python tensorflow tf.nn.conv2d () (4-D`input` given tensor and `filter` calculating 2-D convolution)

From tensorflow\python\ops\gen_nn_ops.py

@tf_export('nn.conv2d')
def conv2d(input, filter, strides, padding, use_cudnn_on_gpu=True, data_format="NHWC", dilations=[1, 1, 1, 1], name=None):
  r"""Computes a 2-D convolution given 4-D `input` and `filter` tensors.
  给定4-D`input`和`filter`张量来计算2-D卷积。

  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:
  给定形状为[[batch,in_height,in_width,in_channels]`的输入张量和形状为
  [[filter_height,filter_width,in_channels,out_channels]`的过滤器/内核张量,
  此操作执行以下操作:

  

  1. Flattens the filter to a 2-D matrix with shape

     `[filter_height * filter_width * in_channels, output_channels]`.
     将过滤器展平为形状为[[filter_height * filter_width * in_channels,
     output_channels]`的二维矩阵。

  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]`.
     从输入张量中提取图像补丁,以形成形状为[[batch,out_height,out_width,
     filter_height * filter_width * in_channels]`的*虚拟*张量。

  3. For each patch, right-multiplies the filter matrix and the image patch

     vector.
     对于每个色块,将滤波器矩阵和图像色块向量右乘。

  

  In detail, with the default NHWC format,
  详细而言,使用默认的NHWC格式,

  
公式1:
      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]`.
  必须具有“步幅[0] =步幅[3] = 1”。 
  对于相同的水平和顶点步幅,在最常见的情况下,“步幅= [1,步幅,步幅,1]”。

  Args:
    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.
      张量 必须是以下类型之一:`half`,`bfloat16`,`float32`,`float64`。 
      一个4-D张量。 维度顺序是根据data_format的值来解释的,有关详细信息,请参见下文。
      
    filter: A `Tensor`. Must have the same type as `input`.
      A 4-D tensor of shape

      `[filter_height, filter_width, in_channels, out_channels]`
      张量,必须和输入类型相同。 形状为[[filter_height,filter_width,
      in_channels,out_channels]`的4-D张量
      
    strides: A list of `ints`.
      1-D tensor of length 4.  The stride of the sliding window for each

      dimension of `input`. The dimension order is determined by the value of

      `data_format`, see below for details.
      `ints'的列表。 一维张量,长度为4。“ input”的每个维度的滑动窗口的步幅。 
      尺寸顺序由data_format的值确定,有关详细信息,请参见下文。
      
    padding: A `string` from: `"SAME", "VALID"`.
      The type of padding algorithm to use.
      来自“ SAME”,“ VALID”`的`string`。 要使用的填充算法的类型。
      
    use_cudnn_on_gpu: An optional `bool`. Defaults to `True`.
    可选的布尔。 默认为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].
          可选字符串,来自“ NHWC”,“ NCHW”。 默认为““ NHWC”`。 
          指定输入和输出数据的数据格式。 
          使用默认格式“ NHWC”时,数据按以下顺序存储:[批,高度,宽度,通道]。 
          或者,格式可以是“ NCHW”,数据存储顺序为:[批,通道,高度,宽度]。
          
    dilations: An optional list of `ints`. Defaults to `[1, 1, 1, 1]`.
      1-D tensor of length 4.  The dilation factor for each dimension of

      `input`. 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 must be 1.
      `ints'的可选列表。 默认为[[1,1,1,1]`。 长度为1的一维张量。
      “输入”的每个维度的膨胀因子。 如果设置为k> 1,则该维度上每个过滤器元素之间将有k-1个跳过的像元。 
      尺寸顺序由data_format的值确定,有关详细信息,请参见上文。 
      批次尺寸和深度尺寸的膨胀必须为1。
      
    name: A name for the operation (optional).
    操作的名称(可选)。

  Returns:
    A `Tensor`. Has the same type as `input`.
    张量 与`input`具有相同的类型。
  """
  _ctx = _context._context
  if _ctx is None or not _ctx._eager_context.is_eager:
    if not isinstance(strides, (list, tuple)):
      raise TypeError(
          "Expected list for 'strides' argument to "
          "'conv2d' Op, not %r." % strides)
    strides = [_execute.make_int(_i, "strides") for _i in strides]
    padding = _execute.make_str(padding, "padding")
    if use_cudnn_on_gpu is None:
      use_cudnn_on_gpu = True
    use_cudnn_on_gpu = _execute.make_bool(use_cudnn_on_gpu, "use_cudnn_on_gpu")
    if data_format is None:
      data_format = "NHWC"
    data_format = _execute.make_str(data_format, "data_format")
    if dilations is None:
      dilations = [1, 1, 1, 1]
    if not isinstance(dilations, (list, tuple)):
      raise TypeError(
          "Expected list for 'dilations' argument to "
          "'conv2d' Op, not %r." % dilations)
    dilations = [_execute.make_int(_i, "dilations") for _i in dilations]
    _, _, _op = _op_def_lib._apply_op_helper(
        "Conv2D", input=input, filter=filter, strides=strides,
        padding=padding, use_cudnn_on_gpu=use_cudnn_on_gpu,
        data_format=data_format, dilations=dilations, name=name)
    _result = _op.outputs[:]
    _inputs_flat = _op.inputs
    _attrs = ("T", _op.get_attr("T"), "strides", _op.get_attr("strides"),
              "use_cudnn_on_gpu", _op.get_attr("use_cudnn_on_gpu"), "padding",
              _op.get_attr("padding"), "data_format",
              _op.get_attr("data_format"), "dilations",
              _op.get_attr("dilations"))
    _execute.record_gradient(
      "Conv2D", _inputs_flat, _attrs, _result, name)
    _result, = _result
    return _result

  else:
    try:
      _result = _pywrap_tensorflow.TFE_Py_FastPathExecute(
        _ctx._context_handle, _ctx._eager_context.device_name, "Conv2D", name,
        _ctx._post_execution_callbacks, input, filter, "strides", strides,
        "use_cudnn_on_gpu", use_cudnn_on_gpu, "padding", padding,
        "data_format", data_format, "dilations", dilations)
      return _result
    except _core._FallbackException:
      return conv2d_eager_fallback(
          input, filter, strides=strides, use_cudnn_on_gpu=use_cudnn_on_gpu,
          padding=padding, data_format=data_format, dilations=dilations,
          name=name, ctx=_ctx)
    except _core._NotOkStatusException as e:
      if name is not None:
        message = e.message + " name: " + name
      else:
        message = e.message
      _six.raise_from(_core._status_to_exception(e.code, message), None)

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