def grad(self, inp, cost_grad):
"""
Notes
-----
The gradient is currently implemented for matrices only.
"""
a, val, offset = inp
grad = cost_grad[0]
height, width = grad.shape
if a.dtype.startswith("complex"):
return [None, None]
# only valid for matrices
wr_a = fill_diagonal_offset(grad, 0, offset)
offset_abs = abs_(offset)
pos_offset_flag = ge(offset, 0)
neg_offset_flag = lt(offset, 0)
min_wh = minimum(width, height)
start = offset * pos_offset_flag + offset_abs * width * neg_offset_flag
num_of_step = minimum(
min_wh,
width * pos_offset_flag + height * neg_offset_flag - offset_abs)
step = a.shape[1] + 1
end = start + step * num_of_step
# input of slice should be integer
start = aet.cast(start, "int32")
step = aet.cast(step, "int32")
end = aet.cast(end, "int32")
wr_val = grad.flatten()[start:end:step].sum()
wr_offset = grad_undefined(
self,
2,
offset,
"offset is not defined for non-integer offset so"
" fill_diagonal_offset(a,val,offset+eps) is undefined",
)
return [wr_a, wr_val, wr_offset]
def infer_shape(self, fgraph, node, shapes):
(x_shape, ) = shapes
M, N = x_shape
K = tm.minimum(M, N)
s_shape = (K, )
if self.compute_uv:
u_shape = (M, M) if self.full_matrices else (M, K)
vt_shape = (N, N) if self.full_matrices else (K, N)
return [u_shape, s_shape, vt_shape]
else:
return [s_shape]
def scan(
fn,
sequences=None,
outputs_info=None,
non_sequences=None,
n_steps=None,
truncate_gradient=-1,
go_backwards=False,
mode=None,
name=None,
profile=False,
allow_gc=None,
strict=False,
return_list=False,
):
"""This function constructs and applies a Scan op to the provided
arguments.
Parameters
----------
fn
``fn`` is a function that describes the operations involved in one
step of ``scan``. ``fn`` should construct variables describing the
output of one iteration step. It should expect as input aesara
variables representing all the slices of the input sequences
and previous values of the outputs, as well as all other arguments
given to scan as ``non_sequences``. The order in which scan passes
these variables to ``fn`` is the following :
* all time slices of the first sequence
* all time slices of the second sequence
* ...
* all time slices of the last sequence
* all past slices of the first output
* all past slices of the second output
* ...
* all past slices of the last output
* all other arguments (the list given as `non_sequences` to
scan)
The order of the sequences is the same as the one in the list
`sequences` given to scan. The order of the outputs is the same
as the order of ``outputs_info``. For any sequence or output the
order of the time slices is the same as the one in which they have
been given as taps. For example if one writes the following :
.. code-block:: python
scan(fn, sequences = [ dict(input= Sequence1, taps = [-3,2,-1])
, Sequence2
, dict(input = Sequence3, taps = 3) ]
, outputs_info = [ dict(initial = Output1, taps = [-3,-5])
, dict(initial = Output2, taps = None)
, Output3 ]
, non_sequences = [ Argument1, Argument2])
``fn`` should expect the following arguments in this given order:
#. ``Sequence1[t-3]``
#. ``Sequence1[t+2]``
#. ``Sequence1[t-1]``
#. ``Sequence2[t]``
#. ``Sequence3[t+3]``
#. ``Output1[t-3]``
#. ``Output1[t-5]``
#. ``Output3[t-1]``
#. ``Argument1``
#. ``Argument2``
The list of ``non_sequences`` can also contain shared variables
used in the function, though ``scan`` is able to figure those
out on its own so they can be skipped. For the clarity of the
code we recommend though to provide them to scan. To some extend
``scan`` can also figure out other ``non sequences`` (not shared)
even if not passed to scan (but used by `fn`). A simple example of
this would be :
.. code-block:: python
import aesara.tensor as aet
W = aet.matrix()
W_2 = W**2
def f(x):
return aet.dot(x,W_2)
The function is expected to return two things. One is a list of
outputs ordered in the same order as ``outputs_info``, with the
difference that there should be only one output variable per
output initial state (even if no tap value is used). Secondly
`fn` should return an update dictionary (that tells how to
update any shared variable after each iteration step). The
dictionary can optionally be given as a list of tuples. There is
no constraint on the order of these two list, ``fn`` can return
either ``(outputs_list, update_dictionary)`` or
``(update_dictionary, outputs_list)`` or just one of the two (in
case the other is empty).
To use ``scan`` as a while loop, the user needs to change the
function ``fn`` such that also a stopping condition is returned.
To do so, he/she needs to wrap the condition in an ``until`` class.
The condition should be returned as a third element, for example:
.. code-block:: python
...
return [y1_t, y2_t], {x:x+1}, until(x < 50)
Note that a number of steps (considered in here as the maximum
number of steps ) is still required even though a condition is
passed (and it is used to allocate memory if needed). = {}):
sequences
``sequences`` is the list of Aesara variables or dictionaries
describing the sequences ``scan`` has to iterate over. If a
sequence is given as wrapped in a dictionary, then a set of optional
information can be provided about the sequence. The dictionary
should have the following keys:
* ``input`` (*mandatory*) -- Aesara variable representing the
sequence.
* ``taps`` -- Temporal taps of the sequence required by ``fn``.
They are provided as a list of integers, where a value ``k``
impiles that at iteration step ``t`` scan will pass to ``fn``
the slice ``t+k``. Default value is ``[0]``
Any Aesara variable in the list ``sequences`` is automatically
wrapped into a dictionary where ``taps`` is set to ``[0]``
outputs_info
``outputs_info`` is the list of Aesara variables or dictionaries
describing the initial state of the outputs computed
recurrently. When this initial states are given as dictionary
optional information can be provided about the output corresponding
to these initial states. The dictionary should have the following
keys:
* ``initial`` -- Aesara variable that represents the initial
state of a given output. In case the output is not computed
recursively (think of a map) and does not require an initial
state this field can be skipped. Given that (only) the previous
time step of the output is used by ``fn``, the initial state
**should have the same shape** as the output and **should not
involve a downcast** of the data type of the output. If multiple
time taps are used, the initial state should have one extra
dimension that should cover all the possible taps. For example
if we use ``-5``, ``-2`` and ``-1`` as past taps, at step 0,
``fn`` will require (by an abuse of notation) ``output[-5]``,
``output[-2]`` and ``output[-1]``. This will be given by
the initial state, which in this case should have the shape
(5,)+output.shape. If this variable containing the initial
state is called ``init_y`` then ``init_y[0]`` *corresponds to*
``output[-5]``. ``init_y[1]`` *correponds to* ``output[-4]``,
``init_y[2]`` corresponds to ``output[-3]``, ``init_y[3]``
coresponds to ``output[-2]``, ``init_y[4]`` corresponds to
``output[-1]``. While this order might seem strange, it comes
natural from splitting an array at a given point. Assume that
we have a array ``x``, and we choose ``k`` to be time step
``0``. Then our initial state would be ``x[:k]``, while the
output will be ``x[k:]``. Looking at this split, elements in
``x[:k]`` are ordered exactly like those in ``init_y``.
* ``taps`` -- Temporal taps of the output that will be pass to
``fn``. They are provided as a list of *negative* integers,
where a value ``k`` implies that at iteration step ``t`` scan
will pass to ``fn`` the slice ``t+k``.
``scan`` will follow this logic if partial information is given:
* If an output is not wrapped in a dictionary, ``scan`` will wrap
it in one assuming that you use only the last step of the output
(i.e. it makes your tap value list equal to [-1]).
* If you wrap an output in a dictionary and you do not provide any
taps but you provide an initial state it will assume that you are
using only a tap value of -1.
* If you wrap an output in a dictionary but you do not provide any
initial state, it assumes that you are not using any form of
taps.
* If you provide a ``None`` instead of a variable or a empty
dictionary ``scan`` assumes that you will not use any taps for
this output (like for example in case of a map)
If ``outputs_info`` is an empty list or None, ``scan`` assumes
that no tap is used for any of the outputs. If information is
provided just for a subset of the outputs an exception is
raised (because there is no convention on how scan should map
the provided information to the outputs of ``fn``)
non_sequences
``non_sequences`` is the list of arguments that are passed to
``fn`` at each steps. One can opt to exclude variable
used in ``fn`` from this list as long as they are part of the
computational graph, though for clarity we encourage not to do so.
n_steps
``n_steps`` is the number of steps to iterate given as an int
or Aesara scalar. If any of the input sequences do not have
enough elements, scan will raise an error. If the *value is 0* the
outputs will have *0 rows*. If n_steps is not provided, ``scan`` will
figure out the amount of steps it should run given its input
sequences. ``n_steps`` < 0 is not supported anymore.
truncate_gradient
``truncate_gradient`` is the number of steps to use in truncated
BPTT. If you compute gradients through a scan op, they are
computed using backpropagation through time. By providing a
different value then -1, you choose to use truncated BPTT instead
of classical BPTT, where you go for only ``truncate_gradient``
number of steps back in time.
go_backwards
``go_backwards`` is a flag indicating if ``scan`` should go
backwards through the sequences. If you think of each sequence
as indexed by time, making this flag True would mean that
``scan`` goes back in time, namely that for any sequence it
starts from the end and goes towards 0.
name
When profiling ``scan``, it is crucial to provide a name for any
instance of ``scan``. The profiler will produce an overall
profile of your code as well as profiles for the computation of
one step of each instance of ``scan``. The ``name`` of the instance
appears in those profiles and can greatly help to disambiguate
information.
mode
It is recommended to leave this argument to None, especially
when profiling ``scan`` (otherwise the results are not going to
be accurate). If you prefer the computations of one step of
``scan`` to be done differently then the entire function, you
can use this parameter to describe how the computations in this
loop are done (see ``aesara.function`` for details about
possible values and their meaning).
profile
Flag or string. If true, or different from the empty string, a
profile object will be created and attached to the inner graph of
scan. In case ``profile`` is True, the profile object will have the
name of the scan instance, otherwise it will have the passed string.
Profile object collect (and print) information only when running the
inner graph with the new cvm linker ( with default modes,
other linkers this argument is useless)
allow_gc
Set the value of allow gc for the internal graph of scan. If
set to None, this will use the value of config.scan__allow_gc.
The full scan behavior related to allocation is determined by
this value and the Aesara flag allow_gc. If the flag allow_gc
is True (default) and this scan parameter allow_gc is False
(default), then we let scan allocate all intermediate memory
on the first iteration, those are not garbage collected them
during that first iteration (this is determined by the scan
allow_gc). This speed up allocation of the following
iteration. But we free all those temp allocation at the end of
all iterations (this is what the Aesara flag allow_gc mean).
If you use preallocate and this scan is on GPU, the speed up
from the scan allow_gc is small. If you are missing memory,
disable the scan allow_gc could help you run graph that
request much memory.
strict
If true, all the shared variables used in ``fn`` must be provided as a
part of ``non_sequences`` or ``sequences``.
return_list
If True, will always return a list, even if there is only 1 output.
Returns
-------
tuple
Tuple of the form (outputs, updates); ``outputs`` is either a
Aesara variable or a list of Aesara variables representing the
outputs of ``scan`` (in the same order as in ``outputs_info``).
``updates`` is a subclass of dictionary specifying the update rules for
all shared variables used in scan.
This dictionary should be passed to ``aesara.function`` when you compile
your function. The change compared to a normal dictionary is that we
validate that keys are SharedVariable and addition of those dictionary
are validated to be consistent.
"""
# General observation : this code is executed only once, at creation
# of the computational graph, so we don't yet need to be smart about
# anything (to speed things up)
##
# Step 1. Wrap all inputs in dictionaries and add default values
##
# check if inputs are just single variables instead of lists
def wrap_into_list(x):
"""
Wrap the input into a list if it is not already a list.
"""
if x is None:
return []
elif not isinstance(x, (list, tuple)):
return [x]
else:
return list(x)
seqs = wrap_into_list(sequences)
outs_info = wrap_into_list(outputs_info)
# Make sure we get rid of numpy arrays or ints or anything like that
# passed as inputs to scan
non_seqs = []
for elem in wrap_into_list(non_sequences):
if not isinstance(elem, Variable):
non_seqs.append(aet.as_tensor_variable(elem))
else:
non_seqs.append(elem)
# If we provided a known number of steps ( before compilation)
# and if that number is 1 or -1, then we can skip the Scan Op,
# and just apply the inner function once
# To do that we check here to see the nature of n_steps
n_fixed_steps = None
if isinstance(n_steps, (float, int)):
n_fixed_steps = int(n_steps)
else:
try:
n_fixed_steps = aet.get_scalar_constant_value(n_steps)
except NotScalarConstantError:
n_fixed_steps = None
# Check n_steps is an int
if hasattr(n_steps, "dtype") and str(n_steps.dtype) not in integer_dtypes:
raise ValueError(
f" n_steps must be an int. dtype provided is {n_steps.dtype}")
# compute number of sequences and number of outputs
n_seqs = len(seqs)
n_outs = len(outs_info)
return_steps = OrderedDict()
# wrap sequences in a dictionary if they are not already dictionaries
for i in range(n_seqs):
if not isinstance(seqs[i], dict):
seqs[i] = OrderedDict([("input", seqs[i]), ("taps", [0])])
elif seqs[i].get("taps", None) is not None:
seqs[i]["taps"] = wrap_into_list(seqs[i]["taps"])
elif seqs[i].get("taps", None) is None:
# seqs dictionary does not have the ``taps`` key
seqs[i]["taps"] = [0]
# wrap outputs info in a dictionary if they are not already in one
for i in range(n_outs):
if outs_info[i] is not None:
if isinstance(outs_info[i], dict):
if outs_info[i].get("return_steps", None) is not None:
raise DeprecationWarning(
"Using `return_steps` has been deprecated. "
"Simply select the entries you need using a "
"subtensor. Scan will optimize memory "
"consumption, so do not worry about that.")
# END
if not isinstance(outs_info[i], dict):
# by default any output has a tap value of -1
outs_info[i] = OrderedDict([("initial", outs_info[i]),
("taps", [-1])])
elif (outs_info[i].get("initial", None) is None
and outs_info[i].get("taps", None) is not None):
# ^ no initial state but taps provided
raise ValueError("If you are using slices of an output "
"you need to provide a initial state "
f"for it: {outs_info[i]}")
elif (outs_info[i].get("initial", None) is not None
and outs_info[i].get("taps", None) is None):
# ^ initial state but taps not provided
if "taps" in outs_info[i]:
# ^ explicitly provided a None for taps
_logger.warning(
f"Output {getattr(outs_info[i]['initial'], 'name', 'None')} (index {i}) has a initial "
"state but taps is explicitly set to None ", )
outs_info[i]["taps"] = [-1]
elif outs_info[i].get("taps", None) is not None:
# Check that taps are valid (< 0 and all dfferent)
taps = outs_info[i]["taps"]
if len(taps) > len(set(taps)):
raise ValueError(
("All the taps must be different in "
" `outputs_info`"),
outs_info[i],
)
for t in taps:
if t >= 0:
raise ValueError(
("All the tap values must be "
"smaller than 0."),
outs_info[i],
)
else:
# if a None is provided as the output info we replace it
# with an empty OrdereDict() to simplify handling
outs_info[i] = OrderedDict()
##
# Step 2. Generate inputs and outputs of the inner functions
# for compiling a dummy function (Iteration #1)
##
# create aesara inputs for the recursive function
# note : this is a first batch of possible inputs that will
# be compiled in a dummy function; we used this dummy
# function to detect shared variables and their updates
# and to construct a new and complete list of inputs and
# outputs
n_seqs = 0
scan_seqs = [] # Variables passed as inputs to the scan op
inner_seqs = [] # Variables passed as inputs to the inner function
inner_slices = [] # Actual slices if scan is removed from the picture
# go through sequences picking up time slices as needed
for i, seq in enumerate(seqs):
# Note that you can have something like no taps for
# a sequence, though is highly unlikely in practice
if "taps" in seq:
# go through the indicated slice
mintap = np.min(seq["taps"])
maxtap = np.max(seq["taps"])
# We cut the sequence such that seq[i] to correspond to
# seq[i-k]. For the purposes of cutting the sequences, we
# need to pretend tap 0 is used to avoid cutting the sequences
# too long if the taps are all lower or all higher than 0.
maxtap_proxy = max(maxtap, 0)
mintap_proxy = min(mintap, 0)
for k in seq["taps"]:
# create one slice of the input
# Later on, if we decide not to use scan because we are
# going for just one step, it makes things easier if we
# compute the correct outputs here. This way we can use
# the output of the lambda expression directly to replace
# the output of scan.
# If not we need to use copies, that will be replaced at
# each frame by the corresponding slice
actual_slice = seq["input"][k - mintap_proxy]
_seq_val = aet.as_tensor_variable(seq["input"])
_seq_val_slice = _seq_val[k - mintap_proxy]
nw_slice = _seq_val_slice.type()
# Try to transfer test_value to the new variable
if config.compute_test_value != "off":
try:
nw_slice.tag.test_value = get_test_value(
_seq_val_slice)
except TestValueError:
if config.compute_test_value != "ignore":
# No need to print a warning or raise an error now,
# it will be done when fn will be called.
_logger.warning(
("Cannot compute test value for "
"the inner function of scan, input value "
"missing {}").format(_seq_val_slice))
# Add names to slices for debugging and pretty printing ..
# that is if the input already has a name
if getattr(seq["input"], "name", None) is not None:
if k > 0:
nw_name = seq["input"].name + f"[t+{int(k)}]"
elif k == 0:
nw_name = seq["input"].name + "[t]"
else:
nw_name = seq["input"].name + f"[t{int(k)}]"
nw_slice.name = nw_name
start = k - mintap_proxy
nw_name = None
if k == maxtap_proxy:
nw_seq = seq["input"][start:]
if getattr(seq["input"], "name", None) is not None:
nw_name = seq["input"].name + f"[{int(start)}:]"
else:
end = -(maxtap_proxy - k)
nw_seq = seq["input"][start:end]
if getattr(seq["input"], "name", None) is not None:
nw_name = seq[
"input"].name + f"[{int(start)}:{int(end)}]"
if go_backwards:
nw_seq = nw_seq[::-1]
scan_seqs.append(nw_seq)
inner_seqs.append(nw_slice)
inner_slices.append(actual_slice)
n_seqs += 1
# Add names -- it helps a lot when debugging
if nw_name is not None:
nw_seq.name = nw_name
# Since we've added all sequences now we need to level them up based on
# n_steps or their different shapes
lengths_vec = []
for seq in scan_seqs:
lengths_vec.append(seq.shape[0])
if not utils.isNaN_or_Inf_or_None(n_steps):
# ^ N_steps should also be considered
lengths_vec.append(aet.as_tensor(n_steps))
if len(lengths_vec) == 0:
# ^ No information about the number of steps
raise ValueError("No information about the number of steps "
"provided. Either provide a value for "
"n_steps argument of scan or provide an input "
"sequence")
# If the user has provided the number of steps, do that regardless ( and
# raise an error if the sequences are not long enough )
if utils.isNaN_or_Inf_or_None(n_steps):
actual_n_steps = lengths_vec[0]
for contestant in lengths_vec[1:]:
actual_n_steps = minimum(actual_n_steps, contestant)
else:
actual_n_steps = aet.as_tensor(n_steps)
scan_seqs = [seq[:actual_n_steps] for seq in scan_seqs]
# Conventions :
# mit_mot = multiple input taps, multiple output taps ( only provided
# by the gradient function )
# mit_sot = multiple input taps, single output tap (t + 0)
# sit_sot = single input tap, single output tap (t + 0)
# nit_sot = no input tap, single output tap (t + 0)
# MIT_MOT -- not provided by the user only by the grad function
n_mit_mot = 0
n_mit_mot_outs = 0
mit_mot_scan_inputs = []
mit_mot_inner_inputs = []
mit_mot_inner_outputs = []
mit_mot_out_slices = []
# SIT_SOT -- provided by the user
n_mit_sot = 0
mit_sot_scan_inputs = []
mit_sot_inner_inputs = []
mit_sot_inner_slices = []
mit_sot_inner_outputs = []
mit_sot_return_steps = OrderedDict()
mit_sot_tap_array = []
mit_sot_rightOrder = []
n_sit_sot = 0
sit_sot_scan_inputs = []
sit_sot_inner_inputs = []
sit_sot_inner_slices = []
sit_sot_inner_outputs = []
sit_sot_return_steps = OrderedDict()
sit_sot_rightOrder = []
# go through outputs picking up time slices as needed
for i, init_out in enumerate(outs_info):
# Note that our convention dictates that if an output uses
# just the previous time step, as a initial state we will only
# provide a tensor of the same dimension as one time step; This
# makes code much cleaner for those who do not use taps. Otherwise
# they would always had to shape_padleft the initial state ..
# which is ugly
if init_out.get("taps", None) == [-1]:
actual_arg = init_out["initial"]
if not isinstance(actual_arg, Variable):
actual_arg = aet.as_tensor_variable(actual_arg)
arg = safe_new(actual_arg)
if isinstance(arg, Constant):
# safe new returns a clone of the constants, but that is not
# what we need for initial states
arg = arg.type()
# Try to transfer test_value to the new variable
if config.compute_test_value != "off":
try:
arg.tag.test_value = get_test_value(actual_arg)
except TestValueError:
if config.compute_test_value != "ignore":
_logger.warning(
("Cannot compute test value for the "
"inner function of scan, test value missing: {}"
).format(actual_arg))
if getattr(init_out["initial"], "name", None) is not None:
arg.name = init_out["initial"].name + "[t-1]"
# We need now to allocate space for storing the output and copy
# the initial state over. We do this using the expand function
# defined in scan utils
sit_sot_scan_inputs.append(
utils.expand_empty(
aet.unbroadcast(shape_padleft(actual_arg), 0),
actual_n_steps,
))
sit_sot_inner_slices.append(actual_arg)
if i in return_steps:
sit_sot_return_steps[n_sit_sot] = return_steps[i]
sit_sot_inner_inputs.append(arg)
sit_sot_rightOrder.append(i)
n_sit_sot += 1
elif init_out.get("taps", None):
if np.any(np.array(init_out.get("taps", [])) > 0):
# Make sure we do not have requests for future values of a
# sequence we can not provide such values
raise ValueError("Can not use future taps of outputs",
init_out)
# go through the taps
mintap = abs(np.min(init_out["taps"]))
mit_sot_tap_array.append(init_out["taps"])
# Sequence
mit_sot_scan_inputs.append(
utils.expand_empty(init_out["initial"][:mintap],
actual_n_steps))
if i in return_steps:
mit_sot_return_steps[n_mit_sot] = return_steps[i]
mit_sot_rightOrder.append(i)
n_mit_sot += 1
for k in init_out["taps"]:
# create a new slice
actual_nw_slice = init_out["initial"][k + mintap]
_init_out_var = aet.as_tensor_variable(init_out["initial"])
_init_out_var_slice = _init_out_var[k + mintap]
nw_slice = _init_out_var_slice.type()
# Try to transfer test_value to the new variable
if config.compute_test_value != "off":
try:
nw_slice.tag.test_value = get_test_value(
_init_out_var_slice)
except TestValueError:
if config.compute_test_value != "ignore":
_logger.warning(
("Cannot compute test value for "
"the inner function of scan, test value "
"missing: {}").format(_init_out_var_slice))
# give it a name or debugging and pretty printing
if getattr(init_out["initial"], "name", None) is not None:
if k > 0:
nw_slice.name = init_out[
"initial"].name + f"[t+{int(k)}]"
elif k == 0:
nw_slice.name = init_out["initial"].name + "[t]"
else:
nw_slice.name = init_out[
"initial"].name + f"[t{int(k)}]"
mit_sot_inner_inputs.append(nw_slice)
mit_sot_inner_slices.append(actual_nw_slice)
# NOTE: there is another case, in which we do not want to provide
# any previous value of the output to the inner function (i.e.
# a map); in that case we do not have to do anything ..
# Re-order args
max_mit_sot = np.max([-1] + mit_sot_rightOrder) + 1
max_sit_sot = np.max([-1] + sit_sot_rightOrder) + 1
n_elems = np.max([max_mit_sot, max_sit_sot])
_ordered_args = [[] for x in range(n_elems)]
offset = 0
for idx in range(n_mit_sot):
n_inputs = len(mit_sot_tap_array[idx])
if n_fixed_steps in [1, -1]:
_ordered_args[
mit_sot_rightOrder[idx]] = mit_sot_inner_slices[offset:offset +
n_inputs]
else:
_ordered_args[
mit_sot_rightOrder[idx]] = mit_sot_inner_inputs[offset:offset +
n_inputs]
offset += n_inputs
for idx in range(n_sit_sot):
if n_fixed_steps in [1, -1]:
_ordered_args[sit_sot_rightOrder[idx]] = [
sit_sot_inner_slices[idx]
]
else:
_ordered_args[sit_sot_rightOrder[idx]] = [
sit_sot_inner_inputs[idx]
]
ordered_args = []
for ls in _ordered_args:
ordered_args += ls
if n_fixed_steps in [1, -1]:
args = inner_slices + ordered_args + non_seqs
else:
args = inner_seqs + ordered_args + non_seqs
# add only the non-shared variables and non-constants to the arguments of
# the dummy function [ a function should not get shared variables or
# constants as input ]
dummy_args = [
arg for arg in args if (not isinstance(arg, SharedVariable)
and not isinstance(arg, Constant))
]
# when we apply the lambda expression we get a mixture of update rules
# and outputs that needs to be separated
condition, outputs, updates = utils.get_updates_and_outputs(fn(*args))
if condition is not None:
as_while = True
else:
as_while = False
##
# Step 3. Check if we actually need scan and remove it if we don't
##
if n_fixed_steps in [1, -1]:
# We do not need to use the scan op anymore, so we can just return
# the outputs and updates we have
if condition is not None:
_logger.warning(
("When the number of steps is fixed and equal "
"to 1, the provided stopping condition, {} is ignored",
).format(condition))
for pos, inner_out in enumerate(outputs):
# we need to see if we need to pad our sequences with an
# unbroadcastable dimension; case example : we return an
# output for which we want all intermediate. If n_steps is 1
# then, if we return the output as given by the innner function
# this will represent only a slice and it will have one
# dimension less.
if isinstance(inner_out.type,
TensorType) and return_steps.get(pos, 0) != 1:
outputs[pos] = aet.unbroadcast(shape_padleft(inner_out), 0)
if return_list is not True and len(outputs) == 1:
outputs = outputs[0]
return (outputs, updates)
##
# Step 4. Compile the dummy function
##
# We can now compile a dummy function just to see what shared variable
# we have and what are their update rules (note that the user has
# the option not to pass the shared variable to scan, so we need to
# pick them manually and add them to scan)
# make the compilation as fast as possible by not applying any
# optimization or conversion to C [ note this region is not important
# for performance so we can do stuff as unoptimal as we wish ]
# extract still missing inputs (there still might be so) and add them
# as non sequences at the end of our args
if condition is not None:
outputs.append(condition)
fake_nonseqs = [x.type() for x in non_seqs]
fake_outputs = clone_replace(outputs,
replace=OrderedDict(
zip(non_seqs, fake_nonseqs)))
all_inputs = filter(
lambda x: (isinstance(x, Variable) and not isinstance(
x, SharedVariable) and not isinstance(x, Constant)),
graph_inputs(fake_outputs),
)
extra_inputs = [x for x in all_inputs if x not in args + fake_nonseqs]
non_seqs += extra_inputs
# Note we do not use all_inputs directly since the order of variables
# in args is quite important
dummy_args += extra_inputs
dummy_outs = outputs
# Perform a try-except to provide a meaningful error message to the
# user if inputs of the inner function are missing.
try:
dummy_f = function(
dummy_args,
dummy_outs,
updates=updates,
mode=Mode(linker="py", optimizer=None),
on_unused_input="ignore",
profile=False,
)
except MissingInputError as err:
msg = ("\nPlease pass this variable to the scan's inner function. Do "
"not forget to also pass it to the `non_sequences` attribute "
"of scan.")
raise MissingInputError(err.args[0] + msg)
##
# Step 5. Re-arange inputs of scan into a more strict order
##
# Step 5.0 Check the outputs of the dummy function to see if they
# match with user provided data
# if the number of outputs to the function does not match the number of
# assumed outputs until now (provided by the user) there can be
# only one explanation: No information is provided for any of the
# outputs (i.e. we are dealing with a map)
tmp_dummy_f_outs = len(dummy_f.maker.outputs)
if as_while:
tmp_dummy_f_outs -= 1
if not (tmp_dummy_f_outs == n_outs or outs_info == []):
raise ValueError("Please provide None as outputs_info for "
"any output that does not feed back into "
"scan (i.e. it behaves like a map) ")
if outs_info == []:
n_outs = len(dummy_f.maker.outputs)
if as_while:
n_outs = n_outs - 1
outs_info = [OrderedDict() for x in range(n_outs)]
# Step 5.1 Outputs with taps different then -1
for i, out in enumerate(outs_info):
if "taps" in out and out["taps"] != [-1]:
mit_sot_inner_outputs.append(outputs[i])
# Step 5.2 Outputs with tap equal to -1
for i, out in enumerate(outs_info):
if "taps" in out and out["taps"] == [-1]:
sit_sot_inner_outputs.append(outputs[i])
# Step 5.3 Outputs that correspond to update rules of shared variables
givens = OrderedDict()
n_shared_outs = 0
shared_scan_inputs = []
shared_inner_inputs = []
shared_inner_outputs = []
sit_sot_shared = []
for input in dummy_f.maker.expanded_inputs:
if isinstance(input.variable, SharedVariable) and input.update:
new_var = safe_new(input.variable)
if getattr(input.variable, "name", None) is not None:
new_var.name = input.variable.name + "_copy"
if isinstance(new_var.type, ops.expandable_types):
sit_sot_inner_inputs.append(new_var)
sit_sot_scan_inputs.append(
utils.expand_empty(
aet.unbroadcast(shape_padleft(input.variable), 0),
actual_n_steps,
))
tensor_update = aet.as_tensor_variable(input.update)
sit_sot_inner_outputs.append(tensor_update)
# Not that pos is not a negative index. The sign of pos is used
# as a flag to indicate if this output should be part of the
# update rules or part of the standard outputs of scan.
# If `pos` is positive than it corresponds to the standard
# outputs of scan and it refers to output of index `pos`. If `pos`
# is negative that it corresponds to update rules of scan and it
# refers to update rule of index -1 - `pos`.
sit_sot_rightOrder.append(-1 - len(sit_sot_shared))
sit_sot_shared.append(input.variable)
givens[input.variable] = new_var
else:
shared_inner_inputs.append(new_var)
shared_scan_inputs.append(input.variable)
shared_inner_outputs.append(input.update)
givens[input.variable] = new_var
n_shared_outs += 1
n_sit_sot = len(sit_sot_inner_inputs)
# Step 5.4 Outputs with no taps used in the input
n_nit_sot = 0
nit_sot_inner_outputs = []
nit_sot_return_steps = OrderedDict()
nit_sot_rightOrder = []
for i, out in enumerate(outs_info):
if "taps" not in out:
nit_sot_inner_outputs.append(outputs[i])
if i in return_steps:
nit_sot_return_steps[n_nit_sot] = return_steps[i]
nit_sot_rightOrder.append(i)
n_nit_sot += 1
# Step 5.5 all other arguments including extra inputs
other_scan_args = []
other_inner_args = []
other_scan_args += [
arg for arg in non_seqs if (not isinstance(arg, SharedVariable)
and not isinstance(arg, Constant))
]
# Step 5.6 all shared variables with no update rules
other_inner_args += [
safe_new(arg, "_copy") for arg in non_seqs if
(not isinstance(arg, SharedVariable) and not isinstance(arg, Constant))
]
givens.update(OrderedDict(zip(other_scan_args, other_inner_args)))
if strict:
non_seqs_set = set(non_sequences if non_sequences is not None else [])
other_shared_scan_args = [
arg.variable for arg in dummy_f.maker.expanded_inputs
if (isinstance(arg.variable, SharedVariable) and not arg.update
and arg.variable in non_seqs_set)
]
other_shared_inner_args = [
safe_new(arg.variable, "_copy")
for arg in dummy_f.maker.expanded_inputs
if (isinstance(arg.variable, SharedVariable) and not arg.update
and arg.variable in non_seqs_set)
]
else:
other_shared_scan_args = [
arg.variable for arg in dummy_f.maker.expanded_inputs
if (isinstance(arg.variable, SharedVariable) and not arg.update)
]
other_shared_inner_args = [
safe_new(arg.variable, "_copy")
for arg in dummy_f.maker.expanded_inputs
if (isinstance(arg.variable, SharedVariable) and not arg.update)
]
givens.update(
OrderedDict(zip(other_shared_scan_args, other_shared_inner_args)))
##
# Step 6. Re-order the outputs and clone them replacing things
# using the givens
##
inner_inputs = (inner_seqs + mit_mot_inner_inputs + mit_sot_inner_inputs +
sit_sot_inner_inputs + shared_inner_inputs +
other_shared_inner_args + other_inner_args)
inner_outs = (mit_mot_inner_outputs + mit_sot_inner_outputs +
sit_sot_inner_outputs + nit_sot_inner_outputs +
shared_inner_outputs)
if condition is not None:
inner_outs.append(condition)
# gpuarray is imported here, instead of being imported on top of
# the file because that would force on the user some dependencies that we
# might do not want to. Currently we are working on removing the
# dependencies on sandbox code completeley.
from aesara import gpuarray
if gpuarray.pygpu_activated:
# very often we end up in this situation when we want to
# replace w with w_copy, where w is a GPU variable
# and w_copy is TensorType. This is caused because shared
# variables are put on GPU right away >:| ,
new_givens = OrderedDict()
for w, w_copy in givens.items():
if isinstance(w.type, gpuarray.GpuArrayType) and isinstance(
w_copy.type, TensorType):
for o in inner_outs:
new_givens = traverse(o, w, w_copy, new_givens)
else:
new_givens[w] = w_copy
else:
new_givens = givens
new_outs = clone_replace(inner_outs, replace=new_givens)
##
# Step 7. Create the Scan Op
##
tap_array = mit_sot_tap_array + [[-1] for x in range(n_sit_sot)]
if allow_gc is None:
allow_gc = config.scan__allow_gc
info = OrderedDict()
info["tap_array"] = tap_array
info["n_seqs"] = n_seqs
info["n_mit_mot"] = n_mit_mot
info["n_mit_mot_outs"] = n_mit_mot_outs
info["mit_mot_out_slices"] = mit_mot_out_slices
info["n_mit_sot"] = n_mit_sot
info["n_sit_sot"] = n_sit_sot
info["n_shared_outs"] = n_shared_outs
info["n_nit_sot"] = n_nit_sot
info["truncate_gradient"] = truncate_gradient
info["name"] = name
info["mode"] = mode
info["destroy_map"] = OrderedDict()
info["gpua"] = False
info["as_while"] = as_while
info["profile"] = profile
info["allow_gc"] = allow_gc
info["strict"] = strict
local_op = Scan(inner_inputs, new_outs, info)
##
# Step 8. Compute the outputs using the scan op
##
_scan_inputs = (scan_seqs + mit_mot_scan_inputs + mit_sot_scan_inputs +
sit_sot_scan_inputs + shared_scan_inputs +
[actual_n_steps for x in range(n_nit_sot)] +
other_shared_scan_args + other_scan_args)
scan_inputs = []
for arg in [actual_n_steps] + _scan_inputs:
try:
arg = aet.as_tensor_variable(arg)
except TypeError:
# This happens for Random States for e.g. but it is a good way
# to make sure all inputs are tensors.
pass
scan_inputs += [arg]
scan_outs = local_op(*scan_inputs)
if type(scan_outs) not in (list, tuple):
scan_outs = [scan_outs]
##
# Step 9. Figure out which outs are update rules for shared variables
# and so on ...
##
update_map = OrderedUpdates()
def remove_dimensions(outs, steps_return, offsets=None):
out_ls = []
for idx, out in enumerate(outs):
if idx in steps_return:
if steps_return[idx] > 1:
out_ls.append(out[-steps_return[idx]:])
else:
out_ls.append(out[-1])
else:
if offsets is None:
out_ls.append(out)
else:
out_ls.append(out[offsets[idx]:])
return out_ls
offset = n_mit_mot
offsets = [abs(np.min(x)) for x in mit_sot_tap_array]
mit_sot_outs = remove_dimensions(scan_outs[offset:offset + n_mit_sot],
mit_sot_return_steps, offsets)
offset += n_mit_sot
offsets = [1 for x in range(n_sit_sot)]
sit_sot_outs = remove_dimensions(scan_outs[offset:offset + n_sit_sot],
sit_sot_return_steps, offsets)
offset += n_sit_sot
nit_sot_outs = remove_dimensions(scan_outs[offset:offset + n_nit_sot],
nit_sot_return_steps)
offset += n_nit_sot
for idx, update_rule in enumerate(scan_outs[offset:offset +
n_shared_outs]):
update_map[shared_scan_inputs[idx]] = update_rule
_scan_out_list = mit_sot_outs + sit_sot_outs + nit_sot_outs
# Step 10. I need to reorder the outputs to be in the order expected by
# the user
rightOrder = mit_sot_rightOrder + sit_sot_rightOrder + nit_sot_rightOrder
scan_out_list = [None] * len(rightOrder)
for idx, pos in enumerate(rightOrder):
if pos >= 0:
scan_out_list[pos] = _scan_out_list[idx]
else:
# Not that pos is not a negative index. The sign of pos is used
# as a flag to indicate if this output should be part of the
# update rules or part of the standard outputs of scan.
# If `pos` is positive than it corresponds to the standard
# outputs of scan and it refers to output of index `pos`. If `pos`
# is negative that it corresponds to update rules of scan and it
# refers to update rule of index -1 - `pos`.
update_map[sit_sot_shared[abs(pos) - 1]] = _scan_out_list[idx][-1]
scan_out_list = [x for x in scan_out_list if x is not None]
if return_list is not True and len(scan_out_list) == 1:
scan_out_list = scan_out_list[0]
elif len(scan_out_list) == 0:
scan_out_list = None
return (scan_out_list, update_map)