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提交 47ab45df authored 作者: Pascal Lamblin's avatar Pascal Lamblin
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Convert some docstrings to numpydoc and improve rendering

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theano/gradient.py
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......@@ -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)
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