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"""
=====================================
Sparse matrices (:mod:`scipy.sparse`)
=====================================
.. currentmodule:: scipy.sparse
SciPy 2-D sparse matrix package.
Contents
========
Sparse matrix classes
---------------------
.. autosummary::
:toctree: generated/
bsr_matrix - Block Sparse Row matrix
coo_matrix - A sparse matrix in COOrdinate format
csc_matrix - Compressed Sparse Column matrix
csr_matrix - Compressed Sparse Row matrix
dia_matrix - Sparse matrix with DIAgonal storage
dok_matrix - Dictionary Of Keys based sparse matrix
lil_matrix - Row-based linked list sparse matrix
Functions
---------
Building sparse matrices:
.. autosummary::
:toctree: generated/
eye - Sparse MxN matrix whose k-th diagonal is all ones
identity - Identity matrix in sparse format
kron - kronecker product of two sparse matrices
kronsum - kronecker sum of sparse matrices
spdiags - Return a sparse matrix from diagonals
tril - Lower triangular portion of a matrix in sparse format
triu - Upper triangular portion of a matrix in sparse format
bmat - Build a sparse matrix from sparse sub-blocks
hstack - Stack sparse matrices horizontally (column wise)
vstack - Stack sparse matrices vertically (row wise)
rand - Random values in a given shape
Identifying sparse matrices:
.. autosummary::
:toctree: generated/
issparse
isspmatrix
isspmatrix_csc
isspmatrix_csr
isspmatrix_bsr
isspmatrix_lil
isspmatrix_dok
isspmatrix_coo
isspmatrix_dia
Graph algorithms:
.. autosummary::
:toctree: generated/
cs_graph_components -- Determine connected components of a graph
Exceptions
----------
.. autosummary::
:toctree: generated/
SparseEfficiencyWarning
SparseWarning
Usage information
=================
There are seven available sparse matrix types:
1. csc_matrix: Compressed Sparse Column format
2. csr_matrix: Compressed Sparse Row format
3. bsr_matrix: Block Sparse Row format
4. lil_matrix: List of Lists format
5. dok_matrix: Dictionary of Keys format
6. coo_matrix: COOrdinate format (aka IJV, triplet format)
7. dia_matrix: DIAgonal format
To construct a matrix efficiently, use either lil_matrix (recommended) or
dok_matrix. The lil_matrix class supports basic slicing and fancy
indexing with a similar syntax to NumPy arrays. As illustrated below,
the COO format may also be used to efficiently construct matrices.
To perform manipulations such as multiplication or inversion, first
convert the matrix to either CSC or CSR format. The lil_matrix format is
row-based, so conversion to CSR is efficient, whereas conversion to CSC
is less so.
All conversions among the CSR, CSC, and COO formats are efficient,
linear-time operations.
Example 1
---------
Construct a 1000x1000 lil_matrix and add some values to it:
>>> from scipy.sparse import lil_matrix
>>> from scipy.sparse.linalg import spsolve
>>> from numpy.linalg import solve, norm
>>> from numpy.random import rand
>>> A = lil_matrix((1000, 1000))
>>> A[0, :100] = rand(100)
>>> A[1, 100:200] = A[0, :100]
>>> A.setdiag(rand(1000))
Now convert it to CSR format and solve A x = b for x:
>>> A = A.tocsr()
>>> b = rand(1000)
>>> x = spsolve(A, b)
Convert it to a dense matrix and solve, and check that the result
is the same:
>>> x_ = solve(A.todense(), b)
Now we can compute norm of the error with:
>>> err = norm(x-x_)
>>> err < 1e-10
True
It should be small :)
Example 2
---------
Construct a matrix in COO format:
>>> from scipy import sparse
>>> from numpy import array
>>> I = array([0,3,1,0])
>>> J = array([0,3,1,2])
>>> V = array([4,5,7,9])
>>> A = sparse.coo_matrix((V,(I,J)),shape=(4,4))
Notice that the indices do not need to be sorted.
Duplicate (i,j) entries are summed when converting to CSR or CSC.
>>> I = array([0,0,1,3,1,0,0])
>>> J = array([0,2,1,3,1,0,0])
>>> V = array([1,1,1,1,1,1,1])
>>> B = sparse.coo_matrix((V,(I,J)),shape=(4,4)).tocsr()
This is useful for constructing finite-element stiffness and mass matrices.
Further Details
---------------
CSR column indices are not necessarily sorted. Likewise for CSC row
indices. Use the .sorted_indices() and .sort_indices() methods when
sorted indices are required (e.g. when passing data to other libraries).
"""
# Original code by Travis Oliphant.
# Modified and extended by Ed Schofield, Robert Cimrman, and Nathan Bell.
from base import *
from csr import *
from csc import *
from lil import *
from dok import *
from coo import *
from dia import *
from bsr import *
from csgraph import *
from construct import *
from extract import *
#from spfuncs import *
__all__ = filter(lambda s:not s.startswith('_'),dir())
from numpy.testing import Tester
test = Tester().test
bench = Tester().bench
|
