#13400: Use strong caches diligently
-------------------------------+--------------------------------------------
Reporter: nbruin | Owner: robertwb
Type: enhancement | Status: new
Priority: major | Milestone: sage-wishlist
Component: coercion | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
-------------------------------+--------------------------------------------
Comment (by nbruin):
Replying to [comment:4 SimonKing]:
> ... it ''is'' cached, mainly.
>
> Do we talk about the same version of sage? Namely, with #11943,
In that case you might want to check if that ticket was properly merged in
the
5.3b2 source, as available in `sage.math.washington.edu:/home/release`.
What I see is
`sage/categories/covariant_functorial_construction.py:359`:
{{{#!python
@cached_method
def is_subcategory(self, C):
"""
.. todo:: doctests + explain why this method is needed
"""
if C is self:
return True
return any(X.is_subcategory(C) for X in self._super_categories)
}}}
if I add `print("is_subcategory(self=%s,C=%s)"%(self,C)")` as a first
statement
I get lines such as:
{{{
is_subcategory(self=Category of subquotients of monoids,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of magmas,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of sets,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of monoids,C=Category of
quotients of semigroups)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
quotients of semigroups)
is_subcategory(self=Category of subquotients of magmas,C=Category of
quotients of semigroups)
is_subcategory(self=Category of subquotients of sets,C=Category of
quotients of semigroups)
is_subcategory(self=Category of quotients of semigroups,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of magmas,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of sets,C=Category of
commutative rings)
is_subcategory(self=Category of quotients of sets,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of sets,C=Category of
commutative rings)
is_subcategory(self=Category of quotients of semigroups,C=Category of
subquotients of monoids)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
subquotients of monoids)
is_subcategory(self=Category of subquotients of magmas,C=Category of
subquotients of monoids)
is_subcategory(self=Category of subquotients of sets,C=Category of
subquotients of monoids)
is_subcategory(self=Category of quotients of sets,C=Category of
subquotients of monoids)
is_subcategory(self=Category of subquotients of sets,C=Category of
subquotients of monoids)
is_subcategory(self=Category of subquotients of monoids,C=Category of
finite enumerated sets)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
finite enumerated sets)
is_subcategory(self=Category of subquotients of magmas,C=Category of
finite enumerated sets)
is_subcategory(self=Category of subquotients of sets,C=Category of finite
enumerated sets)
is_subcategory(self=Category of quotients of semigroups,C=Category of
finite enumerated sets)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
finite enumerated sets)
is_subcategory(self=Category of subquotients of magmas,C=Category of
finite enumerated sets)
is_subcategory(self=Category of subquotients of sets,C=Category of finite
enumerated sets)
is_subcategory(self=Category of quotients of sets,C=Category of finite
enumerated sets)
is_subcategory(self=Category of subquotients of sets,C=Category of finite
enumerated sets)
is_subcategory(self=Category of subquotients of monoids,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of magmas,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of sets,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of monoids,C=Category of
quotients of semigroups)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
quotients of semigroups)
is_subcategory(self=Category of subquotients of magmas,C=Category of
quotients of semigroups)
is_subcategory(self=Category of subquotients of sets,C=Category of
quotients of semigroups)
is_subcategory(self=Category of quotients of semigroups,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of magmas,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of sets,C=Category of
commutative rings)
is_subcategory(self=Category of quotients of sets,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of sets,C=Category of
commutative rings)
is_subcategory(self=Category of quotients of semigroups,C=Category of
subquotients of monoids)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
subquotients of monoids)
is_subcategory(self=Category of subquotients of magmas,C=Category of
subquotients of monoids)
is_subcategory(self=Category of subquotients of sets,C=Category of
subquotients of monoids)
is_subcategory(self=Category of quotients of sets,C=Category of
subquotients of monoids)
is_subcategory(self=Category of subquotients of sets,C=Category of
subquotients of monoids)
is_subcategory(self=Category of subquotients of monoids,C=Category of
finite enumerated sets)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
finite enumerated sets)
is_subcategory(self=Category of subquotients of magmas,C=Category of
finite enumerated sets)
is_subcategory(self=Category of subquotients of sets,C=Category of finite
enumerated sets)
is_subcategory(self=Category of quotients of semigroups,C=Category of
finite enumerated sets)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
finite enumerated sets)
is_subcategory(self=Category of subquotients of magmas,C=Category of
finite enumerated sets)
is_subcategory(self=Category of subquotients of sets,C=Category of finite
enumerated sets)
is_subcategory(self=Category of quotients of sets,C=Category of finite
enumerated sets)
is_subcategory(self=Category of subquotients of sets,C=Category of finite
enumerated sets)
is_subcategory(self=Category of subquotients of monoids,C=Category of
fields)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
fields)
is_subcategory(self=Category of subquotients of magmas,C=Category of
fields)
is_subcategory(self=Category of subquotients of sets,C=Category of fields)
is_subcategory(self=Category of quotients of semigroups,C=Category of
fields)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
fields)
is_subcategory(self=Category of subquotients of magmas,C=Category of
fields)
is_subcategory(self=Category of subquotients of sets,C=Category of fields)
is_subcategory(self=Category of quotients of sets,C=Category of fields)
is_subcategory(self=Category of subquotients of sets,C=Category of fields)
is_subcategory(self=Category of subquotients of monoids,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of magmas,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of sets,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of monoids,C=Category of
quotients of semigroups)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
quotients of semigroups)
is_subcategory(self=Category of subquotients of magmas,C=Category of
quotients of semigroups)
is_subcategory(self=Category of subquotients of sets,C=Category of
quotients of semigroups)
is_subcategory(self=Category of quotients of semigroups,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of magmas,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of sets,C=Category of
commutative rings)
is_subcategory(self=Category of quotients of sets,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of sets,C=Category of
commutative rings)
is_subcategory(self=Category of quotients of semigroups,C=Category of
subquotients of monoids)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
subquotients of monoids)
is_subcategory(self=Category of subquotients of magmas,C=Category of
subquotients of monoids)
is_subcategory(self=Category of subquotients of sets,C=Category of
subquotients of monoids)
is_subcategory(self=Category of quotients of sets,C=Category of
subquotients of monoids)
is_subcategory(self=Category of subquotients of sets,C=Category of
subquotients of monoids)
is_subcategory(self=Category of subquotients of monoids,C=Category of
finite enumerated sets)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
finite enumerated sets)
is_subcategory(self=Category of subquotients of magmas,C=Category of
finite enumerated sets)
is_subcategory(self=Category of subquotients of sets,C=Category of finite
enumerated sets)
is_subcategory(self=Category of quotients of semigroups,C=Category of
finite enumerated sets)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
finite enumerated sets)
is_subcategory(self=Category of subquotients of magmas,C=Category of
finite enumerated sets)
is_subcategory(self=Category of subquotients of sets,C=Category of finite
enumerated sets)
is_subcategory(self=Category of quotients of sets,C=Category of finite
enumerated sets)
is_subcategory(self=Category of subquotients of sets,C=Category of finite
enumerated sets)
is_subcategory(self=Category of subquotients of monoids,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of magmas,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of sets,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of monoids,C=Category of
quotients of semigroups)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
quotients of semigroups)
is_subcategory(self=Category of subquotients of magmas,C=Category of
quotients of semigroups)
is_subcategory(self=Category of subquotients of sets,C=Category of
quotients of semigroups)
is_subcategory(self=Category of quotients of semigroups,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of magmas,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of sets,C=Category of
commutative rings)
is_subcategory(self=Category of quotients of sets,C=Category of
commutative rings)
is_subcategory(self=Category of subquotients of sets,C=Category of
commutative rings)
is_subcategory(self=Category of quotients of semigroups,C=Category of
subquotients of monoids)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
subquotients of monoids)
is_subcategory(self=Category of subquotients of magmas,C=Category of
subquotients of monoids)
is_subcategory(self=Category of subquotients of sets,C=Category of
subquotients of monoids)
is_subcategory(self=Category of quotients of sets,C=Category of
subquotients of monoids)
is_subcategory(self=Category of subquotients of sets,C=Category of
subquotients of monoids)
is_subcategory(self=Category of subquotients of monoids,C=Category of
finite enumerated sets)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
finite enumerated sets)
is_subcategory(self=Category of subquotients of magmas,C=Category of
finite enumerated sets)
is_subcategory(self=Category of subquotients of sets,C=Category of finite
enumerated sets)
is_subcategory(self=Category of quotients of semigroups,C=Category of
finite enumerated sets)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
finite enumerated sets)
is_subcategory(self=Category of subquotients of magmas,C=Category of
finite enumerated sets)
is_subcategory(self=Category of subquotients of sets,C=Category of finite
enumerated sets)
is_subcategory(self=Category of quotients of sets,C=Category of finite
enumerated sets)
is_subcategory(self=Category of subquotients of sets,C=Category of finite
enumerated sets)
is_subcategory(self=Category of subquotients of monoids,C=Category of
fields)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
fields)
is_subcategory(self=Category of subquotients of magmas,C=Category of
fields)
is_subcategory(self=Category of subquotients of sets,C=Category of fields)
is_subcategory(self=Category of quotients of semigroups,C=Category of
fields)
is_subcategory(self=Category of subquotients of semigroups,C=Category of
fields)
is_subcategory(self=Category of subquotients of magmas,C=Category of
fields)
is_subcategory(self=Category of subquotients of sets,C=Category of fields)
is_subcategory(self=Category of quotients of sets,C=Category of fields)
is_subcategory(self=Category of subquotients of sets,C=Category of fields)
}}}
a lot of them, and as you can see, all "static" categories. None of those
funny
dynamically generated ones. If I decorate with `@cached_method` I get
these
lines at startup but not afterwards anymore.
`make ptest` improves (5.3b2 + tickets + cached is_subcategory):
{{{
Total time for all tests: 989.4 seconds
Total time for all tests: 994.4 seconds
}}}
and perhaps more significantly, the multimodular variant above now
profiles to:
multimodular echelonization loop (5.3b2 + tickets + cached
is_subcategory):
{{{
1263618 function calls (1229625 primitive calls) in 5.191 seconds
Ordered by: internal time
ncalls tottime percall cumtime percall filename:lineno(function)
1000 2.176 0.002 4.766 0.005 {method 'echelon_form' of
'sage.matrix.matrix_rational_dense.Matrix_rational_dense' objects}
4994 0.330 0.000 0.590 0.000
matrix_space.py:230(__init__)
2142 0.297 0.000 0.374 0.000
quotient_ring.py:322(__init__)
5000 0.193 0.000 0.946 0.000 matrix_space.py:1180(matrix)
6031 0.186 0.000 0.187 0.000
dynamic_class.py:259(dynamic_class_internal)
2142 0.120 0.000 0.139 0.000 {method 'ideal' of
'sage.rings.ring.Ring' objects}
16880 0.098 0.000 0.106 0.000 {method 'is_prime' of
'sage.rings.integer.Integer' objects}
1000 0.094 0.000 0.094 0.000 {method 'range' of
'sage.rings.integer_ring.IntegerRing_class' objects}
6253 0.088 0.000 0.272 0.000 category.py:112(_join)
18121/6128 0.079 0.000 0.585 0.000
lazy_attribute.py:506(__get__)
1 0.075 0.075 5.193 5.193 <ipython console>:1(test1)
14911 0.069 0.000 0.208 0.000 arith.py:401(is_prime)
130255 0.057 0.000 0.057 0.000 {isinstance}
43753 0.057 0.000 0.072 0.000 weakref.py:55(__getitem__)
10000 0.055 0.000 0.713 0.000
matrix_space.py:154(__classcall__)
2962 0.051 0.000 0.256 0.000 {sage.rings.ring.is_Field}
2000 0.048 0.000 0.235 0.000
arith.py:1051(previous_prime)
2142 0.046 0.000 0.726 0.000
integer_mod_ring.py:191(__init__)
1993 0.043 0.000 0.159 0.000
matrix_space.py:1133(zero_matrix)
4994 0.037 0.000 0.064 0.000
matrix_space.py:904(_get_matrix_class)
6000/1000 0.037 0.000 0.508 0.001
category.py:1023(parent_class)
7000 0.037 0.000 0.048 0.000
category_types.py:261(__init__)
3962 0.036 0.000 0.069 0.000
sageinspect.py:917(sage_getargspec)
19278 0.035 0.000 0.078 0.000 weakref.py:79(__setitem__)
2000 0.033 0.000 0.053 0.000 sequence.py:86(Sequence)
12000 0.030 0.000 0.059 0.000 misc.py:179(cputime)
55239 0.029 0.000 0.058 0.000 category.py:148(<genexpr>)
993 0.028 0.000 0.086 0.000 homset.py:80(Hom)
14911 0.028 0.000 0.033 0.000 all.py:1(arithmetic)
12994/9994 0.028 0.000 0.659 0.000
unique_representation.py:452(__classcall__)
48986 0.026 0.000 0.050 0.000 category.py:150(<genexpr>)
993 0.025 0.000 0.050 0.000 homset.py:353(__init__)
25236 0.025 0.000 0.025 0.000 weakref.py:228(__init__)
38622 0.021 0.000 0.046 0.000
category.py:1102(is_subcategory)
12000 0.021 0.000 0.021 0.000 {resource.getrusage}
12994/9994 0.021 0.000 0.636 0.000
{sage.misc.classcall_metaclass.typecall}
1000 0.019 0.000 0.168 0.000 misc.py:1051(srange)
27378 0.019 0.000 0.029 0.000 weakref.py:223(__new__)
1000 0.017 0.000 0.184 0.000 constructor.py:34(matrix)
}}}
'''Strongly caching matrix spaces''': Wouldn't help much with the current
design.
The primes used in some of the multimodular steps are randomized, so even
when
doing the same computation, you'll end up with other rings.
It might be an idea to keep a cache of good fields for multimodular stuff,
that
get used before trying random primes. That at least saves creating the
fields.
Caching the matrix spaces might be painful, since you don't know which
dimensions you'll need...
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13400#comment:11>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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