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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, to_native, isshape, getdtype
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, ij), [shape=(M, N)])
The arguments 'data' and 'ij' represent three arrays:
1. data[:] the entries of the matrix, in any order
2. ij[0][:] the row indices of the matrix entries
3. ij[1][:] the column indices of the matrix entries
Where ``A[ij[0][k], ij[1][k] = data[k]``. When shape is
not specified, it is inferred from the index arrays
Notes
-----
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 *
>>> from scipy import *
>>> coo_matrix( (3,4), dtype=int8 ).todense()
matrix([[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]], dtype=int8)
>>> row = array([0,3,1,0])
>>> col = array([0,3,1,2])
>>> data = 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 = 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])
>>> 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, dims=None):
_data_matrix.__init__(self)
if dims is not None:
warn("dims is deprecated, use shape instead", DeprecationWarning)
shape=dims
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 != 0).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')
@np.deprecate
def rowcol(self, num):
return (self.row[num], self.col[num])
@np.deprecate
def getdata(self, num):
return self.data[num]
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):
B = np.zeros(self.shape, dtype=self.dtype)
M,N = self.shape
coo_todense(M, N, self.nnz, self.row, self.col, self.data, B.ravel())
return B
def tocsc(self):
"""Return a copy of this matrix in Compressed Sparse Column format
Duplicate entries will be summed together.
Example
-------
>>> 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.
Example
-------
>>> 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(self.dtype,other.dtype) )
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 ] )
from sputils import _isinstance
def isspmatrix_coo( x ):
return _isinstance(x, coo_matrix)
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