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"""Dictionary Of Keys based matrix"""
from __future__ import division, print_function, absolute_import
__docformat__ = "restructuredtext en"
__all__ = ['dok_matrix', 'isspmatrix_dok']
import numpy as np
from scipy.lib.six.moves 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
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, 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
self.update( coo_matrix(arg1, dtype=dtype).todok() )
self.shape = arg1.shape
self.dtype = arg1.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, key):
"""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.
"""
try:
i, j = key
except (ValueError, TypeError):
raise TypeError('index must be a pair of integers or slices')
# Bounds checking
if isintlike(i):
if i < 0:
i += self.shape[0]
if i < 0 or i >= self.shape[0]:
raise IndexError('index out of bounds')
if isintlike(j):
if j < 0:
j += self.shape[1]
if j < 0 or j >= self.shape[1]:
raise IndexError('index out of bounds')
# First deal with the case where both i and j are integers
if isintlike(i) and isintlike(j):
return dict.get(self, (i,j), 0.)
else:
# Either i or j is a slice, sequence, or invalid. If i is a slice
# or sequence, unfold it first and call __getitem__ recursively.
if isinstance(i, slice):
# Is there an easier way to do this?
seq = xrange(i.start or 0, i.stop or self.shape[0], i.step or 1)
elif _is_sequence(i):
seq = i
else:
# Make sure i is an integer. (But allow it to be a subclass of int).
if not isintlike(i):
raise TypeError('index must be a pair of integers or slices')
seq = None
if seq is not None:
# i is a seq
if isintlike(j):
# Create a new matrix of the correct dimensions
first = seq[0]
last = seq[-1]
if first < 0 or first >= self.shape[0] or last < 0 \
or last >= self.shape[0]:
raise IndexError('index out of bounds')
newshape = (last-first+1, 1)
new = dok_matrix(newshape)
# ** This uses linear time in the size m of dimension 0:
# new[0:seq[-1]-seq[0]+1, 0] = \
# [self.get((element, j), 0) for element in seq]
# ** Instead just add the non-zero elements. This uses
# ** linear time in the number of non-zeros:
for (ii, jj) in self.keys():
if jj == j and ii >= first and ii <= last:
dict.__setitem__(new, (ii-first, 0), \
dict.__getitem__(self, (ii,jj)))
else:
###################################
# We should reshape the new matrix here!
###################################
raise NotImplementedError("fancy indexing supported over"
" one axis only")
return new
# Below here, j is a sequence, but i is an integer
if isinstance(j, slice):
# Is there an easier way to do this?
seq = xrange(j.start or 0, j.stop or self.shape[1], j.step or 1)
elif _is_sequence(j):
seq = j
else:
# j is not an integer
raise TypeError("index must be a pair of integers or slices")
# Create a new matrix of the correct dimensions
first = seq[0]
last = seq[-1]
if first < 0 or first >= self.shape[1] or last < 0 \
or last >= self.shape[1]:
raise IndexError("index out of bounds")
newshape = (1, last-first+1)
new = dok_matrix(newshape)
# ** This uses linear time in the size n of dimension 1:
# new[0, 0:seq[-1]-seq[0]+1] = \
# [self.get((i, element), 0) for element in seq]
# ** Instead loop over the non-zero elements. This is slower
# ** if there are many non-zeros
for (ii, jj) in self.keys():
if ii == i and jj >= first and jj <= last:
dict.__setitem__(new, (0, jj-first), \
dict.__getitem__(self, (ii,jj)))
return new
def __setitem__(self, key, value):
try:
i, j = key
except (ValueError, TypeError):
raise TypeError("index must be a pair of integers or slices")
# First deal with the case where both i and j are integers
if isintlike(i) and isintlike(j):
if i < 0:
i += self.shape[0]
if j < 0:
j += self.shape[1]
if i < 0 or i >= self.shape[0] or j < 0 or j >= self.shape[1]:
raise IndexError("index out of bounds")
if np.isscalar(value):
if value == 0:
if (i,j) in self:
del self[(i,j)]
else:
dict.__setitem__(self, (i,j), self.dtype.type(value))
else:
raise ValueError('setting an array element with a sequence')
else:
# Either i or j is a slice, sequence, or invalid. If i is a slice
# or sequence, unfold it first and call __setitem__ recursively.
if isinstance(i, slice):
# Is there an easier way to do this?
seq = xrange(i.start or 0, i.stop or self.shape[0], i.step or 1)
elif _is_sequence(i):
seq = i
else:
# Make sure i is an integer. (But allow it to be a subclass of int).
if not isintlike(i):
raise TypeError("index must be a pair of integers or slices")
seq = None
if seq is not None:
# First see if 'value' is another dok_matrix of the appropriate
# dimensions
if isinstance(value, dok_matrix):
if value.shape[1] == 1:
for element in seq:
self[element, j] = value[element, 0]
else:
raise NotImplementedError("setting a 2-d slice of"
" a dok_matrix is not yet supported")
elif np.isscalar(value):
for element in seq:
self[element, j] = value
else:
# See if value is a sequence
try:
if len(seq) != len(value):
raise ValueError("index and value ranges must"
" have the same length")
except TypeError:
# Not a sequence
raise TypeError("unsupported type for"
" dok_matrix.__setitem__")
# Value is a sequence
for element, val in izip(seq, value):
self[element, j] = val # don't use dict.__setitem__
# here, since we still want to be able to delete
# 0-valued keys, do type checking on 'val' (e.g. if
# it's a rank-1 dense array), etc.
else:
# Process j
if isinstance(j, slice):
seq = xrange(j.start or 0, j.stop or self.shape[1], j.step or 1)
elif _is_sequence(j):
seq = j
else:
# j is not an integer
raise TypeError("index must be a pair of integers or slices")
# First see if 'value' is another dok_matrix of the appropriate
# dimensions
if isinstance(value, dok_matrix):
if value.shape[0] == 1:
for element in seq:
self[i, element] = value[0, element]
else:
raise NotImplementedError("setting a 2-d slice of"
" a dok_matrix is not yet supported")
elif np.isscalar(value):
for element in seq:
self[i, element] = value
else:
# See if value is a sequence
try:
if len(seq) != len(value):
raise ValueError("index and value ranges must have"
" the same length")
except TypeError:
# Not a sequence
raise TypeError("unsupported type for dok_matrix.__setitem__")
else:
for element, val in izip(seq, value):
self[i, element] = val
def __add__(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
#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 the largest of
# the two matrices to be summed. Would this be a good idea?
new = dok_matrix(self.shape, dtype=self.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):
# Multiply this scalar by every element.
new = dok_matrix(self.shape, dtype=self.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:
return NotImplementedError
def __truediv__(self, other):
if isscalarlike(other):
new = dok_matrix(self.shape, dtype=self.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:
return 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 take(self, cols_or_rows, columns=1):
# Extract columns or rows as indictated from matrix
# assume cols_or_rows is sorted
new = dok_matrix(dtype=self.dtype) # what should the dimensions be ?!
indx = int((columns == 1))
N = len(cols_or_rows)
if indx: # columns
for key in self.keys():
num = np.searchsorted(cols_or_rows, key[1])
if num < N:
newkey = (key[0], num)
new[newkey] = self[key]
else:
for key in self.keys():
num = np.searchsorted(cols_or_rows, key[0])
if num < N:
newkey = (num, key[1])
new[newkey] = self[key]
return new
def split(self, cols_or_rows, columns=1):
# Similar to take but returns two arrays, the extracted columns plus
# the resulting array. Assumes cols_or_rows is sorted
base = dok_matrix()
ext = dok_matrix()
indx = int((columns == 1))
if indx:
for key in self.keys():
num = np.searchsorted(cols_or_rows, key[1])
if cols_or_rows[num] == key[1]:
newkey = (key[0], num)
ext[newkey] = self[key]
else:
newkey = (key[0], key[1]-num)
base[newkey] = self[key]
else:
for key in self.keys():
num = np.searchsorted(cols_or_rows, key[0])
if cols_or_rows[num] == key[0]:
newkey = (num, key[1])
ext[newkey] = self[key]
else:
newkey = (key[0]-num, key[1])
base[newkey] = self[key]
return base, ext
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:
data = np.asarray(list(self.values()), dtype=self.dtype)
indices = np.asarray(list(self.keys()), dtype=np.intc).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 isspmatrix_dok(x):
return isinstance(x, dok_matrix)
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