Skip to main content
`Ctrl`+`K`
scipy.sparse.

# dia_array

class scipy.sparse.dia_array(arg1, shape=None, dtype=None, copy=False, *, maxprint=None)

  Sparse array with DIAgonal storage.

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

      where D is a 2-D ndarray

    dia_array(S)

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

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

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

    dia_array((data, offsets), shape=(M, N))

      where the `data[k,:]` stores the diagonal entries for diagonal `offsets[k]` (See example below)

  Attributes:
    data

      DIA format data array of the array

    offsets

      DIA format offset array of the array

    dtype dtype

      Data type of the array

    shape 2-tuple

      Shape of the array

    ndim int

      Number of dimensions (this is always 2)

    `format` str

      Format string for matrix.

    `nnz` int

      Number of stored values, including explicit zeros.

    `size` int

      Number of stored values.

    `T` dia_array

      Transpose.

    `mT` dia_array

      Matrix transpose.

  Methods

  `__len__`() |
  `arcsin`() | Element-wise arcsin.
  `arcsinh`() | Element-wise arcsinh.
  `arctan`() | Element-wise arctan.
  `arctanh`() | Element-wise arctanh.
  `asformat`(format[, copy]) | Return this array/matrix in the passed format.
  `astype`(dtype[, casting, copy]) | Cast the array/matrix 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/matrix.
  `count_nonzero`([axis]) | Number of non-zero entries.
  `deg2rad`() | Element-wise deg2rad.
  `diagonal`([k]) | Returns the kth diagonal of the array/matrix.
  `dot`(other) | Ordinary dot product.
  `expm1`() | Element-wise expm1.
  `floor`() | Element-wise floor.
  `log1p`() | Element-wise log1p.
  `maximum`(other) | Element-wise maximum between this and another array/matrix.
  `mean`([axis, dtype, out]) | Compute the arithmetic mean along the specified axis.
  `minimum`(other) | Element-wise minimum between this and another array/matrix.
  `multiply`(other) | Element-wise multiplication by another array/matrix.
  `nonzero`() | Nonzero indices of the array/matrix.
  `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/matrix without changing its data.
  `resize`(*shape) | Resize the array/matrix in-place to dimensions given by `shape`.
  `rint`() | Element-wise rint.
  `setdiag`(values[, k]) | Set diagonal or off-diagonal elements of the array/matrix.
  `sign`() | Element-wise sign.
  `sin`() | Element-wise sin.
  `sinh`() | Element-wise sinh.
  `sqrt`() | Element-wise sqrt.
  `sum`([axis, dtype, out]) | Sum the array/matrix elements over a given axis.
  `tan`() | Element-wise tan.
  `tanh`() | Element-wise tanh.
  `toarray`([order, out]) | Return a dense ndarray representation of this sparse array/matrix.
  `tobsr`([blocksize, copy]) | Convert this array/matrix to Block Sparse Row format.
  `tocoo`([copy]) | Convert this array/matrix to COOrdinate format.
  `tocsc`([copy]) | Convert this array/matrix to Compressed Sparse Column format.
  `tocsr`([copy]) | Convert this array/matrix to Compressed Sparse Row format.
  `todense`([order, out]) | Return a dense representation of this sparse array.
  `todia`([copy]) | Convert this array/matrix to sparse DIAgonal format.
  `todok`([copy]) | Convert this array/matrix to Dictionary Of Keys format.
  `tolil`([copy]) | Convert this array/matrix to List of Lists format.
  `trace`([offset]) | Returns the sum along diagonals of the sparse array/matrix.
  `transpose`([axes, copy]) | Reverses the dimensions of the sparse array/matrix.
  `trunc`() | Element-wise trunc.

  __add__ |
  __matmul__ |
  __mul__ |
  __pow__ |
  __rmatmul__ |
  __rmul__ |
  __truediv__ |

  Notes

  Sparse arrays can be used in arithmetic operations: they support addition, subtraction, multiplication, division, and matrix power. Sparse arrays with DIAgonal storage do not support slicing.

  Format details

  The `data` array stores the diagonal elements. The alignment of these elements within the rows of `data` depends on their position relative to the main diagonal:

  - Main diagonal (`offsets[i] == 0`): Elements start at column 0.

  - Super-diagonals (`offsets[i] > 0`): Elements are right-aligned (padded with zeros on the left).

  - Sub-diagonals (`offsets[i] < 0`): Elements are left-aligned (padded with zeros on the right).

  Each column of `data` corresponds to a diagonal in the resulting matrix.

  Mathematically, the element at row `r` and column `c` of the matrix is stored in the `data` array at row `i` and column `c - max(0, -offsets[i])`, where `i` is the index of the diagonal in `offsets`.

  Note that if `offsets` is provided in decreasing order, this format matches the BLAS/LAPACK general band format (e.g., as used in `dgbmv`).

  Examples

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

      >>> data = np.array([[1, 2, 3, 4]]).repeat(3, axis=0)
      >>> offsets = np.array([0, -1, 2])
      >>> dia_array((data, offsets), shape=(4, 4)).toarray()
      array([[1, 0, 3, 0],
             [1, 2, 0, 4],
             [0, 2, 3, 0],
             [0, 0, 3, 4]])

      >>> from scipy.sparse import dia_array
      >>> n = 10
      >>> ex = np.ones(n)
      >>> data = np.array([ex, 2 * ex, ex])
      >>> offsets = np.array([-1, 0, 1])
      >>> dia_array((data, offsets), shape=(n, n)).toarray()
      array([[2., 1., 0., ..., 0., 0., 0.],
             [1., 2., 1., ..., 0., 0., 0.],
             [0., 1., 2., ..., 0., 0., 0.],
             ...,
             [0., 0., 0., ..., 2., 1., 0.],
             [0., 0., 0., ..., 1., 2., 1.],
             [0., 0., 0., ..., 0., 1., 2.]])