random¶

Generate MarkovChain and DiscreteDP instances randomly.

quantecon.markov.random.random_discrete_dp(num_states, num_actions, beta=None, k=None, scale=1, sparse=False, sa_pair=False, random_state=None)[source]¶

Generate a DiscreteDP randomly. The reward values are drawn from the normal distribution with mean 0 and standard deviation scale.

Parameters:

num_states : scalar(int): Number of states.
num_actions : scalar(int): Number of actions.
beta : scalar(float), optional(default=None): Discount factor. Randomly chosen from [0, 1) if not specified.
k : scalar(int), optional(default=None): Number of possible next states for each state-action pair. Equal to num_states if not specified.
scale : scalar(float), optional(default=1): Standard deviation of the normal distribution for the reward values.
sparse : bool, optional(default=False): Whether to store the transition probability array in sparse matrix form.
sa_pair : bool, optional(default=False): Whether to represent the data in the state-action pairs formulation. (If sparse=True, automatically set True.)
random_state : int or np.random.RandomState, optional: Random seed (integer) or np.random.RandomState instance to set the initial state of the random number generator for reproducibility. If None, a randomly initialized RandomState is used.

Returns:

ddp : DiscreteDP: An instance of DiscreteDP.

quantecon.markov.random.random_markov_chain(n, k=None, sparse=False, random_state=None)[source]¶

Return a randomly sampled MarkovChain instance with n states, where each state has k states with positive transition probability.

Parameters:

n : scalar(int): Number of states.
k : scalar(int), optional(default=None): Number of states that may be reached from each state with positive probability. Set to n if not specified.
sparse : bool, optional(default=False): Whether to store the transition probability matrix in sparse matrix form.
random_state : int or np.random.RandomState, optional: Random seed (integer) or np.random.RandomState instance to set the initial state of the random number generator for reproducibility. If None, a randomly initialized RandomState is used.

Returns:

mc : MarkovChain

Examples

>>> mc = qe.markov.random_markov_chain(3, random_state=1234)
>>> mc.P
array([[ 0.19151945,  0.43058932,  0.37789123],
       [ 0.43772774,  0.34763084,  0.21464142],
       [ 0.27259261,  0.5073832 ,  0.22002419]])
>>> mc = qe.markov.random_markov_chain(3, k=2, random_state=1234)
>>> mc.P
array([[ 0.19151945,  0.80848055,  0.        ],
       [ 0.        ,  0.62210877,  0.37789123],
       [ 0.56227226,  0.        ,  0.43772774]])

quantecon.markov.random.random_stochastic_matrix(n, k=None, sparse=False, format='csr', random_state=None)[source]¶

Return a randomly sampled n x n stochastic matrix with k nonzero entries for each row.

Parameters:

n : scalar(int): Number of states.
k : scalar(int), optional(default=None): Number of nonzero entries in each row of the matrix. Set to n if not specified.
sparse : bool, optional(default=False): Whether to generate the matrix in sparse matrix form.
format : str, optional(default=’csr’): Sparse matrix format, str in {‘bsr’, ‘csr’, ‘csc’, ‘coo’, ‘lil’, ‘dia’, ‘dok’}. Relevant only when sparse=True.
random_state : int or np.random.RandomState, optional: Random seed (integer) or np.random.RandomState instance to set the initial state of the random number generator for reproducibility. If None, a randomly initialized RandomState is used.

Returns:

P : numpy ndarray or scipy sparse matrix (float, ndim=2): Stochastic matrix.