def root_sum_of_squares(data: torch.Tensor,
dim: Union[int, str] = "coil") -> torch.Tensor:
"""
Compute the root sum of squares (RSS) transform along a given (perhaps named) dimension of the input tensor.
$$x_{\textrm{rss}} = \sqrt{\sum_{i \in \textrm{coil}} |x_i|^2}$$
Parameters
----------
data : torch.Tensor
Input tensor
dim : Union[int, str]
Coil dimension.
Returns
-------
torch.Tensor : RSS of the input tensor.
"""
assert_named(data)
if "complex" in data.names:
assert_complex(data, complex_last=True)
return torch.sqrt((data**2).sum("complex").sum(dim))
else:
return torch.sqrt((data**2).sum(dim))
def modulus_if_complex(data: torch.Tensor) -> torch.Tensor:
"""
Compute modulus if complex-valued.
Parameters
----------
data : torch.Tensor
Returns
-------
torch.Tensor
"""
# TODO: This can be merged with modulus if the tensor is real.
assert_named(data)
if "complex" in data.names:
return modulus(data)
return data
def safe_divide(a: torch.Tensor, b: torch.Tensor) -> torch.Tensor:
"""
Divide a and b safely, set the output to zero where the divisor b is zero.
Parameters
----------
a : torch.Tensor
b : torch.Tensor
Returns
-------
torch.Tensor: the division.
"""
assert_named(a)
assert_named(b)
b = b.align_as(a)
data = torch.where(
b.rename(None) == 0,
torch.tensor([0.0], dtype=a.dtype).to(a.device),
(a / b).rename(None),
).refine_names(*a.names)
return data
