Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
sparse_columns(copy=True)
Return a list of the columns of self as sparse vectors (or free module elements).
INPUT:
•copy - (default: True) if True, return a copy so you can modify it safely
EXAMPLES:
sage: a = matrix(2,3,range(6)); a
[0 1 2]
[3 4 5]
sage: v = a.sparse_columns(); v
[(0, 3), (1, 4), (2, 5)]
sage: v[1].is_sparse()
True
TESTS:
Columns of sparse matrices having no columns were fixed on trac ticket #10714:
sage: m = matrix(10, 0, sparse=True)
sage: m.ncols()
0
sage: m.columns()
[]
Check that the returned columns are immutable as per trac ticket #14874:
sage: m = Mat(ZZ,3,3,sparse=True)(range(9))
sage: v = m.sparse_columns()
sage: map(lambda x: x.is_mutable(), v)
[False, False, False]
sparse_matrix()
If this matrix is dense, return a sparse matrix with the same entries. If this matrix is sparse, return this
matrix (not a copy).
Note: The definition of “dense” and “sparse” in Sage have nothing to do with the number of nonzero
entries. Sparse and dense are properties of the underlying representation of the matrix.
EXAMPLES:
sage: A = MatrixSpace(QQ,2, sparse=False)([1,2,0,1])
sage: A.is_sparse()
False
sage: B = A.sparse_matrix()
sage: B.is_sparse()
True
sage: A
[1 2]
[0 1]
sage: B
[1 2]
[0 1]
sage: A*B
[1 4]
[0 1]
sage: A.parent()
Full MatrixSpace of 2 by 2 dense matrices over Rational Field
112 Chapter 6. Base class for matrices, part 1