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

import torch
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',
    'mm',
    'sum',
    'softmax',
    'log_softmax',
]


def addmm(mat: Tensor, mat1: Tensor, mat2: Tensor,
          beta: float = 1., alpha: float = 1.) -> Tensor:
    r"""
    This function does exact same thing as :func:`torch.addmm` in the forward,
    except that it supports backward for sparse matrix :attr:`mat1`. :attr:`mat1`
    need to have `sparse_dim = 2`. Note that the gradients of :attr:`mat1` is a
    coalesced sparse tensor.

    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`)
    """
    return torch._sparse_addmm(mat, mat1, mat2, beta=beta, alpha=alpha)


def mm(mat1: Tensor, mat2: Tensor) -> Tensor:
    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. :attr:`mat1` need to have `sparse_dim = 2`.
    This function also supports backward for both matrices. Note that the gradients of
    :attr:`mat1` is a coalesced sparse tensor.

    Args:
        mat1 (SparseTensor): the first sparse matrix to be multiplied
        mat2 (Tensor): the second matrix to be multiplied, which could be sparse or dense 

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

    Example::

        >>> a = torch.randn(2, 3).to_sparse().requires_grad_(True)
        >>> a
        tensor(indices=tensor([[0, 0, 0, 1, 1, 1],
                               [0, 1, 2, 0, 1, 2]]),
               values=tensor([ 1.5901,  0.0183, -0.6146,  1.8061, -0.0112,  0.6302]),
               size=(2, 3), nnz=6, layout=torch.sparse_coo, requires_grad=True)

        >>> b = torch.randn(3, 2, requires_grad=True)
        >>> b
        tensor([[-0.6479,  0.7874],
                [-1.2056,  0.5641],
                [-1.1716, -0.9923]], requires_grad=True)

        >>> y = torch.sparse.mm(a, b)
        >>> y
        tensor([[-0.3323,  1.8723],
                [-1.8951,  0.7904]], grad_fn=<SparseAddmmBackward>)
        >>> y.sum().backward()
        >>> a.grad
        tensor(indices=tensor([[0, 0, 0, 1, 1, 1],
                               [0, 1, 2, 0, 1, 2]]),
               values=tensor([ 0.1394, -0.6415, -2.1639,  0.1394, -0.6415, -2.1639]),
               size=(2, 3), nnz=6, layout=torch.sparse_coo)
    """
    if mat1.is_sparse and mat2.is_sparse:
        return torch._sparse_sparse_matmul(mat1, mat2)
    return torch._sparse_mm(mat1, mat2)


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)
        >>> 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)


def softmax(input: Tensor, dim: int, dtype: Optional[DType] = None) -> Tensor:
    r"""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
    """
    return torch._sparse_softmax(input, dim, dtype=dtype)


def log_softmax(input: Tensor, dim: int, dtype: Optional[DType] = None) -> Tensor:
    r"""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
    """
    return torch._sparse_log_softmax(input, dim, dtype=dtype)