# Tensor

The `Tensor` class is probably the most important class in `Torch`. Almost every package depends on this class. It is the class for handling numeric data. As with pretty much anything in Torch7, tensors are serializable.

Multi-dimensional matrix

A `Tensor` is a multi-dimensional matrix. The number of dimensions is unlimited (up to what can be created using LongStorage).

Example:

`````` --- creation of a 4D-tensor 4x5x6x2
z = torch.Tensor(4,5,6,2)
--- for more dimensions, (here a 6D tensor) one can do:
s = torch.LongStorage(6)
s = 4; s = 5; s = 6; s = 2; s = 7; s = 3;
x = torch.Tensor(s)
``````

The number of dimensions of a `Tensor` can be queried by nDimension() or dim(). Size of the `i-th` dimension is returned by size(i). A LongStorage containing all the dimensions can be returned by size().

``````> x:nDimension()
6
> x:size()
4
5
6
2
7
3
[torch.LongStorage of size 6]
``````

Internal data representation

The actual data of a `Tensor` is contained into a Storage. It can be accessed using `storage()`. While the memory of a `Tensor` has to be contained in this unique `Storage`, it might not be contiguous: the first position used in the `Storage` is given by `storageOffset()` (starting at `1`). And the jump needed to go from one element to another element in the `i-th` dimension is given by `stride(i)`. In other words, given a 3D tensor

``````x = torch.Tensor(7,7,7)
``````

accessing the element `(3,4,5)` can be done by

``````> x
``````

or equivalently (but slowly!)

``````> x:storage()[x:storageOffset()
+(3-1)*x:stride(1)+(4-1)*x:stride(2)+(5-1)*x:stride(3)]
``````

One could say that a `Tensor` is a particular way of viewing a `Storage`: a `Storage` only represents a chunk of memory, while the `Tensor` interprets this chunk of memory as having dimensions:

``````x = torch.Tensor(4,5)
s = x:storage()
for i=1,s:size() do -- fill up the Storage
s[i] = i
end
> x -- s is interpreted by x as a 2D matrix
1   2   3   4   5
6   7   8   9  10
11  12  13  14  15
16  17  18  19  20
[torch.DoubleTensor of dimension 4x5]
``````

Note also that in Torch7 elements in the same row [elements along the last dimension] are contiguous in memory for a matrix [tensor]:

``````x = torch.Tensor(4,5)
i = 0

x:apply(function()
i = i + 1
return i
end)

> x
1   2   3   4   5
6   7   8   9  10
11  12  13  14  15
16  17  18  19  20
[torch.DoubleTensor of dimension 4x5]

> x:stride()
5
1  -- element in the last dimension are contiguous!
[torch.LongStorage of size 2]
``````

This is exactly like in C (and not `Fortran`).

Tensors of different types

Actually, several types of `Tensor` exists:

``````ByteTensor -- contains unsigned chars
CharTensor -- contains signed chars
ShortTensor -- contains shorts
IntTensor -- contains ints
LongTensor -- contains longs
FloatTensor -- contains floats
DoubleTensor -- contains doubles
``````

Most numeric operations are implemented only for `FloatTensor` and `DoubleTensor`. Other Tensor types are useful if you want to save memory space.

Default Tensor type

For convenience, an alias `torch.Tensor` is provided, which allows the user to write type-independent scripts, which can then ran after choosing the desired Tensor type with a call like

``````torch.setdefaulttensortype('torch.FloatTensor')
``````

See torch.setdefaulttensortype for more details. By default, the alias "points" on `torch.DoubleTensor`.

Efficient memory management

All tensor operations in this class do not make any memory copy. All these methods transform the existing tensor, or return a new tensor referencing the same storage. This magical behavior is internally obtained by good usage of the stride() and storageOffset(). Example:

``````x = torch.Tensor(5):zero()
> x
0
0
0
0
0
[torch.DoubleTensor of dimension 5]
> x:narrow(1, 2, 3):fill(1) -- narrow() returns a Tensor
-- referencing the same Storage as x
> x
0
1
1
1
0
[torch.Tensor of dimension 5]
``````

If you really need to copy a `Tensor`, you can use the copy() method:

``````y = torch.Tensor(x:size()):copy(x)
``````

Or the convenience method

``````y = x:clone()
``````

We now describe all the methods for `Tensor`. If you want to specify the Tensor type, just replace `Tensor` by the name of the Tensor variant (like `CharTensor`).

## Tensor constructors

Tensor constructors, create new Tensor object, optionally, allocating new memory. By default the elements of a newly allocated memory are not initialized, therefore, might contain arbitrary numbers. Here are several ways to construct a new `Tensor`.

### torch.Tensor()

Returns an empty tensor.

### torch.Tensor(tensor)

Returns a new tensor which reference the same Storage than the given `tensor`. The size, stride, and storage offset are the same than the given tensor.

The new `Tensor` is now going to "view" the same storage as the given `tensor`. As a result, any modification in the elements of the `Tensor` will have a impact on the elements of the given `tensor`, and vice-versa. No memory copy!

``````x = torch.Tensor(2,5):fill(3.14)
> x
3.1400  3.1400  3.1400  3.1400  3.1400
3.1400  3.1400  3.1400  3.1400  3.1400
[torch.DoubleTensor of dimension 2x5]

y = torch.Tensor(x)
> y
3.1400  3.1400  3.1400  3.1400  3.1400
3.1400  3.1400  3.1400  3.1400  3.1400
[torch.DoubleTensor of dimension 2x5]

y:zero()
> x -- elements of x are the same as y!
0 0 0 0 0
0 0 0 0 0
[torch.DoubleTensor of dimension 2x5]
``````

### torch.Tensor(sz1 [,sz2 [,sz3 [,sz4]]]])

Create a tensor up to 4 dimensions. The tensor size will be `sz1 x sz2 x sx3 x sz4`.

### torch.Tensor(sizes, [strides])

Create a tensor of any number of dimensions. The LongStorage `sizes` gives the size in each dimension of the tensor. The optional LongStorage `strides` gives the jump necessary to go from one element to the next one in the each dimension. Of course, `sizes` and `strides` must have the same number of elements. If not given, or if some elements of `strides` are negative, the stride() will be computed such that the tensor is as contiguous as possible in memory.

Example, create a 4D 4x4x3x2 tensor:

``````x = torch.Tensor(torch.LongStorage({4,4,3,2}))
``````

Playing with the strides can give some interesting things:

``````x = torch.Tensor(torch.LongStorage({4}), torch.LongStorage({0})):zero() -- zeroes the tensor
x = 1 -- all elements point to the same address!
> x
1
1
1
1
[torch.DoubleTensor of dimension 4]
``````

Note that negative strides are not allowed, and, if given as argument when constructing the Tensor, will be interpreted as //choose the right stride such that the Tensor is contiguous in memory//.

Note this method cannot be used to create `torch.LongTensor`s. The constructor from a storage will be used:

``````a = torch.LongStorage({1,2}) -- We have a torch.LongStorage containing the values 1 and 2
-- General case for TYPE ~= Long, e.g. for TYPE = Float:
b = torch.FloatTensor(a)
-- Creates a new torch.FloatTensor with 2 dimensions, the first of size 1 and the second of size 2
> b:size()
1
2
[torch.LongStorage of size 2]

-- Special case of torch.LongTensor
c = torch.LongTensor(a)
-- Creates a new torch.LongTensor that uses a as storage and thus contains the values 1 and 2
> c
1
2
[torch.LongTensor of size 2]
``````

### torch.Tensor(storage, [storageOffset, sizes, [strides]])

Returns a tensor which uses the existing Storage `storage`, starting at position `storageOffset` (>=1). The size of each dimension of the tensor is given by the LongStorage `sizes`.

If only `storage` is provided, it will create a 1D Tensor viewing the all Storage.

The jump necessary to go from one element to the next one in each dimension is given by the optional argument LongStorage `strides`. If not given, or if some elements of `strides` are negative, the stride() will be computed such that the tensor is as contiguous as possible in memory.

Any modification in the elements of the `Storage` will have an impact on the elements of the new `Tensor`, and vice-versa. There is no memory copy!

``````-- creates a storage with 10 elements
s = torch.Storage(10):fill(1)

-- we want to see it as a 2x5 tensor
x = torch.Tensor(s, 1, torch.LongStorage{2,5})
> x
1  1  1  1  1
1  1  1  1  1
[torch.DoubleTensor of dimension 2x5]

x:zero()
> s -- the storage contents have been modified
0
0
0
0
0
0
0
0
0
0
[torch.DoubleStorage of size 10]
``````

### torch.Tensor(storage, [storageOffset, sz1 [, st1 ... [, sz4 [, st4]]]])

Convenience constructor (for the previous constructor) assuming a number of dimensions inferior or equal to 4. `szi` is the size in the `i-th` dimension, and `sti` is the stride in the `i-th` dimension.

### torch.Tensor(table)

The argument is assumed to be a Lua array of numbers. The constructor returns a new Tensor of the size of the table, containing all the table elements. The table might be multi-dimensional.

Example:

``````> torch.Tensor({{1,2,3,4}, {5,6,7,8}})
1  2  3  4
5  6  7  8
[torch.DoubleTensor of dimension 2x4]
``````

## A note on function calls

The rest of this guide will present many functions that can be used to manipulate tensors. Most functions have been defined so that they can be called flexibly, either in an object-oriented "method call" style i.e. `src:function(...)` or a more "functional" style `torch.function(src, ...)`, where `src` is a tensor. Note that these different invocations may differ in whether they modify the tensor in-place, or create a new tensor. Additionally, some functions can be called in the form `dst:function(src, ...)` which usually suggests that the result of the operation on the `src` tensor will be stored in the tensor `dst`. Further details are given in the individual function definitions, below, but it should be noted that the documentation is currently incomplete in this regard, and readers are encouraged to experiment in an interactive session.

## Cloning

### [Tensor] clone()

Returns a clone of a tensor. The memory is copied.

``````i = 0
x = torch.Tensor(5):apply(function(x)
i = i + 1
return i
end)
> x
1
2
3
4
5
[torch.DoubleTensor of dimension 5]

-- create a clone of x
y = x:clone()
> y
1
2
3
4
5
[torch.DoubleTensor of dimension 5]

-- fill up y with 1
y:fill(1)
> y
1
1
1
1
1
[torch.DoubleTensor of dimension 5]

-- the contents of x were not changed:
> x
1
2
3
4
5
[torch.DoubleTensor of dimension 5]
``````

### [Tensor] contiguous

• If the given Tensor contents are contiguous in memory, returns the exact same Tensor (no memory copy).
• Otherwise (not contiguous in memory), returns a clone (memory copy).
``````x = torch.Tensor(2,3):fill(1)
> x
1  1  1
1  1  1
[torch.DoubleTensor of dimension 2x3]

-- x is contiguous, so y points to the same thing
y = x:contiguous():fill(2)
> y
2  2  2
2  2  2
[torch.DoubleTensor of dimension 2x3]

-- contents of x have been changed
> x
2  2  2
2  2  2
[torch.DoubleTensor of dimension 2x3]

-- x:t() is not contiguous, so z is a clone
z = x:t():contiguous():fill(3.14)
> z
3.1400  3.1400
3.1400  3.1400
3.1400  3.1400
[torch.DoubleTensor of dimension 3x2]

-- contents of x have not been changed
> x
2  2  2
2  2  2
[torch.DoubleTensor of dimension 2x3]
``````

### [Tensor or string] type(type)

If `type` is `nil`, returns a string containing the type name of the given tensor.

``````= torch.Tensor():type()
torch.DoubleTensor
``````

If `type` is a string describing a Tensor type, and is equal to the given tensor typename, returns the exact same tensor (//no memory copy//).

``````x = torch.Tensor(3):fill(3.14)
> x
3.1400
3.1400
3.1400
[torch.DoubleTensor of dimension 3]

y = x:type('torch.DoubleTensor')
> y
3.1400
3.1400
3.1400
[torch.DoubleTensor of dimension 3]

-- zero y contents
y:zero()

-- contents of x have been changed
> x
0
0
0
[torch.DoubleTensor of dimension 3]

``````

If `type` is a string describing a Tensor type, different from the type name of the given Tensor, returns a new Tensor of the specified type, whose contents corresponds to the contents of the original Tensor, casted to the given type (//memory copy occurs, with possible loss of precision//).

``````x = torch.Tensor(3):fill(3.14)
> x
3.1400
3.1400
3.1400
[torch.DoubleTensor of dimension 3]

y = x:type('torch.IntTensor')
> y
3
3
3
[torch.IntTensor of dimension 3]

``````

### [Tensor] typeAs(tensor)

Convenience method for the type method. Equivalent to

``````type(tensor:type())
``````

### [boolean] isTensor(object)

Returns `true` iff the provided `object` is one of the `torch.*Tensor` types.

``````> torch.isTensor(torch.randn(3,4))
true

> torch.isTensor(torch.randn(3,4))
true

> torch.isTensor(torch.randn(3,4))
false
``````

### [Tensor] byte(), char(), short(), int(), long(), float(), double()

Convenience methods for the type method. For example:

``````x = torch.Tensor(3):fill(3.14)
> x
3.1400
3.1400
3.1400
[torch.DoubleTensor of dimension 3]

-- calling type('torch.IntTensor')
> x:type('torch.IntTensor')
3
3
3
[torch.IntTensor of dimension 3]

-- is equivalent to calling int()
> x:int()
3
3
3
[torch.IntTensor of dimension 3]
``````

## Querying the size and structure

### [number] nDimension()

Returns the number of dimensions in a `Tensor`.

``````x = torch.Tensor(4,5) -- a matrix
> x:nDimension()
2
``````

### [number] dim()

Same as nDimension().

### [number] size(dim)

Returns the size of the specified dimension `dim`. Example:

``````x = torch.Tensor(4,5):zero()
> x
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
[torch.DoubleTensor of dimension 4x5]

> x:size(2) -- gets the number of columns
5
``````

### [LongStorage] size()

Returns a LongStorage containing the size of each dimension of the tensor.

``````x = torch.Tensor(4,5):zero()
> x
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
[torch.DoubleTensor of dimension 4x5]

> x:size()
4
5
[torch.LongStorage of size 2]
``````

### [LongStorage] #self

Same as size() method.

### [number] stride(dim)

Returns the jump necessary to go from one element to the next one in the specified dimension `dim`. Example:

``````x = torch.Tensor(4,5):zero()
> x
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
[torch.DoubleTensor of dimension 4x5]

-- elements in a row are contiguous in memory
> x:stride(2)
1

-- to go from one element to the next one in a column
-- we need here to jump the size of the row
> x:stride(1)
5
``````

Note also that in `Torch` elements in the same row [elements along the last dimension] are contiguous in memory for a matrix [tensor].

### [LongStorage] stride()

Returns the jump necessary to go from one element to the next one in each dimension. Example:

``````x = torch.Tensor(4,5):zero()
> x
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
[torch.DoubleTensor of dimension 4x5]

> x:stride()
5
1 -- elements are contiguous in a row [last dimension]
[torch.LongStorage of size 2]
``````

Note also that in `Torch` elements in the same row [elements along the last dimension] are contiguous in memory for a matrix [tensor].

### [Storage] storage()

Returns the Storage used to store all the elements of the `Tensor`. Basically, a `Tensor` is a particular way of viewing a `Storage`.

``````x = torch.Tensor(4,5)
s = x:storage()
for i=1,s:size() do -- fill up the Storage
s[i] = i
end

> x -- s is interpreted by x as a 2D matrix
1   2   3   4   5
6   7   8   9  10
11  12  13  14  15
16  17  18  19  20
[torch.DoubleTensor of dimension 4x5]
``````

### [boolean] isContiguous()

Returns `true` iff the elements of the `Tensor` are contiguous in memory.

``````-- normal tensors are contiguous in memory
x = torch.randn(4,5)
> x:isContiguous()
true

-- y now "views" the 3rd column of x
-- the storage of y is the same than x
-- so the memory cannot be contiguous
y = x:select(2, 3)
> y:isContiguous()
false

-- the next one, the stride is 5
> y:stride()
5
[torch.LongStorage of size 1]
``````

### [boolean] isSize(storage)

Returns `true` iff the dimensions of the `Tensor` match the elements of the `storage`.

``````x = torch.Tensor(4,5)
y = torch.LongStorage({4,5})
z = torch.LongStorage({5,4,1})
> x:isSize(y)
true

> x:isSize(z)
false

> x:isSize(x:size())
true
``````

### [boolean] isSameSizeAs(tensor)

Returns `true` iff the dimensions of the `Tensor` and the argument `Tensor` are exactly the same.

``````x = torch.Tensor(4,5)
y = torch.Tensor(4,5)
> x:isSameSizeAs(y)
true

y = torch.Tensor(4,6)
> x:isSameSizeAs(y)
false
``````

### [number] nElement()

Returns the number of elements of a tensor.

``````x = torch.Tensor(4,5)
> x:nElement() -- 4x5 = 20!
20
``````

### [number] storageOffset()

Return the first index (starting at 1) used in the tensor's storage.

## Querying elements

Elements of a tensor can be retrieved with the `[index]` operator.

If `index` is a number, `[index]` operator is equivalent to a `select(1, index)`. If the tensor has more than one dimension, this operation returns a slice of the tensor that shares the same underlying storage. If the tensor is a 1D tensor, it returns the value at `index` in this tensor.

If `index` is a table, the table must contain n numbers, where n is the number of dimensions of the Tensor. It will return the element at the given position.

In the same spirit, `index` might be a LongStorage, specifying the position (in the Tensor) of the element to be retrieved.

If `index` is a `ByteTensor` in which each element is 0 or 1 then it acts as a selection mask used to extract a subset of the original tensor. This is particularly useful with logical operators like `torch.le`.

Example:

``````x = torch.Tensor(3,3)
i = 0; x:apply(function() i = i + 1; return i end)
> x
1  2  3
4  5  6
7  8  9
[torch.DoubleTensor of dimension 3x3]

> x -- returns row 2
4
5
6
[torch.DoubleTensor of dimension 3]

> x -- returns row 2, column 3
6

> x[{2,3}] -- another way to return row 2, column 3
6

> x[torch.LongStorage{2,3}] -- yet another way to return row 2, column 3
6

> x[torch.le(x,3)] -- torch.le returns a ByteTensor that acts as a mask
1
2
3
[torch.DoubleTensor of dimension 3]
``````

## Referencing a tensor to an existing tensor or chunk of memory

A `Tensor` being a way of viewing a Storage, it is possible to "set" a `Tensor` such that it views an existing Storage.

Note that if you want to perform a set on an empty `Tensor` like

``````y = torch.Storage(10)
x = torch.Tensor()
x:set(y, 1, 10)
``````

you might want in that case to use one of the equivalent constructor.

``````y = torch.Storage(10)
x = torch.Tensor(y, 1, 10)
``````

### [self] set(tensor)

The `Tensor` is now going to "view" the same storage as the given `tensor`. As the result, any modification in the elements of the `Tensor` will have an impact on the elements of the given `tensor`, and vice-versa. This is an efficient method, as there is no memory copy!

``````x = torch.Tensor(2,5):fill(3.14)
> x
3.1400  3.1400  3.1400  3.1400  3.1400
3.1400  3.1400  3.1400  3.1400  3.1400
[torch.DoubleTensor of dimension 2x5]

y = torch.Tensor():set(x)
> y
3.1400  3.1400  3.1400  3.1400  3.1400
3.1400  3.1400  3.1400  3.1400  3.1400
[torch.DoubleTensor of dimension 2x5]

y:zero()
> x -- elements of x are the same than y!
0 0 0 0 0
0 0 0 0 0
[torch.DoubleTensor of dimension 2x5]
``````

### [boolean] isSetTo(tensor)

Returns true iff the `Tensor` is set to the argument `Tensor`. Note: this is only true if the tensors are the same size, have the same strides and share the same storage and offset.

``````x = torch.Tensor(2,5)
y = torch.Tensor()
> y:isSetTo(x)
false
> y:set(x)
> y:isSetTo(x)
true
> y:t():isSetTo(x)
false -- x and y have different strides
``````

### [self] set(storage, [storageOffset, sizes, [strides]])

The `Tensor` is now going to "view" the given `storage`, starting at position `storageOffset` (>=1) with the given dimension `sizes` and the optional given `strides`. As the result, any modification in the elements of the `Storage` will have a impact on the elements of the `Tensor`, and vice-versa. This is an efficient method, as there is no memory copy!

If only `storage` is provided, the whole storage will be viewed as a 1D Tensor.

``````-- creates a storage with 10 elements
s = torch.Storage(10):fill(1)

-- we want to see it as a 2x5 tensor
sz = torch.LongStorage({2,5})
x = torch.Tensor()
x:set(s, 1, sz)
> x
1  1  1  1  1
1  1  1  1  1
[torch.DoubleTensor of dimension 2x5]

x:zero()
> s -- the storage contents have been modified
0
0
0
0
0
0
0
0
0
0
[torch.DoubleStorage of size 10]
``````

### [self] set(storage, [storageOffset, sz1 [, st1 ... [, sz4 [, st4]]]])

This is a "shortcut" for previous method. It works up to 4 dimensions. `szi` is the size of the `i`-th dimension of the tensor. `sti` is the stride in the `i`-th dimension.

## Copying and initializing

### [self] copy(tensor)

Replace the elements of the `Tensor` by copying the elements of the given `tensor`. The number of elements must match, but the sizes might be different.

``````x = torch.Tensor(4):fill(1)
y = torch.Tensor(2,2):copy(x)
> x
1
1
1
1
[torch.DoubleTensor of dimension 4]

> y
1  1
1  1
[torch.DoubleTensor of dimension 2x2]
``````

If a different type of `tensor` is given, then a type conversion occurs, which, of course, might result in loss of precision.

### [self] fill(value)

Fill the tensor with the given `value`.

``````> torch.DoubleTensor(4):fill(3.14)
3.1400
3.1400
3.1400
3.1400
[torch.DoubleTensor of dimension 4]
``````

### [self] zero()

Fill the tensor with zeros.

``````> torch.Tensor(4):zero()
0
0
0
0
[torch.DoubleTensor of dimension 4]
``````

## Resizing

When resizing to a larger size, the underlying Storage is resized to fit all the elements of the `Tensor`.

When resizing to a smaller size, the underlying Storage is not resized.

Important note: the content of a `Tensor` after resizing is undetermined as strides might have been completely changed. In particular, the elements of the resized tensor are contiguous in memory.

### [self] resizeAs(tensor)

Resize the `tensor` as the given `tensor` (of the same type).

### [self] resize(sizes)

Resize the `tensor` according to the given LongStorage `sizes`.

### [self] resize(sz1 [,sz2 [,sz3 [,sz4]]]])

Convenience method of the previous method, working for a number of dimensions up to 4.

## Extracting sub-tensors

Each of these methods returns a `Tensor` which is a sub-tensor of the given tensor.

For methods `narrow`, `select` and `sub` the returned tensor shares the same `Storage` as the original. Hence, any modification in the memory of the sub-tensor will have an impact on the primary tensor, and vice-versa. These methods are very fast, as they do not involve any memory copy.

For all other methods in this section such as `index`, `indexCopy` etc., since you cannot extract a shared subtensor (technically), a new tensor is returned. If you make changes in this new tensor, they are not reflected in the original tensor.

### [self] narrow(dim, index, size)

Returns a new `Tensor` which is a narrowed version of the current one: the dimension `dim` is narrowed from `index` to `index+size-1`.

``````x = torch.Tensor(5, 6):zero()
> x

0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
[torch.DoubleTensor of dimension 5x6]

y = x:narrow(1, 2, 3) -- narrow dimension 1 from index 2 to index 2+3-1
y:fill(1) -- fill with 1
> y
1  1  1  1  1  1
1  1  1  1  1  1
1  1  1  1  1  1
[torch.DoubleTensor of dimension 3x6]

> x -- memory in x has been modified!
0  0  0  0  0  0
1  1  1  1  1  1
1  1  1  1  1  1
1  1  1  1  1  1
0  0  0  0  0  0
[torch.DoubleTensor of dimension 5x6]
``````

### [Tensor] sub(dim1s, dim1e ... [, dim4s [, dim4e]])

This method is equivalent to do a series of narrow up to the first 4 dimensions. It returns a new `Tensor` which is a sub-tensor going from index `dimis` to `dimie` in the `i`-th dimension. Negative values are interpreted index starting from the end: `-1` is the last index, `-2` is the index before the last index, ...

``````x = torch.Tensor(5, 6):zero()
> x
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
[torch.DoubleTensor of dimension 5x6]

y = x:sub(2,4):fill(1) -- y is sub-tensor of x:
> y                    -- dimension 1 starts at index 2, ends at index 4
1  1  1  1  1  1
1  1  1  1  1  1
1  1  1  1  1  1
[torch.DoubleTensor of dimension 3x6]

> x                    -- x has been modified!
0  0  0  0  0  0
1  1  1  1  1  1
1  1  1  1  1  1
1  1  1  1  1  1
0  0  0  0  0  0
[torch.DoubleTensor of dimension 5x6]

z = x:sub(2,4,3,4):fill(2) -- we now take a new sub-tensor
> z                        -- dimension 1 starts at index 2, ends at index 4
-- dimension 2 starts at index 3, ends at index 4
2  2
2  2
2  2
[torch.DoubleTensor of dimension 3x2]

> x                        -- x has been modified
0  0  0  0  0  0
1  1  2  2  1  1
1  1  2  2  1  1
1  1  2  2  1  1
0  0  0  0  0  0
[torch.DoubleTensor of dimension 5x6]

> y                        -- y has been modified
1  1  2  2  1  1
1  1  2  2  1  1
1  1  2  2  1  1
[torch.DoubleTensor of dimension 3x6]

> y:sub(-1, -1, 3, 4)      -- negative values = bounds
2  2
[torch.DoubleTensor of dimension 1x2]
``````

### [Tensor] select(dim, index)

Returns a new `Tensor` which is a tensor slice at the given `index` in the dimension `dim`. The returned tensor has one less dimension: the dimension `dim` is removed. As a result, it is not possible to `select()` on a 1D tensor.

Note that "selecting" on the first dimension is equivalent to use the [] operator

``````x = torch.Tensor(5,6):zero()
> x
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
[torch.DoubleTensor of dimension 5x6]

y = x:select(1, 2):fill(2) -- select row 2 and fill up
> y
2
2
2
2
2
2
[torch.DoubleTensor of dimension 6]

> x
0  0  0  0  0  0
2  2  2  2  2  2
0  0  0  0  0  0
0  0  0  0  0  0
0  0  0  0  0  0
[torch.DoubleTensor of dimension 5x6]

z = x:select(2,5):fill(5) -- select column 5 and fill up
> z
5
5
5
5
5
[torch.DoubleTensor of dimension 5]

> x
0  0  0  0  5  0
2  2  2  2  5  2
0  0  0  0  5  0
0  0  0  0  5  0
0  0  0  0  5  0
[torch.DoubleTensor of dimension 5x6]
``````

### [Tensor] [{ dim1,dim2,... }] or [{ {dim1s,dim1e}, {dim2s,dim2e} }]

The indexing operator [] can be used to combine narrow/sub and select in a concise and efficient way. It can also be used to copy, and fill (sub) tensors.

This operator also works with an input mask made of a `ByteTensor` with 0 and 1 elements, e.g with a logical operator.

``````x = torch.Tensor(5, 6):zero()
> x
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
[torch.DoubleTensor of dimension 5x6]

x[{ 1,3 }] = 1 -- sets element at (i=1,j=3) to 1
> x
0  0  1  0  0  0
0  0  0  0  0  0
0  0  0  0  0  0
0  0  0  0  0  0
0  0  0  0  0  0
[torch.DoubleTensor of dimension 5x6]

x[{ 2,{2,4} }] = 2  -- sets a slice of 3 elements to 2
> x
0  0  1  0  0  0
0  2  2  2  0  0
0  0  0  0  0  0
0  0  0  0  0  0
0  0  0  0  0  0
[torch.DoubleTensor of dimension 5x6]

x[{ {},4 }] = -1 -- sets the full 4th column to -1
> x
0  0  1 -1  0  0
0  2  2 -1  0  0
0  0  0 -1  0  0
0  0  0 -1  0  0
0  0  0 -1  0  0
[torch.DoubleTensor of dimension 5x6]

x[{ {},2 }] = torch.range(1,5) -- copy a 1D tensor to a slice of x
> x

0  1  1 -1  0  0
0  2  2 -1  0  0
0  3  0 -1  0  0
0  4  0 -1  0  0
0  5  0 -1  0  0
[torch.DoubleTensor of dimension 5x6]

x[torch.lt(x,0)] = -2 -- sets all negative elements to -2 via a mask
> x

0  1  1 -2  0  0
0  2  2 -2  0  0
0  3  0 -2  0  0
0  4  0 -2  0  0
0  5  0 -2  0  0
[torch.DoubleTensor of dimension 5x6]
``````

### [Tensor] index(dim, index)

Returns a new `Tensor` which indexes the original `Tensor` along dimension `dim` using the entries in `torch.LongTensor` `index`. The returned `Tensor` has the same number of dimensions as the original `Tensor`. The returned `Tensor` does not use the same storage as the original `Tensor` -- see below for storing the result in an existing `Tensor`.

``````x = torch.rand(5,5)
> x
0.8020  0.7246  0.1204  0.3419  0.4385
0.0369  0.4158  0.0985  0.3024  0.8186
0.2746  0.9362  0.2546  0.8586  0.6674
0.7473  0.9028  0.1046  0.9085  0.6622
0.1412  0.6784  0.1624  0.8113  0.3949
[torch.DoubleTensor of dimension 5x5]

y = x:index(1,torch.LongTensor{3,1})
> y
0.2746  0.9362  0.2546  0.8586  0.6674
0.8020  0.7246  0.1204  0.3419  0.4385
[torch.DoubleTensor of dimension 2x5]

y:fill(1)
> y
1  1  1  1  1
1  1  1  1  1
[torch.DoubleTensor of dimension 2x5]

> x
0.8020  0.7246  0.1204  0.3419  0.4385
0.0369  0.4158  0.0985  0.3024  0.8186
0.2746  0.9362  0.2546  0.8586  0.6674
0.7473  0.9028  0.1046  0.9085  0.6622
0.1412  0.6784  0.1624  0.8113  0.3949
[torch.DoubleTensor of dimension 5x5]

``````

Note the explicit `index` function is different than the indexing operator `[]`. The indexing operator `[]` is a syntactic shortcut for a series of select and narrow operations, therefore it always returns a new view on the original tensor that shares the same storage. However, the explicit `index` function can not use the same storage.

It is possible to store the result into an existing Tensor with `result:index(source, ...)`:

``````x = torch.rand(5,5)
> x
0.8020  0.7246  0.1204  0.3419  0.4385
0.0369  0.4158  0.0985  0.3024  0.8186
0.2746  0.9362  0.2546  0.8586  0.6674
0.7473  0.9028  0.1046  0.9085  0.6622
0.1412  0.6784  0.1624  0.8113  0.3949
[torch.DoubleTensor of dimension 5x5]

y = torch.Tensor()
y:index(x,1,torch.LongTensor{3,1})
> y
0.2746  0.9362  0.2546  0.8586  0.6674
0.8020  0.7246  0.1204  0.3419  0.4385
[torch.DoubleTensor of dimension 2x5]
``````

### [Tensor] indexCopy(dim, index, tensor)

Copies the elements of `tensor` into the original tensor by selecting the indices in the order given in `index`. The shape of `tensor` must exactly match the elements indexed or an error will be thrown.

``````> x
0.8020  0.7246  0.1204  0.3419  0.4385
0.0369  0.4158  0.0985  0.3024  0.8186
0.2746  0.9362  0.2546  0.8586  0.6674
0.7473  0.9028  0.1046  0.9085  0.6622
0.1412  0.6784  0.1624  0.8113  0.3949
[torch.DoubleTensor of dimension 5x5]

z=torch.Tensor(5,2)
z:select(2,1):fill(-1)
z:select(2,2):fill(-2)
> z
-1 -2
-1 -2
-1 -2
-1 -2
-1 -2
[torch.DoubleTensor of dimension 5x2]

x:indexCopy(2,torch.LongTensor{5,1},z)
> x
-2.0000  0.7246  0.1204  0.3419 -1.0000
-2.0000  0.4158  0.0985  0.3024 -1.0000
-2.0000  0.9362  0.2546  0.8586 -1.0000
-2.0000  0.9028  0.1046  0.9085 -1.0000
-2.0000  0.6784  0.1624  0.8113 -1.0000
[torch.DoubleTensor of dimension 5x5]

``````

Accumulate the elements of `tensor` into the original tensor by adding to the indices in the order given in `index`. The shape of `tensor` must exactly match the elements indexed or an error will be thrown.

``````Example 1

> x
-2.1742  0.5688 -1.0201  0.1383  1.0504
0.0970  0.2169  0.1324  0.9553 -1.9518
-0.7607  0.8947  0.1658 -0.2181 -2.1237
-1.4099  0.2342  0.4549  0.6316 -0.2608
0.0349  0.4713  0.0050  0.1677  0.2103
[torch.DoubleTensor of size 5x5]

z=torch.Tensor(5, 2)
z:select(2,1):fill(-1)
z:select(2,2):fill(-2)
> z
-1 -2
-1 -2
-1 -2
-1 -2
-1 -2
[torch.DoubleTensor of dimension 5x2]

> x
-4.1742  0.5688 -1.0201  0.1383  0.0504
-1.9030  0.2169  0.1324  0.9553 -2.9518
-2.7607  0.8947  0.1658 -0.2181 -3.1237
-3.4099  0.2342  0.4549  0.6316 -1.2608
-1.9651  0.4713  0.0050  0.1677 -0.7897
[torch.DoubleTensor of size 5x5]

Example 2

> a = torch.range(1, 5)
> a
1
2
3
4
5
[torch.DoubleTensor of size 5]

> a:indexAdd(1, torch.LongTensor{1, 1, 3, 3}, torch.range(1, 4))
> a
4
2
10
4
5
[torch.DoubleTensor of size 5]

``````

### [Tensor] indexFill(dim, index, val)

Fills the elements of the original `Tensor` with value `val` by selecting the indices in the order given in `index`.

``````x=torch.rand(5,5)
> x
0.8414  0.4121  0.3934  0.5600  0.5403
0.3029  0.2040  0.7893  0.6079  0.6334
0.3743  0.1389  0.1573  0.1357  0.8460
0.2838  0.9925  0.0076  0.7220  0.5185
0.8739  0.6887  0.4271  0.0385  0.9116
[torch.DoubleTensor of dimension 5x5]

x:indexFill(2,torch.LongTensor{4,2},-10)
> x
0.8414 -10.0000   0.3934 -10.0000   0.5403
0.3029 -10.0000   0.7893 -10.0000   0.6334
0.3743 -10.0000   0.1573 -10.0000   0.8460
0.2838 -10.0000   0.0076 -10.0000   0.5185
0.8739 -10.0000   0.4271 -10.0000   0.9116
[torch.DoubleTensor of dimension 5x5]

``````

### [Tensor] gather(dim, index)

Creates a new `Tensor` from the original tensor by gathering a number of values from each "row", where the rows are along the dimension `dim`. The values in a `LongTensor`, passed as `index`, specify which values to take from each row. Specifically, the resulting `Tensor`, which will have the same size as the `index` tensor, is given by

``````-- dim = 1
result[i][j][k]... = src[index[i][j][k]...][j][k]...

-- dim = 2
result[i][j][k]... = src[i][index[i][j][k]...][k]...

-- etc.
``````

where `src` is the original `Tensor`.

The same number of values are selected from each row, and the same value cannot be selected from a row more than once. The values in the `index` tensor must not be larger than the length of the row, that is they must be between 1 and `src:size(dim)` inclusive. It can be somewhat confusing to ensure that the `index` tensor has the correct shape. Viewed pictorially: Numerically, to give an example, if `src` has size `n x m x p x q`, we are gathering along `dim = 3`, and we wish to gather `k` elements from each row (where `k <= p`) then `index` must have size `n x m x k x q`.

It is possible to store the result into an existing Tensor with `result:gather(src, ...)`.

``````x = torch.rand(5, 5)
> x
0.7259  0.5291  0.4559  0.4367  0.4133
0.0513  0.4404  0.4741  0.0658  0.0653
0.3393  0.1735  0.6439  0.1011  0.7923
0.7606  0.5025  0.5706  0.7193  0.1572
0.1720  0.3546  0.8354  0.8339  0.3025
[torch.DoubleTensor of size 5x5]

y = x:gather(1, torch.LongTensor{{1, 2, 3, 4, 5}, {2, 3, 4, 5, 1}})
> y
0.7259  0.4404  0.6439  0.7193  0.3025
0.0513  0.1735  0.5706  0.8339  0.4133
[torch.DoubleTensor of size 2x5]

z = x:gather(2, torch.LongTensor{{1, 2}, {2, 3}, {3, 4}, {4, 5}, {5, 1}})
> z
0.7259  0.5291
0.4404  0.4741
0.6439  0.1011
0.7193  0.1572
0.3025  0.1720
[torch.DoubleTensor of size 5x2]

``````

### [Tensor] scatter(dim, index, src|val)

Writes all values from tensor `src` or the scalar `val` into `self` at the specified indices. The indices are specified with respect to the given dimension, `dim`, in the manner described in gather. Note that, as for gather, the values of index must be between 1 and `self:size(dim)` inclusive and all values in a row along the specified dimension must be unique.

``````x = torch.rand(2, 5)
> x
0.3227  0.4294  0.8476  0.9414  0.1159
0.7338  0.5185  0.2947  0.0578  0.1273
[torch.DoubleTensor of size 2x5]

y = torch.zeros(3, 5):scatter(1, torch.LongTensor{{1, 2, 3, 1, 1}, {3, 1, 1, 2, 3}}, x)
> y
0.3227  0.5185  0.2947  0.9414  0.1159
0.0000  0.4294  0.0000  0.0578  0.0000
0.7338  0.0000  0.8476  0.0000  0.1273
[torch.DoubleTensor of size 3x5]

z = torch.zeros(2, 4):scatter(2, torch.LongTensor{{3}, {4}}, 1.23)
> z
0.0000  0.0000  1.2300  0.0000
0.0000  0.0000  0.0000  1.2300
[torch.DoubleTensor of size 2x4]

``````

Returns a new Tensor which contains all elements aligned to a `1` in the corresponding `mask`. This `mask` is a `torch.ByteTensor` of zeros and ones. The `mask` and `Tensor` must have the same number of elements. The resulting Tensor will be a 1D tensor of the same type as `Tensor` having size `mask:sum()`.

``````x = torch.range(1,12):double():resize(3,4)
> x
1   2   3   4
5   6   7   8
9  10  11  12
[torch.DoubleTensor of dimension 3x4]

1  0  1  0  0  0
1  1  0  0  0  1
[torch.ByteTensor of dimension 2x6]

> y
1
3
7
8
12
[torch.DoubleTensor of dimension 5]

z = torch.DoubleTensor()
> z
1
3
7
8
12
``````

Note how the dimensions of the above `x`, `mask` and `y` do not match. Also note how an existing tensor `z` can be used to store the results.

Copies the elements of `tensor` into `mask` locations of itself. The masked elements are those elements having a corresponding `1` in the `mask` Tensor. This `mask` is a `torch.ByteTensor` of zeros and ones. The destination `Tensor` and the `mask` Tensor should have the same number of elements. The source `tensor` should have at least as many elements as the number of 1s in the `mask`.

``````x = torch.Tensor({0, 0, 0, 0})
mask = torch.ByteTensor({0, 1, 0, 1})
y = torch.Tensor({10, 20})
print(x)

0
10
0
20
[torch.DoubleTensor of size 4]
``````
``````x = torch.range(1,4):double():resize(2,2)
> x
1  2
3  4
[torch.DoubleTensor of dimension 2x4]

0  0  1  1  1  0  1  0
[torch.ByteTensor of dimension 1x8]

y = torch.DoubleTensor(2,4):fill(-1)
> y
-1 -1 -1 -1
-1 -1 -1 -1
[torch.DoubleTensor of dimension 2x4]

> y
-1 -1  1  2
3 -1  4 -1
[torch.DoubleTensor of dimension 2x4]
``````

Note how the dimensions of the above `x`, `mask` and `y` do not match, but the number of elements do.

Fills the masked elements of itself with value `val`. The masked elements are those elements having a corresponding `1` in the `mask` Tensor. This `mask` is a `torch.ByteTensor` of zeros and ones. The `mask` and `Tensor` must have the same number of elements.

``````x = torch.range(1,4):double():resize(1,4)
> x
1  2  3  4
[torch.DoubleTensor of dimension 1x4]

0  0
1  1
[torch.ByteTensor of dimension 2x2]

> x
1  2 -1 -1
[torch.DoubleTensor of dimension 1x4]

``````

Note how the dimensions of the above `x` and `mask` do not match, but the number of elements do.

Each of these methods returns a `LongTensor` corresponding to the indices of the given search operation.

### [LongTensor] nonzero(tensor)

Finds and returns a `LongTensor` corresponding to the subscript indices of all non-zero elements in `tensor`.

Note that torch uses the first argument on dispatch to determine the return type. Since the first argument is any `torch.TensorType`, but the return type is always `torch.LongTensor`, the function call `torch.nonzero(torch.LongTensor(), tensor)` does not work. However, `tensor.nonzero(torch.LongTensor(), tensor)` does work.

``````> x = torch.rand(4, 4):mul(3):floor():int()
> x
2  0  2  0
0  0  1  2
0  2  2  1
2  1  2  2
[torch.IntTensor of dimension 4x4]

> torch.nonzero(x)
1  1
1  3
2  3
2  4
3  2
3  3
3  4
4  1
4  2
4  3
4  4
[torch.LongTensor of dimension 11x2]

> x:nonzero()
1  1
1  3
2  3
2  4
3  2
3  3
3  4
4  1
4  2
4  3
4  4
[torch.LongTensor of dimension 11x2]

> indices = torch.LongTensor()
> x.nonzero(indices, x)
1  1
1  3
2  3
2  4
3  2
3  3
3  4
4  1
4  2
4  3
4  4
[torch.LongTensor of dimension 11x2]

> x:eq(1):nonzero()
2  3
3  4
4  2
[torch.LongTensor of dimension 3x2]

``````

## Expanding/Replicating/Squeezing Tensors

These methods returns a Tensor which is created by replications of the original tensor.

### [result] expand([result,] sizes)

`sizes` can either be a `torch.LongStorage` or numbers. Expanding a tensor does not allocate new memory, but only creates a new view on the existing tensor where singleton dimensions can be expanded to multiple ones by setting the `stride` to 0. Any dimension that has size 1 can be expanded to arbitrary value without any new memory allocation. Attempting to expand along a dimension that does not have size 1 will result in an error.

``````x = torch.rand(10,1)
> x
0.3837
0.5966
0.0763
0.1896
0.4958
0.6841
0.4038
0.4068
0.1502
0.2239
[torch.DoubleTensor of dimension 10x1]

y = torch.expand(x,10,2)
> y
0.3837  0.3837
0.5966  0.5966
0.0763  0.0763
0.1896  0.1896
0.4958  0.4958
0.6841  0.6841
0.4038  0.4038
0.4068  0.4068
0.1502  0.1502
0.2239  0.2239
[torch.DoubleTensor of dimension 10x2]

y:fill(1)
> y
1  1
1  1
1  1
1  1
1  1
1  1
1  1
1  1
1  1
1  1
[torch.DoubleTensor of dimension 10x2]

> x
1
1
1
1
1
1
1
1
1
1
[torch.DoubleTensor of dimension 10x1]

i=0; y:apply(function() i=i+1;return i end)
> y
2   2
4   4
6   6
8   8
10  10
12  12
14  14
16  16
18  18
20  20
[torch.DoubleTensor of dimension 10x2]

> x
2
4
6
8
10
12
14
16
18
20
[torch.DoubleTensor of dimension 10x1]

``````

### [result] expandAs([result,] tensor)

This is equivalent to `self:expand(tensor:size())`

### [Tensor] repeatTensor([result,] sizes)

`sizes` can either be a `torch.LongStorage` or numbers. Repeating a tensor allocates new memory, unless `result` is provided, in which case its memory is resized. `sizes` specify the number of times the tensor is repeated in each dimension.

```lua x = torch.rand(5)

x 0.7160 0.6514 0.0704 0.7856 0.7452 [torch.DoubleTensor of dimension 5]

torch.repeatTensor(x,3,2) 0.7160 0.6514 0.0704 0.7856 0.7452 0.7160 0.6514 0.0704 0.7856 0.7452 0.7160 0.6514 0.0704 0.7856 0.7452 0.7160 0.6514 0.0704 0.7856 0.7452 0.7160 0.6514 0.0704 0.7856 0.7452 0.7160 0.6514 0.0704 0.7856 0.7452 [torch.DoubleTensor of dimension 3x10]

torch.repeatTensor(x,3,2,1) (1,.,.) = 0.7160 0.6514 0.0704 0.7856 0.7452 0.7160 0.6514 0.0704 0.7856 0.7452

(2,.,.) = 0.7160 0.6514 0.0704 0.7856 0.7452 0.7160 0.6514 0.0704 0.7856 0.7452

(3,.,.) = 0.7160 0.6514 0.0704 0.7856 0.7452 0.7160 0.6514 0.0704 0.7856 0.7452 [torch.DoubleTensor of dimension 3x2x5]

```

### [Tensor] squeeze([dim])

Removes all singleton dimensions of the tensor. If `dim` is given, squeezes only that particular dimension of the tensor.

```lua x=torch.rand(2,1,2,1,2)

x (1,1,1,.,.) = 0.6020 0.8897

(2,1,1,.,.) = 0.4713 0.2645

(1,1,2,.,.) = 0.4441 0.9792

(2,1,2,.,.) = 0.5467 0.8648 [torch.DoubleTensor of dimension 2x1x2x1x2]

torch.squeeze(x) (1,.,.) = 0.6020 0.8897 0.4441 0.9792

(2,.,.) = 0.4713 0.2645 0.5467 0.8648 [torch.DoubleTensor of dimension 2x2x2]

torch.squeeze(x,2) (1,1,.,.) = 0.6020 0.8897

(2,1,.,.) = 0.4713 0.2645

(1,2,.,.) = 0.4441 0.9792

(2,2,.,.) = 0.5467 0.8648 [torch.DoubleTensor of dimension 2x2x1x2]

```

## Manipulating the tensor view

Each of these methods returns a `Tensor` which is another way of viewing the `Storage` of the given tensor. Hence, any modification in the memory of the sub-tensor will have an impact on the primary tensor, and vice-versa.

These methods are very fast, because they do not involve any memory copy.

### [result] view([result,] tensor, sizes)

Creates a view with different dimensions of the storage associated with `tensor`. If `result` is not passed, then a new tensor is returned, otherwise its storage is made to point to storage of `tensor`.

`sizes` can either be a `torch.LongStorage` or numbers. If one of the dimensions is -1, the size of that dimension is inferred from the rest of the elements.

``````x = torch.zeros(4)
> x:view(2,2)
0 0
0 0
[torch.DoubleTensor of dimension 2x2]

> x:view(2,-1)
0 0
0 0
[torch.DoubleTensor of dimension 2x2]

> x:view(torch.LongStorage{2,2})
0 0
0 0
[torch.DoubleTensor of dimension 2x2]

> x
0
0
0
0
[torch.DoubleTensor of dimension 4]
``````

### [result] viewAs([result,] tensor, template)

Creates a view with the same dimensions as `template` of the storage associated with `tensor`. If `result` is not passed, then a new tensor is returned, otherwise its storage is made to point to storage of `tensor`.

``````x = torch.zeros(4)
y = torch.Tensor(2,2)
> x:viewAs(y)
0 0
0 0
[torch.DoubleTensor of dimension 2x2]
``````

### [Tensor] transpose(dim1, dim2)

Returns a tensor where dimensions `dim1` and `dim2` have been swapped. For 2D tensors, the convenience method of t() is available.

``````x = torch.Tensor(3,4):zero()
x:select(2,3):fill(7) -- fill column 3 with 7
> x
0  0  7  0
0  0  7  0
0  0  7  0
[torch.DoubleTensor of dimension 3x4]

y = x:transpose(1,2) -- swap dimension 1 and 2
> y
0  0  0
0  0  0
7  7  7
0  0  0
[torch.DoubleTensor of dimension 4x3]

y:select(2, 3):fill(8) -- fill column 3 with 8
> y
0  0  8
0  0  8
7  7  8
0  0  8
[torch.DoubleTensor of dimension 4x3]

> x -- contents of x have changed as well
0  0  7  0
0  0  7  0
8  8  8  8
[torch.DoubleTensor of dimension 3x4]
``````

### [Tensor] t()

Convenience method of transpose() for 2D tensors. The given tensor must be 2 dimensional. Swap dimensions 1 and 2.

``````x = torch.Tensor(3,4):zero()
x:select(2,3):fill(7)
y = x:t()
> y
0  0  0
0  0  0
7  7  7
0  0  0
[torch.DoubleTensor of dimension 4x3]

> x
0  0  7  0
0  0  7  0
0  0  7  0
[torch.DoubleTensor of dimension 3x4]
``````

### [Tensor] permute(dim1, dim2, ..., dimn)

Generalizes the function transpose() and can be used as a convenience method replacing a sequence of transpose() calls. Returns a tensor where the dimensions were permuted according to the permutation given by (dim1, dim2, ... , dimn). The permutation must be specified fully, i.e. there must be as many parameters as the tensor has dimensions.

``````x = torch.Tensor(3,4,2,5)
> x:size()
3
4
2
5
[torch.LongStorage of size 4]

y = x:permute(2,3,1,4) -- equivalent to y = x:transpose(1,3):transpose(1,2)
> y:size()
4
2
3
5
[torch.LongStorage of size 4]

``````

### [Tensor] unfold(dim, size, step)

Returns a tensor which contains all slices of size `size` in the dimension `dim`. Step between two slices is given by `step`.

If `sizedim` is the original size of dimension `dim`, the size of dimension `dim` in the returned tensor will be `(sizedim - size) / step + 1`

An additional dimension of size `size` is appended in the returned tensor.

``````x = torch.Tensor(7)
for i=1,7 do x[i] = i end
> x
1
2
3
4
5
6
7
[torch.DoubleTensor of dimension 7]

> x:unfold(1, 2, 1)
1  2
2  3
3  4
4  5
5  6
6  7
[torch.DoubleTensor of dimension 6x2]

> x:unfold(1, 2, 2)
1  2
3  4
5  6
[torch.DoubleTensor of dimension 3x2]
``````

## Applying a function to a tensor

These functions apply a function to each element of the tensor on which called the method (self). These methods are much faster than using a `for` loop in `Lua`. The results are stored in `self` (if the function returns something).

### [self] apply(function)

Apply the given function to all elements of self.

The function takes a number (the current element of the tensor) and might return a number, in which case it will be stored in self.

Examples:

``````i = 0
z = torch.Tensor(3,3)
z:apply(function(x)
i = i + 1
return i
end) -- fill up the tensor
> z
1  2  3
4  5  6
7  8  9
[torch.DoubleTensor of dimension 3x3]

z:apply(math.sin) -- apply the sin function
> z
0.8415  0.9093  0.1411
-0.7568 -0.9589 -0.2794
0.6570  0.9894  0.4121
[torch.DoubleTensor of dimension 3x3]

sum = 0
z:apply(function(x)
sum = sum + x
end) -- compute the sum of the elements
> sum
1.9552094821074

> z:sum() -- it is indeed correct!
1.9552094821074
``````

### [self] map(tensor, function(xs, xt))

Apply the given function to all elements of self and `tensor`. The number of elements of both tensors must match, but sizes do not matter.

The function takes two numbers (the current element of self and `tensor`) and might return a number, in which case it will be stored in self.

Example:

``````x = torch.Tensor(3,3)
y = torch.Tensor(9)
i = 0
x:apply(function() i = i + 1; return i end) -- fill-up x
i = 0
y:apply(function() i = i + 1; return i end) -- fill-up y
> x
1  2  3
4  5  6
7  8  9
[torch.DoubleTensor of dimension 3x3]

> y
1
2
3
4
5
6
7
8
9
[torch.DoubleTensor of dimension 9]

x:map(y, function(xx, yy) return xx*yy end) -- element-wise multiplication
> x
1   4   9
16  25  36
49  64  81
[torch.DoubleTensor of dimension 3x3]
``````

### [self] map2(tensor1, tensor2, function(x, xt1, xt2))

Apply the given function to all elements of self, `tensor1` and `tensor2`. The number of elements of all tensors must match, but sizes do not matter.

The function takes three numbers (the current element of self, `tensor1` and `tensor2`) and might return a number, in which case it will be stored in self.

Example:

``````x = torch.Tensor(3,3)
y = torch.Tensor(9)
z = torch.Tensor(3,3)

i = 0; x:apply(function() i = i + 1; return math.cos(i)*math.cos(i) end)
i = 0; y:apply(function() i = i + 1; return i end)
i = 0; z:apply(function() i = i + 1; return i end)

> x
0.2919  0.1732  0.9801
0.4272  0.0805  0.9219
0.5684  0.0212  0.8302
[torch.DoubleTensor of dimension 3x3]

> y
1
2
3
4
5
6
7
8
9
[torch.DoubleTensor of dimension 9]

> z
1  2  3
4  5  6
7  8  9
[torch.DoubleTensor of dimension 3x3]

x:map2(y, z, function(xx, yy, zz) return xx+yy*zz end)
> x
1.2919   4.1732   9.9801
16.4272  25.0805  36.9219
49.5684  64.0212  81.8302
[torch.DoubleTensor of dimension 3x3]
``````

## Dividing a tensor into a table of tensors

These functions divide a Tensor into a table of Tensors.

### [result] split([result,] tensor, size, [dim])

Splits Tensor `tensor` along dimension `dim` into a `result` table of Tensors of size `size` (a number) or less (in the case of the last Tensor). The sizes of the non-`dim` dimensions remain unchanged. Internally, a series of narrows are performed along dimensions `dim`. Argument `dim` defaults to 1.

If `result` is not passed, then a new table is returned, otherwise it is emptied and reused.

Example:

``````x = torch.randn(3,4,5)

> x:split(2,1)
{
1 : DoubleTensor - size: 2x4x5
2 : DoubleTensor - size: 1x4x5
}

> x:split(3,2)
{
1 : DoubleTensor - size: 3x3x5
2 : DoubleTensor - size: 3x1x5
}

> x:split(2,3)
{
1 : DoubleTensor - size: 3x4x2
2 : DoubleTensor - size: 3x4x2
3 : DoubleTensor - size: 3x4x1
}
``````

### [result] chunk([result,] tensor, n, [dim])

Splits Tensor `tensor` into `n` chunks of approximately equal size along dimensions `dim` and returns these as a `result` table of Tensors. Argument `dim` defaults to 1.

This function uses split internally:

``````torch.split(result, tensor, math.ceil(tensor:size(dim)/n), dim)
``````

Example:

``````x = torch.randn(3,4,5)

> x:chunk(2,1)
{
1 : DoubleTensor - size: 2x4x5
2 : DoubleTensor - size: 1x4x5
}

> x:chunk(2,2)
{
1 : DoubleTensor - size: 3x2x5
2 : DoubleTensor - size: 3x2x5
}

> x:chunk(2,3)
{
1 : DoubleTensor - size: 3x4x3
2 : DoubleTensor - size: 3x4x2
}
``````

## LuaJIT FFI access

These functions expose Torch's Tensor and Storage data structures, through LuaJIT FFI. This allows extremely fast access to Tensors and Storages, all from Lua.

### [result] data(tensor, [asnumber])

Returns a LuaJIT FFI pointer to the raw data of the tensor. If `asnumber` is true, then returns the pointer as a `intptr_t` cdata that you can transform to a plain lua number with `tonumber()`.

Accessing the raw data of a Tensor like this is extremely efficient, in fact, it's almost as fast as C in lots of cases.

Example:

``````t = torch.randn(3,2)
> t
0.8008 -0.6103
0.6473 -0.1870
-0.0023 -0.4902
[torch.DoubleTensor of dimension 3x2]

t_data = torch.data(t)
for i = 0,t:nElement()-1 do t_data[i] = 0 end
> t
0 0
0 0
0 0
[torch.DoubleTensor of dimension 3x2]
``````

WARNING: bear in mind that accessing the raw data like this is dangerous, and should only be done on contiguous tensors (if a tensor is not contiguous, then you have to use its size and stride information). Making sure a tensor is contiguous is easy:

``````t = torch.randn(3,2)
t_noncontiguous = t:transpose(1,2)

-- it would be unsafe to work with torch.data(t_noncontiguous)
t_transposed_and_contiguous = t_noncontiguous:contiguous()

-- it is now safe to work with the raw pointer
data = torch.data(t_transposed_and_contiguous)
``````

Last, the pointer can be returned as a plain `intptr_t` cdata. This can be useful to share pointers between threads (warning: this is dangerous, as the second tensor doesn't increment the reference counter on the storage. If the first tensor gets freed, then the data of the second tensor becomes a dangling pointer):

``````t = torch.randn(10)
p = tonumber(torch.data(t,true))
s = torch.Storage(10, p)
tt = torch.Tensor(s)
-- tt and t are a view on the same data.
``````

### [result] cdata(tensor, [asnumber])

Returns a LuaJIT FFI pointer to the C structure of the tensor. Use this with caution, and look at FFI.lua for the members of the tensor

## Reference counting

Tensors are reference-counted. It means that each time an object (C or the Lua state) need to keep a reference over a tensor, the corresponding tensor reference counter will be increased. The reference counter is decreased when the object does not need the tensor anymore.

These methods should be used with extreme care. In general, they should never be called, except if you know what you are doing, as the handling of references is done automatically. They can be useful in threaded environments. Note that these methods are atomic operations.

### retain()

Increment the reference counter of the tensor.

### free()

Decrement the reference counter of the tensor. Free the tensor if the counter is at 0.