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"""Functions to extract parts of sparse matrices """
"""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, copy=True) A.sum_duplicates() # remove explicit zeros nz_mask = A.data != 0 return A.row[nz_mask], A.col[nz_mask], A.data[nz_mask]
"""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 '<class '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 return _masked_coo(A, mask).asformat(format)
"""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 '<class '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 return _masked_coo(A, mask).asformat(format)
row = A.row[mask] col = A.col[mask] data = A.data[mask] return coo_matrix((data, (row, col)), shape=A.shape, dtype=A.dtype) |