618 lines
22 KiB
Python
618 lines
22 KiB
Python
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""" A sparse matrix in COOrdinate or 'triplet' format"""
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__docformat__ = "restructuredtext en"
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__all__ = ['coo_matrix', 'isspmatrix_coo']
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from warnings import warn
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import numpy as np
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from ._sparsetools import coo_tocsr, coo_todense, coo_matvec
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from .base import isspmatrix, SparseEfficiencyWarning, spmatrix
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from .data import _data_matrix, _minmax_mixin
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from .sputils import (upcast, upcast_char, to_native, isshape, getdtype,
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get_index_dtype, downcast_intp_index, check_shape,
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check_reshape_kwargs, matrix)
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import operator
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class coo_matrix(_data_matrix, _minmax_mixin):
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"""
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A sparse matrix in COOrdinate format.
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Also known as the 'ijv' or 'triplet' format.
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This can be instantiated in several ways:
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coo_matrix(D)
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with a dense matrix D
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coo_matrix(S)
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with another sparse matrix S (equivalent to S.tocoo())
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coo_matrix((M, N), [dtype])
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to construct an empty matrix with shape (M, N)
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dtype is optional, defaulting to dtype='d'.
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coo_matrix((data, (i, j)), [shape=(M, N)])
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to construct from three arrays:
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1. data[:] the entries of the matrix, in any order
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2. i[:] the row indices of the matrix entries
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3. j[:] the column indices of the matrix entries
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Where ``A[i[k], j[k]] = data[k]``. When shape is not
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specified, it is inferred from the index arrays
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Attributes
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----------
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dtype : dtype
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Data type of the matrix
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shape : 2-tuple
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Shape of the matrix
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ndim : int
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Number of dimensions (this is always 2)
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nnz
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Number of stored values, including explicit zeros
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data
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COO format data array of the matrix
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row
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COO format row index array of the matrix
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col
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COO format column index array of the matrix
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Notes
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-----
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Sparse matrices can be used in arithmetic operations: they support
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addition, subtraction, multiplication, division, and matrix power.
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Advantages of the COO format
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- facilitates fast conversion among sparse formats
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- permits duplicate entries (see example)
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- very fast conversion to and from CSR/CSC formats
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Disadvantages of the COO format
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- does not directly support:
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+ arithmetic operations
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+ slicing
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Intended Usage
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- COO is a fast format for constructing sparse matrices
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- Once a matrix has been constructed, convert to CSR or
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CSC format for fast arithmetic and matrix vector operations
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- By default when converting to CSR or CSC format, duplicate (i,j)
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entries will be summed together. This facilitates efficient
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construction of finite element matrices and the like. (see example)
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Examples
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--------
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>>> # Constructing an empty matrix
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>>> from scipy.sparse import coo_matrix
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>>> coo_matrix((3, 4), dtype=np.int8).toarray()
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array([[0, 0, 0, 0],
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[0, 0, 0, 0],
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[0, 0, 0, 0]], dtype=int8)
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>>> # Constructing a matrix using ijv format
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>>> row = np.array([0, 3, 1, 0])
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>>> col = np.array([0, 3, 1, 2])
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>>> data = np.array([4, 5, 7, 9])
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>>> coo_matrix((data, (row, col)), shape=(4, 4)).toarray()
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array([[4, 0, 9, 0],
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[0, 7, 0, 0],
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[0, 0, 0, 0],
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[0, 0, 0, 5]])
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>>> # Constructing a matrix with duplicate indices
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>>> row = np.array([0, 0, 1, 3, 1, 0, 0])
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>>> col = np.array([0, 2, 1, 3, 1, 0, 0])
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>>> data = np.array([1, 1, 1, 1, 1, 1, 1])
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>>> coo = coo_matrix((data, (row, col)), shape=(4, 4))
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>>> # Duplicate indices are maintained until implicitly or explicitly summed
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>>> np.max(coo.data)
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1
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>>> coo.toarray()
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array([[3, 0, 1, 0],
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[0, 2, 0, 0],
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[0, 0, 0, 0],
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[0, 0, 0, 1]])
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"""
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format = 'coo'
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def __init__(self, arg1, shape=None, dtype=None, copy=False):
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_data_matrix.__init__(self)
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if isinstance(arg1, tuple):
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if isshape(arg1):
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M, N = arg1
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self._shape = check_shape((M, N))
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idx_dtype = get_index_dtype(maxval=max(M, N))
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self.row = np.array([], dtype=idx_dtype)
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self.col = np.array([], dtype=idx_dtype)
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self.data = np.array([], getdtype(dtype, default=float))
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self.has_canonical_format = True
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else:
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try:
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obj, (row, col) = arg1
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except (TypeError, ValueError):
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raise TypeError('invalid input format')
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if shape is None:
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if len(row) == 0 or len(col) == 0:
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raise ValueError('cannot infer dimensions from zero '
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'sized index arrays')
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M = operator.index(np.max(row)) + 1
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N = operator.index(np.max(col)) + 1
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self._shape = check_shape((M, N))
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else:
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# Use 2 steps to ensure shape has length 2.
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M, N = shape
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self._shape = check_shape((M, N))
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idx_dtype = get_index_dtype(maxval=max(self.shape))
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self.row = np.array(row, copy=copy, dtype=idx_dtype)
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self.col = np.array(col, copy=copy, dtype=idx_dtype)
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self.data = np.array(obj, copy=copy)
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self.has_canonical_format = False
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else:
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if isspmatrix(arg1):
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if isspmatrix_coo(arg1) and copy:
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self.row = arg1.row.copy()
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self.col = arg1.col.copy()
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self.data = arg1.data.copy()
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self._shape = check_shape(arg1.shape)
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else:
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coo = arg1.tocoo()
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self.row = coo.row
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self.col = coo.col
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self.data = coo.data
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self._shape = check_shape(coo.shape)
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self.has_canonical_format = False
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else:
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#dense argument
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M = np.atleast_2d(np.asarray(arg1))
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if M.ndim != 2:
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raise TypeError('expected dimension <= 2 array or matrix')
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self._shape = check_shape(M.shape)
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if shape is not None:
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if check_shape(shape) != self._shape:
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raise ValueError('inconsistent shapes: %s != %s' %
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(shape, self._shape))
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self.row, self.col = M.nonzero()
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self.data = M[self.row, self.col]
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self.has_canonical_format = True
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if dtype is not None:
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self.data = self.data.astype(dtype, copy=False)
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self._check()
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def reshape(self, *args, **kwargs):
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shape = check_shape(args, self.shape)
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order, copy = check_reshape_kwargs(kwargs)
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# Return early if reshape is not required
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if shape == self.shape:
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if copy:
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return self.copy()
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else:
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return self
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nrows, ncols = self.shape
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if order == 'C':
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# Upcast to avoid overflows: the coo_matrix constructor
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# below will downcast the results to a smaller dtype, if
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# possible.
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dtype = get_index_dtype(maxval=(ncols * max(0, nrows - 1) + max(0, ncols - 1)))
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flat_indices = np.multiply(ncols, self.row, dtype=dtype) + self.col
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new_row, new_col = divmod(flat_indices, shape[1])
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elif order == 'F':
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dtype = get_index_dtype(maxval=(nrows * max(0, ncols - 1) + max(0, nrows - 1)))
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flat_indices = np.multiply(nrows, self.col, dtype=dtype) + self.row
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new_col, new_row = divmod(flat_indices, shape[0])
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else:
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raise ValueError("'order' must be 'C' or 'F'")
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# Handle copy here rather than passing on to the constructor so that no
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# copy will be made of new_row and new_col regardless
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if copy:
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new_data = self.data.copy()
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else:
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new_data = self.data
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return coo_matrix((new_data, (new_row, new_col)),
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shape=shape, copy=False)
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reshape.__doc__ = spmatrix.reshape.__doc__
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def getnnz(self, axis=None):
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if axis is None:
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nnz = len(self.data)
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if nnz != len(self.row) or nnz != len(self.col):
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raise ValueError('row, column, and data array must all be the '
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'same length')
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if self.data.ndim != 1 or self.row.ndim != 1 or \
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self.col.ndim != 1:
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raise ValueError('row, column, and data arrays must be 1-D')
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return int(nnz)
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if axis < 0:
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axis += 2
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if axis == 0:
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return np.bincount(downcast_intp_index(self.col),
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minlength=self.shape[1])
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elif axis == 1:
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return np.bincount(downcast_intp_index(self.row),
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minlength=self.shape[0])
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else:
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raise ValueError('axis out of bounds')
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getnnz.__doc__ = spmatrix.getnnz.__doc__
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def _check(self):
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""" Checks data structure for consistency """
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# index arrays should have integer data types
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if self.row.dtype.kind != 'i':
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warn("row index array has non-integer dtype (%s) "
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% self.row.dtype.name)
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if self.col.dtype.kind != 'i':
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warn("col index array has non-integer dtype (%s) "
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% self.col.dtype.name)
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idx_dtype = get_index_dtype(maxval=max(self.shape))
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self.row = np.asarray(self.row, dtype=idx_dtype)
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self.col = np.asarray(self.col, dtype=idx_dtype)
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self.data = to_native(self.data)
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if self.nnz > 0:
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if self.row.max() >= self.shape[0]:
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raise ValueError('row index exceeds matrix dimensions')
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if self.col.max() >= self.shape[1]:
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raise ValueError('column index exceeds matrix dimensions')
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if self.row.min() < 0:
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raise ValueError('negative row index found')
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if self.col.min() < 0:
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raise ValueError('negative column index found')
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def transpose(self, axes=None, copy=False):
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if axes is not None:
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raise ValueError(("Sparse matrices do not support "
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"an 'axes' parameter because swapping "
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"dimensions is the only logical permutation."))
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M, N = self.shape
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return coo_matrix((self.data, (self.col, self.row)),
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shape=(N, M), copy=copy)
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transpose.__doc__ = spmatrix.transpose.__doc__
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def resize(self, *shape):
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shape = check_shape(shape)
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new_M, new_N = shape
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M, N = self.shape
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if new_M < M or new_N < N:
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mask = np.logical_and(self.row < new_M, self.col < new_N)
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if not mask.all():
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self.row = self.row[mask]
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self.col = self.col[mask]
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self.data = self.data[mask]
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self._shape = shape
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resize.__doc__ = spmatrix.resize.__doc__
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def toarray(self, order=None, out=None):
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"""See the docstring for `spmatrix.toarray`."""
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B = self._process_toarray_args(order, out)
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fortran = int(B.flags.f_contiguous)
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if not fortran and not B.flags.c_contiguous:
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raise ValueError("Output array must be C or F contiguous")
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M,N = self.shape
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coo_todense(M, N, self.nnz, self.row, self.col, self.data,
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B.ravel('A'), fortran)
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return B
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def tocsc(self, copy=False):
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"""Convert this matrix to Compressed Sparse Column format
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Duplicate entries will be summed together.
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Examples
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--------
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>>> from numpy import array
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>>> from scipy.sparse import coo_matrix
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>>> row = array([0, 0, 1, 3, 1, 0, 0])
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>>> col = array([0, 2, 1, 3, 1, 0, 0])
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>>> data = array([1, 1, 1, 1, 1, 1, 1])
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>>> A = coo_matrix((data, (row, col)), shape=(4, 4)).tocsc()
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>>> A.toarray()
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array([[3, 0, 1, 0],
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[0, 2, 0, 0],
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[0, 0, 0, 0],
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[0, 0, 0, 1]])
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"""
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from .csc import csc_matrix
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if self.nnz == 0:
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return csc_matrix(self.shape, dtype=self.dtype)
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else:
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M,N = self.shape
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idx_dtype = get_index_dtype((self.col, self.row),
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maxval=max(self.nnz, M))
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row = self.row.astype(idx_dtype, copy=False)
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col = self.col.astype(idx_dtype, copy=False)
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indptr = np.empty(N + 1, dtype=idx_dtype)
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indices = np.empty_like(row, dtype=idx_dtype)
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data = np.empty_like(self.data, dtype=upcast(self.dtype))
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coo_tocsr(N, M, self.nnz, col, row, self.data,
|
||
|
|
indptr, indices, data)
|
||
|
|
|
||
|
|
x = csc_matrix((data, indices, indptr), shape=self.shape)
|
||
|
|
if not self.has_canonical_format:
|
||
|
|
x.sum_duplicates()
|
||
|
|
return x
|
||
|
|
|
||
|
|
def tocsr(self, copy=False):
|
||
|
|
"""Convert this matrix to Compressed Sparse Row format
|
||
|
|
|
||
|
|
Duplicate entries will be summed together.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> 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.toarray()
|
||
|
|
array([[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
|
||
|
|
idx_dtype = get_index_dtype((self.row, self.col),
|
||
|
|
maxval=max(self.nnz, N))
|
||
|
|
row = self.row.astype(idx_dtype, copy=False)
|
||
|
|
col = self.col.astype(idx_dtype, copy=False)
|
||
|
|
|
||
|
|
indptr = np.empty(M + 1, dtype=idx_dtype)
|
||
|
|
indices = np.empty_like(col, dtype=idx_dtype)
|
||
|
|
data = np.empty_like(self.data, dtype=upcast(self.dtype))
|
||
|
|
|
||
|
|
coo_tocsr(M, N, self.nnz, row, col, self.data,
|
||
|
|
indptr, indices, data)
|
||
|
|
|
||
|
|
x = csr_matrix((data, indices, indptr), shape=self.shape)
|
||
|
|
if not self.has_canonical_format:
|
||
|
|
x.sum_duplicates()
|
||
|
|
return x
|
||
|
|
|
||
|
|
def tocoo(self, copy=False):
|
||
|
|
if copy:
|
||
|
|
return self.copy()
|
||
|
|
else:
|
||
|
|
return self
|
||
|
|
|
||
|
|
tocoo.__doc__ = spmatrix.tocoo.__doc__
|
||
|
|
|
||
|
|
def todia(self, copy=False):
|
||
|
|
from .dia import dia_matrix
|
||
|
|
|
||
|
|
self.sum_duplicates()
|
||
|
|
ks = self.col - self.row # the diagonal for each nonzero
|
||
|
|
diags, diag_idx = np.unique(ks, return_inverse=True)
|
||
|
|
|
||
|
|
if len(diags) > 100:
|
||
|
|
# probably undesired, should todia() have a maxdiags parameter?
|
||
|
|
warn("Constructing a DIA matrix with %d diagonals "
|
||
|
|
"is inefficient" % len(diags), SparseEfficiencyWarning)
|
||
|
|
|
||
|
|
#initialize and fill in data array
|
||
|
|
if self.data.size == 0:
|
||
|
|
data = np.zeros((0, 0), dtype=self.dtype)
|
||
|
|
else:
|
||
|
|
data = np.zeros((len(diags), self.col.max()+1), dtype=self.dtype)
|
||
|
|
data[diag_idx, self.col] = self.data
|
||
|
|
|
||
|
|
return dia_matrix((data,diags), shape=self.shape)
|
||
|
|
|
||
|
|
todia.__doc__ = spmatrix.todia.__doc__
|
||
|
|
|
||
|
|
def todok(self, copy=False):
|
||
|
|
from .dok import dok_matrix
|
||
|
|
|
||
|
|
self.sum_duplicates()
|
||
|
|
dok = dok_matrix((self.shape), dtype=self.dtype)
|
||
|
|
dok._update(zip(zip(self.row,self.col),self.data))
|
||
|
|
|
||
|
|
return dok
|
||
|
|
|
||
|
|
todok.__doc__ = spmatrix.todok.__doc__
|
||
|
|
|
||
|
|
def diagonal(self, k=0):
|
||
|
|
rows, cols = self.shape
|
||
|
|
if k <= -rows or k >= cols:
|
||
|
|
return np.empty(0, dtype=self.data.dtype)
|
||
|
|
diag = np.zeros(min(rows + min(k, 0), cols - max(k, 0)),
|
||
|
|
dtype=self.dtype)
|
||
|
|
diag_mask = (self.row + k) == self.col
|
||
|
|
|
||
|
|
if self.has_canonical_format:
|
||
|
|
row = self.row[diag_mask]
|
||
|
|
data = self.data[diag_mask]
|
||
|
|
else:
|
||
|
|
row, _, data = self._sum_duplicates(self.row[diag_mask],
|
||
|
|
self.col[diag_mask],
|
||
|
|
self.data[diag_mask])
|
||
|
|
diag[row + min(k, 0)] = data
|
||
|
|
|
||
|
|
return diag
|
||
|
|
|
||
|
|
diagonal.__doc__ = _data_matrix.diagonal.__doc__
|
||
|
|
|
||
|
|
def _setdiag(self, values, k):
|
||
|
|
M, N = self.shape
|
||
|
|
if values.ndim and not len(values):
|
||
|
|
return
|
||
|
|
idx_dtype = self.row.dtype
|
||
|
|
|
||
|
|
# Determine which triples to keep and where to put the new ones.
|
||
|
|
full_keep = self.col - self.row != k
|
||
|
|
if k < 0:
|
||
|
|
max_index = min(M+k, N)
|
||
|
|
if values.ndim:
|
||
|
|
max_index = min(max_index, len(values))
|
||
|
|
keep = np.logical_or(full_keep, self.col >= max_index)
|
||
|
|
new_row = np.arange(-k, -k + max_index, dtype=idx_dtype)
|
||
|
|
new_col = np.arange(max_index, dtype=idx_dtype)
|
||
|
|
else:
|
||
|
|
max_index = min(M, N-k)
|
||
|
|
if values.ndim:
|
||
|
|
max_index = min(max_index, len(values))
|
||
|
|
keep = np.logical_or(full_keep, self.row >= max_index)
|
||
|
|
new_row = np.arange(max_index, dtype=idx_dtype)
|
||
|
|
new_col = np.arange(k, k + max_index, dtype=idx_dtype)
|
||
|
|
|
||
|
|
# Define the array of data consisting of the entries to be added.
|
||
|
|
if values.ndim:
|
||
|
|
new_data = values[:max_index]
|
||
|
|
else:
|
||
|
|
new_data = np.empty(max_index, dtype=self.dtype)
|
||
|
|
new_data[:] = values
|
||
|
|
|
||
|
|
# Update the internal structure.
|
||
|
|
self.row = np.concatenate((self.row[keep], new_row))
|
||
|
|
self.col = np.concatenate((self.col[keep], new_col))
|
||
|
|
self.data = np.concatenate((self.data[keep], new_data))
|
||
|
|
self.has_canonical_format = False
|
||
|
|
|
||
|
|
# 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)
|
||
|
|
|
||
|
|
def sum_duplicates(self):
|
||
|
|
"""Eliminate duplicate matrix entries by adding them together
|
||
|
|
|
||
|
|
This is an *in place* operation
|
||
|
|
"""
|
||
|
|
if self.has_canonical_format:
|
||
|
|
return
|
||
|
|
summed = self._sum_duplicates(self.row, self.col, self.data)
|
||
|
|
self.row, self.col, self.data = summed
|
||
|
|
self.has_canonical_format = True
|
||
|
|
|
||
|
|
def _sum_duplicates(self, row, col, data):
|
||
|
|
# Assumes (data, row, col) not in canonical format.
|
||
|
|
if len(data) == 0:
|
||
|
|
return row, col, data
|
||
|
|
order = np.lexsort((row, col))
|
||
|
|
row = row[order]
|
||
|
|
col = col[order]
|
||
|
|
data = data[order]
|
||
|
|
unique_mask = ((row[1:] != row[:-1]) |
|
||
|
|
(col[1:] != col[:-1]))
|
||
|
|
unique_mask = np.append(True, unique_mask)
|
||
|
|
row = row[unique_mask]
|
||
|
|
col = col[unique_mask]
|
||
|
|
unique_inds, = np.nonzero(unique_mask)
|
||
|
|
data = np.add.reduceat(data, unique_inds, dtype=self.dtype)
|
||
|
|
return row, col, data
|
||
|
|
|
||
|
|
def eliminate_zeros(self):
|
||
|
|
"""Remove zero entries from the matrix
|
||
|
|
|
||
|
|
This is an *in place* operation
|
||
|
|
"""
|
||
|
|
mask = self.data != 0
|
||
|
|
self.data = self.data[mask]
|
||
|
|
self.row = self.row[mask]
|
||
|
|
self.col = self.col[mask]
|
||
|
|
|
||
|
|
#######################
|
||
|
|
# Arithmetic handlers #
|
||
|
|
#######################
|
||
|
|
|
||
|
|
def _add_dense(self, other):
|
||
|
|
if other.shape != self.shape:
|
||
|
|
raise ValueError('Incompatible shapes.')
|
||
|
|
dtype = upcast_char(self.dtype.char, other.dtype.char)
|
||
|
|
result = np.array(other, dtype=dtype, copy=True)
|
||
|
|
fortran = int(result.flags.f_contiguous)
|
||
|
|
M, N = self.shape
|
||
|
|
coo_todense(M, N, self.nnz, self.row, self.col, self.data,
|
||
|
|
result.ravel('A'), fortran)
|
||
|
|
return matrix(result, copy=False)
|
||
|
|
|
||
|
|
def _mul_vector(self, other):
|
||
|
|
#output array
|
||
|
|
result = np.zeros(self.shape[0], dtype=upcast_char(self.dtype.char,
|
||
|
|
other.dtype.char))
|
||
|
|
coo_matvec(self.nnz, self.row, self.col, self.data, other, result)
|
||
|
|
return result
|
||
|
|
|
||
|
|
def _mul_multivector(self, other):
|
||
|
|
result = np.zeros((other.shape[1], self.shape[0]),
|
||
|
|
dtype=upcast_char(self.dtype.char, other.dtype.char))
|
||
|
|
for i, col in enumerate(other.T):
|
||
|
|
coo_matvec(self.nnz, self.row, self.col, self.data, col, result[i])
|
||
|
|
return result.T.view(type=type(other))
|
||
|
|
|
||
|
|
|
||
|
|
def isspmatrix_coo(x):
|
||
|
|
"""Is x of coo_matrix type?
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
x
|
||
|
|
object to check for being a coo matrix
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
bool
|
||
|
|
True if x is a coo matrix, False otherwise
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> from scipy.sparse import coo_matrix, isspmatrix_coo
|
||
|
|
>>> isspmatrix_coo(coo_matrix([[5]]))
|
||
|
|
True
|
||
|
|
|
||
|
|
>>> from scipy.sparse import coo_matrix, csr_matrix, isspmatrix_coo
|
||
|
|
>>> isspmatrix_coo(csr_matrix([[5]]))
|
||
|
|
False
|
||
|
|
"""
|
||
|
|
return isinstance(x, coo_matrix)
|