"""Functions to extract parts of sparse matrices
"""
__docformat__ = "restructuredtext en"
__all__ = ['find', 'tril', 'triu']
from coo import coo_matrix
def find(A):
"""Return the indices and values of the nonzero elements of a matrix
Parameters
----------
A : dense or sparse matrix
Matrix whose nonzero elements are desired.
Returns
-------
(I,J,V) : tuple of arrays
I,J, and V contain the row indices, column indices, and values
of the nonzero matrix entries.
Example
-------
>>> from scipy.sparse import csr_matrix
>>> A = csr_matrix([[7.0, 8.0, 0],[0, 0, 9.0]])
>>> find(A)
(array([0, 0, 1], dtype=int32), array([0, 1, 2], dtype=int32), array([ 7., 8., 9.]))
"""
A = coo_matrix(A).tocsr() #sums duplicates
A.eliminate_zeros() #removes explicit zeros
A = A.tocoo(copy=False) #(cheaply) convert to COO
return A.row,A.col,A.data
def tril(A, k=0, format=None):
"""Return the lower triangular portion of a matrix in sparse format
Returns the elements on or below the k-th diagonal of the matrix A.
- k = 0 corresponds to the main diagonal
- k > 0 is above the main diagonal
- k < 0 is below the main diagonal
Parameters
----------
A : dense or sparse matrix
Matrix whose lower trianglar portion is desired.
k : integer : optional
The top-most diagonal of the lower triangle.
format : string
Sparse format of the result, e.g. format="csr", etc.
Returns
-------
L : sparse matrix
Lower triangular portion of A in sparse format.
See Also
--------
triu : upper triangle in sparse format
Examples
--------
>>> from scipy.sparse import csr_matrix
>>> A = csr_matrix( [[1,2,0,0,3],[4,5,0,6,7],[0,0,8,9,0]], dtype='int32' )
>>> A.todense()
matrix([[1, 2, 0, 0, 3],
[4, 5, 0, 6, 7],
[0, 0, 8, 9, 0]])
>>> tril(A).todense()
matrix([[1, 0, 0, 0, 0],
[4, 5, 0, 0, 0],
[0, 0, 8, 0, 0]])
>>> tril(A).nnz
4
>>> tril(A, k=1).todense()
matrix([[1, 2, 0, 0, 0],
[4, 5, 0, 0, 0],
[0, 0, 8, 9, 0]])
>>> tril(A, k=-1).todense()
matrix([[0, 0, 0, 0, 0],
[4, 0, 0, 0, 0],
[0, 0, 0, 0, 0]])
>>> tril(A, format='csc')
<3x5 sparse matrix of type '<type 'numpy.int32'>'
with 4 stored elements in Compressed Sparse Column format>
"""
# convert to COOrdinate format where things are easy
A = coo_matrix(A, copy=False)
mask = A.row + k >= A.col
row = A.row[mask]
col = A.col[mask]
data = A.data[mask]
return coo_matrix( (data,(row,col)), shape=A.shape ).asformat(format)
def triu(A, k=0, format=None):
"""Return the upper triangular portion of a matrix in sparse format
Returns the elements on or above the k-th diagonal of the matrix A.
- k = 0 corresponds to the main diagonal
- k > 0 is above the main diagonal
- k < 0 is below the main diagonal
Parameters
----------
A : dense or sparse matrix
Matrix whose upper trianglar portion is desired.
k : integer : optional
The bottom-most diagonal of the upper triangle.
format : string
Sparse format of the result, e.g. format="csr", etc.
Returns
-------
L : sparse matrix
Upper triangular portion of A in sparse format.
See Also
--------
tril : lower triangle in sparse format
Examples
--------
>>> from scipy.sparse import csr_matrix
>>> A = csr_matrix( [[1,2,0,0,3],[4,5,0,6,7],[0,0,8,9,0]], dtype='int32' )
>>> A.todense()
matrix([[1, 2, 0, 0, 3],
[4, 5, 0, 6, 7],
[0, 0, 8, 9, 0]])
>>> triu(A).todense()
matrix([[1, 2, 0, 0, 3],
[0, 5, 0, 6, 7],
[0, 0, 8, 9, 0]])
>>> triu(A).nnz
8
>>> triu(A, k=1).todense()
matrix([[0, 2, 0, 0, 3],
[0, 0, 0, 6, 7],
[0, 0, 0, 9, 0]])
>>> triu(A, k=-1).todense()
matrix([[1, 2, 0, 0, 3],
[4, 5, 0, 6, 7],
[0, 0, 8, 9, 0]])
>>> triu(A, format='csc')
<3x5 sparse matrix of type '<type 'numpy.int32'>'
with 8 stored elements in Compressed Sparse Column format>
"""
# convert to COOrdinate format where things are easy
A = coo_matrix(A, copy=False)
mask = A.row + k <= A.col
row = A.row[mask]
col = A.col[mask]
data = A.data[mask]
return coo_matrix( (data,(row,col)), shape=A.shape ).asformat(format)
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