add some triangular ring solver and asymptotically fast generics #1490
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Additional details and impacted files@@ Coverage Diff @@
## master #1490 +/- ##
==========================================
- Coverage 87.11% 86.95% -0.17%
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Files 112 113 +1
Lines 28786 29023 +237
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+ Hits 25078 25236 +158
- Misses 3708 3787 +79 ☔ View full report in Codecov by Sentry. |
but what do we want?
we have
solve_triu for fields Ax = b
rings (this PR) Ax = b
solve_triu_left rings (this PR) xA = b
All three accept large "b", ie. can solve multiple equations in one.
However, they require "A" to be non-singular square
We also have
can_solve_left_reduced_triu
which can deal with arbitrary matrices "A" in rref, but can only
deal with single row "b"
solve_triu for fields also has flags for the diagonal being 1
if b and A are square, this is asymptotically not optimal as it will
be a n^3/2 algo
I can add test - if we want this "interface"
Note: for triangular, one cannot transpose to reduce one case to the
other
Note: in serious use, should also be supplemented by special
implementations in Nemo/ Flint for nmod and/or ZZ
and friends
fieker
changed the title
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also added module Strassen (see help string) to provide sub-cubic generics |
thofma
reviewed
Dec 1, 2023
src/Matrix-Strassen.jl
Outdated
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| #Examples: | ||
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| ```jldoctest |
There was a problem hiding this comment.
It seems that the doctest is failing
|
We should write down what we want for the "solve" interface or the linear algebra interface at large. I suggest we get the stuff here in, once the doctest is fixed. |
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but what do we want?
we have
solve_triu for fields Ax = b
rings (this PR) Ax = b
solve_triu_left rings (this PR) xA = b
All three accept large "b", ie. can solve multiple equations in one.
However, they require "A" to be non-singular square
We also have
can_solve_left_reduced_triu
which can deal with arbitrary matrices "A" in rref, but can only deal with single row "b"
solve_triu for fields also has flags for the diagonal being 1
if b and A are square, this is asymptotically not optimal as it will be a n^3/2 algo
I can add test - if we want this "interface"
Note: for triangular, one cannot transpose to reduce one case to the
other
Note: in serious use, should also be supplemented by special
implementations in Nemo/ Flint for nmod and/or ZZ
and friends