# The Tensor classes are added to this module by python_tensor.cpp
from typing import Optional, Tuple, List, Union

import torch
from torch._C import _add_docstr, _sparse  # type: ignore[attr-defined]
from torch import Tensor

# A workaround to support both TorchScript and MyPy:
from typing import TYPE_CHECKING
if TYPE_CHECKING:
    from torch.types import _dtype as DType
    DimOrDims = Optional[Union[int, Tuple[int], List[int]]]
else:
    # The JIT doesn't understand Union, nor torch.dtype here
    DType = int
    DimOrDims = Optional[Tuple[int]]


__all__ = [
    'addmm',
    'check_sparse_tensor_invariants',
    'mm',
    'sum',
    'softmax',
    'log_softmax',
]


addmm = _add_docstr(_sparse._sparse_addmm, r"""
sparse.addmm(mat, mat1, mat2, *, beta=1., alpha=1.) -> Tensor

This function does exact same thing as :func:`torch.addmm` in the forward,
except that it supports backward for sparse COO matrix :attr:`mat1`.
When :attr:`mat1` is a COO tensor it must have `sparse_dim = 2`.
When inputs are COO tensors, this function also supports backward for both inputs.

Supports both CSR and COO storage formats.

.. note::
    This function doesn't support computing derivaties with respect to CSR matrices.

Args:
    mat (Tensor): a dense matrix to be added
    mat1 (Tensor): a sparse matrix to be multiplied
    mat2 (Tensor): a dense matrix to be multiplied
    beta (Number, optional): multiplier for :attr:`mat` (:math:`\beta`)
    alpha (Number, optional): multiplier for :math:`mat1 @ mat2` (:math:`\alpha`)
""")


mm = _add_docstr(_sparse._sparse_mm, r"""
    Performs a matrix multiplication of the sparse matrix :attr:`mat1`
    and the (sparse or strided) matrix :attr:`mat2`. Similar to :func:`torch.mm`, if :attr:`mat1` is a
    :math:`(n \times m)` tensor, :attr:`mat2` is a :math:`(m \times p)` tensor, out will be a
    :math:`(n \times p)` tensor.
    When :attr:`mat1` is a COO tensor it must have `sparse_dim = 2`.
    When inputs are COO tensors, this function also supports backward for both inputs.

    Supports both CSR and COO storage formats.

.. note::
    This function doesn't support computing derivaties with respect to CSR matrices.

    This function also additionally accepts an optional :attr:`reduce` argument that allows
    specification of an optional reduction operation, mathematically performs the following operation:

.. math::

    z_{ij} = \bigoplus_{k = 0}^{K - 1} x_{ik} y_{kj}

where :math:`\bigoplus` defines the reduce operator. :attr:`reduce` is implemented only for
CSR storage format on CPU device.

Args:
    mat1 (Tensor): the first sparse matrix to be multiplied
    mat2 (Tensor): the second matrix to be multiplied, which could be sparse or dense
    reduce (str, optional): the reduction operation to apply for non-unique indices
        (:obj:`"sum"`, :obj:`"mean"`, :obj:`"amax"`, :obj:`"amin"`). Default :obj:`"sum"`.

Shape:
    The format of the output tensor of this function follows:
    - sparse x sparse -> sparse
    - sparse x dense -> dense

Example::

    >>> a = torch.tensor([[1., 0, 2], [0, 3, 0]]).to_sparse().requires_grad_()
    >>> a
    tensor(indices=tensor([[0, 0, 1],
                           [0, 2, 1]]),
           values=tensor([1., 2., 3.]),
           size=(2, 3), nnz=3, layout=torch.sparse_coo, requires_grad=True)
    >>> b = torch.tensor([[0, 1.], [2, 0], [0, 0]], requires_grad=True)
    >>> b
    tensor([[0., 1.],
            [2., 0.],
            [0., 0.]], requires_grad=True)
    >>> y = torch.sparse.mm(a, b)
    >>> y
    tensor([[0., 1.],
            [6., 0.]], grad_fn=<SparseAddmmBackward0>)
    >>> y.sum().backward()
    >>> a.grad
    tensor(indices=tensor([[0, 0, 1],
                           [0, 2, 1]]),
           values=tensor([1., 0., 2.]),
           size=(2, 3), nnz=3, layout=torch.sparse_coo)
    >>> c = a.detach().to_sparse_csr()
    >>> c
    tensor(crow_indices=tensor([0, 2, 3]),
           col_indices=tensor([0, 2, 1]),
           values=tensor([1., 2., 3.]), size=(2, 3), nnz=3,
           layout=torch.sparse_csr)
    >>> y1 = torch.sparse.mm(c, b, 'sum')
    >>> y1
    tensor([[0., 1.],
            [6., 0.]], grad_fn=<SparseMmReduceImplBackward0>)
    >>> y2 = torch.sparse.mm(c, b, 'max')
    >>> y2
    tensor([[0., 1.],
            [6., 0.]], grad_fn=<SparseMmReduceImplBackward0>)
""")


sampled_addmm = _add_docstr(_sparse.sparse_sampled_addmm, r"""
sparse.sampled_addmm(input, mat1, mat2, *, beta=1., alpha=1., out=None) -> Tensor

Performs a matrix multiplication of the dense matrices :attr:`mat1` and :attr:`mat2` at the locations
specified by the sparsity pattern of :attr:`input`. The matrix :attr:`input` is added to the final result.

Mathematically this performs the following operation:

.. math::

    \text{out} = \alpha\ (\text{mat1} \mathbin{@} \text{mat2})*\text{spy}(\text{input}) + \beta\ \text{input}

where :math:`\text{spy}(\text{input})` is the sparsity pattern matrix of :attr:`input`, :attr:`alpha`
and :attr:`beta` are the scaling factors.
:math:`\text{spy}(\text{input})` has value 1 at the positions where :attr:`input` has non-zero values, and 0 elsewhere.

.. note::
    :attr:`input` must be a sparse CSR tensor. :attr:`mat1` and :attr:`mat2` must be dense tensors.

Args:
    input (Tensor): a sparse CSR matrix of shape `(m, n)` to be added and used to compute
        the sampled matrix multiplication
    mat1 (Tensor): a dense matrix of shape `(m, k)` to be multiplied
    mat2 (Tensor): a dense matrix of shape `(k, n)` to be multiplied

Keyword args:
    beta (Number, optional): multiplier for :attr:`input` (:math:`\beta`)
    alpha (Number, optional): multiplier for :math:`mat1 @ mat2` (:math:`\alpha`)
    out (Tensor, optional): output tensor. Ignored if `None`. Default: `None`.

Examples::

    >>> input = torch.eye(3, device='cuda').to_sparse_csr()
    >>> mat1 = torch.randn(3, 5, device='cuda')
    >>> mat2 = torch.randn(5, 3, device='cuda')
    >>> torch.sparse.sampled_addmm(input, mat1, mat2)
    tensor(crow_indices=tensor([0, 1, 2, 3]),
        col_indices=tensor([0, 1, 2]),
        values=tensor([ 0.2847, -0.7805, -0.1900]), device='cuda:0',
        size=(3, 3), nnz=3, layout=torch.sparse_csr)
    >>> torch.sparse.sampled_addmm(input, mat1, mat2).to_dense()
    tensor([[ 0.2847,  0.0000,  0.0000],
        [ 0.0000, -0.7805,  0.0000],
        [ 0.0000,  0.0000, -0.1900]], device='cuda:0')
    >>> torch.sparse.sampled_addmm(input, mat1, mat2, beta=0.5, alpha=0.5)
    tensor(crow_indices=tensor([0, 1, 2, 3]),
        col_indices=tensor([0, 1, 2]),
        values=tensor([ 0.1423, -0.3903, -0.0950]), device='cuda:0',
        size=(3, 3), nnz=3, layout=torch.sparse_csr)
""")

def sum(input: Tensor, dim: DimOrDims = None,
        dtype: Optional[DType] = None) -> Tensor:
    r"""
    Returns the sum of each row of the sparse tensor :attr:`input` in the given
    dimensions :attr:`dim`. If :attr:`dim` is a list of dimensions,
    reduce over all of them. When sum over all ``sparse_dim``, this method
    returns a dense tensor instead of a sparse tensor.

    All summed :attr:`dim` are squeezed (see :func:`torch.squeeze`), resulting an output
    tensor having :attr:`dim` fewer dimensions than :attr:`input`.

    During backward, only gradients at ``nnz`` locations of :attr:`input`
    will propagate back. Note that the gradients of :attr:`input` is coalesced.

    Args:
        input (Tensor): the input sparse tensor
        dim (int or tuple of ints): a dimension or a list of dimensions to reduce. Default: reduce
            over all dims.
        dtype (:class:`torch.dtype`, optional): the desired data type of returned Tensor.
            Default: dtype of :attr:`input`.

    Example::

        >>> nnz = 3
        >>> dims = [5, 5, 2, 3]
        >>> I = torch.cat([torch.randint(0, dims[0], size=(nnz,)),
                           torch.randint(0, dims[1], size=(nnz,))], 0).reshape(2, nnz)
        >>> V = torch.randn(nnz, dims[2], dims[3])
        >>> size = torch.Size(dims)
        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
        >>> S = torch.sparse_coo_tensor(I, V, size)
        >>> S
        tensor(indices=tensor([[2, 0, 3],
                               [2, 4, 1]]),
               values=tensor([[[-0.6438, -1.6467,  1.4004],
                               [ 0.3411,  0.0918, -0.2312]],

                              [[ 0.5348,  0.0634, -2.0494],
                               [-0.7125, -1.0646,  2.1844]],

                              [[ 0.1276,  0.1874, -0.6334],
                               [-1.9682, -0.5340,  0.7483]]]),
               size=(5, 5, 2, 3), nnz=3, layout=torch.sparse_coo)

        # when sum over only part of sparse_dims, return a sparse tensor
        >>> torch.sparse.sum(S, [1, 3])
        tensor(indices=tensor([[0, 2, 3]]),
               values=tensor([[-1.4512,  0.4073],
                              [-0.8901,  0.2017],
                              [-0.3183, -1.7539]]),
               size=(5, 2), nnz=3, layout=torch.sparse_coo)

        # when sum over all sparse dim, return a dense tensor
        # with summed dims squeezed
        >>> torch.sparse.sum(S, [0, 1, 3])
        tensor([-2.6596, -1.1450])
    """
    if dtype is None:
        if dim is not None:
            return torch._sparse_sum(input, dim)
        else:
            return torch._sparse_sum(input)
    else:
        if dim is not None:
            return torch._sparse_sum(input, dim, dtype=dtype)
        else:
            return torch._sparse_sum(input, dtype=dtype)


softmax = _add_docstr(_sparse._sparse_softmax, r"""
sparse.softmax(input, dim, *, dtype=None) -> Tensor

Applies a softmax function.

Softmax is defined as:

:math:`\text{Softmax}(x_{i}) = \frac{exp(x_i)}{\sum_j exp(x_j)}`

where :math:`i, j` run over sparse tensor indices and unspecified
entries are ignores. This is equivalent to defining unspecified
entries as negative infinity so that :math:`exp(x_k) = 0` when the
entry with index :math:`k` has not specified.

It is applied to all slices along `dim`, and will re-scale them so
that the elements lie in the range `[0, 1]` and sum to 1.

Args:
    input (Tensor): input
    dim (int): A dimension along which softmax will be computed.
    dtype (:class:`torch.dtype`, optional): the desired data type
        of returned tensor.  If specified, the input tensor is
        casted to :attr:`dtype` before the operation is
        performed. This is useful for preventing data type
        overflows. Default: None
""")


log_softmax = _add_docstr(_sparse._sparse_log_softmax, r"""
sparse.log_softmax(input, dim, *, dtype=None) -> Tensor

Applies a softmax function followed by logarithm.

See :class:`~torch.sparse.softmax` for more details.

Args:
    input (Tensor): input
    dim (int): A dimension along which softmax will be computed.
    dtype (:class:`torch.dtype`, optional): the desired data type
        of returned tensor.  If specified, the input tensor is
        casted to :attr:`dtype` before the operation is
        performed. This is useful for preventing data type
        overflows. Default: None
""")


spdiags = _add_docstr(
    _sparse._spdiags,
    r"""
sparse.spdiags(diagonals, offsets, shape, layout=None) -> Tensor

Creates a sparse 2D tensor by placing the values from rows of
:attr:`diagonals` along specified diagonals of the output

The :attr:`offsets` tensor controls which diagonals are set.

- If :attr:`offsets[i]` = 0, it is the main diagonal
- If :attr:`offsets[i]` < 0, it is below the main diagonal
- If :attr:`offsets[i]` > 0, it is above the main diagonal

The number of rows in :attr:`diagonals` must match the length of :attr:`offsets`,
and an offset may not be repeated.

Args:
    diagonals (Tensor): Matrix storing diagonals row-wise
    offsets (Tensor): The diagonals to be set, stored as a vector
    shape (2-tuple of ints): The desired shape of the result
Keyword args:
    layout (:class:`torch.layout`, optional): The desired layout of the
        returned tensor. ``torch.sparse_coo``, ``torch.sparse_csc`` and ``torch.sparse_csr``
        are supported. Default: ``torch.sparse_coo``

Examples:

Set the main and first two lower diagonals of a matrix::

    >>> diags = torch.arange(9).reshape(3, 3)
    >>> diags
    tensor([[0, 1, 2],
            [3, 4, 5],
            [6, 7, 8]])
    >>> s = torch.sparse.spdiags(diags, torch.tensor([0, -1, -2]), (3, 3))
    >>> s
    tensor(indices=tensor([[0, 1, 2, 1, 2, 2],
                           [0, 1, 2, 0, 1, 0]]),
           values=tensor([0, 1, 2, 3, 4, 6]),
           size=(3, 3), nnz=6, layout=torch.sparse_coo)
    >>> s.to_dense()
    tensor([[0, 0, 0],
            [3, 1, 0],
            [6, 4, 2]])


Change the output layout::

    >>> diags = torch.arange(9).reshape(3, 3)
    >>> diags
    tensor([[0, 1, 2],[3, 4, 5], [6, 7, 8])
    >>> s = torch.sparse.spdiags(diags, torch.tensor([0, -1, -2]), (3, 3), layout=torch.sparse_csr)
    >>> s
    tensor(crow_indices=tensor([0, 1, 3, 6]),