prompt: You will be provided with a partial code base and an issue statement explaining a problem to resolve.
  <issue>
  ZeroMean for Batch Independent Multioutput GP
  I'm following the Batch Independent Multioutput GP example, but instead of using a constant mean, I would like each dimension to use a zero mean (maybe this is a bad idea?).
  
  ```
  class ZeroMeanIndependentMultitaskGPModel(gpytorch.models.ExactGP):
      def __init__(self, train_x, train_y, likelihood, nx):
          super().__init__(train_x, train_y, likelihood)
          self.n = nx     #output dimension
          #self.mean_module = gpytorch.means.MultitaskMean([gpytorch.means.ZeroMean()]*self.n,
          #                                                num_tasks=self.n)
          #self.mean_module = gpytorch.means.ConstantMean(batch_shape=torch.Size([self.n]))
          self.mean_module = gpytorch.means.ZeroMean()
          self.covar_module = gpytorch.kernels.ScaleKernel(
              gpytorch.kernels.RBFKernel(batch_shape=torch.Size([self.n])),
              batch_shape=torch.Size([self.n])
          )
  
      def forward(self, x):
          mean_x = self.mean_module(x) # is this needed for ZeroMean?
          covar_x = self.covar_module(x)
          return gpytorch.distributions.MultitaskMultivariateNormal.from_batch_mvn(
              gpytorch.distributions.MultivariateNormal(mean_x, covar_x)
          )
  ```
  
  
  When training with this, I get the error `RuntimeError: mean should be a matrix or a batch matrix (batch mode)`. It works as intended with constant mean. As you can see, I've tried a couple different things, but they don't seem to work either. I can't seem to find other people with the same issue online. Is it possible to do this with ZeroMean?
  
  
  </issue>
  <code>
  [start of gpytorch/means/zero_mean.py]
  1 #!/usr/bin/env python3
  2 
  3 import torch
  4 
  5 from .mean import Mean
  6 
  7 
  8 class ZeroMean(Mean):
  9     def forward(self, input):
  10         return torch.zeros(input.shape[:-1], dtype=input.dtype, device=input.device)
  11
  [end of gpytorch/means/zero_mean.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/gpytorch/means/zero_mean.py b/gpytorch/means/zero_mean.py
  --- a/gpytorch/means/zero_mean.py
  +++ b/gpytorch/means/zero_mean.py
  @@ -2,9 +2,18 @@
   
   import torch
   
  +from ..utils.broadcasting import _mul_broadcast_shape
   from .mean import Mean
   
   
   class ZeroMean(Mean):
  +    def __init__(self, batch_shape=torch.Size(), **kwargs):
  +        super(ZeroMean, self).__init__()
  +        self.batch_shape = batch_shape
  +
       def forward(self, input):
  -        return torch.zeros(input.shape[:-1], dtype=input.dtype, device=input.device)
  +        mean = torch.zeros(*self.batch_shape, 1, dtype=input.dtype, device=input.device)
  +        if input.shape[:-2] == self.batch_shape:
  +            return mean.expand(input.shape[:-1])
  +        else:
  +            return mean.expand(_mul_broadcast_shape(input.shape[:-1], mean.shape))
  
verification_info: {"golden_diff": "diff --git a/gpytorch/means/zero_mean.py b/gpytorch/means/zero_mean.py\n--- a/gpytorch/means/zero_mean.py\n+++ b/gpytorch/means/zero_mean.py\n@@ -2,9 +2,18 @@\n \n import torch\n \n+from ..utils.broadcasting import _mul_broadcast_shape\n from .mean import Mean\n \n \n class ZeroMean(Mean):\n+    def __init__(self, batch_shape=torch.Size(), **kwargs):\n+        super(ZeroMean, self).__init__()\n+        self.batch_shape = batch_shape\n+\n     def forward(self, input):\n-        return torch.zeros(input.shape[:-1], dtype=input.dtype, device=input.device)\n+        mean = torch.zeros(*self.batch_shape, 1, dtype=input.dtype, device=input.device)\n+        if input.shape[:-2] == self.batch_shape:\n+            return mean.expand(input.shape[:-1])\n+        else:\n+            return mean.expand(_mul_broadcast_shape(input.shape[:-1], mean.shape))\n", "issue": "ZeroMean for Batch Independent Multioutput GP\nI'm following the Batch Independent Multioutput GP example, but instead of using a constant mean, I would like each dimension to use a zero mean (maybe this is a bad idea?).\r\n\r\n```\r\nclass ZeroMeanIndependentMultitaskGPModel(gpytorch.models.ExactGP):\r\n    def __init__(self, train_x, train_y, likelihood, nx):\r\n        super().__init__(train_x, train_y, likelihood)\r\n        self.n = nx     #output dimension\r\n        #self.mean_module = gpytorch.means.MultitaskMean([gpytorch.means.ZeroMean()]*self.n,\r\n        #                                                num_tasks=self.n)\r\n        #self.mean_module = gpytorch.means.ConstantMean(batch_shape=torch.Size([self.n]))\r\n        self.mean_module = gpytorch.means.ZeroMean()\r\n        self.covar_module = gpytorch.kernels.ScaleKernel(\r\n            gpytorch.kernels.RBFKernel(batch_shape=torch.Size([self.n])),\r\n            batch_shape=torch.Size([self.n])\r\n        )\r\n\r\n    def forward(self, x):\r\n        mean_x = self.mean_module(x) # is this needed for ZeroMean?\r\n        covar_x = self.covar_module(x)\r\n        return gpytorch.distributions.MultitaskMultivariateNormal.from_batch_mvn(\r\n            gpytorch.distributions.MultivariateNormal(mean_x, covar_x)\r\n        )\r\n```\r\n\r\n\r\nWhen training with this, I get the error `RuntimeError: mean should be a matrix or a batch matrix (batch mode)`. It works as intended with constant mean. As you can see, I've tried a couple different things, but they don't seem to work either. I can't seem to find other people with the same issue online. Is it possible to do this with ZeroMean?\r\n\n", "before_files": [{"content": "#!/usr/bin/env python3\n\nimport torch\n\nfrom .mean import Mean\n\n\nclass ZeroMean(Mean):\n    def forward(self, input):\n        return torch.zeros(input.shape[:-1], dtype=input.dtype, device=input.device)\n", "path": "gpytorch/means/zero_mean.py"}]}