#15104: Special case modn_dense matrix operations to improve performance
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Reporter: nbruin | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.2
Component: linear algebra | Resolution:
Keywords: | Merged in:
Authors: Nils Bruin, Simon | Reviewers:
King | Work issues: regression in
Report Upstream: N/A | right_kernel_matrix
Branch: | Commit:
u/SimonKing/ticket/15104 | 0f008f9266e3ed6fbd67e7f3d357474825bdb160
Dependencies: | Stopgaps:
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Changes (by SimonKing):
* cc: nthiery (added)
Comment:
It seems to me that the following happens when creating a square matrix
and then computing right kernel:
- The parent of the matrix is ''incompletely'' (by #11900) initialised in
the category of algebras. This will ''not'' trigger the creation of super
categories, as the incomplete category initialisation skips the category's
parent class.
- When computing the kernel, some temporary results are created that are
non-square matrices. Their parents are initialised in the category of
vector spaces.
- The temporary results, their parents and thus also the category of
vector spaces will be garbage collected as soon as the kernel computation
is done. Hence, when we compute another kernel, then the category of
vector spaces is created again. And that's the regression.
I just tested: If one adds the following initialisation method to the
category of algebras, then the regression vanishes:
{{{
def __init__(self, B):
Category_over_base_ring.__init__(self, B)
self._super_categories
}}}
It stores the category of B-modules as an attribute of the category of
B-algebras. Hence, if we create a square matrix M over GF(5), then there
will be a chain of strong references
{{{
M->M.parent()->Algebras(GF(5))->VectorSpaces(GF(5))
}}}
And thus the undue garbage collection of `VectorSpaces(GF(5))`, that seems
to be the cause of the regression, will not take place.
However, I can imagine that some code (number fields and elliptic curves
are the usual suspects) will regress when the creation of the category of
algebras always creates the super categories. After all, an observed
regression was the reason for introducing the incomplete initialisation of
matrix spaces in #11900.
What do you think we should do?
--
Ticket URL: <http://trac.sagemath.org/ticket/15104#comment:30>
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