Speed up square matrix times vector over GF(2) #37375
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…rix_times_vector_over_F2' into speed_up_square_matrix_times_vector_over_F2
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vbraun
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When doing a matrix-times-vector multiplication over F_2, there is some inefficiency caused by calling `VectorSpace` to create a parent for the result. This becomes noticeable when repeatedly multiplying small matrices. When the dimensions are all the same, this can be improved by using the parent of the vector also as the parent for the result. Before: ``` sage: A = random_matrix(GF(2),10^2,10^2) sage: v0 = vector(random_matrix(GF(2),10^2,1)) sage: %timeit A*v0 2.78 µs ± 128 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each) ``` After: ``` sage: A = random_matrix(GF(2),10,10) sage: v0 = vector(random_matrix(GF(2),10,1)) sage: %timeit A*v0 995 ns ± 22.9 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each) ``` URL: sagemath#37375 Reported by: kedlaya Reviewer(s): Lorenz Panny
vbraun
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Feb 19, 2024
When doing a matrix-times-vector multiplication over F_2, there is some
inefficiency caused by calling `VectorSpace` to create a parent for the
result. This becomes noticeable when repeatedly multiplying small
matrices.
When the dimensions are all the same, this can be improved by using the
parent of the vector also as the parent for the result. Before:
```
sage: A = random_matrix(GF(2),10^2,10^2)
sage: v0 = vector(random_matrix(GF(2),10^2,1))
sage: %timeit A*v0
2.78 µs ± 128 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops
each)
```
After:
```
sage: A = random_matrix(GF(2),10,10)
sage: v0 = vector(random_matrix(GF(2),10,1))
sage: %timeit A*v0
995 ns ± 22.9 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops
each)
```
URL: sagemath#37375
Reported by: kedlaya
Reviewer(s): Lorenz Panny
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Just a note, your timing doesn't show anything, since the dimensions are different (one's with |
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Oh! Good catch. But there is still a significant speedup: The reduction in runtime is about |
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I fixed the examples to both use 10 by 10 matrices, as indeed this problem is more acute with small matrices. There seems to be a fixed amount of overhead with matrix/vector creation which is rampant throughout Sage; a broader fix for that would obviate the need for such trickery. |
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When doing a matrix-times-vector multiplication over F_2, there is some inefficiency caused by calling
VectorSpaceto create a parent for the result. This becomes noticeable when repeatedly multiplying small matrices.When the dimensions are all the same, this can be improved by using the parent of the vector also as the parent for the result. Before:
After: