def get_psd_product(self, vector, dtype=None):
    """Function that provides matrix product interface with PSD matrix.

    Args:
      vector: the vector to be multiplied with matrix M

    Returns:
      result_product: Matrix product of M and vector
    """
    # For convenience, think of x as [\alpha, \beta]
    if dtype is None:
      dtype = self.nn_dtype
    vector = tf.cast(vector, self.nn_dtype)
    alpha = tf.reshape(vector[0], shape=[1, 1])
    beta = vector[1:]
    # Computing the product of matrix_h with beta part of vector
    # At first layer, h is simply diagonal
    h_beta = self.get_h_product(beta)

    # Constructing final result using vector_g
    result = tf.concat(
        [
            alpha * self.nu + tf.reduce_sum(tf.multiply(beta, self.vector_g)),
            tf.multiply(alpha, self.vector_g) + h_beta
        ],
        axis=0)
    return tf.cast(result, dtype)