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doc/OnlineDocs/explanation/modeling/dae.rst

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@@ -35,19 +35,19 @@ Pyomo.DAE introduces three new modeling components to Pyomo:
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As will be shown later, differential equations can be declared using
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using these new modeling components along with the standard Pyomo
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:py:class:`Var<.Var>` and
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:py:class:`Constraint<.Constraint>` components.
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:py:class:`.Var` and
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:py:class:`.Constraint` components.
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ContinuousSet
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*************
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This component is used to define continuous bounded domains (for example
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'spatial' or 'time' domains). It is similar to a Pyomo
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:py:class:`Set <.Set>` component and can be used to index things
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:py:class:`.Set` component and can be used to index things
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like variables and constraints. Any number of
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:py:class:`ContinuousSets <pyomo.dae.ContinuousSet>` can be used to index a
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component and components can be indexed by both
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:py:class:`Sets <.Set>` and
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:py:class:`.Set` and
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:py:class:`ContinuousSets <pyomo.dae.ContinuousSet>` in arbitrary order.
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In the current implementation, models with
@@ -112,9 +112,9 @@ abstract Pyomo model using the example data file.
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.. note::
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Most valid ways to declare and initialize a
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:py:class:`Set <.Set>` can be used to
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:py:class:`.Set` can be used to
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declare and initialize a :py:class:`ContinuousSet<pyomo.dae.ContinuousSet>`.
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See the documentation for :py:class:`Set <.Set>` for additional
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See the documentation for :py:class:`.Set` for additional
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options.
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.. warning::
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.. note::
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:py:class:`ContinuousSet <pyomo.dae.ContinuousSet>` components are
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always ordered (sorted) therefore the ``first()`` and ``last()``
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:py:class:`Set <.Set>` methods can be used to access the lower
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:py:class:`.Set` methods can be used to access the lower
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and upper boundaries of the
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:py:class:`ContinuousSet <pyomo.dae.ContinuousSet>` respectively
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@@ -146,7 +146,7 @@ Pyomo model. In each case, the variable being differentiated is supplied
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as the only positional argument and the type of derivative is specified
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using the 'wrt' (or the more verbose 'withrespectto') keyword
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argument. Any keyword argument that is valid for a Pyomo
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:py:class:`Var <.Var>` component may also be specified.
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:py:class:`.Var` component may also be specified.
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.. doctest::
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@@ -182,16 +182,16 @@ argument. Any keyword argument that is valid for a Pyomo
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The 'initialize' keyword argument will initialize the value of a
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derivative and is **not** the same as specifying an initial
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condition. Initial or boundary conditions should be specified using a
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:py:class:`Constraint<.Constraint>` or
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:py:class:`ConstraintList<.ConstraintList>` or
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by fixing the value of a :py:class:`Var<.Var>` at a boundary
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:py:class:`.Constraint` or
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:py:class:`.ConstraintList` or
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by fixing the value of a :py:class:`.Var` at a boundary
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point.
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Declaring Differential Equations
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--------------------------------
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A differential equations is declared as a standard Pyomo
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:py:class:`Constraint<.Constraint>` and is not required to have
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:py:class:`.Constraint` and is not required to have
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any particular form. The following code snippet shows how one might declare
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an ordinary or partial differential equation.
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@@ -226,12 +226,12 @@ an ordinary or partial differential equation.
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... return m.dydt[t, l] == m.dydl2[t, l]
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>>> model.pde = pyo.Constraint(model.t, model.l, rule=_pde_rule)
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By default, a :py:class:`Constraint<.Constraint>` declared over a
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By default, a :py:class:`.Constraint` declared over a
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:py:class:`ContinuousSet<pyomo.dae.ContinuousSet>` will be applied at every
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discretization point contained in the set. Often a modeler does not want to
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enforce a differential equation at one or both boundaries of a continuous
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domain. This may be addressed explicitly in the
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:py:class:`Constraint<.Constraint>` declaration using
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:py:class:`.Constraint` declaration using
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``Constraint.Skip`` as shown above. Alternatively, the desired constraints can
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be deactivated just before the model is sent to a solver as shown below.
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@@ -294,7 +294,7 @@ Declaring Integrals
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:members:
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Declaring an :py:class:`Integral<pyomo.dae.Integral>` component is similar to
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declaring an :py:class:`Expression<.Expression>` component. A
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declaring an :py:class:`.Expression` component. A
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simple example is shown below:
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.. doctest::
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ensure consistency in the ordering and dimension of the indexing sets
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After an :py:class:`Integral<pyomo.dae.Integral>` has been declared, it can be
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used just like a Pyomo :py:class:`Expression<.Expression>`
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used just like a Pyomo :py:class:`.Expression`
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component and can be included in constraints or the objective function as shown
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above.
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@@ -342,7 +342,7 @@ positional argument. This should become more clear with the following example
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showing a double integral over the
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:py:class:`ContinuousSet<pyomo.dae.ContinuousSet>` components ``model.t1`` and
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``model.t2``. In addition, the expression is also indexed by the
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:py:class:`Set<.Set>` ``model.s``. The mathematical representation
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:py:class:`.Set` ``model.s``. The mathematical representation
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and implementation in Pyomo are shown below:
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.. math::
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where :math:`h` is the step size between discretization points or the size of
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each finite element. These equations are generated automatically as
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:py:class:`Constraints<.Constraint>` when the backward
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:py:class:`.Constraint` when the backward
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difference method is applied to a Pyomo model.
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There are several discretization options available to a

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