prompt: We are currently solving the following issue within our repository. Here is the issue text:
  --- BEGIN ISSUE ---
  Scattering 2D doesn't work when using 2^J == image size (TensorFlow backend)
  Similar issues have been reported before (#284, #363) and also fixed (#412) for Torch backend. However, still not working in the tensorflow backend:
  
  test:
  ```python 
  import numpy as np
  from kymatio.tensorflow import Scattering2D
  
  scattering = Scattering2D(J=5, shape=(32, 32))
  test_im = np.ones((1,1,32,32))
  test = scattering.scattering(test_im)
  ```
  
  Gives error:
  ```
        7 scattering = Scattering2D(J=5, shape=(32, 32))
        8 test_im = np.ones((1,1,32,32))
  ----> 9 test = scattering.scattering(test_im)
  
  ~/.local/lib/python3.9/site-packages/kymatio/scattering2d/frontend/tensorflow_frontend.py in scattering(self, input)
       48             input = tf.reshape(input, tf.concat(((-1,), signal_shape), 0))
       49 
  ---> 50             S = scattering2d(input, self.pad, self.unpad, self.backend, self.J, self.L, self.phi, self.psi,
       51                              self.max_order, self.out_type)
       52 
  
  ~/.local/lib/python3.9/site-packages/kymatio/scattering2d/core/scattering2d.py in scattering2d(x, pad, unpad, backend, J, L, phi, psi, max_order, out_type)
       13     out_S_0, out_S_1, out_S_2 = [], [], []
       14 
  ---> 15     U_r = pad(x)
       16 
       17     U_0_c = fft(U_r, 'C2C')
  
  ~/.local/lib/python3.9/site-packages/kymatio/scattering2d/backend/tensorflow_backend.py in __call__(self, x)
       27         paddings = [[0, 0]] * len(x.shape[:-2])
       28         paddings += [[self.pad_size[0], self.pad_size[1]], [self.pad_size[2], self.pad_size[3]]]
  ---> 29         return tf.cast(tf.pad(x, paddings, mode="REFLECT"), tf.complex64)
       30 
       31 def unpad(in_):
  
  ~/.local/lib/python3.9/site-packages/tensorflow/python/util/traceback_utils.py in error_handler(*args, **kwargs)
      151     except Exception as e:
      152       filtered_tb = _process_traceback_frames(e.__traceback__)
  --> 153       raise e.with_traceback(filtered_tb) from None
      154     finally:
      155       del filtered_tb
  
  ~/.local/lib/python3.9/site-packages/tensorflow/python/eager/execute.py in quick_execute(op_name, num_outputs, inputs, attrs, ctx, name)
       56   try:
       57     ctx.ensure_initialized()
  ---> 58     tensors = pywrap_tfe.TFE_Py_Execute(ctx._handle, device_name, op_name,
       59                                         inputs, attrs, num_outputs)
       60   except core._NotOkStatusException as e:
  
  InvalidArgumentError: paddings must be less than the dimension size: 32, 32 not less than 32 [Op:MirrorPad]
  ```
  
  (speculation) So possibly problems with the order of the padding being different in tensorflow from torch. 
  
  Should also probably include some tests for these types of problems like the tests for implemented for Torch in #346 
  
  --- END ISSUE ---
  
  Below are some code segments, each from a relevant file. One or more of these files may contain bugs.
  --- BEGIN FILES ---
  Path: `kymatio/scattering2d/backend/tensorflow_backend.py`
  Content:
  ```
  1 import tensorflow as tf
  2 
  3 from ...backend.tensorflow_backend import TensorFlowBackend
  4 
  5 
  6 class Pad(object):
  7     def __init__(self, pad_size, input_size):
  8         """
  9             Padding which allows to simultaneously pad in a reflection fashion
  10             and map to complex.
  11             Parameters
  12             ----------
  13             pad_size : list of 4 integers
  14                 size of padding to apply.
  15             input_size : list of 2 integers
  16                 size of the original signal
  17         """
  18         self.pad_size = pad_size
  19 
  20     def __call__(self, x):
  21         paddings = [[0, 0]] * len(x.shape[:-2])
  22         paddings += [[self.pad_size[0], self.pad_size[1]], [self.pad_size[2], self.pad_size[3]]]
  23         return tf.pad(x, paddings, mode="REFLECT")
  24 
  25 
  26 class TensorFlowBackend2D(TensorFlowBackend):
  27     Pad = Pad
  28 
  29     @staticmethod
  30     def unpad(in_):
  31         """
  32             Slices the input tensor at indices between 1::-1
  33             Parameters
  34             ----------
  35             in_ : tensor_like
  36                 input tensor
  37             Returns
  38             -------
  39             in_[..., 1:-1, 1:-1]
  40         """
  41         return in_[..., 1:-1, 1:-1]
  42 
  43 
  44     @classmethod
  45     def rfft(cls, x):
  46         cls.real_check(x)
  47         return tf.signal.fft2d(tf.cast(x, tf.complex64), name='rfft2d')
  48 
  49     @classmethod
  50     def irfft(cls, x):
  51         cls.complex_check(x)
  52         return tf.math.real(tf.signal.ifft2d(x, name='irfft2d'))
  53 
  54 
  55     @classmethod
  56     def ifft(cls, x):
  57         cls.complex_check(x)
  58         return tf.signal.ifft2d(x, name='ifft2d')
  59 
  60     @classmethod
  61     def subsample_fourier(cls, x, k):
  62         """ Subsampling of a 2D image performed in the Fourier domain.
  63 
  64         Subsampling in the spatial domain amounts to periodization
  65         in the Fourier domain, hence the formula.
  66 
  67         Parameters
  68         ----------
  69         x : tensor_like
  70             input tensor with at least three dimensions.
  71         k : int
  72             integer such that x is subsampled by k along the spatial variables.
  73 
  74         Returns
  75         -------
  76         out : tensor_like
  77             Tensor such that its Fourier transform is the Fourier
  78             transform of a subsampled version of x, i.e. in
  79             F^{-1}(out)[u1, u2] = F^{-1}(x)[u1 * k, u2 * k]
  80 
  81         """
  82         cls.complex_check(x)
  83 
  84         y = tf.reshape(x, (-1, k, x.shape[1] // k, k, x.shape[2] // k))
  85 
  86         out = tf.reduce_mean(y, axis=(1, 3))
  87         return out
  88 
  89 
  90 backend = TensorFlowBackend2D
  91
  ```
  --- END FILES ---
  
  Please first localize the bug based on the issue statement, and then generate a patch according to the `git diff` format fenced by three backticks.
  
  Here is an example:
  
  ```diff
  diff --git a/examples/server_async.py b/examples/server_async.py
  --- a/examples/server_async.py
  +++ b/examples/server_async.py
  @@ -313,4 +313,4 @@
   
   
   if __name__ == "__main__":
  -    asyncio.run(run_async_server("."), debug=True)
  +    asyncio.run(run_async_server(), debug=True)
  diff --git a/examples/server_sync.py b/examples/server_sync.py
  --- a/examples/server_sync.py
  +++ b/examples/server_sync.py
  @@ -313,5 +313,5 @@
   
   
   if __name__ == "__main__":
  -    server = run_sync_server(".")
  +    server = run_sync_server()
       server.shutdown()
  
  ```
  
golden_diff: diff --git a/kymatio/scattering2d/backend/tensorflow_backend.py b/kymatio/scattering2d/backend/tensorflow_backend.py
  --- a/kymatio/scattering2d/backend/tensorflow_backend.py
  +++ b/kymatio/scattering2d/backend/tensorflow_backend.py
  @@ -16,11 +16,34 @@
                   size of the original signal
           """
           self.pad_size = pad_size
  +        self.input_size = input_size
   
       def __call__(self, x):
  +        pad_size = list(self.pad_size)
  +
  +        # Clone to avoid passing on modifications.
  +        new_pad_size = list(pad_size)
  +
  +        # This handles the case where the padding is equal to the image size.
  +        if pad_size[0] == self.input_size[0]:
  +            new_pad_size[0] -= 1
  +            new_pad_size[1] -= 1
  +        if pad_size[2] == self.input_size[1]:
  +            new_pad_size[2] -= 1
  +            new_pad_size[3] -= 1
  +
           paddings = [[0, 0]] * len(x.shape[:-2])
  -        paddings += [[self.pad_size[0], self.pad_size[1]], [self.pad_size[2], self.pad_size[3]]]
  -        return tf.pad(x, paddings, mode="REFLECT")
  +        paddings += [[new_pad_size[0], new_pad_size[1]], [new_pad_size[2], new_pad_size[3]]]
  +
  +        x_padded = tf.pad(x, paddings, mode="REFLECT")
  +
  +        # Again, special handling for when padding is the same as image size.
  +        if pad_size[0] == self.input_size[0]:
  +            x_padded = tf.concat([tf.expand_dims(x_padded[..., 1, :], axis=-2), x_padded, tf.expand_dims(x_padded[..., x_padded.shape[-2] -2, :], axis=-2)], axis=-2)
  +        if pad_size[2] == self.input_size[1]:
  +            x_padded = tf.concat([tf.expand_dims(x_padded[..., :, 1], axis=-1), x_padded, tf.expand_dims(x_padded[..., :,  x_padded.shape[-1]-2], axis=-1)], axis=-1)
  +
  +        return x_padded
   
   
   class TensorFlowBackend2D(TensorFlowBackend):
  
verification_info: {"golden_diff": "diff --git a/kymatio/scattering2d/backend/tensorflow_backend.py b/kymatio/scattering2d/backend/tensorflow_backend.py\n--- a/kymatio/scattering2d/backend/tensorflow_backend.py\n+++ b/kymatio/scattering2d/backend/tensorflow_backend.py\n@@ -16,11 +16,34 @@\n                 size of the original signal\n         \"\"\"\n         self.pad_size = pad_size\n+        self.input_size = input_size\n \n     def __call__(self, x):\n+        pad_size = list(self.pad_size)\n+\n+        # Clone to avoid passing on modifications.\n+        new_pad_size = list(pad_size)\n+\n+        # This handles the case where the padding is equal to the image size.\n+        if pad_size[0] == self.input_size[0]:\n+            new_pad_size[0] -= 1\n+            new_pad_size[1] -= 1\n+        if pad_size[2] == self.input_size[1]:\n+            new_pad_size[2] -= 1\n+            new_pad_size[3] -= 1\n+\n         paddings = [[0, 0]] * len(x.shape[:-2])\n-        paddings += [[self.pad_size[0], self.pad_size[1]], [self.pad_size[2], self.pad_size[3]]]\n-        return tf.pad(x, paddings, mode=\"REFLECT\")\n+        paddings += [[new_pad_size[0], new_pad_size[1]], [new_pad_size[2], new_pad_size[3]]]\n+\n+        x_padded = tf.pad(x, paddings, mode=\"REFLECT\")\n+\n+        # Again, special handling for when padding is the same as image size.\n+        if pad_size[0] == self.input_size[0]:\n+            x_padded = tf.concat([tf.expand_dims(x_padded[..., 1, :], axis=-2), x_padded, tf.expand_dims(x_padded[..., x_padded.shape[-2] -2, :], axis=-2)], axis=-2)\n+        if pad_size[2] == self.input_size[1]:\n+            x_padded = tf.concat([tf.expand_dims(x_padded[..., :, 1], axis=-1), x_padded, tf.expand_dims(x_padded[..., :,  x_padded.shape[-1]-2], axis=-1)], axis=-1)\n+\n+        return x_padded\n \n \n class TensorFlowBackend2D(TensorFlowBackend):\n", "issue": "Scattering 2D doesn't work when using 2^J == image size (TensorFlow backend)\nSimilar issues have been reported before (#284, #363) and also fixed (#412) for Torch backend. However, still not working in the tensorflow backend:\r\n\r\ntest:\r\n```python \r\nimport numpy as np\r\nfrom kymatio.tensorflow import Scattering2D\r\n\r\nscattering = Scattering2D(J=5, shape=(32, 32))\r\ntest_im = np.ones((1,1,32,32))\r\ntest = scattering.scattering(test_im)\r\n```\r\n\r\nGives error:\r\n```\r\n      7 scattering = Scattering2D(J=5, shape=(32, 32))\r\n      8 test_im = np.ones((1,1,32,32))\r\n----> 9 test = scattering.scattering(test_im)\r\n\r\n~/.local/lib/python3.9/site-packages/kymatio/scattering2d/frontend/tensorflow_frontend.py in scattering(self, input)\r\n     48             input = tf.reshape(input, tf.concat(((-1,), signal_shape), 0))\r\n     49 \r\n---> 50             S = scattering2d(input, self.pad, self.unpad, self.backend, self.J, self.L, self.phi, self.psi,\r\n     51                              self.max_order, self.out_type)\r\n     52 \r\n\r\n~/.local/lib/python3.9/site-packages/kymatio/scattering2d/core/scattering2d.py in scattering2d(x, pad, unpad, backend, J, L, phi, psi, max_order, out_type)\r\n     13     out_S_0, out_S_1, out_S_2 = [], [], []\r\n     14 \r\n---> 15     U_r = pad(x)\r\n     16 \r\n     17     U_0_c = fft(U_r, 'C2C')\r\n\r\n~/.local/lib/python3.9/site-packages/kymatio/scattering2d/backend/tensorflow_backend.py in __call__(self, x)\r\n     27         paddings = [[0, 0]] * len(x.shape[:-2])\r\n     28         paddings += [[self.pad_size[0], self.pad_size[1]], [self.pad_size[2], self.pad_size[3]]]\r\n---> 29         return tf.cast(tf.pad(x, paddings, mode=\"REFLECT\"), tf.complex64)\r\n     30 \r\n     31 def unpad(in_):\r\n\r\n~/.local/lib/python3.9/site-packages/tensorflow/python/util/traceback_utils.py in error_handler(*args, **kwargs)\r\n    151     except Exception as e:\r\n    152       filtered_tb = _process_traceback_frames(e.__traceback__)\r\n--> 153       raise e.with_traceback(filtered_tb) from None\r\n    154     finally:\r\n    155       del filtered_tb\r\n\r\n~/.local/lib/python3.9/site-packages/tensorflow/python/eager/execute.py in quick_execute(op_name, num_outputs, inputs, attrs, ctx, name)\r\n     56   try:\r\n     57     ctx.ensure_initialized()\r\n---> 58     tensors = pywrap_tfe.TFE_Py_Execute(ctx._handle, device_name, op_name,\r\n     59                                         inputs, attrs, num_outputs)\r\n     60   except core._NotOkStatusException as e:\r\n\r\nInvalidArgumentError: paddings must be less than the dimension size: 32, 32 not less than 32 [Op:MirrorPad]\r\n```\r\n\r\n(speculation) So possibly problems with the order of the padding being different in tensorflow from torch. \r\n\r\nShould also probably include some tests for these types of problems like the tests for implemented for Torch in #346 \n", "before_files": [{"content": "import tensorflow as tf\n\nfrom ...backend.tensorflow_backend import TensorFlowBackend\n\n\nclass Pad(object):\n    def __init__(self, pad_size, input_size):\n        \"\"\"\n            Padding which allows to simultaneously pad in a reflection fashion\n            and map to complex.\n            Parameters\n            ----------\n            pad_size : list of 4 integers\n                size of padding to apply.\n            input_size : list of 2 integers\n                size of the original signal\n        \"\"\"\n        self.pad_size = pad_size\n\n    def __call__(self, x):\n        paddings = [[0, 0]] * len(x.shape[:-2])\n        paddings += [[self.pad_size[0], self.pad_size[1]], [self.pad_size[2], self.pad_size[3]]]\n        return tf.pad(x, paddings, mode=\"REFLECT\")\n\n\nclass TensorFlowBackend2D(TensorFlowBackend):\n    Pad = Pad\n\n    @staticmethod\n    def unpad(in_):\n        \"\"\"\n            Slices the input tensor at indices between 1::-1\n            Parameters\n            ----------\n            in_ : tensor_like\n                input tensor\n            Returns\n            -------\n            in_[..., 1:-1, 1:-1]\n        \"\"\"\n        return in_[..., 1:-1, 1:-1]\n\n\n    @classmethod\n    def rfft(cls, x):\n        cls.real_check(x)\n        return tf.signal.fft2d(tf.cast(x, tf.complex64), name='rfft2d')\n\n    @classmethod\n    def irfft(cls, x):\n        cls.complex_check(x)\n        return tf.math.real(tf.signal.ifft2d(x, name='irfft2d'))\n\n\n    @classmethod\n    def ifft(cls, x):\n        cls.complex_check(x)\n        return tf.signal.ifft2d(x, name='ifft2d')\n\n    @classmethod\n    def subsample_fourier(cls, x, k):\n        \"\"\" Subsampling of a 2D image performed in the Fourier domain.\n\n        Subsampling in the spatial domain amounts to periodization\n        in the Fourier domain, hence the formula.\n\n        Parameters\n        ----------\n        x : tensor_like\n            input tensor with at least three dimensions.\n        k : int\n            integer such that x is subsampled by k along the spatial variables.\n\n        Returns\n        -------\n        out : tensor_like\n            Tensor such that its Fourier transform is the Fourier\n            transform of a subsampled version of x, i.e. in\n            F^{-1}(out)[u1, u2] = F^{-1}(x)[u1 * k, u2 * k]\n\n        \"\"\"\n        cls.complex_check(x)\n\n        y = tf.reshape(x, (-1, k, x.shape[1] // k, k, x.shape[2] // k))\n\n        out = tf.reduce_mean(y, axis=(1, 3))\n        return out\n\n\nbackend = TensorFlowBackend2D\n", "path": "kymatio/scattering2d/backend/tensorflow_backend.py"}], "after_files": [{"content": "import tensorflow as tf\n\nfrom ...backend.tensorflow_backend import TensorFlowBackend\n\n\nclass Pad(object):\n    def __init__(self, pad_size, input_size):\n        \"\"\"\n            Padding which allows to simultaneously pad in a reflection fashion\n            and map to complex.\n            Parameters\n            ----------\n            pad_size : list of 4 integers\n                size of padding to apply.\n            input_size : list of 2 integers\n                size of the original signal\n        \"\"\"\n        self.pad_size = pad_size\n        self.input_size = input_size\n\n    def __call__(self, x):\n        pad_size = list(self.pad_size)\n\n        # Clone to avoid passing on modifications.\n        new_pad_size = list(pad_size)\n\n        # This handles the case where the padding is equal to the image size.\n        if pad_size[0] == self.input_size[0]:\n            new_pad_size[0] -= 1\n            new_pad_size[1] -= 1\n        if pad_size[2] == self.input_size[1]:\n            new_pad_size[2] -= 1\n            new_pad_size[3] -= 1\n\n        paddings = [[0, 0]] * len(x.shape[:-2])\n        paddings += [[new_pad_size[0], new_pad_size[1]], [new_pad_size[2], new_pad_size[3]]]\n\n        x_padded = tf.pad(x, paddings, mode=\"REFLECT\")\n\n        # Again, special handling for when padding is the same as image size.\n        if pad_size[0] == self.input_size[0]:\n            x_padded = tf.concat([tf.expand_dims(x_padded[..., 1, :], axis=-2), x_padded, tf.expand_dims(x_padded[..., x_padded.shape[-2] -2, :], axis=-2)], axis=-2)\n        if pad_size[2] == self.input_size[1]:\n            x_padded = tf.concat([tf.expand_dims(x_padded[..., :, 1], axis=-1), x_padded, tf.expand_dims(x_padded[..., :,  x_padded.shape[-1]-2], axis=-1)], axis=-1)\n\n        return x_padded\n\n\nclass TensorFlowBackend2D(TensorFlowBackend):\n    Pad = Pad\n\n    @staticmethod\n    def unpad(in_):\n        \"\"\"\n            Slices the input tensor at indices between 1::-1\n            Parameters\n            ----------\n            in_ : tensor_like\n                input tensor\n            Returns\n            -------\n            in_[..., 1:-1, 1:-1]\n        \"\"\"\n        return in_[..., 1:-1, 1:-1]\n\n\n    @classmethod\n    def rfft(cls, x):\n        cls.real_check(x)\n        return tf.signal.fft2d(tf.cast(x, tf.complex64), name='rfft2d')\n\n    @classmethod\n    def irfft(cls, x):\n        cls.complex_check(x)\n        return tf.math.real(tf.signal.ifft2d(x, name='irfft2d'))\n\n\n    @classmethod\n    def ifft(cls, x):\n        cls.complex_check(x)\n        return tf.signal.ifft2d(x, name='ifft2d')\n\n    @classmethod\n    def subsample_fourier(cls, x, k):\n        \"\"\" Subsampling of a 2D image performed in the Fourier domain.\n\n        Subsampling in the spatial domain amounts to periodization\n        in the Fourier domain, hence the formula.\n\n        Parameters\n        ----------\n        x : tensor_like\n            input tensor with at least three dimensions.\n        k : int\n            integer such that x is subsampled by k along the spatial variables.\n\n        Returns\n        -------\n        out : tensor_like\n            Tensor such that its Fourier transform is the Fourier\n            transform of a subsampled version of x, i.e. in\n            F^{-1}(out)[u1, u2] = F^{-1}(x)[u1 * k, u2 * k]\n\n        \"\"\"\n        cls.complex_check(x)\n\n        y = tf.reshape(x, (-1, k, x.shape[1] // k, k, x.shape[2] // k))\n\n        out = tf.reduce_mean(y, axis=(1, 3))\n        return out\n\n\nbackend = TensorFlowBackend2D\n", "path": "kymatio/scattering2d/backend/tensorflow_backend.py"}]}