Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

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Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1 sage: A.T [1 3] [2 4] sage: A.subdivide(None, 1); A [1|2] [3|4] sage: A.transpose() [1 3] [---] [2 4] 280 Chapter 10. Base class for dense matrices
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] 2 281
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Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

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