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()

```

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

{"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"}]}