Skip to content

HTTPS clone URL

Subversion checkout URL

You can clone with HTTPS or Subversion.

Download ZIP
Fetching contributors…

Cannot retrieve contributors at this time

511 lines (428 sloc) 17.187 kb
"""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 numpy as np
from scipy.lib.six import zip as izip, xrange
from scipy.lib.six import iteritems
from .base import spmatrix, isspmatrix
from .sputils import (isdense, getdtype, isshape, isintlike, isscalarlike,
upcast, upcast_scalar, IndexMixin, get_index_dtype)
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
--------
>>> from scipy.sparse import *
>>> from scipy import *
>>> S = dok_matrix((5,5), dtype=float32)
>>> for i in range(5):
>>> for j in range(5):
>>> S[i,j] = i+j # Update element
"""
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 = (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)
self.update(arg1)
self.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()
self.update(d)
self.shape = arg1.shape
self.dtype = d.dtype
def getnnz(self):
return dict.__len__(self)
nnz = property(fget=getnnz)
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.
"""
i, j = self._unpack_index(index)
i_intlike = isintlike(i)
j_intlike = isintlike(j)
if i_intlike and j_intlike:
# Scalar index case
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), 0.)
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[0] 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 a in xrange(i.shape[0]):
for b in xrange(i.shape[1]):
v = dict.get(self, (i[a,b], j[a,b]), 0.)
if v != 0:
dict.__setitem__(newdok, (a, b), 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 self.keys():
# 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[0] 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):
# First check if argument is a scalar
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 i in xrange(M):
for j in xrange(N):
aij = self.get((i, j), 0) + other
if aij != 0:
new[i, j] = aij
# new.dtype.char = self.dtype.char
elif isinstance(other, dok_matrix):
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)
new.update(self)
for key in other.keys():
new[key] += other[key]
elif isspmatrix(other):
csc = self.tocsc()
new = csc + other
elif isdense(other):
new = self.todense() + other
else:
raise TypeError("data type not understood")
return new
def __radd__(self, other):
# First check if argument is a scalar
if isscalarlike(other):
new = dok_matrix(self.shape, dtype=self.dtype)
# Add this scalar to every element.
M, N = self.shape
for i in xrange(M):
for j in xrange(N):
aij = self.get((i, j), 0) + other
if aij != 0:
new[i, j] = aij
elif isinstance(other, dok_matrix):
if other.shape != self.shape:
raise ValueError("matrix dimensions are not equal")
new = dok_matrix(self.shape, dtype=self.dtype)
new.update(self)
for key in other:
new[key] += other[key]
elif isspmatrix(other):
csc = self.tocsc()
new = csc + other
elif isdense(other):
new = other + self.todense()
else:
raise TypeError("data type not understood")
return new
def __neg__(self):
new = dok_matrix(self.shape, dtype=self.dtype)
for key in self.keys():
new[key] = -self[key]
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)
for (key, val) in iteritems(self):
new[key] = val * other
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
M,N = self.shape
n_vecs = other.shape[1] # number of column vectors
result = np.zeros((M,n_vecs), dtype=upcast(self.dtype,other.dtype))
for (i,j),v in iteritems(self):
result[i,:] += v * other[j,:]
return result
def __imul__(self, other):
if isscalarlike(other):
# Multiply this scalar by every element.
for (key, val) in iteritems(self):
self[key] = val * other
# new.dtype.char = self.dtype.char
return self
else:
raise NotImplementedError
def __truediv__(self, other):
if isscalarlike(other):
res_dtype = upcast_scalar(self.dtype, other)
new = dok_matrix(self.shape, dtype=res_dtype)
# Multiply this scalar by every element.
for (key, val) in iteritems(self):
new[key] = val / other
# new.dtype.char = self.dtype.char
return new
else:
return self.tocsr() / other
def __itruediv__(self, other):
if isscalarlike(other):
# Multiply this scalar by every element.
for (key, val) in iteritems(self):
self[key] = val / other
return self
else:
raise NotImplementedError
# 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):
""" Return the transpose
"""
M, N = self.shape
new = dok_matrix((N, M), dtype=self.dtype)
for key, value in iteritems(self):
new[key[1], key[0]] = value
return new
def conjtransp(self):
""" Return the conjugate transpose
"""
M, N = self.shape
new = dok_matrix((N, M), dtype=self.dtype)
for key, value in iteritems(self):
new[key[1], key[0]] = np.conj(value)
return new
def copy(self):
new = dok_matrix(self.shape, dtype=self.dtype)
new.update(self)
return new
def getrow(self, i):
"""Returns a copy of row i of the matrix as a (1 x n)
DOK matrix.
"""
out = self.__class__((1, self.shape[1]), dtype=self.dtype)
for j in range(self.shape[1]):
out[0, j] = self[i, j]
return out
def getcol(self, j):
"""Returns a copy of column j of the matrix as a (m x 1)
DOK matrix.
"""
out = self.__class__((self.shape[0], 1), dtype=self.dtype)
for i in range(self.shape[0]):
out[i, 0] = self[i, j]
return out
def tocoo(self):
""" Return a copy of this matrix in COOrdinate format"""
from .coo import coo_matrix
if self.nnz == 0:
return coo_matrix(self.shape, dtype=self.dtype)
else:
idx_dtype = get_index_dtype(maxval=max(self.shape[0], self.shape[1]))
data = np.asarray(_list(self.values()), dtype=self.dtype)
indices = np.asarray(_list(self.keys()), dtype=idx_dtype).T
return coo_matrix((data,indices), shape=self.shape, dtype=self.dtype)
def todok(self,copy=False):
if copy:
return self.copy()
else:
return self
def tocsr(self):
""" Return a copy of this matrix in Compressed Sparse Row format"""
return self.tocoo().tocsr()
def tocsc(self):
""" Return a copy of this matrix in Compressed Sparse Column format"""
return self.tocoo().tocsc()
def toarray(self, order=None, out=None):
"""See the docstring for `spmatrix.toarray`."""
return self.tocoo().toarray(order=order, out=out)
def resize(self, shape):
""" Resize the matrix in-place to dimensions given by 'shape'.
Any non-zero elements that lie outside the new shape are removed.
"""
if not isshape(shape):
raise TypeError("dimensions must be a 2-tuple of positive"
" integers")
newM, newN = shape
M, N = self.shape
if newM < M or newN < N:
# Remove all elements outside new dimensions
for (i, j) in list(self.keys()):
if i >= newM or j >= newN:
del self[i, j]
self._shape = shape
def _list(x):
"""Force x to a list."""
if not isinstance(x, list):
x = list(x)
return x
def isspmatrix_dok(x):
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)
Jump to Line
Something went wrong with that request. Please try again.