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remove .at() from docs
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docs/source/point-evaluation.rst

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@@ -356,90 +356,6 @@ be created. Any existing immersed vertex-only mesh will have been created
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using the previous tolerance and will be unaffected by the change.
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``Function.at``
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------------------------------
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.. warning::
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The following API is deprecated and will be removed in a future release.
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Please use the primary API described above.
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The :meth:`~.Function.at` method is designed for simple interrogation of a :class:`~.Function` with
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a few points.
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.. code-block:: python3
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# evaluate f at a 1-dimensional point
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f.at(0.3)
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# evaluate f at two 1-dimensional points, or at one 2-dimensional point
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# (depending on f's geometric dimension)
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f.at(0.2, 0.4)
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# evaluate f at one 2-dimensional point
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f.at([0.2, 0.4])
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# evaluate f at two 2-dimensional points
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f.at([0.2, 0.4], [1.2, 0.5])
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# evaluate f at two 2-dimensional points (same as above)
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f.at([[0.2, 0.4], [1.2, 0.5]])
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While in these examples we have only shown lists, other *iterables*
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such as tuples and ``numpy`` arrays are also accepted. The following
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are equivalent:
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.. code-block:: python3
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f.at(0.2, 0.4)
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f.at((0.2, 0.4))
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f.at([0.2, 0.4])
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f.at(numpy.array([0.2, 0.4]))
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For a single point, the result is a ``numpy`` array, or a tuple of
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``numpy`` arrays in case of *mixed* functions. When evaluating
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multiple points, the result is a list of values for each point.
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To summarise:
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* Single point, non-mixed: ``numpy`` array
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* Single point, mixed: tuple of ``numpy`` arrays
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* Multiple points, non-mixed: list of ``numpy`` arrays
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* Multiple points, mixed: list of tuples of ``numpy`` arrays
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Points outside the domain
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~~~~~~~~~~~~~~~~~~~~~~~~~
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When any point is outside the domain of the function,
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:py:class:`.PointNotInDomainError` exception is raised. If
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``dont_raise=True`` is passed to :meth:`~.Function.at`, the result is
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``None`` for those points which fall outside the domain.
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.. code-block:: python3
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mesh = UnitIntervalMesh(8)
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f = mesh.coordinates
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f.at(1.2) # raises exception
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f.at(1.2, dont_raise=True) # returns None
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f.at(0.5, 1.2) # raises exception
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f.at(0.5, 1.2, dont_raise=True) # returns [0.5, None]
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Evaluation with a distributed mesh
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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There is limited support for :meth:`~.Function.at` when running Firedrake
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in parallel. There is no special API, but there are some restrictions:
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* Point evaluation is a *collective* operation.
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* Each process must ask for the same list of points.
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* Each process will get the same values.
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If ``RuntimeError: Point evaluation gave different results across processes.``
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is raised, try lowering the :ref:`mesh tolerance <tolerance>`.
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UFL API
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-------
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