:py:mod:`tlm_adjoint.firedrake.interpolation`
=============================================

.. py:module:: tlm_adjoint.firedrake.interpolation

.. autoapi-nested-parse::

   Interpolation operations with Firedrake.

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Module Contents
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.. py:class:: ExprInterpolation(x, rhs)




   
   Represents interpolation of `rhs` onto the space for `x`.

   The forward residual :math:`\mathcal{F}` is defined so that :math:`\partial
   \mathcal{F} / \partial x` is the identity.

   :arg x: The forward solution.
   :arg rhs: A :class:`ufl.core.expr.Expr` defining the expression to
       interpolate onto the space for `x`. Should not depend on `x`.















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   .. py:method:: drop_references()

      
      Drop references to variables which store values.
















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   .. py:method:: forward_solve(x, deps=None)

      
      Compute the forward solution.

      Can assume that the currently active :class:`.EquationManager` is
      paused.

      :arg X: A variable or a :class:`Sequence` of variables storing the
          solution. May define an initial guess, and should be set by this
          method.
      :arg deps: A :class:`tuple` of variables, defining values for
          dependencies. Only the elements corresponding to `X` may be
          modified. `self.dependencies()` should be used if not supplied.















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   .. py:method:: adjoint_derivative_action(nl_deps, dep_index, adj_x)

      
      Return the action of the adjoint of a derivative of the forward
      residual on the adjoint solution. This is the *negative* of an adjoint
      right-hand-side term.

      :arg nl_deps: A :class:`Sequence` of variables defining values for
          non-linear dependencies. Should not be modified.
      :arg dep_index: An :class:`int`. The derivative is defined by
          differentiation of the forward residual with respect to
          `self.dependencies()[dep_index]`.
      :arg adj_X: The adjoint solution. A variable or a :class:`Sequence` of
          variables. Should not be modified.
      :returns: The action of the adjoint of a derivative on the adjoint
          solution. Will be passed to
          :func:`.subtract_adjoint_derivative_action`, and valid types depend
          upon the adjoint variable type. Typically this will be a variable,
          or a two element :class:`tuple` `(alpha, F)`, where `alpha` is a
          :class:`numbers.Complex` and `F` a variable, with the value defined
          by the product of `alpha` and `F`.















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   .. py:method:: adjoint_jacobian_solve(adj_x, nl_deps, b)

      
      Compute an adjoint solution.

      :arg adj_X: Either `None`, or a variable or :class:`Sequence` of
          variables defining the initial guess for an iterative solve. May be
          modified or returned.
      :arg nl_deps: A :class:`Sequence` of variables defining values for
          non-linear dependencies. Should not be modified.
      :arg B: The right-hand-side. A variable or :class:`Sequence` of
          variables storing the value of the right-hand-side. May be modified
          or returned.
      :returns: A variable or :class:`Sequence` of variables storing the
          value of the adjoint solution. May return `None` to indicate a
          value of zero.















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   .. py:method:: tangent_linear(tlm_map)

      
      Derive an :class:`.Equation` corresponding to a tangent-linear
      operation.

      :arg tlm_map: A :class:`.TangentLinearMap` storing values for
          tangent-linear variables.
      :returns: An :class:`.Equation`, corresponding to the tangent-linear
          operation.















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