Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

CHAPTER
ELEVEN
BASE CLASS FOR SPARSE MATRICES
Base class for sparse matrices
class sage.matrix.matrix_sparse.Matrix_sparse
Bases: sage.matrix.matrix.Matrix
The initialization routine of the Matrix base class ensures that it sets the attributes self._parent, self._base_ring,
self._nrows, self._ncols. It sets the latter ones by accessing the relevant information on parent, which is often
slower than what a more specific subclass can do.
Subclasses of Matrix can safely skip calling Matrix.__init__ provided they take care of initializing these attributes
themselves.
The private attributes self._is_immutable and self._cache are implicitly initialized to valid values upon memory
allocation.
EXAMPLES:
sage: import sage.matrix.matrix0
sage: A = sage.matrix.matrix0.Matrix(MatrixSpace(QQ,2))
sage: type(A)
antitranspose()
apply_map(phi, R=None, sparse=True)
Apply the given map phi (an arbitrary Python function or callable object) to this matrix. If R is not given,
automatically determine the base ring of the resulting matrix.
INPUT: sparse – False to make the output a dense matrix; default True
•phi - arbitrary Python function or callable object
•R - (optional) ring
OUTPUT: a matrix over R
EXAMPLES:
sage: m = matrix(ZZ, 10000, {(1,2): 17}, sparse=True)
sage: k. = GF(9)
sage: f = lambda x: k(x)
sage: n = m.apply_map(f)
sage: n.parent()
Full MatrixSpace of 10000 by 10000 sparse matrices over Finite Field in a of size 3^2
sage: n[1,2]
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