Coverage for /pythoncovmergedfiles/medio/medio/usr/local/lib/python3.9/dist-packages/scipy/sparse/__init__.py: 100%
20 statements
« prev ^ index » next coverage.py v7.3.1, created at 2023-09-23 06:43 +0000
1"""
2=====================================
3Sparse matrices (:mod:`scipy.sparse`)
4=====================================
6.. currentmodule:: scipy.sparse
8.. toctree::
9 :hidden:
11 sparse.csgraph
12 sparse.linalg
14SciPy 2-D sparse array package for numeric data.
16.. note::
18 This package is switching to an array interface, compatible with
19 NumPy arrays, from the older matrix interface. We recommend that
20 you use the array objects (`bsr_array`, `coo_array`, etc.) for
21 all new work.
23 When using the array interface, please note that:
25 - ``x * y`` no longer performs matrix multiplication, but
26 element-wise multiplication (just like with NumPy arrays). To
27 make code work with both arrays and matrices, use ``x @ y`` for
28 matrix multiplication.
29 - Operations such as `sum`, that used to produce dense matrices, now
30 produce arrays, whose multiplication behavior differs similarly.
31 - Sparse arrays currently must be two-dimensional. This also means
32 that all *slicing* operations on these objects must produce
33 two-dimensional results, or they will result in an error. This
34 will be addressed in a future version.
36 The construction utilities (`eye`, `kron`, `random`, `diags`, etc.)
37 have not yet been ported, but their results can be wrapped into arrays::
39 A = csr_array(eye(3))
41Contents
42========
44Sparse array classes
45--------------------
47.. autosummary::
48 :toctree: generated/
50 bsr_array - Block Sparse Row array
51 coo_array - A sparse array in COOrdinate format
52 csc_array - Compressed Sparse Column array
53 csr_array - Compressed Sparse Row array
54 dia_array - Sparse array with DIAgonal storage
55 dok_array - Dictionary Of Keys based sparse array
56 lil_array - Row-based list of lists sparse array
57 sparray - Sparse array base class
59Sparse matrix classes
60---------------------
62.. autosummary::
63 :toctree: generated/
65 bsr_matrix - Block Sparse Row matrix
66 coo_matrix - A sparse matrix in COOrdinate format
67 csc_matrix - Compressed Sparse Column matrix
68 csr_matrix - Compressed Sparse Row matrix
69 dia_matrix - Sparse matrix with DIAgonal storage
70 dok_matrix - Dictionary Of Keys based sparse matrix
71 lil_matrix - Row-based list of lists sparse matrix
72 spmatrix - Sparse matrix base class
74Functions
75---------
77Building sparse arrays:
79.. autosummary::
80 :toctree: generated/
82 diags_array - Return a sparse array from diagonals
84Building sparse matrices:
86.. autosummary::
87 :toctree: generated/
89 eye - Sparse MxN matrix whose k-th diagonal is all ones
90 identity - Identity matrix in sparse format
91 kron - kronecker product of two sparse matrices
92 kronsum - kronecker sum of sparse matrices
93 diags - Return a sparse matrix from diagonals
94 spdiags - Return a sparse matrix from diagonals
95 block_diag - Build a block diagonal sparse matrix
96 tril - Lower triangular portion of a matrix in sparse format
97 triu - Upper triangular portion of a matrix in sparse format
98 block - Build a sparse array from sub-blocks
99 bmat - Build a sparse matrix from sub-blocks
100 hstack - Stack sparse matrices horizontally (column wise)
101 vstack - Stack sparse matrices vertically (row wise)
102 rand - Random values in a given shape
103 random - Random values in a given shape
105Save and load sparse matrices:
107.. autosummary::
108 :toctree: generated/
110 save_npz - Save a sparse matrix to a file using ``.npz`` format.
111 load_npz - Load a sparse matrix from a file using ``.npz`` format.
113Sparse matrix tools:
115.. autosummary::
116 :toctree: generated/
118 find
120Identifying sparse matrices:
122.. autosummary::
123 :toctree: generated/
125 issparse
126 isspmatrix
127 isspmatrix_csc
128 isspmatrix_csr
129 isspmatrix_bsr
130 isspmatrix_lil
131 isspmatrix_dok
132 isspmatrix_coo
133 isspmatrix_dia
135Submodules
136----------
138.. autosummary::
140 csgraph - Compressed sparse graph routines
141 linalg - sparse linear algebra routines
143Exceptions
144----------
146.. autosummary::
147 :toctree: generated/
149 SparseEfficiencyWarning
150 SparseWarning
153Usage information
154=================
156There are seven available sparse array types:
158 1. `csc_array`: Compressed Sparse Column format
159 2. `csr_array`: Compressed Sparse Row format
160 3. `bsr_array`: Block Sparse Row format
161 4. `lil_array`: List of Lists format
162 5. `dok_array`: Dictionary of Keys format
163 6. `coo_array`: COOrdinate format (aka IJV, triplet format)
164 7. `dia_array`: DIAgonal format
166To construct an array efficiently, use either `dok_array` or `lil_array`.
167The `lil_array` class supports basic slicing and fancy indexing with a
168similar syntax to NumPy arrays. As illustrated below, the COO format
169may also be used to efficiently construct arrays. Despite their
170similarity to NumPy arrays, it is **strongly discouraged** to use NumPy
171functions directly on these arrays because NumPy may not properly convert
172them for computations, leading to unexpected (and incorrect) results. If you
173do want to apply a NumPy function to these arrays, first check if SciPy has
174its own implementation for the given sparse array class, or **convert the
175sparse array to a NumPy array** (e.g., using the ``toarray`` method of the
176class) first before applying the method.
178To perform manipulations such as multiplication or inversion, first
179convert the array to either CSC or CSR format. The `lil_array` format is
180row-based, so conversion to CSR is efficient, whereas conversion to CSC
181is less so.
183All conversions among the CSR, CSC, and COO formats are efficient,
184linear-time operations.
186Matrix vector product
187---------------------
188To do a vector product between a sparse array and a vector simply use
189the array ``dot`` method, as described in its docstring:
191>>> import numpy as np
192>>> from scipy.sparse import csr_array
193>>> A = csr_array([[1, 2, 0], [0, 0, 3], [4, 0, 5]])
194>>> v = np.array([1, 0, -1])
195>>> A.dot(v)
196array([ 1, -3, -1], dtype=int64)
198.. warning:: As of NumPy 1.7, ``np.dot`` is not aware of sparse arrays,
199 therefore using it will result on unexpected results or errors.
200 The corresponding dense array should be obtained first instead:
202 >>> np.dot(A.toarray(), v)
203 array([ 1, -3, -1], dtype=int64)
205 but then all the performance advantages would be lost.
207The CSR format is especially suitable for fast matrix vector products.
209Example 1
210---------
211Construct a 1000x1000 `lil_array` and add some values to it:
213>>> from scipy.sparse import lil_array
214>>> from scipy.sparse.linalg import spsolve
215>>> from numpy.linalg import solve, norm
216>>> from numpy.random import rand
218>>> A = lil_array((1000, 1000))
219>>> A[0, :100] = rand(100)
220>>> A[1, 100:200] = A[0, :100]
221>>> A.setdiag(rand(1000))
223Now convert it to CSR format and solve A x = b for x:
225>>> A = A.tocsr()
226>>> b = rand(1000)
227>>> x = spsolve(A, b)
229Convert it to a dense array and solve, and check that the result
230is the same:
232>>> x_ = solve(A.toarray(), b)
234Now we can compute norm of the error with:
236>>> err = norm(x-x_)
237>>> err < 1e-10
238True
240It should be small :)
243Example 2
244---------
246Construct an array in COO format:
248>>> from scipy import sparse
249>>> from numpy import array
250>>> I = array([0,3,1,0])
251>>> J = array([0,3,1,2])
252>>> V = array([4,5,7,9])
253>>> A = sparse.coo_array((V,(I,J)),shape=(4,4))
255Notice that the indices do not need to be sorted.
257Duplicate (i,j) entries are summed when converting to CSR or CSC.
259>>> I = array([0,0,1,3,1,0,0])
260>>> J = array([0,2,1,3,1,0,0])
261>>> V = array([1,1,1,1,1,1,1])
262>>> B = sparse.coo_array((V,(I,J)),shape=(4,4)).tocsr()
264This is useful for constructing finite-element stiffness and mass matrices.
266Further details
267---------------
269CSR column indices are not necessarily sorted. Likewise for CSC row
270indices. Use the ``.sorted_indices()`` and ``.sort_indices()`` methods when
271sorted indices are required (e.g., when passing data to other libraries).
273"""
275# Original code by Travis Oliphant.
276# Modified and extended by Ed Schofield, Robert Cimrman,
277# Nathan Bell, and Jake Vanderplas.
279import warnings as _warnings
281from ._base import *
282from ._csr import *
283from ._csc import *
284from ._lil import *
285from ._dok import *
286from ._coo import *
287from ._dia import *
288from ._bsr import *
289from ._construct import *
290from ._extract import *
291from ._matrix import spmatrix
292from ._matrix_io import *
294# For backward compatibility with v0.19.
295from . import csgraph
297# Deprecated namespaces, to be removed in v2.0.0
298from . import (
299 base, bsr, compressed, construct, coo, csc, csr, data, dia, dok, extract,
300 lil, sparsetools, sputils
301)
303__all__ = [s for s in dir() if not s.startswith('_')]
305# Filter PendingDeprecationWarning for np.matrix introduced with numpy 1.15
306_warnings.filterwarnings('ignore', message='the matrix subclass is not the recommended way')
308from scipy._lib._testutils import PytestTester
309test = PytestTester(__name__)
310del PytestTester