add padding function to imgScalePadding()
This commit is contained in:
@@ -1,298 +0,0 @@
|
||||
"""
|
||||
=====================================
|
||||
Sparse matrices (:mod:`scipy.sparse`)
|
||||
=====================================
|
||||
|
||||
.. currentmodule:: scipy.sparse
|
||||
|
||||
SciPy 2-D sparse array package for numeric data.
|
||||
|
||||
.. note::
|
||||
|
||||
This package is switching to an array interface, compatible with
|
||||
NumPy arrays, from the older matrix interface. We recommend that
|
||||
you use the array objects (`bsr_array`, `coo_array`, etc.) for
|
||||
all new work.
|
||||
|
||||
When using the array interface, please note that:
|
||||
|
||||
- ``x * y`` no longer performs matrix multiplication, but
|
||||
element-wise multiplication (just like with NumPy arrays). To
|
||||
make code work with both arrays and matrices, use ``x @ y`` for
|
||||
matrix multiplication.
|
||||
- Operations such as `sum`, that used to produce dense matrices, now
|
||||
produce arrays, whose multiplication behavior differs similarly.
|
||||
- Sparse arrays currently must be two-dimensional. This also means
|
||||
that all *slicing* operations on these objects must produce
|
||||
two-dimensional results, or they will result in an error. This
|
||||
will be addressed in a future version.
|
||||
|
||||
The construction utilities (`eye`, `kron`, `random`, `diags`, etc.)
|
||||
have not yet been ported, but their results can be wrapped into arrays::
|
||||
|
||||
A = csr_array(eye(3))
|
||||
|
||||
Contents
|
||||
========
|
||||
|
||||
Sparse array classes
|
||||
--------------------
|
||||
|
||||
.. autosummary::
|
||||
:toctree: generated/
|
||||
|
||||
bsr_array - Block Sparse Row array
|
||||
coo_array - A sparse array in COOrdinate format
|
||||
csc_array - Compressed Sparse Column array
|
||||
csr_array - Compressed Sparse Row array
|
||||
dia_array - Sparse array with DIAgonal storage
|
||||
dok_array - Dictionary Of Keys based sparse array
|
||||
lil_array - Row-based list of lists sparse array
|
||||
|
||||
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 list of lists sparse matrix
|
||||
spmatrix - Sparse matrix base class
|
||||
|
||||
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
|
||||
diags - Return a sparse matrix from diagonals
|
||||
spdiags - Return a sparse matrix from diagonals
|
||||
block_diag - Build a block diagonal sparse matrix
|
||||
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
|
||||
random - Random values in a given shape
|
||||
|
||||
Save and load sparse matrices:
|
||||
|
||||
.. autosummary::
|
||||
:toctree: generated/
|
||||
|
||||
save_npz - Save a sparse matrix to a file using ``.npz`` format.
|
||||
load_npz - Load a sparse matrix from a file using ``.npz`` format.
|
||||
|
||||
Sparse matrix tools:
|
||||
|
||||
.. autosummary::
|
||||
:toctree: generated/
|
||||
|
||||
find
|
||||
|
||||
Identifying sparse matrices:
|
||||
|
||||
.. autosummary::
|
||||
:toctree: generated/
|
||||
|
||||
issparse
|
||||
isspmatrix
|
||||
isspmatrix_csc
|
||||
isspmatrix_csr
|
||||
isspmatrix_bsr
|
||||
isspmatrix_lil
|
||||
isspmatrix_dok
|
||||
isspmatrix_coo
|
||||
isspmatrix_dia
|
||||
|
||||
Submodules
|
||||
----------
|
||||
|
||||
.. autosummary::
|
||||
|
||||
csgraph - Compressed sparse graph routines
|
||||
linalg - sparse linear algebra routines
|
||||
|
||||
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 dok_matrix or lil_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. Despite their
|
||||
similarity to NumPy arrays, it is **strongly discouraged** to use NumPy
|
||||
functions directly on these matrices because NumPy may not properly convert
|
||||
them for computations, leading to unexpected (and incorrect) results. If you
|
||||
do want to apply a NumPy function to these matrices, first check if SciPy has
|
||||
its own implementation for the given sparse matrix class, or **convert the
|
||||
sparse matrix to a NumPy array** (e.g., using the `toarray()` method of the
|
||||
class) first before applying the method.
|
||||
|
||||
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.
|
||||
|
||||
Matrix vector product
|
||||
---------------------
|
||||
To do a vector product between a sparse matrix and a vector simply use
|
||||
the matrix `dot` method, as described in its docstring:
|
||||
|
||||
>>> import numpy as np
|
||||
>>> from scipy.sparse import csr_matrix
|
||||
>>> A = csr_matrix([[1, 2, 0], [0, 0, 3], [4, 0, 5]])
|
||||
>>> v = np.array([1, 0, -1])
|
||||
>>> A.dot(v)
|
||||
array([ 1, -3, -1], dtype=int64)
|
||||
|
||||
.. warning:: As of NumPy 1.7, `np.dot` is not aware of sparse matrices,
|
||||
therefore using it will result on unexpected results or errors.
|
||||
The corresponding dense array should be obtained first instead:
|
||||
|
||||
>>> np.dot(A.toarray(), v)
|
||||
array([ 1, -3, -1], dtype=int64)
|
||||
|
||||
but then all the performance advantages would be lost.
|
||||
|
||||
The CSR format is specially suitable for fast matrix vector products.
|
||||
|
||||
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.toarray(), 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,
|
||||
# Nathan Bell, and Jake Vanderplas.
|
||||
|
||||
import warnings as _warnings
|
||||
|
||||
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 ._construct import *
|
||||
from ._extract import *
|
||||
from ._matrix_io import *
|
||||
|
||||
from ._arrays import (
|
||||
csr_array, csc_array, lil_array, dok_array, coo_array, dia_array, bsr_array
|
||||
)
|
||||
|
||||
# For backward compatibility with v0.19.
|
||||
from . import csgraph
|
||||
|
||||
# Deprecated namespaces, to be removed in v2.0.0
|
||||
from . import (
|
||||
base, bsr, compressed, construct, coo, csc, csr, data, dia, dok, extract,
|
||||
lil, sparsetools, sputils
|
||||
)
|
||||
|
||||
__all__ = [s for s in dir() if not s.startswith('_')]
|
||||
|
||||
# Filter PendingDeprecationWarning for np.matrix introduced with numpy 1.15
|
||||
_warnings.filterwarnings('ignore', message='the matrix subclass is not the recommended way')
|
||||
|
||||
from scipy._lib._testutils import PytestTester
|
||||
test = PytestTester(__name__)
|
||||
del PytestTester
|
||||
Reference in New Issue
Block a user