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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 _log_multivariate_normal_density_diag(X, means, covars):
 """Compute Gaussian log-density at X for a diagonal model."""

    n_samples, n_dim = X.shape
    lpr = -0.5 * (n_dim * np.log(2 * np.pi) + np.sum(np.log(covars), 1)
                  + np.sum((means ** 2) / covars, 1)
                  - 2 * np.dot(X, (means / covars).T)
                  + np.dot(X ** 2, (1.0 / covars).T))
    return lpr