def bincount(x, weights=None, minlength=None, assert_nonneg=False):
"""Count number of occurrences of each value in array of ints.
The number of bins (of size 1) is one larger than the largest
value in x. If minlength is specified, there will be at least
this number of bins in the output array (though it will be longer
if necessary, depending on the contents of x). Each bin gives the
number of occurrences of its index value in x. If weights is
specified the input array is weighted by it, i.e. if a value n
is found at position i, out[n] += weight[i] instead of out[n] += 1.
Parameters
----------
x : 1 dimension, nonnegative ints
weights : array of the same shape as x with corresponding weights.
Optional.
minlength : A minimum number of bins for the output array.
Optional.
assert_nonneg : A flag that inserts an assert_op to check if
every input x is nonnegative.
Optional.
.. versionadded:: 0.6
"""
if x.ndim != 1:
raise TypeError("Inputs must be of dimension 1.")
if assert_nonneg:
assert_op = Assert("Input to bincount has negative values!")
x = assert_op(x, aet_all(x >= 0))
max_value = aet.cast(x.max() + 1, "int64")
if minlength is not None:
max_value = maximum(max_value, minlength)
# Note: we do not use inc_subtensor(out[x], ...) in the following lines,
# since out[x] raises an exception if the indices (x) are int8.
if weights is None:
out = aet.zeros([max_value], dtype=x.dtype)
out = advanced_inc_subtensor1(out, 1, x)
else:
out = aet.zeros([max_value], dtype=weights.dtype)
out = advanced_inc_subtensor1(out, weights, x)
return out
def to_one_hot(y, nb_class, dtype=None):
"""
Return a matrix where each row correspond to the one hot
encoding of each element in y.
Parameters
----------
y
A vector of integer value between 0 and nb_class - 1.
nb_class : int
The number of class in y.
dtype : data-type
The dtype of the returned matrix. Default floatX.
Returns
-------
object
A matrix of shape (y.shape[0], nb_class), where each row ``i`` is
the one hot encoding of the corresponding ``y[i]`` value.
"""
ret = aet.zeros((y.shape[0], nb_class), dtype=dtype)
ret = set_subtensor(ret[aet.arange(y.shape[0]), y], 1)
return ret
def scan_checkpoints(
fn,
sequences=None,
outputs_info=None,
non_sequences=None,
name="checkpointscan_fn",
n_steps=None,
save_every_N=10,
padding=True,
):
"""Scan function that uses less memory, but is more restrictive.
In :func:`~aesara.scan`, if you compute the gradient of the output
with respect to the input, you will have to store the intermediate
results at each time step, which can be prohibitively huge. This
function allows to do ``save_every_N`` steps of forward computations
without storing the intermediate results, and to recompute them during
the gradient computation.
Notes
-----
Current assumptions:
* Every sequence has the same length.
* If ``n_steps`` is specified, it has the same value as the length of
any sequence.
* The value of ``save_every_N`` divides the number of steps the scan
will run without remainder.
* Only singly-recurrent and non-recurrent outputs are used.
No multiple recurrences.
* Only the last timestep of any output will ever be used.
Parameters
----------
fn
``fn`` is a function that describes the operations involved in one
step of ``scan``. See the documentation of :func:`~aesara.scan`
for more information.
sequences
``sequences`` is the list of Aesara variables or dictionaries
describing the sequences ``scan`` has to iterate over. All
sequences must be the same length in this version of ``scan``.
outputs_info
``outputs_info`` is the list of Aesara variables or dictionaries
describing the initial state of the outputs computed
recurrently.
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 (> 0). If any of the input sequences do not have
enough elements, scan will raise an error. If n_steps is not provided,
``scan`` will figure out the amount of steps it should run given its
input sequences.
save_every_N
``save_every_N`` is the number of steps to go without storing
the computations of ``scan`` (ie they will have to be recomputed
during the gradient computation).
padding
If the length of the sequences is not a multiple of ``save_every_N``,
the sequences will be zero padded to make this version of ``scan``
work properly, but will also result in a memory copy. It can be
avoided by setting ``padding`` to False, but you need to make
sure the length of the sequences is a multiple of ``save_every_N``.
Returns
-------
tuple
Tuple of the form ``(outputs, updates)`` as in :func:`~aesara.scan`, but
with a small change: It only contain the output at each
``save_every_N`` step. The time steps that are not returned by
this function will be recomputed during the gradient computation
(if any).
See Also
--------
:func:`~aesara.scan`: Looping in Aesara.
"""
# Standardize the format of input arguments
if sequences is None:
sequences = []
elif not isinstance(sequences, list):
sequences = [sequences]
if not isinstance(outputs_info, list):
outputs_info = [outputs_info]
if non_sequences is None:
non_sequences = []
elif not isinstance(non_sequences, list):
non_sequences = [non_sequences]
# Check that outputs_info has no taps:
for element in outputs_info:
if isinstance(element, dict) and "taps" in element:
raise RuntimeError("scan_checkpoints doesn't work with taps.")
# Determine how many steps the original scan would run
if n_steps is None:
n_steps = sequences[0].shape[0]
# Compute the number of steps of the outer scan
o_n_steps = at.cast(ceil(n_steps / save_every_N), "int64")
# Compute the number of steps of the inner scan
i_n_steps = save_every_N * at.ones((o_n_steps, ), "int64")
mod = n_steps % save_every_N
last_n_steps = at.switch(eq(mod, 0), save_every_N, mod)
i_n_steps = set_subtensor(i_n_steps[-1], last_n_steps)
# Pad the sequences if needed
if padding:
# Since padding could be an empty tensor, Join returns a view of s.
join = Join(view=0)
for i, s in enumerate(sequences):
n = s.shape[0] % save_every_N
z = at.zeros((n, s.shape[1:]), dtype=s.dtype)
sequences[i] = join(0, [s, z])
# Establish the input variables of the outer scan
o_sequences = [
s.reshape(
[s.shape[0] / save_every_N, save_every_N] +
[s.shape[i] for i in range(1, s.ndim)],
s.ndim + 1,
) for s in sequences
]
o_sequences.append(i_n_steps)
new_nitsots = [i for i in outputs_info if i is None]
o_nonsequences = non_sequences
def outer_step(*args):
# Separate the received arguments into their respective (seq, outputs
# from previous iterations, nonseqs) categories
i_sequences = list(args[:len(o_sequences)])
i_prev_outputs = list(args[len(o_sequences):-len(o_nonsequences)])
i_non_sequences = list(args[-len(o_nonsequences):])
i_outputs_infos = i_prev_outputs + [
None,
] * len(new_nitsots)
# Call the user-provided function with the proper arguments
results, updates = scan(
fn=fn,
sequences=i_sequences[:-1],
outputs_info=i_outputs_infos,
non_sequences=i_non_sequences,
name=name + "_inner",
n_steps=i_sequences[-1],
)
if not isinstance(results, list):
results = [results]
# Keep only the last timestep of every output but keep all the updates
if not isinstance(results, list):
return results[-1], updates
else:
return [r[-1] for r in results], updates
results, updates = scan(
fn=outer_step,
sequences=o_sequences,
outputs_info=outputs_info,
non_sequences=o_nonsequences,
name=name + "_outer",
n_steps=o_n_steps,
allow_gc=True,
)
return results, updates
def neibs2images(neibs, neib_shape, original_shape, mode="valid"):
"""
Function :func:`neibs2images <aesara.sandbox.neighbours.neibs2images>`
performs the inverse operation of
:func:`images2neibs <aesara.sandbox.neighbours.neibs2images>`. It inputs
the output of :func:`images2neibs <aesara.sandbox.neighbours.neibs2images>`
and reconstructs its input.
Parameters
----------
neibs : 2d tensor
Like the one obtained by
:func:`images2neibs <aesara.sandbox.neighbours.neibs2images>`.
neib_shape
`neib_shape` that was used in
:func:`images2neibs <aesara.sandbox.neighbours.neibs2images>`.
original_shape
Original shape of the 4d tensor given to
:func:`images2neibs <aesara.sandbox.neighbours.neibs2images>`
Returns
-------
object
Reconstructs the input of
:func:`images2neibs <aesara.sandbox.neighbours.neibs2images>`,
a 4d tensor of shape `original_shape`.
Notes
-----
Currently, the function doesn't support tensors created with
`neib_step` different from default value. This means that it may be
impossible to compute the gradient of a variable gained by
:func:`images2neibs <aesara.sandbox.neighbours.neibs2images>` w.r.t.
its inputs in this case, because it uses
:func:`images2neibs <aesara.sandbox.neighbours.neibs2images>` for
gradient computation.
Examples
--------
Example, which uses a tensor gained in example for
:func:`images2neibs <aesara.sandbox.neighbours.neibs2images>`:
.. code-block:: python
im_new = neibs2images(neibs, (5, 5), im_val.shape)
# Aesara function definition
inv_window = aesara.function([neibs], im_new)
# Function application
im_new_val = inv_window(neibs_val)
.. note:: The code will output the initial image array.
"""
neibs = as_tensor_variable(neibs)
neib_shape = as_tensor_variable(neib_shape)
original_shape = as_tensor_variable(original_shape)
new_neib_shape = stack(
[original_shape[-1] // neib_shape[1], neib_shape[1]])
output_2d = images2neibs(neibs.dimshuffle("x", "x", 0, 1),
new_neib_shape,
mode=mode)
if mode == "ignore_borders":
# We use set_subtensor to accept original_shape we can't infer
# the shape and still raise error when it don't have the right
# shape.
valid_shape = original_shape
valid_shape = set_subtensor(
valid_shape[2], (valid_shape[2] // neib_shape[0]) * neib_shape[0])
valid_shape = set_subtensor(
valid_shape[3], (valid_shape[3] // neib_shape[1]) * neib_shape[1])
output_4d = output_2d.reshape(valid_shape, ndim=4)
# padding the borders with zeros
for d in (2, 3):
pad_shape = list(output_4d.shape)
pad_shape[d] = original_shape[d] - valid_shape[d]
output_4d = concatenate([output_4d, zeros(pad_shape)], axis=d)
elif mode == "valid":
# TODO: we do not implement all mode with this code.
# Add a check for the good cases.
output_4d = output_2d.reshape(original_shape, ndim=4)
else:
raise NotImplementedError(f"neibs2images do not support mode={mode}")
return output_4d
def grad(self, inp, grads):
x, neib_shape, neib_step = inp
(gz, ) = grads
if self.mode in ("valid", "ignore_borders"):
if (neib_shape is neib_step or neib_shape == neib_step or
# Aesara Constant == do not compare the data
# the equals function do that.
(hasattr(neib_shape, "equals") and neib_shape.equals(neib_step)
)):
return [
neibs2images(gz, neib_shape, x.shape, mode=self.mode),
grad_undefined(self, 1, neib_shape),
grad_undefined(self, 2, neib_step),
]
if self.mode in ["valid"]:
# Iterate over neighborhood positions, summing contributions.
def pos2map(pidx, pgz, prior_result, neib_shape, neib_step):
"""
Helper function that adds gradient contribution from a single
neighborhood position i,j.
pidx = Index of position within neighborhood.
pgz = Gradient of shape (batch_size*num_channels*neibs)
prior_result = Shape (batch_size, num_channnels, rows, cols)
neib_shape = Number of rows, cols in a neighborhood.
neib_step = Step sizes from image2neibs.
"""
nrows, ncols = neib_shape
rstep, cstep = neib_step
batch_size, num_channels, rows, cols = prior_result.shape
i = pidx // ncols
j = pidx - (i * ncols)
# This position does not touch some img pixels in valid mode.
result_indices = prior_result[:, :,
i:(rows - nrows + i + 1):rstep,
j:(cols - ncols + j + 1):cstep, ]
newshape = ((batch_size, num_channels) +
((rows - nrows) // rstep + 1, ) +
((cols - ncols) // cstep + 1, ))
return inc_subtensor(result_indices, pgz.reshape(newshape))
indices = arange(neib_shape[0] * neib_shape[1])
pgzs = gz.dimshuffle((1, 0))
result, _ = aesara.scan(
fn=pos2map,
sequences=[indices, pgzs],
outputs_info=zeros(x.shape),
non_sequences=[neib_shape, neib_step],
)
grad_input = result[-1]
return [
grad_input,
grad_undefined(self, 1, neib_shape),
grad_undefined(self, 2, neib_step),
]
return [
grad_not_implemented(self, 0, x),
grad_undefined(self, 1, neib_shape),
grad_undefined(self, 2, neib_step),
]
