qfeval_functions.functions.mulmean

mulmean(x, y, dim=(), keepdim=False, *, _ddof=0)[source]

Compute the mean of element-wise product in a memory-efficient way.

This function calculates the mean of the element-wise product of two tensors (x * y).mean(dim) without creating the intermediate product tensor in memory. This is particularly useful when working with large tensors where memory efficiency is critical, or when broadcasting between tensors would result in a very large intermediate tensor.

The function is mathematically equivalent to (x * y).mean(dim) but uses a more memory-efficient implementation that avoids materializing the full product tensor.

Parameters:

x (Tensor) – The first input tensor.
y (Tensor) – The second input tensor. Must be broadcastable with x.
dim (Union[int, Tuple[int, ...]]) – The dimension(s) along which to compute the mean. If not specified (default is empty tuple), the mean is computed over all dimensions.
keepdim (bool) – Whether the output tensor has dim retained or not. Default is False.
_ddof (int) – Delta degrees of freedom for internal calculations. The divisor used is N - _ddof, where N is the number of elements. Default is 0. This is an internal parameter.

Returns:

The mean of the element-wise product. The shape depends on the input dimensions, dim, and keepdim parameters.

Return type:

Tensor

Example

>>> # Simple element-wise product mean
>>> x = torch.tensor([1.0, 2.0, 3.0, 4.0])
>>> y = torch.tensor([2.0, 3.0, 4.0, 5.0])
>>> QF.mulmean(x, y)
tensor(10.)

>>> # Equivalent to (x * y).mean()
>>> torch.allclose(QF.mulmean(x, y), (x * y).mean())
True

>>> # 2D tensors with specific dimension
>>> x = torch.tensor([[1.0, 2.0], [3.0, 4.0]])
>>> y = torch.tensor([[2.0, 1.0], [1.0, 2.0]])
>>> QF.mulmean(x, y, dim=1)
tensor([2.0000, 5.5000])

>>> # Broadcasting example
>>> x = torch.randn(1000, 1)
>>> y = torch.randn(1, 1000)
>>> # Memory-efficient: doesn't create 1000x1000 intermediate tensor
>>> result = QF.mulmean(x, y)

>>> # With keepdim
>>> x = torch.tensor([[[1.0, 2.0]], [[3.0, 4.0]]])
>>> y = torch.tensor([[[2.0, 1.0]], [[1.0, 2.0]]])
>>> QF.mulmean(x, y, dim=(1, 2), keepdim=True)
tensor([[[2.0000]],

        [[5.5000]]])