Convert some docstrings to numpydoc and improve rendering

theano/gradient.py

@@ -44,6 +44,7 @@ grad_time = 0
 def format_as(use_list, use_tuple, outputs):
     """
     Formats the outputs according to the flags `use_list` and `use_tuple`.
+
     If `use_list` is True, `outputs` is returned as a list (if `outputs`
     is not a list or a tuple then it is converted in a one element list).
     If `use_tuple` is True, `outputs` is returned as a tuple (if `outputs`
@@ -163,20 +164,23 @@ disconnected_type = DisconnectedType()
 def Rop(f, wrt, eval_points, disconnected_outputs="raise",
         return_disconnected="zero"):
     """
-    Computes the R operation on `f` wrt to `wrt` evaluated at points given
-    in `eval_points`. Mathematically this stands for the jacobian of `f` wrt
+    Computes the R operation on `f` wrt to `wrt` at `eval_points`.
+
+    Mathematically this stands for the jacobian of `f` wrt
     to `wrt` right muliplied by the eval points.
 
-    :type f: Variable or list of Variables
-             `f` stands for the output of the computational graph to which you
-             want to apply the R operator
-    :type wrt: Variable or list of `Variables`s
-               variables for which you compute the R operator of the expression
-               described by `f`
-    :type eval_points: Variable or list of Variables
-                       evalutation points for each of the variables in `wrt`
-    :type disconnected_outputs: str
-        Defines the behaviour if some of the variables in `f` are
+    Parameters
+    ----------
+    f: :class:`~theano.gof.graph.Variable` or list of Variables
+        `f` stands for the output of the computational graph to which you
+        want to apply the R operator
+    wrt: :class:`~theano.gof.graph.Variable` or list of Variables
+        variables for which you compute the R operator of the expression
+        described by `f`
+    eval_points: :class:`~theano.gof.graph.Variable` or list of Variables
+        evalutation points for each of the variables in `wrt`
+    disconnected_outputs: str
+        Defines the behaviour if some of the variables in `f`
         have no dependency on any of the variable in `wrt` (or if
         all links are non-differentiable). The possible values are:
 
@@ -184,16 +188,18 @@ def Rop(f, wrt, eval_points, disconnected_outputs="raise",
         - 'warn': consider the gradient zero, and print a warning.
         - 'raise': raise DisconnectedInputError.
 
-    :type return_disconnected : {'zero', 'None', 'Disconnected'}
+    return_disconnected : {'zero', 'None', 'Disconnected'}
         - 'zero' : If wrt[i] is disconnected, return value i will be
-                   wrt[i].zeros_like()
+          wrt[i].zeros_like()
         - 'None' : If wrt[i] is disconnected, return value i will be
-                   None
+          None
         - 'Disconnected' : returns variables of type DisconnectedType
 
-    :rtype: :class:`~theano.gof.Variable` or list/tuple of Variables depending on type of f
-    :return: symbolic expression such that
-        R_op[i] = sum_j ( d f[i] / d wrt[j]) eval_point[j]
+    Returns
+    -------
+    :class:`~theano.gof.graph.Variable` or list/tuple of Variables depending on type of f
+        Symbolic expression such that
+        R_op[i] = sum_j (d f[i] / d wrt[j]) eval_point[j]
         where the indices in that expression are magic multidimensional
         indices that specify both the position within a list and all
         coordinates of the tensor element in the last.
@@ -349,22 +355,27 @@ def Rop(f, wrt, eval_points, disconnected_outputs="raise",
 def Lop(f, wrt, eval_points, consider_constant=None,
         disconnected_inputs='raise'):
     """
-    Computes the L operation on `f` wrt to `wrt` evaluated at points given
-    in `eval_points`. Mathematically this stands for the jacobian of `f` wrt
+    Computes the L operation on `f` wrt to `wrt` at `eval_points`.
+
+    Mathematically this stands for the jacobian of `f` wrt
     to `wrt` left muliplied by the eval points.
 
-    :type f: Variable or list of Variables
+    Parameters
+    ----------
+    f: :class:`~theano.gof.graph.Variable` or list of Variables
         `f` stands for the output of the computational graph to which you
         want to apply the L operator
-    :type wrt: Variable or list of `Variables`s
+    wrt: :class:`~theano.gof.graph.Variable` or list of Variables
         variables for which you compute the L operator of the expression
         described by `f`
-    :type eval_points: Variable or list of Variables
-                        evalutation points for each of the variables in `f`
+    eval_points: :class:`~theano.gof.graph.Variable` or list of Variables
+        evalutation points for each of the variables in `f`
 
-    :rtype: :class:`~theano.gof.Variable` or list/tuple of Variables depending on type of f
-    :return: symbolic expression such that
-        L_op[i] = sum_i ( d f[i] / d wrt[j]) eval_point[i]
+    Returns
+    -------
+    :class:`~theano.gof.Variable` or list/tuple of Variables depending on type of f
+        Symbolic expression such that
+        L_op[i] = sum_i (d f[i] / d wrt[j]) eval_point[i]
         where the indices in that expression are magic multidimensional
         indices that specify both the position within a list and all
         coordinates of the tensor element in the last
@@ -414,10 +425,10 @@ def grad(cost, wrt, consider_constant=None,
 
     Parameters
     ----------
-    cost : :class:`~theano.gof.Variable` scalar (0-dimensional) tensor variable or None
+    cost : :class:`~theano.gof.graph.Variable` scalar (0-dimensional) tensor variable or None
         Value with respect to which we are differentiating.  May be
         `None` if known_grads is provided.
-    wrt : :class:`~theano.gof.Variable` or list of Variables
+    wrt : :class:`~theano.gof.graph.Variable` or list of Variables
         term[s] for which we want gradients
     consider_constant : list of variables
         expressions not to backpropagate through
@@ -439,9 +450,9 @@ def grad(cost, wrt, consider_constant=None,
         variables but do not know the original cost.
     return_disconnected : {'zero', 'None', 'Disconnected'}
         - 'zero' : If wrt[i] is disconnected, return value i will be
-                   wrt[i].zeros_like()
+          wrt[i].zeros_like()
         - 'None' : If wrt[i] is disconnected, return value i will be
-                   None
+          None
         - 'Disconnected' : returns variables of type DisconnectedType
     null_gradients : {'raise', 'return'}
         Defines the behaviour if some of the variables in `wrt` have a
@@ -453,7 +464,7 @@ def grad(cost, wrt, consider_constant=None,
     Returns
     -------
     variable or list/tuple of variables (matches `wrt`)
-        symbolic expression of gradient of `cost` with respect to each
+        Symbolic expression of gradient of `cost` with respect to each
         of the `wrt` terms.  If an element of `wrt` is not
         differentiable with respect to the output, then a zero
         variable is returned.
@@ -670,50 +681,46 @@ def subgraph_grad(wrt, end, start=None, cost=None, details=False):
             next_grad = dict(zip(grad_ends[i], next_grad))
             param_grads.extend(param_grad)
 
-    :type wrt: list of variables
-    :param wrt:
-      Gradients are computed with respect to `wrt`.
+    Parameters
+    ----------
 
-    :type end: list of variables
-    :param end:
-      Theano variables at which to end gradient descent (they are
-      considered constant in theano.grad).  For convenience, the
-      gradients with respect to these variables are also returned.
+    wrt: list of variables
+        Gradients are computed with respect to `wrt`.
 
-    :type start: dictionary of variables
-    :param start:
-      If not None, a dictionary mapping variables to their
-      gradients. This is useful when the gradient on some variables
-      are known. These are used to compute the gradients backwards up
-      to the variables in `end` (they are used as known_grad in
-      theano.grad).
+    end: list of variables
+        Theano variables at which to end gradient descent (they are
+        considered constant in theano.grad).  For convenience, the
+        gradients with respect to these variables are also returned.
 
-    :type cost: :class:`~theano.gof.Variable` scalar (0-dimensional) variable
-    :param cost:
-      Additional costs for which to compute the gradients.  For
-      example, these could be weight decay, an l1 constraint, MSE,
-      NLL, etc. May optionally be None if start is provided.  Warning
-      : If the gradients of `cost` with respect to any of the `start`
-      variables is already part of the `start` dictionary, then it may
-      be counted twice with respect to `wrt` and `end`.
+    start: dictionary of variables
+        If not None, a dictionary mapping variables to their
+        gradients. This is useful when the gradient on some variables
+        are known. These are used to compute the gradients backwards up
+        to the variables in `end` (they are used as known_grad in
+        theano.grad).
 
-      .. warning::
+    cost: :class:`~theano.gof.Variable` scalar (0-dimensional) variable
+        Additional costs for which to compute the gradients.  For
+        example, these could be weight decay, an l1 constraint, MSE,
+        NLL, etc. May optionally be None if start is provided.
 
-        If the gradients of `cost` with respect to any of the `start`
-        variables is already part of the `start` dictionary, then it
-        may be counted twice with respect to `wrt` and `end`.
+        .. warning::
 
+            If the gradients of `cost` with respect to any of the `start`
+            variables is already part of the `start` dictionary, then it
+            may be counted twice with respect to `wrt` and `end`.
 
-    :type details: bool
-    :param details:
-      When True, additionally returns the list of gradients from
-      `start` and of `cost`, respectively, with respect to `wrt` (not
-      `end`).
+    details: bool
+        When True, additionally returns the list of gradients from
+        `start` and of `cost`, respectively, with respect to `wrt` (not
+        `end`).
 
-    :rtype: Tuple of 2 or 4 Lists of Variables
+    Returns
+    -------
+    Tuple of 2 or 4 Lists of Variables
+        Returns lists of gradients with respect to `wrt` and `end`,
+        respectively.
 
-    :return: Returns lists of gradients with respect to `wrt` and `end`,
-            respectively.
 
     .. versionadded:: 0.7
     '''
@@ -1813,26 +1820,31 @@ verify_grad.E_grad = GradientError
 def jacobian(expression, wrt, consider_constant=None,
              disconnected_inputs='raise'):
     """
-    :type expression: Vector (1-dimensional) Variable
-    :type wrt: Variable or list of Variables
+    Compute the full Jacobian
 
-    :param consider_constant: a list of expressions not to backpropagate
-        through
+    Parameters
+    ----------
+    expression: Vector (1-dimensional) :class:`~theano.gof.graph.Variable`
+    wrt: :class:`~theano.gof.graph.Variable` or list of Variables
+    consider_constant:
+        a list of expressions not to backpropagate through
 
-    :type disconnected_inputs: string
-    :param disconnected_inputs: Defines the behaviour if some of the variables
+    disconnected_inputs: string
+        Defines the behaviour if some of the variables
         in ``wrt`` are not part of the computational graph computing ``cost``
         (or if all links are non-differentiable). The possible values are:
+
         - 'ignore': considers that the gradient on these parameters is zero.
         - 'warn': consider the gradient zero, and print a warning.
         - 'raise': raise an exception.
 
-    :return: either a instance of Variable or list/tuple of Variables
-            (depending upon `wrt`) repesenting the jacobian of `expression`
-            with respect to (elements of) `wrt`. If an element of `wrt` is not
-            differentiable with respect to the output, then a zero
-            variable is returned. The return value is of same type
-            as `wrt`: a list/tuple or TensorVariable in all cases.
+    Returns
+    -------
+    :class:`~theano.gof.graph.Variable` or list/tuple of Variables (depending upon `wrt`)
+        The jacobian of `expression` with respect to (elements of) `wrt`.
+        If an element of `wrt` is not differentiable with respect to the
+        output, then a zero variable is returned. The return value is
+        of same type as `wrt`: a list/tuple or TensorVariable in all cases.
     """
     from theano.tensor import arange
     # Check inputs have the right format
@@ -1886,27 +1898,29 @@ def jacobian(expression, wrt, consider_constant=None,
 def hessian(cost, wrt, consider_constant=None,
             disconnected_inputs='raise'):
     """
-    :type cost: Scalar (0-dimensional) Variable.
-    :type wrt: Vector (1-dimensional tensor) 'Variable' or list of
-               vectors (1-dimensional tensors) Variables
-
-    :param consider_constant: a list of expressions not to backpropagate
-        through
-
-    :type disconnected_inputs: string
-    :param disconnected_inputs: Defines the behaviour if some of the variables
+    Parameters
+    ----------
+    cost: Scalar (0-dimensional) variable.
+    wrt: Vector (1-dimensional tensor) 'Variable' or list of
+    vectors (1-dimensional tensors) Variables
+    consider_constant:
+        a list of expressions not to backpropagate through
+    disconnected_inputs: string
+        Defines the behaviour if some of the variables
         in ``wrt`` are not part of the computational graph computing ``cost``
         (or if all links are non-differentiable). The possible values are:
+
         - 'ignore': considers that the gradient on these parameters is zero.
         - 'warn': consider the gradient zero, and print a warning.
         - 'raise': raise an exception.
 
-    :return: either a instance of Variable or list/tuple of Variables
-            (depending upon `wrt`) repressenting the Hessian of the `cost`
-            with respect to (elements of) `wrt`. If an element of `wrt` is not
-            differentiable with respect to the output, then a zero
-            variable is returned. The return value is of same type
-            as `wrt`: a list/tuple or TensorVariable in all cases.
+    Returns
+    -------
+    :class:`~theano.gof.graph.Variable` or list/tuple of Variables
+        The Hessian of the `cost` with respect to (elements of) `wrt`.
+        If an element of `wrt` is not differentiable with respect to the
+        output, then a zero variable is returned. The return value is
+        of same type as `wrt`: a list/tuple or TensorVariable in all cases.
     """
     from theano.tensor import arange
     # Check inputs have the right format
@@ -2034,10 +2048,16 @@ def zero_grad(x):
     through with a value of zero. In other words, the gradient of
     the expression is truncated to 0.
 
-    :param x: A Theano expression whose gradient should be truncated.
+    Parameters
+    ----------
+    x: :class:`~theano.gof.graph.Variable`
+        A Theano expression whose gradient should be truncated.
 
-    :return: The expression is returned unmodified, but its gradient
-        is now truncated to 0.
+    Returns
+    -------
+    :class:`~theano.gof.graph.Variable`
+        An expression equivalent to ``x``, with its gradient
+        truncated to 0.
     """
     return zero_grad_(x)
 
@@ -2058,18 +2078,24 @@ undefined_grad_ = UndefinedGrad()
 
 def undefined_grad(x):
     """
-    Consider the gradient of this variable undefined and
-    generate an error message if its gradient is taken.
+    Consider the gradient of this variable undefined.
+
+    This will generate an error message if its gradient is taken.
 
     The expression itself is unaffected, but when its gradient is
     computed, or the gradient of another expression that this
     expression is a subexpression of, an error message will be generated
     specifying such gradient is not defined.
 
-    :param x: A Theano expression whose gradient should be undefined.
+    Parameters
+    ----------
+    x: :class:`~theano.gof.graph.Variable`
+        A Theano expression whose gradient should be undefined.
 
-    :return: The expression is returned unmodified, but its gradient
-        is now undefined.
+    Returns
+    -------
+    :class:`~theano.gof.graph.Variable`
+        An expression equivalent to ``x``, with its gradient undefined.
     """
     return undefined_grad_(x)
 
@@ -2090,8 +2116,9 @@ disconnected_grad_ = DisconnectedGrad()
 
 def disconnected_grad(x):
     """
-    Consider an expression constant when computing gradients,
-    while effectively not backpropagating through it.
+    Consider an expression constant when computing gradients.
+
+    It will effectively not backpropagating through it.
 
     The expression itself is unaffected, but when its gradient is
     computed, or the gradient of another expression that this
@@ -2101,11 +2128,17 @@ def disconnected_grad(x):
     has to go through the underlying computational graph related to the
     expression.
 
-    :param x: A Theano expression whose gradient should not be
-              backpropagated through.
+    Parameters
+    ----------
+    x: :class:`~theano.gof.graph.Variable`
+        A Theano expression whose gradient should not be
+        backpropagated through.
 
-    :return: The expression is returned unmodified, but its gradient
-        is now effectively truncated to 0.
+    Returns
+    -------
+    :class:`~theano.gof.graph.Variable`
+        An expression equivalent to ``x``, with its gradient
+        now effectively truncated to 0.
     """
     return disconnected_grad_(x)
 
@@ -2133,23 +2166,28 @@ def grad_clip(x, lower_bound, upper_bound):
 
     This is an elemwise operation.
 
-    :param x: the variable we want its gradient inputs clipped
-    :param lower_bound: The lower bound of the gradient value
-    :param upper_bound: The upper bound of the gradient value.
-
-    :examples:
-
-        x = theano.tensor.scalar()
-
-        z = theano.tensor.grad(grad_clip(x, -1, 1)**2, x)
-        z2 = theano.tensor.grad(x**2, x)
-
-        f = theano.function([x], outputs = [z, z2])
-
-        print(f(2.0))  # output (1.0, 4.0)
-
-    :note: We register an opt in tensor/opt.py that remove the GradClip.
-       So it have 0 cost in the forward and only do work in the grad.
+    Parameters
+    ----------
+    x:
+        The variable we want its gradient inputs clipped
+    lower_bound:
+        The lower bound of the gradient value
+    upper_bound:
+        The upper bound of the gradient value.
+
+    Examples
+    --------
+    >>> x = theano.tensor.scalar()
+    >>> z = theano.tensor.grad(grad_clip(x, -1, 1)**2, x)
+    >>> z2 = theano.tensor.grad(x**2, x)
+    >>> f = theano.function([x], outputs = [z, z2])
+    >>> print(f(2.0))
+    [array(1.0), array(4.0)]
+
+    Note
+    ----
+    We register an opt in tensor/opt.py that remove the GradClip.
+    So it have 0 cost in the forward and only do work in the grad.
 
     """
     return GradClip(lower_bound, upper_bound)(x)
@@ -2167,21 +2205,25 @@ def grad_scale(x, multiplier):
     """
     This op scale or inverse the gradient in the backpropagation.
 
-    :param x: the variable we want its gradient inputs scale
-    :param multiplier: scale of the gradient
-
-    :examples:
-
-        x = theano.tensor.fscalar()
-        fx = theano.tensor.sin(x)
-
-        fp = theano.tensor.grad(fx, wrt=x)
-        fprime = theano.function([x], fp)
-        print(fprime(2))#-0.416
-
-        f_inverse=grad_scale(fx,-1.)
-        fpp = theano.tensor.grad(f_inverse, wrt=x)
-        fpprime = theano.function([x], fpp)
-        print(fpprime(2))#0.416
+    Parameters
+    ----------
+    x:
+        The variable we want its gradient inputs scale
+    multiplier:
+        Scale of the gradient
+
+    Examples
+    --------
+    >>> x = theano.tensor.fscalar()
+    >>> fx = theano.tensor.sin(x)
+    >>> fp = theano.tensor.grad(fx, wrt=x)
+    >>> fprime = theano.function([x], fp)
+    >>> print(fprime(2))  # doctest: +ELLIPSIS
+    -0.416...
+    >>> f_inverse=grad_scale(fx, -1.)
+    >>> fpp = theano.tensor.grad(f_inverse, wrt=x)
+    >>> fpprime = theano.function([x], fpp)
+    >>> print(fpprime(2))  # doctest: +ELLIPSIS
+    0.416...
     """
     return GradScale(multiplier)(x)