Random MarkovChain

examples/lucas_stokey.py

@@ -9,7 +9,7 @@
 from scipy.optimize import fmin_slsqp
 from scipy.interpolate import UnivariateSpline
 from quantecon import compute_fixed_point
-from quantecon.mc_tools import mc_sample_path
+from quantecon.markov import mc_sample_path
 
 
 class Planners_Allocation_Sequential(object):

quantecon/__init__.py

@@ -9,21 +9,22 @@
 from .estspec import smooth, periodogram, ar_periodogram
 from .graph_tools import DiGraph
 from .gridtools import cartesian, mlinspace
-from .gth_solve import gth_solve
 from .kalman import Kalman
 from .lae import LAE
 from .arma import ARMA
 from .lqcontrol import LQ
 from .lqnash import nnash
 from .lss import LinearStateSpace
 from .matrix_eqn import solve_discrete_lyapunov, solve_discrete_riccati
-from .mc_tools import MarkovChain, mc_compute_stationary, mc_sample_path
 from .quadsums import var_quadratic_sum, m_quadratic_sum
+#->Propose Delete From Top Level
+from .markov import MarkovChain, random_markov_chain, random_stochastic_matrix, gth_solve, tauchen 	 #Promote to keep current examples working
+from .markov import mc_compute_stationary, mc_sample_path 							#Imports that Should be Deprecated with markov package
+#<-
 from .rank_nullspace import rank_est, nullspace
 from .robustlq import RBLQ
-from .tauchen import approx_markov
 from . import quad as quad
-from .utilities import searchsorted
+from .util import searchsorted
 
 #Add Version Attribute
 from .version import version as __version__

quantecon/markov/__init__.py

@@ -0,0 +1,9 @@
+"""
+Markov Chain SubPackge API
+"""
+
+from .core import MarkovChain
+from .core import mc_compute_stationary, mc_sample_path 			#-Future Deprecation-#
+from .gth_solve import gth_solve
+from .random import random_markov_chain, random_stochastic_matrix
+from .approximation import tauchen

quantecon/tauchen.py → quantecon/markov/approximation.py

@@ -1,8 +1,10 @@
 """
-Filename: tauchen.py
+Filename: approximation.py
 
 Authors: Thomas Sargent, John Stachurski
 
+tauchen
+-------
 Discretizes Gaussian linear AR(1) processes via Tauchen's method
 
 """
@@ -11,7 +13,7 @@
 from scipy.stats import norm
 
 
-def approx_markov(rho, sigma_u, m=3, n=7):
+def tauchen(rho, sigma_u, m=3, n=7):
     """
     Computes the Markov matrix associated with a discretized version of
     the linear Gaussian AR(1) process

quantecon/mc_tools.py → quantecon/markov/core.py

@@ -2,7 +2,7 @@
 Authors: Chase Coleman, Spencer Lyon, Daisuke Oyama, Tom Sargent,
          John Stachurski
 
-Filename: mc_tools.py
+Filename: core.py
 
 This file contains some useful objects for handling a finite-state
 discrete-time Markov chain.
@@ -88,12 +88,12 @@
 import numpy as np
 from fractions import gcd
 import sys
-from .graph_tools import DiGraph
 from .gth_solve import gth_solve
+from ..graph_tools import DiGraph
 
 # -Check if Numba is Available- #
-from .external import numba_installed, jit
-from .utilities import searchsorted
+from ..external import numba_installed, jit
+from ..util import searchsorted
 
 
 class MarkovChain(object):

quantecon/gth_solve.py → quantecon/markov/gth_solve.py

@@ -10,7 +10,7 @@
 import numpy as np
 from numba import jit
 
-from .external import numba_installed, jit
+from ..external import numba_installed, jit
 if not numba_installed:
     try:
         xrange

quantecon/markov/random.py

@@ -0,0 +1,141 @@
+"""
+Filename: random.py
+
+Author: Daisuke Oyama
+
+Generate a MarkovChain randomly.
+
+"""
+import numpy as np
+import scipy.sparse
+
+from .core import MarkovChain
+from ..external import numba_installed, jit
+from ..util import check_random_state
+from ..random import (
+    probvec, sample_without_replacement
+)
+
+
+def random_markov_chain(n, k=None, sparse=False, random_state=None):
+    """
+    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. (Sparse format is not yet implemented.)
+
+    random_state : scalar(int) or np.random.RandomState,
+                   optional(default=None)
+        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]])
+
+    """
+    if sparse:
+        raise NotImplementedError
+    P = random_stochastic_matrix(n, k, sparse, format='csr',
+                                 random_state=random_state)
+    mc = MarkovChain(P)
+    return mc
+
+
+def random_stochastic_matrix(n, k=None, sparse=False, format='csr',
+                             random_state=None):
+    """
+    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 in {'bsr', 'csr', 'csc', 'coo', 'lil', 'dia', 'dok'},
+             optional(default='csr')
+        Sparse matrix format. Relevant only when sparse=True.
+
+    random_state : scalar(int) or np.random.RandomState,
+                   optional(default=None)
+        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.
+
+    See also
+    --------
+    random_markov_chain : Return a random MarkovChain instance.
+
+    """
+    if not (isinstance(n, int) and n > 0):
+        raise ValueError('n must be a positive integer')
+    if k is None:
+        k = n
+    if not (isinstance(k, int) and 0 < k <= n):
+        raise ValueError('k must be an integer with 0 < k <= n')
+
+    # n prob vectors of dimension k, shape (n, k)
+    probvecs = probvec(n, k, random_state=random_state)
+
+    if k == n:
+        P = probvecs
+        if sparse:
+            return scipy.sparse.coo_matrix(P).asformat(format)
+        else:
+            return P
+
+    # if k < n:
+    rows = np.repeat(np.arange(n), k)
+    cols = \
+        sample_without_replacement(
+            n, k, num_trials=n, random_state=random_state
+        ).ravel()
+    data = probvecs.ravel()
+
+    if sparse:
+        P = scipy.sparse.coo_matrix((data, (rows, cols)), shape=(n, n))
+        return P.asformat(format)
+    else:
+        P = np.zeros((n, n))
+        P[rows, cols] = data
+        return P

quantecon/tests/test_tauchen.py → quantecon/markov/tests/test_approximation.py

@@ -1,28 +1,28 @@
 """
-Filename: test_tauchen.py
+Filename: test_approximation.py
 Authors: Chase Coleman
 Date: 07/18/2014
 
-Tests for tauchen.py file
+Tests for approximation.py file (i.e. tauchen)
 
 """
 import sys
 import os
 import unittest
 import numpy as np
 from numpy.testing import assert_allclose
-from quantecon.tauchen import approx_markov
+from quantecon.markov import tauchen
 
 
-class TestApproxMarkov(unittest.TestCase):
+class TestTauchen(unittest.TestCase):
 
     def setUp(self):
         self.rho, self.sigma_u = np.random.rand(2)
         self.n = np.random.random_integers(3, 25)
         self.m = np.random.random_integers(4)
         self.tol = 1e-12
 
-        self.x, self.P = approx_markov(self.rho, self.sigma_u, self.m, self.n)
+        self.x, self.P = tauchen(self.rho, self.sigma_u, self.m, self.n)
 
     def tearDown(self):
         del self.x
@@ -51,5 +51,5 @@ def test_states_sum_0(self):
 
 
 if __name__ == '__main__':
-    suite = unittest.TestLoader().loadTestsFromTestCase(TestApproxMarkov)
+    suite = unittest.TestLoader().loadTestsFromTestCase(TestTauchen)
     unittest.TextTestRunner(verbosity=2, stream=sys.stderr).run(suite)

quantecon/tests/test_mc_tools.py → quantecon/markov/tests/test_core.py

@@ -13,11 +13,11 @@
 from numpy.testing import assert_allclose, assert_array_equal
 from nose.tools import eq_, raises
 
-from quantecon.mc_tools import (
+from quantecon.markov import (
     MarkovChain, mc_compute_stationary, mc_sample_path
 )
 
-from ..external import numba_installed, jit
+from quantecon.external import numba_installed, jit
 
 
 def list_of_array_equal(s, t):

quantecon/tests/test_gth_solve.py → quantecon/markov/tests/test_gth_solve.py

@@ -11,7 +11,7 @@
 from numpy.testing import assert_array_equal
 from nose.tools import eq_, ok_, raises
 
-from quantecon.gth_solve import gth_solve
+from quantecon.markov import gth_solve
 
 
 TOL = 1e-15