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""" A sparse matrix in COOrdinate or 'triplet' format"""
__docformat__ = "restructuredtext en"
__all__ = ['coo_matrix', 'isspmatrix_coo']
from warnings import warn
import numpy as np
from sparsetools import coo_tocsr, coo_todense, coo_matvec
from base import isspmatrix
from data import _data_matrix
from sputils import upcast, upcast_char, to_native, isshape, getdtype, isintlike
class coo_matrix(_data_matrix):
"""
A sparse matrix in COOrdinate format.
Also known as the 'ijv' or 'triplet' format.
This can be instantiated in several ways:
coo_matrix(D)
with a dense matrix D
coo_matrix(S)
with another sparse matrix S (equivalent to S.tocoo())
coo_matrix((M, N), [dtype])
to construct an empty matrix with shape (M, N)
dtype is optional, defaulting to dtype='d'.
coo_matrix((data, (i, j)), [shape=(M, N)])
to construct from three arrays:
1. data[:] the entries of the matrix, in any order
2. i[:] the row indices of the matrix entries
3. j[:] the column indices of the matrix entries
Where ``A[i[k], j[k]] = data[k]``. When shape is not
specified, it is inferred from the index arrays
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
data
COO format data array of the matrix
row
COO format row index array of the matrix
col
COO format column index array of the matrix
Notes
-----
Sparse matrices can be used in arithmetic operations: they support
addition, subtraction, multiplication, division, and matrix power.
Advantages of the COO format
- facilitates fast conversion among sparse formats
- permits duplicate entries (see example)
- very fast conversion to and from CSR/CSC formats
Disadvantages of the COO format
- does not directly support:
+ arithmetic operations
+ slicing
Intended Usage
- COO is a fast format for constructing sparse matrices
- Once a matrix has been constructed, convert to CSR or
CSC format for fast arithmetic and matrix vector operations
- By default when converting to CSR or CSC format, duplicate (i,j)
entries will be summed together. This facilitates efficient
construction of finite element matrices and the like. (see example)
Examples
--------
>>> from scipy.sparse import coo_matrix
>>> coo_matrix((3,4), dtype=np.int8).todense()
matrix([[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]], dtype=int8)
>>> row = np.array([0,3,1,0])
>>> col = np.array([0,3,1,2])
>>> data = np.array([4,5,7,9])
>>> coo_matrix((data,(row,col)), shape=(4,4)).todense()
matrix([[4, 0, 9, 0],
[0, 7, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 5]])
>>> # example with duplicates
>>> row = np.array([0,0,1,3,1,0,0])
>>> col = np.array([0,2,1,3,1,0,0])
>>> data = np.array([1,1,1,1,1,1,1])
>>> coo_matrix((data, (row,col)), shape=(4,4)).todense()
matrix([[3, 0, 1, 0],
[0, 2, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 1]])
"""
def __init__(self, arg1, shape=None, dtype=None, copy=False):
_data_matrix.__init__(self)
if isinstance(arg1, tuple):
if isshape(arg1):
M, N = arg1
self.shape = (M,N)
self.row = np.array([], dtype=np.intc)
self.col = np.array([], dtype=np.intc)
self.data = np.array([], getdtype(dtype, default=float))
else:
try:
obj, ij = arg1
except:
raise TypeError('invalid input format')
try:
if len(ij) != 2:
raise TypeError
except TypeError:
raise TypeError('invalid input format')
self.row = np.array(ij[0], copy=copy, dtype=np.intc)
self.col = np.array(ij[1], copy=copy, dtype=np.intc)
self.data = np.array( obj, copy=copy)
if shape is None:
if len(self.row) == 0 or len(self.col) == 0:
raise ValueError('cannot infer dimensions from zero sized index arrays')
M = self.row.max() + 1
N = self.col.max() + 1
self.shape = (M, N)
else:
# Use 2 steps to ensure shape has length 2.
M, N = shape
self.shape = (M, N)
elif arg1 is None:
# Initialize an empty matrix.
if not isinstance(shape, tuple) or not isintlike(shape[0]):
raise TypeError('dimensions not understood')
warn('coo_matrix(None, shape=(M,N)) is deprecated, ' \
'use coo_matrix( (M,N) ) instead', DeprecationWarning)
self.shape = shape
self.data = np.array([], getdtype(dtype, default=float))
self.row = np.array([], dtype=np.intc)
self.col = np.array([], dtype=np.intc)
else:
if isspmatrix(arg1):
if isspmatrix_coo(arg1) and copy:
self.row = arg1.row.copy()
self.col = arg1.col.copy()
self.data = arg1.data.copy()
self.shape = arg1.shape
else:
coo = arg1.tocoo()
self.row = coo.row
self.col = coo.col
self.data = coo.data
self.shape = coo.shape
else:
#dense argument
try:
M = np.atleast_2d(np.asarray(arg1))
except:
raise TypeError('invalid input format')
if np.rank(M) != 2:
raise TypeError('expected rank <= 2 array or matrix')
self.shape = M.shape
self.row, self.col = M.nonzero()
self.data = M[self.row, self.col]
if dtype is not None:
self.data = self.data.astype(dtype)
self._check()
def getnnz(self):
nnz = len(self.data)
if nnz != len(self.row) or nnz != len(self.col):
raise ValueError('row, column, and data array must all be the same length')
if np.rank(self.data) != 1 or np.rank(self.row) != 1 or np.rank(self.col) != 1:
raise ValueError('row, column, and data arrays must have rank 1')
return nnz
nnz = property(fget=getnnz)
def _check(self):
""" Checks data structure for consistency """
nnz = self.nnz
# index arrays should have integer data types
if self.row.dtype.kind != 'i':
warn("row index array has non-integer dtype (%s) " \
% self.row.dtype.name )
if self.col.dtype.kind != 'i':
warn("col index array has non-integer dtype (%s) " \
% self.col.dtype.name )
# only support 32-bit ints for now
self.row = np.asarray(self.row, dtype=np.intc)
self.col = np.asarray(self.col, dtype=np.intc)
self.data = to_native(self.data)
if nnz > 0:
if self.row.max() >= self.shape[0]:
raise ValueError('row index exceedes matrix dimensions')
if self.col.max() >= self.shape[1]:
raise ValueError('column index exceedes matrix dimensions')
if self.row.min() < 0:
raise ValueError('negative row index found')
if self.col.min() < 0:
raise ValueError('negative column index found')
def transpose(self, copy=False):
M,N = self.shape
return coo_matrix((self.data, (self.col, self.row)), shape=(N,M), copy=copy)
def toarray(self, order=None, out=None):
"""See the docstring for `spmatrix.toarray`."""
B = self._process_toarray_args(order, out)
fortran = int(B.flags.f_contiguous)
if not fortran and not B.flags.c_contiguous:
raise ValueError("Output array must be C or F contiguous")
M,N = self.shape
coo_todense(M, N, self.nnz, self.row, self.col, self.data,
B.ravel('A'), fortran)
return B
def tocsc(self):
"""Return a copy of this matrix in Compressed Sparse Column format
Duplicate entries will be summed together.
Examples
--------
>>> from numpy import array
>>> from scipy.sparse import coo_matrix
>>> row = array([0,0,1,3,1,0,0])
>>> col = array([0,2,1,3,1,0,0])
>>> data = array([1,1,1,1,1,1,1])
>>> A = coo_matrix( (data,(row,col)), shape=(4,4)).tocsc()
>>> A.todense()
matrix([[3, 0, 1, 0],
[0, 2, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 1]])
"""
from csc import csc_matrix
if self.nnz == 0:
return csc_matrix(self.shape, dtype=self.dtype)
else:
M,N = self.shape
indptr = np.empty(N + 1, dtype=np.intc)
indices = np.empty(self.nnz, dtype=np.intc)
data = np.empty(self.nnz, dtype=upcast(self.dtype))
coo_tocsr(N, M, self.nnz, \
self.col, self.row, self.data, \
indptr, indices, data)
A = csc_matrix((data, indices, indptr), shape=self.shape)
A.sum_duplicates()
return A
def tocsr(self):
"""Return a copy of this matrix in Compressed Sparse Row format
Duplicate entries will be summed together.
Examples
--------
>>> from numpy import array
>>> from scipy.sparse import coo_matrix
>>> row = array([0,0,1,3,1,0,0])
>>> col = array([0,2,1,3,1,0,0])
>>> data = array([1,1,1,1,1,1,1])
>>> A = coo_matrix( (data,(row,col)), shape=(4,4)).tocsr()
>>> A.todense()
matrix([[3, 0, 1, 0],
[0, 2, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 1]])
"""
from csr import csr_matrix
if self.nnz == 0:
return csr_matrix(self.shape, dtype=self.dtype)
else:
M,N = self.shape
indptr = np.empty(M + 1, dtype=np.intc)
indices = np.empty(self.nnz, dtype=np.intc)
data = np.empty(self.nnz, dtype=upcast(self.dtype))
coo_tocsr(M, N, self.nnz, \
self.row, self.col, self.data, \
indptr, indices, data)
A = csr_matrix((data, indices, indptr), shape=self.shape)
A.sum_duplicates()
return A
def tocoo(self, copy=False):
if copy:
return self.copy()
else:
return self
def todia(self):
from dia import dia_matrix
ks = self.col - self.row #the diagonal for each nonzero
diags = np.unique(ks)
if len(diags) > 100:
#probably undesired, should we do something?
#should todia() have a maxdiags parameter?
pass
#initialize and fill in data array
data = np.zeros( (len(diags), self.col.max()+1), dtype=self.dtype)
data[ np.searchsorted(diags,ks), self.col ] = self.data
return dia_matrix((data,diags), shape=self.shape)
def todok(self):
from itertools import izip
from dok import dok_matrix
dok = dok_matrix((self.shape), dtype=self.dtype)
dok.update( izip(izip(self.row,self.col),self.data) )
return dok
# needed by _data_matrix
def _with_data(self,data,copy=True):
"""Returns a matrix with the same sparsity structure as self,
but with different data. By default the index arrays
(i.e. .row and .col) are copied.
"""
if copy:
return coo_matrix( (data, (self.row.copy(), self.col.copy()) ), \
shape=self.shape, dtype=data.dtype)
else:
return coo_matrix( (data, (self.row, self.col) ), \
shape=self.shape, dtype=data.dtype)
###########################
# Multiplication handlers #
###########################
def _mul_vector(self, other):
#output array
result = np.zeros( self.shape[0], dtype=upcast_char(self.dtype.char,
other.dtype.char) )
coo_matvec(self.nnz, self.row, self.col, self.data, other, result)
return result
def _mul_multivector(self, other):
return np.hstack( [ self._mul_vector(col).reshape(-1,1) for col in other.T ] )
def isspmatrix_coo( x ):
return isinstance(x, coo_matrix)
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