def theano_dtw(batch, compiled_dtw, pack_batch=True):
"""
Calls the provided compiled Theano DTW function using the appropriate mechanims (batching inputs when supported else
submitted the sequence pairs one-at-a-time).
:param batch: The sequence pairs whose DTW distances are to be calculated.
:param compiled_dtw: The compiled DTW function to use.
:param pack_batch: Whether the batch should be packed or not (i.e. the input dimensionality supported by
compiled_dtw). If pack_batch=True then compiled_dtw must accept 3D (batched) inputs else
compiled_dtw must accept 2D (non-batched) inputs.
:return: The DTW distances between all the sequence pairs in batch.
"""
assert compiled_dtw is not None
assert isinstance(pack_batch, bool)
dtype = utility.get_standard_dtype()
def dtw(validated_batch):
if pack_batch:
# A validated batch input to this method is still in "list of pairs" format. To use the batched DTW function
# we must pack those pairs into a single 3D tensor. The tensor size is determined by the maximum sequence
# lengths on each side of the pairs. All shorter sequences are zero padded to fill the tensor. An integer
# array is constructed to inform the DTW function how long the sequences are on each side.
max_lengths = [
max(lengths)
for lengths in zip(*((len(x1), len(x2))
for x1, x2 in validated_batch))
]
batch_size = len(validated_batch)
input_size = validated_batch[0][0].shape[1]
packed_x1 = numpy.zeros((max_lengths[0], batch_size, input_size),
dtype=dtype)
packed_x2 = numpy.zeros((max_lengths[1], batch_size, input_size),
dtype=dtype)
x1_lengths = numpy.empty(batch_size, dtype='int32')
x2_lengths = numpy.empty(batch_size, dtype='int32')
for index, (x1, x2) in enumerate(validated_batch):
packed_x1[:len(x1), index, :] = x1
packed_x2[:len(x2), index, :] = x2
x1_lengths[index] = len(x1)
x2_lengths[index] = len(x2)
outputs = compiled_dtw(packed_x1, packed_x2, x1_lengths,
x2_lengths)
_check_outputs(outputs)
return [float(output) for output in outputs[0]]
# If we're not packing the batch then we need to submit them one at a time.
results = []
for x1, x2 in validated_batch:
outputs = compiled_dtw(x1, x2, len(x1), len(x2))
_check_outputs(outputs)
results.append(float(outputs[0]))
return results
return _common_dtw(batch, dtw)
def theano_symbolic_dtw(x1, x2, x1_lengths, x2_lengths, distance_function=cosine, normalize=True, debug_level=None,
eps=None):
"""
A symbolic implementation of DTW that supports batches of sequence pairs.
Returns a scalar if ndim == 2 and a vector of size x1.shape[1] if ndim == 3
This is slow! About 90 times slower than the Cython implementation using the parameters below.
:param x1: A tensor containing the first side of the sequence pairs to be aligned.
:param x2: A tensor containing the second side of the sequence pairs to be aligned.
:param x1_lengths: An integer vector identifying the lengths of the sequences in x1
:param x2_lengths: An integer vector identifying the lengths of the sequences in x2
:param distance_function: The symbolic distance function to use (e.g. a reference to a function in
distance).
:param normalize: Whether the DTW distances should be sequence length normalized.
:param debug_level: The debug level to use (see above for explanation).
:param eps: The minimum value to use inside the distance function. Set to the machine epsilon if None.
:return: The DTW distances for every sequence pair in the batch.
"""
if eps is None:
eps = numpy.dtype(theano.config.floatX).type(numpy.finfo(float).eps)
assert 0 <= x1_lengths.ndim == x2_lengths.ndim <= 1
assert isinstance(normalize, bool)
ndim = x1.ndim
assert 2 <= ndim == x2.ndim <= 3
# Ensure x2 is the shorter input to minimize the number of scan iterations
x1_shorter_than_x2 = tt.le(x1.shape[0], x2.shape[0])
x1, x2 = _swap(x1_shorter_than_x2, x1, x2, 'x1', 'x2', debug_level)
x1_lengths, x2_lengths = _swap(x1_shorter_than_x2, x1_lengths, x2_lengths, 'x1_lengths', 'x2_lengths', debug_level)
# Compute distances between x1 sequences and paired x2 sequences
d = distance_function(x1, x2, eps)
# Iterate over the temporal slices of x2. See dtw_outer_step for an explanation of the other inputs to this scan
# operation
x1_indexes = tt.arange(x1.shape[0], dtype=DTYPE_INT64)
results, _ = theano.scan(_create_dtw_outer_step(distance_function, debug_level), sequences=[x1_indexes, d],
outputs_info=[
tt.zeros_like(x2[:, :, 0] if x2.ndim == 3 else x2[:, 0], dtype=theano.config.floatX)],
non_sequences=[x1_lengths, x2_lengths])
result = results[x1_lengths - 1, x2_lengths - 1, tt.arange(x1.shape[1])] if x2.ndim == 3 else results[
x1_lengths - 1, x2_lengths - 1]
result = _debug(result, 'theano_symbolic_dtw.result', debug_level)
assert result.ndim == x1_lengths.ndim
# Length normalize the distances if requested to do so
if normalize:
result = _debug(result / tt.cast(x1_lengths + x2_lengths, dtype=utility.get_standard_dtype()),
'theano_symbolic_dtw.norm_result', debug_level)
return result
def theano_dtw(batch, compiled_dtw, pack_batch=True):
"""
Calls the provided compiled Theano DTW function using the appropriate mechanims (batching inputs when supported else
submitted the sequence pairs one-at-a-time).
:param batch: The sequence pairs whose DTW distances are to be calculated.
:param compiled_dtw: The compiled DTW function to use.
:param pack_batch: Whether the batch should be packed or not (i.e. the input dimensionality supported by
compiled_dtw). If pack_batch=True then compiled_dtw must accept 3D (batched) inputs else
compiled_dtw must accept 2D (non-batched) inputs.
:return: The DTW distances between all the sequence pairs in batch.
"""
assert compiled_dtw is not None
assert isinstance(pack_batch, bool)
dtype = utility.get_standard_dtype()
def dtw(validated_batch):
if pack_batch:
# A validated batch input to this method is still in "list of pairs" format. To use the batched DTW function
# we must pack those pairs into a single 3D tensor. The tensor size is determined by the maximum sequence
# lengths on each side of the pairs. All shorter sequences are zero padded to fill the tensor. An integer
# array is constructed to inform the DTW function how long the sequences are on each side.
max_lengths = [max(lengths) for lengths in zip(*((len(x1), len(x2)) for x1, x2 in validated_batch))]
batch_size = len(validated_batch)
input_size = validated_batch[0][0].shape[1]
packed_x1 = numpy.zeros((max_lengths[0], batch_size, input_size), dtype=dtype)
packed_x2 = numpy.zeros((max_lengths[1], batch_size, input_size), dtype=dtype)
x1_lengths = numpy.empty(batch_size, dtype='int32')
x2_lengths = numpy.empty(batch_size, dtype='int32')
for index, (x1, x2) in enumerate(validated_batch):
packed_x1[:len(x1), index, :] = x1
packed_x2[:len(x2), index, :] = x2
x1_lengths[index] = len(x1)
x2_lengths[index] = len(x2)
outputs = compiled_dtw(packed_x1, packed_x2, x1_lengths, x2_lengths)
_check_outputs(outputs)
return [float(output) for output in outputs[0]]
# If we're not packing the batch then we need to submit them one at a time.
results = []
for x1, x2 in validated_batch:
outputs = compiled_dtw(x1, x2, len(x1), len(x2))
_check_outputs(outputs)
results.append(float(outputs[0]))
return results
return _common_dtw(batch, dtw)
def _var(name,
test_value_shape,
debug_name_prefix,
debug_level,
dtype=None,
test_value_getter=lambda shape: numpy.random.randn(*shape)):
"""
Creates a new symbolic variable with the given name and generates a synthetic test value of the requested shape. The
resulting Theano variable is wrapped in a Debug operation.
:param name: The name of the variable to be created.
:param test_value_shape: The shape of the test value.
:param debug_name_prefix: Used in naming the Debug operation.
:param debug_level: The debug level to use (see above for explanation).
:param dtype: The type of the variable being created. Defaults to whatever is returned by
utility.get_standard_dtype.
:param test_value_getter: A method for generating test values. Defaults to zero mean unit variance Gaussian values.
:return: The newly created Theano variable.
"""
if dtype is None:
dtype = utility.get_standard_dtype()
if len(test_value_shape) == 0:
x = tt.scalar(name, dtype=dtype)
elif len(test_value_shape) == 1:
x = tt.vector(name, dtype=dtype)
elif len(test_value_shape) == 2:
x = tt.matrix(name, dtype=dtype)
elif len(test_value_shape) == 3:
x = tt.tensor3(name, dtype=dtype)
else:
raise Exception('Unsupported number of dimensions: ' +
str(len(test_value_shape)))
if debug_level > 0:
x.tag.test_value = test_value_getter(test_value_shape)
if len(test_value_shape) == 0:
x.tag.test_value = numpy.dtype(dtype).type(x.tag.test_value)
else:
x.tag.test_value = x.tag.test_value.astype(dtype)
return x, _debug(x, '%s.%s' % (debug_name_prefix, name), debug_level)
def _var(name, test_value_shape, debug_name_prefix, debug_level, dtype=None,
test_value_getter=lambda shape: numpy.random.randn(*shape)):
"""
Creates a new symbolic variable with the given name and generates a synthetic test value of the requested shape. The
resulting Theano variable is wrapped in a Debug operation.
:param name: The name of the variable to be created.
:param test_value_shape: The shape of the test value.
:param debug_name_prefix: Used in naming the Debug operation.
:param debug_level: The debug level to use (see above for explanation).
:param dtype: The type of the variable being created. Defaults to whatever is returned by
utility.get_standard_dtype.
:param test_value_getter: A method for generating test values. Defaults to zero mean unit variance Gaussian values.
:return: The newly created Theano variable.
"""
if dtype is None:
dtype = utility.get_standard_dtype()
if len(test_value_shape) == 0:
x = tt.scalar(name, dtype=dtype)
elif len(test_value_shape) == 1:
x = tt.vector(name, dtype=dtype)
elif len(test_value_shape) == 2:
x = tt.matrix(name, dtype=dtype)
elif len(test_value_shape) == 3:
x = tt.tensor3(name, dtype=dtype)
else:
raise Exception('Unsupported number of dimensions: ' + str(len(test_value_shape)))
if debug_level > 0:
x.tag.test_value = test_value_getter(test_value_shape)
if len(test_value_shape) == 0:
x.tag.test_value = numpy.dtype(dtype).type(x.tag.test_value)
else:
x.tag.test_value = x.tag.test_value.astype(dtype)
return x, _debug(x, '%s.%s' % (debug_name_prefix, name), debug_level)
def theano_symbolic_dtw(x1,
x2,
x1_lengths,
x2_lengths,
distance_function=cosine,
normalize=True,
debug_level=None,
eps=None):
"""
A symbolic implementation of DTW that supports batches of sequence pairs.
Returns a scalar if ndim == 2 and a vector of size x1.shape[1] if ndim == 3
This is slow! About 90 times slower than the Cython implementation using the parameters below.
:param x1: A tensor containing the first side of the sequence pairs to be aligned.
:param x2: A tensor containing the second side of the sequence pairs to be aligned.
:param x1_lengths: An integer vector identifying the lengths of the sequences in x1
:param x2_lengths: An integer vector identifying the lengths of the sequences in x2
:param distance_function: The symbolic distance function to use (e.g. a reference to a function in
distance).
:param normalize: Whether the DTW distances should be sequence length normalized.
:param debug_level: The debug level to use (see above for explanation).
:param eps: The minimum value to use inside the distance function. Set to the machine epsilon if None.
:return: The DTW distances for every sequence pair in the batch.
"""
if eps is None:
eps = numpy.dtype(theano.config.floatX).type(numpy.finfo(float).eps)
assert 0 <= x1_lengths.ndim == x2_lengths.ndim <= 1
assert isinstance(normalize, bool)
ndim = x1.ndim
assert 2 <= ndim == x2.ndim <= 3
# Ensure x2 is the shorter input to minimize the number of scan iterations
x1_shorter_than_x2 = tt.le(x1.shape[0], x2.shape[0])
x1, x2 = _swap(x1_shorter_than_x2, x1, x2, 'x1', 'x2', debug_level)
x1_lengths, x2_lengths = _swap(x1_shorter_than_x2, x1_lengths, x2_lengths,
'x1_lengths', 'x2_lengths', debug_level)
# Compute distances between x1 sequences and paired x2 sequences
d = distance_function(x1, x2, eps)
# Iterate over the temporal slices of x2. See dtw_outer_step for an explanation of the other inputs to this scan
# operation
x1_indexes = tt.arange(x1.shape[0], dtype=DTYPE_INT64)
results, _ = theano.scan(
_create_dtw_outer_step(distance_function, debug_level),
sequences=[x1_indexes, d],
outputs_info=[
tt.zeros_like(x2[:, :, 0] if x2.ndim == 3 else x2[:, 0],
dtype=theano.config.floatX)
],
non_sequences=[x1_lengths, x2_lengths])
result = results[x1_lengths - 1, x2_lengths - 1,
tt.arange(x1.shape[1])] if x2.ndim == 3 else results[
x1_lengths - 1, x2_lengths - 1]
result = _debug(result, 'theano_symbolic_dtw.result', debug_level)
assert result.ndim == x1_lengths.ndim
# Length normalize the distances if requested to do so
if normalize:
result = _debug(
result / tt.cast(x1_lengths + x2_lengths,
dtype=utility.get_standard_dtype()),
'theano_symbolic_dtw.norm_result', debug_level)
return result
