock is the clock that has the highest resolution out of the clocks in the
+system. It is normally a typedef to either the system clock or the steady clock
+but can be its own independent clock. This is important as when using these
+conversions as the types you get in python for this clock might be different
+depending on the system.
+If it is a typedef of the system clock, python will get datetime objects, but if
+it is a different clock they will be timedelta objects.
+
+Conversions Provided
+--------------------
+
+.. rubric:: C++ to Python
+
+- ``std::chrono::system_clock::time_point`` → ``datetime.datetime``
+    System clock times are converted to python datetime instances. They are
+    in the local timezone, but do not have any timezone information attached
+    to them (they are naive datetime objects).
+
+- ``std::chrono::duration`` → ``datetime.timedelta``
+    Durations are converted to timedeltas, any precision in the duration
+    greater than microseconds is lost by rounding towards zero.
+
+- ``std::chrono::[other_clocks]::time_point`` → ``datetime.timedelta``
+    Any clock time that is not the system clock is converted to a time delta.
+    This timedelta measures the time from the clocks epoch to now.
+
+.. rubric:: Python to C++
+
+- ``datetime.datetime`` → ``std::chrono::system_clock::time_point``
+    Date/time objects are converted into system clock timepoints. Any
+    timezone information is ignored and the type is treated as a naive
+    object.
+
+- ``datetime.timedelta`` → ``std::chrono::duration``
+    Time delta are converted into durations with microsecond precision.
+
+- ``datetime.timedelta`` → ``std::chrono::[other_clocks]::time_point``
+    Time deltas that are converted into clock timepoints are treated as
+    the amount of time from the start of the clocks epoch.
+
+- ``float`` → ``std::chrono::duration``
+    Floats that are passed to C++ as durations be interpreted as a number of
+    seconds. These will be converted to the duration using ``duration_cast``
+    from the float.
+
+- ``float`` → ``std::chrono::[other_clocks]::time_point``
+    Floats that are passed to C++ as time points will be interpreted as the
+    number of seconds from the start of the clocks epoch.

docs/advanced/cast/custom.rst

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+Custom type casters
+===================
+
+In very rare cases, applications may require custom type casters that cannot be
+expressed using the abstractions provided by pybind11, thus requiring raw
+Python C API calls. This is fairly advanced usage and should only be pursued by
+experts who are familiar with the intricacies of Python reference counting.
+
+The following snippets demonstrate how this works for a very simple ``inty``
+type that that should be convertible from Python types that provide a
+``__int__(self)`` method.
+
+.. code-block:: cpp
+
+    struct inty { long long_value; };
+
+    void print(inty s) {
+        std::cout << s.long_value << std::endl;
+    }
+
+The following Python snippet demonstrates the intended usage from the Python side:
+
+.. code-block:: python
+
+    class A:
+        def __int__(self):
+            return 123
+
+    from example import print
+    print(A())
+
+To register the necessary conversion routines, it is necessary to add
+a partial overload to the ``pybind11::detail::type_caster<T>`` template.
+Although this is an implementation detail, adding partial overloads to this
+type is explicitly allowed.
+
+.. code-block:: cpp
+
+    namespace pybind11 { namespace detail {
+        template <> struct type_caster<inty> {
+        public:
+            /**
+             * This macro establishes the name 'inty' in
+             * function signatures and declares a local variable
+             * 'value' of type inty
+             */
+            PYBIND11_TYPE_CASTER(inty, _("inty"));
+
+            /**
+             * Conversion part 1 (Python->C++): convert a PyObject into a inty
+             * instance or return false upon failure. The second argument
+             * indicates whether implicit conversions should be applied.
+             */
+            bool load(handle src, bool) {
+                /* Extract PyObject from handle */
+                PyObject *source = src.ptr();
+                /* Try converting into a Python integer value */
+                PyObject *tmp = PyNumber_Long(source);
+                if (!tmp)
+                    return false;
+                /* Now try to convert into a C++ int */
+                value.long_value = PyLong_AsLong(tmp);
+                Py_DECREF(tmp);
+                /* Ensure return code was OK (to avoid out-of-range errors etc) */
+                return !(value.long_value == -1 && !PyErr_Occurred());
+            }
+
+            /**
+             * Conversion part 2 (C++ -> Python): convert an inty instance into
+             * a Python object. The second and third arguments are used to
+             * indicate the return value policy and parent object (for
+             * ``return_value_policy::reference_internal``) and are generally
+             * ignored by implicit casters.
+             */
+            static handle cast(inty src, return_value_policy /* policy */, handle /* parent */) {
+                return PyLong_FromLong(src.long_value);
+            }
+        };
+    }} // namespace pybind11::detail

docs/advanced/cast/eigen.rst

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+Eigen
+=====
+
+`Eigen <http://eigen.tuxfamily.org>`_ is C++ header-based library for dense and
+sparse linear algebra. Due to its popularity and widespread adoption, pybind11
+provides transparent conversion support between Eigen and Scientific Python linear
+algebra data types.
+
+Specifically, when including the optional header file :file:`pybind11/eigen.h`,
+pybind11 will automatically and transparently convert
+
+1. Static and dynamic Eigen dense vectors and matrices to instances of
+   ``numpy.ndarray`` (and vice versa).
+
+2. Returned matrix expressions such as blocks (including columns or rows) and
+   diagonals will be converted to ``numpy.ndarray`` of the expression
+   values.
+
+3. Returned matrix-like objects such as Eigen::DiagonalMatrix or
+   Eigen::SelfAdjointView will be converted to ``numpy.ndarray`` containing the
+   expressed value.
+
+4. Eigen sparse vectors and matrices to instances of
+   ``scipy.sparse.csr_matrix``/``scipy.sparse.csc_matrix`` (and vice versa).
+
+This makes it possible to bind most kinds of functions that rely on these types.
+One major caveat are functions that take Eigen matrices *by reference* and modify
+them somehow, in which case the information won't be propagated to the caller.
+
+.. code-block:: cpp
+
+    /* The Python bindings of these functions won't replicate
+       the intended effect of modifying the function arguments */
+    void scale_by_2(Eigen::Vector3f &v) {
+        v *= 2;
+    }
+    void scale_by_2(Eigen::Ref<Eigen::MatrixXd> &v) {
+        v *= 2;
+    }
+
+To see why this is, refer to the section on :ref:`opaque` (although that
+section specifically covers STL data types, the underlying issue is the same).
+The :ref:`numpy` sections discuss an efficient alternative for exposing the
+underlying native Eigen types as opaque objects in a way that still integrates
+with NumPy and SciPy.
+
+.. seealso::
+
+    The file :file:`tests/test_eigen.cpp` contains a complete example that
+    shows how to pass Eigen sparse and dense data types in more detail.

docs/advanced/cast/functional.rst

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+Functional
+##########
+
+The following features must be enabled by including :file:`pybind11/functional.h`.
+
+
+Callbacks and passing anonymous functions
+=========================================
+
+The C++11 standard brought lambda functions and the generic polymorphic
+function wrapper ``std::function<>`` to the C++ programming language, which
+enable powerful new ways of working with functions. Lambda functions come in
+two flavors: stateless lambda function resemble classic function pointers that
+link to an anonymous piece of code, while stateful lambda functions
+additionally depend on captured variables that are stored in an anonymous
+*lambda closure object*.
+
+Here is a simple example of a C++ function that takes an arbitrary function
+(stateful or stateless) with signature ``int -> int`` as an argument and runs
+it with the value 10.
+
+.. code-block:: cpp
+
+    int func_arg(const std::function<int(int)> &f) {
+        return f(10);
+    }
+
+The example below is more involved: it takes a function of signature ``int -> int``
+and returns another function of the same kind. The return value is a stateful
+lambda function, which stores the value ``f`` in the capture object and adds 1 to
+its return value upon execution.
+
+.. code-block:: cpp
+
+    std::function<int(int)> func_ret(const std::function<int(int)> &f) {
+        return [f](int i) {
+            return f(i) + 1;
+        };
+    }
+
+This example demonstrates using python named parameters in C++ callbacks which
+requires using ``py::cpp_function`` as a wrapper. Usage is similar to defining
+methods of classes:
+
+.. code-block:: cpp
+
+    py::cpp_function func_cpp() {
+        return py::cpp_function([](int i) { return i+1; },
+           py::arg("number"));
+    }
+
+After including the extra header file :file:`pybind11/functional.h`, it is almost
+trivial to generate binding code for all of these functions.
+
+.. code-block:: cpp
+
+    #include <pybind11/functional.h>
+
+    PYBIND11_PLUGIN(example) {
+        py::module m("example", "pybind11 example plugin");
+
+        m.def("func_arg", &func_arg);
+        m.def("func_ret", &func_ret);
+        m.def("func_cpp", &func_cpp);
+
+        return m.ptr();
+    }
+
+The following interactive session shows how to call them from Python.
+
+.. code-block:: pycon
+
+    $ python
+    >>> import example
+    >>> def square(i):
+    ...     return i * i
+    ...
+    >>> example.func_arg(square)
+    100L
+    >>> square_plus_1 = example.func_ret(square)
+    >>> square_plus_1(4)
+    17L
+    >>> plus_1 = func_cpp()
+    >>> plus_1(number=43)
+    44L
+
+.. warning::
+
+    Keep in mind that passing a function from C++ to Python (or vice versa)
+    will instantiate a piece of wrapper code that translates function
+    invocations between the two languages. Naturally, this translation
+    increases the computational cost of each function call somewhat. A
+    problematic situation can arise when a function is copied back and forth
+    between Python and C++ many times in a row, in which case the underlying
+    wrappers will accumulate correspondingly. The resulting long sequence of
+    C++ -> Python -> C++ -> ... roundtrips can significantly decrease
+    performance.
+
+    There is one exception: pybind11 detects case where a stateless function
+    (i.e. a function pointer or a lambda function without captured variables)
+    is passed as an argument to another C++ function exposed in Python. In this
+    case, there is no overhead. Pybind11 will extract the underlying C++
+    function pointer from the wrapped function to sidestep a potential C++ ->
+    Python -> C++ roundtrip. This is demonstrated in :file:`tests/test_callbacks.cpp`.
+
+.. note::
+
+    This functionality is very useful when generating bindings for callbacks in
+    C++ libraries (e.g. GUI libraries, asynchronous networking libraries, etc.).
+
+    The file :file:`tests/test_callbacks.cpp` contains a complete example
+    that demonstrates how to work with callbacks and anonymous functions in
+    more detail.