539 lines
18 KiB
Python
539 lines
18 KiB
Python
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"""Dictionary Of Keys based matrix"""
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from __future__ import division, print_function, absolute_import
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__docformat__ = "restructuredtext en"
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__all__ = ['dok_matrix', 'isspmatrix_dok']
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import functools
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import operator
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import itertools
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import numpy as np
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from scipy._lib.six import zip as izip, xrange, iteritems, iterkeys, itervalues
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from .base import spmatrix, isspmatrix
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from .sputils import (isdense, getdtype, isshape, isintlike, isscalarlike,
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upcast, upcast_scalar, IndexMixin, get_index_dtype,
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check_shape)
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try:
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from operator import isSequenceType as _is_sequence
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except ImportError:
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def _is_sequence(x):
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return (hasattr(x, '__len__') or hasattr(x, '__next__')
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or hasattr(x, 'next'))
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class dok_matrix(spmatrix, IndexMixin, dict):
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"""
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Dictionary Of Keys based sparse matrix.
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This is an efficient structure for constructing sparse
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matrices incrementally.
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This can be instantiated in several ways:
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dok_matrix(D)
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with a dense matrix, D
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dok_matrix(S)
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with a sparse matrix, S
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dok_matrix((M,N), [dtype])
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create the matrix with initial shape (M,N)
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dtype is optional, defaulting to dtype='d'
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Attributes
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----------
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dtype : dtype
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Data type of the matrix
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shape : 2-tuple
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Shape of the matrix
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ndim : int
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Number of dimensions (this is always 2)
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nnz
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Number of nonzero elements
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Notes
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-----
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Sparse matrices can be used in arithmetic operations: they support
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addition, subtraction, multiplication, division, and matrix power.
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Allows for efficient O(1) access of individual elements.
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Duplicates are not allowed.
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Can be efficiently converted to a coo_matrix once constructed.
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Examples
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--------
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>>> import numpy as np
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>>> from scipy.sparse import dok_matrix
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>>> S = dok_matrix((5, 5), dtype=np.float32)
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>>> for i in range(5):
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... for j in range(5):
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... S[i, j] = i + j # Update element
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"""
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format = 'dok'
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def __init__(self, arg1, shape=None, dtype=None, copy=False):
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dict.__init__(self)
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spmatrix.__init__(self)
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self.dtype = getdtype(dtype, default=float)
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if isinstance(arg1, tuple) and isshape(arg1): # (M,N)
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M, N = arg1
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self._shape = check_shape((M, N))
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elif isspmatrix(arg1): # Sparse ctor
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if isspmatrix_dok(arg1) and copy:
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arg1 = arg1.copy()
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else:
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arg1 = arg1.todok()
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if dtype is not None:
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arg1 = arg1.astype(dtype)
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dict.update(self, arg1)
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self._shape = check_shape(arg1.shape)
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self.dtype = arg1.dtype
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else: # Dense ctor
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try:
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arg1 = np.asarray(arg1)
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except:
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raise TypeError('Invalid input format.')
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if len(arg1.shape) != 2:
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raise TypeError('Expected rank <=2 dense array or matrix.')
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from .coo import coo_matrix
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d = coo_matrix(arg1, dtype=dtype).todok()
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dict.update(self, d)
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self._shape = check_shape(arg1.shape)
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self.dtype = d.dtype
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def update(self, val):
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# Prevent direct usage of update
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raise NotImplementedError("Direct modification to dok_matrix element "
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"is not allowed.")
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def _update(self, data):
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"""An update method for dict data defined for direct access to
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`dok_matrix` data. Main purpose is to be used for effcient conversion
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from other spmatrix classes. Has no checking if `data` is valid."""
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return dict.update(self, data)
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def set_shape(self, shape):
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new_matrix = self.reshape(shape, copy=False).asformat(self.format)
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self.__dict__ = new_matrix.__dict__
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dict.clear(self)
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dict.update(self, new_matrix)
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shape = property(fget=spmatrix.get_shape, fset=set_shape)
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def getnnz(self, axis=None):
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if axis is not None:
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raise NotImplementedError("getnnz over an axis is not implemented "
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"for DOK format.")
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return dict.__len__(self)
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def count_nonzero(self):
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return sum(x != 0 for x in itervalues(self))
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getnnz.__doc__ = spmatrix.getnnz.__doc__
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count_nonzero.__doc__ = spmatrix.count_nonzero.__doc__
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def __len__(self):
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return dict.__len__(self)
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def get(self, key, default=0.):
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"""This overrides the dict.get method, providing type checking
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but otherwise equivalent functionality.
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"""
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try:
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i, j = key
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assert isintlike(i) and isintlike(j)
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except (AssertionError, TypeError, ValueError):
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raise IndexError('Index must be a pair of integers.')
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if (i < 0 or i >= self.shape[0] or j < 0 or j >= self.shape[1]):
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raise IndexError('Index out of bounds.')
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return dict.get(self, key, default)
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def __getitem__(self, index):
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"""If key=(i, j) is a pair of integers, return the corresponding
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element. If either i or j is a slice or sequence, return a new sparse
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matrix with just these elements.
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"""
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zero = self.dtype.type(0)
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i, j = self._unpack_index(index)
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i_intlike = isintlike(i)
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j_intlike = isintlike(j)
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if i_intlike and j_intlike:
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i = int(i)
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j = int(j)
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if i < 0:
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i += self.shape[0]
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if i < 0 or i >= self.shape[0]:
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raise IndexError('Index out of bounds.')
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if j < 0:
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j += self.shape[1]
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if j < 0 or j >= self.shape[1]:
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raise IndexError('Index out of bounds.')
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return dict.get(self, (i,j), zero)
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elif ((i_intlike or isinstance(i, slice)) and
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(j_intlike or isinstance(j, slice))):
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# Fast path for slicing very sparse matrices
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i_slice = slice(i, i+1) if i_intlike else i
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j_slice = slice(j, j+1) if j_intlike else j
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i_indices = i_slice.indices(self.shape[0])
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j_indices = j_slice.indices(self.shape[1])
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i_seq = xrange(*i_indices)
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j_seq = xrange(*j_indices)
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newshape = (len(i_seq), len(j_seq))
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newsize = _prod(newshape)
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if len(self) < 2*newsize and newsize != 0:
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# Switch to the fast path only when advantageous
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# (count the iterations in the loops, adjust for complexity)
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#
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# We also don't handle newsize == 0 here (if
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# i/j_intlike, it can mean index i or j was out of
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# bounds)
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return self._getitem_ranges(i_indices, j_indices, newshape)
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i, j = self._index_to_arrays(i, j)
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if i.size == 0:
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return dok_matrix(i.shape, dtype=self.dtype)
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min_i = i.min()
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if min_i < -self.shape[0] or i.max() >= self.shape[0]:
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raise IndexError('Index (%d) out of range -%d to %d.' %
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(i.min(), self.shape[0], self.shape[0]-1))
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if min_i < 0:
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i = i.copy()
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i[i < 0] += self.shape[0]
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min_j = j.min()
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if min_j < -self.shape[1] or j.max() >= self.shape[1]:
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raise IndexError('Index (%d) out of range -%d to %d.' %
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(j.min(), self.shape[1], self.shape[1]-1))
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if min_j < 0:
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j = j.copy()
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j[j < 0] += self.shape[1]
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newdok = dok_matrix(i.shape, dtype=self.dtype)
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for key in itertools.product(xrange(i.shape[0]), xrange(i.shape[1])):
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v = dict.get(self, (i[key], j[key]), zero)
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if v:
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dict.__setitem__(newdok, key, v)
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return newdok
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def _getitem_ranges(self, i_indices, j_indices, shape):
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# performance golf: we don't want Numpy scalars here, they are slow
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i_start, i_stop, i_stride = map(int, i_indices)
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j_start, j_stop, j_stride = map(int, j_indices)
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newdok = dok_matrix(shape, dtype=self.dtype)
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for (ii, jj) in iterkeys(self):
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# ditto for numpy scalars
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ii = int(ii)
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jj = int(jj)
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a, ra = divmod(ii - i_start, i_stride)
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if a < 0 or a >= shape[0] or ra != 0:
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continue
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b, rb = divmod(jj - j_start, j_stride)
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if b < 0 or b >= shape[1] or rb != 0:
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continue
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dict.__setitem__(newdok, (a, b),
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dict.__getitem__(self, (ii, jj)))
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return newdok
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def __setitem__(self, index, x):
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if isinstance(index, tuple) and len(index) == 2:
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# Integer index fast path
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i, j = index
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if (isintlike(i) and isintlike(j) and 0 <= i < self.shape[0]
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and 0 <= j < self.shape[1]):
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v = np.asarray(x, dtype=self.dtype)
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if v.ndim == 0 and v != 0:
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dict.__setitem__(self, (int(i), int(j)), v[()])
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return
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i, j = self._unpack_index(index)
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i, j = self._index_to_arrays(i, j)
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if isspmatrix(x):
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x = x.toarray()
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# Make x and i into the same shape
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x = np.asarray(x, dtype=self.dtype)
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x, _ = np.broadcast_arrays(x, i)
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if x.shape != i.shape:
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raise ValueError("Shape mismatch in assignment.")
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if np.size(x) == 0:
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return
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min_i = i.min()
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if min_i < -self.shape[0] or i.max() >= self.shape[0]:
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raise IndexError('Index (%d) out of range -%d to %d.' %
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(i.min(), self.shape[0], self.shape[0]-1))
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if min_i < 0:
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i = i.copy()
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i[i < 0] += self.shape[0]
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min_j = j.min()
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if min_j < -self.shape[1] or j.max() >= self.shape[1]:
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raise IndexError('Index (%d) out of range -%d to %d.' %
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(j.min(), self.shape[1], self.shape[1]-1))
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if min_j < 0:
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j = j.copy()
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j[j < 0] += self.shape[1]
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dict.update(self, izip(izip(i.flat, j.flat), x.flat))
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if 0 in x:
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zeroes = x == 0
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for key in izip(i[zeroes].flat, j[zeroes].flat):
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if dict.__getitem__(self, key) == 0:
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# may have been superseded by later update
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del self[key]
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def __add__(self, other):
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if isscalarlike(other):
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res_dtype = upcast_scalar(self.dtype, other)
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new = dok_matrix(self.shape, dtype=res_dtype)
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# Add this scalar to every element.
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M, N = self.shape
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for key in itertools.product(xrange(M), xrange(N)):
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aij = dict.get(self, (key), 0) + other
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if aij:
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new[key] = aij
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# new.dtype.char = self.dtype.char
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elif isspmatrix_dok(other):
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if other.shape != self.shape:
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raise ValueError("Matrix dimensions are not equal.")
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# We could alternatively set the dimensions to the largest of
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# the two matrices to be summed. Would this be a good idea?
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res_dtype = upcast(self.dtype, other.dtype)
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new = dok_matrix(self.shape, dtype=res_dtype)
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dict.update(new, self)
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with np.errstate(over='ignore'):
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dict.update(new,
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((k, new[k] + other[k]) for k in iterkeys(other)))
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elif isspmatrix(other):
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csc = self.tocsc()
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new = csc + other
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elif isdense(other):
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new = self.todense() + other
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else:
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return NotImplemented
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return new
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def __radd__(self, other):
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if isscalarlike(other):
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new = dok_matrix(self.shape, dtype=self.dtype)
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M, N = self.shape
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for key in itertools.product(xrange(M), xrange(N)):
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aij = dict.get(self, (key), 0) + other
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if aij:
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new[key] = aij
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elif isspmatrix_dok(other):
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if other.shape != self.shape:
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raise ValueError("Matrix dimensions are not equal.")
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new = dok_matrix(self.shape, dtype=self.dtype)
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dict.update(new, self)
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dict.update(new,
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((k, self[k] + other[k]) for k in iterkeys(other)))
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elif isspmatrix(other):
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csc = self.tocsc()
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new = csc + other
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elif isdense(other):
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new = other + self.todense()
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else:
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return NotImplemented
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|
|
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)
|