# Shapes and Shaping

TensorFlow provides several operations that you can use to determine the shape of a tensor and change the shape of a tensor.

### tf.shape(input, name=None)

Returns the shape of a tensor.

This operation returns a 1-D integer tensor representing the shape of input.

For example:

# 't' is [[[1, 1, 1], [2, 2, 2]], [[3, 3, 3], [4, 4, 4]]]
shape(t) ==> [2, 2, 3]

##### Args:
• input: A Tensor or SparseTensor.
• name: A name for the operation (optional).
##### Returns:

A Tensor of type int32.

### tf.size(input, name=None)

Returns the size of a tensor.

This operation returns an integer representing the number of elements in input.

For example:

# 't' is [[[1, 1, 1], [2, 2, 2]], [[3, 3, 3], [4, 4, 4]]]]
size(t) ==> 12

##### Args:
• input: A Tensor or SparseTensor.
• name: A name for the operation (optional).
##### Returns:

A Tensor of type int32.

### tf.rank(input, name=None)

Returns the rank of a tensor.

This operation returns an integer representing the rank of input.

For example:

# 't' is [[[1, 1, 1], [2, 2, 2]], [[3, 3, 3], [4, 4, 4]]]
# shape of tensor 't' is [2, 2, 3]
rank(t) ==> 3


Note: The rank of a tensor is not the same as the rank of a matrix. The rank of a tensor is the number of indices required to uniquely select each element of the tensor. Rank is also known as "order", "degree", or "ndims."

##### Args:
• input: A Tensor or SparseTensor.
• name: A name for the operation (optional).
##### Returns:

A Tensor of type int32.

### tf.reshape(tensor, shape, name=None)

Reshapes a tensor.

Given tensor, this operation returns a tensor that has the same values as tensor with shape shape.

If one component of shape is the special value -1, the size of that dimension is computed so that the total size remains constant. In particular, a shape of [-1] flattens into 1-D. At most one component of shape can be -1.

If shape is 1-D or higher, then the operation returns a tensor with shape shape filled with the values of tensor. In this case, the number of elements implied by shape must be the same as the number of elements in tensor.

For example:

# tensor 't' is [1, 2, 3, 4, 5, 6, 7, 8, 9]
# tensor 't' has shape [9]
reshape(t, [3, 3]) ==> [[1, 2, 3],
[4, 5, 6],
[7, 8, 9]]

# tensor 't' is [[[1, 1], [2, 2]],
#                [[3, 3], [4, 4]]]
# tensor 't' has shape [2, 2, 2]
reshape(t, [2, 4]) ==> [[1, 1, 2, 2],
[3, 3, 4, 4]]

# tensor 't' is [[[1, 1, 1],
#                 [2, 2, 2]],
#                [[3, 3, 3],
#                 [4, 4, 4]],
#                [[5, 5, 5],
#                 [6, 6, 6]]]
# tensor 't' has shape [3, 2, 3]
# pass '[-1]' to flatten 't'
reshape(t, [-1]) ==> [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6]

# -1 can also be used to infer the shape

# -1 is inferred to be 9:
reshape(t, [2, -1]) ==> [[1, 1, 1, 2, 2, 2, 3, 3, 3],
[4, 4, 4, 5, 5, 5, 6, 6, 6]]
# -1 is inferred to be 2:
reshape(t, [-1, 9]) ==> [[1, 1, 1, 2, 2, 2, 3, 3, 3],
[4, 4, 4, 5, 5, 5, 6, 6, 6]]
# -1 is inferred to be 3:
reshape(t, [ 2, -1, 3]) ==> [[[1, 1, 1],
[2, 2, 2],
[3, 3, 3]],
[[4, 4, 4],
[5, 5, 5],
[6, 6, 6]]]

# tensor 't' is [7]
# shape [] reshapes to a scalar
reshape(t, []) ==> 7

##### Args:
• tensor: A Tensor.
• shape: A Tensor of type int32. Defines the shape of the output tensor.
• name: A name for the operation (optional).
##### Returns:

A Tensor. Has the same type as tensor.

### tf.squeeze(input, squeeze_dims=None, name=None)

Removes dimensions of size 1 from the shape of a tensor.

Given a tensor input, this operation returns a tensor of the same type with all dimensions of size 1 removed. If you don't want to remove all size 1 dimensions, you can remove specific size 1 dimensions by specifying squeeze_dims.

For example:

# 't' is a tensor of shape [1, 2, 1, 3, 1, 1]
shape(squeeze(t)) ==> [2, 3]


Or, to remove specific size 1 dimensions:

# 't' is a tensor of shape [1, 2, 1, 3, 1, 1]
shape(squeeze(t, [2, 4])) ==> [1, 2, 3, 1]

##### Args:
• input: A Tensor. The input to squeeze.
• squeeze_dims: An optional list of ints. Defaults to []. If specified, only squeezes the dimensions listed. The dimension index starts at 0. It is an error to squeeze a dimension that is not 1.
• name: A name for the operation (optional).
##### Returns:

A Tensor. Has the same type as input. Contains the same data as input, but has one or more dimensions of size 1 removed.

### tf.expand_dims(input, dim, name=None)

Inserts a dimension of 1 into a tensor's shape.

Given a tensor input, this operation inserts a dimension of 1 at the dimension index dim of input's shape. The dimension index dim starts at zero; if you specify a negative number for dim it is counted backward from the end.

This operation is useful if you want to add a batch dimension to a single element. For example, if you have a single image of shape [height, width, channels], you can make it a batch of 1 image with expand_dims(image, 0), which will make the shape [1, height, width, channels].

Other examples:

# 't' is a tensor of shape [2]
shape(expand_dims(t, 0)) ==> [1, 2]
shape(expand_dims(t, 1)) ==> [2, 1]
shape(expand_dims(t, -1)) ==> [2, 1]

# 't2' is a tensor of shape [2, 3, 5]
shape(expand_dims(t2, 0)) ==> [1, 2, 3, 5]
shape(expand_dims(t2, 2)) ==> [2, 3, 1, 5]
shape(expand_dims(t2, 3)) ==> [2, 3, 5, 1]


This operation requires that:

-1-input.dims() <= dim <= input.dims()

This operation is related to squeeze(), which removes dimensions of size 1.

##### Args:
• input: A Tensor.
• dim: A Tensor of type int32. 0-D (scalar). Specifies the dimension index at which to expand the shape of input.
• name: A name for the operation (optional).
##### Returns:

A Tensor. Has the same type as input. Contains the same data as input, but its shape has an additional dimension of size 1 added.

### tf.meshgrid(*args, **kwargs)

Broadcasts parameters for evaluation on an N-D grid.

Given N one-dimensional coordinate arrays *args, returns a list outputs of N-D coordinate arrays for evaluating expressions on an N-D grid.

Notes:

meshgrid supports cartesian ('xy') and matrix ('ij') indexing conventions. When the indexing argument is set to 'xy' (the default), the broadcasting instructions for the first two dimensions are swapped.

Examples:

Calling X, Y = meshgrid(x, y) with the tensors

  x = [1, 2, 3]
y = [4, 5, 6]


results in

  X = [[1, 1, 1],
[2, 2, 2],
[3, 3, 3]]
Y = [[4, 5, 6],
[4, 5, 6],
[4, 5, 6]]

##### Args:
• *args: Tensors with rank 1
• indexing: Either 'xy' or 'ij' (optional, default: 'xy')
• name: A name for the operation (optional).
##### Returns:
• outputs: A list of N Tensors with rank N