bluemira.equilibria.optimisation.problem._tikhonov
==================================================

.. py:module:: bluemira.equilibria.optimisation.problem._tikhonov


Classes
-------

.. autoapisummary::

   bluemira.equilibria.optimisation.problem._tikhonov.TikhonovCurrentCOP
   bluemira.equilibria.optimisation.problem._tikhonov.UnconstrainedTikhonovCurrentGradientCOP


Module Contents
---------------

.. py:class:: TikhonovCurrentCOP(eq: bluemira.equilibria.equilibrium.Equilibrium, targets: bluemira.equilibria.optimisation.constraints.MagneticConstraintSet, gamma: float, opt_algorithm: bluemira.optimisation.AlgorithmType = Algorithm.SLSQP, opt_conditions: dict[str, float | int] | None = None, opt_parameters: dict[str, float] | None = None, max_currents: numpy.typing.ArrayLike | None = None, constraints: list[bluemira.equilibria.optimisation.constraints.UpdateableConstraint] | None = None)

   Bases: :py:obj:`bluemira.equilibria.optimisation.problem.base.EqCoilsetOptimisationProblem`

   .. autoapi-inheritance-diagram:: bluemira.equilibria.optimisation.problem._tikhonov.TikhonovCurrentCOP
      :parts: 1
      :private-bases:


   Coilset OptimisationProblem for coil currents subject to maximum current bounds.

   Coilset currents optimised using objectives.regularised_lsq_objective as
   objective function.

   :param eq: Equilibrium object (used to update magnetic field targets)
              with Coilset to optimise.
   :param targets: Set of magnetic field targets to use in objective function.
   :param gamma: Tikhonov regularisation parameter in units of [A⁻¹].
   :param opt_algorithm: Optimiser algorithm
   :param opt_conditions: optimiser conditions
                          for defaults see
                          :class:`~bluemira.optimisation._algorithm.AlgorithDefaultTolerances`
                          along with `max_eval=100`
   :param opt_parameters: optimisation parameters
   :param max_currents: Maximum allowed current for each independent coil current in coilset [A].
                        If specified as a float, the float will set the maximum allowed current
                        for all coils.
   :param constraints: Optional list of UpdatableConstraint objects storing
                       information about constraints that must be satisfied
                       during the coilset optimisation, to be provided to the
                       optimiser.


   .. py:attribute:: gamma


   .. py:method:: optimise(x0=None, *, fixed_coils=True, keep_history: bool = False, check_constraints: bool = False, verbose: bool = False) -> bluemira.equilibria.optimisation.problem.base.CoilsetOptimiserResult

      Solve the optimisation problem

      :param fixed_coils: Whether or not to update to coilset response matrices

      :returns: Optimised CoilSet
      :rtype: coilset



.. py:class:: UnconstrainedTikhonovCurrentGradientCOP(eq: bluemira.equilibria.equilibrium.Equilibrium, targets: bluemira.equilibria.optimisation.constraints.MagneticConstraintSet, gamma: float, opt_algorithm: bluemira.optimisation.AlgorithmType = Algorithm.SLSQP, opt_conditions: dict[str, float | int] | None = None, opt_parameters: dict[str, float] | None = None, max_currents: numpy.typing.ArrayLike | None = None)

   Bases: :py:obj:`bluemira.equilibria.optimisation.problem.base.EqCoilsetOptimisationProblem`

   .. autoapi-inheritance-diagram:: bluemira.equilibria.optimisation.problem._tikhonov.UnconstrainedTikhonovCurrentGradientCOP
      :parts: 1
      :private-bases:


   Unbounded, unconstrained, analytically optimised current gradient vector for minimal
   error to the L2-norm of a set of magnetic constraints (used here as targets).

   This is useful for getting a preliminary Equilibrium

   :param eq: Equilibrium object (used to update magnetic field targets)
              with Coilset to optimise.
   :param targets: Set of magnetic constraints to minimise the error for
   :param gamma: Tikhonov regularisation parameter [1/A]


   .. py:attribute:: gamma


   .. py:method:: optimise(**_) -> bluemira.equilibria.optimisation.problem.base.CoilsetOptimiserResult

      Optimise the prescribed problem.

      .. rubric:: Notes

      The weight vector is used to scale the response matrix and
      constraint vector. The weights are assumed to be uncorrelated, such that the
      weight matrix W_ij used to define (for example) the least-squares objective
      function (Ax - b)ᵀ W (Ax - b), is diagonal, such that
      weights[i] = w[i] = sqrt(W[i,i]).