# scipy.sparse.coo_matrix

class scipy.sparse.coo_matrix(arg1, shape=None, dtype=None, copy=False)

  A sparse matrix in COOrdinate format.

  Also known as the ‘ijv’ or ‘triplet’ format.

  This can be instantiated in several ways:
    coo_array(D)

      with a dense matrix D

    coo_array(S)

      with another sparse matrix S (equivalent to S.tocoo())

    coo_array((M, N), [dtype])

      to construct an empty matrix with shape (M, N) dtype is optional, defaulting to dtype=’d’.

    coo_array((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

  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 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 indices sorted by row, then column.

    - There are no duplicate entries (i.e. duplicate (i,j) locations)

    - Arrays MAY have explicit zeros.

  Examples

      >>> # Constructing an empty matrix
      >>> 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 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_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 matrix with duplicate indices
      >>> 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 indices 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]])

  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`

      Number of stored values, including explicit zeros.

    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

  Methods

  `__len__`() |
  `__mul__`(other) |
  `arcsin`() | Element-wise arcsin.
  `arcsinh`() | Element-wise arcsinh.
  `arctan`() | Element-wise arctan.
  `arctanh`() | Element-wise arctanh.
  `argmax`([axis, out]) | Return indices of maximum elements along an axis.
  `argmin`([axis, out]) | Return indices of minimum elements along an axis.
  `asformat`(format[, copy]) | Return this array in the passed format.
  `asfptype`() | Upcast array to a floating point format (if necessary)
  `astype`(dtype[, casting, copy]) | Cast the array elements to a specified type.
  `ceil`() | Element-wise ceil.
  `conj`([copy]) | Element-wise complex conjugation.
  `conjugate`([copy]) | Element-wise complex conjugation.
  `copy`() | Returns a copy of this array.
  `count_nonzero`() | Number of non-zero entries, equivalent to
  `deg2rad`() | Element-wise deg2rad.
  `diagonal`([k]) | Returns the kth diagonal of the array.
  `dot`(other) | Ordinary dot product
  `eliminate_zeros`() | Remove zero entries from the matrix
  `expm1`() | Element-wise expm1.
  `floor`() | Element-wise floor.
  `getH`() | Return the Hermitian transpose of this array.
  `get_shape`() | Get the shape of the matrix
  `getcol`(j) | Returns a copy of column j of the array, as an (m x 1) sparse array (column vector).
  `getformat`() | Matrix storage format
  `getmaxprint`() | Maximum number of elements to display when printed.
  `getnnz`([axis]) | Number of stored values, including explicit zeros.
  `getrow`(i) | Returns a copy of row i of the array, as a (1 x n) sparse array (row vector).
  `log1p`() | Element-wise log1p.
  `max`([axis, out]) | Return the maximum of the matrix or maximum along an axis.
  `maximum`(other) | Element-wise maximum between this and another array.
  `mean`([axis, dtype, out]) | Compute the arithmetic mean along the specified axis.
  `min`([axis, out]) | Return the minimum of the matrix or maximum along an axis.
  `minimum`(other) | Element-wise minimum between this and another array.
  `multiply`(other) | Point-wise multiplication by another array
  `nanmax`([axis, out]) | Return the maximum of the matrix or maximum along an axis, ignoring any NaNs.
  `nanmin`([axis, out]) | Return the minimum of the matrix or minimum along an axis, ignoring any NaNs.
  `nonzero`() | nonzero indices
  `power`(n[, dtype]) | This function performs element-wise power.
  `rad2deg`() | Element-wise rad2deg.
  `reshape`(self, shape[, order, copy]) | Gives a new shape to a sparse array without changing its data.
  `resize`(*shape) | Resize the array in-place to dimensions given by `shape`
  `rint`() | Element-wise rint.
  `set_shape`(shape) | Set the shape of the matrix in-place
  `setdiag`(values[, k]) | Set diagonal or off-diagonal elements of the array.
  `sign`() | Element-wise sign.
  `sin`() | Element-wise sin.
  `sinh`() | Element-wise sinh.
  `sqrt`() | Element-wise sqrt.
  `sum`([axis, dtype, out]) | Sum the array elements over a given axis.
  `sum_duplicates`() | Eliminate duplicate matrix entries by adding them together
  `tan`() | Element-wise tan.
  `tanh`() | Element-wise tanh.
  `toarray`([order, out]) | See the docstring for _spbase.toarray.
  `tobsr`([blocksize, copy]) | Convert this array to Block Sparse Row format.
  `tocoo`([copy]) | Convert this array to COOrdinate format.
  `tocsc`([copy]) | Convert this matrix to Compressed Sparse Column format
  `tocsr`([copy]) | Convert this matrix to Compressed Sparse Row format
  `todense`([order, out]) | Return a dense matrix representation of this sparse array.
  `todia`([copy]) | Convert this array to sparse DIAgonal format.
  `todok`([copy]) | Convert this array to Dictionary Of Keys format.
  `tolil`([copy]) | Convert this array to List of Lists format.
  `trace`([offset]) | Returns the sum along diagonals of the sparse array.
  `transpose`([axes, copy]) | Reverses the dimensions of the sparse array.
  `trunc`() | Element-wise trunc.