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"""Functions to extract parts of sparse matrices |
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""" |
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__docformat__ = "restructuredtext en" |
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__all__ = ['find', 'tril', 'triu'] |
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from ._coo import coo_matrix, coo_array |
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from ._base import sparray |
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def find(A): |
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"""Return the indices and values of the nonzero elements of a matrix |
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Parameters |
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---------- |
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A : dense or sparse array or matrix |
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Matrix whose nonzero elements are desired. |
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Returns |
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------- |
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(I,J,V) : tuple of arrays |
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I,J, and V contain the row indices, column indices, and values |
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of the nonzero entries. |
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Examples |
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-------- |
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>>> from scipy.sparse import csr_array, find |
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>>> A = csr_array([[7.0, 8.0, 0],[0, 0, 9.0]]) |
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>>> find(A) |
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(array([0, 0, 1], dtype=int32), |
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array([0, 1, 2], dtype=int32), |
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array([ 7., 8., 9.])) |
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""" |
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A = coo_array(A, copy=True) |
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A.sum_duplicates() |
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nz_mask = A.data != 0 |
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return A.row[nz_mask], A.col[nz_mask], A.data[nz_mask] |
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def tril(A, k=0, format=None): |
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"""Return the lower triangular portion of a sparse array or matrix |
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Returns the elements on or below the k-th diagonal of A. |
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- k = 0 corresponds to the main diagonal |
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- k > 0 is above the main diagonal |
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- k < 0 is below the main diagonal |
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Parameters |
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---------- |
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A : dense or sparse array or matrix |
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Matrix whose lower trianglar portion is desired. |
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k : integer : optional |
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The top-most diagonal of the lower triangle. |
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format : string |
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Sparse format of the result, e.g. format="csr", etc. |
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Returns |
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------- |
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L : sparse matrix |
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Lower triangular portion of A in sparse format. |
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See Also |
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-------- |
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triu : upper triangle in sparse format |
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Examples |
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-------- |
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>>> from scipy.sparse import csr_array, tril |
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>>> A = csr_array([[1, 2, 0, 0, 3], [4, 5, 0, 6, 7], [0, 0, 8, 9, 0]], |
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... dtype='int32') |
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>>> A.toarray() |
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array([[1, 2, 0, 0, 3], |
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[4, 5, 0, 6, 7], |
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[0, 0, 8, 9, 0]], dtype=int32) |
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>>> tril(A).toarray() |
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array([[1, 0, 0, 0, 0], |
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[4, 5, 0, 0, 0], |
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[0, 0, 8, 0, 0]], dtype=int32) |
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>>> tril(A).nnz |
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4 |
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>>> tril(A, k=1).toarray() |
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array([[1, 2, 0, 0, 0], |
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[4, 5, 0, 0, 0], |
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[0, 0, 8, 9, 0]], dtype=int32) |
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>>> tril(A, k=-1).toarray() |
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array([[0, 0, 0, 0, 0], |
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[4, 0, 0, 0, 0], |
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[0, 0, 0, 0, 0]], dtype=int32) |
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>>> tril(A, format='csc') |
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<Compressed Sparse Column sparse array of dtype 'int32' |
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with 4 stored elements and shape (3, 5)> |
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""" |
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coo_sparse = coo_array if isinstance(A, sparray) else coo_matrix |
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A = coo_sparse(A, copy=False) |
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mask = A.row + k >= A.col |
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row = A.row[mask] |
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col = A.col[mask] |
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data = A.data[mask] |
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new_coo = coo_sparse((data, (row, col)), shape=A.shape, dtype=A.dtype) |
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return new_coo.asformat(format) |
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def triu(A, k=0, format=None): |
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"""Return the upper triangular portion of a sparse array or matrix |
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Returns the elements on or above the k-th diagonal of A. |
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- k = 0 corresponds to the main diagonal |
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- k > 0 is above the main diagonal |
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- k < 0 is below the main diagonal |
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Parameters |
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---------- |
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A : dense or sparse array or matrix |
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Matrix whose upper trianglar portion is desired. |
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k : integer : optional |
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The bottom-most diagonal of the upper triangle. |
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format : string |
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Sparse format of the result, e.g. format="csr", etc. |
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Returns |
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------- |
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L : sparse array or matrix |
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Upper triangular portion of A in sparse format. |
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Sparse array if A is a sparse array, otherwise matrix. |
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See Also |
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-------- |
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tril : lower triangle in sparse format |
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Examples |
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-------- |
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>>> from scipy.sparse import csr_array, triu |
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>>> A = csr_array([[1, 2, 0, 0, 3], [4, 5, 0, 6, 7], [0, 0, 8, 9, 0]], |
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... dtype='int32') |
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>>> A.toarray() |
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array([[1, 2, 0, 0, 3], |
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[4, 5, 0, 6, 7], |
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[0, 0, 8, 9, 0]], dtype=int32) |
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>>> triu(A).toarray() |
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array([[1, 2, 0, 0, 3], |
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[0, 5, 0, 6, 7], |
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[0, 0, 8, 9, 0]], dtype=int32) |
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>>> triu(A).nnz |
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8 |
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>>> triu(A, k=1).toarray() |
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array([[0, 2, 0, 0, 3], |
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[0, 0, 0, 6, 7], |
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[0, 0, 0, 9, 0]], dtype=int32) |
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>>> triu(A, k=-1).toarray() |
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array([[1, 2, 0, 0, 3], |
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[4, 5, 0, 6, 7], |
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[0, 0, 8, 9, 0]], dtype=int32) |
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>>> triu(A, format='csc') |
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<Compressed Sparse Column sparse array of dtype 'int32' |
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with 8 stored elements and shape (3, 5)> |
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""" |
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coo_sparse = coo_array if isinstance(A, sparray) else coo_matrix |
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A = coo_sparse(A, copy=False) |
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mask = A.row + k <= A.col |
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row = A.row[mask] |
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col = A.col[mask] |
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data = A.data[mask] |
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new_coo = coo_sparse((data, (row, col)), shape=A.shape, dtype=A.dtype) |
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return new_coo.asformat(format) |
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