venv/lib/python3.10/site-packages/scipy/sparse/_coo.py

""" A sparse matrix in COOrdinate or 'triplet' format"""

__docformat__ = "restructuredtext en"

__all__ = ['coo_array', 'coo_matrix', 'isspmatrix_coo']

import math
from warnings import warn

import numpy as np

from .._lib._util import copy_if_needed
from ._matrix import spmatrix
from ._sparsetools import coo_tocsr, coo_todense, coo_matvec
from ._base import issparse, SparseEfficiencyWarning, _spbase, sparray
from ._data import _data_matrix, _minmax_mixin
from ._sputils import (upcast_char, to_native, isshape, getdtype,
                       getdata, downcast_intp_index, get_index_dtype,
                       check_shape, check_reshape_kwargs)

import operator


class _coo_base(_data_matrix, _minmax_mixin):
    _format = 'coo'

    def __init__(self, arg1, shape=None, dtype=None, copy=False):
        _data_matrix.__init__(self)
        is_array = isinstance(self, sparray)
        if not copy:
            copy = copy_if_needed

        if isinstance(arg1, tuple):
            if isshape(arg1, allow_1d=is_array):
                self._shape = check_shape(arg1, allow_1d=is_array)
                idx_dtype = self._get_index_dtype(maxval=max(self._shape))
                data_dtype = getdtype(dtype, default=float)
                self.coords = tuple(np.array([], dtype=idx_dtype)
                                     for _ in range(len(self._shape)))
                self.data = np.array([], dtype=data_dtype)
                self.has_canonical_format = True
            else:
                try:
                    obj, coords = arg1
                except (TypeError, ValueError) as e:
                    raise TypeError('invalid input format') from e

                if shape is None:
                    if any(len(idx) == 0 for idx in coords):
                        raise ValueError('cannot infer dimensions from zero '
                                         'sized index arrays')
                    shape = tuple(operator.index(np.max(idx)) + 1
                                  for idx in coords)
                self._shape = check_shape(shape, allow_1d=is_array)

                idx_dtype = self._get_index_dtype(coords,
                                                  maxval=max(self.shape),
                                                  check_contents=True)
                self.coords = tuple(np.array(idx, copy=copy, dtype=idx_dtype)
                                     for idx in coords)
                self.data = getdata(obj, copy=copy, dtype=dtype)
                self.has_canonical_format = False
        else:
            if issparse(arg1):
                if arg1.format == self.format and copy:
                    self.coords = tuple(idx.copy() for idx in arg1.coords)
                    self.data = arg1.data.copy()
                    self._shape = check_shape(arg1.shape, allow_1d=is_array)
                    self.has_canonical_format = arg1.has_canonical_format
                else:
                    coo = arg1.tocoo()
                    self.coords = tuple(coo.coords)
                    self.data = coo.data
                    self._shape = check_shape(coo.shape, allow_1d=is_array)
                    self.has_canonical_format = False
            else:
                # dense argument
                M = np.asarray(arg1)
                if not is_array:
                    M = np.atleast_2d(M)
                    if M.ndim != 2:
                        raise TypeError('expected dimension <= 2 array or matrix')

                self._shape = check_shape(M.shape, allow_1d=is_array)
                if shape is not None:
                    if check_shape(shape, allow_1d=is_array) != self._shape:
                        message = f'inconsistent shapes: {shape} != {self._shape}'
                        raise ValueError(message)
                index_dtype = self._get_index_dtype(maxval=max(self._shape))
                coords = M.nonzero()
                self.coords = tuple(idx.astype(index_dtype, copy=False)
                                     for idx in coords)
                self.data = M[coords]
                self.has_canonical_format = True

        if dtype is not None:
            self.data = self.data.astype(dtype, copy=False)

        self._check()

    @property
    def row(self):
        if self.ndim > 1:
            return self.coords[-2]
        result = np.zeros_like(self.col)
        result.setflags(write=False)
        return result


    @row.setter
    def row(self, new_row):
        if self.ndim < 2:
            raise ValueError('cannot set row attribute of a 1-dimensional sparse array')
        new_row = np.asarray(new_row, dtype=self.coords[-2].dtype)
        self.coords = self.coords[:-2] + (new_row,) + self.coords[-1:]

    @property
    def col(self):
        return self.coords[-1]

    @col.setter
    def col(self, new_col):
        new_col = np.asarray(new_col, dtype=self.coords[-1].dtype)
        self.coords = self.coords[:-1] + (new_col,)

    def reshape(self, *args, **kwargs):
        is_array = isinstance(self, sparray)
        shape = check_shape(args, self.shape, allow_1d=is_array)
        order, copy = check_reshape_kwargs(kwargs)

        # Return early if reshape is not required
        if shape == self.shape:
            if copy:
                return self.copy()
            else:
                return self

        # When reducing the number of dimensions, we need to be careful about
        # index overflow. This is why we can't simply call
        # `np.ravel_multi_index()` followed by `np.unravel_index()` here.
        flat_coords = _ravel_coords(self.coords, self.shape, order=order)
        if len(shape) == 2:
            if order == 'C':
                new_coords = divmod(flat_coords, shape[1])
            else:
                new_coords = divmod(flat_coords, shape[0])[::-1]
        else:
            new_coords = np.unravel_index(flat_coords, shape, order=order)

        # Handle copy here rather than passing on to the constructor so that no
        # copy will be made of `new_coords` regardless.
        if copy:
            new_data = self.data.copy()
        else:
            new_data = self.data

        return self.__class__((new_data, new_coords), shape=shape, copy=False)

    reshape.__doc__ = _spbase.reshape.__doc__

    def _getnnz(self, axis=None):
        if axis is None or (axis == 0 and self.ndim == 1):
            nnz = len(self.data)
            if any(len(idx) != nnz for idx in self.coords):
                raise ValueError('all index and data arrays must have the '
                                 'same length')

            if self.data.ndim != 1 or any(idx.ndim != 1 for idx in self.coords):
                raise ValueError('row, column, and data arrays must be 1-D')

            return int(nnz)

        if axis < 0:
            axis += self.ndim
        if axis >= self.ndim:
            raise ValueError('axis out of bounds')
        if self.ndim > 2:
            raise NotImplementedError('per-axis nnz for COO arrays with >2 '
                                      'dimensions is not supported')
        return np.bincount(downcast_intp_index(self.coords[1 - axis]),
                           minlength=self.shape[1 - axis])

    _getnnz.__doc__ = _spbase._getnnz.__doc__

    def _check(self):
        """ Checks data structure for consistency """
        if self.ndim != len(self.coords):
            raise ValueError('mismatching number of index arrays for shape; '
                             f'got {len(self.coords)}, expected {self.ndim}')

        # index arrays should have integer data types
        for i, idx in enumerate(self.coords):
            if idx.dtype.kind != 'i':
                warn(f'index array {i} has non-integer dtype ({idx.dtype.name})',
                     stacklevel=3)

        idx_dtype = self._get_index_dtype(self.coords, maxval=max(self.shape))
        self.coords = tuple(np.asarray(idx, dtype=idx_dtype)
                             for idx in self.coords)
        self.data = to_native(self.data)

        if self.nnz > 0:
            for i, idx in enumerate(self.coords):
                if idx.max() >= self.shape[i]:
                    raise ValueError(f'axis {i} index {idx.max()} exceeds '
                                     f'matrix dimension {self.shape[i]}')
                if idx.min() < 0:
                    raise ValueError(f'negative axis {i} index: {idx.min()}')

    def transpose(self, axes=None, copy=False):
        if axes is None:
            axes = range(self.ndim)[::-1]
        elif isinstance(self, sparray):
            if len(axes) != self.ndim:
                raise ValueError("axes don't match matrix dimensions")
            if len(set(axes)) != self.ndim:
                raise ValueError("repeated axis in transpose")
        elif axes != (1, 0):
            raise ValueError("Sparse matrices do not support an 'axes' "
                             "parameter because swapping dimensions is the "
                             "only logical permutation.")

        permuted_shape = tuple(self._shape[i] for i in axes)
        permuted_coords = tuple(self.coords[i] for i in axes)
        return self.__class__((self.data, permuted_coords),
                              shape=permuted_shape, copy=copy)

    transpose.__doc__ = _spbase.transpose.__doc__

    def resize(self, *shape) -> None:
        is_array = isinstance(self, sparray)
        shape = check_shape(shape, allow_1d=is_array)

        # Check for added dimensions.
        if len(shape) > self.ndim:
            flat_coords = _ravel_coords(self.coords, self.shape)
            max_size = math.prod(shape)
            self.coords = np.unravel_index(flat_coords[:max_size], shape)
            self.data = self.data[:max_size]
            self._shape = shape
            return

        # Check for removed dimensions.
        if len(shape) < self.ndim:
            tmp_shape = (
                self._shape[:len(shape) - 1]  # Original shape without last axis
                + (-1,)  # Last axis is used to flatten the array
                + (1,) * (self.ndim - len(shape))  # Pad with ones
            )
            tmp = self.reshape(tmp_shape)
            self.coords = tmp.coords[:len(shape)]
            self._shape = tmp.shape[:len(shape)]

        # Handle truncation of existing dimensions.
        is_truncating = any(old > new for old, new in zip(self.shape, shape))
        if is_truncating:
            mask = np.logical_and.reduce([
                idx < size for idx, size in zip(self.coords, shape)
            ])
            if not mask.all():
                self.coords = tuple(idx[mask] for idx in self.coords)
                self.data = self.data[mask]

        self._shape = shape

    resize.__doc__ = _spbase.resize.__doc__

    def toarray(self, order=None, out=None):
        B = self._process_toarray_args(order, out)
        fortran = int(B.flags.f_contiguous)
        if not fortran and not B.flags.c_contiguous:
            raise ValueError("Output array must be C or F contiguous")
        if self.ndim > 2:
            raise ValueError("Cannot densify higher-rank sparse array")
        # This handles both 0D and 1D cases correctly regardless of the
        # original shape.
        M, N = self._shape_as_2d
        coo_todense(M, N, self.nnz, self.row, self.col, self.data,
                    B.ravel('A'), fortran)
        # Note: reshape() doesn't copy here, but does return a new array (view).
        return B.reshape(self.shape)

    toarray.__doc__ = _spbase.toarray.__doc__

    def tocsc(self, copy=False):
        """Convert this array/matrix to Compressed Sparse Column format

        Duplicate entries will be summed together.

        Examples
        --------
        >>> from numpy import array
        >>> from scipy.sparse import coo_array
        >>> row  = array([0, 0, 1, 3, 1, 0, 0])
        >>> col  = array([0, 2, 1, 3, 1, 0, 0])
        >>> data = array([1, 1, 1, 1, 1, 1, 1])
        >>> A = coo_array((data, (row, col)), shape=(4, 4)).tocsc()
        >>> A.toarray()
        array([[3, 0, 1, 0],
               [0, 2, 0, 0],
               [0, 0, 0, 0],
               [0, 0, 0, 1]])

        """
        if self.ndim != 2:
            raise ValueError("Cannot convert a 1d sparse array to csc format")
        if self.nnz == 0:
            return self._csc_container(self.shape, dtype=self.dtype)
        else:
            from ._csc import csc_array
            indptr, indices, data, shape = self._coo_to_compressed(csc_array._swap)

            x = self._csc_container((data, indices, indptr), shape=shape)
            if not self.has_canonical_format:
                x.sum_duplicates()
            return x

    def tocsr(self, copy=False):
        """Convert this array/matrix to Compressed Sparse Row format

        Duplicate entries will be summed together.

        Examples
        --------
        >>> from numpy import array
        >>> from scipy.sparse import coo_array
        >>> row  = array([0, 0, 1, 3, 1, 0, 0])
        >>> col  = array([0, 2, 1, 3, 1, 0, 0])
        >>> data = array([1, 1, 1, 1, 1, 1, 1])
        >>> A = coo_array((data, (row, col)), shape=(4, 4)).tocsr()
        >>> A.toarray()
        array([[3, 0, 1, 0],
               [0, 2, 0, 0],
               [0, 0, 0, 0],
               [0, 0, 0, 1]])

        """
        if self.ndim != 2:
            raise ValueError("Cannot convert a 1d sparse array to csr format")
        if self.nnz == 0:
            return self._csr_container(self.shape, dtype=self.dtype)
        else:
            from ._csr import csr_array
            indptr, indices, data, shape = self._coo_to_compressed(csr_array._swap)

            x = self._csr_container((data, indices, indptr), shape=self.shape)
            if not self.has_canonical_format:
                x.sum_duplicates()
            return x

    def _coo_to_compressed(self, swap):
        """convert (shape, coords, data) to (indptr, indices, data, shape)"""
        M, N = swap(self.shape)
        major, minor = swap(self.coords)
        nnz = len(major)
        # convert idx_dtype intc to int32 for pythran.
        # tested in scipy/optimize/tests/test__numdiff.py::test_group_columns
        idx_dtype = self._get_index_dtype(self.coords, maxval=max(self.nnz, N))
        major = major.astype(idx_dtype, copy=False)
        minor = minor.astype(idx_dtype, copy=False)

        indptr = np.empty(M + 1, dtype=idx_dtype)
        indices = np.empty_like(minor, dtype=idx_dtype)
        data = np.empty_like(self.data, dtype=self.dtype)

        coo_tocsr(M, N, nnz, major, minor, self.data, indptr, indices, data)
        return indptr, indices, data, self.shape

    def tocoo(self, copy=False):
        if copy:
            return self.copy()
        else:
            return self

    tocoo.__doc__ = _spbase.tocoo.__doc__

    def todia(self, copy=False):
        if self.ndim != 2:
            raise ValueError("Cannot convert a 1d sparse array to dia format")
        self.sum_duplicates()
        ks = self.col - self.row  # the diagonal for each nonzero
        diags, diag_idx = np.unique(ks, return_inverse=True)

        if len(diags) > 100:
            # probably undesired, should todia() have a maxdiags parameter?
            warn("Constructing a DIA matrix with %d diagonals "
                 "is inefficient" % len(diags),
                 SparseEfficiencyWarning, stacklevel=2)

        #initialize and fill in data array
        if self.data.size == 0:
            data = np.zeros((0, 0), dtype=self.dtype)
        else:
            data = np.zeros((len(diags), self.col.max()+1), dtype=self.dtype)
            data[diag_idx, self.col] = self.data

        return self._dia_container((data, diags), shape=self.shape)

    todia.__doc__ = _spbase.todia.__doc__

    def todok(self, copy=False):
        self.sum_duplicates()
        dok = self._dok_container(self.shape, dtype=self.dtype)
        # ensure that 1d coordinates are not tuples
        if self.ndim == 1:
            coords = self.coords[0]
        else:
            coords = zip(*self.coords)

        dok._dict = dict(zip(coords, self.data))
        return dok

    todok.__doc__ = _spbase.todok.__doc__

    def diagonal(self, k=0):
        if self.ndim != 2:
            raise ValueError("diagonal requires two dimensions")
        rows, cols = self.shape
        if k <= -rows or k >= cols:
            return np.empty(0, dtype=self.data.dtype)
        diag = np.zeros(min(rows + min(k, 0), cols - max(k, 0)),
                        dtype=self.dtype)
        diag_mask = (self.row + k) == self.col

        if self.has_canonical_format:
            row = self.row[diag_mask]
            data = self.data[diag_mask]
        else:
            inds = tuple(idx[diag_mask] for idx in self.coords)
            (row, _), data = self._sum_duplicates(inds, self.data[diag_mask])
        diag[row + min(k, 0)] = data

        return diag

    diagonal.__doc__ = _data_matrix.diagonal.__doc__

    def _setdiag(self, values, k):
        if self.ndim != 2:
            raise ValueError("setting a diagonal requires two dimensions")
        M, N = self.shape
        if values.ndim and not len(values):
            return
        idx_dtype = self.row.dtype

        # Determine which triples to keep and where to put the new ones.
        full_keep = self.col - self.row != k
        if k < 0:
            max_index = min(M+k, N)
            if values.ndim:
                max_index = min(max_index, len(values))
            keep = np.logical_or(full_keep, self.col >= max_index)
            new_row = np.arange(-k, -k + max_index, dtype=idx_dtype)
            new_col = np.arange(max_index, dtype=idx_dtype)
        else:
            max_index = min(M, N-k)
            if values.ndim:
                max_index = min(max_index, len(values))
            keep = np.logical_or(full_keep, self.row >= max_index)
            new_row = np.arange(max_index, dtype=idx_dtype)
            new_col = np.arange(k, k + max_index, dtype=idx_dtype)

        # Define the array of data consisting of the entries to be added.
        if values.ndim:
            new_data = values[:max_index]
        else:
            new_data = np.empty(max_index, dtype=self.dtype)
            new_data[:] = values

        # Update the internal structure.
        self.coords = (np.concatenate((self.row[keep], new_row)),
                       np.concatenate((self.col[keep], new_col)))
        self.data = np.concatenate((self.data[keep], new_data))
        self.has_canonical_format = False

    # needed by _data_matrix
    def _with_data(self, data, copy=True):
        """Returns a matrix with the same sparsity structure as self,
        but with different data. By default the index arrays are copied.
        """
        if copy:
            coords = tuple(idx.copy() for idx in self.coords)
        else:
            coords = self.coords
        return self.__class__((data, coords), shape=self.shape, dtype=data.dtype)

    def sum_duplicates(self) -> None:
        """Eliminate duplicate entries by adding them together

        This is an *in place* operation
        """
        if self.has_canonical_format:
            return
        summed = self._sum_duplicates(self.coords, self.data)
        self.coords, self.data = summed
        self.has_canonical_format = True

    def _sum_duplicates(self, coords, data):
        # Assumes coords not in canonical format.
        if len(data) == 0:
            return coords, data
        # Sort coords w.r.t. rows, then cols. This corresponds to C-order,
        # which we rely on for argmin/argmax to return the first index in the
        # same way that numpy does (in the case of ties).
        order = np.lexsort(coords[::-1])
        coords = tuple(idx[order] for idx in coords)
        data = data[order]
        unique_mask = np.logical_or.reduce([
            idx[1:] != idx[:-1] for idx in coords
        ])
        unique_mask = np.append(True, unique_mask)
        coords = tuple(idx[unique_mask] for idx in coords)
        unique_inds, = np.nonzero(unique_mask)
        data = np.add.reduceat(data, unique_inds, dtype=self.dtype)
        return coords, data

    def eliminate_zeros(self):
        """Remove zero entries from the array/matrix

        This is an *in place* operation
        """
        mask = self.data != 0
        self.data = self.data[mask]
        self.coords = tuple(idx[mask] for idx in self.coords)

    #######################
    # Arithmetic handlers #
    #######################

    def _add_dense(self, other):
        if other.shape != self.shape:
            raise ValueError(f'Incompatible shapes ({self.shape} and {other.shape})')
        dtype = upcast_char(self.dtype.char, other.dtype.char)
        result = np.array(other, dtype=dtype, copy=True)
        fortran = int(result.flags.f_contiguous)
        M, N = self._shape_as_2d
        coo_todense(M, N, self.nnz, self.row, self.col, self.data,
                    result.ravel('A'), fortran)
        return self._container(result, copy=False)

    def _matmul_vector(self, other):
        result_shape = self.shape[0] if self.ndim > 1 else 1
        result = np.zeros(result_shape,
                          dtype=upcast_char(self.dtype.char, other.dtype.char))

        if self.ndim == 2:
            col = self.col
            row = self.row
        elif self.ndim == 1:
            col = self.coords[0]
            row = np.zeros_like(col)
        else:
            raise NotImplementedError(
                f"coo_matvec not implemented for ndim={self.ndim}")

        coo_matvec(self.nnz, row, col, self.data, other, result)
        # Array semantics return a scalar here, not a single-element array.
        if isinstance(self, sparray) and result_shape == 1:
            return result[0]
        return result

    def _matmul_multivector(self, other):
        result_dtype = upcast_char(self.dtype.char, other.dtype.char)
        if self.ndim == 2:
            result_shape = (other.shape[1], self.shape[0])
            col = self.col
            row = self.row
        elif self.ndim == 1:
            result_shape = (other.shape[1],)
            col = self.coords[0]
            row = np.zeros_like(col)
        else:
            raise NotImplementedError(
                f"coo_matvec not implemented for ndim={self.ndim}")

        result = np.zeros(result_shape, dtype=result_dtype)
        for i, other_col in enumerate(other.T):
            coo_matvec(self.nnz, row, col, self.data, other_col, result[i:i + 1])
        return result.T.view(type=type(other))


def _ravel_coords(coords, shape, order='C'):
    """Like np.ravel_multi_index, but avoids some overflow issues."""
    if len(coords) == 1:
        return coords[0]
    # Handle overflow as in https://github.com/scipy/scipy/pull/9132
    if len(coords) == 2:
        nrows, ncols = shape
        row, col = coords
        if order == 'C':
            maxval = (ncols * max(0, nrows - 1) + max(0, ncols - 1))
            idx_dtype = get_index_dtype(maxval=maxval)
            return np.multiply(ncols, row, dtype=idx_dtype) + col
        elif order == 'F':
            maxval = (nrows * max(0, ncols - 1) + max(0, nrows - 1))
            idx_dtype = get_index_dtype(maxval=maxval)
            return np.multiply(nrows, col, dtype=idx_dtype) + row
        else:
            raise ValueError("'order' must be 'C' or 'F'")
    return np.ravel_multi_index(coords, shape, order=order)


def isspmatrix_coo(x):
    """Is `x` of coo_matrix type?

    Parameters
    ----------
    x
        object to check for being a coo matrix

    Returns
    -------
    bool
        True if `x` is a coo matrix, False otherwise

    Examples
    --------
    >>> from scipy.sparse import coo_array, coo_matrix, csr_matrix, isspmatrix_coo
    >>> isspmatrix_coo(coo_matrix([[5]]))
    True
    >>> isspmatrix_coo(coo_array([[5]]))
    False
    >>> isspmatrix_coo(csr_matrix([[5]]))
    False
    """
    return isinstance(x, coo_matrix)


# This namespace class separates array from matrix with isinstance
class coo_array(_coo_base, sparray):
    """
    A sparse array in COOrdinate format.

    Also known as the 'ijv' or 'triplet' format.

    This can be instantiated in several ways:
        coo_array(D)
            where D is an ndarray

        coo_array(S)
            with another sparse array or matrix S (equivalent to S.tocoo())

        coo_array(shape, [dtype])
            to construct an empty sparse array with shape `shape`
            dtype is optional, defaulting to dtype='d'.

        coo_array((data, coords), [shape])
            to construct from existing data and index arrays:
                1. data[:]       the entries of the sparse array, in any order
                2. coords[i][:]  the axis-i coordinates of the data entries

            Where ``A[coords] = data``, and coords is a tuple of index arrays.
            When shape is not specified, it is inferred from the index arrays.

    Attributes
    ----------
    dtype : dtype
        Data type of the sparse array
    shape : tuple of integers
        Shape of the sparse array
    ndim : int
        Number of dimensions of the sparse array
    nnz
    size
    data
        COO format data array of the sparse array
    coords
        COO format tuple of index arrays
    has_canonical_format : bool
        Whether the matrix has sorted coordinates and no duplicates
    format
    T

    Notes
    -----

    Sparse arrays can be used in arithmetic operations: they support
    addition, subtraction, multiplication, division, and matrix power.

    Advantages of the COO format
        - facilitates fast conversion among sparse formats
        - permits duplicate entries (see example)
        - very fast conversion to and from CSR/CSC formats

    Disadvantages of the COO format
        - does not directly support:
            + arithmetic operations
            + slicing

    Intended Usage
        - COO is a fast format for constructing sparse arrays
        - Once a COO array has been constructed, convert to CSR or
          CSC format for fast arithmetic and matrix vector operations
        - By default when converting to CSR or CSC format, duplicate (i,j)
          entries will be summed together.  This facilitates efficient
          construction of finite element matrices and the like. (see example)

    Canonical format
        - Entries and coordinates sorted by row, then column.
        - There are no duplicate entries (i.e. duplicate (i,j) locations)
        - Data arrays MAY have explicit zeros.

    Examples
    --------

    >>> # Constructing an empty sparse array
    >>> import numpy as np
    >>> from scipy.sparse import coo_array
    >>> coo_array((3, 4), dtype=np.int8).toarray()
    array([[0, 0, 0, 0],
           [0, 0, 0, 0],
           [0, 0, 0, 0]], dtype=int8)

    >>> # Constructing a sparse array using ijv format
    >>> row  = np.array([0, 3, 1, 0])
    >>> col  = np.array([0, 3, 1, 2])
    >>> data = np.array([4, 5, 7, 9])
    >>> coo_array((data, (row, col)), shape=(4, 4)).toarray()
    array([[4, 0, 9, 0],
           [0, 7, 0, 0],
           [0, 0, 0, 0],
           [0, 0, 0, 5]])

    >>> # Constructing a sparse array with duplicate coordinates
    >>> row  = np.array([0, 0, 1, 3, 1, 0, 0])
    >>> col  = np.array([0, 2, 1, 3, 1, 0, 0])
    >>> data = np.array([1, 1, 1, 1, 1, 1, 1])
    >>> coo = coo_array((data, (row, col)), shape=(4, 4))
    >>> # Duplicate coordinates are maintained until implicitly or explicitly summed
    >>> np.max(coo.data)
    1
    >>> coo.toarray()
    array([[3, 0, 1, 0],
           [0, 2, 0, 0],
           [0, 0, 0, 0],
           [0, 0, 0, 1]])

    """


class coo_matrix(spmatrix, _coo_base):
    """
    A sparse matrix in COOrdinate format.

    Also known as the 'ijv' or 'triplet' format.

    This can be instantiated in several ways:
        coo_matrix(D)
            where D is a 2-D ndarray

        coo_matrix(S)
            with another sparse array or matrix S (equivalent to S.tocoo())

        coo_matrix((M, N), [dtype])
            to construct an empty matrix with shape (M, N)
            dtype is optional, defaulting to dtype='d'.

        coo_matrix((data, (i, j)), [shape=(M, N)])
            to construct from three arrays:
                1. data[:]   the entries of the matrix, in any order
                2. i[:]      the row indices of the matrix entries
                3. j[:]      the column indices of the matrix entries

            Where ``A[i[k], j[k]] = data[k]``.  When shape is not
            specified, it is inferred from the index arrays

    Attributes
    ----------
    dtype : dtype
        Data type of the matrix
    shape : 2-tuple
        Shape of the matrix
    ndim : int
        Number of dimensions (this is always 2)
    nnz
    size
    data
        COO format data array of the matrix
    row
        COO format row index array of the matrix
    col
        COO format column index array of the matrix
    has_canonical_format : bool
        Whether the matrix has sorted indices and no duplicates
    format
    T

    Notes
    -----

    Sparse matrices can be used in arithmetic operations: they support
    addition, subtraction, multiplication, division, and matrix power.

    Advantages of the COO format
        - facilitates fast conversion among sparse formats
        - permits duplicate entries (see example)
        - very fast conversion to and from CSR/CSC formats

    Disadvantages of the COO format
        - does not directly support:
            + arithmetic operations
            + slicing

    Intended Usage
        - COO is a fast format for constructing sparse matrices
        - Once a COO matrix has been constructed, convert to CSR or
          CSC format for fast arithmetic and matrix vector operations
        - By default when converting to CSR or CSC format, duplicate (i,j)
          entries will be summed together.  This facilitates efficient
          construction of finite element matrices and the like. (see example)

    Canonical format
        - Entries and coordinates sorted by row, then column.
        - There are no duplicate entries (i.e. duplicate (i,j) locations)
        - Data arrays MAY have explicit zeros.

    Examples
    --------

    >>> # Constructing an empty matrix
    >>> import numpy as np
    >>> from scipy.sparse import coo_matrix
    >>> coo_matrix((3, 4), dtype=np.int8).toarray()
    array([[0, 0, 0, 0],
           [0, 0, 0, 0],
           [0, 0, 0, 0]], dtype=int8)

    >>> # Constructing a matrix using ijv format
    >>> row  = np.array([0, 3, 1, 0])
    >>> col  = np.array([0, 3, 1, 2])
    >>> data = np.array([4, 5, 7, 9])
    >>> coo_matrix((data, (row, col)), shape=(4, 4)).toarray()
    array([[4, 0, 9, 0],
           [0, 7, 0, 0],
           [0, 0, 0, 0],
           [0, 0, 0, 5]])

    >>> # Constructing a matrix with duplicate coordinates
    >>> row  = np.array([0, 0, 1, 3, 1, 0, 0])
    >>> col  = np.array([0, 2, 1, 3, 1, 0, 0])
    >>> data = np.array([1, 1, 1, 1, 1, 1, 1])
    >>> coo = coo_matrix((data, (row, col)), shape=(4, 4))
    >>> # Duplicate coordinates are maintained until implicitly or explicitly summed
    >>> np.max(coo.data)
    1
    >>> coo.toarray()
    array([[3, 0, 1, 0],
           [0, 2, 0, 0],
           [0, 0, 0, 0],
           [0, 0, 0, 1]])

    """

    def __setstate__(self, state):
        if 'coords' not in state:
            # For retro-compatibility with the previous attributes
            # storing nnz coordinates for 2D COO matrix.
            state['coords'] = (state.pop('row'), state.pop('col'))
        self.__dict__.update(state)