diff --git a/.github/CODEOWNERS b/.github/CODEOWNERS index 76e1d6dad0..7cf2c0a4f5 100644 --- a/.github/CODEOWNERS +++ b/.github/CODEOWNERS @@ -1,5 +1,5 @@ -# Set Ivar Stefansson and Eirik Keilegavlen as global owners -* @keileg @IvarStefansson +# Set Ivar Stefansson, Omar Duran, and Eirik Keilegavlen as global owners +* @keileg @IvarStefansson @OmarDuran # Make vlipovac code owner of the docs folder -docs/* @vlipovac +/docs/* @vlipovac diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml index 6d74d3be63..06c6427fab 100644 --- a/.github/workflows/ci.yml +++ b/.github/workflows/ci.yml @@ -27,7 +27,7 @@ jobs: # https://help.github.com/en/actions/language-and-framework-guides/using-python-with-github-actions#specifying-a-python-version strategy: matrix: - python-version: ["3.8", "3.9", "3.10"] # TODO: Change 3.10.6 to 3.10 when mypy error is fixed + python-version: ["3.8", "3.9", "3.10"] # Complete all versions in matrix even if one fails. fail-fast: false @@ -53,9 +53,8 @@ jobs: # Cache the full python environment, this is more efficient than just caching pip # https://blog.allenai.org/python-caching-in-github-actions-e9452698e98d path: ${{ env.pythonLocation }} - key: ${{ env.pythonLocation }}-pip-${{ hashFiles('**/requirements-dev.txt') }} - restore-keys: | - ${{ runner.os }}-pip- + # Hash both ordinary requirements and those specific for developmnet. + key: ${{ env.pythonLocation }}-${{ hashFiles('setup.py') }}-${{ hashFiles('**/requirements.txt', '**/requirements-dev.txt') }} - name: Cache mypy uses: actions/cache@v3 @@ -66,7 +65,10 @@ jobs: - name: Install external libraries run: | - sudo apt-get install libglu1-mesa libgeos-dev + # Various packages that must be installed + # Install libffi v7. This was (seemed to be) necessary in Nov 2022. The reason could be that + # ubuntu-latest was updated, libffi was removed, and scipy complained. + sudo apt-get install libglu1-mesa libgeos-dev libffi7 export LD_LIBRARY_PATH=/usr/local/lib64/:$LD_LIBRARY_PATH - name: Install requirements @@ -97,14 +99,14 @@ jobs: if: ${{ always() }} run: flake8 src - - name: mypy - if: ${{ always() }} - run: mypy src --cache-dir mypy-cache-${{ matrix.python-version}} - - name: unit tests if: ${{always()}} run: pytest tests/unit + - name: mypy + if: ${{ always() }} + run: mypy src --cache-dir mypy-cache-${{ matrix.python-version}} + - name: integration tests if: ${{always()}} run: pytest tests/integration diff --git a/docs/conf.py b/docs/conf.py index 41c8922279..d88adb838c 100644 --- a/docs/conf.py +++ b/docs/conf.py @@ -40,9 +40,10 @@ # extensions coming with Sphinx (named 'sphinx.ext.*') or your custom # ones. extensions = [ + 'sphinx.ext.napoleon', 'sphinx.ext.autodoc', + # 'sphinx_autodoc_typehints', # this moves type links from signature to docstring 'sphinx.ext.intersphinx', - 'sphinx.ext.napoleon', 'sphinx.ext.todo', 'sphinx.ext.viewcode', ] @@ -62,28 +63,38 @@ # -- Options for HTML output ------------------------------------------------------------------ # The theme to use for HTML and HTML Help pages. Currently set to theme of Python 2 docs -html_theme = "nature" +html_theme = "sphinx_rtd_theme" # Add any paths that contain custom static files (such as style sheets) here, # relative to this directory. They are copied after the builtin static files, # so a file named "default.css" will overwrite the builtin "default.css". -html_static_path = ["static"] - -# Customize the html theme here. Supported customization depends on the chosen HTML theme, -# but unknown entries will cause no error when compiling. -html_theme_options = { - # "rightsidebar": "false", - # "relbarbgcolor": "black", - # "externalrefs": "true", - # "bodyfont": "Arial", - # "headfont": "Arial", -} +html_static_path = [] html_short_title = "PorePy" html_split_index = True html_copy_source = False html_show_sourcelink = False html_show_sphinx = False +html_baseurl = 'https://pmgbergen.github.io/porepy/' + +# relative path to project logo, to be displayed on docs webpage +# html_logo = '' + +# theme-specific customization, read the docs of respective theme +html_theme_options = { + 'logo_only': False, + 'display_version': True, + 'prev_next_buttons_location': 'bottom', + 'style_external_links': True, + 'vcs_pageview_mode': '', + 'style_nav_header_background': '#2980B9', + # Toc options + 'collapse_navigation': False, + 'sticky_navigation': True, + 'navigation_depth': 4, + 'includehidden': True, + 'titles_only': False +} # -- Autodoc Settings ------------------------------------------------------------------------- @@ -96,9 +107,21 @@ # orders the members of an object group wise, e.g. private, special or public methods autodoc_member_order = "groupwise" # alphabetical-groupwise-bysource +# Avoid double appearance of documentation if child member has no docs +autodoc_inherit_docstrings = False + +# do not evaluate default arguments, leave as is +autodoc_preserve_defaults = True + # type hints will be shortened: porepy.grids.grid.Grid -> Grid autodoc_typehints_format = "short" +# uses type hints in signatures for e.g. linking (default) +autodoc_typehints = "signature" + +# display types in signature which are documented, or all (by default) +autodoc_typehints_description_target = 'all' # all-documented + # default configurations for all autodoc directives autodoc_default_options = { "members": True, @@ -109,14 +132,15 @@ "no-value": False } -# uses type hints in signatures for e.g. linking (default) -autodoc_typehints = "signature" - -# Avoid double appearance of documentation if child member has no docs -autodoc_inherit_docstrings = False - # Used to shorten the parsing of type hint aliases -autodoc_type_aliases = {} +# NOTE: As of now, hyperlinking to type aliases is an open issue +# see https://github.com/sphinx-doc/sphinx/issues/10785 +autodoc_type_aliases = { + 'ArrayLike': 'ArrayLike', + 'NDArray': 'NDArray', + 'DTypeLike': 'DTypeLike', + 'ExampleArrayLike': 'ExampleArrayLike', +} # -- Napoleon Settings ------------------------------------------------------------------------ @@ -125,16 +149,27 @@ # napoleon_include_init_with_doc = False # napoleon_include_private_with_doc = False # napoleon_include_special_with_doc = False -napoleon_use_admonition_for_examples = False -napoleon_use_admonition_for_notes = False -napoleon_use_admonition_for_references = False +napoleon_use_admonition_for_examples = True +napoleon_use_admonition_for_notes = True +napoleon_use_admonition_for_references = True napoleon_use_ivar = False napoleon_use_param = True +napoleon_use_keyword = True napoleon_use_rtype = True -napoleon_preprocess_types = False -napoleon_type_aliases = None +napoleon_preprocess_types = True +napoleon_type_aliases = { +} napoleon_attr_annotations = True +# -- Autodoc typehints settings --------------------------------------------------------------- + +# typehints_fully_qualified = False +# always_document_param_types = False +# typehints_document_rtype = True +# typehints_use_rtype = False +# typehints_defaults = 'braces' +# simplify_optional_unions = False + # -- Intersphinx Settings --------------------------------------------------------------------- intersphinx_mapping = { @@ -149,5 +184,3 @@ todo_include_todos = True todo_emit_warnings = False todo_link_only = False - -# -- Viewcode Settings ------------------------------------------------------------------------ diff --git a/docs/docsrc/howto/howto-docstring.rst b/docs/docsrc/howto/howto-docstring.rst index bdc0ce5aaf..79b822c964 100644 --- a/docs/docsrc/howto/howto-docstring.rst +++ b/docs/docsrc/howto/howto-docstring.rst @@ -40,6 +40,10 @@ Directives Next to plain text, the content of your documentation can be created using *directives*, followed by a block of indented text. +Directives are structural blocks inside the text of a documentation. +They provide specific formatting for sections dedicated to e.g., function parameters, +return values or exmaple code. + For example, the *note* directive in plain rst code :: .. note:: Implementation @@ -142,40 +146,60 @@ As a consequence, **we abstain from including type hints in docstrings** and kee This rule does not exclude custom linking and referencing in-text, where a developer feels the necessity to do so. +.. rubric:: Google style directives + +Google style directives are aliases for standard directives, which simplify the usage and syntax. +Besides the obligatory declaration of parameters, return values and raised errors, +the PorePy style encourages the use of other sections to provide notes, example code usage, references, etc. + +For a list of all supported Google style directives, +`see Google style docstring sections `_. + +The compulsory order of directives inside a docstring is: + + 1. Examples, Note, ... + 2. References, See Also + 3. Parameters + 4. Returns/ Yields + 5. Raises + +Other rules: + + * When using Google Style directives do not type additional text **between** and **after** the + directives References/See Also, Parameters, Returns/Yields and Raises. + * End every docstring with a blank line before \"\"\". This is especially important after + the *Returns:* directive and its indented block. + +.. note:: + The Google Style directives are only valid when used inside docstrings, + but not so when used in .rst files. Keep this in mind, in case you deal with the .rst + structure of the webpage. Documenting variables --------------------- -.. autodata:: example_docstrings.module_level_var_1 +.. autodata:: example_docstrings.example_var_1 + +.. autodata:: example_docstrings.example_var_2 -.. autodata:: example_docstrings.module_level_var_2 +.. autodata:: example_docstrings.example_var_3 -.. autodata:: example_docstrings.module_level_var_3 +.. autodata:: example_docstrings.ExampleArrayLike Documenting functions --------------------- -.. autofunction:: example_docstrings.module_level_function_1 +.. autofunction:: example_docstrings.example_function_1 -.. autofunction:: example_docstrings.module_level_function_2 +.. autofunction:: example_docstrings.example_function_2 -.. autofunction:: example_docstrings.module_level_function_3 +.. autofunction:: example_docstrings.example_function_3 -.. autofunction:: example_docstrings.module_level_function_4 +.. autofunction:: example_docstrings.example_function_4 -.. autofunction:: example_docstrings.example_generator +.. autofunction:: example_docstrings.example_function_5 -.. rubric:: Directives inside docstrings - -* Write the directive blocks in the following order - 1. Examples, Note - 2. Parameters - 3. Returns/ Yields - 4. Raises -* When using Google Style directives do not type additional text **between** and **after** the - directives Parameters, Returns/Yields and Raises. -* End every docstring with a blank line before \"\"\". This is especially important after - the *Returns:* directive and its indented block. +.. autofunction:: example_docstrings.example_generator Documenting classes ------------------- diff --git a/docs/doctrees/docsrc/howto/howto-docstring.doctree b/docs/doctrees/docsrc/howto/howto-docstring.doctree index 351ddae7f9..f61886f5f2 100644 Binary files a/docs/doctrees/docsrc/howto/howto-docstring.doctree and b/docs/doctrees/docsrc/howto/howto-docstring.doctree differ diff --git a/docs/doctrees/docsrc/porepy/numerics/ad/numerics-ad.doctree b/docs/doctrees/docsrc/porepy/numerics/ad/numerics-ad.doctree index b13d7130c9..9185717384 100644 Binary files a/docs/doctrees/docsrc/porepy/numerics/ad/numerics-ad.doctree and b/docs/doctrees/docsrc/porepy/numerics/ad/numerics-ad.doctree differ diff --git a/docs/doctrees/docsrc/porepy/numerics/numerics.doctree b/docs/doctrees/docsrc/porepy/numerics/numerics.doctree index 8283a8f69a..3eaa453acf 100644 Binary files a/docs/doctrees/docsrc/porepy/numerics/numerics.doctree and b/docs/doctrees/docsrc/porepy/numerics/numerics.doctree differ diff --git a/docs/doctrees/environment.pickle b/docs/doctrees/environment.pickle index c8965603f2..6d79f4e30f 100644 Binary files a/docs/doctrees/environment.pickle and b/docs/doctrees/environment.pickle differ diff --git a/docs/doctrees/index.doctree b/docs/doctrees/index.doctree index 2ec7d51be1..d083a91530 100644 Binary files a/docs/doctrees/index.doctree and b/docs/doctrees/index.doctree differ diff --git a/docs/example_docstrings.py b/docs/example_docstrings.py index 0e9890e76a..9f2270a9c5 100644 --- a/docs/example_docstrings.py +++ b/docs/example_docstrings.py @@ -44,7 +44,8 @@ """ from __future__ import annotations -from typing import Generator, Literal, Optional +from typing import Generator, Literal, Optional, Union +from numpy.typing import ArrayLike, NDArray, DTypeLike import numpy as np import scipy.sparse as sps @@ -52,11 +53,11 @@ import porepy as pp -module_level_var_1: str = "var" +example_var_1: str = "var" """Variables at the module level are documented inline after declaration.""" -module_level_var_2: int = 1 +example_var_2: int = 1 """Multi-line docstrings are also valid. You might want to use multiline docstrings when a more detailed description @@ -96,7 +97,7 @@ """ -module_level_var_3: int = 42 +example_var_3: int = 42 """int: **DO NOT** start the docstring with ``int:``, i.e. with type hints. This will render the below ``Type: int``, which is unnecessary due to the already present @@ -107,20 +108,24 @@ .. code:: Python - module_level_var_3: int = 1 + example_var_3: int = 1 \"\"\"This is var 3.\"\"\" **DO NOT:** .. code:: Python - module_level_var_3 = 1 + example_var_3 = 1 \"\"\"int: This is var 3.\"\"\" """ -def module_level_function_1(arg1: int, arg2: str, arg3: bool) -> bool: +ExampleArrayLike = Union[list, np.ndarray] +"""This is a custom type alias, including lists and numpy's ``ndarray``.""" + + +def example_function_1(arg1: int, arg2: str, arg3: bool) -> bool: """A short description of the functionality must fit in the first line. Detailed description can be given next if necessary. The extended description @@ -133,10 +138,10 @@ def module_level_function_1(arg1: int, arg2: str, arg3: bool) -> bool: Note: You can find the ``[source]`` link in the upper right corner of this function's - documentation and take a look at the Python and rst source code of this docstring, + signature and inspect the Python and rst source code of this docstring, as well as for every docstring that follows. - The return value can be described using the Google Style directive *Returns:*. + The return value must be documented using the Google Style directive *Returns:*. Parameters: arg1: Description of arg1. @@ -161,21 +166,25 @@ def module_level_function_1(arg1: int, arg2: str, arg3: bool) -> bool: return (arg1 > len(arg2)) and arg3 -def module_level_function_2( +def example_function_2( optional_arg: Optional[int] = None, *args, **kwargs ) -> None: - """Optional arguments must be type-hinted using :class:`typing.Optional`. + """This function demonstrates linking to objects inside docstrings, optional arguments and + the *Raises:* directive. + + Optional arguments must be type-hinted using :obj:`typing.Optional`. As evident, you can link objects in-text. You can also link functions like - :meth:`module_level_function_1`. + :meth:`example_function_1`. Note the different usage of ``:obj:`` and ``:class:`` for + objects in third-party packages and objects in PorePy. If ``*args`` or ``**kwargs`` are accepted, they must be listed as ``*args`` and ``**kwargs`` in the *Parameters* directive. Note: - We note that this function returns ``None`` as per signature. - This is the default return value of Python and as such does not need documentation. - I.e., we can omit the *Returns:* directive. However, it is important to explicitly + This function returns ``None`` as per signature. + It is the default return value of Python and as such does not need documentation. + I.e., we can omit the *Returns:* directive. However, it is obligatory to explicitly specify the None return in the signature. Parameters: @@ -203,15 +212,13 @@ def module_level_function_2( pass -def module_level_function_3( +def example_function_3( mdg: pp.MixedDimensionalGrid, vector: np.ndarray, matrix: sps.spmatrix, option: Literal["A", "B", "C"] = "A", ) -> sps.spmatrix: - """We demonstrate here the intra- and inter-doc linking to non-base-type Python objects - in the signature, - as well as how to document special requirements for the arguments. + """This function demonstrates how to document special requirements for input arguments. Parameters: mdg: A mixed-dimensional grid. Notice the usage of the acronym ``mdg``. @@ -219,13 +226,12 @@ def module_level_function_3( We use the type hint brackets to indicate its supposed length. The required length is ``num_cells``, the number of cells. If unclear to what the number refers, explain. - E.g. where ``num_cells`` denotes the number of cells in ``mdg``. matrix (shape=(3, num_cells)): This argument is a sparse matrix with 3 rows and ``num_cells`` columns. option (optional): This argument has admissible values and a default value. it can only be a string ``'A'``, ``'B'`` or ``'C'``. For such admissible values use - :class:`typing.literal` to denote them in the signature. + :obj:`typing.Literal` to denote them in the signature. Since it has a default value, we mark it with ``(optional)``. Returns: @@ -246,11 +252,11 @@ def module_level_function_3( pass -def module_level_function_4( +def example_function_4( vector: np.ndarray, matrix: sps.spmatrix, -) -> tuple[sps.spmatrix, np.ndarray] | None: - """Functions with multiple return values need better description in the *Returns:* +) -> tuple[sps.spmatrix, np.ndarray]: + """This function demonstrates how to document multiple return values in the *Returns:* directive. Parameters: @@ -261,18 +267,41 @@ def module_level_function_4( Every returned object needs a description. We can use the same structure as for the parameters: indented block per returned object or value. - spmatrix: + spmatrix ``(shape=(3, nd))``: Though technically the tuple is a single object, it often is of - importance what the tuple contains. + importance what the tuple contains. If the returned object has noteworthy + characteristic, explain them next to the bullet header, the same way as for + parameters. ndarray: - We therefore use again the definition list structure with indented blocks to + Use the definition list structure with indented blocks to describe the content individually. This makes of course only sense if the tuple is of fixed length and/or contains objects of various types. - None: - The same rules hold for union return types. - Raises: - ValueError: If ``option`` is not in ``{'A', 'B', 'C'}``. + """ + pass + + +def example_function_5( + array_like: ArrayLike, + ndarray_like: NDArray, + dtype_like: DTypeLike, +) -> ExampleArrayLike: + """This function demonstrates type annotations using custom type aliases, including those + from third-party packages. + + For Sphinx to display type aliases without parsing their complete expression, + a configuration is needed which maps the type alias to its source. + + When encountering type aliases, which are not already covered by the configuration of + PorePy's docs, please contact the core developers. + + Parameters: + array_like: an argument of type :obj:`~numpy.typing.ArrayLike` + ndarray_like: an argument of type :obj:`~numpy.typing.NDArray` + dtype_like: an argument of type :obj:`~numpy.typing.DTypeLike` + + Returns: + a value of a custom array type :data:`ExampleArrayLike`. """ pass @@ -283,11 +312,8 @@ def example_generator(n: int) -> Generator[int, None, None]: Their usage is equivalent, indicating only that this is a generator object, not a regular function. - Examples: - The Google Style offers an *Examples:* directives where you can write text but also - include inline examples of code usage, without the special code directive from Sphinx. - An indented block with the content has to follow the directive. Like all for all - directives, a blank line after the indented block signalizes the end of the directive. + Example: + Here we demonstrate the usage of ``example_generator`` using the *Example:* directive: >>> print([i for i in example_generator(4)]) [0, 1, 2, 3] @@ -313,8 +339,31 @@ class ExampleClass: *Note:* directives can be used the same way as for functions. - At the end follows obligatory the *Parameters:* directive and a *Raises:* directive, - if errors are raised in the constructor for some reason. + Example: + Using the *Example:* directive, you can provide simplified python syntax using ``>>>`` + on how to instantiate the class for example: + + >>> import example_docstrings as ed + >>> A = ed.ExampleClass() + >>> print(type(A)) + + + Use the *References:* and *See Also:* directives to provide links to sources or + inspirations for your implementation. + + For readability reasons, we impose the same rules on the order of directives as for + functions. Meaning references/ see also, followed by parameters, return/yield and raises + must be placed at the end with no additional text in between. + + References: + 1. `Basic Google Style + `_. + + See Also: + `Same, but in different directive + `_. Parameters: arg1: first argument. diff --git a/docs/html/.buildinfo b/docs/html/.buildinfo index 8acfaebd74..acd5db00f9 100644 --- a/docs/html/.buildinfo +++ b/docs/html/.buildinfo @@ -1,4 +1,4 @@ # Sphinx build info version 1 # This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done. -config: 73117507a055de80d3e2cd9377d56e97 +config: 21375f1304e0c230cf7e7ff241e18de7 tags: 645f666f9bcd5a90fca523b33c5a78b7 diff --git a/docs/html/_modules/example_docstrings.html b/docs/html/_modules/example_docstrings.html index 1a70ca4af4..7bd9254e83 100644 --- a/docs/html/_modules/example_docstrings.html +++ b/docs/html/_modules/example_docstrings.html @@ -1,41 +1,79 @@ - - - - - - - example_docstrings — PorePy 1.5 documentation - - - - - - - + + + + + example_docstrings — PorePy 1.5 documentation + + + + + + + + + + + + - - - -
-
-
-
- + + + +
+ + +
+ +
+
+
+ +
+
+
+
+

Source code for example_docstrings

 """
 Welcome to the *How-To* on creating documentation for your functions, classes and submodules.
@@ -83,7 +121,8 @@ 
Source code for example_docstrings
 """
 from __future__ import annotations
 
-from typing import Generator, Literal, Optional
+from typing import Generator, Literal, Optional, Union
+from numpy.typing import ArrayLike, NDArray, DTypeLike
 
 import numpy as np
 import scipy.sparse as sps
@@ -91,11 +130,11 @@ 
Source code for example_docstrings
 import porepy as pp
 
 
-module_level_var_1: str = "var"
+example_var_1: str = "var"
 """Variables at the module level are documented inline after declaration."""
 
 
-module_level_var_2: int = 1
+example_var_2: int = 1
 """Multi-line docstrings are also valid.
 
 You might want to use multiline docstrings when a more detailed description
@@ -135,7 +174,7 @@ 
Source code for example_docstrings
 """
 
 
-module_level_var_3: int = 42
+example_var_3: int = 42
 """int: **DO NOT** start the docstring with ``int:``, i.e. with type hints.
 
 This will render the below ``Type: int``, which is unnecessary due to the already present
@@ -146,20 +185,24 @@ 
Source code for example_docstrings
 
 .. code:: Python
 
-    module_level_var_3: int = 1
+    example_var_3: int = 1
     \"\"\"This is var 3.\"\"\"
 
 **DO NOT:**
 
 .. code:: Python
 
-    module_level_var_3 = 1
+    example_var_3 = 1
     \"\"\"int: This is var 3.\"\"\"
 
 """
 
 
-
[docs]def module_level_function_1(arg1: int, arg2: str, arg3: bool) -> bool:
+ExampleArrayLike = Union[list, np.ndarray]
+"""This is a custom type alias, including lists and numpy's ``ndarray``."""
+
+
+
[docs]def example_function_1(arg1: int, arg2: str, arg3: bool) -> bool:
     """A short description of the functionality must fit in the first line.
 
     Detailed description can be given next if necessary. The extended description
@@ -172,10 +215,10 @@ 
Source code for example_docstrings
 
     Note:
         You can find the ``[source]`` link in the upper right corner of this function's
-        documentation and take a look at the Python and rst source code of this docstring,
+        signature and inspect the Python and rst source code of this docstring,
         as well as for every docstring that follows.
 
-    The return value can be described using the Google Style directive *Returns:*.
+    The return value must be documented using the Google Style directive *Returns:*.
 
     Parameters:
         arg1: Description of arg1.
@@ -200,21 +243,25 @@ 
Source code for example_docstrings
     return (arg1 > len(arg2)) and arg3

 
 
-
[docs]def module_level_function_2(
+
[docs]def example_function_2(
     optional_arg: Optional[int] = None, *args, **kwargs
 ) -> None:
-    """Optional arguments must be type-hinted using :class:`typing.Optional`.
+    """This function demonstrates linking to objects inside docstrings, optional arguments and
+    the *Raises:* directive.
+    
+    Optional arguments must be type-hinted using :obj:`typing.Optional`.
 
     As evident, you can link objects in-text. You can also link functions like
-    :meth:`module_level_function_1`.
+    :meth:`example_function_1`. Note the different usage of ``:obj:`` and ``:class:`` for
+    objects in third-party packages and objects in PorePy.
 
     If ``*args`` or ``**kwargs`` are accepted,
     they must be listed as ``*args`` and ``**kwargs`` in the *Parameters* directive.
 
     Note:
-        We note that this function returns ``None`` as per signature.
-        This is the default return value of Python and as such does not need documentation.
-        I.e., we can omit the *Returns:* directive. However, it is important to explicitly
+        This function returns ``None`` as per signature.
+        It is the default return value of Python and as such does not need documentation.
+        I.e., we can omit the *Returns:* directive. However, it is obligatory to explicitly
         specify the None return in the signature.
 
     Parameters:
@@ -242,15 +289,13 @@ 
Source code for example_docstrings
     pass

 
 
-
[docs]def module_level_function_3(
+
[docs]def example_function_3(
     mdg: pp.MixedDimensionalGrid,
     vector: np.ndarray,
     matrix: sps.spmatrix,
     option: Literal["A", "B", "C"] = "A",
 ) -> sps.spmatrix:
-    """We demonstrate here the intra- and inter-doc linking to non-base-type Python objects
-    in the signature,
-    as well as how to document special requirements for the arguments.
+    """This function demonstrates how to document special requirements for input arguments.
 
     Parameters:
         mdg: A mixed-dimensional grid. Notice the usage of the acronym ``mdg``.
@@ -258,13 +303,12 @@ 
Source code for example_docstrings
             We use the type hint brackets to indicate its supposed length.
             The required length is ``num_cells``, the number of cells. If unclear to what the
             number refers, explain.
-
             E.g. where ``num_cells`` denotes the number of cells in ``mdg``.
         matrix (shape=(3, num_cells)): This argument is a sparse matrix with 3 rows and
             ``num_cells`` columns.
         option (optional): This argument has admissible values and a default value.
             it can only be a string ``'A'``, ``'B'`` or ``'C'``. For such admissible values use
-            :class:`typing.literal` to denote them in the signature.
+            :obj:`typing.Literal` to denote them in the signature.
             Since it has a default value, we mark it with ``(optional)``.
 
     Returns:
@@ -285,11 +329,11 @@ 
Source code for example_docstrings
     pass

 
 
-
[docs]def module_level_function_4(
+
[docs]def example_function_4(
     vector: np.ndarray,
     matrix: sps.spmatrix,
-) -> tuple[sps.spmatrix, np.ndarray] | None:
-    """Functions with multiple return values need better description in the *Returns:*
+) -> tuple[sps.spmatrix, np.ndarray]:
+    """This function demonstrates how to document multiple return values in the *Returns:*
     directive.
 
     Parameters:
@@ -300,18 +344,41 @@ 
Source code for example_docstrings
         Every returned object needs a description. We can use the same structure as for
         the parameters: indented block per returned object or value.
 
-        spmatrix:
+        spmatrix ``(shape=(3, nd))``:
             Though technically the tuple is a single object, it often is of
-            importance what the tuple contains.
+            importance what the tuple contains. If the returned object has noteworthy
+            characteristic, explain them next to the bullet header, the same way as for
+            parameters.
         ndarray:
-            We therefore use again the definition list structure with indented blocks to
+            Use the definition list structure with indented blocks to
             describe the content individually. This makes of course only sense if the tuple
             is of fixed length and/or contains objects of various types.
-        None:
-            The same rules hold for union return types.
 
-    Raises:
-        ValueError: If ``option`` is not in ``{'A', 'B', 'C'}``.
+    """
+    pass

+
+
+
[docs]def example_function_5(
+    array_like: ArrayLike,
+    ndarray_like: NDArray,
+    dtype_like: DTypeLike,
+) -> ExampleArrayLike:
+    """This function demonstrates type annotations using custom type aliases, including those
+    from third-party packages.
+
+    For Sphinx to display type aliases without parsing their complete expression,
+    a configuration is needed which maps the type alias to its source.
+
+    When encountering type aliases, which are not already covered by the configuration of
+    PorePy's docs, please contact the core developers.
+
+    Parameters:
+        array_like: an argument of type :obj:`~numpy.typing.ArrayLike`
+        ndarray_like: an argument of type :obj:`~numpy.typing.NDArray`
+        dtype_like: an argument of type :obj:`~numpy.typing.DTypeLike`
+
+    Returns:
+        a value of a custom array type :data:`ExampleArrayLike`.
 
     """
     pass

@@ -322,11 +389,8 @@ 
Source code for example_docstrings
     Their usage is equivalent, indicating only that this is a generator object, not a regular
     function.
 
-    Examples:
-        The Google Style offers an *Examples:* directives where you can write text but also
-        include inline examples of code usage, without the special code directive from Sphinx.
-        An indented block with the content has to follow the directive. Like all for all
-        directives, a blank line after the indented block signalizes the end of the directive.
+    Example:
+        Here we demonstrate the usage of ``example_generator`` using the *Example:* directive:
 
         >>> print([i for i in example_generator(4)])
         [0, 1, 2, 3]
@@ -352,8 +416,31 @@ 
Source code for example_docstrings
 
     *Note:* directives can be used the same way as for functions.
 
-    At the end follows obligatory the *Parameters:* directive and a *Raises:* directive,
-    if errors are raised in the constructor for some reason.
+    Example:
+        Using the *Example:* directive, you can provide simplified python syntax using ``>>>``
+        on how to instantiate the class for example:
+
+        >>> import example_docstrings as ed
+        >>> A = ed.ExampleClass()
+        >>> print(type(A))
+        <class 'example_docstrings.ExampleClass'>
+
+    Use the *References:* and *See Also:* directives to provide links to sources or
+    inspirations for your implementation.
+
+    For readability reasons, we impose the same rules on the order of directives as for
+    functions. Meaning references/ see also, followed by parameters, return/yield and raises
+    must be placed at the end with no additional text in between.
+
+    References:
+        1. `Basic Google Style 
+           <https://www.sphinx-doc.org/en/master/usage/extensions/
+           example_google.html#example-google>`_.
+
+    See Also:
+        `Same, but in different directive 
+        <https://www.sphinx-doc.org/en/master/usage/extensions/
+        example_google.html#example-google>`_.
 
     Parameters:
         arg1: first argument.
@@ -502,42 +589,28 @@ 
Source code for example_docstrings
         pass

 

 
-            

+           

           

+          

+
+  

+
+  

+    
© Copyright 2022 UiB Center for Modeling of Coupled Subsurface Dynamics, GNU LESSER GENERAL PUBLIC LICENSE Version 3, 29 June 2007..

+  

+
+   
+
+

         

       

-      
-      

-    

-    
-    
-  
+
+
+ + + \ No newline at end of file diff --git a/docs/html/_modules/index.html b/docs/html/_modules/index.html index c49564d4dc..3ca07ae90f 100644 --- a/docs/html/_modules/index.html +++ b/docs/html/_modules/index.html @@ -1,40 +1,78 @@ - - - - - - - Overview: module code — PorePy 1.5 documentation - - - - - - - + + + + + Overview: module code — PorePy 1.5 documentation + + + + + + + + + + + + - - + + + +
+ -
-
-
-
- +
+ +
+
+
+
    +
    • +
  • Overview: module code
    • +
  • +
    • +
+
+
+
+
+

All modules for which code is available

-
+
+
+ +
+ +
+

© Copyright 2022 UiB Center for Modeling of Coupled Subsurface Dynamics, GNU LESSER GENERAL PUBLIC LICENSE Version 3, 29 June 2007..

+
+ + + +
- -
-
- - - + +
+ + + \ No newline at end of file diff --git a/docs/html/_modules/porepy/numerics/ad/functions.html b/docs/html/_modules/porepy/numerics/ad/functions.html index eec93677b9..d6c720093b 100644 --- a/docs/html/_modules/porepy/numerics/ad/functions.html +++ b/docs/html/_modules/porepy/numerics/ad/functions.html @@ -301,8 +301,15 @@

Source code for porepy.numerics.ad.functions

[docs]def heaviside_smooth(var, eps: float = 1e-3):
-    """
-    Smooth (regularized) version of the Heaviside function.
+    """Smooth (regularized) version of the Heaviside function.
+
+    Note:
+        The analytical expression for the smooth version Heaviside function reads:
+            ``H_eps(x) = (1/2) * (1 + (2/pi) * arctan(x/eps))``,
+        with its derivative smoothly approximating the Dirac delta function:
+            ``d(H(x))/dx = delta_eps = (1/pi) * (eps / (eps^2 + x^2))``.
+
+        Reference: https://ieeexplore.ieee.org/document/902291
 
     Parameters:
         var: Input array.
@@ -313,14 +320,6 @@ 
Source code for porepy.numerics.ad.functions
        Regularized heaviside function (and its Jacobian if applicable) in form of a
         Ad_array or ndarray (depending on the input).
 
-    Note:
-        The analytical expression for the smooth version Heaviside function reads:
-            ``H_eps(x) = (1/2) * (1 + (2/pi) * arctan(x/eps))``,
-        with its derivative smoothly approximating the Dirac delta function:
-            ``d(H(x))/dx = delta_eps = (1/pi) * (eps / (eps^2 + x^2))``.
-
-        Reference: https://ieeexplore.ieee.org/document/902291
-
     """
     if isinstance(var, Ad_array):
         val = 0.5 * (1 + 2 * np.pi ** (-1) * np.arctan(var.val * eps ** (-1)))
@@ -353,7 +352,7 @@ 
Source code for porepy.numerics.ad.functions
    wrapped in a pp.ad.Array, whereas the first argument is expected to be an
     Ad_array originating from a pp.ad.Operator.
 
-    Args:
+    Parameters:
         var0: First argument to the maximum function.
         var1: Second argument.
 
@@ -384,10 +383,10 @@ 
Source code for porepy.numerics.ad.functions
    Returns 1 if ``var.val`` is within absolute tolerance = ``tol`` of zero.
     The derivative is set to zero independent of ``var.val``.
 
-    Notes:
+    Note:
         See module level documentation on how to wrap functions like this in ``ad.Function``.
 
-    Args:
+    Parameters:
         tol: Absolute tolerance for comparison with 0 using np.isclose.
         var: Ad operator (variable or expression).
 
diff --git a/docs/html/_modules/porepy/numerics/ad/operator_functions.html b/docs/html/_modules/porepy/numerics/ad/operator_functions.html
index 5012f5b220..f72688343b 100644
--- a/docs/html/_modules/porepy/numerics/ad/operator_functions.html
+++ b/docs/html/_modules/porepy/numerics/ad/operator_functions.html
@@ -47,7 +47,7 @@ 
Source code for porepy.numerics.ad.operator_functions
import abc
 from functools import partial
-from typing import Callable, List, Optional, Type, Union
+from typing import Callable, Optional, Type, Union
 
 import numpy as np
 import scipy.sparse as sps
@@ -127,7 +127,7 @@ 
Source code for porepy.numerics.ad.operator_functions
self._operation: Operation = Operation.evaluate
         self._set_tree()
 
-
[docs]    def __call__(self, *args: pp.ad.Operator | Ad_array):
+
[docs]    def __call__(self, *args: pp.ad.Operator | Ad_array) -> pp.ad.Operator:
         """Renders this function operator callable, fulfilling its notion as 'function'.
 
         Parameters:
@@ -360,7 +360,7 @@ 
Source code for porepy.numerics.ad.operator_functions
self,
         func: Callable,
         name: str,
-        multipliers: Union[List[float], float],
+        multipliers: float | list[float],
         array_compatible: bool = False,
     ):
         super().__init__(func, name, array_compatible)
@@ -625,7 +625,7 @@ 
Source code for porepy.numerics.ad.operator_functions
# This will trigger the function evaluation.
         return partial(self.__call__, binding_instance)

 
-
[docs]    def ad_wrapper(self, *args, **kwargs) -> AbstractFunction:
+
[docs]    def ad_wrapper(self, *args, **kwargs) -> Operator:
         """Actual wrapper function.
         Constructs the necessary AD-Operator class wrapping the decorated callable
         and performs the evaluation/call.
diff --git a/docs/html/_modules/porepy/numerics/ad/operators.html b/docs/html/_modules/porepy/numerics/ad/operators.html
index 19b81c777e..7482e10f8e 100644
--- a/docs/html/_modules/porepy/numerics/ad/operators.html
+++ b/docs/html/_modules/porepy/numerics/ad/operators.html
@@ -293,9 +293,6 @@ 
Source code for porepy.numerics.ad.operators
"""Perform the ``discretize`` function of all child operators which are discretizations
         using data from mdg.
 
-        IMPLEMENTATION NOTE: The discretizations was identified at initialization of
-        Expression - it is now done here to accommodate updates (?) and
-
         """
         unique_discretizations: dict[
             _ad_utils.MergedOperator, GridLike
@@ -781,7 +778,7 @@ 
Source code for porepy.numerics.ad.operators
self,
         dof_manager: pp.DofManager,
         state: Optional[np.ndarray] = None,
-    ) -> Ad_array:
+    ):
         """Evaluate the residual and Jacobian matrix for a given state.
 
         Parameters:
diff --git a/docs/html/_modules/typing.html b/docs/html/_modules/typing.html
new file mode 100644
index 0000000000..9343d64333
--- /dev/null
+++ b/docs/html/_modules/typing.html
@@ -0,0 +1,2307 @@
+
+
+
+  
+  
+  typing — PorePy 1.5 documentation
+      
+      
+  
+  
+        
+        
+        
+        
+        
+    
+    
+     
+
+
+ 
+  

+    
+
+    

+
+      

+        

+          

+  
+  

+

+          

+           

+             
+  
Source code for typing
+"""
+The typing module: Support for gradual typing as defined by PEP 484.
+
+At large scale, the structure of the module is following:
+* Imports and exports, all public names should be explicitly added to __all__.
+* Internal helper functions: these should never be used in code outside this module.
+* _SpecialForm and its instances (special forms): Any, NoReturn, ClassVar, Union, Optional
+* Two classes whose instances can be type arguments in addition to types: ForwardRef and TypeVar
+* The core of internal generics API: _GenericAlias and _VariadicGenericAlias, the latter is
+  currently only used by Tuple and Callable. All subscripted types like X[int], Union[int, str],
+  etc., are instances of either of these classes.
+* The public counterpart of the generics API consists of two classes: Generic and Protocol.
+* Public helper functions: get_type_hints, overload, cast, no_type_check,
+  no_type_check_decorator.
+* Generic aliases for collections.abc ABCs and few additional protocols.
+* Special types: NewType, NamedTuple, TypedDict.
+* Wrapper submodules for re and io related types.
+"""
+
+from abc import abstractmethod, ABCMeta
+import collections
+import collections.abc
+import contextlib
+import functools
+import operator
+import re as stdlib_re  # Avoid confusion with the re we export.
+import sys
+import types
+from types import WrapperDescriptorType, MethodWrapperType, MethodDescriptorType, GenericAlias
+
+# Please keep __all__ alphabetized within each category.
+__all__ = [
+    # Super-special typing primitives.
+    'Annotated',
+    'Any',
+    'Callable',
+    'ClassVar',
+    'Final',
+    'ForwardRef',
+    'Generic',
+    'Literal',
+    'Optional',
+    'Protocol',
+    'Tuple',
+    'Type',
+    'TypeVar',
+    'Union',
+
+    # ABCs (from collections.abc).
+    'AbstractSet',  # collections.abc.Set.
+    'ByteString',
+    'Container',
+    'ContextManager',
+    'Hashable',
+    'ItemsView',
+    'Iterable',
+    'Iterator',
+    'KeysView',
+    'Mapping',
+    'MappingView',
+    'MutableMapping',
+    'MutableSequence',
+    'MutableSet',
+    'Sequence',
+    'Sized',
+    'ValuesView',
+    'Awaitable',
+    'AsyncIterator',
+    'AsyncIterable',
+    'Coroutine',
+    'Collection',
+    'AsyncGenerator',
+    'AsyncContextManager',
+
+    # Structural checks, a.k.a. protocols.
+    'Reversible',
+    'SupportsAbs',
+    'SupportsBytes',
+    'SupportsComplex',
+    'SupportsFloat',
+    'SupportsIndex',
+    'SupportsInt',
+    'SupportsRound',
+
+    # Concrete collection types.
+    'ChainMap',
+    'Counter',
+    'Deque',
+    'Dict',
+    'DefaultDict',
+    'List',
+    'OrderedDict',
+    'Set',
+    'FrozenSet',
+    'NamedTuple',  # Not really a type.
+    'TypedDict',  # Not really a type.
+    'Generator',
+
+    # One-off things.
+    'AnyStr',
+    'cast',
+    'final',
+    'get_args',
+    'get_origin',
+    'get_type_hints',
+    'NewType',
+    'no_type_check',
+    'no_type_check_decorator',
+    'NoReturn',
+    'overload',
+    'runtime_checkable',
+    'Text',
+    'TYPE_CHECKING',
+]
+
+# The pseudo-submodules 're' and 'io' are part of the public
+# namespace, but excluded from __all__ because they might stomp on
+# legitimate imports of those modules.
+
+
+def _type_convert(arg):
+    """For converting None to type(None), and strings to ForwardRef."""
+    if arg is None:
+        return type(None)
+    if isinstance(arg, str):
+        return ForwardRef(arg)
+    return arg
+
+
+def _type_check(arg, msg, is_argument=True):
+    """Check that the argument is a type, and return it (internal helper).
+
+    As a special case, accept None and return type(None) instead. Also wrap strings
+    into ForwardRef instances. Consider several corner cases, for example plain
+    special forms like Union are not valid, while Union[int, str] is OK, etc.
+    The msg argument is a human-readable error message, e.g::
+
+        "Union[arg, ...]: arg should be a type."
+
+    We append the repr() of the actual value (truncated to 100 chars).
+    """
+    invalid_generic_forms = (Generic, Protocol)
+    if is_argument:
+        invalid_generic_forms = invalid_generic_forms + (ClassVar, Final)
+
+    arg = _type_convert(arg)
+    if (isinstance(arg, _GenericAlias) and
+            arg.__origin__ in invalid_generic_forms):
+        raise TypeError(f"{arg} is not valid as type argument")
+    if arg in (Any, NoReturn):
+        return arg
+    if isinstance(arg, _SpecialForm) or arg in (Generic, Protocol):
+        raise TypeError(f"Plain {arg} is not valid as type argument")
+    if isinstance(arg, (type, TypeVar, ForwardRef)):
+        return arg
+    if not callable(arg):
+        raise TypeError(f"{msg} Got {arg!r:.100}.")
+    return arg
+
+
+def _type_repr(obj):
+    """Return the repr() of an object, special-casing types (internal helper).
+
+    If obj is a type, we return a shorter version than the default
+    type.__repr__, based on the module and qualified name, which is
+    typically enough to uniquely identify a type.  For everything
+    else, we fall back on repr(obj).
+    """
+    if isinstance(obj, types.GenericAlias):
+        return repr(obj)
+    if isinstance(obj, type):
+        if obj.__module__ == 'builtins':
+            return obj.__qualname__
+        return f'{obj.__module__}.{obj.__qualname__}'
+    if obj is ...:
+        return('...')
+    if isinstance(obj, types.FunctionType):
+        return obj.__name__
+    return repr(obj)
+
+
+def _collect_type_vars(types):
+    """Collect all type variable contained in types in order of
+    first appearance (lexicographic order). For example::
+
+        _collect_type_vars((T, List[S, T])) == (T, S)
+    """
+    tvars = []
+    for t in types:
+        if isinstance(t, TypeVar) and t not in tvars:
+            tvars.append(t)
+        if isinstance(t, (_GenericAlias, GenericAlias)):
+            tvars.extend([t for t in t.__parameters__ if t not in tvars])
+    return tuple(tvars)
+
+
+def _check_generic(cls, parameters, elen):
+    """Check correct count for parameters of a generic cls (internal helper).
+    This gives a nice error message in case of count mismatch.
+    """
+    if not elen:
+        raise TypeError(f"{cls} is not a generic class")
+    alen = len(parameters)
+    if alen != elen:
+        raise TypeError(f"Too {'many' if alen > elen else 'few'} parameters for {cls};"
+                        f" actual {alen}, expected {elen}")
+
+
+def _deduplicate(params):
+    # Weed out strict duplicates, preserving the first of each occurrence.
+    all_params = set(params)
+    if len(all_params) < len(params):
+        new_params = []
+        for t in params:
+            if t in all_params:
+                new_params.append(t)
+                all_params.remove(t)
+        params = new_params
+        assert not all_params, all_params
+    return params
+
+
+def _remove_dups_flatten(parameters):
+    """An internal helper for Union creation and substitution: flatten Unions
+    among parameters, then remove duplicates.
+    """
+    # Flatten out Union[Union[...], ...].
+    params = []
+    for p in parameters:
+        if isinstance(p, _UnionGenericAlias):
+            params.extend(p.__args__)
+        elif isinstance(p, tuple) and len(p) > 0 and p[0] is Union:
+            params.extend(p[1:])
+        else:
+            params.append(p)
+
+    return tuple(_deduplicate(params))
+
+
+def _flatten_literal_params(parameters):
+    """An internal helper for Literal creation: flatten Literals among parameters"""
+    params = []
+    for p in parameters:
+        if isinstance(p, _LiteralGenericAlias):
+            params.extend(p.__args__)
+        else:
+            params.append(p)
+    return tuple(params)
+
+
+_cleanups = []
+
+
+def _tp_cache(func=None, /, *, typed=False):
+    """Internal wrapper caching __getitem__ of generic types with a fallback to
+    original function for non-hashable arguments.
+    """
+    def decorator(func):
+        cached = functools.lru_cache(typed=typed)(func)
+        _cleanups.append(cached.cache_clear)
+
+        @functools.wraps(func)
+        def inner(*args, **kwds):
+            try:
+                return cached(*args, **kwds)
+            except TypeError:
+                pass  # All real errors (not unhashable args) are raised below.
+            return func(*args, **kwds)
+        return inner
+
+    if func is not None:
+        return decorator(func)
+
+    return decorator
+
+def _eval_type(t, globalns, localns, recursive_guard=frozenset()):
+    """Evaluate all forward references in the given type t.
+    For use of globalns and localns see the docstring for get_type_hints().
+    recursive_guard is used to prevent prevent infinite recursion
+    with recursive ForwardRef.
+    """
+    if isinstance(t, ForwardRef):
+        return t._evaluate(globalns, localns, recursive_guard)
+    if isinstance(t, (_GenericAlias, GenericAlias)):
+        ev_args = tuple(_eval_type(a, globalns, localns, recursive_guard) for a in t.__args__)
+        if ev_args == t.__args__:
+            return t
+        if isinstance(t, GenericAlias):
+            return GenericAlias(t.__origin__, ev_args)
+        else:
+            return t.copy_with(ev_args)
+    return t
+
+
+class _Final:
+    """Mixin to prohibit subclassing"""
+
+    __slots__ = ('__weakref__',)
+
+    def __init_subclass__(self, /, *args, **kwds):
+        if '_root' not in kwds:
+            raise TypeError("Cannot subclass special typing classes")
+
+class _Immutable:
+    """Mixin to indicate that object should not be copied."""
+    __slots__ = ()
+
+    def __copy__(self):
+        return self
+
+    def __deepcopy__(self, memo):
+        return self
+
+
+# Internal indicator of special typing constructs.
+# See __doc__ instance attribute for specific docs.
+class _SpecialForm(_Final, _root=True):
+    __slots__ = ('_name', '__doc__', '_getitem')
+
+    def __init__(self, getitem):
+        self._getitem = getitem
+        self._name = getitem.__name__
+        self.__doc__ = getitem.__doc__
+
+    def __mro_entries__(self, bases):
+        raise TypeError(f"Cannot subclass {self!r}")
+
+    def __repr__(self):
+        return 'typing.' + self._name
+
+    def __reduce__(self):
+        return self._name
+
+    def __call__(self, *args, **kwds):
+        raise TypeError(f"Cannot instantiate {self!r}")
+
+    def __instancecheck__(self, obj):
+        raise TypeError(f"{self} cannot be used with isinstance()")
+
+    def __subclasscheck__(self, cls):
+        raise TypeError(f"{self} cannot be used with issubclass()")
+
+    @_tp_cache
+    def __getitem__(self, parameters):
+        return self._getitem(self, parameters)
+
+
+class _LiteralSpecialForm(_SpecialForm, _root=True):
+    @_tp_cache(typed=True)
+    def __getitem__(self, parameters):
+        return self._getitem(self, parameters)
+
+
+@_SpecialForm
+def Any(self, parameters):
+    """Special type indicating an unconstrained type.
+
+    - Any is compatible with every type.
+    - Any assumed to have all methods.
+    - All values assumed to be instances of Any.
+
+    Note that all the above statements are true from the point of view of
+    static type checkers. At runtime, Any should not be used with instance
+    or class checks.
+    """
+    raise TypeError(f"{self} is not subscriptable")
+
+@_SpecialForm
+def NoReturn(self, parameters):
+    """Special type indicating functions that never return.
+    Example::
+
+      from typing import NoReturn
+
+      def stop() -> NoReturn:
+          raise Exception('no way')
+
+    This type is invalid in other positions, e.g., ``List[NoReturn]``
+    will fail in static type checkers.
+    """
+    raise TypeError(f"{self} is not subscriptable")
+
+@_SpecialForm
+def ClassVar(self, parameters):
+    """Special type construct to mark class variables.
+
+    An annotation wrapped in ClassVar indicates that a given
+    attribute is intended to be used as a class variable and
+    should not be set on instances of that class. Usage::
+
+      class Starship:
+          stats: ClassVar[Dict[str, int]] = {} # class variable
+          damage: int = 10                     # instance variable
+
+    ClassVar accepts only types and cannot be further subscribed.
+
+    Note that ClassVar is not a class itself, and should not
+    be used with isinstance() or issubclass().
+    """
+    item = _type_check(parameters, f'{self} accepts only single type.')
+    return _GenericAlias(self, (item,))
+
+@_SpecialForm
+def Final(self, parameters):
+    """Special typing construct to indicate final names to type checkers.
+
+    A final name cannot be re-assigned or overridden in a subclass.
+    For example:
+
+      MAX_SIZE: Final = 9000
+      MAX_SIZE += 1  # Error reported by type checker
+
+      class Connection:
+          TIMEOUT: Final[int] = 10
+
+      class FastConnector(Connection):
+          TIMEOUT = 1  # Error reported by type checker
+
+    There is no runtime checking of these properties.
+    """
+    item = _type_check(parameters, f'{self} accepts only single type.')
+    return _GenericAlias(self, (item,))
+
+@_SpecialForm
+def Union(self, parameters):
+    """Union type; Union[X, Y] means either X or Y.
+
+    To define a union, use e.g. Union[int, str].  Details:
+    - The arguments must be types and there must be at least one.
+    - None as an argument is a special case and is replaced by
+      type(None).
+    - Unions of unions are flattened, e.g.::
+
+        Union[Union[int, str], float] == Union[int, str, float]
+
+    - Unions of a single argument vanish, e.g.::
+
+        Union[int] == int  # The constructor actually returns int
+
+    - Redundant arguments are skipped, e.g.::
+
+        Union[int, str, int] == Union[int, str]
+
+    - When comparing unions, the argument order is ignored, e.g.::
+
+        Union[int, str] == Union[str, int]
+
+    - You cannot subclass or instantiate a union.
+    - You can use Optional[X] as a shorthand for Union[X, None].
+    """
+    if parameters == ():
+        raise TypeError("Cannot take a Union of no types.")
+    if not isinstance(parameters, tuple):
+        parameters = (parameters,)
+    msg = "Union[arg, ...]: each arg must be a type."
+    parameters = tuple(_type_check(p, msg) for p in parameters)
+    parameters = _remove_dups_flatten(parameters)
+    if len(parameters) == 1:
+        return parameters[0]
+    return _UnionGenericAlias(self, parameters)
+
+@_SpecialForm
+def Optional(self, parameters):
+    """Optional type.
+
+    Optional[X] is equivalent to Union[X, None].
+    """
+    arg = _type_check(parameters, f"{self} requires a single type.")
+    return Union[arg, type(None)]
+
+@_LiteralSpecialForm
+def Literal(self, parameters):
+    """Special typing form to define literal types (a.k.a. value types).
+
+    This form can be used to indicate to type checkers that the corresponding
+    variable or function parameter has a value equivalent to the provided
+    literal (or one of several literals):
+
+      def validate_simple(data: Any) -> Literal[True]:  # always returns True
+          ...
+
+      MODE = Literal['r', 'rb', 'w', 'wb']
+      def open_helper(file: str, mode: MODE) -> str:
+          ...
+
+      open_helper('/some/path', 'r')  # Passes type check
+      open_helper('/other/path', 'typo')  # Error in type checker
+
+    Literal[...] cannot be subclassed. At runtime, an arbitrary value
+    is allowed as type argument to Literal[...], but type checkers may
+    impose restrictions.
+    """
+    # There is no '_type_check' call because arguments to Literal[...] are
+    # values, not types.
+    if not isinstance(parameters, tuple):
+        parameters = (parameters,)
+
+    parameters = _flatten_literal_params(parameters)
+
+    try:
+        parameters = tuple(p for p, _ in _deduplicate(list(_value_and_type_iter(parameters))))
+    except TypeError:  # unhashable parameters
+        pass
+
+    return _LiteralGenericAlias(self, parameters)
+
+
+class ForwardRef(_Final, _root=True):
+    """Internal wrapper to hold a forward reference."""
+
+    __slots__ = ('__forward_arg__', '__forward_code__',
+                 '__forward_evaluated__', '__forward_value__',
+                 '__forward_is_argument__')
+
+    def __init__(self, arg, is_argument=True):
+        if not isinstance(arg, str):
+            raise TypeError(f"Forward reference must be a string -- got {arg!r}")
+        try:
+            code = compile(arg, '<string>', 'eval')
+        except SyntaxError:
+            raise SyntaxError(f"Forward reference must be an expression -- got {arg!r}")
+        self.__forward_arg__ = arg
+        self.__forward_code__ = code
+        self.__forward_evaluated__ = False
+        self.__forward_value__ = None
+        self.__forward_is_argument__ = is_argument
+
+    def _evaluate(self, globalns, localns, recursive_guard):
+        if self.__forward_arg__ in recursive_guard:
+            return self
+        if not self.__forward_evaluated__ or localns is not globalns:
+            if globalns is None and localns is None:
+                globalns = localns = {}
+            elif globalns is None:
+                globalns = localns
+            elif localns is None:
+                localns = globalns
+            type_ =_type_check(
+                eval(self.__forward_code__, globalns, localns),
+                "Forward references must evaluate to types.",
+                is_argument=self.__forward_is_argument__,
+            )
+            self.__forward_value__ = _eval_type(
+                type_, globalns, localns, recursive_guard | {self.__forward_arg__}
+            )
+            self.__forward_evaluated__ = True
+        return self.__forward_value__
+
+    def __eq__(self, other):
+        if not isinstance(other, ForwardRef):
+            return NotImplemented
+        if self.__forward_evaluated__ and other.__forward_evaluated__:
+            return (self.__forward_arg__ == other.__forward_arg__ and
+                    self.__forward_value__ == other.__forward_value__)
+        return self.__forward_arg__ == other.__forward_arg__
+
+    def __hash__(self):
+        return hash(self.__forward_arg__)
+
+    def __repr__(self):
+        return f'ForwardRef({self.__forward_arg__!r})'
+
+
+class TypeVar(_Final, _Immutable, _root=True):
+    """Type variable.
+
+    Usage::
+
+      T = TypeVar('T')  # Can be anything
+      A = TypeVar('A', str, bytes)  # Must be str or bytes
+
+    Type variables exist primarily for the benefit of static type
+    checkers.  They serve as the parameters for generic types as well
+    as for generic function definitions.  See class Generic for more
+    information on generic types.  Generic functions work as follows:
+
+      def repeat(x: T, n: int) -> List[T]:
+          '''Return a list containing n references to x.'''
+          return [x]*n
+
+      def longest(x: A, y: A) -> A:
+          '''Return the longest of two strings.'''
+          return x if len(x) >= len(y) else y
+
+    The latter example's signature is essentially the overloading
+    of (str, str) -> str and (bytes, bytes) -> bytes.  Also note
+    that if the arguments are instances of some subclass of str,
+    the return type is still plain str.
+
+    At runtime, isinstance(x, T) and issubclass(C, T) will raise TypeError.
+
+    Type variables defined with covariant=True or contravariant=True
+    can be used to declare covariant or contravariant generic types.
+    See PEP 484 for more details. By default generic types are invariant
+    in all type variables.
+
+    Type variables can be introspected. e.g.:
+
+      T.__name__ == 'T'
+      T.__constraints__ == ()
+      T.__covariant__ == False
+      T.__contravariant__ = False
+      A.__constraints__ == (str, bytes)
+
+    Note that only type variables defined in global scope can be pickled.
+    """
+
+    __slots__ = ('__name__', '__bound__', '__constraints__',
+                 '__covariant__', '__contravariant__', '__dict__')
+
+    def __init__(self, name, *constraints, bound=None,
+                 covariant=False, contravariant=False):
+        self.__name__ = name
+        if covariant and contravariant:
+            raise ValueError("Bivariant types are not supported.")
+        self.__covariant__ = bool(covariant)
+        self.__contravariant__ = bool(contravariant)
+        if constraints and bound is not None:
+            raise TypeError("Constraints cannot be combined with bound=...")
+        if constraints and len(constraints) == 1:
+            raise TypeError("A single constraint is not allowed")
+        msg = "TypeVar(name, constraint, ...): constraints must be types."
+        self.__constraints__ = tuple(_type_check(t, msg) for t in constraints)
+        if bound:
+            self.__bound__ = _type_check(bound, "Bound must be a type.")
+        else:
+            self.__bound__ = None
+        try:
+            def_mod = sys._getframe(1).f_globals.get('__name__', '__main__')  # for pickling
+        except (AttributeError, ValueError):
+            def_mod = None
+        if def_mod != 'typing':
+            self.__module__ = def_mod
+
+    def __repr__(self):
+        if self.__covariant__:
+            prefix = '+'
+        elif self.__contravariant__:
+            prefix = '-'
+        else:
+            prefix = '~'
+        return prefix + self.__name__
+
+    def __reduce__(self):
+        return self.__name__
+
+
+def _is_dunder(attr):
+    return attr.startswith('__') and attr.endswith('__')
+
+class _BaseGenericAlias(_Final, _root=True):
+    """The central part of internal API.
+
+    This represents a generic version of type 'origin' with type arguments 'params'.
+    There are two kind of these aliases: user defined and special. The special ones
+    are wrappers around builtin collections and ABCs in collections.abc. These must
+    have 'name' always set. If 'inst' is False, then the alias can't be instantiated,
+    this is used by e.g. typing.List and typing.Dict.
+    """
+    def __init__(self, origin, *, inst=True, name=None):
+        self._inst = inst
+        self._name = name
+        self.__origin__ = origin
+        self.__slots__ = None  # This is not documented.
+
+    def __call__(self, *args, **kwargs):
+        if not self._inst:
+            raise TypeError(f"Type {self._name} cannot be instantiated; "
+                            f"use {self.__origin__.__name__}() instead")
+        result = self.__origin__(*args, **kwargs)
+        try:
+            result.__orig_class__ = self
+        except AttributeError:
+            pass
+        return result
+
+    def __mro_entries__(self, bases):
+        res = []
+        if self.__origin__ not in bases:
+            res.append(self.__origin__)
+        i = bases.index(self)
+        for b in bases[i+1:]:
+            if isinstance(b, _BaseGenericAlias) or issubclass(b, Generic):
+                break
+        else:
+            res.append(Generic)
+        return tuple(res)
+
+    def __getattr__(self, attr):
+        # We are careful for copy and pickle.
+        # Also for simplicity we just don't relay all dunder names
+        if '__origin__' in self.__dict__ and not _is_dunder(attr):
+            return getattr(self.__origin__, attr)
+        raise AttributeError(attr)
+
+    def __setattr__(self, attr, val):
+        if _is_dunder(attr) or attr in ('_name', '_inst', '_nparams'):
+            super().__setattr__(attr, val)
+        else:
+            setattr(self.__origin__, attr, val)
+
+    def __instancecheck__(self, obj):
+        return self.__subclasscheck__(type(obj))
+
+    def __subclasscheck__(self, cls):
+        raise TypeError("Subscripted generics cannot be used with"
+                        " class and instance checks")
+
+
+# Special typing constructs Union, Optional, Generic, Callable and Tuple
+# use three special attributes for internal bookkeeping of generic types:
+# * __parameters__ is a tuple of unique free type parameters of a generic
+#   type, for example, Dict[T, T].__parameters__ == (T,);
+# * __origin__ keeps a reference to a type that was subscripted,
+#   e.g., Union[T, int].__origin__ == Union, or the non-generic version of
+#   the type.
+# * __args__ is a tuple of all arguments used in subscripting,
+#   e.g., Dict[T, int].__args__ == (T, int).
+
+
+class _GenericAlias(_BaseGenericAlias, _root=True):
+    def __init__(self, origin, params, *, inst=True, name=None):
+        super().__init__(origin, inst=inst, name=name)
+        if not isinstance(params, tuple):
+            params = (params,)
+        self.__args__ = tuple(... if a is _TypingEllipsis else
+                              () if a is _TypingEmpty else
+                              a for a in params)
+        self.__parameters__ = _collect_type_vars(params)
+        if not name:
+            self.__module__ = origin.__module__
+
+    def __eq__(self, other):
+        if not isinstance(other, _GenericAlias):
+            return NotImplemented
+        return (self.__origin__ == other.__origin__
+                and self.__args__ == other.__args__)
+
+    def __hash__(self):
+        return hash((self.__origin__, self.__args__))
+
+    @_tp_cache
+    def __getitem__(self, params):
+        if self.__origin__ in (Generic, Protocol):
+            # Can't subscript Generic[...] or Protocol[...].
+            raise TypeError(f"Cannot subscript already-subscripted {self}")
+        if not isinstance(params, tuple):
+            params = (params,)
+        msg = "Parameters to generic types must be types."
+        params = tuple(_type_check(p, msg) for p in params)
+        _check_generic(self, params, len(self.__parameters__))
+
+        subst = dict(zip(self.__parameters__, params))
+        new_args = []
+        for arg in self.__args__:
+            if isinstance(arg, TypeVar):
+                arg = subst[arg]
+            elif isinstance(arg, (_GenericAlias, GenericAlias)):
+                subparams = arg.__parameters__
+                if subparams:
+                    subargs = tuple(subst[x] for x in subparams)
+                    arg = arg[subargs]
+            new_args.append(arg)
+        return self.copy_with(tuple(new_args))
+
+    def copy_with(self, params):
+        return self.__class__(self.__origin__, params, name=self._name, inst=self._inst)
+
+    def __repr__(self):
+        if self._name:
+            name = 'typing.' + self._name
+        else:
+            name = _type_repr(self.__origin__)
+        args = ", ".join([_type_repr(a) for a in self.__args__])
+        return f'{name}[{args}]'
+
+    def __reduce__(self):
+        if self._name:
+            origin = globals()[self._name]
+        else:
+            origin = self.__origin__
+        args = tuple(self.__args__)
+        if len(args) == 1 and not isinstance(args[0], tuple):
+            args, = args
+        return operator.getitem, (origin, args)
+
+    def __mro_entries__(self, bases):
+        if self._name:  # generic version of an ABC or built-in class
+            return super().__mro_entries__(bases)
+        if self.__origin__ is Generic:
+            if Protocol in bases:
+                return ()
+            i = bases.index(self)
+            for b in bases[i+1:]:
+                if isinstance(b, _BaseGenericAlias) and b is not self:
+                    return ()
+        return (self.__origin__,)
+
+
+# _nparams is the number of accepted parameters, e.g. 0 for Hashable,
+# 1 for List and 2 for Dict.  It may be -1 if variable number of
+# parameters are accepted (needs custom __getitem__).
+
+class _SpecialGenericAlias(_BaseGenericAlias, _root=True):
+    def __init__(self, origin, nparams, *, inst=True, name=None):
+        if name is None:
+            name = origin.__name__
+        super().__init__(origin, inst=inst, name=name)
+        self._nparams = nparams
+        if origin.__module__ == 'builtins':
+            self.__doc__ = f'A generic version of {origin.__qualname__}.'
+        else:
+            self.__doc__ = f'A generic version of {origin.__module__}.{origin.__qualname__}.'
+
+    @_tp_cache
+    def __getitem__(self, params):
+        if not isinstance(params, tuple):
+            params = (params,)
+        msg = "Parameters to generic types must be types."
+        params = tuple(_type_check(p, msg) for p in params)
+        _check_generic(self, params, self._nparams)
+        return self.copy_with(params)
+
+    def copy_with(self, params):
+        return _GenericAlias(self.__origin__, params,
+                             name=self._name, inst=self._inst)
+
+    def __repr__(self):
+        return 'typing.' + self._name
+
+    def __subclasscheck__(self, cls):
+        if isinstance(cls, _SpecialGenericAlias):
+            return issubclass(cls.__origin__, self.__origin__)
+        if not isinstance(cls, _GenericAlias):
+            return issubclass(cls, self.__origin__)
+        return super().__subclasscheck__(cls)
+
+    def __reduce__(self):
+        return self._name
+
+
+class _CallableGenericAlias(_GenericAlias, _root=True):
+    def __repr__(self):
+        assert self._name == 'Callable'
+        if len(self.__args__) == 2 and self.__args__[0] is Ellipsis:
+            return super().__repr__()
+        return (f'typing.Callable'
+                f'[[{", ".join([_type_repr(a) for a in self.__args__[:-1]])}], '
+                f'{_type_repr(self.__args__[-1])}]')
+
+    def __reduce__(self):
+        args = self.__args__
+        if not (len(args) == 2 and args[0] is ...):
+            args = list(args[:-1]), args[-1]
+        return operator.getitem, (Callable, args)
+
+
+class _CallableType(_SpecialGenericAlias, _root=True):
+    def copy_with(self, params):
+        return _CallableGenericAlias(self.__origin__, params,
+                                     name=self._name, inst=self._inst)
+
+    def __getitem__(self, params):
+        if not isinstance(params, tuple) or len(params) != 2:
+            raise TypeError("Callable must be used as "
+                            "Callable[[arg, ...], result].")
+        args, result = params
+        # This relaxes what args can be on purpose to allow things like
+        # PEP 612 ParamSpec.  Responsibility for whether a user is using
+        # Callable[...] properly is deferred to static type checkers.
+        if isinstance(args, list):
+            params = (tuple(args), result)
+        else:
+            params = (args, result)
+        return self.__getitem_inner__(params)
+
+    @_tp_cache
+    def __getitem_inner__(self, params):
+        args, result = params
+        msg = "Callable[args, result]: result must be a type."
+        result = _type_check(result, msg)
+        if args is Ellipsis:
+            return self.copy_with((_TypingEllipsis, result))
+        if not isinstance(args, tuple):
+            args = (args,)
+        args = tuple(_type_convert(arg) for arg in args)
+        params = args + (result,)
+        return self.copy_with(params)
+
+
+class _TupleType(_SpecialGenericAlias, _root=True):
+    @_tp_cache
+    def __getitem__(self, params):
+        if params == ():
+            return self.copy_with((_TypingEmpty,))
+        if not isinstance(params, tuple):
+            params = (params,)
+        if len(params) == 2 and params[1] is ...:
+            msg = "Tuple[t, ...]: t must be a type."
+            p = _type_check(params[0], msg)
+            return self.copy_with((p, _TypingEllipsis))
+        msg = "Tuple[t0, t1, ...]: each t must be a type."
+        params = tuple(_type_check(p, msg) for p in params)
+        return self.copy_with(params)
+
+
+class _UnionGenericAlias(_GenericAlias, _root=True):
+    def copy_with(self, params):
+        return Union[params]
+
+    def __eq__(self, other):
+        if not isinstance(other, _UnionGenericAlias):
+            return NotImplemented
+        return set(self.__args__) == set(other.__args__)
+
+    def __hash__(self):
+        return hash(frozenset(self.__args__))
+
+    def __repr__(self):
+        args = self.__args__
+        if len(args) == 2:
+            if args[0] is type(None):
+                return f'typing.Optional[{_type_repr(args[1])}]'
+            elif args[1] is type(None):
+                return f'typing.Optional[{_type_repr(args[0])}]'
+        return super().__repr__()
+
+
+def _value_and_type_iter(parameters):
+    return ((p, type(p)) for p in parameters)
+
+
+class _LiteralGenericAlias(_GenericAlias, _root=True):
+
+    def __eq__(self, other):
+        if not isinstance(other, _LiteralGenericAlias):
+            return NotImplemented
+
+        return set(_value_and_type_iter(self.__args__)) == set(_value_and_type_iter(other.__args__))
+
+    def __hash__(self):
+        return hash(frozenset(_value_and_type_iter(self.__args__)))
+
+
+class Generic:
+    """Abstract base class for generic types.
+
+    A generic type is typically declared by inheriting from
+    this class parameterized with one or more type variables.
+    For example, a generic mapping type might be defined as::
+
+      class Mapping(Generic[KT, VT]):
+          def __getitem__(self, key: KT) -> VT:
+              ...
+          # Etc.
+
+    This class can then be used as follows::
+
+      def lookup_name(mapping: Mapping[KT, VT], key: KT, default: VT) -> VT:
+          try:
+              return mapping[key]
+          except KeyError:
+              return default
+    """
+    __slots__ = ()
+    _is_protocol = False
+
+    @_tp_cache
+    def __class_getitem__(cls, params):
+        if not isinstance(params, tuple):
+            params = (params,)
+        if not params and cls is not Tuple:
+            raise TypeError(
+                f"Parameter list to {cls.__qualname__}[...] cannot be empty")
+        msg = "Parameters to generic types must be types."
+        params = tuple(_type_check(p, msg) for p in params)
+        if cls in (Generic, Protocol):
+            # Generic and Protocol can only be subscripted with unique type variables.
+            if not all(isinstance(p, TypeVar) for p in params):
+                raise TypeError(
+                    f"Parameters to {cls.__name__}[...] must all be type variables")
+            if len(set(params)) != len(params):
+                raise TypeError(
+                    f"Parameters to {cls.__name__}[...] must all be unique")
+        else:
+            # Subscripting a regular Generic subclass.
+            _check_generic(cls, params, len(cls.__parameters__))
+        return _GenericAlias(cls, params)
+
+    def __init_subclass__(cls, *args, **kwargs):
+        super().__init_subclass__(*args, **kwargs)
+        tvars = []
+        if '__orig_bases__' in cls.__dict__:
+            error = Generic in cls.__orig_bases__
+        else:
+            error = Generic in cls.__bases__ and cls.__name__ != 'Protocol'
+        if error:
+            raise TypeError("Cannot inherit from plain Generic")
+        if '__orig_bases__' in cls.__dict__:
+            tvars = _collect_type_vars(cls.__orig_bases__)
+            # Look for Generic[T1, ..., Tn].
+            # If found, tvars must be a subset of it.
+            # If not found, tvars is it.
+            # Also check for and reject plain Generic,
+            # and reject multiple Generic[...].
+            gvars = None
+            for base in cls.__orig_bases__:
+                if (isinstance(base, _GenericAlias) and
+                        base.__origin__ is Generic):
+                    if gvars is not None:
+                        raise TypeError(
+                            "Cannot inherit from Generic[...] multiple types.")
+                    gvars = base.__parameters__
+            if gvars is not None:
+                tvarset = set(tvars)
+                gvarset = set(gvars)
+                if not tvarset <= gvarset:
+                    s_vars = ', '.join(str(t) for t in tvars if t not in gvarset)
+                    s_args = ', '.join(str(g) for g in gvars)
+                    raise TypeError(f"Some type variables ({s_vars}) are"
+                                    f" not listed in Generic[{s_args}]")
+                tvars = gvars
+        cls.__parameters__ = tuple(tvars)
+
+
+class _TypingEmpty:
+    """Internal placeholder for () or []. Used by TupleMeta and CallableMeta
+    to allow empty list/tuple in specific places, without allowing them
+    to sneak in where prohibited.
+    """
+
+
+class _TypingEllipsis:
+    """Internal placeholder for ... (ellipsis)."""
+
+
+_TYPING_INTERNALS = ['__parameters__', '__orig_bases__',  '__orig_class__',
+                     '_is_protocol', '_is_runtime_protocol']
+
+_SPECIAL_NAMES = ['__abstractmethods__', '__annotations__', '__dict__', '__doc__',
+                  '__init__', '__module__', '__new__', '__slots__',
+                  '__subclasshook__', '__weakref__', '__class_getitem__']
+
+# These special attributes will be not collected as protocol members.
+EXCLUDED_ATTRIBUTES = _TYPING_INTERNALS + _SPECIAL_NAMES + ['_MutableMapping__marker']
+
+
+def _get_protocol_attrs(cls):
+    """Collect protocol members from a protocol class objects.
+
+    This includes names actually defined in the class dictionary, as well
+    as names that appear in annotations. Special names (above) are skipped.
+    """
+    attrs = set()
+    for base in cls.__mro__[:-1]:  # without object
+        if base.__name__ in ('Protocol', 'Generic'):
+            continue
+        annotations = getattr(base, '__annotations__', {})
+        for attr in list(base.__dict__.keys()) + list(annotations.keys()):
+            if not attr.startswith('_abc_') and attr not in EXCLUDED_ATTRIBUTES:
+                attrs.add(attr)
+    return attrs
+
+
+def _is_callable_members_only(cls):
+    # PEP 544 prohibits using issubclass() with protocols that have non-method members.
+    return all(callable(getattr(cls, attr, None)) for attr in _get_protocol_attrs(cls))
+
+
+def _no_init(self, *args, **kwargs):
+    if type(self)._is_protocol:
+        raise TypeError('Protocols cannot be instantiated')
+
+
+def _allow_reckless_class_cheks():
+    """Allow instance and class checks for special stdlib modules.
+
+    The abc and functools modules indiscriminately call isinstance() and
+    issubclass() on the whole MRO of a user class, which may contain protocols.
+    """
+    try:
+        return sys._getframe(3).f_globals['__name__'] in ['abc', 'functools']
+    except (AttributeError, ValueError):  # For platforms without _getframe().
+        return True
+
+
+_PROTO_WHITELIST = {
+    'collections.abc': [
+        'Callable', 'Awaitable', 'Iterable', 'Iterator', 'AsyncIterable',
+        'Hashable', 'Sized', 'Container', 'Collection', 'Reversible',
+    ],
+    'contextlib': ['AbstractContextManager', 'AbstractAsyncContextManager'],
+}
+
+
+class _ProtocolMeta(ABCMeta):
+    # This metaclass is really unfortunate and exists only because of
+    # the lack of __instancehook__.
+    def __instancecheck__(cls, instance):
+        # We need this method for situations where attributes are
+        # assigned in __init__.
+        if ((not getattr(cls, '_is_protocol', False) or
+                _is_callable_members_only(cls)) and
+                issubclass(instance.__class__, cls)):
+            return True
+        if cls._is_protocol:
+            if all(hasattr(instance, attr) and
+                    # All *methods* can be blocked by setting them to None.
+                    (not callable(getattr(cls, attr, None)) or
+                     getattr(instance, attr) is not None)
+                    for attr in _get_protocol_attrs(cls)):
+                return True
+        return super().__instancecheck__(instance)
+
+
+class Protocol(Generic, metaclass=_ProtocolMeta):
+    """Base class for protocol classes.
+
+    Protocol classes are defined as::
+
+        class Proto(Protocol):
+            def meth(self) -> int:
+                ...
+
+    Such classes are primarily used with static type checkers that recognize
+    structural subtyping (static duck-typing), for example::
+
+        class C:
+            def meth(self) -> int:
+                return 0
+
+        def func(x: Proto) -> int:
+            return x.meth()
+
+        func(C())  # Passes static type check
+
+    See PEP 544 for details. Protocol classes decorated with
+    @typing.runtime_checkable act as simple-minded runtime protocols that check
+    only the presence of given attributes, ignoring their type signatures.
+    Protocol classes can be generic, they are defined as::
+
+        class GenProto(Protocol[T]):
+            def meth(self) -> T:
+                ...
+    """
+    __slots__ = ()
+    _is_protocol = True
+    _is_runtime_protocol = False
+
+    def __init_subclass__(cls, *args, **kwargs):
+        super().__init_subclass__(*args, **kwargs)
+
+        # Determine if this is a protocol or a concrete subclass.
+        if not cls.__dict__.get('_is_protocol', False):
+            cls._is_protocol = any(b is Protocol for b in cls.__bases__)
+
+        # Set (or override) the protocol subclass hook.
+        def _proto_hook(other):
+            if not cls.__dict__.get('_is_protocol', False):
+                return NotImplemented
+
+            # First, perform various sanity checks.
+            if not getattr(cls, '_is_runtime_protocol', False):
+                if _allow_reckless_class_cheks():
+                    return NotImplemented
+                raise TypeError("Instance and class checks can only be used with"
+                                " @runtime_checkable protocols")
+            if not _is_callable_members_only(cls):
+                if _allow_reckless_class_cheks():
+                    return NotImplemented
+                raise TypeError("Protocols with non-method members"
+                                " don't support issubclass()")
+            if not isinstance(other, type):
+                # Same error message as for issubclass(1, int).
+                raise TypeError('issubclass() arg 1 must be a class')
+
+            # Second, perform the actual structural compatibility check.
+            for attr in _get_protocol_attrs(cls):
+                for base in other.__mro__:
+                    # Check if the members appears in the class dictionary...
+                    if attr in base.__dict__:
+                        if base.__dict__[attr] is None:
+                            return NotImplemented
+                        break
+
+                    # ...or in annotations, if it is a sub-protocol.
+                    annotations = getattr(base, '__annotations__', {})
+                    if (isinstance(annotations, collections.abc.Mapping) and
+                            attr in annotations and
+                            issubclass(other, Generic) and other._is_protocol):
+                        break
+                else:
+                    return NotImplemented
+            return True
+
+        if '__subclasshook__' not in cls.__dict__:
+            cls.__subclasshook__ = _proto_hook
+
+        # We have nothing more to do for non-protocols...
+        if not cls._is_protocol:
+            return
+
+        # ... otherwise check consistency of bases, and prohibit instantiation.
+        for base in cls.__bases__:
+            if not (base in (object, Generic) or
+                    base.__module__ in _PROTO_WHITELIST and
+                    base.__name__ in _PROTO_WHITELIST[base.__module__] or
+                    issubclass(base, Generic) and base._is_protocol):
+                raise TypeError('Protocols can only inherit from other'
+                                ' protocols, got %r' % base)
+        cls.__init__ = _no_init
+
+
+class _AnnotatedAlias(_GenericAlias, _root=True):
+    """Runtime representation of an annotated type.
+
+    At its core 'Annotated[t, dec1, dec2, ...]' is an alias for the type 't'
+    with extra annotations. The alias behaves like a normal typing alias,
+    instantiating is the same as instantiating the underlying type, binding
+    it to types is also the same.
+    """
+    def __init__(self, origin, metadata):
+        if isinstance(origin, _AnnotatedAlias):
+            metadata = origin.__metadata__ + metadata
+            origin = origin.__origin__
+        super().__init__(origin, origin)
+        self.__metadata__ = metadata
+
+    def copy_with(self, params):
+        assert len(params) == 1
+        new_type = params[0]
+        return _AnnotatedAlias(new_type, self.__metadata__)
+
+    def __repr__(self):
+        return "typing.Annotated[{}, {}]".format(
+            _type_repr(self.__origin__),
+            ", ".join(repr(a) for a in self.__metadata__)
+        )
+
+    def __reduce__(self):
+        return operator.getitem, (
+            Annotated, (self.__origin__,) + self.__metadata__
+        )
+
+    def __eq__(self, other):
+        if not isinstance(other, _AnnotatedAlias):
+            return NotImplemented
+        return (self.__origin__ == other.__origin__
+                and self.__metadata__ == other.__metadata__)
+
+    def __hash__(self):
+        return hash((self.__origin__, self.__metadata__))
+
+
+class Annotated:
+    """Add context specific metadata to a type.
+
+    Example: Annotated[int, runtime_check.Unsigned] indicates to the
+    hypothetical runtime_check module that this type is an unsigned int.
+    Every other consumer of this type can ignore this metadata and treat
+    this type as int.
+
+    The first argument to Annotated must be a valid type.
+
+    Details:
+
+    - It's an error to call `Annotated` with less than two arguments.
+    - Nested Annotated are flattened::
+
+        Annotated[Annotated[T, Ann1, Ann2], Ann3] == Annotated[T, Ann1, Ann2, Ann3]
+
+    - Instantiating an annotated type is equivalent to instantiating the
+    underlying type::
+
+        Annotated[C, Ann1](5) == C(5)
+
+    - Annotated can be used as a generic type alias::
+
+        Optimized = Annotated[T, runtime.Optimize()]
+        Optimized[int] == Annotated[int, runtime.Optimize()]
+
+        OptimizedList = Annotated[List[T], runtime.Optimize()]
+        OptimizedList[int] == Annotated[List[int], runtime.Optimize()]
+    """
+
+    __slots__ = ()
+
+    def __new__(cls, *args, **kwargs):
+        raise TypeError("Type Annotated cannot be instantiated.")
+
+    @_tp_cache
+    def __class_getitem__(cls, params):
+        if not isinstance(params, tuple) or len(params) < 2:
+            raise TypeError("Annotated[...] should be used "
+                            "with at least two arguments (a type and an "
+                            "annotation).")
+        msg = "Annotated[t, ...]: t must be a type."
+        origin = _type_check(params[0], msg)
+        metadata = tuple(params[1:])
+        return _AnnotatedAlias(origin, metadata)
+
+    def __init_subclass__(cls, *args, **kwargs):
+        raise TypeError(
+            "Cannot subclass {}.Annotated".format(cls.__module__)
+        )
+
+
+def runtime_checkable(cls):
+    """Mark a protocol class as a runtime protocol.
+
+    Such protocol can be used with isinstance() and issubclass().
+    Raise TypeError if applied to a non-protocol class.
+    This allows a simple-minded structural check very similar to
+    one trick ponies in collections.abc such as Iterable.
+    For example::
+
+        @runtime_checkable
+        class Closable(Protocol):
+            def close(self): ...
+
+        assert isinstance(open('/some/file'), Closable)
+
+    Warning: this will check only the presence of the required methods,
+    not their type signatures!
+    """
+    if not issubclass(cls, Generic) or not cls._is_protocol:
+        raise TypeError('@runtime_checkable can be only applied to protocol classes,'
+                        ' got %r' % cls)
+    cls._is_runtime_protocol = True
+    return cls
+
+
+def cast(typ, val):
+    """Cast a value to a type.
+
+    This returns the value unchanged.  To the type checker this
+    signals that the return value has the designated type, but at
+    runtime we intentionally don't check anything (we want this
+    to be as fast as possible).
+    """
+    return val
+
+
+def _get_defaults(func):
+    """Internal helper to extract the default arguments, by name."""
+    try:
+        code = func.__code__
+    except AttributeError:
+        # Some built-in functions don't have __code__, __defaults__, etc.
+        return {}
+    pos_count = code.co_argcount
+    arg_names = code.co_varnames
+    arg_names = arg_names[:pos_count]
+    defaults = func.__defaults__ or ()
+    kwdefaults = func.__kwdefaults__
+    res = dict(kwdefaults) if kwdefaults else {}
+    pos_offset = pos_count - len(defaults)
+    for name, value in zip(arg_names[pos_offset:], defaults):
+        assert name not in res
+        res[name] = value
+    return res
+
+
+_allowed_types = (types.FunctionType, types.BuiltinFunctionType,
+                  types.MethodType, types.ModuleType,
+                  WrapperDescriptorType, MethodWrapperType, MethodDescriptorType)
+
+
+def get_type_hints(obj, globalns=None, localns=None, include_extras=False):
+    """Return type hints for an object.
+
+    This is often the same as obj.__annotations__, but it handles
+    forward references encoded as string literals, adds Optional[t] if a
+    default value equal to None is set and recursively replaces all
+    'Annotated[T, ...]' with 'T' (unless 'include_extras=True').
+
+    The argument may be a module, class, method, or function. The annotations
+    are returned as a dictionary. For classes, annotations include also
+    inherited members.
+
+    TypeError is raised if the argument is not of a type that can contain
+    annotations, and an empty dictionary is returned if no annotations are
+    present.
+
+    BEWARE -- the behavior of globalns and localns is counterintuitive
+    (unless you are familiar with how eval() and exec() work).  The
+    search order is locals first, then globals.
+
+    - If no dict arguments are passed, an attempt is made to use the
+      globals from obj (or the respective module's globals for classes),
+      and these are also used as the locals.  If the object does not appear
+      to have globals, an empty dictionary is used.
+
+    - If one dict argument is passed, it is used for both globals and
+      locals.
+
+    - If two dict arguments are passed, they specify globals and
+      locals, respectively.
+    """
+
+    if getattr(obj, '__no_type_check__', None):
+        return {}
+    # Classes require a special treatment.
+    if isinstance(obj, type):
+        hints = {}
+        for base in reversed(obj.__mro__):
+            if globalns is None:
+                base_globals = sys.modules[base.__module__].__dict__
+            else:
+                base_globals = globalns
+            ann = base.__dict__.get('__annotations__', {})
+            for name, value in ann.items():
+                if value is None:
+                    value = type(None)
+                if isinstance(value, str):
+                    value = ForwardRef(value, is_argument=False)
+                value = _eval_type(value, base_globals, localns)
+                hints[name] = value
+        return hints if include_extras else {k: _strip_annotations(t) for k, t in hints.items()}
+
+    if globalns is None:
+        if isinstance(obj, types.ModuleType):
+            globalns = obj.__dict__
+        else:
+            nsobj = obj
+            # Find globalns for the unwrapped object.
+            while hasattr(nsobj, '__wrapped__'):
+                nsobj = nsobj.__wrapped__
+            globalns = getattr(nsobj, '__globals__', {})
+        if localns is None:
+            localns = globalns
+    elif localns is None:
+        localns = globalns
+    hints = getattr(obj, '__annotations__', None)
+    if hints is None:
+        # Return empty annotations for something that _could_ have them.
+        if isinstance(obj, _allowed_types):
+            return {}
+        else:
+            raise TypeError('{!r} is not a module, class, method, '
+                            'or function.'.format(obj))
+    defaults = _get_defaults(obj)
+    hints = dict(hints)
+    for name, value in hints.items():
+        if value is None:
+            value = type(None)
+        if isinstance(value, str):
+            value = ForwardRef(value)
+        value = _eval_type(value, globalns, localns)
+        if name in defaults and defaults[name] is None:
+            value = Optional[value]
+        hints[name] = value
+    return hints if include_extras else {k: _strip_annotations(t) for k, t in hints.items()}
+
+
+def _strip_annotations(t):
+    """Strips the annotations from a given type.
+    """
+    if isinstance(t, _AnnotatedAlias):
+        return _strip_annotations(t.__origin__)
+    if isinstance(t, _GenericAlias):
+        stripped_args = tuple(_strip_annotations(a) for a in t.__args__)
+        if stripped_args == t.__args__:
+            return t
+        return t.copy_with(stripped_args)
+    if isinstance(t, GenericAlias):
+        stripped_args = tuple(_strip_annotations(a) for a in t.__args__)
+        if stripped_args == t.__args__:
+            return t
+        return GenericAlias(t.__origin__, stripped_args)
+    return t
+
+
+def get_origin(tp):
+    """Get the unsubscripted version of a type.
+
+    This supports generic types, Callable, Tuple, Union, Literal, Final, ClassVar
+    and Annotated. Return None for unsupported types. Examples::
+
+        get_origin(Literal[42]) is Literal
+        get_origin(int) is None
+        get_origin(ClassVar[int]) is ClassVar
+        get_origin(Generic) is Generic
+        get_origin(Generic[T]) is Generic
+        get_origin(Union[T, int]) is Union
+        get_origin(List[Tuple[T, T]][int]) == list
+    """
+    if isinstance(tp, _AnnotatedAlias):
+        return Annotated
+    if isinstance(tp, (_BaseGenericAlias, GenericAlias)):
+        return tp.__origin__
+    if tp is Generic:
+        return Generic
+    return None
+
+
+def get_args(tp):
+    """Get type arguments with all substitutions performed.
+
+    For unions, basic simplifications used by Union constructor are performed.
+    Examples::
+        get_args(Dict[str, int]) == (str, int)
+        get_args(int) == ()
+        get_args(Union[int, Union[T, int], str][int]) == (int, str)
+        get_args(Union[int, Tuple[T, int]][str]) == (int, Tuple[str, int])
+        get_args(Callable[[], T][int]) == ([], int)
+    """
+    if isinstance(tp, _AnnotatedAlias):
+        return (tp.__origin__,) + tp.__metadata__
+    if isinstance(tp, (_GenericAlias, GenericAlias)):
+        res = tp.__args__
+        if tp.__origin__ is collections.abc.Callable and res[0] is not Ellipsis:
+            res = (list(res[:-1]), res[-1])
+        return res
+    return ()
+
+
+def no_type_check(arg):
+    """Decorator to indicate that annotations are not type hints.
+
+    The argument must be a class or function; if it is a class, it
+    applies recursively to all methods and classes defined in that class
+    (but not to methods defined in its superclasses or subclasses).
+
+    This mutates the function(s) or class(es) in place.
+    """
+    if isinstance(arg, type):
+        arg_attrs = arg.__dict__.copy()
+        for attr, val in arg.__dict__.items():
+            if val in arg.__bases__ + (arg,):
+                arg_attrs.pop(attr)
+        for obj in arg_attrs.values():
+            if isinstance(obj, types.FunctionType):
+                obj.__no_type_check__ = True
+            if isinstance(obj, type):
+                no_type_check(obj)
+    try:
+        arg.__no_type_check__ = True
+    except TypeError:  # built-in classes
+        pass
+    return arg
+
+
+def no_type_check_decorator(decorator):
+    """Decorator to give another decorator the @no_type_check effect.
+
+    This wraps the decorator with something that wraps the decorated
+    function in @no_type_check.
+    """
+
+    @functools.wraps(decorator)
+    def wrapped_decorator(*args, **kwds):
+        func = decorator(*args, **kwds)
+        func = no_type_check(func)
+        return func
+
+    return wrapped_decorator
+
+
+def _overload_dummy(*args, **kwds):
+    """Helper for @overload to raise when called."""
+    raise NotImplementedError(
+        "You should not call an overloaded function. "
+        "A series of @overload-decorated functions "
+        "outside a stub module should always be followed "
+        "by an implementation that is not @overload-ed.")
+
+
+def overload(func):
+    """Decorator for overloaded functions/methods.
+
+    In a stub file, place two or more stub definitions for the same
+    function in a row, each decorated with @overload.  For example:
+
+      @overload
+      def utf8(value: None) -> None: ...
+      @overload
+      def utf8(value: bytes) -> bytes: ...
+      @overload
+      def utf8(value: str) -> bytes: ...
+
+    In a non-stub file (i.e. a regular .py file), do the same but
+    follow it with an implementation.  The implementation should *not*
+    be decorated with @overload.  For example:
+
+      @overload
+      def utf8(value: None) -> None: ...
+      @overload
+      def utf8(value: bytes) -> bytes: ...
+      @overload
+      def utf8(value: str) -> bytes: ...
+      def utf8(value):
+          # implementation goes here
+    """
+    return _overload_dummy
+
+
+def final(f):
+    """A decorator to indicate final methods and final classes.
+
+    Use this decorator to indicate to type checkers that the decorated
+    method cannot be overridden, and decorated class cannot be subclassed.
+    For example:
+
+      class Base:
+          @final
+          def done(self) -> None:
+              ...
+      class Sub(Base):
+          def done(self) -> None:  # Error reported by type checker
+                ...
+
+      @final
+      class Leaf:
+          ...
+      class Other(Leaf):  # Error reported by type checker
+          ...
+
+    There is no runtime checking of these properties.
+    """
+    return f
+
+
+# Some unconstrained type variables.  These are used by the container types.
+# (These are not for export.)
+T = TypeVar('T')  # Any type.
+KT = TypeVar('KT')  # Key type.
+VT = TypeVar('VT')  # Value type.
+T_co = TypeVar('T_co', covariant=True)  # Any type covariant containers.
+V_co = TypeVar('V_co', covariant=True)  # Any type covariant containers.
+VT_co = TypeVar('VT_co', covariant=True)  # Value type covariant containers.
+T_contra = TypeVar('T_contra', contravariant=True)  # Ditto contravariant.
+# Internal type variable used for Type[].
+CT_co = TypeVar('CT_co', covariant=True, bound=type)
+
+# A useful type variable with constraints.  This represents string types.
+# (This one *is* for export!)
+AnyStr = TypeVar('AnyStr', bytes, str)
+
+
+# Various ABCs mimicking those in collections.abc.
+_alias = _SpecialGenericAlias
+
+Hashable = _alias(collections.abc.Hashable, 0)  # Not generic.
+Awaitable = _alias(collections.abc.Awaitable, 1)
+Coroutine = _alias(collections.abc.Coroutine, 3)
+AsyncIterable = _alias(collections.abc.AsyncIterable, 1)
+AsyncIterator = _alias(collections.abc.AsyncIterator, 1)
+Iterable = _alias(collections.abc.Iterable, 1)
+Iterator = _alias(collections.abc.Iterator, 1)
+Reversible = _alias(collections.abc.Reversible, 1)
+Sized = _alias(collections.abc.Sized, 0)  # Not generic.
+Container = _alias(collections.abc.Container, 1)
+Collection = _alias(collections.abc.Collection, 1)
+Callable = _CallableType(collections.abc.Callable, 2)
+Callable.__doc__ = \
+    """Callable type; Callable[[int], str] is a function of (int) -> str.
+
+    The subscription syntax must always be used with exactly two
+    values: the argument list and the return type.  The argument list
+    must be a list of types or ellipsis; the return type must be a single type.
+
+    There is no syntax to indicate optional or keyword arguments,
+    such function types are rarely used as callback types.
+    """
+AbstractSet = _alias(collections.abc.Set, 1, name='AbstractSet')
+MutableSet = _alias(collections.abc.MutableSet, 1)
+# NOTE: Mapping is only covariant in the value type.
+Mapping = _alias(collections.abc.Mapping, 2)
+MutableMapping = _alias(collections.abc.MutableMapping, 2)
+Sequence = _alias(collections.abc.Sequence, 1)
+MutableSequence = _alias(collections.abc.MutableSequence, 1)
+ByteString = _alias(collections.abc.ByteString, 0)  # Not generic
+# Tuple accepts variable number of parameters.
+Tuple = _TupleType(tuple, -1, inst=False, name='Tuple')
+Tuple.__doc__ = \
+    """Tuple type; Tuple[X, Y] is the cross-product type of X and Y.
+
+    Example: Tuple[T1, T2] is a tuple of two elements corresponding
+    to type variables T1 and T2.  Tuple[int, float, str] is a tuple
+    of an int, a float and a string.
+
+    To specify a variable-length tuple of homogeneous type, use Tuple[T, ...].
+    """
+List = _alias(list, 1, inst=False, name='List')
+Deque = _alias(collections.deque, 1, name='Deque')
+Set = _alias(set, 1, inst=False, name='Set')
+FrozenSet = _alias(frozenset, 1, inst=False, name='FrozenSet')
+MappingView = _alias(collections.abc.MappingView, 1)
+KeysView = _alias(collections.abc.KeysView, 1)
+ItemsView = _alias(collections.abc.ItemsView, 2)
+ValuesView = _alias(collections.abc.ValuesView, 1)
+ContextManager = _alias(contextlib.AbstractContextManager, 1, name='ContextManager')
+AsyncContextManager = _alias(contextlib.AbstractAsyncContextManager, 1, name='AsyncContextManager')
+Dict = _alias(dict, 2, inst=False, name='Dict')
+DefaultDict = _alias(collections.defaultdict, 2, name='DefaultDict')
+OrderedDict = _alias(collections.OrderedDict, 2)
+Counter = _alias(collections.Counter, 1)
+ChainMap = _alias(collections.ChainMap, 2)
+Generator = _alias(collections.abc.Generator, 3)
+AsyncGenerator = _alias(collections.abc.AsyncGenerator, 2)
+Type = _alias(type, 1, inst=False, name='Type')
+Type.__doc__ = \
+    """A special construct usable to annotate class objects.
+
+    For example, suppose we have the following classes::
+
+      class User: ...  # Abstract base for User classes
+      class BasicUser(User): ...
+      class ProUser(User): ...
+      class TeamUser(User): ...
+
+    And a function that takes a class argument that's a subclass of
+    User and returns an instance of the corresponding class::
+
+      U = TypeVar('U', bound=User)
+      def new_user(user_class: Type[U]) -> U:
+          user = user_class()
+          # (Here we could write the user object to a database)
+          return user
+
+      joe = new_user(BasicUser)
+
+    At this point the type checker knows that joe has type BasicUser.
+    """
+
+
+@runtime_checkable
+class SupportsInt(Protocol):
+    """An ABC with one abstract method __int__."""
+    __slots__ = ()
+
+    @abstractmethod
+    def __int__(self) -> int:
+        pass
+
+
+@runtime_checkable
+class SupportsFloat(Protocol):
+    """An ABC with one abstract method __float__."""
+    __slots__ = ()
+
+    @abstractmethod
+    def __float__(self) -> float:
+        pass
+
+
+@runtime_checkable
+class SupportsComplex(Protocol):
+    """An ABC with one abstract method __complex__."""
+    __slots__ = ()
+
+    @abstractmethod
+    def __complex__(self) -> complex:
+        pass
+
+
+@runtime_checkable
+class SupportsBytes(Protocol):
+    """An ABC with one abstract method __bytes__."""
+    __slots__ = ()
+
+    @abstractmethod
+    def __bytes__(self) -> bytes:
+        pass
+
+
+@runtime_checkable
+class SupportsIndex(Protocol):
+    """An ABC with one abstract method __index__."""
+    __slots__ = ()
+
+    @abstractmethod
+    def __index__(self) -> int:
+        pass
+
+
+@runtime_checkable
+class SupportsAbs(Protocol[T_co]):
+    """An ABC with one abstract method __abs__ that is covariant in its return type."""
+    __slots__ = ()
+
+    @abstractmethod
+    def __abs__(self) -> T_co:
+        pass
+
+
+@runtime_checkable
+class SupportsRound(Protocol[T_co]):
+    """An ABC with one abstract method __round__ that is covariant in its return type."""
+    __slots__ = ()
+
+    @abstractmethod
+    def __round__(self, ndigits: int = 0) -> T_co:
+        pass
+
+
+def _make_nmtuple(name, types, module, defaults = ()):
+    fields = [n for n, t in types]
+    types = {n: _type_check(t, f"field {n} annotation must be a type")
+             for n, t in types}
+    nm_tpl = collections.namedtuple(name, fields,
+                                    defaults=defaults, module=module)
+    nm_tpl.__annotations__ = nm_tpl.__new__.__annotations__ = types
+    return nm_tpl
+
+
+# attributes prohibited to set in NamedTuple class syntax
+_prohibited = frozenset({'__new__', '__init__', '__slots__', '__getnewargs__',
+                         '_fields', '_field_defaults',
+                         '_make', '_replace', '_asdict', '_source'})
+
+_special = frozenset({'__module__', '__name__', '__annotations__'})
+
+
+class NamedTupleMeta(type):
+
+    def __new__(cls, typename, bases, ns):
+        assert bases[0] is _NamedTuple
+        types = ns.get('__annotations__', {})
+        default_names = []
+        for field_name in types:
+            if field_name in ns:
+                default_names.append(field_name)
+            elif default_names:
+                raise TypeError(f"Non-default namedtuple field {field_name} "
+                                f"cannot follow default field"
+                                f"{'s' if len(default_names) > 1 else ''} "
+                                f"{', '.join(default_names)}")
+        nm_tpl = _make_nmtuple(typename, types.items(),
+                               defaults=[ns[n] for n in default_names],
+                               module=ns['__module__'])
+        # update from user namespace without overriding special namedtuple attributes
+        for key in ns:
+            if key in _prohibited:
+                raise AttributeError("Cannot overwrite NamedTuple attribute " + key)
+            elif key not in _special and key not in nm_tpl._fields:
+                setattr(nm_tpl, key, ns[key])
+        return nm_tpl
+
+
+def NamedTuple(typename, fields=None, /, **kwargs):
+    """Typed version of namedtuple.
+
+    Usage in Python versions >= 3.6::
+
+        class Employee(NamedTuple):
+            name: str
+            id: int
+
+    This is equivalent to::
+
+        Employee = collections.namedtuple('Employee', ['name', 'id'])
+
+    The resulting class has an extra __annotations__ attribute, giving a
+    dict that maps field names to types.  (The field names are also in
+    the _fields attribute, which is part of the namedtuple API.)
+    Alternative equivalent keyword syntax is also accepted::
+
+        Employee = NamedTuple('Employee', name=str, id=int)
+
+    In Python versions <= 3.5 use::
+
+        Employee = NamedTuple('Employee', [('name', str), ('id', int)])
+    """
+    if fields is None:
+        fields = kwargs.items()
+    elif kwargs:
+        raise TypeError("Either list of fields or keywords"
+                        " can be provided to NamedTuple, not both")
+    try:
+        module = sys._getframe(1).f_globals.get('__name__', '__main__')
+    except (AttributeError, ValueError):
+        module = None
+    return _make_nmtuple(typename, fields, module=module)
+
+_NamedTuple = type.__new__(NamedTupleMeta, 'NamedTuple', (), {})
+
+def _namedtuple_mro_entries(bases):
+    if len(bases) > 1:
+        raise TypeError("Multiple inheritance with NamedTuple is not supported")
+    assert bases[0] is NamedTuple
+    return (_NamedTuple,)
+
+NamedTuple.__mro_entries__ = _namedtuple_mro_entries
+
+
+class _TypedDictMeta(type):
+    def __new__(cls, name, bases, ns, total=True):
+        """Create new typed dict class object.
+
+        This method is called when TypedDict is subclassed,
+        or when TypedDict is instantiated. This way
+        TypedDict supports all three syntax forms described in its docstring.
+        Subclasses and instances of TypedDict return actual dictionaries.
+        """
+        for base in bases:
+            if type(base) is not _TypedDictMeta:
+                raise TypeError('cannot inherit from both a TypedDict type '
+                                'and a non-TypedDict base class')
+        tp_dict = type.__new__(_TypedDictMeta, name, (dict,), ns)
+
+        annotations = {}
+        own_annotations = ns.get('__annotations__', {})
+        own_annotation_keys = set(own_annotations.keys())
+        msg = "TypedDict('Name', {f0: t0, f1: t1, ...}); each t must be a type"
+        own_annotations = {
+            n: _type_check(tp, msg) for n, tp in own_annotations.items()
+        }
+        required_keys = set()
+        optional_keys = set()
+
+        for base in bases:
+            annotations.update(base.__dict__.get('__annotations__', {}))
+            required_keys.update(base.__dict__.get('__required_keys__', ()))
+            optional_keys.update(base.__dict__.get('__optional_keys__', ()))
+
+        annotations.update(own_annotations)
+        if total:
+            required_keys.update(own_annotation_keys)
+        else:
+            optional_keys.update(own_annotation_keys)
+
+        tp_dict.__annotations__ = annotations
+        tp_dict.__required_keys__ = frozenset(required_keys)
+        tp_dict.__optional_keys__ = frozenset(optional_keys)
+        if not hasattr(tp_dict, '__total__'):
+            tp_dict.__total__ = total
+        return tp_dict
+
+    __call__ = dict  # static method
+
+    def __subclasscheck__(cls, other):
+        # Typed dicts are only for static structural subtyping.
+        raise TypeError('TypedDict does not support instance and class checks')
+
+    __instancecheck__ = __subclasscheck__
+
+
+def TypedDict(typename, fields=None, /, *, total=True, **kwargs):
+    """A simple typed namespace. At runtime it is equivalent to a plain dict.
+
+    TypedDict creates a dictionary type that expects all of its
+    instances to have a certain set of keys, where each key is
+    associated with a value of a consistent type. This expectation
+    is not checked at runtime but is only enforced by type checkers.
+    Usage::
+
+        class Point2D(TypedDict):
+            x: int
+            y: int
+            label: str
+
+        a: Point2D = {'x': 1, 'y': 2, 'label': 'good'}  # OK
+        b: Point2D = {'z': 3, 'label': 'bad'}           # Fails type check
+
+        assert Point2D(x=1, y=2, label='first') == dict(x=1, y=2, label='first')
+
+    The type info can be accessed via the Point2D.__annotations__ dict, and
+    the Point2D.__required_keys__ and Point2D.__optional_keys__ frozensets.
+    TypedDict supports two additional equivalent forms::
+
+        Point2D = TypedDict('Point2D', x=int, y=int, label=str)
+        Point2D = TypedDict('Point2D', {'x': int, 'y': int, 'label': str})
+
+    By default, all keys must be present in a TypedDict. It is possible
+    to override this by specifying totality.
+    Usage::
+
+        class point2D(TypedDict, total=False):
+            x: int
+            y: int
+
+    This means that a point2D TypedDict can have any of the keys omitted.A type
+    checker is only expected to support a literal False or True as the value of
+    the total argument. True is the default, and makes all items defined in the
+    class body be required.
+
+    The class syntax is only supported in Python 3.6+, while two other
+    syntax forms work for Python 2.7 and 3.2+
+    """
+    if fields is None:
+        fields = kwargs
+    elif kwargs:
+        raise TypeError("TypedDict takes either a dict or keyword arguments,"
+                        " but not both")
+
+    ns = {'__annotations__': dict(fields)}
+    try:
+        # Setting correct module is necessary to make typed dict classes pickleable.
+        ns['__module__'] = sys._getframe(1).f_globals.get('__name__', '__main__')
+    except (AttributeError, ValueError):
+        pass
+
+    return _TypedDictMeta(typename, (), ns, total=total)
+
+_TypedDict = type.__new__(_TypedDictMeta, 'TypedDict', (), {})
+TypedDict.__mro_entries__ = lambda bases: (_TypedDict,)
+
+
+def NewType(name, tp):
+    """NewType creates simple unique types with almost zero
+    runtime overhead. NewType(name, tp) is considered a subtype of tp
+    by static type checkers. At runtime, NewType(name, tp) returns
+    a dummy function that simply returns its argument. Usage::
+
+        UserId = NewType('UserId', int)
+
+        def name_by_id(user_id: UserId) -> str:
+            ...
+
+        UserId('user')          # Fails type check
+
+        name_by_id(42)          # Fails type check
+        name_by_id(UserId(42))  # OK
+
+        num = UserId(5) + 1     # type: int
+    """
+
+    def new_type(x):
+        return x
+
+    new_type.__name__ = name
+    new_type.__supertype__ = tp
+    return new_type
+
+
+# Python-version-specific alias (Python 2: unicode; Python 3: str)
+Text = str
+
+
+# Constant that's True when type checking, but False here.
+TYPE_CHECKING = False
+
+
+class IO(Generic[AnyStr]):
+    """Generic base class for TextIO and BinaryIO.
+
+    This is an abstract, generic version of the return of open().
+
+    NOTE: This does not distinguish between the different possible
+    classes (text vs. binary, read vs. write vs. read/write,
+    append-only, unbuffered).  The TextIO and BinaryIO subclasses
+    below capture the distinctions between text vs. binary, which is
+    pervasive in the interface; however we currently do not offer a
+    way to track the other distinctions in the type system.
+    """
+
+    __slots__ = ()
+
+    @property
+    @abstractmethod
+    def mode(self) -> str:
+        pass
+
+    @property
+    @abstractmethod
+    def name(self) -> str:
+        pass
+
+    @abstractmethod
+    def close(self) -> None:
+        pass
+
+    @property
+    @abstractmethod
+    def closed(self) -> bool:
+        pass
+
+    @abstractmethod
+    def fileno(self) -> int:
+        pass
+
+    @abstractmethod
+    def flush(self) -> None:
+        pass
+
+    @abstractmethod
+    def isatty(self) -> bool:
+        pass
+
+    @abstractmethod
+    def read(self, n: int = -1) -> AnyStr:
+        pass
+
+    @abstractmethod
+    def readable(self) -> bool:
+        pass
+
+    @abstractmethod
+    def readline(self, limit: int = -1) -> AnyStr:
+        pass
+
+    @abstractmethod
+    def readlines(self, hint: int = -1) -> List[AnyStr]:
+        pass
+
+    @abstractmethod
+    def seek(self, offset: int, whence: int = 0) -> int:
+        pass
+
+    @abstractmethod
+    def seekable(self) -> bool:
+        pass
+
+    @abstractmethod
+    def tell(self) -> int:
+        pass
+
+    @abstractmethod
+    def truncate(self, size: int = None) -> int:
+        pass
+
+    @abstractmethod
+    def writable(self) -> bool:
+        pass
+
+    @abstractmethod
+    def write(self, s: AnyStr) -> int:
+        pass
+
+    @abstractmethod
+    def writelines(self, lines: List[AnyStr]) -> None:
+        pass
+
+    @abstractmethod
+    def __enter__(self) -> 'IO[AnyStr]':
+        pass
+
+    @abstractmethod
+    def __exit__(self, type, value, traceback) -> None:
+        pass
+
+
+class BinaryIO(IO[bytes]):
+    """Typed version of the return of open() in binary mode."""
+
+    __slots__ = ()
+
+    @abstractmethod
+    def write(self, s: Union[bytes, bytearray]) -> int:
+        pass
+
+    @abstractmethod
+    def __enter__(self) -> 'BinaryIO':
+        pass
+
+
+class TextIO(IO[str]):
+    """Typed version of the return of open() in text mode."""
+
+    __slots__ = ()
+
+    @property
+    @abstractmethod
+    def buffer(self) -> BinaryIO:
+        pass
+
+    @property
+    @abstractmethod
+    def encoding(self) -> str:
+        pass
+
+    @property
+    @abstractmethod
+    def errors(self) -> Optional[str]:
+        pass
+
+    @property
+    @abstractmethod
+    def line_buffering(self) -> bool:
+        pass
+
+    @property
+    @abstractmethod
+    def newlines(self) -> Any:
+        pass
+
+    @abstractmethod
+    def __enter__(self) -> 'TextIO':
+        pass
+
+
+class io:
+    """Wrapper namespace for IO generic classes."""
+
+    __all__ = ['IO', 'TextIO', 'BinaryIO']
+    IO = IO
+    TextIO = TextIO
+    BinaryIO = BinaryIO
+
+
+io.__name__ = __name__ + '.io'
+sys.modules[io.__name__] = io
+
+Pattern = _alias(stdlib_re.Pattern, 1)
+Match = _alias(stdlib_re.Match, 1)
+
+class re:
+    """Wrapper namespace for re type aliases."""
+
+    __all__ = ['Pattern', 'Match']
+    Pattern = Pattern
+    Match = Match
+
+
+re.__name__ = __name__ + '.re'
+sys.modules[re.__name__] = re
+

+
+           

+          

+          

+
+  

+
+  

+    
© Copyright 2022 UiB Center for Modeling of Coupled Subsurface Dynamics, GNU LESSER GENERAL PUBLIC LICENSE Version 3, 29 June 2007..

+  

+
+   
+
+

+        

+      

+    

+  

+   
+
+
+
\ No newline at end of file
diff --git a/docs/html/_static/basic.css b/docs/html/_static/basic.css
index 4e9a9f1fac..eeb0519a69 100644
--- a/docs/html/_static/basic.css
+++ b/docs/html/_static/basic.css
@@ -236,6 +236,16 @@ div.body p, div.body dd, div.body li, div.body blockquote {
 a.headerlink {
     visibility: hidden;
 }
+a.brackets:before,
+span.brackets > a:before{
+    content: "[";
+}
+
+a.brackets:after,
+span.brackets > a:after {
+    content: "]";
+}
+
 
 h1:hover > a.headerlink,
 h2:hover > a.headerlink,
@@ -324,15 +334,11 @@ aside.sidebar {
 p.sidebar-title {
     font-weight: bold;
 }
-nav.contents,
-aside.topic,
 div.admonition, div.topic, blockquote {
     clear: left;
 }
 
 /* -- topics ---------------------------------------------------------------- */
-nav.contents,
-aside.topic,
 div.topic {
     border: 1px solid #ccc;
     padding: 7px;
@@ -371,8 +377,6 @@ div.body p.centered {
 
 div.sidebar > :last-child,
 aside.sidebar > :last-child,
-nav.contents > :last-child,
-aside.topic > :last-child,
 div.topic > :last-child,
 div.admonition > :last-child {
     margin-bottom: 0;
@@ -380,8 +384,6 @@ div.admonition > :last-child {
 
 div.sidebar::after,
 aside.sidebar::after,
-nav.contents::after,
-aside.topic::after,
 div.topic::after,
 div.admonition::after,
 blockquote::after {
@@ -606,26 +608,19 @@ ol.simple p,
 ul.simple p {
     margin-bottom: 0;
 }
-aside.footnote > span,
-div.citation > span {
+dl.footnote > dt,
+dl.citation > dt {
     float: left;
+    margin-right: 0.5em;
 }
-aside.footnote > span:last-of-type,
-div.citation > span:last-of-type {
-  padding-right: 0.5em;
-}
-aside.footnote > p {
-  margin-left: 2em;
-}
-div.citation > p {
-  margin-left: 4em;
-}
-aside.footnote > p:last-of-type,
-div.citation > p:last-of-type {
+
+dl.footnote > dd,
+dl.citation > dd {
     margin-bottom: 0em;
 }
-aside.footnote > p:last-of-type:after,
-div.citation > p:last-of-type:after {
+
+dl.footnote > dd:after,
+dl.citation > dd:after {
     content: "";
     clear: both;
 }
@@ -641,6 +636,10 @@ dl.field-list > dt {
     padding-left: 0.5em;
     padding-right: 5px;
 }
+dl.field-list > dt:after {
+    content: ":";
+}
+
 
 dl.field-list > dd {
     padding-left: 0.5em;
diff --git a/docs/html/_static/css/badge_only.css b/docs/html/_static/css/badge_only.css
new file mode 100644
index 0000000000..c718cee441
--- /dev/null
+++ b/docs/html/_static/css/badge_only.css
@@ -0,0 +1 @@
+.clearfix{*zoom:1}.clearfix:after,.clearfix:before{display:table;content:""}.clearfix:after{clear:both}@font-face{font-family:FontAwesome;font-style:normal;font-weight:400;src:url(fonts/fontawesome-webfont.eot?674f50d287a8c48dc19ba404d20fe713?#iefix) format("embedded-opentype"),url(fonts/fontawesome-webfont.woff2?af7ae505a9eed503f8b8e6982036873e) format("woff2"),url(fonts/fontawesome-webfont.woff?fee66e712a8a08eef5805a46892932ad) format("woff"),url(fonts/fontawesome-webfont.ttf?b06871f281fee6b241d60582ae9369b9) format("truetype"),url(fonts/fontawesome-webfont.svg?912ec66d7572ff821749319396470bde#FontAwesome) format("svg")}.fa:before{font-family:FontAwesome;font-style:normal;font-weight:400;line-height:1}.fa:before,a .fa{text-decoration:inherit}.fa:before,a .fa,li .fa{display:inline-block}li .fa-large:before{width:1.875em}ul.fas{list-style-type:none;margin-left:2em;text-indent:-.8em}ul.fas li .fa{width:.8em}ul.fas li .fa-large:before{vertical-align:baseline}.fa-book:before,.icon-book:before{content:"\f02d"}.fa-caret-down:before,.icon-caret-down:before{content:"\f0d7"}.fa-caret-up:before,.icon-caret-up:before{content:"\f0d8"}.fa-caret-left:before,.icon-caret-left:before{content:"\f0d9"}.fa-caret-right:before,.icon-caret-right:before{content:"\f0da"}.rst-versions{position:fixed;bottom:0;left:0;width:300px;color:#fcfcfc;background:#1f1d1d;font-family:Lato,proxima-nova,Helvetica Neue,Arial,sans-serif;z-index:400}.rst-versions a{color:#2980b9;text-decoration:none}.rst-versions .rst-badge-small{display:none}.rst-versions .rst-current-version{padding:12px;background-color:#272525;display:block;text-align:right;font-size:90%;cursor:pointer;color:#27ae60}.rst-versions .rst-current-version:after{clear:both;content:"";display:block}.rst-versions .rst-current-version .fa{color:#fcfcfc}.rst-versions .rst-current-version .fa-book,.rst-versions .rst-current-version .icon-book{float:left}.rst-versions .rst-current-version.rst-out-of-date{background-color:#e74c3c;color:#fff}.rst-versions .rst-current-version.rst-active-old-version{background-color:#f1c40f;color:#000}.rst-versions.shift-up{height:auto;max-height:100%;overflow-y:scroll}.rst-versions.shift-up .rst-other-versions{display:block}.rst-versions .rst-other-versions{font-size:90%;padding:12px;color:grey;display:none}.rst-versions .rst-other-versions hr{display:block;height:1px;border:0;margin:20px 0;padding:0;border-top:1px solid #413d3d}.rst-versions .rst-other-versions dd{display:inline-block;margin:0}.rst-versions .rst-other-versions dd a{display:inline-block;padding:6px;color:#fcfcfc}.rst-versions.rst-badge{width:auto;bottom:20px;right:20px;left:auto;border:none;max-width:300px;max-height:90%}.rst-versions.rst-badge .fa-book,.rst-versions.rst-badge .icon-book{float:none;line-height:30px}.rst-versions.rst-badge.shift-up .rst-current-version{text-align:right}.rst-versions.rst-badge.shift-up .rst-current-version .fa-book,.rst-versions.rst-badge.shift-up .rst-current-version .icon-book{float:left}.rst-versions.rst-badge>.rst-current-version{width:auto;height:30px;line-height:30px;padding:0 6px;display:block;text-align:center}@media screen and (max-width:768px){.rst-versions{width:85%;display:none}.rst-versions.shift{display:block}}
\ No newline at end of file
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format("woff2"),url(fonts/Roboto-Slab-Bold.woff?bed5564a116b05148e3b3bea6fb1162a) format("woff");font-display:block}
\ No newline at end of file
diff --git a/docs/html/_static/doctools.js b/docs/html/_static/doctools.js
index c3db08d1c3..527b876ca6 100644
--- a/docs/html/_static/doctools.js
+++ b/docs/html/_static/doctools.js
@@ -10,6 +10,13 @@
  */
 "use strict";
 
+const BLACKLISTED_KEY_CONTROL_ELEMENTS = new Set([
+  "TEXTAREA",
+  "INPUT",
+  "SELECT",
+  "BUTTON",
+]);
+
 const _ready = (callback) => {
   if (document.readyState !== "loading") {
     callback();
@@ -18,73 +25,11 @@ const _ready = (callback) => {
   }
 };
 
-/**
- * highlight a given string on a node by wrapping it in
- * span elements with the given class name.
- */
-const _highlight = (node, addItems, text, className) => {
-  if (node.nodeType === Node.TEXT_NODE) {
-    const val = node.nodeValue;
-    const parent = node.parentNode;
-    const pos = val.toLowerCase().indexOf(text);
-    if (
-      pos >= 0 &&
-      !parent.classList.contains(className) &&
-      !parent.classList.contains("nohighlight")
-    ) {
-      let span;
-
-      const closestNode = parent.closest("body, svg, foreignObject");
-      const isInSVG = closestNode && closestNode.matches("svg");
-      if (isInSVG) {
-        span = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
-      } else {
-        span = document.createElement("span");
-        span.classList.add(className);
-      }
-
-      span.appendChild(document.createTextNode(val.substr(pos, text.length)));
-      parent.insertBefore(
-        span,
-        parent.insertBefore(
-          document.createTextNode(val.substr(pos + text.length)),
-          node.nextSibling
-        )
-      );
-      node.nodeValue = val.substr(0, pos);
-
-      if (isInSVG) {
-        const rect = document.createElementNS(
-          "http://www.w3.org/2000/svg",
-          "rect"
-        );
-        const bbox = parent.getBBox();
-        rect.x.baseVal.value = bbox.x;
-        rect.y.baseVal.value = bbox.y;
-        rect.width.baseVal.value = bbox.width;
-        rect.height.baseVal.value = bbox.height;
-        rect.setAttribute("class", className);
-        addItems.push({ parent: parent, target: rect });
-      }
-    }
-  } else if (node.matches && !node.matches("button, select, textarea")) {
-    node.childNodes.forEach((el) => _highlight(el, addItems, text, className));
-  }
-};
-const _highlightText = (thisNode, text, className) => {
-  let addItems = [];
-  _highlight(thisNode, addItems, text, className);
-  addItems.forEach((obj) =>
-    obj.parent.insertAdjacentElement("beforebegin", obj.target)
-  );
-};
-
 /**
  * Small JavaScript module for the documentation.
  */
 const Documentation = {
   init: () => {
-    Documentation.highlightSearchWords();
     Documentation.initDomainIndexTable();
     Documentation.initOnKeyListeners();
   },
@@ -126,51 +71,6 @@ const Documentation = {
     Documentation.LOCALE = catalog.locale;
   },
 
-  /**
-   * highlight the search words provided in the url in the text
-   */
-  highlightSearchWords: () => {
-    const highlight =
-      new URLSearchParams(window.location.search).get("highlight") || "";
-    const terms = highlight.toLowerCase().split(/\s+/).filter(x => x);
-    if (terms.length === 0) return; // nothing to do
-
-    // There should never be more than one element matching "div.body"
-    const divBody = document.querySelectorAll("div.body");
-    const body = divBody.length ? divBody[0] : document.querySelector("body");
-    window.setTimeout(() => {
-      terms.forEach((term) => _highlightText(body, term, "highlighted"));
-    }, 10);
-
-    const searchBox = document.getElementById("searchbox");
-    if (searchBox === null) return;
-    searchBox.appendChild(
-      document
-        .createRange()
-        .createContextualFragment(
-          '
' +
-            '' +
-            Documentation.gettext("Hide Search Matches") +
-            "
"
-        )
-    );
-  },
-
-  /**
-   * helper function to hide the search marks again
-   */
-  hideSearchWords: () => {
-    document
-      .querySelectorAll("#searchbox .highlight-link")
-      .forEach((el) => el.remove());
-    document
-      .querySelectorAll("span.highlighted")
-      .forEach((el) => el.classList.remove("highlighted"));
-    const url = new URL(window.location);
-    url.searchParams.delete("highlight");
-    window.history.replaceState({}, "", url);
-  },
-
   /**
    * helper function to focus on search bar
    */
@@ -210,15 +110,11 @@ const Documentation = {
     )
       return;
 
-    const blacklistedElements = new Set([
-      "TEXTAREA",
-      "INPUT",
-      "SELECT",
-      "BUTTON",
-    ]);
     document.addEventListener("keydown", (event) => {
-      if (blacklistedElements.has(document.activeElement.tagName)) return; // bail for input elements
-      if (event.altKey || event.ctrlKey || event.metaKey) return; // bail with special keys
+      // bail for input elements
+      if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return;
+      // bail with special keys
+      if (event.altKey || event.ctrlKey || event.metaKey) return;
 
       if (!event.shiftKey) {
         switch (event.key) {
@@ -240,10 +136,6 @@ const Documentation = {
               event.preventDefault();
             }
             break;
-          case "Escape":
-            if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) break;
-            Documentation.hideSearchWords();
-            event.preventDefault();
         }
       }
 
diff --git a/docs/html/_static/js/badge_only.js b/docs/html/_static/js/badge_only.js
new file mode 100644
index 0000000000..526d7234b6
--- /dev/null
+++ b/docs/html/_static/js/badge_only.js
@@ -0,0 +1 @@
+!function(e){var t={};function r(n){if(t[n])return t[n].exports;var o=t[n]={i:n,l:!1,exports:{}};return e[n].call(o.exports,o,o.exports,r),o.l=!0,o.exports}r.m=e,r.c=t,r.d=function(e,t,n){r.o(e,t)||Object.defineProperty(e,t,{enumerable:!0,get:n})},r.r=function(e){"undefined"!=typeof Symbol&&Symbol.toStringTag&&Object.defineProperty(e,Symbol.toStringTag,{value:"Module"}),Object.defineProperty(e,"__esModule",{value:!0})},r.t=function(e,t){if(1&t&&(e=r(e)),8&t)return e;if(4&t&&"object"==typeof e&&e&&e.__esModule)return e;var n=Object.create(null);if(r.r(n),Object.defineProperty(n,"default",{enumerable:!0,value:e}),2&t&&"string"!=typeof e)for(var o in e)r.d(n,o,function(t){return e[t]}.bind(null,o));return n},r.n=function(e){var t=e&&e.__esModule?function(){return e.default}:function(){return e};return r.d(t,"a",t),t},r.o=function(e,t){return Object.prototype.hasOwnProperty.call(e,t)},r.p="",r(r.s=4)}({4:function(e,t,r){}});
\ No newline at end of file
diff --git a/docs/html/_static/js/html5shiv-printshiv.min.js b/docs/html/_static/js/html5shiv-printshiv.min.js
new file mode 100644
index 0000000000..2b43bd062e
--- /dev/null
+++ b/docs/html/_static/js/html5shiv-printshiv.min.js
@@ -0,0 +1,4 @@
+/**
+* @preserve HTML5 Shiv 3.7.3-pre | @afarkas @jdalton @jon_neal @rem | MIT/GPL2 Licensed
+*/
+!function(a,b){function c(a,b){var c=a.createElement("p"),d=a.getElementsByTagName("head")[0]||a.documentElement;return c.innerHTML="x",d.insertBefore(c.lastChild,d.firstChild)}function d(){var a=y.elements;return"string"==typeof a?a.split(" "):a}function e(a,b){var c=y.elements;"string"!=typeof c&&(c=c.join(" ")),"string"!=typeof a&&(a=a.join(" ")),y.elements=c+" "+a,j(b)}function f(a){var b=x[a[v]];return b||(b={},w++,a[v]=w,x[w]=b),b}function g(a,c,d){if(c||(c=b),q)return c.createElement(a);d||(d=f(c));var e;return e=d.cache[a]?d.cache[a].cloneNode():u.test(a)?(d.cache[a]=d.createElem(a)).cloneNode():d.createElem(a),!e.canHaveChildren||t.test(a)||e.tagUrn?e:d.frag.appendChild(e)}function h(a,c){if(a||(a=b),q)return a.createDocumentFragment();c=c||f(a);for(var e=c.frag.cloneNode(),g=0,h=d(),i=h.length;i>g;g++)e.createElement(h[g]);return e}function i(a,b){b.cache||(b.cache={},b.createElem=a.createElement,b.createFrag=a.createDocumentFragment,b.frag=b.createFrag()),a.createElement=function(c){return y.shivMethods?g(c,a,b):b.createElem(c)},a.createDocumentFragment=Function("h,f","return function(){var n=f.cloneNode(),c=n.createElement;h.shivMethods&&("+d().join().replace(/[\w\-:]+/g,function(a){return b.createElem(a),b.frag.createElement(a),'c("'+a+'")'})+");return n}")(y,b.frag)}function j(a){a||(a=b);var d=f(a);return!y.shivCSS||p||d.hasCSS||(d.hasCSS=!!c(a,"article,aside,dialog,figcaption,figure,footer,header,hgroup,main,nav,section{display:block}mark{background:#FF0;color:#000}template{display:none}")),q||i(a,d),a}function k(a){for(var b,c=a.getElementsByTagName("*"),e=c.length,f=RegExp("^(?:"+d().join("|")+")$","i"),g=[];e--;)b=c[e],f.test(b.nodeName)&&g.push(b.applyElement(l(b)));return g}function l(a){for(var b,c=a.attributes,d=c.length,e=a.ownerDocument.createElement(A+":"+a.nodeName);d--;)b=c[d],b.specified&&e.setAttribute(b.nodeName,b.nodeValue);return e.style.cssText=a.style.cssText,e}function m(a){for(var b,c=a.split("{"),e=c.length,f=RegExp("(^|[\\s,>+~])("+d().join("|")+")(?=[[\\s,>+~#.:]|$)","gi"),g="$1"+A+"\\:$2";e--;)b=c[e]=c[e].split("}"),b[b.length-1]=b[b.length-1].replace(f,g),c[e]=b.join("}");return c.join("{")}function n(a){for(var b=a.length;b--;)a[b].removeNode()}function o(a){function b(){clearTimeout(g._removeSheetTimer),d&&d.removeNode(!0),d=null}var d,e,g=f(a),h=a.namespaces,i=a.parentWindow;return!B||a.printShived?a:("undefined"==typeof h[A]&&h.add(A),i.attachEvent("onbeforeprint",function(){b();for(var f,g,h,i=a.styleSheets,j=[],l=i.length,n=Array(l);l--;)n[l]=i[l];for(;h=n.pop();)if(!h.disabled&&z.test(h.media)){try{f=h.imports,g=f.length}catch(o){g=0}for(l=0;g>l;l++)n.push(f[l]);try{j.push(h.cssText)}catch(o){}}j=m(j.reverse().join("")),e=k(a),d=c(a,j)}),i.attachEvent("onafterprint",function(){n(e),clearTimeout(g._removeSheetTimer),g._removeSheetTimer=setTimeout(b,500)}),a.printShived=!0,a)}var p,q,r="3.7.3",s=a.html5||{},t=/^<|^(?:button|map|select|textarea|object|iframe|option|optgroup)$/i,u=/^(?:a|b|code|div|fieldset|h1|h2|h3|h4|h5|h6|i|label|li|ol|p|q|span|strong|style|table|tbody|td|th|tr|ul)$/i,v="_html5shiv",w=0,x={};!function(){try{var a=b.createElement("a");a.innerHTML="",p="hidden"in a,q=1==a.childNodes.length||function(){b.createElement("a");var a=b.createDocumentFragment();return"undefined"==typeof a.cloneNode||"undefined"==typeof a.createDocumentFragment||"undefined"==typeof a.createElement}()}catch(c){p=!0,q=!0}}();var y={elements:s.elements||"abbr article aside audio bdi canvas data datalist details dialog figcaption figure footer header hgroup main mark meter nav output picture progress section summary template time video",version:r,shivCSS:s.shivCSS!==!1,supportsUnknownElements:q,shivMethods:s.shivMethods!==!1,type:"default",shivDocument:j,createElement:g,createDocumentFragment:h,addElements:e};a.html5=y,j(b);var z=/^$|\b(?:all|print)\b/,A="html5shiv",B=!q&&function(){var c=b.documentElement;return!("undefined"==typeof b.namespaces||"undefined"==typeof b.parentWindow||"undefined"==typeof c.applyElement||"undefined"==typeof c.removeNode||"undefined"==typeof a.attachEvent)}();y.type+=" print",y.shivPrint=o,o(b),"object"==typeof module&&module.exports&&(module.exports=y)}("undefined"!=typeof window?window:this,document);
\ No newline at end of file
diff --git a/docs/html/_static/js/html5shiv.min.js b/docs/html/_static/js/html5shiv.min.js
new file mode 100644
index 0000000000..cd1c674f5e
--- /dev/null
+++ b/docs/html/_static/js/html5shiv.min.js
@@ -0,0 +1,4 @@
+/**
+* @preserve HTML5 Shiv 3.7.3 | @afarkas @jdalton @jon_neal @rem | MIT/GPL2 Licensed
+*/
+!function(a,b){function c(a,b){var c=a.createElement("p"),d=a.getElementsByTagName("head")[0]||a.documentElement;return c.innerHTML="x",d.insertBefore(c.lastChild,d.firstChild)}function d(){var a=t.elements;return"string"==typeof a?a.split(" "):a}function e(a,b){var c=t.elements;"string"!=typeof c&&(c=c.join(" ")),"string"!=typeof a&&(a=a.join(" ")),t.elements=c+" "+a,j(b)}function f(a){var b=s[a[q]];return b||(b={},r++,a[q]=r,s[r]=b),b}function g(a,c,d){if(c||(c=b),l)return c.createElement(a);d||(d=f(c));var e;return e=d.cache[a]?d.cache[a].cloneNode():p.test(a)?(d.cache[a]=d.createElem(a)).cloneNode():d.createElem(a),!e.canHaveChildren||o.test(a)||e.tagUrn?e:d.frag.appendChild(e)}function h(a,c){if(a||(a=b),l)return a.createDocumentFragment();c=c||f(a);for(var e=c.frag.cloneNode(),g=0,h=d(),i=h.length;i>g;g++)e.createElement(h[g]);return e}function i(a,b){b.cache||(b.cache={},b.createElem=a.createElement,b.createFrag=a.createDocumentFragment,b.frag=b.createFrag()),a.createElement=function(c){return t.shivMethods?g(c,a,b):b.createElem(c)},a.createDocumentFragment=Function("h,f","return function(){var n=f.cloneNode(),c=n.createElement;h.shivMethods&&("+d().join().replace(/[\w\-:]+/g,function(a){return b.createElem(a),b.frag.createElement(a),'c("'+a+'")'})+");return n}")(t,b.frag)}function j(a){a||(a=b);var d=f(a);return!t.shivCSS||k||d.hasCSS||(d.hasCSS=!!c(a,"article,aside,dialog,figcaption,figure,footer,header,hgroup,main,nav,section{display:block}mark{background:#FF0;color:#000}template{display:none}")),l||i(a,d),a}var k,l,m="3.7.3-pre",n=a.html5||{},o=/^<|^(?:button|map|select|textarea|object|iframe|option|optgroup)$/i,p=/^(?:a|b|code|div|fieldset|h1|h2|h3|h4|h5|h6|i|label|li|ol|p|q|span|strong|style|table|tbody|td|th|tr|ul)$/i,q="_html5shiv",r=0,s={};!function(){try{var a=b.createElement("a");a.innerHTML="",k="hidden"in a,l=1==a.childNodes.length||function(){b.createElement("a");var a=b.createDocumentFragment();return"undefined"==typeof a.cloneNode||"undefined"==typeof a.createDocumentFragment||"undefined"==typeof a.createElement}()}catch(c){k=!0,l=!0}}();var t={elements:n.elements||"abbr article aside audio bdi canvas data datalist details dialog figcaption figure footer header hgroup main mark meter nav output picture progress section summary template time video",version:m,shivCSS:n.shivCSS!==!1,supportsUnknownElements:l,shivMethods:n.shivMethods!==!1,type:"default",shivDocument:j,createElement:g,createDocumentFragment:h,addElements:e};a.html5=t,j(b),"object"==typeof module&&module.exports&&(module.exports=t)}("undefined"!=typeof window?window:this,document);
\ No newline at end of file
diff --git a/docs/html/_static/js/theme.js b/docs/html/_static/js/theme.js
new file mode 100644
index 0000000000..1fddb6ee4a
--- /dev/null
+++ b/docs/html/_static/js/theme.js
@@ -0,0 +1 @@
+!function(n){var e={};function t(i){if(e[i])return e[i].exports;var o=e[i]={i:i,l:!1,exports:{}};return n[i].call(o.exports,o,o.exports,t),o.l=!0,o.exports}t.m=n,t.c=e,t.d=function(n,e,i){t.o(n,e)||Object.defineProperty(n,e,{enumerable:!0,get:i})},t.r=function(n){"undefined"!=typeof Symbol&&Symbol.toStringTag&&Object.defineProperty(n,Symbol.toStringTag,{value:"Module"}),Object.defineProperty(n,"__esModule",{value:!0})},t.t=function(n,e){if(1&e&&(n=t(n)),8&e)return n;if(4&e&&"object"==typeof n&&n&&n.__esModule)return n;var i=Object.create(null);if(t.r(i),Object.defineProperty(i,"default",{enumerable:!0,value:n}),2&e&&"string"!=typeof n)for(var o in n)t.d(i,o,function(e){return n[e]}.bind(null,o));return i},t.n=function(n){var e=n&&n.__esModule?function(){return n.default}:function(){return n};return t.d(e,"a",e),e},t.o=function(n,e){return Object.prototype.hasOwnProperty.call(n,e)},t.p="",t(t.s=0)}([function(n,e,t){t(1),n.exports=t(3)},function(n,e,t){(function(){var e="undefined"!=typeof window?window.jQuery:t(2);n.exports.ThemeNav={navBar:null,win:null,winScroll:!1,winResize:!1,linkScroll:!1,winPosition:0,winHeight:null,docHeight:null,isRunning:!1,enable:function(n){var t=this;void 0===n&&(n=!0),t.isRunning||(t.isRunning=!0,e((function(e){t.init(e),t.reset(),t.win.on("hashchange",t.reset),n&&t.win.on("scroll",(function(){t.linkScroll||t.winScroll||(t.winScroll=!0,requestAnimationFrame((function(){t.onScroll()})))})),t.win.on("resize",(function(){t.winResize||(t.winResize=!0,requestAnimationFrame((function(){t.onResize()})))})),t.onResize()})))},enableSticky:function(){this.enable(!0)},init:function(n){n(document);var e=this;this.navBar=n("div.wy-side-scroll:first"),this.win=n(window),n(document).on("click","[data-toggle='wy-nav-top']",(function(){n("[data-toggle='wy-nav-shift']").toggleClass("shift"),n("[data-toggle='rst-versions']").toggleClass("shift")})).on("click",".wy-menu-vertical .current ul li a",(function(){var t=n(this);n("[data-toggle='wy-nav-shift']").removeClass("shift"),n("[data-toggle='rst-versions']").toggleClass("shift"),e.toggleCurrent(t),e.hashChange()})).on("click","[data-toggle='rst-current-version']",(function(){n("[data-toggle='rst-versions']").toggleClass("shift-up")})),n("table.docutils:not(.field-list,.footnote,.citation)").wrap("
"),n("table.docutils.footnote").wrap("
"),n("table.docutils.citation").wrap("
"),n(".wy-menu-vertical ul").not(".simple").siblings("a").each((function(){var t=n(this);expand=n(''),expand.on("click",(function(n){return e.toggleCurrent(t),n.stopPropagation(),!1})),t.prepend(expand)}))},reset:function(){var n=encodeURI(window.location.hash)||"#";try{var e=$(".wy-menu-vertical"),t=e.find('[href="'+n+'"]');if(0===t.length){var i=$('.document [id="'+n.substring(1)+'"]').closest("div.section");0===(t=e.find('[href="#'+i.attr("id")+'"]')).length&&(t=e.find('[href="#"]'))}if(t.length>0){$(".wy-menu-vertical .current").removeClass("current").attr("aria-expanded","false"),t.addClass("current").attr("aria-expanded","true"),t.closest("li.toctree-l1").parent().addClass("current").attr("aria-expanded","true");for(let n=1;n<=10;n++)t.closest("li.toctree-l"+n).addClass("current").attr("aria-expanded","true");t[0].scrollIntoView()}}catch(n){console.log("Error expanding nav for anchor",n)}},onScroll:function(){this.winScroll=!1;var n=this.win.scrollTop(),e=n+this.winHeight,t=this.navBar.scrollTop()+(n-this.winPosition);n<0||e>this.docHeight||(this.navBar.scrollTop(t),this.winPosition=n)},onResize:function(){this.winResize=!1,this.winHeight=this.win.height(),this.docHeight=$(document).height()},hashChange:function(){this.linkScroll=!0,this.win.one("hashchange",(function(){this.linkScroll=!1}))},toggleCurrent:function(n){var e=n.closest("li");e.siblings("li.current").removeClass("current").attr("aria-expanded","false"),e.siblings().find("li.current").removeClass("current").attr("aria-expanded","false");var t=e.find("> ul li");t.length&&(t.removeClass("current").attr("aria-expanded","false"),e.toggleClass("current").attr("aria-expanded",(function(n,e){return"true"==e?"false":"true"})))}},"undefined"!=typeof window&&(window.SphinxRtdTheme={Navigation:n.exports.ThemeNav,StickyNav:n.exports.ThemeNav}),function(){for(var n=0,e=["ms","moz","webkit","o"],t=0;t {
 const _escapeRegExp = (string) =>
   string.replace(/[.*+\-?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string
 
-const _displayItem = (item, highlightTerms, searchTerms) => {
+const _displayItem = (item, searchTerms) => {
   const docBuilder = DOCUMENTATION_OPTIONS.BUILDER;
   const docUrlRoot = DOCUMENTATION_OPTIONS.URL_ROOT;
   const docFileSuffix = DOCUMENTATION_OPTIONS.FILE_SUFFIX;
   const docLinkSuffix = DOCUMENTATION_OPTIONS.LINK_SUFFIX;
   const showSearchSummary = DOCUMENTATION_OPTIONS.SHOW_SEARCH_SUMMARY;
 
-  const [docName, title, anchor, descr] = item;
+  const [docName, title, anchor, descr, score, _filename] = item;
 
   let listItem = document.createElement("li");
   let requestUrl;
@@ -82,10 +82,9 @@ const _displayItem = (item, highlightTerms, searchTerms) => {
     requestUrl = docUrlRoot + docName + docFileSuffix;
     linkUrl = docName + docLinkSuffix;
   }
-  const params = new URLSearchParams();
-  params.set("highlight", [...highlightTerms].join(" "));
   let linkEl = listItem.appendChild(document.createElement("a"));
-  linkEl.href = linkUrl + "?" + params.toString() + anchor;
+  linkEl.href = linkUrl + anchor;
+  linkEl.dataset.score = score;
   linkEl.innerHTML = title;
   if (descr)
     listItem.appendChild(document.createElement("span")).innerHTML =
@@ -96,7 +95,7 @@ const _displayItem = (item, highlightTerms, searchTerms) => {
       .then((data) => {
         if (data)
           listItem.appendChild(
-            Search.makeSearchSummary(data, searchTerms, highlightTerms)
+            Search.makeSearchSummary(data, searchTerms)
           );
       });
   Search.output.appendChild(listItem);
@@ -116,15 +115,14 @@ const _finishSearch = (resultCount) => {
 const _displayNextItem = (
   results,
   resultCount,
-  highlightTerms,
   searchTerms
 ) => {
   // results left, load the summary and display it
   // this is intended to be dynamic (don't sub resultsCount)
   if (results.length) {
-    _displayItem(results.pop(), highlightTerms, searchTerms);
+    _displayItem(results.pop(), searchTerms);
     setTimeout(
-      () => _displayNextItem(results, resultCount, highlightTerms, searchTerms),
+      () => _displayNextItem(results, resultCount, searchTerms),
       5
     );
   }
@@ -237,6 +235,12 @@ const Search = {
    * execute search (requires search index to be loaded)
    */
   query: (query) => {
+    const filenames = Search._index.filenames;
+    const docNames = Search._index.docnames;
+    const titles = Search._index.titles;
+    const allTitles = Search._index.alltitles;
+    const indexEntries = Search._index.indexentries;
+
     // stem the search terms and add them to the correct list
     const stemmer = new Stemmer();
     const searchTerms = new Set();
@@ -264,6 +268,10 @@ const Search = {
       }
     });
 
+    if (SPHINX_HIGHLIGHT_ENABLED) {  // set in sphinx_highlight.js
+      localStorage.setItem("sphinx_highlight_terms", [...highlightTerms].join(" "))
+    }
+
     // console.debug("SEARCH: searching for:");
     // console.info("required: ", [...searchTerms]);
     // console.info("excluded: ", [...excludedTerms]);
@@ -272,6 +280,40 @@ const Search = {
     let results = [];
     _removeChildren(document.getElementById("search-progress"));
 
+    const queryLower = query.toLowerCase();
+    for (const [title, foundTitles] of Object.entries(allTitles)) {
+      if (title.toLowerCase().includes(queryLower) && (queryLower.length >= title.length/2)) {
+        for (const [file, id] of foundTitles) {
+          let score = Math.round(100 * queryLower.length / title.length)
+          results.push([
+            docNames[file],
+            titles[file] !== title ? `${titles[file]} > ${title}` : title,
+            id !== null ? "#" + id : "",
+            null,
+            score,
+            filenames[file],
+          ]);
+        }
+      }
+    }
+
+    // search for explicit entries in index directives
+    for (const [entry, foundEntries] of Object.entries(indexEntries)) {
+      if (entry.includes(queryLower) && (queryLower.length >= entry.length/2)) {
+        for (const [file, id] of foundEntries) {
+          let score = Math.round(100 * queryLower.length / entry.length)
+          results.push([
+            docNames[file],
+            titles[file],
+            id ? "#" + id : "",
+            null,
+            score,
+            filenames[file],
+          ]);
+        }
+      }
+    }
+
     // lookup as object
     objectTerms.forEach((term) =>
       results.push(...Search.performObjectSearch(term, objectTerms))
@@ -318,7 +360,7 @@ const Search = {
     // console.info("search results:", Search.lastresults);
 
     // print the results
-    _displayNextItem(results, results.length, highlightTerms, searchTerms);
+    _displayNextItem(results, results.length, searchTerms);
   },
 
   /**
@@ -399,8 +441,8 @@ const Search = {
     // prepare search
     const terms = Search._index.terms;
     const titleTerms = Search._index.titleterms;
-    const docNames = Search._index.docnames;
     const filenames = Search._index.filenames;
+    const docNames = Search._index.docnames;
     const titles = Search._index.titles;
 
     const scoreMap = new Map();
@@ -497,11 +539,9 @@ const Search = {
   /**
    * helper function to return a node containing the
    * search summary for a given text. keywords is a list
-   * of stemmed words, highlightWords is the list of normal, unstemmed
-   * words. the first one is used to find the occurrence, the
-   * latter for highlighting it.
+   * of stemmed words.
    */
-  makeSearchSummary: (htmlText, keywords, highlightWords) => {
+  makeSearchSummary: (htmlText, keywords) => {
     const text = Search.htmlToText(htmlText);
     if (text === "") return null;
 
@@ -519,10 +559,6 @@ const Search = {
     summary.classList.add("context");
     summary.textContent = top + text.substr(startWithContext, 240).trim() + tail;
 
-    highlightWords.forEach((highlightWord) =>
-      _highlightText(summary, highlightWord, "highlighted")
-    );
-
     return summary;
   },
 };
diff --git a/docs/html/_static/sphinx_highlight.js b/docs/html/_static/sphinx_highlight.js
new file mode 100644
index 0000000000..aae669d7ea
--- /dev/null
+++ b/docs/html/_static/sphinx_highlight.js
@@ -0,0 +1,144 @@
+/* Highlighting utilities for Sphinx HTML documentation. */
+"use strict";
+
+const SPHINX_HIGHLIGHT_ENABLED = true
+
+/**
+ * highlight a given string on a node by wrapping it in
+ * span elements with the given class name.
+ */
+const _highlight = (node, addItems, text, className) => {
+  if (node.nodeType === Node.TEXT_NODE) {
+    const val = node.nodeValue;
+    const parent = node.parentNode;
+    const pos = val.toLowerCase().indexOf(text);
+    if (
+      pos >= 0 &&
+      !parent.classList.contains(className) &&
+      !parent.classList.contains("nohighlight")
+    ) {
+      let span;
+
+      const closestNode = parent.closest("body, svg, foreignObject");
+      const isInSVG = closestNode && closestNode.matches("svg");
+      if (isInSVG) {
+        span = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
+      } else {
+        span = document.createElement("span");
+        span.classList.add(className);
+      }
+
+      span.appendChild(document.createTextNode(val.substr(pos, text.length)));
+      parent.insertBefore(
+        span,
+        parent.insertBefore(
+          document.createTextNode(val.substr(pos + text.length)),
+          node.nextSibling
+        )
+      );
+      node.nodeValue = val.substr(0, pos);
+
+      if (isInSVG) {
+        const rect = document.createElementNS(
+          "http://www.w3.org/2000/svg",
+          "rect"
+        );
+        const bbox = parent.getBBox();
+        rect.x.baseVal.value = bbox.x;
+        rect.y.baseVal.value = bbox.y;
+        rect.width.baseVal.value = bbox.width;
+        rect.height.baseVal.value = bbox.height;
+        rect.setAttribute("class", className);
+        addItems.push({ parent: parent, target: rect });
+      }
+    }
+  } else if (node.matches && !node.matches("button, select, textarea")) {
+    node.childNodes.forEach((el) => _highlight(el, addItems, text, className));
+  }
+};
+const _highlightText = (thisNode, text, className) => {
+  let addItems = [];
+  _highlight(thisNode, addItems, text, className);
+  addItems.forEach((obj) =>
+    obj.parent.insertAdjacentElement("beforebegin", obj.target)
+  );
+};
+
+/**
+ * Small JavaScript module for the documentation.
+ */
+const SphinxHighlight = {
+
+  /**
+   * highlight the search words provided in localstorage in the text
+   */
+  highlightSearchWords: () => {
+    if (!SPHINX_HIGHLIGHT_ENABLED) return;  // bail if no highlight
+
+    // get and clear terms from localstorage
+    const url = new URL(window.location);
+    const highlight =
+        localStorage.getItem("sphinx_highlight_terms")
+        || url.searchParams.get("highlight")
+        || "";
+    localStorage.removeItem("sphinx_highlight_terms")
+    url.searchParams.delete("highlight");
+    window.history.replaceState({}, "", url);
+
+    // get individual terms from highlight string
+    const terms = highlight.toLowerCase().split(/\s+/).filter(x => x);
+    if (terms.length === 0) return; // nothing to do
+
+    // There should never be more than one element matching "div.body"
+    const divBody = document.querySelectorAll("div.body");
+    const body = divBody.length ? divBody[0] : document.querySelector("body");
+    window.setTimeout(() => {
+      terms.forEach((term) => _highlightText(body, term, "highlighted"));
+    }, 10);
+
+    const searchBox = document.getElementById("searchbox");
+    if (searchBox === null) return;
+    searchBox.appendChild(
+      document
+        .createRange()
+        .createContextualFragment(
+          '
' +
+            '' +
+            _("Hide Search Matches") +
+            "
"
+        )
+    );
+  },
+
+  /**
+   * helper function to hide the search marks again
+   */
+  hideSearchWords: () => {
+    document
+      .querySelectorAll("#searchbox .highlight-link")
+      .forEach((el) => el.remove());
+    document
+      .querySelectorAll("span.highlighted")
+      .forEach((el) => el.classList.remove("highlighted"));
+    localStorage.removeItem("sphinx_highlight_terms")
+  },
+
+  initEscapeListener: () => {
+    // only install a listener if it is really needed
+    if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) return;
+
+    document.addEventListener("keydown", (event) => {
+      // bail for input elements
+      if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return;
+      // bail with special keys
+      if (event.shiftKey || event.altKey || event.ctrlKey || event.metaKey) return;
+      if (DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS && (event.key === "Escape")) {
+        SphinxHighlight.hideSearchWords();
+        event.preventDefault();
+      }
+    });
+  },
+};
+
+_ready(SphinxHighlight.highlightSearchWords);
+_ready(SphinxHighlight.initEscapeListener);
diff --git a/docs/html/docsrc/howto/howto-docstring.html b/docs/html/docsrc/howto/howto-docstring.html
index 3ee7add2df..f70c80bc80 100644
--- a/docs/html/docsrc/howto/howto-docstring.html
+++ b/docs/html/docsrc/howto/howto-docstring.html
@@ -1,47 +1,82 @@
-
 
-
-
-  
-    
-    
-
-    1. How-To docstring — PorePy 1.5 documentation
-    
-    
-    
-    
-    
-    
-    
+
+
+  
+
+  
+  1. How-To docstring — PorePy 1.5 documentation
+      
+      
+    
+  
+  
+        
+        
+        
+        
+        
+        
+    
     
     
      
-  
-      
-
-    

-      

-        

-          

-            
+
+
+ 
+  

+    
+
+    

+
+      

+        

+          

+  
    
+      
    • 
+      
  • 1. How-To docstring
    • 
+      
  • 
+      
    • 
+  

+  

+

+          

+           

+             
   

-
1. How-To docstring

+
1. How-To docstring

 
Welcome to the How-To on creating documentation for your functions, classes and submodules.
 Here we explain shortly how the documentation works and give examples for how to write proper
 docstrings.

@@ -75,7 +110,7 @@ 
Navigation

 This will be done in a next step. Before that, familiarize yourself with the various directives
 and their options beforehand.

 

-
1.1. Docstring-Basics

+
1.1. Docstring-Basics

 
    
 
  1. Python docstrings are started and ended using a triple """, and are placed below the
 declaration of an object.
    
@@ -103,9 +138,12 @@ 
    1.1. Docstring-Basics
-
    1.1.1. Directives
    
+
    1.1.1. Directives
    
 
    Next to plain text, the content of your documentation can be created using directives,
 followed by a block of indented text.
    
+
    Directives are structural blocks inside the text of a documentation.
+They provide specific formatting for sections dedicated to e.g., function parameters,
+return values or exmaple code.
    
 
    For example, the note directive in plain rst code
    
 
    .. note:: Implementation
 
@@ -170,7 +208,7 @@ 
    1.1.1. Directives
 

 

-
1.2. PorePy style

+
1.2. PorePy style

 
As mentioned above, the PorePy style is Google Style with minor changes. These changes involve
 the developer team’s principles of good code and aesthetics. They also involve the project’s
 style guide, especially naming conventions. For more information check out the
@@ -199,17 +237,48 @@ 
1.2. PorePy styleAs a consequence, we abstain from including type hints in docstrings and keep them light.

 
This rule does not exclude custom linking and referencing in-text, where a developer feels the
 necessity to do so.

+
Google style directives

+
Google style directives are aliases for standard directives, which simplify the usage and syntax.
+Besides the obligatory declaration of parameters, return values and raised errors,
+the PorePy style encourages the use of other sections to provide notes, example code usage, references, etc.

+
For a list of all supported Google style directives,
+see Google style docstring sections.

+
The compulsory order of directives inside a docstring is:

+

+
    
+
  1. Examples, Note, …
    2. 
+
  2. References, See Also
    3. 
+
  3. Parameters
    4. 
+
  4. Returns/ Yields
    5. 
+
  5. Raises
    6. 
+

+

+
Other rules:

+

+
    
+
  • When using Google Style directives do not type additional text between and after the
+directives References/See Also, Parameters, Returns/Yields and Raises.
    • 
+
  • End every docstring with a blank line before """. This is especially important after
+the Returns: directive and its indented block.
    • 
+

+

+

+
Note

+
The Google Style directives are only valid when used inside docstrings,
+but not so when used in .rst files. Keep this in mind, in case you deal with the .rst
+structure of the webpage.

+

 

-
1.2.1. Documenting variables

+
1.2.1. Documenting variables

 

-

-module_level_var_1: str

+

+example_var_1: str

 
Variables at the module level are documented inline after declaration.

 

 
 

-

-module_level_var_2: int

+

+example_var_2: int

 
Multi-line docstrings are also valid.

 
You might want to use multiline docstrings when a more detailed description
 of the variable is required.

@@ -241,35 +310,42 @@ 
1.2.1. Documenting variables
-

-module_level_var_3: int

+

+example_var_3: int

 
DO NOT start the docstring with int:, i.e. with type hints.

 
This will render the below Type: int, which is unnecessary due to the already present
 annotation after the variable name. As you can test above, clicking on int will forward you
 to the right documentation.

 
DO:

-
module_level_var_3: int = 1
+
example_var_3: int = 1
 """This is var 3."""
 

 

 
DO NOT:

-
module_level_var_3 = 1
+
example_var_3 = 1
 """int: This is var 3."""
 

 

 

-
Type:

+
Type

 
int

 

 

 

 
+

+

+ExampleArrayLike

+
This is a custom type alias, including lists and numpy’s ndarray.

+
alias of Union[list, ndarray]

+

+
 

 

-
1.2.2. Documenting functions

+
1.2.2. Documenting functions

 

-

-module_level_function_1(arg1: int, arg2: str, arg3: bool) → bool[source]

+

+example_function_1(arg1: int, arg2: str, arg3: bool) → bool[source]

 
A short description of the functionality must fit in the first line.

 
Detailed description can be given next if necessary. The extended description
 can of course span several lines.

@@ -279,12 +355,12 @@ 
1.2.2. Documenting functions
 
Note

 
You can find the [source] link in the upper right corner of this function’s
-documentation and take a look at the Python and rst source code of this docstring,
+signature and inspect the Python and rst source code of this docstring,
 as well as for every docstring that follows.

 

-
The return value can be described using the Google Style directive Returns:.

+
The return value must be documented using the Google Style directive Returns:.

 

-
Parameters:

+
Parameters

 

 

-
Returns:

+
Returns

 
Describe the return value here. Multiple lines can be used and you have
 to indent the lines.

 
DO NOT use type hints here as they are present in the signature.

@@ -306,24 +382,27 @@ 
1.2.2. Documenting functions
-

-module_level_function_2(optional_arg: Optional[int] = None, *args, **kwargs) → None[source]

-
Optional arguments must be type-hinted using typing.Optional.

+

+example_function_2(optional_arg: Optional[int] = None, *args, **kwargs) → None[source]

+
This function demonstrates linking to objects inside docstrings, optional arguments and
+the Raises: directive.

+
Optional arguments must be type-hinted using typing.Optional.

 
As evident, you can link objects in-text. You can also link functions like
-module_level_function_1().

+example_function_1(). Note the different usage of :obj: and :class: for
+objects in third-party packages and objects in PorePy.

 
If *args or **kwargs are accepted,
 they must be listed as *args and **kwargs in the Parameters directive.

 

 
Note

-
We note that this function returns None as per signature.
-This is the default return value of Python and as such does not need documentation.
-I.e., we can omit the Returns: directive. However, it is important to explicitly
+
This function returns None as per signature.
+It is the default return value of Python and as such does not need documentation.
+I.e., we can omit the Returns: directive. However, it is obligatory to explicitly
 specify the None return in the signature.

 

 

-
Parameters:

+
Parameters

 
    
-
  • optional_arg (optional) – Description of optional_arg.
+
  • optional_arg (optional) – Description of optional_arg.
 The default value is described at the end.
 Use easily spottable wording like ‘Defaults to None.’ and mark the argument using
 (optional) after the name.
    • 
@@ -338,7 +417,7 @@ 
    1.2.2. Documenting functionsRaises:
+
    Raises
    
 
      
 
    • ValueError – You can use the the Google Style directive Raises: to describe error
     sources you have programmed. Here for example we can raise a value error
@@ -351,30 +430,27 @@ 
      1.2.2. Documenting functions
-
      
-module_level_function_3(mdg: MixedDimensionalGrid, vector: ndarray, matrix: spmatrix, option: Literal['A', 'B', 'C'] = 'A') → spmatrix[source]
      
-
      We demonstrate here the intra- and inter-doc linking to non-base-type Python objects
-in the signature,
-as well as how to document special requirements for the arguments.
      
+
      
+example_function_3(mdg: MixedDimensionalGrid, vector: ndarray, matrix: spmatrix, option: Literal['A', 'B', 'C'] = 'A') → spmatrix[source]
      
+
      This function demonstrates how to document special requirements for input arguments.
      
 
      
-
      Parameters:
      
+
      Parameters
      
 
        
 
      • mdg – A mixed-dimensional grid. Notice the usage of the acronym mdg.
        • 
-
      • vector (len=num_cells) – 
        This vector’s special requirement is a certain length.
+
      • vector (len=num_cells) – This vector’s special requirement is a certain length.
 We use the type hint brackets to indicate its supposed length.
 The required length is num_cells, the number of cells. If unclear to what the
-number refers, explain.
        
-
        E.g. where num_cells denotes the number of cells in mdg.
        
-
        • 
-
      • matrix (shape=(3, num_cells)) – This argument is a sparse matrix with 3 rows and
+number refers, explain.
+E.g. where num_cells denotes the number of cells in mdg.
        • 
+
      • matrix (shape=(3, num_cells)) – This argument is a sparse matrix with 3 rows and
 num_cells columns.
        • 
-
      • option (optional) – This argument has admissible values and a default value.
+
      • option (optional) – This argument has admissible values and a default value.
 it can only be a string 'A', 'B' or 'C'. For such admissible values use
-typing.literal to denote them in the signature.
+typing.Literal to denote them in the signature.
 Since it has a default value, we mark it with (optional).
        • 
 
      
 
      
-
      Returns:
      
+
      Returns
      
 
      Describe the return value here. You can also describe its dependence on the value of
 option here, or alternatively in the extended description at the beginning of the
 docstring.
      
@@ -386,91 +462,93 @@ 
      1.2.2. Documenting functionsRaises:
+
      Raises
      
 
      ValueError – If option is not in {'A', 'B', 'C'}.
      
 
      
 
      
 

 
 

-

-module_level_function_4(vector: np.ndarray, matrix: sps.spmatrix) → tuple[sps.spmatrix, np.ndarray] | None[source]

-
Functions with multiple return values need better description in the Returns:
+

+example_function_4(vector: ndarray, matrix: spmatrix) → tuple[scipy.sparse._base.spmatrix, numpy.ndarray][source]

+
This function demonstrates how to document multiple return values in the Returns:
 directive.

 

-
Parameters:

+
Parameters

 
    
 
  • vector – some vector
    • 
 
  • matrix – some matrix
    • 
 

 

-
Returns:

+
Returns

 
Every returned object needs a description. We can use the same structure as for
 the parameters: indented block per returned object or value.

 

-
spmatrix:
Though technically the tuple is a single object, it often is of
-importance what the tuple contains.

+
spmatrix (shape=(3, nd)):
Though technically the tuple is a single object, it often is of
+importance what the tuple contains. If the returned object has noteworthy
+characteristic, explain them next to the bullet header, the same way as for
+parameters.

 

-
ndarray:
We therefore use again the definition list structure with indented blocks to
+
ndarray:
Use the definition list structure with indented blocks to
 describe the content individually. This makes of course only sense if the tuple
 is of fixed length and/or contains objects of various types.

 

-
None:
The same rules hold for union return types.

-

 

 

 

-
Raises:

-
ValueError – If option is not in {'A', 'B', 'C'}.

+

+

+
+

+

+example_function_5(array_like: ArrayLike, ndarray_like: NDArray, dtype_like: DTypeLike) → ExampleArrayLike[source]

+
This function demonstrates type annotations using custom type aliases, including those
+from third-party packages.

+
For Sphinx to display type aliases without parsing their complete expression,
+a configuration is needed which maps the type alias to its source.

+
When encountering type aliases, which are not already covered by the configuration of
+PorePy’s docs, please contact the core developers.

+

+
Parameters

+
    
+
  • array_like – an argument of type ArrayLike
    • 
+
  • ndarray_like – an argument of type NDArray
    • 
+
  • dtype_like – an argument of type DTypeLike
    • 
+

+

+
Returns

+
a value of a custom array type ExampleArrayLike.

 

 

 

 
 

 

-example_generator(n: int) → Generator[int, None, None][source]

+example_generator(n: int) → Generator[int, None, None][source]
 
When documenting a generator, use the Yields: directive instead of Returns:.
 Their usage is equivalent, indicating only that this is a generator object, not a regular
 function.

-
Examples

-
The Google Style offers an Examples: directives where you can write text but also
-include inline examples of code usage, without the special code directive from Sphinx.
-An indented block with the content has to follow the directive. Like all for all
-directives, a blank line after the indented block signalizes the end of the directive.

+

+
Example

+
Here we demonstrate the usage of example_generator using the Example: directive:

 
>>> print([i for i in example_generator(4)])
 [0, 1, 2, 3]
 

 

+

 

-
Parameters:

+
Parameters

 
n – Some upper integer limit.

 

-
Yields:

+
Yields

 
numbers until n is reached.

 

 

 

 
-
Directives inside docstrings

-
    
-
  • 
-
    Write the directive blocks in the following order
      
-
    1. Examples, Note
      2. 
-
    2. Parameters
      3. 
-
    3. Returns/ Yields
      4. 
-
    4. Raises
      5. 
-
    
-
    
-
    
-
    • 
-
  • When using Google Style directives do not type additional text between and after the
-directives Parameters, Returns/Yields and Raises.
    • 
-
  • End every docstring with a blank line before """. This is especially important after
-the Returns: directive and its indented block.
    • 
-

 

 

-
1.2.3. Documenting classes

+
1.2.3. Documenting classes

 
When documenting classes, three aspects have to be considered.

 
Documenting Constructor Arguments

 
In PorePy, the constructor description is to be included in the class-docstring, not in the
@@ -532,17 +610,41 @@ 
1.2.3. Documenting classesExample class documentation

 

 

-class ExampleClass(arg1: int, arg2: str)[source]

+class ExampleClass(arg1: int, arg2: str)[source]
 
Bases: object

 
A quick purpose of the class is to be provided in the first line.

 
After the first line, a broader, multi-line description of the class can follow. It can
 contain multiple paragraphs as well as elements like code snippets.

 
Example: directives are encouraged to demonstrate the usage of a class.

 
Note: directives can be used the same way as for functions.

-
At the end follows obligatory the Parameters: directive and a Raises: directive,
-if errors are raised in the constructor for some reason.

+

+
Example

+
Using the Example: directive, you can provide simplified python syntax using >>>
+on how to instantiate the class for example:

+
>>> import example_docstrings as ed
+>>> A = ed.ExampleClass()
+>>> print(type(A))
+<class 'example_docstrings.ExampleClass'>
+

+

+

+
Use the References: and See Also: directives to provide links to sources or
+inspirations for your implementation.

+
For readability reasons, we impose the same rules on the order of directives as for
+functions. Meaning references/ see also, followed by parameters, return/yield and raises
+must be placed at the end with no additional text in between.

+

+
References

+
    
+
  1. Basic Google Style.
    2. 
+

+

+

+
See also

+
Same, but in different directive.

+

 

-
Parameters:

+
Parameters

 

 
 

 

-example_method(arg: bool) → bool[source]

+example_method(arg: bool) → bool[source]
 
A short description of the method must fit in the first line.

 
A more elaborate description can follow afterwards.

 

-
Parameters:

+
Parameters

 
arg – The first argument (even though self is technically the first one).

 

-
Returns:

+
Returns

 
True.

 

 

@@ -573,25 +675,25 @@ 
1.2.3. Documenting classes
 

-static example_static_method() → None[source]

+static example_static_method() → None[source]
 
This is the docstring of a static method.

 
Note the absence of self.

 

 
 

 

-attribute_1: int

+attribute_1: int
 
This is how to properly document an instance-level attribute in the constructor.

 

 
 

 

-attribute_2: str

+attribute_2: str
 
This is an instance-level attribute with a redundant field ‘Type:’ caused by
 type hints in the docstring. The type should only be given by its annotation.
 DO NOT use type hints in docstrings (cannot repeat often enough).

 

-
Type:

+
Type

 
str

 

 

@@ -599,7 +701,7 @@ 
1.2.3. Documenting classes
 

-attribute_3: dict[str, int]

+attribute_3: dict[str, int]
 
Some attributes are calculated during construction, possibly in a separate method.

 
Document nevertheless what the attribute contains and what it is used for etc.,
 but leave the documentation of how it is calculated to the separate method.

@@ -607,7 +709,7 @@ 
1.2.3. Documenting classes
 

-class_attribute_1: int = 1

+class_attribute_1: int = 1
 
This is how to properly document a class-level attribute.

 
The value 1 is shown in the docs, because it is static upon class type creation and Sphinx
 realizes that.

@@ -615,12 +717,12 @@ 
1.2.3. Documenting classes
 

-class_attribute_2: str = 'A'

+class_attribute_2: str = 'A'
 
This is a class attribute with a redundant field ‘Type:’ caused by type hints
 in the docstring. The type should only be given by its annotation.
 DO NOT use type hints in docstrings.

 

-
Type:

+
Type

 
str

 

 

@@ -628,13 +730,13 @@ 
1.2.3. Documenting classes
 

-property readonly_property: str

+property readonly_property: str
 
Document properties only in their getter-methods.

 

 
 

 

-property readwrite_property: str

+property readwrite_property: str
 
Properties with both a getter and setter should only be documented in their
 getter method.

 
If the setter method contains notable behavior, it should be
@@ -645,7 +747,7 @@ 
1.2.3. Documenting classes
-
1.2.4. Module-level documentation

+
1.2.4. Module-level documentation

 
Module level documentation can be achieved by writing a docstring at the very top of a file.
 Subpackages i.e., folders containing an __init__ file and multiple modules, have their
 docstring at the top of the __init__ file.
@@ -662,69 +764,30 @@ 
1.2.4. Module-level documentation
 
 
-            

+           

           

-        

-      

-      
-    
-    
-  
+    
+  

+   
+
+
 
\ No newline at end of file
diff --git a/docs/html/docsrc/porepy/numerics/ad/numerics-ad.html b/docs/html/docsrc/porepy/numerics/ad/numerics-ad.html
index 7927a6d774..8a2e8599c2 100644
--- a/docs/html/docsrc/porepy/numerics/ad/numerics-ad.html
+++ b/docs/html/docsrc/porepy/numerics/ad/numerics-ad.html
@@ -1,59 +1,91 @@
-
 
-
-
-  
-    
-    
-
-    Automatic Differentiation — PorePy 1.5 documentation
-    
-    
-    
-    
-    
-    
-    
+
+
+  
+
+  
+  Automatic Differentiation — PorePy 1.5 documentation
+      
+      
+    
+  
+  
+        
+        
+        
+        
+        
+        
+    
     
     
     
      
-  
-      
-
-    

-      

-        

-          

-            
+
+
+ 
+  

+    
+
+    

+
+      

+        

+          

+  
    
+      
    • 
+          
  • Numerics
    • 
+      
  • Automatic Differentiation
    • 
+      
  • 
+      
    • 
+  

+  

+

+          

+           

+             
   

-
Automatic Differentiation

+
Automatic Differentiation

 
The AD framework (Algorithmic or Automatic Differentiation) allows an object-oriented
 representation of variables and other mathematical terms, which appear in equations
 and models. The goal as for any AD framework is to provide a cheap and automated evaluation
 of derivatives, to be utilized in numerical approximation techniques.

 
All classes and functions can be accessed as shown in the following example:

 

-
Access to AD submodule

+
Access to AD submodule

 
import porepy as pp
 
 a = pp.ad.Scalar(1.)
@@ -90,36 +122,36 @@ 
Automatic Differentiation
-
Elemental AD data structures

+
Elemental AD data structures

 

 

-class Ad_array(val=1.0, jac=0.0)[source]

+class Ad_array(val=1.0, jac=0.0)[source]
 
Bases: object

 

 

-copy()[source]

+copy()[source]
 

 
 

 

-diagvec_mul_jac(a)[source]

+diagvec_mul_jac(a)[source]
 

 
 

 

-full_jac()[source]

+full_jac()[source]
 

 
 

 

-jac_mul_diagvec(a)[source]

+jac_mul_diagvec(a)[source]
 

 
 

 
 

 

-class Operator(name: Optional[str] = None, subdomains: Optional[list[porepy.grids.grid.Grid]] = None, interfaces: Optional[list[porepy.grids.mortar_grid.MortarGrid]] = None, tree: Optional[Tree] = None)[source]

+class Operator(name: Optional[str] = None, subdomains: Optional[list[porepy.grids.grid.Grid]] = None, interfaces: Optional[list[porepy.grids.mortar_grid.MortarGrid]] = None, tree: Optional[Tree] = None)[source]
 
Bases: object

 
Parent class for all AD operators.

 
This class is not meant to be initiated directly, rather the various
@@ -128,13 +160,13 @@ 
Elemental AD data structures
-
Parameters:

+
Parameters

 

 
 

 

-evaluate(dof_manager: DofManager, state: Optional[ndarray] = None) → Ad_array[source]

+evaluate(dof_manager: DofManager, state: Optional[ndarray] = None)[source]
 
Evaluate the residual and Jacobian matrix for a given state.

 

-
Parameters:

+
Parameters

 
    
 
  • dof_manager – Used to represent the problem. Will be used
 to parse the sub-operators that combine to form this operator.
    • 
-
  • state (optional) – State vector for which the residual and its
+
  • state (optional) – State vector for which the residual and its
 derivatives should be formed. If not provided, the state will be pulled from
 the previous iterate (if this exists), or alternatively from the state
 at the previous time step.
    • 
 

 

-
Returns:

+
Returns

 
A representation of the residual and Jacobian in form of an AD Array.
 Note that the Jacobian matrix need not be invertible, or even square;
 this depends on the operator.

@@ -175,11 +205,11 @@ 
Elemental AD data structures
 

-is_leaf() → bool[source]

+is_leaf() → bool[source]
 
Check if this operator is a leaf in the tree-representation of an expression.

 
Note that this implies that the method parse() is expected to be implemented.

 

-
Returns:

+
Returns

 
True if the operator has no children.

 

 

@@ -187,7 +217,7 @@ 
Elemental AD data structures
 

-parse(mdg: MixedDimensionalGrid) → Any[source]

+parse(mdg: MixedDimensionalGrid) → Any[source]
 
Translate the operator into a numerical expression.

 
Subclasses that represent atomic operators (leaves in a tree-representation of
 an operator) should override this method to return e.g. a number, an array or a
@@ -195,10 +225,10 @@ 
Elemental AD data structuresevaluate().

 

-
Parameters:

+
Parameters

 
mdg – Mixed-dimensional grid on which this operator is to be parsed.

 

-
Returns:

+
Returns

 
A numerical format representing this operator;s values on given domain.

 

 

@@ -206,14 +236,14 @@ 
Elemental AD data structures
 

-previous_timestep() → Operator[source]

+previous_timestep() → Operator[source]
 
Return an operator that represents the value of this operator at the previous
 timestep.

 
The operator tree at the previous time step is created as a shallow copy, and will
 thus be identical to the original operator, except that all time dependent operators
 are evaluated at the previous time step.

 

-
Returns:

+
Returns

 
A copy of self, with all time dependent operators evaluated at the previous
 time step.

 

@@ -222,10 +252,10 @@ 
Elemental AD data structures
 

-set_name(name: str) → None[source]

+set_name(name: str) → None[source]
 
Reset this object’s name originally passed at instantiation.

 

-
Parameters:

+
Parameters

 
name – the new name to be assigned.

 

 

@@ -233,13 +263,13 @@ 
Elemental AD data structures
 

-viz()[source]

+viz()[source]
 
Draws a visualization of the operator tree that has this operator as its root.

 

 
 

 

-interfaces: list[porepy.grids.mortar_grid.MortarGrid]

+interfaces: list[porepy.grids.mortar_grid.MortarGrid]
 
List of mortar grids in the mixed-dimensional grid on which the operator is defined,
 passed at instantiation.

 
Will be empty for operators not associated with specific subdomains.

@@ -247,7 +277,7 @@ 
Elemental AD data structures
 

-subdomains: list[porepy.grids.grid.Grid]

+subdomains: list[porepy.grids.grid.Grid]
 
List of subdomains on which the operator is defined, passed at instantiation.

 
Will be empty for operators not associated with specific subdomains.

 

@@ -256,13 +286,14 @@ 
Elemental AD data structures
-
Common mathematical functions

+
Common mathematical functions

 
This module contains functions to be wrapped in a
 Function and used as part
 of compound Operator, i.e. as (terms of) equations.

 
Some functions depend on non-ad objects. This requires that the function f be wrapped
 in an ad.Function using partial evaluation:

-
Examples

+

+
Examples

 
>>> from functools import partial
 >>> AdFunction = pp.ad.Function(partial(f, other_parameter), "name")
 >>> equation: pp.ad.Operator = AdFunction(var) - 2 * var
@@ -272,63 +303,66 @@ 
Elemental AD data structuresAdFunction is a
 Function` implies that upon parsing,
 the argument passed to f will be an Ad_array.

+

 

 

-class RegularizedHeaviside(regularization: Callable)[source]

+class RegularizedHeaviside(regularization: Callable)[source]
 
Bases: object

 

 
 

 

-abs(var)[source]

+abs(var)[source]
 

 
 

 

-arccos(var)[source]

+arccos(var)[source]
 

 
 

 

-arccosh(var)[source]

+arccosh(var)[source]
 

 
 

 

-arcsin(var)[source]

+arcsin(var)[source]
 

 
 

 

-arcsinh(var)[source]

+arcsinh(var)[source]
 

 
 

 

-arctan(var)[source]

+arctan(var)[source]
 

 
 

 

-arctanh(var)[source]

+arctanh(var)[source]
 

 
 

 

-characteristic_function(tol: float, var: Ad_array)[source]

+characteristic_function(tol: float, var: Ad_array)[source]
 
Characteristic function of an ad variable.

 
Returns 1 if var.val is within absolute tolerance = tol of zero.
 The derivative is set to zero independent of var.val.

-
Notes

+

+
Note

 
See module level documentation on how to wrap functions like this in ad.Function.

+

 

-
Parameters:

+
Parameters

 
    
 
  • tol – Absolute tolerance for comparison with 0 using np.isclose.
    • 
 
  • var – Ad operator (variable or expression).
    • 
 

 

-
Returns:

+
Returns

 
The characteristic function of var with appropriate val and jac attributes.

 

 

@@ -336,41 +370,28 @@ 
Elemental AD data structures
 

-cos(var)[source]

+cos(var)[source]
 

 
 

 

-cosh(var)[source]

+cosh(var)[source]
 

 
 

 

-exp(var)[source]

+exp(var)[source]
 

 
 

 

-heaviside(var, zerovalue: float = 0.5)[source]

+heaviside(var, zerovalue: float = 0.5)[source]
 

 
 

 

-heaviside_smooth(var, eps: float = 0.001)[source]

+heaviside_smooth(var, eps: float = 1e-3)[source]
 
Smooth (regularized) version of the Heaviside function.

-

-
Parameters:

-
    
-
  • var – Input array.
    • 
-
  • eps (optional) – Regularization parameter. The function will converge to the
-Heaviside function in the limit when eps --> 0. The default is 1e-3.
    • 
-

-

-
Returns:

-
Regularized heaviside function (and its Jacobian if applicable) in form of a
-Ad_array or ndarray (depending on the input).

-

-

 

 
Note

 

@@ -381,11 +402,24 @@ 
Elemental AD data structureshttps://ieeexplore.ieee.org/document/902291

 

+

+
Parameters

+
    
+
  • var – Input array.
    • 
+
  • eps (optional) – Regularization parameter. The function will converge to the
+Heaviside function in the limit when eps --> 0. The default is 1e-3.
    • 
+

+

+
Returns

+
Regularized heaviside function (and its Jacobian if applicable) in form of a
+Ad_array or ndarray (depending on the input).

+

+

 

 
 

 

-l2_norm(dim: int, var: Ad_array) → Ad_array[source]

+l2_norm(dim: int, var: Ad_array) → Ad_array[source]
 
L2 norm of a vector variable.

 
For the example of dim=3 components and n vectors, the ordering is assumed
 to be [u0, v0, w0, u1, v1, w1, ..., un, vn, wn]

@@ -395,13 +429,13 @@ 
Elemental AD data structures
-
Parameters:

+
Parameters

 
    
 
  • dim – Dimension, i.e. number of vector components.
    • 
 
  • var – Ad operator (variable or expression) which is argument of the norm function.
    • 
 

 

-
Returns:

+
Returns

 
The norm of var with appropriate val and jac attributes.

 

 

@@ -409,24 +443,24 @@ 
Elemental AD data structures
 

-log(var)[source]

+log(var)[source]
 

 
 

 

-maximum(var0: pp.ad.Ad_array, var1: pp.ad.Ad_array | np.ndarray) → pp.ad.Ad_array[source]

+maximum(var0: pp.ad.Ad_array, var1: pp.ad.Ad_array | np.ndarray) → pp.ad.Ad_array[source]
 
Ad maximum function represented as an Ad_array.

 
The second argument is allowed to be constant, with a numpy array originally
 wrapped in a pp.ad.Array, whereas the first argument is expected to be an
 Ad_array originating from a pp.ad.Operator.

 

-
Parameters:

+
Parameters

 
    
 
  • var0 – First argument to the maximum function.
    • 
 
  • var1 – Second argument.
    • 
 

 

-
Returns:

+
Returns

 
The maximum of var0 and var1 with appropriate val and jac attributes.

 

 

@@ -434,35 +468,35 @@ 
Elemental AD data structures
 

-sign(var)[source]

+sign(var)[source]
 

 
 

 

-sin(var)[source]

+sin(var)[source]
 

 
 

 

-sinh(var)[source]

+sinh(var)[source]
 

 
 

 

-tan(var)[source]

+tan(var)[source]
 

 
 

 

-tanh(var)[source]

+tanh(var)[source]
 

 
 

 

-
AD-representation of constant scalars, vectors and matrices

+
AD-representation of constant scalars, vectors and matrices

 

 

-class Scalar(value: float, name: Optional[str] = None)[source]

+class Scalar(value: float, name: Optional[str] = None)[source]
 
Bases: Operator

 
Ad representation of a scalar.

 
This is a shallow wrapper around a real scalar. It may be useful to combine
@@ -473,10 +507,10 @@ 
AD-representation of constant scalars, vectors and matrices
 

-parse(mdg: MixedDimensionalGrid) → float[source]

+parse(mdg: MixedDimensionalGrid) → float[source]
 
See Operator.parse().

 

-
Returns:

+
Returns

 
The wrapped number.

 

 

@@ -484,7 +518,7 @@ 
AD-representation of constant scalars, vectors and matrices
 

-interfaces: list[porepy.grids.mortar_grid.MortarGrid]

+interfaces: list[porepy.grids.mortar_grid.MortarGrid]
 
List of mortar grids in the mixed-dimensional grid on which the operator is defined,
 passed at instantiation.

 
Will be empty for operators not associated with specific subdomains.

@@ -492,7 +526,7 @@ 
AD-representation of constant scalars, vectors and matrices
 

-subdomains: list[porepy.grids.grid.Grid]

+subdomains: list[porepy.grids.grid.Grid]
 
List of subdomains on which the operator is defined, passed at instantiation.

 
Will be empty for operators not associated with specific subdomains.

 

@@ -501,7 +535,7 @@ 
AD-representation of constant scalars, vectors and matrices
 

-class Array(values: ndarray, name: Optional[str] = None)[source]

+class Array(values: ndarray, name: Optional[str] = None)[source]
 
Bases: Operator

 
AD representation of a constant numpy array.

 
For sparse matrices, use Matrix instead.
@@ -509,16 +543,16 @@ 
AD-representation of constant scalars, vectors and matrices
-
Parameters:

+
Parameters

 
values – Numpy array to be represented.

 

 
 

 

-parse(mdg: MixedDimensionalGrid) → ndarray[source]

+parse(mdg: MixedDimensionalGrid) → ndarray[source]
 
See Operator.parse().

 

-
Returns:

+
Returns

 
The wrapped array.

 

 

@@ -526,7 +560,7 @@ 
AD-representation of constant scalars, vectors and matrices
 

-interfaces: list[porepy.grids.mortar_grid.MortarGrid]

+interfaces: list[porepy.grids.mortar_grid.MortarGrid]
 
List of mortar grids in the mixed-dimensional grid on which the operator is defined,
 passed at instantiation.

 
Will be empty for operators not associated with specific subdomains.

@@ -534,7 +568,7 @@ 
AD-representation of constant scalars, vectors and matrices
 

-subdomains: list[porepy.grids.grid.Grid]

+subdomains: list[porepy.grids.grid.Grid]
 
List of subdomains on which the operator is defined, passed at instantiation.

 
Will be empty for operators not associated with specific subdomains.

 

@@ -543,7 +577,7 @@ 
AD-representation of constant scalars, vectors and matrices
 

-class TimeDependentArray(name: str, subdomains: Optional[list[porepy.grids.grid.Grid]] = None, interfaces: Optional[list[porepy.grids.mortar_grid.MortarGrid]] = None, previous_timestep: bool = False)[source]

+class TimeDependentArray(name: str, subdomains: Optional[list[porepy.grids.grid.Grid]] = None, interfaces: Optional[list[porepy.grids.mortar_grid.MortarGrid]] = None, previous_timestep: bool = False)[source]
 
Bases: Array

 
An Ad-wrapper around a time-dependent numpy array.

 
The array is tied to a MixedDimensionalGrid, and is distributed among the data
@@ -556,7 +590,7 @@ 
AD-representation of constant scalars, vectors and matrices
-
Parameters:

+
Parameters

 

 
 
-            

+           

           

-        

-      

-      
-    
-    
-  
+    

+  

+   
+
+
 
\ No newline at end of file
diff --git a/docs/html/docsrc/porepy/numerics/numerics.html b/docs/html/docsrc/porepy/numerics/numerics.html
index c1a060e8cf..0748131f60 100644
--- a/docs/html/docsrc/porepy/numerics/numerics.html
+++ b/docs/html/docsrc/porepy/numerics/numerics.html
@@ -1,51 +1,83 @@
-
 
+
+
+  
 
-
-  
-    
-    
-
-    Numerics — PorePy 1.5 documentation
-    
-    
-    
-    
-    
-    
-    
+  
+  Numerics — PorePy 1.5 documentation
+      
+      
+    
+  
+  
+        
+        
+        
+        
+        
+        
+    
     
     
     
-     
-  
-      
+     
+
+
+ 
+  

+    
 
-    

-      

-        

-          

-            
+    

+
+      

+        

+          

+  
    
+      
    • 
+      
  • Numerics
    • 
+      
  • 
+      
    • 
+  

+  

+

+          

+           

+             
   

-
Numerics

+
Numerics

 

 
Submodules

 
    
@@ -55,57 +87,31 @@ 
    Numerics

+           

           

-        

-      

-      
-    
-    
-  
+    

+  

+   
+
+
 
\ No newline at end of file
diff --git a/docs/html/genindex-A.html b/docs/html/genindex-A.html
index 3795ed1c4a..c4f2937923 100644
--- a/docs/html/genindex-A.html
+++ b/docs/html/genindex-A.html
@@ -1,41 +1,79 @@
 
-
 
-
-
-  
-    
-    
-    Index — PorePy 1.5 documentation
-    
-    
-    
-    
-    
-    
-    
+
+
+  
+  
+  Index — PorePy 1.5 documentation
+      
+      
+    
+  
+  
+        
+        
+        
+        
+        
+        
+    
     
      
-  
-      
+
 
-    

-      

-        

-          

-            
+ 
+  

+    
+
+    

+
+      

+        

+          

+  
    
+      
    • 
+      
  • Index
    • 
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Index – V

 
@@ -51,41 +89,28 @@ 
Index – V

 
 
 
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© Copyright 2022 UiB Center for Modeling of Coupled Subsurface Dynamics, GNU LESSER GENERAL PUBLIC LICENSE Version 3, 29 June 2007..

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© Copyright 2022 UiB Center for Modeling of Coupled Subsurface Dynamics, GNU LESSER GENERAL PUBLIC LICENSE Version 3, 29 June 2007..

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Index

 
@@ -169,6 +207,16 @@ 
E

         
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-
 
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-    Index — PorePy 1.5 documentation
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@@ -66,41 +104,28 @@ 
    Index
    
    
    
 
 
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    © Copyright 2022 UiB Center for Modeling of Coupled Subsurface Dynamics, GNU LESSER GENERAL PUBLIC LICENSE Version 3, 29 June 2007..
    
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@@ -1,47 +1,82 @@
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+
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-
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+      
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    Welcome to PorePy!
    
+ 
+  
    
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+
    PorePy Documentation
    
 
    PorePy is a research code that is mainly developed at the Department of Mathematics at the University of Bergen.
 The code is aimed at simulation of multiphysics processes in fractured porous media.
 Specifically, the code is typically applied to
    
@@ -54,7 +89,7 @@ 
    Welcome to PorePy!
-
    What is PorePy good at?
    
+
    What is PorePy good at?
    
 
    The main strengths of PorePy are:
    
 
      
 
    • Natural representation of variables and processes in fracture networks, and on the fracture-matrix interface.
      • 
@@ -70,7 +105,7 @@ 
      What is PorePy good at?
 
    
 
    
-
    What is PorePy not so good at?
    
+
    What is PorePy not so good at?
    
 
      
 
    • No native support for linear and non-linear solvers. This will be improved in the near future.
      • 
 
    • Few standardized setups are available; mostly, the user is responsible for specifying problems and discretizations.
@@ -81,10 +116,8 @@ 
      What is PorePy not so good at?
-
      The PorePy package
      
+
      The PorePy package
      
 
      PorePy is divided into the following modules
      
 
      
 
        
@@ -96,7 +129,7 @@ 
        The PorePy package
-
        For developers
        
+
        For developers
        
 
        Below you will find guidelines and instructions for developing activities in PorePy.
 All new developers are required to familiarize themselves with the How-To-X sections before
 attempting a pull-request.
        
@@ -107,72 +140,41 @@ 
        For developers
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        Indices and tables
        
+
        Indices and tables
        
 
+
    
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    Python Module Index
    
 
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"porepy.numerics.ad.operators.Matrix.transpose"]], "viz() (operator method)": [[1, "porepy.numerics.ad.operators.Operator.viz"]]}})
\ No newline at end of file
diff --git a/docs/index.rst b/docs/index.rst
index 1e9ef010d7..8391065a1c 100644
--- a/docs/index.rst
+++ b/docs/index.rst
@@ -1,5 +1,6 @@
-Welcome to PorePy!
-==================
+====================
+PorePy Documentation
+====================
 
 PorePy is a research code that is mainly developed at the Department of Mathematics at the University of Bergen.
 The code is aimed at simulation of multiphysics processes in fractured porous media.