prompt: We are currently solving the following issue within our repository. Here is the issue text:
  --- BEGIN ISSUE ---
  GPU implementation of transpose_sequence is too slow
  As @jnory mentioned in #1174, `transpose_sequence` is too slow. We need to make a single kernel to make a transposed matrix.
  
  
  --- END ISSUE ---
  
  Below are some code segments, each from a relevant file. One or more of these files may contain bugs.
  --- BEGIN FILES ---
  Path: `chainer/functions/array/transpose_sequence.py`
  Content:
  ```
  1 import numpy
  2 
  3 from chainer import cuda
  4 from chainer import function
  5 from chainer.utils import type_check
  6 
  7 
  8 def _transpose(xs, length):
  9     xp = cuda.get_array_module(*xs)
  10     lengths = numpy.zeros(length, dtype='i')
  11     for i, x in enumerate(xs):
  12         lengths[0:len(x)] = i + 1
  13     dtype = xs[0].dtype
  14     unit = xs[0].shape[1:]
  15     outs = tuple([xp.empty((l,) + unit, dtype=dtype) for l in lengths])
  16 
  17     for i, x in enumerate(xs):
  18         for p, xi in enumerate(x):
  19             outs[p][i] = xi
  20 
  21     return outs
  22 
  23 
  24 class TransposeSequence(function.Function):
  25 
  26     """Function that transposes a list of Variables."""
  27 
  28     def check_type_forward(self, xs_type):
  29         for p, n in zip(xs_type, xs_type[1:]):
  30             type_check.expect(
  31                 p.shape[0] >= n.shape[0],
  32                 p.shape[1:] == n.shape[1:],
  33             )
  34 
  35     def forward(self, xs):
  36         if len(xs) == 0:
  37             return ()
  38         return _transpose(xs, len(xs[0]))
  39 
  40     def backward(self, xs, gs):
  41         return _transpose(gs, len(xs))
  42 
  43 
  44 def transpose_sequence(xs):
  45     """Transpose a list of Variables.
  46 
  47     This function transposes a list of :class:`~chainer.Variable` s and returns
  48     a list of :class:`Variable` s.
  49     For exampe a user gives ``[(0, 1, 2, 3), (4, 5), (6)]``, the function
  50     returns ``[(0, 4, 6), (1, 5), (2), (3)]``.
  51     Note that a given list needs to be sorted by each length of
  52     :class:`~chainer.Variable`.
  53 
  54     Args:
  55         xs (list of ~chainer.Variable): Variables to transpose.
  56 
  57     Returns:
  58         tuple or Variable: Transposed list.
  59     """
  60     ys = TransposeSequence()(*xs)
  61     if not isinstance(ys, tuple):
  62         ys = (ys,)
  63     return ys
  64
  ```
  --- 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/chainer/functions/array/transpose_sequence.py b/chainer/functions/array/transpose_sequence.py
  --- a/chainer/functions/array/transpose_sequence.py
  +++ b/chainer/functions/array/transpose_sequence.py
  @@ -6,17 +6,55 @@
   
   
   def _transpose(xs, length):
  -    xp = cuda.get_array_module(*xs)
  -    lengths = numpy.zeros(length, dtype='i')
  -    for i, x in enumerate(xs):
  -        lengths[0:len(x)] = i + 1
  -    dtype = xs[0].dtype
  -    unit = xs[0].shape[1:]
  -    outs = tuple([xp.empty((l,) + unit, dtype=dtype) for l in lengths])
  +    if length == 0:
  +        return ()
   
  +    xp = cuda.get_array_module(*xs)
  +    lengths = numpy.empty(length, dtype='i')
  +    end = length
       for i, x in enumerate(xs):
  -        for p, xi in enumerate(x):
  -            outs[p][i] = xi
  +        lengths[len(x):end] = i
  +        end = len(x)
  +    lengths[0:end] = len(xs)
  +
  +    if xp is numpy:
  +        dtype = xs[0].dtype
  +        unit = xs[0].shape[1:]
  +
  +        outs = tuple([xp.empty((l,) + unit, dtype=dtype) for l in lengths])
  +        for i, x in enumerate(xs):
  +            for p, xi in enumerate(x):
  +                outs[p][i] = xi
  +
  +    else:
  +        offsets1 = numpy.empty(len(xs) + 1, dtype='i')
  +        offsets1[0] = 0
  +        numpy.cumsum([len(x) for x in xs], out=offsets1[1:])
  +
  +        offsets2 = numpy.empty(length + 1, dtype='i')
  +        offsets2[0] = 0
  +        numpy.cumsum(lengths, dtype='i', out=offsets2[1:])
  +
  +        x = xp.concatenate(xs, axis=0)
  +        o = xp.empty_like(x)
  +        unit = xs[0].size // len(xs[0])
  +        size = length * len(xs) * unit
  +        cuda.elementwise(
  +            'int32 len, int32 unit, raw int32 off1, raw int32 off2, raw T vs',
  +            'raw T hs',
  +            '''
  +            int ind = i / unit;
  +            int off = i - ind * unit;
  +            int y = ind / len;
  +            int x = ind - y * len;
  +            if (off2[x] + y < off2[x + 1]) {
  +              hs[(off2[x] + y) * unit + off] = vs[(off1[y] + x) * unit + off];
  +            }
  +            ''',
  +            'transpose_sequence'
  +        )(length, unit, cuda.to_gpu(offsets1), cuda.to_gpu(offsets2), x, o,
  +          size=size)
  +        outs = tuple(xp.split(o, offsets2[1:-1]))
   
       return outs
  
verification_info: {"golden_diff": "diff --git a/chainer/functions/array/transpose_sequence.py b/chainer/functions/array/transpose_sequence.py\n--- a/chainer/functions/array/transpose_sequence.py\n+++ b/chainer/functions/array/transpose_sequence.py\n@@ -6,17 +6,55 @@\n \n \n def _transpose(xs, length):\n-    xp = cuda.get_array_module(*xs)\n-    lengths = numpy.zeros(length, dtype='i')\n-    for i, x in enumerate(xs):\n-        lengths[0:len(x)] = i + 1\n-    dtype = xs[0].dtype\n-    unit = xs[0].shape[1:]\n-    outs = tuple([xp.empty((l,) + unit, dtype=dtype) for l in lengths])\n+    if length == 0:\n+        return ()\n \n+    xp = cuda.get_array_module(*xs)\n+    lengths = numpy.empty(length, dtype='i')\n+    end = length\n     for i, x in enumerate(xs):\n-        for p, xi in enumerate(x):\n-            outs[p][i] = xi\n+        lengths[len(x):end] = i\n+        end = len(x)\n+    lengths[0:end] = len(xs)\n+\n+    if xp is numpy:\n+        dtype = xs[0].dtype\n+        unit = xs[0].shape[1:]\n+\n+        outs = tuple([xp.empty((l,) + unit, dtype=dtype) for l in lengths])\n+        for i, x in enumerate(xs):\n+            for p, xi in enumerate(x):\n+                outs[p][i] = xi\n+\n+    else:\n+        offsets1 = numpy.empty(len(xs) + 1, dtype='i')\n+        offsets1[0] = 0\n+        numpy.cumsum([len(x) for x in xs], out=offsets1[1:])\n+\n+        offsets2 = numpy.empty(length + 1, dtype='i')\n+        offsets2[0] = 0\n+        numpy.cumsum(lengths, dtype='i', out=offsets2[1:])\n+\n+        x = xp.concatenate(xs, axis=0)\n+        o = xp.empty_like(x)\n+        unit = xs[0].size // len(xs[0])\n+        size = length * len(xs) * unit\n+        cuda.elementwise(\n+            'int32 len, int32 unit, raw int32 off1, raw int32 off2, raw T vs',\n+            'raw T hs',\n+            '''\n+            int ind = i / unit;\n+            int off = i - ind * unit;\n+            int y = ind / len;\n+            int x = ind - y * len;\n+            if (off2[x] + y < off2[x + 1]) {\n+              hs[(off2[x] + y) * unit + off] = vs[(off1[y] + x) * unit + off];\n+            }\n+            ''',\n+            'transpose_sequence'\n+        )(length, unit, cuda.to_gpu(offsets1), cuda.to_gpu(offsets2), x, o,\n+          size=size)\n+        outs = tuple(xp.split(o, offsets2[1:-1]))\n \n     return outs\n", "issue": "GPU implementation of transpose_sequence is too slow\nAs @jnory mentioned in #1174, `transpose_sequence` is too slow. We need to make a single kernel to make a transposed matrix.\n\n", "before_files": [{"content": "import numpy\n\nfrom chainer import cuda\nfrom chainer import function\nfrom chainer.utils import type_check\n\n\ndef _transpose(xs, length):\n    xp = cuda.get_array_module(*xs)\n    lengths = numpy.zeros(length, dtype='i')\n    for i, x in enumerate(xs):\n        lengths[0:len(x)] = i + 1\n    dtype = xs[0].dtype\n    unit = xs[0].shape[1:]\n    outs = tuple([xp.empty((l,) + unit, dtype=dtype) for l in lengths])\n\n    for i, x in enumerate(xs):\n        for p, xi in enumerate(x):\n            outs[p][i] = xi\n\n    return outs\n\n\nclass TransposeSequence(function.Function):\n\n    \"\"\"Function that transposes a list of Variables.\"\"\"\n\n    def check_type_forward(self, xs_type):\n        for p, n in zip(xs_type, xs_type[1:]):\n            type_check.expect(\n                p.shape[0] >= n.shape[0],\n                p.shape[1:] == n.shape[1:],\n            )\n\n    def forward(self, xs):\n        if len(xs) == 0:\n            return ()\n        return _transpose(xs, len(xs[0]))\n\n    def backward(self, xs, gs):\n        return _transpose(gs, len(xs))\n\n\ndef transpose_sequence(xs):\n    \"\"\"Transpose a list of Variables.\n\n    This function transposes a list of :class:`~chainer.Variable` s and returns\n    a list of :class:`Variable` s.\n    For exampe a user gives ``[(0, 1, 2, 3), (4, 5), (6)]``, the function\n    returns ``[(0, 4, 6), (1, 5), (2), (3)]``.\n    Note that a given list needs to be sorted by each length of\n    :class:`~chainer.Variable`.\n\n    Args:\n        xs (list of ~chainer.Variable): Variables to transpose.\n\n    Returns:\n        tuple or Variable: Transposed list.\n    \"\"\"\n    ys = TransposeSequence()(*xs)\n    if not isinstance(ys, tuple):\n        ys = (ys,)\n    return ys\n", "path": "chainer/functions/array/transpose_sequence.py"}], "after_files": [{"content": "import numpy\n\nfrom chainer import cuda\nfrom chainer import function\nfrom chainer.utils import type_check\n\n\ndef _transpose(xs, length):\n    if length == 0:\n        return ()\n\n    xp = cuda.get_array_module(*xs)\n    lengths = numpy.empty(length, dtype='i')\n    end = length\n    for i, x in enumerate(xs):\n        lengths[len(x):end] = i\n        end = len(x)\n    lengths[0:end] = len(xs)\n\n    if xp is numpy:\n        dtype = xs[0].dtype\n        unit = xs[0].shape[1:]\n\n        outs = tuple([xp.empty((l,) + unit, dtype=dtype) for l in lengths])\n        for i, x in enumerate(xs):\n            for p, xi in enumerate(x):\n                outs[p][i] = xi\n\n    else:\n        offsets1 = numpy.empty(len(xs) + 1, dtype='i')\n        offsets1[0] = 0\n        numpy.cumsum([len(x) for x in xs], out=offsets1[1:])\n\n        offsets2 = numpy.empty(length + 1, dtype='i')\n        offsets2[0] = 0\n        numpy.cumsum(lengths, dtype='i', out=offsets2[1:])\n\n        x = xp.concatenate(xs, axis=0)\n        o = xp.empty_like(x)\n        unit = xs[0].size // len(xs[0])\n        size = length * len(xs) * unit\n        cuda.elementwise(\n            'int32 len, int32 unit, raw int32 off1, raw int32 off2, raw T vs',\n            'raw T hs',\n            '''\n            int ind = i / unit;\n            int off = i - ind * unit;\n            int y = ind / len;\n            int x = ind - y * len;\n            if (off2[x] + y < off2[x + 1]) {\n              hs[(off2[x] + y) * unit + off] = vs[(off1[y] + x) * unit + off];\n            }\n            ''',\n            'transpose_sequence'\n        )(length, unit, cuda.to_gpu(offsets1), cuda.to_gpu(offsets2), x, o,\n          size=size)\n        outs = tuple(xp.split(o, offsets2[1:-1]))\n\n    return outs\n\n\nclass TransposeSequence(function.Function):\n\n    \"\"\"Function that transposes a list of Variables.\"\"\"\n\n    def check_type_forward(self, xs_type):\n        for p, n in zip(xs_type, xs_type[1:]):\n            type_check.expect(\n                p.shape[0] >= n.shape[0],\n                p.shape[1:] == n.shape[1:],\n            )\n\n    def forward(self, xs):\n        if len(xs) == 0:\n            return ()\n        return _transpose(xs, len(xs[0]))\n\n    def backward(self, xs, gs):\n        return _transpose(gs, len(xs))\n\n\ndef transpose_sequence(xs):\n    \"\"\"Transpose a list of Variables.\n\n    This function transposes a list of :class:`~chainer.Variable` s and returns\n    a list of :class:`Variable` s.\n    For exampe a user gives ``[(0, 1, 2, 3), (4, 5), (6)]``, the function\n    returns ``[(0, 4, 6), (1, 5), (2), (3)]``.\n    Note that a given list needs to be sorted by each length of\n    :class:`~chainer.Variable`.\n\n    Args:\n        xs (list of ~chainer.Variable): Variables to transpose.\n\n    Returns:\n        tuple or Variable: Transposed list.\n    \"\"\"\n    ys = TransposeSequence()(*xs)\n    if not isinstance(ys, tuple):\n        ys = (ys,)\n    return ys\n", "path": "chainer/functions/array/transpose_sequence.py"}]}