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# scipy.sparse.bsr_matrix

class `scipy.sparse.``bsr_matrix`(arg1, shape=None, dtype=None, copy=False, blocksize=None)

  Block Sparse Row matrix

  This can be instantiated in several ways:
    bsr_matrix(D, [blocksize=(R,C)])
      where D is a dense matrix or 2-D ndarray.
    bsr_matrix(S, [blocksize=(R,C)])
      with another sparse matrix S (equivalent to S.tobsr())
    bsr_matrix((M, N), [blocksize=(R,C), dtype])
      to construct an empty matrix with shape (M, N) dtype is optional, defaulting to dtype=’d’.
    bsr_matrix((data, ij), [blocksize=(R,C), shape=(M, N)])
      where `data` and `ij` satisfy `a[ij[0, k], ij[1, k]] = data[k]`
    bsr_matrix((data, indices, indptr), [shape=(M, N)])
      is the standard BSR representation where the block column indices for row i are stored in `indices[indptr[i]:indptr[i+1]]` and their corresponding block values are stored in `data[ indptr[i]: indptr[i+1] ]`. If the shape parameter is not supplied, the matrix dimensions are inferred from the index arrays.

  Notes

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

  Summary of BSR format

  The Block Compressed Row (BSR) format is very similar to the Compressed Sparse Row (CSR) format. BSR is appropriate for sparse matrices with dense sub matrices like the last example below. Block matrices often arise in vector-valued finite element discretizations. In such cases, BSR is considerably more efficient than CSR and CSC for many sparse arithmetic operations.

  Blocksize

  The blocksize (R,C) must evenly divide the shape of the matrix (M,N). That is, R and C must satisfy the relationship `M % R = 0` and `N % C = 0`.

  If no blocksize is specified, a simple heuristic is applied to determine an appropriate blocksize.

  Examples

      >>> from scipy.sparse import bsr_matrix
      >>> bsr_matrix((3, 4), dtype=np.int8).toarray()
      array([[0, 0, 0, 0],
             [0, 0, 0, 0],
             [0, 0, 0, 0]], dtype=int8)

      >>> row = np.array([0, 0, 1, 2, 2, 2])
      >>> col = np.array([0, 2, 2, 0, 1, 2])
      >>> data = np.array([1, 2, 3 ,4, 5, 6])
      >>> bsr_matrix((data, (row, col)), shape=(3, 3)).toarray()
      array([[1, 0, 2],
             [0, 0, 3],
             [4, 5, 6]])

      >>> indptr = np.array([0, 2, 3, 6])
      >>> indices = np.array([0, 2, 2, 0, 1, 2])
      >>> data = np.array([1, 2, 3, 4, 5, 6]).repeat(4).reshape(6, 2, 2)
      >>> bsr_matrix((data,indices,indptr), shape=(6, 6)).toarray()
      array([[1, 1, 0, 0, 2, 2],
             [1, 1, 0, 0, 2, 2],
             [0, 0, 0, 0, 3, 3],
             [0, 0, 0, 0, 3, 3],
             [4, 4, 5, 5, 6, 6],
             [4, 4, 5, 5, 6, 6]])

  Attributes

  `has_sorted_indices` | Determine whether the matrix has sorted indices

  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 nonzero elements
  data | Data array of the matrix
  indices | BSR format index array
  indptr | BSR format index pointer array
  blocksize | Block size of the matrix

  Methods

  `arcsin`() | Element-wise arcsin.
  `arcsinh`() | Element-wise arcsinh.
  `arctan`() | Element-wise arctan.
  `arctanh`() | Element-wise arctanh.
  `asformat`(format) | Return this matrix in a given sparse format
  `asfptype`() | Upcast matrix to a floating point format (if necessary)
  `astype`(t) |
  `ceil`() | Element-wise ceil.
  `check_format`([full_check]) | check whether the matrix format is valid
  `conj`() |
  `conjugate`() |
  `copy`() |
  `deg2rad`() | Element-wise deg2rad.
  `diagonal`() | Returns the main diagonal of the matrix
  `dot`(other) | Ordinary dot product
  `eliminate_zeros`() |
  `expm1`() | Element-wise expm1.
  `floor`() | Element-wise floor.
  `getH`() |
  `get_shape`() |
  `getcol`(j) | Returns a copy of column j of the matrix, as an (m x 1) sparse matrix (column vector).
  `getdata`(ind) |
  `getformat`() |
  `getmaxprint`() |
  `getnnz`() |
  `getrow`(i) | Returns a copy of row i of the matrix, as a (1 x n) sparse matrix (row vector).
  `log1p`() | Element-wise log1p.
  `matmat`(other) |
  `matvec`(other) |
  `max`([axis]) | Maximum of the elements of this matrix.
  `maximum`(other) |
  `mean`([axis]) | Average the matrix over the given axis.
  `min`([axis]) | Minimum of the elements of this matrix.
  `minimum`(other) |
  `multiply`(other) | Point-wise multiplication by another matrix, vector, or scalar.
  `nonzero`() | nonzero indices
  `power`(n[, dtype]) | This function performs element-wise power.
  `prune`() | Remove empty space after all non-zero elements.
  `rad2deg`() | Element-wise rad2deg.
  `reshape`(shape) |
  `rint`() | Element-wise rint.
  `set_shape`(shape) |
  `setdiag`(values[, k]) | Set diagonal or off-diagonal elements of the array.
  `sign`() | Element-wise sign.
  `sin`() | Element-wise sin.
  `sinh`() | Element-wise sinh.
  `sort_indices`() | Sort the indices of this matrix in place
  `sorted_indices`() | Return a copy of this matrix with sorted indices
  `sqrt`() | Element-wise sqrt.
  `sum`([axis]) | Sum the matrix over the given axis.
  `sum_duplicates`() |
  `tan`() | Element-wise tan.
  `tanh`() | Element-wise tanh.
  `toarray`([order, out]) | See the docstring for `spmatrix.toarray`.
  `tobsr`([blocksize, copy]) |
  `tocoo`([copy]) | Convert this matrix to COOrdinate format.
  `tocsc`() |
  `tocsr`() |
  `todense`([order, out]) | Return a dense matrix representation of this matrix.
  `todia`() |
  `todok`() |
  `tolil`() |
  `transpose`() |
  `trunc`() | Element-wise trunc.