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# tf.nn.conv2d

Computes a 2-D convolution given 4-D `input` and `filter` tensors.

Given an input tensor of shape `[batch, in_height, in_width, in_channels]` and a filter / kernel tensor of shape `[filter_height, filter_width, in_channels, out_channels]`, this op performs the following:

1. Flattens the filter to a 2-D matrix with shape `[filter_height * filter_width * in_channels, output_channels]`.
2. Extracts image patches from the input tensor to form a virtual tensor of shape ```[batch, out_height, out_width, filter_height * filter_width * in_channels]```.
3. For each patch, right-multiplies the filter matrix and the image patch vector.

In detail, with the default NHWC format,

``````output[b, i, j, k] =
sum_{di, dj, q} input[b, strides[1] * i + di, strides[2] * j + dj, q]

* filter[di, dj, q, k]
``````

Must have `strides[0] = strides[3] = 1`. For the most common case of the same horizontal and vertices strides, `strides = [1, stride, stride, 1]`.

`input` A `Tensor`. Must be one of the following types: `half`, `bfloat16`, `float32`, `float64`. A 4-D tensor. The dimension order is interpreted according to the value of `data_format`, see below for details.
`filter` A `Tensor`. Must have the same type as `input`. A 4-D tensor of shape `[filter_height, filter_width, in_channels, out_channels]`
`strides` An int or list of `ints` that has length `1`, `2` or `4`. The stride of the sliding window for each dimension of `input`. If a single value is given it is replicated in the `H` and `W` dimension. By default the `N` and `C` dimensions are set to 1. The dimension order is determined by the value of `data_format`, see below for details.
`padding` Either the `string` `"SAME"` or `"VALID"` indicating the type of padding algorithm to use, or a list indicating the explicit paddings at the start and end of each dimension. When explicit padding is used and data_format is `"NHWC"`, this should be in the form ```[[0, 0], [pad_top, pad_bottom], [pad_left, pad_right], [0, 0]]```. When explicit padding used and data_format is `"NCHW"`, this should be in the form ```[[0, 0], [0, 0], [pad_top, pad_bottom], [pad_left, pad_right]]```.
`use_cudnn_on_gpu` An optional `bool`. Defaults to `True`.
`data_format` An optional `string` from: `"NHWC", "NCHW"`. Defaults to `"NHWC"`. Specify the data format of the input and output data. With the default format "NHWC", the data is stored in the order of: [batch, height, width, channels]. Alternatively, the format could be "NCHW", the data storage order of: [batch, channels, height, width].
`dilations` An int or list of `ints` that has length `1`, `2` or `4`, defaults to 1. The dilation factor for each dimension of`input`. If a single value is given it is replicated in the `H` and `W` dimension. By default the `N` and `C` dimensions are set to 1. If set to k > 1, there will be k-1 skipped cells between each filter element on that dimension. The dimension order is determined by the value of `data_format`, see above for details. Dilations in the batch and depth dimensions if a 4-d tensor must be 1.
`name` A name for the operation (optional).
`filters` Alias for filter.

A `Tensor`. Has the same type as `input`.

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