def scatter_std(src, index, dim=-1, out=None, dim_size=None, unbiased=True):
r"""
|
.. image:: https://raw.githubusercontent.com/rusty1s/pytsd/
master/docs/source/_figures/std.svg?sanitize=true
:align: center
:width: 400px
|
Computes the standard-deviation from all values from the :attr:`src` tensor
into :attr:`out` at the indices specified in the :attr:`index` tensor along
a given axis :attr:`dim` (`cf.` :meth:`~tsd.scatter_add`).
For one-dimensional tensors, the operation computes
.. math::
\mathrm{out}_i = \sqrt{\frac{\sum_j {\left( x_j - \overline{x}_i
\right)}^2}{N_i - 1}}
where :math:`\sum_j` is over :math:`j` such that
:math:`\mathrm{index}_j = i`. :math:`N_i` and :math:`\overline{x}_i`
indicate the number of indices referencing :math:`i` and their mean value,
respectively.
Args:
src (Tensor): The source tensor.
index (LongTensor): The indices of elements to scatter.
dim (int, optional): The axis along which to index.
(default: :obj:`-1`)
out (Tensor, optional): The destination tensor. (default: :obj:`None`)
dim_size (int, optional): If :attr:`out` is not given, automatically
create output with size :attr:`dim_size` at dimension :attr:`dim`.
If :attr:`dim_size` is not given, a minimal sized output tensor is
returned. (default: :obj:`None`)
unbiased (bool, optional): If set to :obj:`False`, then the standard-
deviation will be calculated via the biased estimator.
(default: :obj:`True`)
:rtype: :class:`Tensor`
"""
src, out, index, dim = gen(src, index, dim, out, dim_size, fill_value=0)
tmp = None if out is None else out.clone().fill_(0)
tmp = scatter_add(src, index, dim, tmp, dim_size)
count = None if out is None else out.clone().fill_(0)
count = scatter_add(torch.ones_like(src), index, dim, count, dim_size)
mean = tmp / count.clamp(min=1)
var = (src - mean.gather(dim, index))
var = var * var
out = scatter_add(var, index, dim, out, dim_size)
out = out / (count - 1 if unbiased else count).clamp(min=1)
out = torch.sqrt(out)
return out
def scatter_div(src, index, dim=-1, out=None, dim_size=None, fill_value=1):
r"""
|
.. image:: https://raw.githubusercontent.com/rusty1s/pytsd/
master/docs/source/_figures/div.svg?sanitize=true
:align: center
:width: 400px
|
Divides all values from the :attr:`src` tensor into :attr:`out` at the
indices specified in the :attr:`index` tensor along a given axis
:attr:`dim`.If multiple indices reference the same location, their
**contributions divide** (`cf.` :meth:`~tsd.scatter_add`).
For one-dimensional tensors, the operation computes
.. math::
\mathrm{out}_i = \mathrm{out}_i \cdot \prod_j
\frac{1}{\mathrm{src}_j}
where :math:`\prod_j` is over :math:`j` such that
:math:`\mathrm{index}_j = i`.
Args:
src (Tensor): The source tensor.
index (LongTensor): The indices of elements to scatter.
dim (int, optional): The axis along which to index.
(default: :obj:`-1`)
out (Tensor, optional): The destination tensor. (default: :obj:`None`)
dim_size (int, optional): If :attr:`out` is not given, automatically
create output with size :attr:`dim_size` at dimension :attr:`dim`.
If :attr:`dim_size` is not given, a minimal sized output tensor is
returned. (default: :obj:`None`)
fill_value (int, optional): If :attr:`out` is not given, automatically
fill output tensor with :attr:`fill_value`. (default: :obj:`1`)
:rtype: :class:`Tensor`
.. testsetup::
import torch
.. testcode::
from tsd import scatter_div
src = torch.Tensor([[2, 1, 1, 4, 2], [1, 2, 1, 2, 4]]).float()
index = torch.tensor([[4, 5, 4, 2, 3], [0, 0, 2, 2, 1]])
out = src.new_ones((2, 6))
out = scatter_div(src, index, out=out)
print(out)
.. testoutput::
tensor([[1.0000, 1.0000, 0.2500, 0.5000, 0.5000, 1.0000],
[0.5000, 0.2500, 0.5000, 1.0000, 1.0000, 1.0000]])
"""
src, out, index, dim = gen(src, index, dim, out, dim_size, fill_value)
if src.size(dim) == 0: # pragma: no cover
return out
return ScatterDiv.apply(out, src, index, dim)
def scatter_min(src, index, dim=-1, out=None, dim_size=None, fill_value=None):
r"""
|
.. image:: https://raw.githubusercontent.com/rusty1s/pytsd/
master/docs/source/_figures/min.svg?sanitize=true
:align: center
:width: 400px
|
Minimizes all values from the :attr:`src` tensor into :attr:`out` at the
indices specified in the :attr:`index` tensor along a given axis
:attr:`dim`.If multiple indices reference the same location, their
**contributions minimize** (`cf.` :meth:`~tsd.scatter_add`).
The second return tensor contains index location in :attr:`src` of each
minimum value (known as argmin).
For one-dimensional tensors, the operation computes
.. math::
\mathrm{out}_i = \min(\mathrm{out}_i, \min_j(\mathrm{src}_j))
where :math:`\min_j` is over :math:`j` such that
:math:`\mathrm{index}_j = i`.
Args:
src (Tensor): The source tensor.
index (LongTensor): The indices of elements to scatter.
dim (int, optional): The axis along which to index.
(default: :obj:`-1`)
out (Tensor, optional): The destination tensor. (default: :obj:`None`)
dim_size (int, optional): If :attr:`out` is not given, automatically
create output with size :attr:`dim_size` at dimension :attr:`dim`.
If :attr:`dim_size` is not given, a minimal sized output tensor is
returned. (default: :obj:`None`)
fill_value (int, optional): If :attr:`out` is not given, automatically
fill output tensor with :attr:`fill_value`. (default: :obj:`None`)
fill_value (int, optional): If :attr:`out` is not given, automatically
fill output tensor with :attr:`fill_value`. If set to :obj:`None`,
the output tensor is filled with the greatest possible value of
:obj:`src.dtype`. (default: :obj:`None`)
:rtype: (:class:`Tensor`, :class:`LongTensor`)
.. testsetup::
import torch
.. testcode::
from tsd import scatter_min
src = torch.Tensor([[-2, 0, -1, -4, -3], [0, -2, -1, -3, -4]])
index = torch.tensor([[ 4, 5, 4, 2, 3], [0, 0, 2, 2, 1]])
out = src.new_zeros((2, 6))
out, argmin = scatter_min(src, index, out=out)
print(out)
print(argmin)
.. testoutput::
tensor([[ 0., 0., -4., -3., -2., 0.],
[-2., -4., -3., 0., 0., 0.]])
tensor([[-1, -1, 3, 4, 0, 1],
[ 1, 4, 3, -1, -1, -1]])
"""
if fill_value is None:
op = torch.finfo if torch.is_floating_point(src) else torch.iinfo
fill_value = op(src.dtype).max
src, out, index, dim = gen(src, index, dim, out, dim_size, fill_value)
if src.size(dim) == 0: # pragma: no cover
return out, index.new_full(out.size(), -1)
return ScatterMin.apply(out, src, index, dim)
def scatter_add(src, index, dim=-1, out=None, dim_size=None, fill_value=0):
r"""
|
.. image:: https://raw.githubusercontent.com/rusty1s/pytorch_scatter/
master/docs/source/_figures/add.svg?sanitize=true
:align: center
:width: 400px
|
Sums all values from the :attr:`src` tensor into :attr:`out` at the indices
specified in the :attr:`index` tensor along a given axis :attr:`dim`. For
each value in :attr:`src`, its output index is specified by its index in
:attr:`input` for dimensions outside of :attr:`dim` and by the
corresponding value in :attr:`index` for dimension :attr:`dim`. If
multiple indices reference the same location, their **contributions add**.
Formally, if :attr:`src` and :attr:`index` are n-dimensional tensors with
size :math:`(x_0, ..., x_{i-1}, x_i, x_{i+1}, ..., x_{n-1})` and
:attr:`dim` = `i`, then :attr:`out` must be an n-dimensional tensor with
size :math:`(x_0, ..., x_{i-1}, y, x_{i+1}, ..., x_{n-1})`. Moreover, the
values of :attr:`index` must be between `0` and `out.size(dim) - 1`.
Both :attr:`src` and :attr:`index` are broadcasted in case their dimensions
do not match.
For one-dimensional tensors, the operation computes
.. math::
\mathrm{out}_i = \mathrm{out}_i + \sum_j \mathrm{src}_j
where :math:`\sum_j` is over :math:`j` such that
:math:`\mathrm{index}_j = i`.
Args:
src (Tensor): The source tensor.
index (LongTensor): The indices of elements to scatter.
dim (int, optional): The axis along which to index.
(default: :obj:`-1`)
out (Tensor, optional): The destination tensor. (default: :obj:`None`)
dim_size (int, optional): If :attr:`out` is not given, automatically
create output with size :attr:`dim_size` at dimension :attr:`dim`.
If :attr:`dim_size` is not given, a minimal sized output tensor is
returned. (default: :obj:`None`)
fill_value (int, optional): If :attr:`out` is not given, automatically
fill output tensor with :attr:`fill_value`. (default: :obj:`0`)
:rtype: :class:`Tensor`
.. testsetup::
import torch
.. testcode::
from torch_scatter import scatter_add
src = torch.Tensor([[2, 0, 1, 4, 3], [0, 2, 1, 3, 4]])
index = torch.tensor([[4, 5, 4, 2, 3], [0, 0, 2, 2, 1]])
out = src.new_zeros((2, 6))
out = scatter_add(src, index, out=out)
print(out)
.. testoutput::
tensor([[0., 0., 4., 3., 3., 0.],
[2., 4., 4., 0., 0., 0.]])
"""
src, out, index, dim = gen(src, index, dim, out, dim_size, fill_value)
return out.scatter_add_(dim, index, src)