scipy.sparse 文档如何查找及使用
如果想真正的查看底层的代码，以及每一种存储方式的优缺点请点击：https://github.com/scipy/scipy/blob/v1.1.0/scipy/sparse/
下面以dok_matrix为例，源代码网址：https://github.com/scipy/scipy/blob/v1.1.0/scipy/sparse/dok.py
"""Dictionary Of Keys based matrix"""
from __future__ import division, print_function, absolute_import
__docformat__ = "restructuredtext en"
__all__ = ['dok_matrix', 'isspmatrix_dok']
import functools
import operator
import itertools
import numpy as np
from scipy._lib.six import zip as izip, xrange, iteritems, iterkeys, itervalues
from .base import spmatrix, isspmatrix
from .sputils import (isdense, getdtype, isshape, isintlike, isscalarlike,
upcast, upcast_scalar, IndexMixin, get_index_dtype,
check_shape)
try:
from operator import isSequenceType as _is_sequence
except ImportError:
def _is_sequence(x):
return (hasattr(x, '__len__') or hasattr(x, '__next__')
or hasattr(x, 'next'))
class dok_matrix(spmatrix, IndexMixin, dict):
"""
Dictionary Of Keys based sparse matrix.
This is an efficient structure for constructing sparse
matrices incrementally.
This can be instantiated in several ways:
dok_matrix(D)
with a dense matrix, D
dok_matrix(S)
with a sparse matrix, S
dok_matrix((M,N), [dtype])
create the matrix with initial shape (M,N)
dtype is optional, defaulting to dtype='d'
Attributes
----------
dtype : dtype
Data type of the matrix
shape : 2-tuple
Shape of the matrix
ndim : int
Number of dimensions (this is always 2)
nnz
Number of nonzero elements
Notes
-----
Sparse matrices can be used in arithmetic operations: they support
addition, subtraction, multiplication, division, and matrix power.
Allows for efficient O(1) access of individual elements.
Duplicates are not allowed.
Can be efficiently converted to a coo_matrix once constructed.
Examples
--------
>>> import numpy as np
>>> from scipy.sparse import dok_matrix
>>> S = dok_matrix((5, 5), dtype=np.float32)
>>> for i in range(5):
... for j in range(5):
... S[i, j] = i + j # Update element
"""
format = 'dok'
def __init__(self, arg1, shape=None, dtype=None, copy=False):
dict.__init__(self)
spmatrix.__init__(self)
self.dtype = getdtype(dtype, default=float)
if isinstance(arg1, tuple) and isshape(arg1): # (M,N)
M, N = arg1
self._shape = check_shape((M, N))
elif isspmatrix(arg1): # Sparse ctor
if isspmatrix_dok(arg1) and copy:
arg1 = arg1.copy()
else:
arg1 = arg1.todok()
if dtype is not None:
arg1 = arg1.astype(dtype)
dict.update(self, arg1)
self._shape = check_shape(arg1.shape)
self.dtype = arg1.dtype
else: # Dense ctor
try:
arg1 = np.asarray(arg1)
except:
raise TypeError('Invalid input format.')
if len(arg1.shape) != 2:
raise TypeError('Expected rank <=2 dense array or matrix.')
from .coo import coo_matrix
d = coo_matrix(arg1, dtype=dtype).todok()
dict.update(self, d)
self._shape = check_shape(arg1.shape)
self.dtype = d.dtype
def update(self, val):
# Prevent direct usage of update
raise NotImplementedError("Direct modification to dok_matrix element "
"is not allowed.")
def _update(self, data):
"""An update method for dict data defined for direct access to
`dok_matrix` data. Main purpose is to be used for effcient conversion
from other spmatrix classes. Has no checking if `data` is valid."""
return dict.update(self, data)
def set_shape(self, shape):
new_matrix = self.reshape(shape, copy=False).asformat(self.format)
self.__dict__ = new_matrix.__dict__
dict.clear(self)
dict.update(self, new_matrix)
shape = property(fget=spmatrix.get_shape, fset=set_shape)
def getnnz(self, axis=None):
if axis is not None:
raise NotImplementedError("getnnz over an axis is not implemented "
"for DOK format.")
return dict.__len__(self)
def count_nonzero(self):
return sum(x != 0 for x in itervalues(self))
getnnz.__doc__ = spmatrix.getnnz.__doc__
count_nonzero.__doc__ = spmatrix.count_nonzero.__doc__
def __len__(self):
return dict.__len__(self)
def get(self, key, default=0.):
"""This overrides the dict.get method, providing type checking
but otherwise equivalent functionality.
"""
try:
i, j = key
assert isintlike(i) and isintlike(j)
except (AssertionError, TypeError, ValueError):
raise IndexError('Index must be a pair of integers.')
if (i < 0 or i >= self.shape[0] or j < 0 or j >= self.shape[1]):
raise IndexError('Index out of bounds.')
return dict.get(self, key, default)
def __getitem__(self, index):
"""If key=(i, j) is a pair of integers, return the corresponding
element. If either i or j is a slice or sequence, return a new sparse
matrix with just these elements.
"""
zero = self.dtype.type(0)
i, j = self._unpack_index(index)
i_intlike = isintlike(i)
j_intlike = isintlike(j)
if i_intlike and j_intlike:
i = int(i)
j = int(j)
if i < 0:
i += self.shape[0]
if i < 0 or i >= self.shape[0]:
raise IndexError('Index out of bounds.')
if j < 0:
j += self.shape[1]
if j < 0 or j >= self.shape[1]:
raise IndexError('Index out of bounds.')
return dict.get(self, (i,j), zero)
elif ((i_intlike or isinstance(i, slice)) and
(j_intlike or isinstance(j, slice))):
# Fast path for slicing very sparse matrices
i_slice = slice(i, i+1) if i_intlike else i
j_slice = slice(j, j+1) if j_intlike else j
i_indices = i_slice.indices(self.shape[0])
j_indices = j_slice.indices(self.shape[1])
i_seq = xrange(*i_indices)
j_seq = xrange(*j_indices)
newshape = (len(i_seq), len(j_seq))
newsize = _prod(newshape)
if len(self) < 2*newsize and newsize != 0:
# Switch to the fast path only when advantageous
# (count the iterations in the loops, adjust for complexity)
#
# We also don't handle newsize == 0 here (if
# i/j_intlike, it can mean index i or j was out of
# bounds)
return self._getitem_ranges(i_indices, j_indices, newshape)
i, j = self._index_to_arrays(i, j)
if i.size == 0:
return dok_matrix(i.shape, dtype=self.dtype)
min_i = i.min()
if min_i < -self.shape[0] or i.max() >= self.shape[0]:
raise IndexError('Index (%d) out of range -%d to %d.' %
(i.min(), self.shape[0], self.shape[0]-1))
if min_i < 0:
i = i.copy()
i[i < 0] += self.shape[0]
min_j = j.min()
if min_j < -self.shape[1] or j.max() >= self.shape[1]:
raise IndexError('Index (%d) out of range -%d to %d.' %
(j.min(), self.shape[1], self.shape[1]-1))
if min_j < 0:
j = j.copy()
j[j < 0] += self.shape[1]
newdok = dok_matrix(i.shape, dtype=self.dtype)
for key in itertools.product(xrange(i.shape[0]), xrange(i.shape[1])):
v = dict.get(self, (i[key], j[key]), zero)
if v:
dict.__setitem__(newdok, key, v)
return newdok
def _getitem_ranges(self, i_indices, j_indices, shape):
# performance golf: we don't want Numpy scalars here, they are slow
i_start, i_stop, i_stride = map(int, i_indices)
j_start, j_stop, j_stride = map(int, j_indices)
newdok = dok_matrix(shape, dtype=self.dtype)
for (ii, jj) in iterkeys(self):
# ditto for numpy scalars
ii = int(ii)
jj = int(jj)
a, ra = divmod(ii - i_start, i_stride)
if a < 0 or a >= shape[0] or ra != 0:
continue
b, rb = divmod(jj - j_start, j_stride)
if b < 0 or b >= shape[1] or rb != 0:
continue
dict.__setitem__(newdok, (a, b),
dict.__getitem__(self, (ii, jj)))
return newdok
def __setitem__(self, index, x):
if isinstance(index, tuple) and len(index) == 2:
# Integer index fast path
i, j = index
if (isintlike(i) and isintlike(j) and 0 <= i < self.shape[0]
and 0 <= j < self.shape[1]):
v = np.asarray(x, dtype=self.dtype)
if v.ndim == 0 and v != 0:
dict.__setitem__(self, (int(i), int(j)), v[()])
return
i, j = self._unpack_index(index)
i, j = self._index_to_arrays(i, j)
if isspmatrix(x):
x = x.toarray()
# Make x and i into the same shape
x = np.asarray(x, dtype=self.dtype)
x, _ = np.broadcast_arrays(x, i)
if x.shape != i.shape:
raise ValueError("Shape mismatch in assignment.")
if np.size(x) == 0:
return
min_i = i.min()
if min_i < -self.shape[0] or i.max() >= self.shape[0]:
raise IndexError('Index (%d) out of range -%d to %d.' %
(i.min(), self.shape[0], self.shape[0]-1))
if min_i < 0:
i = i.copy()
i[i < 0] += self.shape[0]
min_j = j.min()
if min_j < -self.shape[1] or j.max() >= self.shape[1]:
raise IndexError('Index (%d) out of range -%d to %d.' %
(j.min(), self.shape[1], self.shape[1]-1))
if min_j < 0:
j = j.copy()
j[j < 0] += self.shape[1]
dict.update(self, izip(izip(i.flat, j.flat), x.flat))
if 0 in x:
zeroes = x == 0
for key in izip(i[zeroes].flat, j[zeroes].flat):
if dict.__getitem__(self, key) == 0:
# may have been superseded by later update
del self[key]
def __add__(self, other):
if isscalarlike(other):
res_dtype = upcast_scalar(self.dtype, other)
new = dok_matrix(self.shape, dtype=res_dtype)
# Add this scalar to every element.
M, N = self.shape
for key in itertools.product(xrange(M), xrange(N)):
aij = dict.get(self, (key), 0) + other
if aij:
new[key] = aij
# new.dtype.char = self.dtype.char
elif isspmatrix_dok(other):
if other.shape != self.shape:
raise ValueError("Matrix dimensions are not equal.")
# We could alternatively set the dimensions to the largest of
# the two matrices to be summed. Would this be a good idea?
res_dtype = upcast(self.dtype, other.dtype)
new = dok_matrix(self.shape, dtype=res_dtype)
dict.update(new, self)
with np.errstate(over='ignore'):
dict.update(new,
((k, new[k] + other[k]) for k in iterkeys(other)))
elif isspmatrix(other):
csc = self.tocsc()
new = csc + other
elif isdense(other):
new = self.todense() + other
else:
return NotImplemented
return new
def __radd__(self, other):
if isscalarlike(other):
new = dok_matrix(self.shape, dtype=self.dtype)
M, N = self.shape
for key in itertools.product(xrange(M), xrange(N)):
aij = dict.get(self, (key), 0) + other
if aij:
new[key] = aij
elif isspmatrix_dok(other):
if other.shape != self.shape:
raise ValueError("Matrix dimensions are not equal.")
new = dok_matrix(self.shape, dtype=self.dtype)
dict.update(new, self)
dict.update(new,
((k, self[k] + other[k]) for k in iterkeys(other)))
elif isspmatrix(other):
csc = self.tocsc()
new = csc + other
elif isdense(other):
new = other + self.todense()
else:
return NotImplemented
return new
def __neg__(self):
if self.dtype.kind == 'b':
raise NotImplementedError('Negating a sparse boolean matrix is not'
' supported.')
new = dok_matrix(self.shape, dtype=self.dtype)
dict.update(new, ((k, -self[k]) for k in iterkeys(self)))
return new
def _mul_scalar(self, other):
res_dtype = upcast_scalar(self.dtype, other)
# Multiply this scalar by every element.
new = dok_matrix(self.shape, dtype=res_dtype)
dict.update(new, ((k, v * other) for k, v in iteritems(self)))
return new
def _mul_vector(self, other):
# matrix * vector
result = np.zeros(self.shape[0], dtype=upcast(self.dtype, other.dtype))
for (i, j), v in iteritems(self):
result[i] += v * other[j]
return result
def _mul_multivector(self, other):
# matrix * multivector
result_shape = (self.shape[0], other.shape[1])
result_dtype = upcast(self.dtype, other.dtype)
result = np.zeros(result_shape, dtype=result_dtype)
for (i, j), v in iteritems(self):
result[i,:] += v * other[j,:]
return result
def __imul__(self, other):
if isscalarlike(other):
dict.update(self, ((k, v * other) for k, v in iteritems(self)))
return self
return NotImplemented
def __truediv__(self, other):
if isscalarlike(other):
res_dtype = upcast_scalar(self.dtype, other)
new = dok_matrix(self.shape, dtype=res_dtype)
dict.update(new, ((k, v / other) for k, v in iteritems(self)))
return new
return self.tocsr() / other
def __itruediv__(self, other):
if isscalarlike(other):
dict.update(self, ((k, v / other) for k, v in iteritems(self)))
return self
return NotImplemented
def __reduce__(self):
# this approach is necessary because __setstate__ is called after
# __setitem__ upon unpickling and since __init__ is not called there
# is no shape attribute hence it is not possible to unpickle it.
return dict.__reduce__(self)
# What should len(sparse) return? For consistency with dense matrices,
# perhaps it should be the number of rows? For now it returns the number
# of non-zeros.
def transpose(self, axes=None, copy=False):
if axes is not None:
raise ValueError("Sparse matrices do not support "
"an 'axes' parameter because swapping "
"dimensions is the only logical permutation.")
M, N = self.shape
new = dok_matrix((N, M), dtype=self.dtype, copy=copy)
dict.update(new, (((right, left), val)
for (left, right), val in iteritems(self)))
return new
transpose.__doc__ = spmatrix.transpose.__doc__
def conjtransp(self):
"""Return the conjugate transpose."""
M, N = self.shape
new = dok_matrix((N, M), dtype=self.dtype)
dict.update(new, (((right, left), np.conj(val))
for (left, right), val in iteritems(self)))
return new
def copy(self):
new = dok_matrix(self.shape, dtype=self.dtype)
dict.update(new, self)
return new
copy.__doc__ = spmatrix.copy.__doc__
def getrow(self, i):
"""Returns the i-th row as a (1 x n) DOK matrix."""
new = dok_matrix((1, self.shape[1]), dtype=self.dtype)
dict.update(new, (((0, j), self[i, j]) for j in xrange(self.shape[1])))
return new
def getcol(self, j):
"""Returns the j-th column as a (m x 1) DOK matrix."""
new = dok_matrix((self.shape[0], 1), dtype=self.dtype)
dict.update(new, (((i, 0), self[i, j]) for i in xrange(self.shape[0])))
return new
def tocoo(self, copy=False):
from .coo import coo_matrix
if self.nnz == 0:
return coo_matrix(self.shape, dtype=self.dtype)
idx_dtype = get_index_dtype(maxval=max(self.shape))
data = np.fromiter(itervalues(self), dtype=self.dtype, count=self.nnz)
row = np.fromiter((i for i, _ in iterkeys(self)), dtype=idx_dtype, count=self.nnz)
col = np.fromiter((j for _, j in iterkeys(self)), dtype=idx_dtype, count=self.nnz)
A = coo_matrix((data, (row, col)), shape=self.shape, dtype=self.dtype)
A.has_canonical_format = True
return A
tocoo.__doc__ = spmatrix.tocoo.__doc__
def todok(self, copy=False):
if copy:
return self.copy()
return self
todok.__doc__ = spmatrix.todok.__doc__
def tocsc(self, copy=False):
return self.tocoo(copy=False).tocsc(copy=copy)
tocsc.__doc__ = spmatrix.tocsc.__doc__
def resize(self, *shape):
shape = check_shape(shape)
newM, newN = shape
M, N = self.shape
if newM < M or newN < N:
# Remove all elements outside new dimensions
for (i, j) in list(iterkeys(self)):
if i >= newM or j >= newN:
del self[i, j]
self._shape = shape
resize.__doc__ = spmatrix.resize.__doc__
def isspmatrix_dok(x):
"""Is x of dok_matrix type?
Parameters
----------
x
object to check for being a dok matrix
Returns
-------
bool
True if x is a dok matrix, False otherwise
Examples
--------
>>> from scipy.sparse import dok_matrix, isspmatrix_dok
>>> isspmatrix_dok(dok_matrix([[5]]))
True
>>> from scipy.sparse import dok_matrix, csr_matrix, isspmatrix_dok
>>> isspmatrix_dok(csr_matrix([[5]]))
False
"""
return isinstance(x, dok_matrix)
def _prod(x):
"""Product of a list of numbers; ~40x faster vs np.prod for Python tuples"""
if len(x) == 0:
return 1
return functools.reduce(operator.mul, x)说实话，个人觉着源代码中写的注释，比下面提供的Reference Guide有用的多，其中有关于每一中格式的优缺点分析，使用的实例等等，建议需要的仔细阅读。帮助文档仅供参考，哈哈。
帮助文档请点击：https://docs.scipy.org/doc/scipy/reference/sparse.html