SciPy

scipy.sparse.diags

scipy.sparse.diags(diagonals, offsets, shape=None, format=None, dtype=None)[source]

Construct a sparse matrix from diagonals.

Parameters:

diagonals : sequence of array_like

Sequence of arrays containing the matrix diagonals, corresponding to offsets.

offsets : sequence of int

Diagonals to set:
  • k = 0 the main diagonal
  • k > 0 the k-th upper diagonal
  • k < 0 the k-th lower diagonal

shape : tuple of int, optional

Shape of the result. If omitted, a square matrix large enough to contain the diagonals is returned.

format : {“dia”, “csr”, “csc”, “lil”, ...}, optional

Matrix format of the result. By default (format=None) an appropriate sparse matrix format is returned. This choice is subject to change.

dtype : dtype, optional

Data type of the matrix.

See also

spdiags
construct matrix from diagonals

Notes

This function differs from spdiags in the way it handles off-diagonals.

The result from diags is the sparse equivalent of:

np.diag(diagonals[0], offsets[0])
+ ...
+ np.diag(diagonals[k], offsets[k])

Repeated diagonal offsets are disallowed.

New in version 0.11.

Examples

>>> from scipy.sparse import diags
>>> diagonals = [[1, 2, 3, 4], [1, 2, 3], [1, 2]]
>>> diags(diagonals, [0, -1, 2]).toarray()
array([[1, 0, 1, 0],
       [1, 2, 0, 2],
       [0, 2, 3, 0],
       [0, 0, 3, 4]])

Broadcasting of scalars is supported (but shape needs to be specified):

>>> diags([1, -2, 1], [-1, 0, 1], shape=(4, 4)).toarray()
array([[-2.,  1.,  0.,  0.],
       [ 1., -2.,  1.,  0.],
       [ 0.,  1., -2.,  1.],
       [ 0.,  0.,  1., -2.]])

If only one diagonal is wanted (as in numpy.diag), the following works as well:

>>> diags([1, 2, 3], 1).toarray()
array([[ 0.,  1.,  0.,  0.],
       [ 0.,  0.,  2.,  0.],
       [ 0.,  0.,  0.,  3.],
       [ 0.,  0.,  0.,  0.]])

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