prompt: You will be provided with a partial code base and an issue statement explaining a problem to resolve.
  <issue>
  Shape of output value of `concat` is list in GPU
  `cuda.empty([1])` makes a `GPUArray` with `list` shape. It causes a type invalid error.
  
  https://github.com/pfnet/chainer/blob/master/chainer/functions/concat.py#L69
  
  
  </issue>
  <code>
  [start of chainer/functions/concat.py]
  1 import numpy
  2 
  3 from chainer import cuda
  4 from chainer import function
  5 from chainer.utils import type_check
  6 
  7 _args = 'const float* x, float* y, int cdimx, int cdimy, int rdim, int coffset'
  8 _preamble = '''
  9 #define COPY(statement) \
  10     int l   = i / (rdim * cdimx);  \
  11     int c   = i / rdim % cdimx + coffset;  \
  12     int r   = i % rdim;  \
  13     int idx = r + rdim * (c + cdimy * l);  \
  14     statement;
  15 '''
  16 
  17 
  18 class Concat(function.Function):
  19 
  20     """Concatenate multiple tensors towards specified axis."""
  21 
  22     # concat along the channel dimension by default
  23     def __init__(self, axis=1):
  24         self.axis = axis
  25 
  26     def check_type_forward(self, in_types):
  27         type_check.expect(in_types.size() > 0)
  28         type_check.expect(in_types[0].ndim >
  29                           type_check.Variable(self.axis, 'axis'))
  30 
  31         ndim = in_types[0].ndim.eval()
  32         for i in range(1, in_types.size().eval()):
  33             type_check.expect(
  34                 in_types[0].dtype == in_types[i].dtype,
  35                 in_types[0].ndim == in_types[i].ndim,
  36             )
  37             for d in range(0, ndim):
  38                 if d == self.axis:
  39                     continue
  40                 type_check.expect(in_types[0].shape[d] == in_types[i].shape[d])
  41 
  42     def check_type_backward(self, in_types, out_types):
  43         type_check.expect(
  44             in_types.size() > 0,
  45             out_types.size() == 1,
  46         )
  47         y_type, = out_types
  48 
  49         type_check.expect(y_type.dtype == in_types[0].dtype)
  50         ndim = in_types[0].ndim.eval()
  51         concat_size = sum(typ.shape[self.axis] for typ in in_types)
  52         type_check.expect(concat_size == y_type.shape[self.axis])
  53 
  54         for d in range(0, ndim):
  55             if d == self.axis:
  56                 continue
  57             type_check.expect(y_type.shape[d] == in_types[0].shape[d])
  58 
  59     def forward_cpu(self, xs):
  60         return numpy.concatenate(xs, axis=self.axis),
  61 
  62     def forward_gpu(self, xs):
  63         # TODO(beam2d): Unify the process into a single kernel.
  64         shape = list(xs[0].shape)
  65         for x in xs[1:]:
  66             shape[self.axis] += x.shape[self.axis]
  67         self.shape = shape
  68 
  69         y = cuda.empty(shape, dtype=xs[0].dtype)
  70         self.cdimy = y.shape[self.axis]
  71         self.rdim = numpy.prod(shape[self.axis + 1:], dtype=int)
  72 
  73         coffset = 0
  74         kernel = cuda.elementwise(
  75             _args, 'COPY(y[idx] = x[i])', 'concat_fwd', preamble=_preamble)
  76         for x in xs:
  77             cdimx = x.shape[self.axis]
  78             kernel(x, y, cdimx, self.cdimy, self.rdim, coffset)
  79             coffset += cdimx
  80 
  81         return y,
  82 
  83     def backward_cpu(self, xs, gy):
  84         sizes = numpy.array([x.shape[self.axis] for x in xs[:-1]]).cumsum()
  85         return numpy.split(gy[0], sizes, axis=self.axis)
  86 
  87     def backward_gpu(self, xs, gy):
  88         gxs = tuple(cuda.empty_like(x) for x in xs)
  89 
  90         coffset = 0
  91         kernel = cuda.elementwise(
  92             _args, 'COPY(x[i] = y[idx])', 'concat_bwd', preamble=_preamble)
  93         for gx in gxs:
  94             cdimx = gx.shape[self.axis]
  95             kernel(gx, gy[0], cdimx, self.cdimy, self.rdim, coffset)
  96             coffset += cdimx
  97 
  98         return gxs
  99 
  100 
  101 def concat(xs, axis=1):
  102     """Concatenates given variables along an axis.
  103 
  104     Args:
  105         xs (tuple of Variables): Variables to be concatenated.
  106         axis (int): Axis that the input arrays are concatenated along.
  107 
  108     Returns:
  109         ~chainer.Variable: Output variable.
  110 
  111     """
  112     return Concat(axis=axis)(*xs)
  113
  [end of chainer/functions/concat.py]
  </code>
  
  I need you to solve this issue by generating a single patch file that I can apply directly to this repository using git apply. Please respond with a single patch file in the following format.
  <patch>
  diff --git a/file.py b/file.py
  --- a/file.py
  +++ b/file.py
  @@ -1,27 +1,35 @@
   def euclidean(a, b):
  -    while b:
  -        a, b = b, a % b
  -    return a
  +    if b == 0:
  +        return a
  +    return euclidean(b, a % b)
   
   
   def bresenham(x0, y0, x1, y1):
       points = []
       dx = abs(x1 - x0)
       dy = abs(y1 - y0)
  -    sx = 1 if x0 < x1 else -1
  -    sy = 1 if y0 < y1 else -1
  -    err = dx - dy
  +    x, y = x0, y0
  +    sx = -1 if x0 > x1 else 1
  +    sy = -1 if y0 > y1 else 1
   
  -    while True:
  -        points.append((x0, y0))
  -        if x0 == x1 and y0 == y1:
  -            break
  -        e2 = 2 * err
  -        if e2 > -dy:
  -            err -= dy
  -            x0 += sx
  -        if e2 < dx:
  -            err += dx
  -            y0 += sy
  +    if dx > dy:
  +        err = dx / 2.0
  +        while x != x1:
  +            points.append((x, y))
  +            err -= dy
  +            if err < 0:
  +                y += sy
  +                err += dx
  +            x += sx
  +    else:
  +        err = dy / 2.0
  +        while y != y1:
  +            points.append((x, y))
  +            err -= dx
  +            if err < 0:
  +                x += sx
  +                err += dy
  +            y += sy
  +
  +    points.append((x, y))
       return points
  
  </patch>
golden_diff: diff --git a/chainer/functions/concat.py b/chainer/functions/concat.py
  --- a/chainer/functions/concat.py
  +++ b/chainer/functions/concat.py
  @@ -64,6 +64,7 @@
           shape = list(xs[0].shape)
           for x in xs[1:]:
               shape[self.axis] += x.shape[self.axis]
  +        shape = tuple(shape)
           self.shape = shape
   
           y = cuda.empty(shape, dtype=xs[0].dtype)
  
verification_info: {"golden_diff": "diff --git a/chainer/functions/concat.py b/chainer/functions/concat.py\n--- a/chainer/functions/concat.py\n+++ b/chainer/functions/concat.py\n@@ -64,6 +64,7 @@\n         shape = list(xs[0].shape)\n         for x in xs[1:]:\n             shape[self.axis] += x.shape[self.axis]\n+        shape = tuple(shape)\n         self.shape = shape\n \n         y = cuda.empty(shape, dtype=xs[0].dtype)\n", "issue": "Shape of output value of `concat` is list in GPU\n`cuda.empty([1])` makes a `GPUArray` with `list` shape. It causes a type invalid error.\n\nhttps://github.com/pfnet/chainer/blob/master/chainer/functions/concat.py#L69\n\n", "before_files": [{"content": "import numpy\n\nfrom chainer import cuda\nfrom chainer import function\nfrom chainer.utils import type_check\n\n_args = 'const float* x, float* y, int cdimx, int cdimy, int rdim, int coffset'\n_preamble = '''\n#define COPY(statement) \\\n    int l   = i / (rdim * cdimx);  \\\n    int c   = i / rdim % cdimx + coffset;  \\\n    int r   = i % rdim;  \\\n    int idx = r + rdim * (c + cdimy * l);  \\\n    statement;\n'''\n\n\nclass Concat(function.Function):\n\n    \"\"\"Concatenate multiple tensors towards specified axis.\"\"\"\n\n    # concat along the channel dimension by default\n    def __init__(self, axis=1):\n        self.axis = axis\n\n    def check_type_forward(self, in_types):\n        type_check.expect(in_types.size() > 0)\n        type_check.expect(in_types[0].ndim >\n                          type_check.Variable(self.axis, 'axis'))\n\n        ndim = in_types[0].ndim.eval()\n        for i in range(1, in_types.size().eval()):\n            type_check.expect(\n                in_types[0].dtype == in_types[i].dtype,\n                in_types[0].ndim == in_types[i].ndim,\n            )\n            for d in range(0, ndim):\n                if d == self.axis:\n                    continue\n                type_check.expect(in_types[0].shape[d] == in_types[i].shape[d])\n\n    def check_type_backward(self, in_types, out_types):\n        type_check.expect(\n            in_types.size() > 0,\n            out_types.size() == 1,\n        )\n        y_type, = out_types\n\n        type_check.expect(y_type.dtype == in_types[0].dtype)\n        ndim = in_types[0].ndim.eval()\n        concat_size = sum(typ.shape[self.axis] for typ in in_types)\n        type_check.expect(concat_size == y_type.shape[self.axis])\n\n        for d in range(0, ndim):\n            if d == self.axis:\n                continue\n            type_check.expect(y_type.shape[d] == in_types[0].shape[d])\n\n    def forward_cpu(self, xs):\n        return numpy.concatenate(xs, axis=self.axis),\n\n    def forward_gpu(self, xs):\n        # TODO(beam2d): Unify the process into a single kernel.\n        shape = list(xs[0].shape)\n        for x in xs[1:]:\n            shape[self.axis] += x.shape[self.axis]\n        self.shape = shape\n\n        y = cuda.empty(shape, dtype=xs[0].dtype)\n        self.cdimy = y.shape[self.axis]\n        self.rdim = numpy.prod(shape[self.axis + 1:], dtype=int)\n\n        coffset = 0\n        kernel = cuda.elementwise(\n            _args, 'COPY(y[idx] = x[i])', 'concat_fwd', preamble=_preamble)\n        for x in xs:\n            cdimx = x.shape[self.axis]\n            kernel(x, y, cdimx, self.cdimy, self.rdim, coffset)\n            coffset += cdimx\n\n        return y,\n\n    def backward_cpu(self, xs, gy):\n        sizes = numpy.array([x.shape[self.axis] for x in xs[:-1]]).cumsum()\n        return numpy.split(gy[0], sizes, axis=self.axis)\n\n    def backward_gpu(self, xs, gy):\n        gxs = tuple(cuda.empty_like(x) for x in xs)\n\n        coffset = 0\n        kernel = cuda.elementwise(\n            _args, 'COPY(x[i] = y[idx])', 'concat_bwd', preamble=_preamble)\n        for gx in gxs:\n            cdimx = gx.shape[self.axis]\n            kernel(gx, gy[0], cdimx, self.cdimy, self.rdim, coffset)\n            coffset += cdimx\n\n        return gxs\n\n\ndef concat(xs, axis=1):\n    \"\"\"Concatenates given variables along an axis.\n\n    Args:\n        xs (tuple of Variables): Variables to be concatenated.\n        axis (int): Axis that the input arrays are concatenated along.\n\n    Returns:\n        ~chainer.Variable: Output variable.\n\n    \"\"\"\n    return Concat(axis=axis)(*xs)\n", "path": "chainer/functions/concat.py"}]}