#16116: Multiplication of dense cyclotomic matrices should be faster
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Reporter: jipilab | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.4
Component: number fields | Resolution:
Keywords: cyclotomic field, matrix, | Merged in:
multiplication, benchmark, days57 | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: |
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Comment (by tscrim):
We also have a related issue:
{{{
sage: R = CyclotomicField(12)
sage: M = matrix.random(R, 40,40)
sage: N = matrix.random(R, 3, 3)
sage: %time K = M.tensor_product(N)
CPU times: user 5.75 s, sys: 28.4 ms, total: 5.78 s
Wall time: 5.73 s
sage: R.defining_polynomial()
x^4 - x^2 + 1
sage: type(M)
<type 'sage.matrix.matrix_cyclo_dense.Matrix_cyclo_dense'>
sage: R = NumberField(x^4 - x^2 + 1, 'a')
sage: M = matrix.random(R, 40,40)
sage: N = matrix.random(R, 3, 3)
sage: %time K = M.tensor_product(N)
CPU times: user 225 ms, sys: 16.4 ms, total: 241 ms
Wall time: 232 ms
sage: type(M)
<type 'sage.matrix.matrix_generic_dense.Matrix_generic_dense'>
}}}
Where the issue is coming from having a scalar times a matrix. Here's some
profiling info of doing it over the cyclotomic field:
{{{
594202 1.806 0.000 3.620 0.000
number_field.py:9200(_element_constructor_)
594202 0.816 0.000 1.171 0.000
number_field.py:6628(_coerce_non_number_field_element_in)
4184691 0.569 0.000 0.569 0.000 {isinstance}
}}}
This is nowhere to be found when doing it over the number field. (For very
small matrices this isn't a problem per se, but it still is visible when
profiling.)
So my conclusion is that we are doing something wrong with how we handle
multiplication with cyclotomics in the matrix versus our generic dense
cases.
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Ticket URL: <http://trac.sagemath.org/ticket/16116#comment:14>
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