scipy.sparse.

dia_array#

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

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

dtypedtype

Data type of the array

shape2-tuple

Shape of the array

ndimint

Number of dimensions (this is always 2)

formatstr

Format string for matrix.

nnzint

Number of stored values, including explicit zeros.

sizeint

Number of stored values.

Tdia_array

Transpose.

mTdia_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.]])
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