.. _LinearCombinationVariable:


Linear combination variable
---------------------------


 

This variable describes a linear combination  :math:`c_0 + c_1 \cdot y_1 + \cdots + c_N \cdot y_N` of :math:`N` inputs  :math:`y_1, y_2, \cdots, y_N` stemming either from a surrogate with :math:`N` inputs or from any set of :math:`N` variables.

.. _ActiveLearning.LinearCombination.name:


name (str)
""""""""""
   The name of the variable under which it can be addressed by other variables or objectives. The name must be distinct from any surrogate name. 

   Default: ``'v'``

.. _ActiveLearning.LinearCombination.coefficients:


coefficients (list)
"""""""""""""""""""
   List of coefficients :math:`(c_0, c_1, ..., c_N)`  that determines the linear combination. Any entry of the list can be either a numbers or a string that determines an expression depending only on variables  without uncertainty  (e.g. parameter names of the design space). 

   Default: Average of the inputs, i.e. :math:`c_0=0, c_1 = c_2 = \dots = c_N = \frac{1}{N}`.

   .. admonition:: Example

      Mixed expression and numeric coefficients for  :math:`N=3` inputs.  Here, ``param1, param2`` are parameters of the  design space and not variable names.

      .. code-block:: python

         ['sin(param1)^2 + cos(param2)^2',0.1,-123.0]


.. _ActiveLearning.LinearCombination.inputs:


inputs (list[str])
""""""""""""""""""
   List of the names of surrogates or other  variables. The sum of the output dimensions of the surrogates  and the output dimensions of the variables must add up to `N`. 

   Default: This value has no default and must be provided