def update_alpha(self, gammat, rho):
        """
        Update parameters for the Dirichlet prior on the per-document
        topic weights `alpha` given the last `gammat`.

        Uses Newton's method: http://www.stanford.edu/~jhuang11/research/dirichlet/dirichlet.pdf

        """
        N = float(len(gammat))
        logphat = sum(dirichlet_expectation(gamma) for gamma in gammat) / N
        dalpha = numpy.copy(self.alpha)
        gradf = N * (psi(numpy.sum(self.alpha)) - psi(self.alpha) + logphat)

        c = N * polygamma(1, numpy.sum(self.alpha))
        q = -N * polygamma(1, self.alpha)

        b = numpy.sum(gradf / q) / ( 1 / c + numpy.sum(1 / q))

        dalpha = -(gradf - b) / q

        if all(rho() * dalpha + self.alpha > 0):
            self.alpha += rho() * dalpha
        else:
            logger.warning("updated alpha not positive")
        logger.info("optimized alpha %s" % list(self.alpha))

        return self.alpha
dataset/ETHPy150Open largelymfs/topical_word_embeddings/TWE-1/gensim/models/ldamodel.py/LdaModel.update_alpha/original