FreeModule(ZZ, 2000).random_element() is far slower than it should be

[sagetrac-cwitty]

Currently, random_element on a FreeModule constructs a basis, even if we know the basis is trivial. The attached patch fixes this for FreeModule_ambient and subclasses.

Before:

sage: K = FreeModule(ZZ, 2000)
sage: get_memory_usage()
118.60546875
sage: %time _ = K.random_element()
CPU times: user 1.45 s, sys: 0.12 s, total: 1.57 s
Wall time: 1.57 s
sage: get_memory_usage()
225.56640625

After:

sage: K = FreeModule(ZZ, 2000)
sage: get_memory_usage()
118.60546875
sage: %time _ = K.random_element()
CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s
Wall time: 0.00 s
sage: get_memory_usage()
118.60546875
sage: timeit('K.random_element()')
125 loops, best of 3: 2.32 ms per loop

A 600-fold speedup.

Component: linear algebra

Issue created by migration from https://trac.sagemath.org/ticket/3652

[ncalexan]

comment:1

Attachment: trac3652-free-module-random-speedup.patch.gz

Applies nicely and does speed up the operation on my system.

[sagetrac-mabshoff]

comment:2

Merged in Sage 3.1.alpha1