prompt: We are currently solving the following issue within our repository. Here is the issue text:
  --- BEGIN ISSUE ---
  Fix the shape of return value of F.det
  Currently, return value of `det` is `xp.array` whose shape is `(1, )`, not a scalar.
  
  ```
  In [16]: a = chainer.Variable(numpy.random.uniform(-1, 1, (3, 3)).astype(numpy.float32))
  In [17]: chainer.functions.det(a).data
  Out[17]: array([-0.80874199], dtype=float32)
  ```
  
  But the document says the return value should be `chainer.Variable` whose data have the shape `()`.
  
  
  --- 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/math/det.py`
  Content:
  ```
  1 import numpy
  2 
  3 from chainer import cuda
  4 from chainer import function
  5 from chainer.functions.array import reshape
  6 from chainer.functions.math import inv
  7 from chainer.functions.math import matmul
  8 from chainer import utils
  9 from chainer.utils import type_check
  10 
  11 
  12 def _det_gpu(b):
  13     # We do a batched LU decomposition on the GPU to compute
  14     # and compute the determinant by multiplying the diagonal.
  15     # Change the shape of the array to be size=1 minibatch if necessary.
  16     # Also copy the matrix as the elments will be modified in-place.
  17     a = matmul._as_batch_mat(b).copy()
  18     n = a.shape[1]
  19     n_matrices = len(a)
  20     # Pivot array
  21     p = cuda.cupy.zeros((n_matrices, n), dtype='int32')
  22     # Output array
  23     # These arrays hold information on the execution success
  24     # or if the matrix was singular.
  25     info1 = cuda.cupy.zeros(n_matrices, dtype=numpy.intp)
  26     ap = matmul._mat_ptrs(a)
  27     _, lda = matmul._get_ld(a)
  28     cuda.cublas.sgetrfBatched(cuda.Device().cublas_handle, n, ap.data.ptr, lda,
  29                               p.data.ptr, info1.data.ptr, n_matrices)
  30     det = cuda.cupy.prod(a.diagonal(axis1=1, axis2=2), axis=1)
  31     # The determinant is equal to the product of the diagonal entries
  32     # of `a` where the sign of `a` is flipped depending on whether
  33     # the pivot array is equal to its index.
  34     rng = cuda.cupy.arange(1, n + 1, dtype='int32')
  35     parity = cuda.cupy.sum(p != rng, axis=1) % 2
  36     sign = 1. - 2. * parity.astype('float32')
  37     success = cuda.cupy.all(info1 == 0)
  38     return det * sign, success
  39 
  40 
  41 class BatchDet(function.Function):
  42 
  43     @property
  44     def label(self):
  45         return 'det'
  46 
  47     def check_type_forward(self, in_types):
  48         type_check.expect(in_types.size() == 1)
  49         a_type, = in_types
  50         a_type = matmul._convert_type(a_type)
  51         type_check.expect(a_type.dtype.kind == 'f')
  52         # Only a minibatch of 2D array shapes allowed.
  53         type_check.expect(a_type.ndim == 3)
  54         # Matrix inversion only allowed for square matrices
  55         # so assert the last two dimensions are equal.
  56         type_check.expect(a_type.shape[-1] == a_type.shape[-2])
  57 
  58     def forward_cpu(self, x):
  59         self.detx = utils.force_array(numpy.linalg.det(x[0]))
  60         return self.detx,
  61 
  62     def forward_gpu(self, x):
  63         self.detx, success = _det_gpu(x[0])
  64         if not success:
  65             raise ValueError('Singular Matrix')
  66         return self.detx,
  67 
  68     def backward_cpu(self, x, gy):
  69         x, = x
  70         gy, = gy
  71         grad = (gy[:, None, None] * self.detx[:, None, None] *
  72                 numpy.linalg.inv(x.transpose((0, 2, 1))))
  73         return utils.force_array(grad),
  74 
  75     def backward_gpu(self, x, gy):
  76         x, = x
  77         gy, = gy
  78         grad = (gy[:, None, None] * self.detx[:, None, None] *
  79                 inv._inv_gpu(x.transpose((0, 2, 1))))
  80         return utils.force_array(grad),
  81 
  82 
  83 def batch_det(a):
  84     """Computes the determinant of a batch of square matrices.
  85 
  86     Args:
  87         a (Variable): Input array to compute the determinant for.
  88         The first dimension should iterate over each matrix and be
  89         of the batchsize.
  90 
  91     Returns:
  92         ~chainer.Variable: vector of determinants for every matrix
  93         in the batch.
  94 
  95     """
  96     return BatchDet()(a)
  97 
  98 
  99 def det(a):
  100     """Computes the determinant of a single square matrix.
  101 
  102     Args:
  103         a (Variable): Input array to compute the determinant for.
  104 
  105     Returns:
  106         ~chainer.Variable: Scalar determinant of the matrix a.
  107 
  108     """
  109     shape = (1, len(a.data), a.data.shape[1])
  110     batched_a = reshape.Reshape(shape)(a)
  111     batched_det = BatchDet()(batched_a)
  112     return reshape.Reshape((1, ))(batched_det)
  113
  ```
  --- 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/math/det.py b/chainer/functions/math/det.py
  --- a/chainer/functions/math/det.py
  +++ b/chainer/functions/math/det.py
  @@ -109,4 +109,4 @@
       shape = (1, len(a.data), a.data.shape[1])
       batched_a = reshape.Reshape(shape)(a)
       batched_det = BatchDet()(batched_a)
  -    return reshape.Reshape((1, ))(batched_det)
  +    return reshape.Reshape(())(batched_det)
  
verification_info: {"golden_diff": "diff --git a/chainer/functions/math/det.py b/chainer/functions/math/det.py\n--- a/chainer/functions/math/det.py\n+++ b/chainer/functions/math/det.py\n@@ -109,4 +109,4 @@\n     shape = (1, len(a.data), a.data.shape[1])\n     batched_a = reshape.Reshape(shape)(a)\n     batched_det = BatchDet()(batched_a)\n-    return reshape.Reshape((1, ))(batched_det)\n+    return reshape.Reshape(())(batched_det)\n", "issue": "Fix the shape of return value of F.det\nCurrently, return value of `det` is `xp.array` whose shape is `(1, )`, not a scalar.\n\n```\nIn [16]: a = chainer.Variable(numpy.random.uniform(-1, 1, (3, 3)).astype(numpy.float32))\nIn [17]: chainer.functions.det(a).data\nOut[17]: array([-0.80874199], dtype=float32)\n```\n\nBut the document says the return value should be `chainer.Variable` whose data have the shape `()`.\n\n", "before_files": [{"content": "import numpy\n\nfrom chainer import cuda\nfrom chainer import function\nfrom chainer.functions.array import reshape\nfrom chainer.functions.math import inv\nfrom chainer.functions.math import matmul\nfrom chainer import utils\nfrom chainer.utils import type_check\n\n\ndef _det_gpu(b):\n    # We do a batched LU decomposition on the GPU to compute\n    # and compute the determinant by multiplying the diagonal.\n    # Change the shape of the array to be size=1 minibatch if necessary.\n    # Also copy the matrix as the elments will be modified in-place.\n    a = matmul._as_batch_mat(b).copy()\n    n = a.shape[1]\n    n_matrices = len(a)\n    # Pivot array\n    p = cuda.cupy.zeros((n_matrices, n), dtype='int32')\n    # Output array\n    # These arrays hold information on the execution success\n    # or if the matrix was singular.\n    info1 = cuda.cupy.zeros(n_matrices, dtype=numpy.intp)\n    ap = matmul._mat_ptrs(a)\n    _, lda = matmul._get_ld(a)\n    cuda.cublas.sgetrfBatched(cuda.Device().cublas_handle, n, ap.data.ptr, lda,\n                              p.data.ptr, info1.data.ptr, n_matrices)\n    det = cuda.cupy.prod(a.diagonal(axis1=1, axis2=2), axis=1)\n    # The determinant is equal to the product of the diagonal entries\n    # of `a` where the sign of `a` is flipped depending on whether\n    # the pivot array is equal to its index.\n    rng = cuda.cupy.arange(1, n + 1, dtype='int32')\n    parity = cuda.cupy.sum(p != rng, axis=1) % 2\n    sign = 1. - 2. * parity.astype('float32')\n    success = cuda.cupy.all(info1 == 0)\n    return det * sign, success\n\n\nclass BatchDet(function.Function):\n\n    @property\n    def label(self):\n        return 'det'\n\n    def check_type_forward(self, in_types):\n        type_check.expect(in_types.size() == 1)\n        a_type, = in_types\n        a_type = matmul._convert_type(a_type)\n        type_check.expect(a_type.dtype.kind == 'f')\n        # Only a minibatch of 2D array shapes allowed.\n        type_check.expect(a_type.ndim == 3)\n        # Matrix inversion only allowed for square matrices\n        # so assert the last two dimensions are equal.\n        type_check.expect(a_type.shape[-1] == a_type.shape[-2])\n\n    def forward_cpu(self, x):\n        self.detx = utils.force_array(numpy.linalg.det(x[0]))\n        return self.detx,\n\n    def forward_gpu(self, x):\n        self.detx, success = _det_gpu(x[0])\n        if not success:\n            raise ValueError('Singular Matrix')\n        return self.detx,\n\n    def backward_cpu(self, x, gy):\n        x, = x\n        gy, = gy\n        grad = (gy[:, None, None] * self.detx[:, None, None] *\n                numpy.linalg.inv(x.transpose((0, 2, 1))))\n        return utils.force_array(grad),\n\n    def backward_gpu(self, x, gy):\n        x, = x\n        gy, = gy\n        grad = (gy[:, None, None] * self.detx[:, None, None] *\n                inv._inv_gpu(x.transpose((0, 2, 1))))\n        return utils.force_array(grad),\n\n\ndef batch_det(a):\n    \"\"\"Computes the determinant of a batch of square matrices.\n\n    Args:\n        a (Variable): Input array to compute the determinant for.\n        The first dimension should iterate over each matrix and be\n        of the batchsize.\n\n    Returns:\n        ~chainer.Variable: vector of determinants for every matrix\n        in the batch.\n\n    \"\"\"\n    return BatchDet()(a)\n\n\ndef det(a):\n    \"\"\"Computes the determinant of a single square matrix.\n\n    Args:\n        a (Variable): Input array to compute the determinant for.\n\n    Returns:\n        ~chainer.Variable: Scalar determinant of the matrix a.\n\n    \"\"\"\n    shape = (1, len(a.data), a.data.shape[1])\n    batched_a = reshape.Reshape(shape)(a)\n    batched_det = BatchDet()(batched_a)\n    return reshape.Reshape((1, ))(batched_det)\n", "path": "chainer/functions/math/det.py"}], "after_files": [{"content": "import numpy\n\nfrom chainer import cuda\nfrom chainer import function\nfrom chainer.functions.array import reshape\nfrom chainer.functions.math import inv\nfrom chainer.functions.math import matmul\nfrom chainer import utils\nfrom chainer.utils import type_check\n\n\ndef _det_gpu(b):\n    # We do a batched LU decomposition on the GPU to compute\n    # and compute the determinant by multiplying the diagonal.\n    # Change the shape of the array to be size=1 minibatch if necessary.\n    # Also copy the matrix as the elments will be modified in-place.\n    a = matmul._as_batch_mat(b).copy()\n    n = a.shape[1]\n    n_matrices = len(a)\n    # Pivot array\n    p = cuda.cupy.zeros((n_matrices, n), dtype='int32')\n    # Output array\n    # These arrays hold information on the execution success\n    # or if the matrix was singular.\n    info1 = cuda.cupy.zeros(n_matrices, dtype=numpy.intp)\n    ap = matmul._mat_ptrs(a)\n    _, lda = matmul._get_ld(a)\n    cuda.cublas.sgetrfBatched(cuda.Device().cublas_handle, n, ap.data.ptr, lda,\n                              p.data.ptr, info1.data.ptr, n_matrices)\n    det = cuda.cupy.prod(a.diagonal(axis1=1, axis2=2), axis=1)\n    # The determinant is equal to the product of the diagonal entries\n    # of `a` where the sign of `a` is flipped depending on whether\n    # the pivot array is equal to its index.\n    rng = cuda.cupy.arange(1, n + 1, dtype='int32')\n    parity = cuda.cupy.sum(p != rng, axis=1) % 2\n    sign = 1. - 2. * parity.astype('float32')\n    success = cuda.cupy.all(info1 == 0)\n    return det * sign, success\n\n\nclass BatchDet(function.Function):\n\n    @property\n    def label(self):\n        return 'det'\n\n    def check_type_forward(self, in_types):\n        type_check.expect(in_types.size() == 1)\n        a_type, = in_types\n        a_type = matmul._convert_type(a_type)\n        type_check.expect(a_type.dtype.kind == 'f')\n        # Only a minibatch of 2D array shapes allowed.\n        type_check.expect(a_type.ndim == 3)\n        # Matrix inversion only allowed for square matrices\n        # so assert the last two dimensions are equal.\n        type_check.expect(a_type.shape[-1] == a_type.shape[-2])\n\n    def forward_cpu(self, x):\n        self.detx = utils.force_array(numpy.linalg.det(x[0]))\n        return self.detx,\n\n    def forward_gpu(self, x):\n        self.detx, success = _det_gpu(x[0])\n        if not success:\n            raise ValueError('Singular Matrix')\n        return self.detx,\n\n    def backward_cpu(self, x, gy):\n        x, = x\n        gy, = gy\n        grad = (gy[:, None, None] * self.detx[:, None, None] *\n                numpy.linalg.inv(x.transpose((0, 2, 1))))\n        return utils.force_array(grad),\n\n    def backward_gpu(self, x, gy):\n        x, = x\n        gy, = gy\n        grad = (gy[:, None, None] * self.detx[:, None, None] *\n                inv._inv_gpu(x.transpose((0, 2, 1))))\n        return utils.force_array(grad),\n\n\ndef batch_det(a):\n    \"\"\"Computes the determinant of a batch of square matrices.\n\n    Args:\n        a (Variable): Input array to compute the determinant for.\n        The first dimension should iterate over each matrix and be\n        of the batchsize.\n\n    Returns:\n        ~chainer.Variable: vector of determinants for every matrix\n        in the batch.\n\n    \"\"\"\n    return BatchDet()(a)\n\n\ndef det(a):\n    \"\"\"Computes the determinant of a single square matrix.\n\n    Args:\n        a (Variable): Input array to compute the determinant for.\n\n    Returns:\n        ~chainer.Variable: Scalar determinant of the matrix a.\n\n    \"\"\"\n    shape = (1, len(a.data), a.data.shape[1])\n    batched_a = reshape.Reshape(shape)(a)\n    batched_det = BatchDet()(batched_a)\n    return reshape.Reshape(())(batched_det)\n", "path": "chainer/functions/math/det.py"}]}