Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
sage: random_matrix(ZZ, 5, x=-10, y=10, density=0.75)
[-6 1 0 0 0]
[ 9 0 0 4 1]
[-6 0 0 -8 0]
[ 0 4 0 6 0]
[ 1 -9 0 0 -8]
sage: random_matrix(ZZ, 5, x=20, y=30, density=0.75)
[ 0 28 0 27 0]
[25 28 20 0 0]
[ 0 21 0 21 0]
[ 0 28 22 0 0]
[ 0 0 0 26 24]
It is possible to construct sparse matrices, where it may now be advisable (but not required) to control the density
of nonzero entries.
sage: A=random_matrix(ZZ, 5, 5)
sage: A.is_sparse()
False
sage: A=random_matrix(ZZ, 5, 5, sparse=True)
sage: A.is_sparse()
True
sage: random_matrix(ZZ, 5, 5, density=0.3, sparse=True)
[ 4 0 0 0 -1]
[ 0 0 0 0 -7]
[ 0 0 2 0 0]
[ 0 0 1 0 -4]
[ 0 0 0 0 0]
For algorithm testing you might want to control the number of bits, say 10,000 entries, each limited to 16 bits.
sage: A = random_matrix(ZZ, 100, 100, x=2^16); A
100 x 100 dense matrix over Integer Ring (type ’print A.str()’ to see all of the entries)
Random rational matrices. Now num_bound and den_bound control the generation of random elements, by
specifying limits on the absolute value of numerators and denominators (respectively). Entries will be positive
and negative (map the absolute value function through the entries to get all positive values), and zeros are
avoided unless the density is set. If either the numerator or denominator bound (or both) is not used, then the
values default to the distribution for ZZ described above that is most frequently positive or negative one.
sage: random_matrix(QQ, 2, 8, num_bound=20, den_bound=4)
[ -1/2 6 13 -12 -2/3 -1/4 5 5]
[ -9/2 5/3 19 15/2 19/2 20/3 -13/4 0]
sage: random_matrix(QQ, 4, density = 0.5, sparse=True)
[ 0 71 0 -1/2]
[ 0 0 0 0]
[31/85 0 -31/2 0]
[ 1 -1/4 0 0]
sage: A = random_matrix(QQ, 3, 10, num_bound = 99, den_bound = 99)
sage: positives = map(abs, A.list())
sage: matrix(QQ, 3, 10, positives)
[61/18 47/41 1/22 1/2 75/68 6/7 1 1/2 72/41 7/3]
[33/13 9/2 40/21 45/46 17/22 1 70/79 97/71 7/24 12/5]
[ 13/8 8/25 1/3 61/14 92/45 4/85 3/38 95/16 82/71 1/5]
48 Chapter 2. Matrix Constructor