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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 feature_TIC_correlation(self):
 r"""Instantaneous correlation matrix between mean-free input features and TICs Denoting the input features as :math:`X_i` and the TICs as :math:`\theta_j`, the instantaneous, linear correlation between them can be written as .. math:: \mathbf{Corr}(X_i - \mu_i, \mathbf{\theta}_j) = \frac{1}{\sigma_{X_i - \mu_i}}\sum_l \sigma_{(X_i - \mu_i)(X_l - \mu_l} \mathbf{U}_{li} The matrix :math:`\mathbf{U}` is the matrix containing, as column vectors, the eigenvectors of the TICA generalized eigenvalue problem . Returns ------- feature_TIC_correlation : ndarray(n,m) correlation matrix between input features and TICs. There is a row for each feature and a column for each TIC. """

        feature_sigma = np.sqrt(np.diag(self.cov))
        return np.dot(self.cov, self.eigenvectors[:, : self.dimension()]) / feature_sigma[:, np.newaxis]