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# scipy/scipy

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 """Functions to extract parts of sparse matrices """ from __future__ import division, print_function, absolute_import __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. Examples -------- >>> from scipy.sparse import csr_matrix, find >>> 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, tril >>> A = csr_matrix([[1, 2, 0, 0, 3], [4, 5, 0, 6, 7], [0, 0, 8, 9, 0]], ... dtype='int32') >>> A.toarray() array([[1, 2, 0, 0, 3], [4, 5, 0, 6, 7], [0, 0, 8, 9, 0]]) >>> tril(A).toarray() array([[1, 0, 0, 0, 0], [4, 5, 0, 0, 0], [0, 0, 8, 0, 0]]) >>> tril(A).nnz 4 >>> tril(A, k=1).toarray() array([[1, 2, 0, 0, 0], [4, 5, 0, 0, 0], [0, 0, 8, 9, 0]]) >>> tril(A, k=-1).toarray() array([[0, 0, 0, 0, 0], [4, 0, 0, 0, 0], [0, 0, 0, 0, 0]]) >>> tril(A, format='csc') <3x5 sparse matrix of type '' 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, triu >>> A = csr_matrix([[1, 2, 0, 0, 3], [4, 5, 0, 6, 7], [0, 0, 8, 9, 0]], ... dtype='int32') >>> A.toarray() array([[1, 2, 0, 0, 3], [4, 5, 0, 6, 7], [0, 0, 8, 9, 0]]) >>> triu(A).toarray() array([[1, 2, 0, 0, 3], [0, 5, 0, 6, 7], [0, 0, 8, 9, 0]]) >>> triu(A).nnz 8 >>> triu(A, k=1).toarray() array([[0, 2, 0, 0, 3], [0, 0, 0, 6, 7], [0, 0, 0, 9, 0]]) >>> triu(A, k=-1).toarray() array([[1, 2, 0, 0, 3], [4, 5, 0, 6, 7], [0, 0, 8, 9, 0]]) >>> triu(A, format='csc') <3x5 sparse matrix of type '' 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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