Matrix exponential slower in Julia 0.7 / 1.0?

General Usage Performance
1

In Julia 0.6.4:

julia> @btime expm([1 0; 2 0])
  3.601 μs (46 allocations: 4.55 KiB)

In Julia 0.7 and 1.0:

julia> @btime exp([1 0; 2 0])
  16.710 μs (67 allocations: 4.55 KiB)

Any idea what’s causing this? Perhaps the implementation changed as part of the rename?

2 Likes
2

I could reproduce.

3

Thanks. I filed a github issue.

4

By the way, if tiny matrix exponentials are actually your target use case, then StaticArrays are 40X faster than even the 0.6 version:

julia> using StaticArrays

julia> m = @SMatrix [1 0; 2 0]
2×2 SArray{Tuple{2,2},Int64,2,4}:
 1  0
 2  0

julia> using BenchmarkTools

julia> @btime exp($m)
  87.196 ns (0 allocations: 0 bytes)
2×2 SArray{Tuple{2,2},Float64,2,4}:
 2.71828  0.0
 3.43656  1.0
6 Likes
5

Thanks. That’s very interesting.

6

And thanks to @kristoffer.carlsson for the quick resolution of the github issue!

7

Can someone explain this, by the way?

julia> m = @SMatrix [1 0; 2 0];

julia> @btime exp($m);
  93.038 ns (0 allocations: 0 bytes)

julia> @btime exp(@SMatrix [1 0; 2 0]);
  60.237 ns (0 allocations: 0 bytes)

This seems backwards to me.

8

It is not backwards. It is the difference between

f(m) = exp(m)

and

f() = exp(@SMatrix [1 0; 2 0]);

In the second, the matrix is a known constant and the function can be further optimized.

1 Like