scipy.sparse.

dia_matrix#

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

Sparse matrix with DIAgonal storage.

Warning

SciPy sparse is shifting from a sparse matrix interface to a sparse array interface. In the next few releases we expect to deprecate the sparse matrix interface. For documentation of the matrix interface, see the spmatrix interface docs. For guidance on converting existing code to sparse arrays, see Migration from spmatrix to sparray.

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

where D is a 2-D ndarray

dia_matrix(S)

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

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

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

dia_matrix((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 matrix

offsets

DIA format offset array of the matrix

dtypedtype

Data type of the matrix

shape2-tuple

Shape of the matrix

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_matrix

Transpose.

mTdia_matrix

Matrix transpose.

Methods

__len__()

__mul__(other)

__pow__(power)

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.

asfptype()

Upcast matrix to a floating point format (if necessary)

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.

getH()

Return the Hermitian transpose of this matrix.

get_shape()

Get the shape of the matrix

getcol(j)

Returns a copy of column j of the matrix, as an (m x 1) sparse matrix (column vector).

getformat()

Matrix storage format

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.

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.

set_shape(shape)

Set the shape of the matrix in-place

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 matrix.

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__

__rmatmul__

__rmul__

__truediv__

Notes

Sparse matrices 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_matrix
>>> dia_matrix((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_matrix((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_matrix
>>> n = 10
>>> ex = np.ones(n)
>>> data = np.array([ex, 2 * ex, ex])
>>> offsets = np.array([-1, 0, 1])
>>> dia_matrix((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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