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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def coupling_matrix(self, lmax, nwin=None, weights=None, mode='full'):
 """ Return the coupling matrix of the first nwin tapers. This matrix relates the global power spectrum to the expectation of the localized multitaper spectrum. Usage ----- Mmt = x.coupling_matrix(lmax, [nwin, weights, mode]) Returns ------- Mmt : ndarray, shape (lmax+lwin+1, lmax+1) or (lmax+1, lmax+1) or (lmax-lwin+1, lmax+1) Parameters lmax : int Spherical harmonic bandwidth of the global power spectrum. nwin : int, optional, default = x.nwin Number of tapers used in the mutlitaper spectral analysis. weights : ndarray, optional, default = x.weights Taper weights used with the multitaper spectral analyses. mode : str, opitonal, default = 'full' 'full' returns a biased output spectrum of size lmax+lwin+1. The input spectrum is assumed to be zero for degrees l>lmax. 'same' returns a biased output spectrum with the same size (lmax+1) as the input spectrum. The input spectrum is assumed to be zero for degrees l>lmax. 'valid' returns a biased spectrum with size lmax-lwin+1. This returns only that part of the biased spectrum that is not influenced by the input spectrum beyond degree lmax. """

        if weights is not None:
            if nwin is not None:
                if len(weights) != nwin:
                    raise ValueError(
                        'Length of weights must be equal to nwin. ' +
                        'len(weights) = {:d}, nwin = {:d}'.format(len(weights),
                                                                  nwin))
            else:
                if len(weights) != self.nwin:
                    raise ValueError(
                        'Length of weights must be equal to nwin. ' +
                        'len(weights) = {:d}, nwin = {:d}'.format(len(weights),
                                                                  self.nwin))

        if mode == 'full':
            return self._coupling_matrix(lmax, nwin=nwin, weights=weights)
        elif mode == 'same':
            cmatrix = self._coupling_matrix(lmax, nwin=nwin,
                                            weights=weights)
            return cmatrix[:lmax+1, :]
        elif mode == 'valid':
            cmatrix = self._coupling_matrix(lmax, nwin=nwin,
                                            weights=weights)
            return cmatrix[:lmax - self.lwin+1, :]
        else:
            raise ValueError("mode has to be 'full', 'same' or 'valid', not "
                             "{}".format(mode))