tensor.elemwise
– Tensor Elemwise¶

class
theano.tensor.elemwise.
CAReduce
(scalar_op, axis=None)[source]¶ CAReduce = Commutative Associative Reduce Reduces a scalar operation along the specified axis(es). (The scalar op should be both commutative and assocative)
The output will have the same shape as the input minus the reduced dimensions. It will contain the variable of accumulating all values over the reduced dimensions using the specified scalar op.
Parameters:  scalar_op – A binary scalar op with only one output. It must be commutative and associative.
 axis –
 The dimension along which we want to reduce
 List of dimensions that we want to reduce
 If None, all dimensions are reduced
Notes
CAReduce(add) # sum (ie, acts like the numpy sum operation) CAReduce(mul) # product CAReduce(maximum) # max CAReduce(minimum) # min CAReduce(or_) # any # not lazy CAReduce(and_) # all # not lazy CAReduce(xor) # a bit at 1 tell that there was an odd number of # bit at that position that where 1. 0 it was an # even number ...
In order to (eventually) optimize memory usage patterns, CAReduce makes zero guarantees on the order in which it iterates over the dimensions and the elements of the array(s). Therefore, to ensure consistent variables, the scalar operation represented by the reduction must be both commutative and associative (eg add, multiply, maximum, binary or/and/xor  but not subtract, divide or power).

c_code
(node, name, inames, onames, sub)[source]¶ Return the C implementation of an Op.
Returns C code that does the computation associated to this Op, given names for the inputs and outputs.
Parameters:  node (Apply instance) – The node for which we are compiling the current c_code. The same Op may be used in more than one node.
 name (str) – A name that is automatically assigned and guaranteed to be unique.
 inputs (list of strings) – There is a string for each input of the function, and the string is the name of a C variable pointing to that input. The type of the variable depends on the declared type of the input. There is a corresponding python variable that can be accessed by prepending “py_” to the name in the list.
 outputs (list of strings) – Each string is the name of a C variable where the Op should store its output. The type depends on the declared type of the output. There is a corresponding python variable that can be accessed by prepending “py_” to the name in the list. In some cases the outputs will be preallocated and the value of the variable may be prefilled. The value for an unallocated output is typedependent.
 sub (dict of strings) – Extra symbols defined in CLinker sub symbols (such as ‘fail’). WRITEME

c_code_cache_version_apply
(node)[source]¶ Return a tuple of integers indicating the version of this Op.
An empty tuple indicates an ‘unversioned’ Op that will not be cached between processes.
The cache mechanism may erase cached modules that have been superceded by newer versions. See ModuleCache for details.
See also
Notes
This function overrides c_code_cache_version unless it explicitly calls c_code_cache_version. The default implementation simply calls c_code_cache_version and ignores the node argument.

c_headers
(**kwargs)[source]¶ Return a list of header files required by code returned by this class.
These strings will be prefixed with
#include
and inserted at the beginning of the C source code.Strings in this list that start neither with
<
nor"
will be enclosed in doublequotes.Examples
 def c_headers(self, **kwargs):
 return [‘<iostream>’, ‘<math.h>’, ‘/full/path/to/header.h’]

make_node
(input)[source]¶ Construct an Apply node that represent the application of this operation to the given inputs.
This must be implemented by subclasses.
Returns: node – The constructed Apply node. Return type: Apply

perform
(node, inp, out)[source]¶ Calculate the function on the inputs and put the variables in the output storage.
Parameters:  node (Apply) – The symbolic Apply node that represents this computation.
 inputs (Sequence) – Immutable sequence of nonsymbolic/numeric inputs. These are the values of each Variable in node.inputs.
 output_storage (list of list) – List of mutable singleelement lists (do not change the length of these lists). Each sublist corresponds to value of each Variable in node.outputs. The primary purpose of this method is to set the values of these sublists.
 params (tuple) – A tuple containing the values of each entry in __props__.
Notes
The output_storage list might contain data. If an element of output_storage is not None, it has to be of the right type, for instance, for a TensorVariable, it has to be a NumPy ndarray with the right number of dimensions and the correct dtype. Its shape and stride pattern can be arbitrary. It is not guaranteed that such preset values were produced by a previous call to this Op.perform; they could’ve been allocated by another Op’s perform method. A Op is free to reuse output_storage as it sees fit, or to discard it and allocate new memory.

class
theano.tensor.elemwise.
CAReduceDtype
(scalar_op, axis=None, dtype=None, acc_dtype=None)[source]¶ Reduces a scalar operation along the specified axis(es).
This subclass of CAReduce accepts an additional “dtype” parameter, that specifies which dtype the output should be.
It also accepts an optional “acc_dtype”, which specify the dtype that will be used for the accumulation.
So, the accumulation will be done into a tensor of dtype “acc_dtype”, then it will be casted into “dtype” and returned.
If no dtype is provided, one will be inferred so as not to lose too much precision.
Parameters:  scalar_op – A binary scalar op with only one output. It must be commutative and associative.
 axis –
 the dimension along which we want to reduce
 list of dimensions that we want to reduce
 if None, all dimensions are reduced
 dtype –
The dtype of the returned tensor. If None, then we use the default dtype which is the same as the input tensor’s dtype except when:
 the input dtype is a signed integer of precision < 64 bit, in which case we use int64
 the input dtype is an unsigned integer of precision < 64 bit, in which case we use uint64
This default dtype does _not_ depend on the value of “acc_dtype”. This behavior is similar in spirit to that of numpy (except numpy uses the default machine integer while we always use 64 bit integers to avoid platformdependent behavior).
 acc_dtype –
The dtype of the internal accumulator. If None (default), we use the dtype in the list below, or the input dtype if its precision is higher:
 for int dtypes, we use at least int64;
 for uint dtypes, we use at least uint64;
 for float dtypes, we use at least float64;
 for complex dtypes, we use at least complex128.

class
theano.tensor.elemwise.
DimShuffle
(input_broadcastable, new_order, inplace=True)[source]¶ Allows to reorder the dimensions of a tensor or insert or remove broadcastable dimensions.
In the following examples, ‘x’ means that we insert a broadcastable dimension and a numerical index represents the dimension of the same rank in the tensor passed to perform.
Parameters:  input_broadcastable – The expected broadcastable pattern of the input
 new_order – A list representing the relationship between the input’s dimensions and the output’s dimensions. Each element of the list can either be an index or ‘x’. Indices must be encoded as python integers, not theano symbolic integers.
 inplace (bool, optional) – If True (default), the output will be a view of the input.
Notes
If j = new_order[i] is an index, the output’s ith dimension will be the input’s jth dimension. If new_order[i] is x, the output’s ith dimension will be 1 and Broadcast operations will be allowed to do broadcasting over that dimension.
If input.broadcastable[i] == False then i must be found in new_order. Broadcastable dimensions, on the other hand, can be discarded.
DimShuffle((False, False, False), ['x', 2, 'x', 0, 1])
This op will only work on 3d tensors with no broadcastable dimensions. The first dimension will be broadcastable, then we will have the third dimension of the input tensor as the second of the resulting tensor, etc. If the tensor has shape (20, 30, 40), the resulting tensor will have dimensions (1, 40, 1, 20, 30). (AxBxC tensor is mapped to 1xCx1xAxB tensor)
DimShuffle((True, False), [1])
This op will only work on 2d tensors with the first dimension broadcastable. The second dimension of the input tensor will be the first dimension of the resulting tensor. If the tensor has shape (1, 20), the resulting tensor will have shape (20, ).
Examples
DimShuffle((), ['x']) # make a 0d (scalar) into a 1d vector DimShuffle((False, False), [0, 1]) # identity DimShuffle((False, False), [1, 0]) # inverts the 1st and 2nd dimensions DimShuffle((False,), ['x', 0]) # make a row out of a 1d vector # (N to 1xN) DimShuffle((False,), [0, 'x']) # make a column out of a 1d vector # (N to Nx1) DimShuffle((False, False, False), [2, 0, 1]) # AxBxC to CxAxB DimShuffle((False, False), [0, 'x', 1]) # AxB to Ax1xB DimShuffle((False, False), [1, 'x', 0]) # AxB to Bx1xA
The reordering of the dimensions can be done with the numpy.transpose function. Adding, subtracting dimensions can be done with reshape.

R_op
(inputs, eval_points)[source]¶ Construct a graph for the Roperator.
This method is primarily used by Rop
Suppose the op outputs
[ f_1(inputs), …, f_n(inputs) ]
Parameters:  inputs (a Variable or list of Variables) –
 eval_points – A Variable or list of Variables with the same length as inputs. Each element of eval_points specifies the value of the corresponding input at the point where the R op is to be evaluated.
Returns:  rval[i] should be Rop(f=f_i(inputs),
wrt=inputs, eval_points=eval_points)
Return type: list of n elements

grad
(inp, grads)[source]¶ Construct a graph for the gradient with respect to each input variable.
Each returned Variable represents the gradient with respect to that input computed based on the symbolic gradients with respect to each output. If the output is not differentiable with respect to an input, then this method should return an instance of type NullType for that input.
Parameters:  inputs (list of Variable) – The input variables.
 output_grads (list of Variable) – The gradients of the output variables.
Returns: grads – The gradients with respect to each Variable in inputs.
Return type: list of Variable

make_node
(_input)[source]¶ Construct an Apply node that represent the application of this operation to the given inputs.
This must be implemented by subclasses.
Returns: node – The constructed Apply node. Return type: Apply

perform
(node, inp, out, params)[source]¶ Calculate the function on the inputs and put the variables in the output storage.
Parameters:  node (Apply) – The symbolic Apply node that represents this computation.
 inputs (Sequence) – Immutable sequence of nonsymbolic/numeric inputs. These are the values of each Variable in node.inputs.
 output_storage (list of list) – List of mutable singleelement lists (do not change the length of these lists). Each sublist corresponds to value of each Variable in node.outputs. The primary purpose of this method is to set the values of these sublists.
 params (tuple) – A tuple containing the values of each entry in __props__.
Notes
The output_storage list might contain data. If an element of output_storage is not None, it has to be of the right type, for instance, for a TensorVariable, it has to be a NumPy ndarray with the right number of dimensions and the correct dtype. Its shape and stride pattern can be arbitrary. It is not guaranteed that such preset values were produced by a previous call to this Op.perform; they could’ve been allocated by another Op’s perform method. A Op is free to reuse output_storage as it sees fit, or to discard it and allocate new memory.

class
theano.tensor.elemwise.
Elemwise
(scalar_op, inplace_pattern=None, name=None, nfunc_spec=None, openmp=None)[source]¶ Generalizes a scalar op to tensors.
All the inputs must have the same number of dimensions. When the Op is performed, for each dimension, each input’s size for that dimension must be the same. As a special case, it can also be 1 but only if the input’s broadcastable flag is True for that dimension. In that case, the tensor is (virtually) replicated along that dimension to match the size of the others.
The dtypes of the outputs mirror those of the scalar Op that is being generalized to tensors. In particular, if the calculations for an output are done inplace on an input, the output type must be the same as the corresponding input type (see the doc of ScalarOp to get help about controlling the output type)
Parameters:  scalar_op – An instance of a subclass of ScalarOp which works uniquely on scalars.
 inplace_pattern – A dictionary that maps the index of an output to the index of an input so the output is calculated inplace using the input’s storage. (Just like destroymap, but without the lists.)
 nfunc_spec – Either None or a tuple of three elements, (nfunc_name, nin, nout) such that getattr(numpy, nfunc_name) implements this operation, takes nin inputs and nout outputs. Note that nin cannot always be inferred from the scalar op’s own nin field because that value is sometimes 0 (meaning a variable number of inputs), whereas the numpy function may not have varargs.
Notes
Elemwise(add) represents + on tensors (x + y)Elemwise(add, {0 : 0}) represents the += operation (x += y)Elemwise(add, {0 : 1}) represents += on the second argument (y += x)Elemwise(mul)(rand(10, 5), rand(1, 5)) the second input is completed along the first dimension to match the first inputElemwise(true_div)(rand(10, 5), rand(10, 1)) same but along the second dimensionElemwise(int_div)(rand(1, 5), rand(10, 1)) the output has size (10, 5)Elemwise(log)(rand(3, 4, 5))
L_op
(inputs, outs, ograds)[source]¶ Construct a graph for the Loperator.
This method is primarily used by Lop and dispatches to Op.grad by default.
The Loperator computes a row vector times the Jacobian. The mathematical relationship is . The Loperator is also supported for generic tensors (not only for vectors).
Parameters:  inputs (list of Variable) –
 outputs (list of Variable) –
 output_grads (list of Variable) –

R_op
(inputs, eval_points)[source]¶ Construct a graph for the Roperator.
This method is primarily used by Rop
Suppose the op outputs
[ f_1(inputs), …, f_n(inputs) ]
Parameters:  inputs (a Variable or list of Variables) –
 eval_points – A Variable or list of Variables with the same length as inputs. Each element of eval_points specifies the value of the corresponding input at the point where the R op is to be evaluated.
Returns:  rval[i] should be Rop(f=f_i(inputs),
wrt=inputs, eval_points=eval_points)
Return type: list of n elements

c_code
(node, nodename, inames, onames, sub)[source]¶ Return the C implementation of an Op.
Returns C code that does the computation associated to this Op, given names for the inputs and outputs.
Parameters:  node (Apply instance) – The node for which we are compiling the current c_code. The same Op may be used in more than one node.
 name (str) – A name that is automatically assigned and guaranteed to be unique.
 inputs (list of strings) – There is a string for each input of the function, and the string is the name of a C variable pointing to that input. The type of the variable depends on the declared type of the input. There is a corresponding python variable that can be accessed by prepending “py_” to the name in the list.
 outputs (list of strings) – Each string is the name of a C variable where the Op should store its output. The type depends on the declared type of the output. There is a corresponding python variable that can be accessed by prepending “py_” to the name in the list. In some cases the outputs will be preallocated and the value of the variable may be prefilled. The value for an unallocated output is typedependent.
 sub (dict of strings) – Extra symbols defined in CLinker sub symbols (such as ‘fail’). WRITEME

c_code_cache_version_apply
(node)[source]¶ Return a tuple of integers indicating the version of this Op.
An empty tuple indicates an ‘unversioned’ Op that will not be cached between processes.
The cache mechanism may erase cached modules that have been superceded by newer versions. See ModuleCache for details.
See also
Notes
This function overrides c_code_cache_version unless it explicitly calls c_code_cache_version. The default implementation simply calls c_code_cache_version and ignores the node argument.

c_support_code
(**kwargs)[source]¶ Return utility code for use by a Variable or Op.
This is included at global scope prior to the rest of the code for this class.
Question: How many times will this support code be emitted for a graph with many instances of the same type?
Returns: Return type: str

c_support_code_apply
(node, nodename)[source]¶ Return Applyspecialized utility code for use by an Op that will be inserted at global scope.
Parameters:  node (Apply) – The node in the graph being compiled.
 name (str) – A string or number that serves to uniquely identify this node. Symbol names defined by this support code should include the name, so that they can be called from the CLinkerOp.c_code, and so that they do not cause name collisions.
Notes
This function is called in addition to CLinkerObject.c_support_code and will supplement whatever is returned from there.

get_output_info
(dim_shuffle, *inputs)[source]¶ Return the outputs dtype and broadcastable pattern and the dimshuffled niputs.

make_node
(*inputs)[source]¶ If the inputs have different number of dimensions, their shape is leftcompleted to the greatest number of dimensions with 1s using DimShuffle.

perform
(node, inputs, output_storage)[source]¶ Calculate the function on the inputs and put the variables in the output storage.
Parameters:  node (Apply) – The symbolic Apply node that represents this computation.
 inputs (Sequence) – Immutable sequence of nonsymbolic/numeric inputs. These are the values of each Variable in node.inputs.
 output_storage (list of list) – List of mutable singleelement lists (do not change the length of these lists). Each sublist corresponds to value of each Variable in node.outputs. The primary purpose of this method is to set the values of these sublists.
 params (tuple) – A tuple containing the values of each entry in __props__.
Notes
The output_storage list might contain data. If an element of output_storage is not None, it has to be of the right type, for instance, for a TensorVariable, it has to be a NumPy ndarray with the right number of dimensions and the correct dtype. Its shape and stride pattern can be arbitrary. It is not guaranteed that such preset values were produced by a previous call to this Op.perform; they could’ve been allocated by another Op’s perform method. A Op is free to reuse output_storage as it sees fit, or to discard it and allocate new memory.

prepare_node
(node, storage_map, compute_map, impl)[source]¶ Make any special modifications that the Op needs before doing Op.make_thunk.
This can modify the node inplace and should return nothing.
It can be called multiple time with different impl. It is the op responsibility to don’t reprepare the node when it isn’t good to do so.

theano.tensor.elemwise.
scalar_elemwise
(*symbol, nfunc=None, nin=None, nout=None, symbolname=None)[source]¶ Replace a symbol definition with an Elemwisewrapped version of the corresponding scalar Op.
If it is not
None
, the nfunc argument should be a string such thatgetattr(numpy, nfunc)
implements a vectorized version of the Elemwise operation. nin is the number of inputs expected by that function, and nout is the number of destination inputs it takes. That is, the function should take nin + nout inputs. nout == 0 means that the numpy function does not take a NumPy array argument to put its result in.