netsse.analys.emep.norm_resp
============================

.. py:function:: netsse.analys.emep.norm_resp(Rxy_ReIm, TRF, S1D, f, mn=None, ReIm=None, Na=None, axy=None)

   Normalizes the response spectra and transfer functions for application of the EMEP method.

   .. note::
       The normalization factors are found in Bendat & Piersol (2010).

   :param Rxy_ReIm: Response spectra as a function of frequency ``f``, considering `Nxy` pairs of responses.
   :type Rxy_ReIm: array_like of shape (Nfreq,Nxy)
   :param TRF: Transfer functions for `Nresp` different responses, as functions of wave direction and frequency ``f``.
   :type TRF: Multidimensional array of shape (Nresp,Ntheta,Nfreq)
   :param S1D: 1-D wave spectrum, as a function of frequency ``f``.
   :type S1D: array_like of shape (Nfreq,)
   :param f: Vector of wave frequencies.
   :type f: array_like of shape (Nfreq,)
   :param mn: Definition of the considered responses in ``Rxy_ReIm``. Elements in ``mn`` correspond to the indices of the pairs of
              responses along the first dimension of ``TRF``, i.e., from 0 to `Nresp`-1.
              Default is ``None``; in that case, the response pairs are ordered in the following order (illustrated for `Nresp = 3`):

              ``Rxy_ReIm = [Re(R00),Re(R11),Re(R22),Re(R01),Re(R02),Re(R12),Im(R01),Im(R02),Im(R12)]``

              ``mn = [[0, 0], [1, 1], [2, 2], [0, 1], [0, 2], [1, 2], [0, 1], [0, 2], [1, 2]]``
   :type mn: array_like of shape (Nxy,2), optional
   :param ReIm: Vector indicating whether the real part (``'R'``) or imaginary part (``'I'``) of the response cross-spectrum is considered
                in ``Rxy_ReIm``.
                Default is ``None``; in that case, the real and imaginary parts of the response pairs are ordered in the order
                shown above, thus:

                ``ReIm = ['R', 'R', 'R', 'R', 'R', 'R', 'I', 'I', 'I']``
   :type ReIm: array_like of shape (Nxy,) or (Nxy,1), optional
   :param Na: Number of the ensembled average for computation of the response spectra variance. Default is ``None``, for which case ``Na = 1``.
   :type Na: str, or array_like of shape (Nxy,), optional
   :param axy: Additional weights (must be positive). Any weight greater than zero increases the importance given to a corresponding pair of
               responses in the EMEP method. Default is ``None``, for which case the weights are set to zero.
   :type axy: array_like of shape (Nxy,), optional

   :returns: * **Rxy_ReIm_n** (*array_like of shape (Nfreq,Nxy)*) -- Normalized version of the response spectra.
             * **Hn** (*array_like of shape (Ntheta,Nfreq,Nxy)*) -- Normalized version of the real and imaginary parts of the product of the transfer functions for pairs of responses.
               The real and imaginary parts for the pairs of responses are output in the same order as ``Rxy_ReIm``.

   .. seealso::

      :obj:`emep`
          Extended Maximum Entropy Principle (EMEP) method for reconstructing the directional spreading function based on the cross-power spectra of measured wave-induced responses.

   .. rubric:: References

   Bendat, J. S., & Piersol, A. G. (2010). Random Data: Analysis and Measurement Procedures. In Measurement Science and
   Technology (Vol. 11, Issue 12). Wiley. https://doi.org/10.1002/9781118032428

   .. rubric:: Example

   >>> Rxy_ReIm_n, Hn = norm_resp(Rxy_ReIm,TRF,S1D,f,mn=None,ReIm=None,Na=None,axy=None)