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Sparse matrices (`scipy.sparse`)

# 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

  `shape` | Get shape of a matrix.
  `nnz` | Number of stored values, including explicit zeros.
  `has_sorted_indices` | Determine whether the matrix has sorted indices

  dtype | (dtype) Data type of the matrix
  ndim | (int) Number of dimensions (this is always 2)
  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.
  `argmax`([axis, out]) | Return indices of minimum elements along an axis.
  `argmin`([axis, out]) | Return indices of minimum elements along an axis.
  `asformat`(format) | Return this matrix in a given sparse format
  `asfptype`() | Upcast matrix to a floating point format (if necessary)
  `astype`(t) | Cast the matrix elements to a specified type.
  `ceil`() | Element-wise ceil.
  `check_format`([full_check]) | check whether the matrix format is valid
  `conj`() | Element-wise complex conjugation.
  `conjugate`() | Element-wise complex conjugation.
  `copy`() | Returns a copy of this matrix.
  `count_nonzero`() | Number of non-zero entries, equivalent to
  `deg2rad`() | Element-wise deg2rad.
  `diagonal`() | Returns the main diagonal of the matrix
  `dot`(other) | Ordinary dot product
  `eliminate_zeros`() | Remove zero elements in-place.
  `expm1`() | Element-wise expm1.
  `floor`() | Element-wise floor.
  `getH`() | Return the Hermitian transpose of this matrix.
  `get_shape`() | Get shape of a matrix.
  `getcol`(j) | Returns a copy of column j of the matrix, as an (m x 1) sparse matrix (column vector).
  `getformat`() | Format of a matrix representation as a string.
  `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 matrix, as a (1 x n) sparse matrix (row vector).
  `log1p`() | Element-wise log1p.
  `matmat`(*args, **kwds) | `matmat` is deprecated!
  `matvec`(*args, **kwds) | `matvec` is deprecated!
  `max`([axis, out]) | Return the maximum of the matrix or maximum along an axis.
  `maximum`(other) | Element-wise maximum between this and another matrix.
  `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 matrix.
  `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[, order]) | Gives a new shape to a sparse matrix without changing its data.
  `rint`() | Element-wise rint.
  `set_shape`(shape) | See `reshape`.
  `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, dtype, out]) | Sum the matrix 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 `spmatrix.toarray`.
  `tobsr`([blocksize, copy]) | Convert this matrix into Block Sparse Row Format.
  `tocoo`([copy]) | Convert this matrix 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 matrix.
  `todia`([copy]) | Convert this matrix to sparse DIAgonal format.
  `todok`([copy]) | Convert this matrix to Dictionary Of Keys format.
  `tolil`([copy]) | Convert this matrix to LInked List format.
  `transpose`([axes, copy]) | Reverses the dimensions of the sparse matrix.
  `trunc`() | Element-wise trunc.