Пример #1
0
def is_neg(var):
    """
    Match a variable with the `-x` pattern.

    :param var: The Variable to analyze.

    :return: `x` if `var` is of the form `-x`, or None otherwise.
    """
    apply = var.owner
    if not apply:
        return None
    # First match against `tensor.neg`.
    if apply.op == tensor.neg:
        return apply.inputs[0]
    # Then match against a multiplication by -1.
    if apply.op == tensor.mul and len(apply.inputs) >= 2:
        for idx, mul_input in enumerate(apply.inputs):
            try:
                constant = opt.get_scalar_constant_value(mul_input)
                is_minus_1 = numpy.allclose(constant, -1)
            except NotScalarConstantError:
                is_minus_1 = False
            if is_minus_1:
                # Found a multiplication by -1.
                if len(apply.inputs) == 2:
                    # Only return the other input.
                    return apply.inputs[1 - idx]
                else:
                    # Return the multiplication of all other inputs.
                    return tensor.mul(*(apply.inputs[0:idx] +
                                        apply.inputs[idx + 1:]))
    # No match.
    return None
Пример #2
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 def fibby_of_zero(node):
     if node.op == fibby:
         x = node.inputs[0]
         try:
             if numpy.all(0 == get_scalar_constant_value(x)):
                 return [x]
         except NotScalarConstantError:
             pass
Пример #3
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 def fibby_of_zero(node):
     if node.op == fibby:
         x = node.inputs[0]
         try:
             if numpy.all(0 == get_scalar_constant_value(x)):
                 return [x]
         except NotScalarConstantError:
             pass
Пример #4
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def _is_1(expr):
    """rtype bool. True iff expr is a constant close to 1
    """
    try:
        v = opt.get_scalar_constant_value(expr)
        return numpy.allclose(v, 1)
    except tensor.NotScalarConstantError:
        return False
Пример #5
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def _is_1(expr):
    """

    Returns
    -------
    bool
        True iff expr is a constant close to 1.

    """
    try:
        v = opt.get_scalar_constant_value(expr)
        return np.allclose(v, 1)
    except tensor.NotScalarConstantError:
        return False
Пример #6
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def _is_1(expr):
    """

    Returns
    -------
    bool
        True iff expr is a constant close to 1.

    """
    try:
        v = opt.get_scalar_constant_value(expr)
        return np.allclose(v, 1)
    except tensor.NotScalarConstantError:
        return False
Пример #7
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def local_1msigmoid(node):
    """
    1-sigm(x) -> sigm(-x)
    """
    if node.op == tensor.sub:
        sub_l, sub_r = node.inputs
        if len(sub_r.clients) > 1:
            return  # graph is using both sigm and 1-sigm
        if sub_r.owner and sub_r.owner.op == sigmoid:
            try:
                val_l = opt.get_scalar_constant_value(sub_l)
            except Exception, e:
                return
            if numpy.allclose(numpy.sum(val_l), 1):
                return [sigmoid(-sub_r.owner.inputs[0])]
Пример #8
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def local_1msigmoid(node):
    """
    1-sigm(x) -> sigm(-x)

    """
    if node.op == tensor.sub:
        sub_l, sub_r = node.inputs
        if len(sub_r.clients) > 1:
            return  # graph is using both sigm and 1-sigm
        if sub_r.owner and sub_r.owner.op == sigmoid:
            try:
                val_l = opt.get_scalar_constant_value(sub_l)
            except tensor.NotScalarConstantError:
                return
            if np.allclose(np.sum(val_l), 1):
                out = sigmoid(-sub_r.owner.inputs[0])
                copy_stack_trace([sub_r, node.outputs[0]], out)
                return [out]
Пример #9
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def local_1msigmoid(node):
    """
    1-sigm(x) -> sigm(-x)

    """
    if node.op == tensor.sub:
        sub_l, sub_r = node.inputs
        if len(sub_r.clients) > 1:
            return  # graph is using both sigm and 1-sigm
        if sub_r.owner and sub_r.owner.op == sigmoid:
            try:
                val_l = opt.get_scalar_constant_value(sub_l)
            except tensor.NotScalarConstantError:
                return
            if np.allclose(np.sum(val_l), 1):
                out = sigmoid(-sub_r.owner.inputs[0])
                copy_stack_trace([sub_r, node.outputs[0]], out)
                return [out]
Пример #10
0
def get_dummy_args(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):
    ################################################################## P1>
    # 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, gof.Variable):
            non_seqs.append(tensor.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, integer_types)):
        n_fixed_steps = int(n_steps)
    else:
        try:
            n_fixed_steps = opt.get_scalar_constant_value(n_steps)
        except tensor.basic.NotScalarConstantError:
            n_fixed_steps = None

    # Check n_steps is an int
    if (hasattr(n_steps, 'dtype')
            and str(n_steps.dtype)[:3] not in ('uin', 'int')):
        raise ValueError(' n_steps must be an int. dtype provided '
                         'is %s' % 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 xrange(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 xrange(n_outs):
        if outs_info[i] is not None:
            if isinstance(outs_info[i], dict):
                # DEPRECATED :
                if outs_info[i].get('return_steps', None) is not None:
                    raise ValueError(
                        "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 '
                                  '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(
                        'Output %s ( index %d) has a initial '
                        'state but taps is explicitly set to None ',
                        getattr(outs_info[i]['initial'], 'name', 'None'), i)
                outs_info[i]['taps'] = [-1]
        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 theano 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 = numpy.min(seq['taps'])
            maxtap = numpy.max(seq['taps'])
            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]
                _seq_val = tensor.as_tensor_variable(seq['input'])
                _seq_val_slice = _seq_val[k - mintap]
                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 = gof.Op._get_test_value(
                            _seq_val_slice)
                    except AttributeError as e:
                        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.info(
                                ('Cannot compute test value for '
                                 'the inner function of scan, input value '
                                 'missing %s'), e)

                # 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 + '[t+%d]' % k
                    elif k == 0:
                        nw_name = seq['input'].name + '[t]'
                    else:
                        nw_name = seq['input'].name + '[t%d]' % k
                    nw_slice.name = nw_name

                # 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)
                start = (k - mintap_proxy)
                if k == maxtap_proxy:
                    nw_seq = seq['input'][start:]
                else:
                    end = -(maxtap_proxy - k)
                    nw_seq = seq['input'][start: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

    # 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 scan_utils.isNaN_or_Inf_or_None(n_steps):
        # ^ N_steps should also be considered
        lengths_vec.append(tensor.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 scan_utils.isNaN_or_Inf_or_None(n_steps):
        actual_n_steps = lengths_vec[0]
        for contestant in lengths_vec[1:]:
            actual_n_steps = tensor.minimum(actual_n_steps, contestant)
    else:
        actual_n_steps = tensor.as_tensor(n_steps)

    # Add names -- it helps a lot when debugging

    for (nw_seq, seq) in zip(scan_seqs, seqs):
        if getattr(seq['input'], 'name', None) is not None:
            nw_seq.name = seq['input'].name + '[%d:]' % k

    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 = []
    mit_mot_rightOrder = []

    # 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, tensor.Variable):
                actual_arg = tensor.as_tensor_variable(actual_arg)
            arg = safe_new(actual_arg)
            if isinstance(arg, tensor.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 = gof.Op._get_test_value(actual_arg)
                except AttributeError as e:
                    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.info(
                            ('Cannot compute test value for the '
                             'inner function of scan, input value missing %s'),
                            e)

            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(
                scan_utils.expand_empty(
                    tensor.unbroadcast(tensor.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 numpy.any(numpy.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(numpy.min(init_out['taps']))
            mit_sot_tap_array.append(init_out['taps'])
            idx_offset = abs(numpy.min(init_out['taps']))
            # Sequence
            mit_sot_scan_inputs.append(
                scan_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 = tensor.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 = gof.Op._get_test_value(
                            _init_out_var_slice)
                    except AttributeError as e:
                        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.info(
                                ('Cannot compute test value for '
                                 'the inner function of scan, input value '
                                 'missing. %s'), e)

                # 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 +
                                         '[t+%d]' % k)
                    elif k == 0:
                        nw_slice.name = init_out['initial'].name + '[t]'
                    else:
                        nw_slice.name = (init_out['initial'].name +
                                         '[t%d]' % 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 = numpy.max([-1] + mit_sot_rightOrder) + 1
    max_sit_sot = numpy.max([-1] + sit_sot_rightOrder) + 1
    n_elems = numpy.max([max_mit_sot, max_sit_sot])
    _ordered_args = [[] for x in xrange(n_elems)]
    offset = 0
    for idx in xrange(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 xrange(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, tensor.Constant))
    ]
    ################################################################## P1<
    return dummy_args, locals()
Пример #11
0
def scan(fn,
         sequences=None,
         states=None,
         params=None,
         n_steps=None,
         mode=None,
         name=None,
         profile=False,
         allow_gc=None):
    """
    Similar to Theano's official scan, this function gives the user more
    control over the scan op, avoiding certain difficulties that arose from
    missing optimizations.

    :param fn: lambda function that describes one step of scan (see the
        official Theano scan function)
    :param sequences: similar to the official Theano's scan. This version
        of scan does not support taps for the sequences (it can only be a
        list of tensor). Scan assumes that sequences have the right length
        and it does not check for this.
    :param states: similar to outputs_info of the official scan function.
        There is one crucial difference though, namely that the `initial`
        key in the dictionary has been replace by 'membuf' key. This
        reflects the change of meaning. Instead of passing to scan just
        the initial steps misisng, one has now to pass a memory buffer in
        which scan will try to store its output. In this memory buffer the
        first entries should be set to the initial states of the
        corresponding states.
        Providing a memory buffer that has less entries then the number of
        steps, mneans scan will only use that amount of memory. The user has
        to match the memory buffer size with the number of steps, otherwise
        scan will produce wrong results. Also if gradients are to be
        computed through the scan, the memory buffer should have the same
        length as the number of steps.
        For states that do not require a initial state, one has to provide a
        dictionary with a single key 'steps' that says how many intermediate
        results to store. See examples below for more insight.
    :param n_steps: This parameter is mandatory and it will represent the
        number of steps scan will do (scan will not check sequences or any
        other source of information to figure out how many steps it needs
        to do).
    :param mode: Same as for the official scan
    :param name: Same as for the official scan
    :param profile: Same as for the official scan

    Note:
     - there is no truncate / go_backwards anymore !
     - the outputs returned by scan contain the initial states as well (i.e.
     if I loop over k steps, with my smallest tap for an output -3 and keep
     al intermediate results, my output will be of length k+3

     Examples:
         (a) if you do not want to store any intermediate results (just the
         last one)

         # The memory buffer can be the initial state, just that we need to
         # add one extra dimension in front of it
         state = TT.unbroadcast(TT.shape_padleft(x0),0)
         out,_ = scan(lambda x:x+1, states = state, n_steps = 5)
         # Once we got our result we need to remove the extra dimension
         out = out[0]

        (b) if you want to keep every intermediate results

        state = TT.alloc(TT.constant(0), 6, x0.shape[0])
        state = TT.set_subtensor(state[0], x0)
        out,_ = scan(lambda x:x+1, states = state, n_steps = 5)
        out = out[1:]

    """
    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(states)
    if allow_gc is None:
        allow_gc = config.scan.allow_gc

    # 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(params):
        if not isinstance(elem, gof.Variable):
            non_seqs.append(tensor.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 = opt.get_scalar_constant_value(n_steps)
        except tensor.basic.NotScalarConstantError:
            n_fixed_steps = None

    # Check n_steps is an int
    if (hasattr(n_steps, 'dtype')
            and str(n_steps.dtype)[:3] not in ('uin', 'int')):
        raise ValueError(' n_steps must be an int. dtype provided '
                         'is %s' % n_steps.dtype)

    # compute number of sequences and number of outputs
    n_seqs = len(seqs)
    n_outs = len(outs_info)

    return_steps = OrderedDict()
    # wrap outputs info in a dictionary if they are not already in one
    for i in xrange(n_outs):
        if outs_info[i] is not None:
            if not isinstance(outs_info[i], dict):
                # by default any output has a tap value of -1
                outs_info[i] = dict(membuf=outs_info[i], taps=[-1])
            elif (not outs_info[i].get('membuf', None)
                  and outs_info[i].get('taps', None)):
                # ^ no initial state but taps provided
                raise ValueError(('If you are using slices of an output '
                                  'you need to provide a memory buffer for '
                                  'the state '), outs_info[i])
            elif (outs_info[i].get('membuf', None)
                  and not outs_info[i].get('taps', None)):
                # ^ initial state but taps not provided
                if 'taps' in outs_info[i]:
                    # ^ explicitly provided a None for taps
                    _logger.warning(
                        'Output %s (index %d) has a memory '
                        'buffer but taps is explicitly set to None ',
                        getattr(outs_info[i]['membuf'], 'name', 'None'), i)
                outs_info[i]['taps'] = [-1]
        else:
            # if a None is provided as the output info we replace it
            # with an dict(steps=n_steps) to simplify handling
            outs_info[i] = dict(steps=n_steps)

    ##
    ###   Step 2. Generate inputs and outputs of the inner functions
    ###           for compiling a dummy function (Iteration #1)
    ##

    # create theano 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):
        if isinstance(seq, dict):
            seq = seq['input']
        actual_slice = seq[0]
        _seq_val = tensor.as_tensor_variable(seq)
        _seq_val_slice = _seq_val[0]

        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 = gof.Op._get_test_value(
                    _seq_val_slice)
            except AttributeError, e:
                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.info(('Cannot compute test value for '
                                  'the inner function of scan, input value '
                                  'missing %s'), e)

        if seq.name:
            nw_slice.name = seq.name + '[t]'
        scan_seqs.append(_seq_val)
        inner_seqs.append(nw_slice)
        inner_slices.append(actual_slice)

        n_seqs += 1
Пример #12
0
def scan(fn,
         sequences=None,
         states=None,
         params=None,
         n_steps=None,
         mode=None,
         name=None,
         profile=False,
         allow_gc=None):
    """
    Similar to Theano's official scan, this function gives the user more
    control over the scan op, avoiding certain difficulties that arose from
    missing optimizations.

    :param fn: lambda function that describes one step of scan (see the
        official Theano scan function)
    :param sequences: similar to the official Theano's scan. This version
        of scan does not support taps for the sequences (it can only be a
        list of tensor). Scan assumes that sequences have the right length
        and it does not check for this.
    :param states: similar to outputs_info of the official scan function.
        There is one crucial difference though, namely that the `initial`
        key in the dictionary has been replace by 'membuf' key. This
        reflects the change of meaning. Instead of passing to scan just
        the initial steps misisng, one has now to pass a memory buffer in
        which scan will try to store its output. In this memory buffer the
        first entries should be set to the initial states of the
        corresponding states.
        Providing a memory buffer that has less entries then the number of
        steps, mneans scan will only use that amount of memory. The user has
        to match the memory buffer size with the number of steps, otherwise
        scan will produce wrong results. Also if gradients are to be
        computed through the scan, the memory buffer should have the same
        length as the number of steps.
        For states that do not require a initial state, one has to provide a
        dictionary with a single key 'steps' that says how many intermediate
        results to store. See examples below for more insight.
    :param n_steps: This parameter is mandatory and it will represent the
        number of steps scan will do (scan will not check sequences or any
        other source of information to figure out how many steps it needs
        to do).
    :param mode: Same as for the official scan
    :param name: Same as for the official scan
    :param profile: Same as for the official scan

    Note:
     - there is no truncate / go_backwards anymore !
     - the outputs returned by scan contain the initial states as well (i.e.
     if I loop over k steps, with my smallest tap for an output -3 and keep
     al intermediate results, my output will be of length k+3

     Examples:
         (a) if you do not want to store any intermediate results (just the
         last one)

         # The memory buffer can be the initial state, just that we need to
         # add one extra dimension in front of it
         state = TT.unbroadcast(TT.shape_padleft(x0),0)
         out,_ = scan(lambda x:x+1, states = state, n_steps = 5)
         # Once we got our result we need to remove the extra dimension
         out = out[0]

        (b) if you want to keep every intermediate results

        state = TT.alloc(TT.constant(0), 6, x0.shape[0])
        state = TT.set_subtensor(state[0], x0)
        out,_ = scan(lambda x:x+1, states = state, n_steps = 5)
        out = out[1:]

    """
    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(states)
    if allow_gc is None:
        allow_gc = config.scan.allow_gc

    # 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(params):
        if not isinstance(elem, gof.Variable):
            non_seqs.append(tensor.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 = opt.get_scalar_constant_value(n_steps)
        except tensor.basic.NotScalarConstantError:
            n_fixed_steps = None

    # Check n_steps is an int
    if (hasattr(n_steps, 'dtype') and
        str(n_steps.dtype)[:3] not in ('uin', 'int')):
        raise ValueError(' n_steps must be an int. dtype provided '
                         'is %s' % n_steps.dtype)

    # compute number of sequences and number of outputs
    n_seqs = len(seqs)
    n_outs = len(outs_info)

    return_steps = OrderedDict()
    # wrap outputs info in a dictionary if they are not already in one
    for i in xrange(n_outs):
        if outs_info[i] is not None:
            if not isinstance(outs_info[i], dict):
                # by default any output has a tap value of -1
                outs_info[i] = dict(membuf=outs_info[i], taps=[-1])
            elif (not outs_info[i].get('membuf', None) and
                    outs_info[i].get('taps', None)):
                # ^ no initial state but taps provided
                raise ValueError(('If you are using slices of an output '
                                  'you need to provide a memory buffer for '
                                  'the state '), outs_info[i])
            elif (outs_info[i].get('membuf', None) and
                  not outs_info[i].get('taps', None)):
                # ^ initial state but taps not provided
                if 'taps' in outs_info[i]:
                    # ^ explicitly provided a None for taps
                    _logger.warning(
                            'Output %s (index %d) has a memory '
                            'buffer but taps is explicitly set to None ',
                            getattr(outs_info[i]['membuf'], 'name', 'None'),
                            i)
                outs_info[i]['taps'] = [-1]
        else:
            # if a None is provided as the output info we replace it
            # with an dict(steps=n_steps) to simplify handling
            outs_info[i] = dict(steps=n_steps)

    ##
    # Step 2. Generate inputs and outputs of the inner functions
    # for compiling a dummy function (Iteration #1)
    ##

    # create theano 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):
        if isinstance(seq, dict):
            seq = seq['input']
        actual_slice = seq[0]
        _seq_val = tensor.as_tensor_variable(seq)
        _seq_val_slice = _seq_val[0]

        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 = gof.Op._get_test_value(
                    _seq_val_slice)
            except AttributeError as e:
                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.info(('Cannot compute test value for '
                        'the inner function of scan, input value '
                        'missing %s'), e)

        if seq.name:
            nw_slice.name = seq.name + '[t]'
        scan_seqs.append(_seq_val)
        inner_seqs.append(nw_slice)
        inner_slices.append(actual_slice)

        n_seqs += 1

    actual_n_steps = tensor.as_tensor(n_steps)

    # 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 = []
    mit_mot_rightOrder = []

    # 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 = []
    nit_sot_steps = []
    # 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

        # Note, 'taps' might not be in the dictionary
        if 'taps' in init_out and init_out['taps'] == [-1]:

            actual_arg = init_out['membuf']
            arg = safe_new(init_out['membuf'][0])
            if isinstance(arg, tensor.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 = gof.Op._get_test_value(actual_arg)
                except AttributeError as e:
                    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.info(('Cannot compute test value for the '
                            'inner function of scan, input value missing %s'),
                                     e)

            if getattr(init_out['membuf'], 'name', None) is not None:
                arg.name = init_out['membuf'].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(actual_arg)
            sit_sot_inner_slices.append(actual_arg[0])
            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 numpy.any(numpy.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(numpy.min(init_out['taps']))
            mit_sot_tap_array.append(init_out['taps'])
            idx_offset = abs(numpy.min(init_out['taps']))
            # Sequence
            mit_sot_scan_inputs.append(init_out['membuf'])

            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['membuf'][k + mintap]
                _init_out_var = tensor.as_tensor_variable(init_out['membuf'])
                _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 = gof.Op._get_test_value(
                            _init_out_var_slice)
                    except AttributeError as e:
                        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.info(('Cannot compute test value for '
                                'the inner function of scan, input value '
                                'missing. %s'), e)

                # give it a name or debugging and pretty printing
                if getattr(init_out['membuf'], 'name', None) is not None:
                    if k > 0:
                        nw_slice.name = (init_out['membuf'].name +
                                            '[t+%d]' % k)
                    elif k == 0:
                        nw_slice.name = init_out['membuf'].name + '[t]'
                    else:
                        nw_slice.name = (init_out['membuf'].name +
                                            '[t%d]' % k)
                mit_sot_inner_inputs.append(nw_slice)
                mit_sot_inner_slices.append(actual_nw_slice)
        else:
            pass

    # Re-order args
    max_mit_sot = numpy.max([-1] + mit_sot_rightOrder) + 1
    max_sit_sot = numpy.max([-1] + sit_sot_rightOrder) + 1
    n_elems = numpy.max([max_mit_sot, max_sit_sot])
    _ordered_args = [[] for x in xrange(n_elems)]
    offset = 0
    for idx in xrange(n_mit_sot):
        n_inputs = len(mit_sot_tap_array[idx])
        if n_fixed_steps == 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 xrange(n_sit_sot):
        if n_fixed_steps == 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 == 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, tensor.Constant))]
    # when we apply the lambda expression we get a mixture of update rules
    # and outputs that needs to be separated
    lambda_result = fn(*args)
    condition, outputs, updates = scan_utils.get_updates_and_outputs(
                                                                lambda_result)
    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 == 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, ',
                    str(condition), ' is ignored'))

        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, tensor.TensorType) and
                return_steps.get(pos, 0) != 1):
                outputs[pos] = tensor.unbroadcast(
                    tensor.shape_padleft(inner_out), 0)
        if 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
    fake_nonseqs = [x.type() for x in non_seqs]
    fake_outputs = scan_utils.clone(outputs + updates.values(),
                                    replace=dict(zip(non_seqs,
                                                     fake_nonseqs)))
    all_inputs = itertools.ifilter(
        lambda x: (isinstance(x, gof.Variable) and
                   not isinstance(x, SharedVariable) and
                   not isinstance(x, gof.Constant)),
        gof.graph.inputs(fake_outputs))
    extra_inputs = filter(lambda x: x not in args + fake_nonseqs,
                                    all_inputs)
    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
    if condition is not None:
        dummy_outs.append(condition)

    # If we use a regular dict here, the results are non-deterministic
    if not isinstance(updates, (list, tuple)):
        if isinstance(updates, dict) and \
            not isinstance(updates, OrderedDict):
                warnings.warn("Using non-deterministic dictionary.")

    dummy_f = function(dummy_args,
                       dummy_outs,
                       updates=updates,
                       mode=compile.mode.Mode(linker='py',
                                              optimizer=None),
                      on_unused_input='ignore')

    ##
    # 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 output_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 = [dict(steps=n_steps) for x in xrange(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 = []
    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'
            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

    # 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 not 'taps' 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)
            nit_sot_steps.append(out['steps'])
            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, tensor.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, tensor.Constant))]

    givens.update(dict(zip(other_scan_args, other_inner_args)))
    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(dict(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)
    new_givens = OrderedDict()
    for w, w_copy in givens.iteritems():
        new_givens[w] = w.type.filter_variable(w_copy)

    new_outs = scan_utils.clone(inner_outs, replace=new_givens)

    ##
    # Step 7. Create the Scan Op
    ##

    tap_array = mit_sot_tap_array + [[-1] for x in xrange(n_sit_sot)]
    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'] = -1
    info['name'] = name
    info['mode'] = mode
    info['destroy_map'] = OrderedDict()
    info['inplace'] = False
    info['gpu'] = False
    info['as_while'] = as_while
    info['profile'] = profile
    info['_scan_savemem_visited'] = True
    info['allow_gc'] = allow_gc

    local_op = scan_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 +
                    nit_sot_steps +
                    other_shared_scan_args +
                    other_scan_args)

    scan_inputs = []
    for arg in [actual_n_steps] + _scan_inputs:
        if not isinstance(arg, gof.Variable):
            arg = tensor.as_tensor_variable(arg)
        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()

    offset = n_mit_mot
    offsets = [abs(numpy.min(x)) for x in mit_sot_tap_array]
    mit_sot_outs = scan_outs[offset:offset + n_mit_sot]

    offset += n_mit_sot
    offsets = [1 for x in xrange(n_sit_sot)]
    sit_sot_outs = scan_outs[offset:offset + n_sit_sot]

    offset += n_sit_sot
    nit_sot_outs = scan_outs[offset:offset + n_nit_sot]

    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):
        scan_out_list[pos] = _scan_out_list[idx]
    if len(scan_out_list) == 1:
        scan_out_list = scan_out_list[0]
    elif len(scan_out_list) == 0:
        scan_out_list = None

    assert isinstance(update_map, OrderedDict)
    return (scan_out_list, update_map)
Пример #13
0
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):
    """
    This function constructs and applies a Scan op to the provided
    arguments.

    :param 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 theano
        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 otuput
        * ...
        * 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 theano.tensor as TT
            W   = TT.matrix()
            W_2 = W**2
            def f(x):
                return TT.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}, theano.scan_module.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). = {}):

    :param sequences:
        ``sequences`` is the list of Theano 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*) -- Theano 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 Theano variable in the list ``sequences`` is automatically
        wrapped into a dictionary where ``taps`` is set to ``[0]``


    :param outputs_info:
        ``outputs_info`` is the list of Theano 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`` -- Theano 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``)


    :param 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.


    :param n_steps:
        ``n_steps`` is the number of steps to iterate given as an int
        or Theano 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 the value is negative, ``scan``
        will run backwards in time. If the ``go_backwards`` flag is already
        set and also ``n_steps`` is negative, ``scan`` will run forward
        in time. If n_steps is not provided, ``scan`` will figure
        out the amount of steps it should run given its input sequences.


    :param 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.


    :param 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.


    :param 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.

    :param 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 ``theano.function`` for details about
        possible values and their meaning).

    :param 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)

    :param 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.

    :param strict:
        If true, all the shared variables used in ``fn`` must be provided as a
        part of ``non_sequences`` or ``sequences``. 

    :rtype: tuple
    :return: tuple of the form (outputs, updates); ``outputs`` is either a
             Theano variable or a list of Theano 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 ``theano.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, gof.Variable):
            non_seqs.append(tensor.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 = opt.get_scalar_constant_value(n_steps)
        except tensor.basic.NotScalarConstantError:
            n_fixed_steps = None

    # Check n_steps is an int
    if (hasattr(n_steps, 'dtype') and
        str(n_steps.dtype)[:3] not in ('uin', 'int')):
        raise ValueError(' n_steps must be an int. dtype provided '
                         'is %s' % 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 xrange(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 xrange(n_outs):
        if outs_info[i] is not None:
            if isinstance(outs_info[i], dict):
                # DEPRECATED :
                if outs_info[i].get('return_steps', None) is not None:
                    raise ValueError(
                            "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 '
                                  '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('Output %s ( index %d) has a initial '
                            'state but taps is explicitly set to None ',
                             getattr(outs_info[i]['initial'], 'name', 'None'),
                             i)
                outs_info[i]['taps'] = [-1]
        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 theano 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 = numpy.min(seq['taps'])
            maxtap = numpy.max(seq['taps'])
            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]
                _seq_val = tensor.as_tensor_variable(seq['input'])
                _seq_val_slice = _seq_val[k - mintap]
                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 = gof.Op._get_test_value(
                            _seq_val_slice)
                    except AttributeError as e:
                        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.info(('Cannot compute test value for '
                                'the inner function of scan, input value '
                                'missing %s'), e)

                # 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 + '[t+%d]' % k
                    elif k == 0:
                        nw_name = seq['input'].name + '[t]'
                    else:
                        nw_name = seq['input'].name + '[t%d]' % k
                    nw_slice.name = nw_name

                # We cut the sequence such that seq[i] to correspond to
                # seq[i-k]
                if maxtap < 0:
                    offset = abs(maxtap)
                else:
                    offset = 0
                if maxtap == mintap and maxtap != 0:
                    if maxtap < 0:
                        nw_seq = seq['input'][:maxtap]
                    else:
                        nw_seq = seq['input'][maxtap:]
                elif maxtap - k != 0:
                    nw_seq = seq['input'][offset + k - mintap: -(maxtap - k)]
                else:
                    nw_seq = seq['input'][offset + k - mintap:]
                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

    # 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 scan_utils.isNaN_or_Inf_or_None(n_steps):
        # ^ N_steps should also be considered
        lengths_vec.append(tensor.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 scan_utils.isNaN_or_Inf_or_None(n_steps):
        actual_n_steps = lengths_vec[0]
        for contestant in lengths_vec[1:]:
            actual_n_steps = tensor.minimum(actual_n_steps, contestant)
    else:
        actual_n_steps = tensor.as_tensor(n_steps)

    # Add names -- it helps a lot when debugging

    for (nw_seq, seq) in zip(scan_seqs, seqs):
        if getattr(seq['input'], 'name', None) is not None:
            nw_seq.name = seq['input'].name + '[%d:]' % k

    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 = []
    mit_mot_rightOrder = []

    # 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, tensor.Variable):
                actual_arg = tensor.as_tensor_variable(actual_arg)
            arg = safe_new(actual_arg)
            if isinstance(arg, tensor.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 = gof.Op._get_test_value(actual_arg)
                except AttributeError as e:
                    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.info(('Cannot compute test value for the '
                            'inner function of scan, input value missing %s'),
                                     e)

            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(
                scan_utils.expand(
                    tensor.unbroadcast(
                        tensor.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 numpy.any(numpy.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(numpy.min(init_out['taps']))
            mit_sot_tap_array.append(init_out['taps'])
            idx_offset = abs(numpy.min(init_out['taps']))
            # Sequence
            mit_sot_scan_inputs.append(
                scan_utils.expand(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 = tensor.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 = gof.Op._get_test_value(
                            _init_out_var_slice)
                    except AttributeError as e:
                        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.info(('Cannot compute test value for '
                                'the inner function of scan, input value '
                                'missing. %s'), e)

                # 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 +
                                            '[t+%d]' % k)
                    elif k == 0:
                        nw_slice.name = init_out['initial'].name + '[t]'
                    else:
                        nw_slice.name = (init_out['initial'].name +
                                            '[t%d]' % 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 = numpy.max([-1] + mit_sot_rightOrder) + 1
    max_sit_sot = numpy.max([-1] + sit_sot_rightOrder) + 1
    n_elems = numpy.max([max_mit_sot, max_sit_sot])
    _ordered_args = [[] for x in xrange(n_elems)]
    offset = 0
    for idx in xrange(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 xrange(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, tensor.Constant))]
    # when we apply the lambda expression we get a mixture of update rules
    # and outputs that needs to be separated

    condition, outputs, updates = scan_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, ',
                    str(condition), ' is ignored'))

        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, tensor.TensorType) and
                return_steps.get(pos, 0) != 1):
                outputs[pos] = tensor.unbroadcast(
                    tensor.shape_padleft(inner_out), 0)
        if 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
    fake_nonseqs = [x.type() for x in non_seqs]
    fake_outputs = scan_utils.clone(outputs,
                                    replace=OrderedDict(zip(non_seqs,
                                                     fake_nonseqs)))
    all_inputs = itertools.ifilter(
        lambda x: (isinstance(x, gof.Variable) and
                   not isinstance(x, SharedVariable) and
                   not isinstance(x, gof.Constant)),
        gof.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
    if condition is not None:
        dummy_outs.append(condition)
    dummy_f = function(dummy_args,
                       dummy_outs,
                       updates=updates,
                       mode=compile.mode.Mode(linker='py',
                                              optimizer=None),
                       on_unused_input='ignore',
                       profile=False)

    ##
    # 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 xrange(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(
                    scan_utils.expand(
                        tensor.unbroadcast(
                            tensor.shape_padleft(input.variable), 0),
                        actual_n_steps))
                tensor_update = tensor.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 not 'taps' 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, tensor.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, tensor.Constant))]

    givens.update(OrderedDict(zip(other_scan_args, other_inner_args)))

    if strict:
        non_seqs_set = set(non_sequences if non_sequences != 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)
    # Cuda is imported here, instead of being imported on top of the file
    # because forces 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 theano.sandbox import cuda
    if cuda.cuda_available:
        # very often we end up in this situation when we want to
        # replace w with w_copy, where w is CudaNdarray
        # and w_copy is TensorType. This is caused because shared
        # variables are put on GPU right aways >:| ,
        new_givens = OrderedDict()

        for w, w_copy in givens.iteritems():
            if (isinstance(w.type, cuda.CudaNdarrayType)
                and isinstance(w_copy.type, tensor.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 = scan_utils.clone(inner_outs, replace=new_givens)

    ##
    # Step 7. Create the Scan Op
    ##

    tap_array = mit_sot_tap_array + [[-1] for x in xrange(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['gpu'] = False
    info['as_while'] = as_while
    info['profile'] = profile
    info['allow_gc'] = allow_gc
    info['strict'] = strict
    if strict:
        warnings.warn('In the strict mode, all neccessary shared variables '
                      'must be passed as a part of non_sequences', Warning)

    local_op = scan_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 xrange(n_nit_sot)] +
                    other_shared_scan_args +
                    other_scan_args)

    scan_inputs = []
    for arg in [actual_n_steps] + _scan_inputs:
        try:
            arg = tensor.as_tensor_variable(arg)
        except TypeError:
            # This happens for Random States for e.g. but it is a good way
            # to make sure no input is a cuda ndarrays
            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(numpy.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 xrange(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 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)
Пример #14
0
def scan(fn,
         sequences=None,
         states=None,
         params=None,
         n_steps=None,
         mode=None,
         name=None,
         profile=False):
    """
    Similar to Theano's official scan, this function gives the user more
    control over the scan op, avoiding certain difficulties that arose from
    missing optimizations.

    :param fn: lambda function that describes one step of scan (see the
        official Theano scan function)
    :param sequences: similar to the official Theano's scan. This version
        of scan does not support taps for the sequences (it can only be a
        list of tensor). Scan assumes that sequences have the right length
        and it does not check for this.
    :param states: similar to outputs_info of the official scan function.
        There is one crucial difference though, namely that the `initial`
        key in the dictionary has been replace by 'membuf' key. This
        reflects the change of meaning. Instead of passing to scan just
        the initial steps misisng, one has now to pass a memory buffer in
        which scan will try to store its output. In this memory buffer the
        first entries should be set to the initial states of the
        corresponding states.
        Providing a memory buffer that has less entries then the number of
        steps, mneans scan will only use that amount of memory. The user has
        to match the memory buffer size with the number of steps, otherwise
        scan will produce wrong results. Also if gradients are to be
        computed through the scan, the memory buffer should have the same
        length as the number of steps.
        For states that do not require a initial state, one has to provide a
        dictionary with a single key 'steps' that says how many intermediate
        results to store. See examples below for more insight.
    :param n_steps: This parameter is mandatory and it will represent the
        number of steps scan will do (scan will not check sequences or any
        other source of information to figure out how many steps it needs
        to do).
    :param mode: Same as for the official scan
    :param name: Same as for the official scan
    :param profile: Same as for the official scan

    Note:
     - there is no truncate / go_backwards anymore !
     - the outputs returned by scan contain the initial states as well (i.e.
     if I loop over k steps, with my smallest tap for an output -3 and keep
     al intermediate results, my output will be of length k+3

     Examples:
         (a) if you do not want to store any intermediate results (just the
         last one)

         # The memory buffer can be the initial state, just that we need to
         # add one extra dimension in front of it
         state = TT.unbroadcast(TT.shape_padleft(x0),0)
         out,_ = scan(lambda x:x+1, states = state, n_steps = 5)
         # Once we got our result we need to remove the extra dimension
         out = out[0]

        (b) if you want to keep every intermediate results

        state = TT.alloc(TT.constant(0), 6, x0.shape[0])
        state = TT.set_subtensor(state[0], x0)
        out,_ = scan(lambda x:x+1, states = state, n_steps = 5)
        out = out[1:]

    """
    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(states)

    # 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(params):
        if not isinstance(elem, gof.Variable):
            non_seqs.append(tensor.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 = opt.get_scalar_constant_value(n_steps)
        except tensor.basic.NotScalarConstantError:
            n_fixed_steps = None

    # Check n_steps is an int
    if (hasattr(n_steps, 'dtype') and
        str(n_steps.dtype)[:3] not in ('uin', 'int')):
        raise ValueError(' n_steps must be an int. dtype provided '
                         'is %s' % n_steps.dtype)

    # compute number of sequences and number of outputs
    n_seqs = len(seqs)
    n_outs = len(outs_info)

    return_steps = OrderedDict()
    # wrap outputs info in a dictionary if they are not already in one
    for i in xrange(n_outs):
        if outs_info[i] is not None:
            if not isinstance(outs_info[i], dict):
                # by default any output has a tap value of -1
                outs_info[i] = dict(membuf=outs_info[i], taps=[-1])
            elif (not outs_info[i].get('membuf', None) and
                    outs_info[i].get('taps', None)):
                # ^ no initial state but taps provided
                raise ValueError(('If you are using slices of an output '
                                  'you need to provide a memory buffer for '
                                  'the state '), outs_info[i])
            elif (outs_info[i].get('membuf', None) and
                  not outs_info[i].get('taps', None)):
                # ^ initial state but taps not provided
                if 'taps' in outs_info[i]:
                    # ^ explicitly provided a None for taps
                    _logger.warning(
                            'Output %s (index %d) has a memory '
                            'buffer but taps is explicitly set to None ',
                            getattr(outs_info[i]['membuf'], 'name', 'None'),
                            i)
                outs_info[i]['taps'] = [-1]
        else:
            # if a None is provided as the output info we replace it
            # with an dict(steps=n_steps) to simplify handling
            outs_info[i] = dict(steps=n_steps)

    ##
    ###   Step 2. Generate inputs and outputs of the inner functions
    ###           for compiling a dummy function (Iteration #1)
    ##

    # create theano 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):
        actual_slice = seq[0]
        _seq_val = tensor.as_tensor_variable(seq)
        _seq_val_slice = _seq_val[0]
        # Try to transfer test_value to the new variable
        if config.compute_test_value != 'off':
            try:
                nw_slice.tag.test_value = gof.Op._get_test_value(
                    _seq_val_slice)
            except AttributeError, e:
                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.info(('Cannot compute test value for '
                        'the inner function of scan, input value '
                        'missing %s'), e)

        nw_slice = _seq_val_slice.type()
        if seq.name:
            nw_slice.name = seq.name + '[t]'
        scan_seqs.append(_seq_val)
        inner_seqs.append(nw_slice)
        inner_slices.append(actual_slice)

        n_seqs += 1
Пример #15
0
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):
    """
    This function constructs and applies a Scan op to the provided
    arguments.

    :param 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 theano
        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 otuput
        * ...
        * 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 theano.tensor as TT
            W   = TT.matrix()
            W_2 = W**2
            def f(x):
                return TT.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}, theano.scan_module.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). = {}):

    :param sequences:
        ``sequences`` is the list of Theano 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*) -- Theano 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 Theano variable in the list ``sequences`` is automatically
        wrapped into a dictionary where ``taps`` is set to ``[0]``


    :param outputs_info:
        ``outputs_info`` is the list of Theano 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`` -- Theano 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``)


    :param 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.


    :param n_steps:
        ``n_steps`` is the number of steps to iterate given as an int
        or Theano 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 the value is negative, ``scan``
        will run backwards in time. If the ``go_backwards`` flag is already
        set and also ``n_steps`` is negative, ``scan`` will run forward
        in time. If n_steps is not provided, ``scan`` will figure
        out the amount of steps it should run given its input sequences.


    :param 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.


    :param 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.


    :param 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.

    :param 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 ``theano.function`` for details about
        possible values and their meaning).

    :param 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)

    :param 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.

    :param strict:
        If true, all the shared variables used in ``fn`` must be provided as a
        part of ``non_sequences`` or ``sequences``. 

    :rtype: tuple
    :return: tuple of the form (outputs, updates); ``outputs`` is either a
             Theano variable or a list of Theano 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 ``theano.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, gof.Variable):
            non_seqs.append(tensor.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 = opt.get_scalar_constant_value(n_steps)
        except tensor.basic.NotScalarConstantError:
            n_fixed_steps = None

    # Check n_steps is an int
    if (hasattr(n_steps, 'dtype') and
        str(n_steps.dtype)[:3] not in ('uin', 'int')):
        raise ValueError(' n_steps must be an int. dtype provided '
                         'is %s' % 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 xrange(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 xrange(n_outs):
        if outs_info[i] is not None:
            if isinstance(outs_info[i], dict):
                # DEPRECATED :
                if outs_info[i].get('return_steps', None) is not None:
                    raise ValueError(
                            "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 '
                                  '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('Output %s ( index %d) has a initial '
                            'state but taps is explicitly set to None ',
                             getattr(outs_info[i]['initial'], 'name', 'None'),
                             i)
                outs_info[i]['taps'] = [-1]
        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 theano 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 = numpy.min(seq['taps'])
            maxtap = numpy.max(seq['taps'])
            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]
                _seq_val = tensor.as_tensor_variable(seq['input'])
                _seq_val_slice = _seq_val[k - mintap]
                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 = gof.Op._get_test_value(
                            _seq_val_slice)
                    except AttributeError, e:
                        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.info(('Cannot compute test value for '
                                'the inner function of scan, input value '
                                'missing %s'), e)

                # 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 + '[t+%d]' % k
                    elif k == 0:
                        nw_name = seq['input'].name + '[t]'
                    else:
                        nw_name = seq['input'].name + '[t%d]' % k
                    nw_slice.name = nw_name

                # We cut the sequence such that seq[i] to correspond to
                # seq[i-k]
                if maxtap < 0:
                    offset = abs(maxtap)
                else:
                    offset = 0
                if maxtap == mintap and maxtap != 0:
                    if maxtap < 0:
                        nw_seq = seq['input'][:maxtap]
                    else:
                        nw_seq = seq['input'][maxtap:]
                elif maxtap - k != 0:
                    nw_seq = seq['input'][offset + k - mintap: -(maxtap - k)]
                else:
                    nw_seq = seq['input'][offset + k - mintap:]
                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
Пример #16
0
def scan(fn,
         sequences=None,
         outputs_info=None,
         non_sequences=None,
         n_steps=None,
         truncate_gradient=-1,
         go_backwards=False,
         mode=None,
         name=None,
         options=None,
         profile=False):
    """
    This function constructs and applies a Scan op to the provided
    arguments.

    :param 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 theano
        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 otuput
        * ...
        * 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, Argument 2])

        ``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 theano.tensor as TT
            W   = TT.matrix()
            W_2 = W**2
            def f(x):
                return TT.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}, theano.scan_module.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). = {}):

    :param sequences:
        ``sequences`` is the list of Theano 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*) -- Theano 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 Theano variable in the list ``sequences`` is automatically
        wrapped into a dictionary where ``taps`` is set to ``[0]``


    :param outputs_info:
        ``outputs_info`` is the list of Theano 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`` -- Theano 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 a initial
          state this field can be skiped. 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. 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``)


    :param 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.


    :param n_steps:
        ``n_steps`` is the number of steps to iterate given as an int
        or Theano 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 the value is negative, ``scan``
        will run backwards in time. If the ``go_backwards`` flag is already
        set and also ``n_steps`` is negative, ``scan`` will run forward
        in time. If n stpes is not provided, ``scan`` will figure
        out the amount of steps it should run given its input sequences.


    :param 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.


    :param 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.


    :param 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.

    :param 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 ``theano.function`` for details about
        possible values and their meaning).

    :param 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)

    :rtype: tuple
    :return: tuple of the form (outputs, updates); ``outputs`` is either a
             Theano variable or a list of Theano 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 ``theano.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.
    """
    # Note : see the internal documentation of the scan op for naming
    # conventions and all other details
    if options is None:
        options = {}
    rvals = scan_utils.canonical_arguments(sequences,
                                           outputs_info,
                                           non_sequences,
                                           go_backwards,
                                           n_steps)
    inputs, states_and_outputs_info, parameters, T = rvals
    # 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
    T_value = None
    if isinstance(n_steps, (float, int)):
        T_value = int(n_steps)
    else:
        try:
            T_value = opt.get_scalar_constant_value(n_steps)
        except (TypeError, AttributeError):
            T_value = None

    if T_value in (1, -1):
        return one_step_scan(fn,
                             inputs,
                             states_and_outputs_info,
                             parameters,
                             truncate_gradient)

    # 1. Variable representing the current time step
    t = scalar_shared(numpy.int64(0), name='t')

    # 2. Allocate memory for the states of scan.
    mintaps = []
    lengths = []
    for pos, arg_info in enumerate(states_and_outputs_info):
        if arg_info.get('taps', None) == [-1]:
            mintaps.append(1)
            lengths.append(scalar_shared(numpy.int64(0),
                                         name='l%d' % pos))
            arg_info['initial'] = scan_utils.expand(tensor.unbroadcast(
                    tensor.shape_padleft(arg_info['initial']), 0), T)
        elif arg_info.get('taps', None):
            if numpy.any(numpy.array(arg_info.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',
                                 arg_info)
            mintap = abs(numpy.min(arg_info['taps']))
            lengths.append(scalar_shared(numpy.int64(0),
                                         name='l%d' % pos))
            mintaps.append(mintap)
            arg_info['initial'] = scan_utils.expand(
                arg_info['initial'][:mintap], T)
        else:
            mintaps.append(0)
            lengths.append(scalar_shared(numpy.int64(0),
                                         name='l%d' % pos))

    # 3. Generate arguments for the function passed to scan. This will
    # function will return the outputs that need to be computed at every
    # timesteps
    inputs_slices = [input[t] for input in inputs]
    states_slices = []
    for n, state in enumerate(states_and_outputs_info):
        # Check if it is actually a state and not an output
        if mintaps[n] != 0:
            for k in state['taps']:
                states_slices.append(
                    state['initial'][(t + mintaps[n] + k) % lengths[n]])

    # 4. Construct outputs that are to be computed by the inner
    # function of scan
    args = inputs_slices + states_slices + parameters
    cond, states_and_outputs, updates = \
            scan_utils.get_updates_and_outputs(fn(*args))

    # User is allowed to provide no information if it only behaves like a
    # map
    if (len(states_and_outputs) != len(states_and_outputs_info) and
        len(states_and_outputs_info) == 0):
        mintaps = [0] * len(states_and_outputs)

    # 5. Construct the scan op
    # 5.1 Construct list of shared variables with updates (those that
    # can be treated as states (i.e. of TensorType) and those that can not
    # (like Random States)

    if cond is not None:
        _cond = [cond]
    else:
        _cond = []
    rvals = rebuild_collect_shared(
        states_and_outputs + _cond,
        updates=updates,
        rebuild_strict=True,
        copy_inputs_over=True,
        no_default_updates=False)

    # extracting the arguments
    input_variables, cloned_outputs, other_rval = rvals
    clone_d, update_d, update_expr, shared_inputs = other_rval
    additional_input_states = []
    additional_output_states = []
    additional_lengths = []
    additional_mintaps = []
    original_numeric_shared_variables = []

    non_numeric_input_states = []
    non_numeric_output_states = []
    original_non_numeric_shared_variables = []
    pos = len(lengths)
    for sv in shared_inputs:
        if sv in update_d:
            if isinstance(sv, (TensorVariable, TensorSharedVariable)):
                # We can treat it as a sit sot
                nw_state = scan_utils.expand(
                    tensor.unbroadcast(tensor.shape_padleft(sv), 0), T)
                additional_lengths.append(scalar_shared(numpy.int64(0),
                                                       name='l%d' % pos))
                pos = pos + 1
                additional_mintaps.append(1)
                additional_input_states.append(nw_state)
                additional_output_states.append(
                    scan_utils.clone(tensor.set_subtensor(
                        nw_state[(t + 1) % additional_lengths[-1]],
                        update_d[sv])))
                original_numeric_shared_variables.append(sv)
            else:
                non_numeric_input_states.append(sv)
                non_numeric_output_states.append(update_d[sv])
                original_non_numeric_shared_variables.append(sv)

    # Replace shared variables in the update
    _additional_output_states = []
    replace = {}
    for sv, buf in zip(original_numeric_shared_variables,
                       additional_input_states):
        replace[sv] = buf[t]
    for out in additional_output_states:
        _additional_output_states.append(
            scan_utils.clone(out, replace=replace))
    additional_output_states = _additional_output_states

    # 5.2 Collect inputs/outputs of the inner function
    inputs = []
    outputs = []
    for n, mintap in enumerate(mintaps):
        if mintap != 0:
            input_state = states_and_outputs_info[n]['initial']
            inputs.append(input_state)
            outputs.append(
                tensor.set_subtensor(
                    input_state[(t + mintap) % lengths[n]],
                    states_and_outputs[n]))
        else:
            mem_buffer = scan_utils.allocate_memory(
                T, states_and_outputs_info[n], states_and_outputs[n])
            inputs.append(output)
            outputs.append(
                tensor.set_subtensor(output[t % lengths[n]],
                                     states_and_outputs[n]))
    inputs.extend(additional_input_states)
    outputs.extend(additional_output_states)
    lengths.extend(additional_lengths)
    mintaps.extend(additional_mintaps)
    inputs.extend(non_numeric_input_states)
    outputs.extend(non_numeric_output_states)
    all_other_inputs = gof.graph.inputs(outputs)
    parameters = [x for x in all_other_inputs
                  if (x not in inputs and x not in lengths and x is not t
                      and isinstance(x, gof.Variable) and
                      not isinstance(x, gof.Constant))]
    inputs.extend(parameters)
    # 5.3 Construct the the options dictionary
    options['name'] = name
    options['profile'] = profile
    options['mode'] = mode
    options['inplace'] = False
    options['gpu'] = False
    options['truncate_gradient'] = truncate_gradient
    options['hash_inner_graph'] = 0
    # 5.4 Construct the ScanOp instance
    local_op = scan_op.ScanOp(inputs=inputs,
                              outputs=outputs,
                              lengths=lengths,
                              switches=[],
                              mintaps=mintaps,
                              index=t,
                              options=options,
                              as_repeatUntil=cond)
    # Note that we get here all the outputs followed by the update rules to
    # the shared variables we had in our scan
    # we know that we have (in this given order):
    #   * len(states_and_outputs) real outputs
    #   * len(additional_input_states) updates for numeric shared variable
    #   * len(non_numeric_input_states) updates for non numeric shared
    #   variables
    scan_inputs = [T] + inputs
    scan_outputs_update_rules = scan_utils.to_list(local_op(*scan_inputs))
    # 5.5 Collect outputs and add permutation object
    scan_outputs = []
    for pos in xrange(len(states_and_outputs)):
        out = scan_utils.ScanPermutation(mintaps[pos])(
            scan_outputs_update_rules[pos], t)
        scan_outputs.append(out[mintaps[pos]:])
    # 5.6 Construct updates dictionary
    update_rules = scan_outputs_update_rules[len(states_and_outputs):]
    updates = {}
    for v, u in izip(original_numeric_shared_variables,
                     update_rules[:len(additional_input_states)]):
        updates[v] = u[-1]
    for v, u in izip(original_non_numeric_shared_variables,
                     update_rules[len(additional_input_states):]):
        updates[v] = u
    # Step 5.7 We are done and can return everything back to the user
    return scan_outputs, updates
Пример #17
0
def scan(
    fn, sequences=None, states=None, params=None, n_steps=None, mode=None, name=None, profile=False, allow_gc=None
):
    """
    Similar to Theano's official scan, this function gives the user more
    control over the scan op, avoiding certain difficulties that arose from
    missing optimizations.

    :param fn: lambda function that describes one step of scan (see the
        official Theano scan function)
    :param sequences: similar to the official Theano's scan. This version
        of scan does not support taps for the sequences (it can only be a
        list of tensor). Scan assumes that sequences have the right length
        and it does not check for this.
    :param states: similar to outputs_info of the official scan function.
        There is one crucial difference though, namely that the `initial`
        key in the dictionary has been replace by 'membuf' key. This
        reflects the change of meaning. Instead of passing to scan just
        the initial steps misisng, one has now to pass a memory buffer in
        which scan will try to store its output. In this memory buffer the
        first entries should be set to the initial states of the
        corresponding states.
        Providing a memory buffer that has less entries then the number of
        steps, mneans scan will only use that amount of memory. The user has
        to match the memory buffer size with the number of steps, otherwise
        scan will produce wrong results. Also if gradients are to be
        computed through the scan, the memory buffer should have the same
        length as the number of steps.
        For states that do not require a initial state, one has to provide a
        dictionary with a single key 'steps' that says how many intermediate
        results to store. See examples below for more insight.
    :param n_steps: This parameter is mandatory and it will represent the
        number of steps scan will do (scan will not check sequences or any
        other source of information to figure out how many steps it needs
        to do).
    :param mode: Same as for the official scan
    :param name: Same as for the official scan
    :param profile: Same as for the official scan

    Note:
     - there is no truncate / go_backwards anymore !
     - the outputs returned by scan contain the initial states as well (i.e.
     if I loop over k steps, with my smallest tap for an output -3 and keep
     al intermediate results, my output will be of length k+3

     Examples:
         (a) if you do not want to store any intermediate results (just the
         last one)

         # The memory buffer can be the initial state, just that we need to
         # add one extra dimension in front of it
         state = TT.unbroadcast(TT.shape_padleft(x0),0)
         out,_ = scan(lambda x:x+1, states = state, n_steps = 5)
         # Once we got our result we need to remove the extra dimension
         out = out[0]

        (b) if you want to keep every intermediate results

        state = TT.alloc(TT.constant(0), 6, x0.shape[0])
        state = TT.set_subtensor(state[0], x0)
        out,_ = scan(lambda x:x+1, states = state, n_steps = 5)
        out = out[1:]

    """

    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(states)
    if allow_gc is None:
        allow_gc = config.scan.allow_gc

    # 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(params):
        if not isinstance(elem, gof.Variable):
            non_seqs.append(tensor.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 = opt.get_scalar_constant_value(n_steps)
        except tensor.basic.NotScalarConstantError:
            n_fixed_steps = None

    # Check n_steps is an int
    if hasattr(n_steps, "dtype") and str(n_steps.dtype)[:3] not in ("uin", "int"):
        raise ValueError(" n_steps must be an int. dtype provided " "is %s" % n_steps.dtype)

    # compute number of sequences and number of outputs
    n_seqs = len(seqs)
    n_outs = len(outs_info)

    return_steps = OrderedDict()
    # wrap outputs info in a dictionary if they are not already in one
    for i in xrange(n_outs):
        if outs_info[i] is not None:
            if not isinstance(outs_info[i], dict):
                # by default any output has a tap value of -1
                outs_info[i] = dict(membuf=outs_info[i], taps=[-1])
            elif not outs_info[i].get("membuf", None) and outs_info[i].get("taps", None):
                # ^ no initial state but taps provided
                raise ValueError(
                    ("If you are using slices of an output " "you need to provide a memory buffer for " "the state "),
                    outs_info[i],
                )
            elif outs_info[i].get("membuf", None) and not outs_info[i].get("taps", None):
                # ^ initial state but taps not provided
                if "taps" in outs_info[i]:
                    # ^ explicitly provided a None for taps
                    _logger.warning(
                        "Output %s (index %d) has a memory " "buffer but taps is explicitly set to None ",
                        getattr(outs_info[i]["membuf"], "name", "None"),
                        i,
                    )
                outs_info[i]["taps"] = [-1]
        else:
            # if a None is provided as the output info we replace it
            # with an dict(steps=n_steps) to simplify handling
            outs_info[i] = dict(steps=n_steps)

    ##
    # Step 2. Generate inputs and outputs of the inner functions
    # for compiling a dummy function (Iteration #1)
    ##

    # create theano 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):
        if isinstance(seq, dict):
            seq = seq["input"]
        actual_slice = seq[0]
        _seq_val = tensor.as_tensor_variable(seq)
        _seq_val_slice = _seq_val[0]

        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 = gof.Op._get_test_value(_seq_val_slice)
            except AttributeError as e:
                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.info(
                        ("Cannot compute test value for " "the inner function of scan, input value " "missing %s"), e
                    )

        if seq.name:
            nw_slice.name = seq.name + "[t]"
        scan_seqs.append(_seq_val)
        inner_seqs.append(nw_slice)
        inner_slices.append(actual_slice)

        n_seqs += 1

    actual_n_steps = tensor.as_tensor(n_steps)

    # 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 = []
    mit_mot_rightOrder = []

    # 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 = []
    nit_sot_steps = []
    # 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

        # Note, 'taps' might not be in the dictionary
        if "taps" in init_out and init_out["taps"] == [-1]:

            actual_arg = init_out["membuf"]
            arg = safe_new(init_out["membuf"][0])
            if isinstance(arg, tensor.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 = gof.Op._get_test_value(actual_arg)
                except AttributeError as e:
                    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.info(
                            ("Cannot compute test value for the " "inner function of scan, input value missing %s"), e
                        )

            if getattr(init_out["membuf"], "name", None) is not None:
                arg.name = init_out["membuf"].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(actual_arg)
            sit_sot_inner_slices.append(actual_arg[0])
            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 numpy.any(numpy.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(numpy.min(init_out["taps"]))
            mit_sot_tap_array.append(init_out["taps"])
            idx_offset = abs(numpy.min(init_out["taps"]))
            # Sequence
            mit_sot_scan_inputs.append(init_out["membuf"])

            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["membuf"][k + mintap]
                _init_out_var = tensor.as_tensor_variable(init_out["membuf"])
                _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 = gof.Op._get_test_value(_init_out_var_slice)
                    except AttributeError as e:
                        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.info(
                                (
                                    "Cannot compute test value for "
                                    "the inner function of scan, input value "
                                    "missing. %s"
                                ),
                                e,
                            )

                # give it a name or debugging and pretty printing
                if getattr(init_out["membuf"], "name", None) is not None:
                    if k > 0:
                        nw_slice.name = init_out["membuf"].name + "[t+%d]" % k
                    elif k == 0:
                        nw_slice.name = init_out["membuf"].name + "[t]"
                    else:
                        nw_slice.name = init_out["membuf"].name + "[t%d]" % k
                mit_sot_inner_inputs.append(nw_slice)
                mit_sot_inner_slices.append(actual_nw_slice)
        else:
            pass

    # Re-order args
    max_mit_sot = numpy.max([-1] + mit_sot_rightOrder) + 1
    max_sit_sot = numpy.max([-1] + sit_sot_rightOrder) + 1
    n_elems = numpy.max([max_mit_sot, max_sit_sot])
    _ordered_args = [[] for x in xrange(n_elems)]
    offset = 0
    for idx in xrange(n_mit_sot):
        n_inputs = len(mit_sot_tap_array[idx])
        if n_fixed_steps == 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 xrange(n_sit_sot):
        if n_fixed_steps == 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 == 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, tensor.Constant))]
    # when we apply the lambda expression we get a mixture of update rules
    # and outputs that needs to be separated
    lambda_result = fn(*args)
    condition, outputs, updates = scan_utils.get_updates_and_outputs(lambda_result)
    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 == 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, ",
                    str(condition),
                    " is ignored",
                )
            )

        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, tensor.TensorType) and return_steps.get(pos, 0) != 1:
                outputs[pos] = tensor.unbroadcast(tensor.shape_padleft(inner_out), 0)
        if 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
    fake_nonseqs = [x.type() for x in non_seqs]
    fake_outputs = scan_utils.clone(outputs + updates.values(), replace=dict(zip(non_seqs, fake_nonseqs)))
    all_inputs = itertools.ifilter(
        lambda x: (
            isinstance(x, gof.Variable) and not isinstance(x, SharedVariable) and not isinstance(x, gof.Constant)
        ),
        gof.graph.inputs(fake_outputs),
    )
    extra_inputs = filter(lambda x: x not in args + fake_nonseqs, all_inputs)
    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
    if condition is not None:
        dummy_outs.append(condition)

    # If we use a regular dict here, the results are non-deterministic
    if not isinstance(updates, (list, tuple)):
        if isinstance(updates, dict) and not isinstance(updates, OrderedDict):
            warnings.warn("Using non-deterministic dictionary.")

    dummy_f = function(
        dummy_args,
        dummy_outs,
        updates=updates,
        mode=compile.mode.Mode(linker="py", optimizer=None),
        on_unused_input="ignore",
    )

    ##
    # 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 output_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 = [dict(steps=n_steps) for x in xrange(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 = []
    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"
            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

    # 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 not "taps" 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)
            nit_sot_steps.append(out["steps"])
            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, tensor.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, tensor.Constant))
    ]

    givens.update(dict(zip(other_scan_args, other_inner_args)))
    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(dict(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)
    new_givens = OrderedDict()
    for w, w_copy in givens.iteritems():
        new_givens[w] = w.type.filter_variable(w_copy)

    new_outs = scan_utils.clone(inner_outs, replace=new_givens)

    ##
    # Step 7. Create the Scan Op
    ##

    tap_array = mit_sot_tap_array + [[-1] for x in xrange(n_sit_sot)]
    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"] = -1
    info["name"] = name
    info["mode"] = mode
    info["destroy_map"] = OrderedDict()
    info["inplace"] = False
    info["gpu"] = False
    info["as_while"] = as_while
    info["profile"] = profile
    info["_scan_savemem_visited"] = True
    info["allow_gc"] = allow_gc

    local_op = scan_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
        + nit_sot_steps
        + other_shared_scan_args
        + other_scan_args
    )

    scan_inputs = []
    for arg in [actual_n_steps] + _scan_inputs:
        if not isinstance(arg, gof.Variable):
            arg = tensor.as_tensor_variable(arg)
        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()

    offset = n_mit_mot
    offsets = [abs(numpy.min(x)) for x in mit_sot_tap_array]
    mit_sot_outs = scan_outs[offset : offset + n_mit_sot]

    offset += n_mit_sot
    offsets = [1 for x in xrange(n_sit_sot)]
    sit_sot_outs = scan_outs[offset : offset + n_sit_sot]

    offset += n_sit_sot
    nit_sot_outs = scan_outs[offset : offset + n_nit_sot]

    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):
        scan_out_list[pos] = _scan_out_list[idx]
    if len(scan_out_list) == 1:
        scan_out_list = scan_out_list[0]
    elif len(scan_out_list) == 0:
        scan_out_list = None

    assert isinstance(update_map, OrderedDict)
    return (scan_out_list, update_map)