Merge pull request #204 from QuantEcon/ddp-fix

DiscreteDP: further fix in docstring

Author: mmcky

quantecon/markov/ddp.py

@@ -23,16 +23,16 @@
   \Delta(S)`, where :math:`q(s'|s, a)` is the probability that the state
   in the next period is :math:`s'` when the current state is :math:`s`
   and the action chosen is :math:`a`; and
-* discount factor :math:`\beta \in [0, 1)`.
+* discount factor :math:`0 \leq \beta < 1`.
 
 For a policy function :math:`\sigma`, let :math:`r_{\sigma}` and
 :math:`Q_{\sigma}` be the reward vector and the transition probability
 matrix for :math:`\sigma`, which are defined by :math:`r_{\sigma}(s) =
 r(s, \sigma(s))` and :math:`Q_{\sigma}(s, s') = q(s'|s, \sigma(s))`,
 respectively. The policy value function :math:`v_{\sigma}` for
-:math`\sigma` is defined by
+:math:`\sigma` is defined by
 
-..math::
+.. math::
 
     v_{\sigma}(s) = \sum_{t=0}^{\infty}
                     \beta^t (Q_{\sigma}^t r_{\sigma})(s)
@@ -45,23 +45,23 @@
 
 The *Bellman equation* is written as
 
-..math::
+.. math::
 
     v(s) = \max_{a \in A(s)} r(s, a)
            + \beta \sum_{s' \in S} q(s'|s, a) v(s') \quad (s \in S).
 
 The *Bellman operator* :math:`T` is defined by the right hand side of
 the Bellman equation:
 
-..math::
+.. math::
 
     (T v)(s) = \max_{a \in A(s)} r(s, a)
                + \beta \sum_{s' \in S} q(s'|s, a) v(s') \quad (s \in S).
 
 For a policy function :math:`\sigma`, the operator :math:`T_{\sigma}` is
 defined by
 
-..math::
+.. math::
 
     (T_{\sigma} v)(s) = r(s, \sigma(s))
                         + \beta \sum_{s' \in S} q(s'|s, \sigma(s)) v(s')
@@ -117,7 +117,7 @@
 
 
 class DiscreteDP(object):
-    """
+    r"""
     Class for dealing with a discrete dynamic program.
 
     There are two ways to represent the data for instantiating a
@@ -165,7 +165,7 @@ class DiscreteDP(object):
         Transition probability array.
 
     beta : scalar(float)
-        Discount factor. Must be in [0, 1).
+        Discount factor. Must be 0 <= beta < 1.
 
     s_indices : array_like(int, ndim=1), optional(default=None)
         Array containing the indices of the states.
@@ -297,7 +297,7 @@ def __init__(self, R, Q, beta, s_indices=None, a_indices=None):
             raise ValueError('R must be 1- or 2-dimensional')
 
         msg_dimension = 'dimensions of R and Q must be either 1 and 2, ' \
-                        'of 2 and 3'
+                        'or 2 and 3'
         msg_shape = 'shapes of R and Q must be either (n, m) and (n, m, n), ' \
                     'or (L,) and (L, n)'