# tf.space_to_batch_nd

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SpaceToBatch for N-D tensors of type T.

#### View aliases


**Compat aliases for migration**

See
[Migration guide](https://www.tensorflow.org/guide/migrate) for
more details.

[`tf.compat.v1.manip.space_to_batch_nd`](https://www.tensorflow.org/api_docs/python/tf/space_to_batch_nd), [`tf.compat.v1.space_to_batch_nd`](https://www.tensorflow.org/api_docs/python/tf/space_to_batch_nd)

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    tf.space_to_batch_nd(
        input, block_shape, paddings, name=None
    )

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.

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]]`:

    x = [[[[1], [2]], [[3], [4]]]]

The output tensor has shape `[4, 1, 1, 1]` and value:

    [[[[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]]`:

    x = [[[[1, 2, 3], [4, 5, 6]],
          [[7, 8, 9], [10, 11, 12]]]]

The output tensor has shape `[4, 1, 1, 3]` and value:

    [[[[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]]`:

    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:

    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]]`:

    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:

    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.

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| ## 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`. |
| `name` | A name for the operation (optional). |

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| ## Returns ||
|---|---|
| A `Tensor`. Has the same type as `input`. ||

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