### `tf.space_to_batch_nd(input, block_shape, paddings, name=None)` {#space_to_batch_nd}
SpaceToBatch for N-D tensors of type T.
This operation divides "spatial" dimensions `[1, ..., M]` of the input into a
grid of blocks of shape `block_shape`, and interleaves these blocks with the
"batch" dimension (0) such that in the output, the spatial dimensions
`[1, ..., M]` correspond to the position within the grid, and the batch
dimension combines both the position within a spatial block and the original
batch position. Prior to division into blocks, the spatial dimensions of the
input are optionally zero padded according to `paddings`. See below for a
precise description.
##### Args:
* `input`: A `Tensor`.
N-D with shape `input_shape = [batch] + spatial_shape + remaining_shape`,
where spatial_shape has `M` dimensions.
* `block_shape`: A `Tensor`. Must be one of the following types: `int32`, `int64`.
1-D with shape `[M]`, all values must be >= 1.
* `paddings`: A `Tensor`. Must be one of the following types: `int32`, `int64`.
2-D with shape `[M, 2]`, all values must be >= 0.
`paddings[i] = [pad_start, pad_end]` specifies the padding for input dimension
`i + 1`, which corresponds to spatial dimension `i`. It is required that
`block_shape[i]` divides `input_shape[i + 1] + pad_start + pad_end`.
This operation is equivalent to the following steps:
1. Zero-pad the start and end of dimensions `[1, ..., M]` of the
input according to `paddings` to produce `padded` of shape `padded_shape`.
2. Reshape `padded` to `reshaped_padded` of shape:
[batch] +
[padded_shape[1] / block_shape[0],
block_shape[0],
...,
padded_shape[M] / block_shape[M-1],
block_shape[M-1]] +
remaining_shape
3. Permute dimensions of `reshaped_padded` to produce
`permuted_reshaped_padded` of shape:
block_shape +
[batch] +
[padded_shape[1] / block_shape[0],
...,
padded_shape[M] / block_shape[M-1]] +
remaining_shape
4. Reshape `permuted_reshaped_padded` to flatten `block_shape` into the batch
dimension, producing an output tensor of shape:
[batch * prod(block_shape)] +
[padded_shape[1] / block_shape[0],
...,
padded_shape[M] / block_shape[M-1]] +
remaining_shape
Some examples:
(1) For the following input of shape `[1, 2, 2, 1]`, `block_shape = [2, 2]`, and
`paddings = [[0, 0], [0, 0]]`:
```prettyprint
x = [[[[1], [2]], [[3], [4]]]]
```
The output tensor has shape `[4, 1, 1, 1]` and value:
```prettyprint
[[[[1]]], [[[2]]], [[[3]]], [[[4]]]]
```
(2) For the following input of shape `[1, 2, 2, 3]`, `block_shape = [2, 2]`, and
`paddings = [[0, 0], [0, 0]]`:
```prettyprint
x = [[[[1, 2, 3], [4, 5, 6]],
[[7, 8, 9], [10, 11, 12]]]]
```
The output tensor has shape `[4, 1, 1, 3]` and value:
```prettyprint
[[[1, 2, 3]], [[4, 5, 6]], [[7, 8, 9]], [[10, 11, 12]]]
```
(3) For the following input of shape `[1, 4, 4, 1]`, `block_shape = [2, 2]`, and
`paddings = [[0, 0], [0, 0]]`:
```prettyprint
x = [[[[1], [2], [3], [4]],
[[5], [6], [7], [8]],
[[9], [10], [11], [12]],
[[13], [14], [15], [16]]]]
```
The output tensor has shape `[4, 2, 2, 1]` and value:
```prettyprint
x = [[[[1], [3]], [[9], [11]]],
[[[2], [4]], [[10], [12]]],
[[[5], [7]], [[13], [15]]],
[[[6], [8]], [[14], [16]]]]
```
(4) For the following input of shape `[2, 2, 4, 1]`, block_shape = `[2, 2]`, and
paddings = `[[0, 0], [2, 0]]`:
```prettyprint
x = [[[[1], [2], [3], [4]],
[[5], [6], [7], [8]]],
[[[9], [10], [11], [12]],
[[13], [14], [15], [16]]]]
```
The output tensor has shape `[8, 1, 3, 1]` and value:
```prettyprint
x = [[[[0], [1], [3]]], [[[0], [9], [11]]],
[[[0], [2], [4]]], [[[0], [10], [12]]],
[[[0], [5], [7]]], [[[0], [13], [15]]],
[[[0], [6], [8]]], [[[0], [14], [16]]]]
```
Among others, this operation is useful for reducing atrous convolution into
regular convolution.
* `name`: A name for the operation (optional).
##### Returns:
A `Tensor`. Has the same type as `input`.