# Specifying ode solver options to speed up compute time

**URL:** <https://discourse.julialang.org/t/specifying-ode-solver-options-to-speed-up-compute-time/61784>\
**Category:** New to Julia\
**Tags:** question\
**Created:** [May 25, 2021, 2:26pm UTC](https://discourse.julialang.org/t/specifying-ode-solver-options-to-speed-up-compute-time/61784 "2021-05-25T14:26:58Z")\
**Posts on this page:** 20\
**Page:** 1

<div class="post-metadata">

**Author:** ![Deepa](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/deepa/32/23385_2.png) [@Deepa](https://discourse.julialang.org/u/Deepa)\
**Post date:** [May 25, 2021, 2:26pm UTC](https://discourse.julialang.org/t/specifying-ode-solver-options-to-speed-up-compute-time/61784/1 "2021-05-25T14:26:58Z")

</div>

Hello All,

This is a follow up to my question posted [here](https://scicomp.stackexchange.com/questions/37440/specifying-ode-solver-options-to-speed-up-compute-time).

I’ve installed Julia in windows and I am running the following code (posted in the above-mentioned link) via the Julia plugin instaled in Pycharm.

```julia
using DifferentialEquations, BenchmarkTools

mat1=[
       1 -2 1 0 0 0 0 0 0 0;
       0 1 -2 1 0 0 0 0 0 0;
       0 0 1 -2 1 0 0 0 0 0;
       0 0 0 1 -2 1 0 0 0 0;
       0 0 0 0 1 -2 1 0 0 0;
       0 0 0 0 0 1 -2 1 0 0;
       0 0 0 0 0 0 1 -2 1 0;
       0 0 0 0 0 0 0 1 -2 1;
       ];

mat2 = [
        1 -1 0 0 0 0 0 0 0 0;
        0 1 -1 0 0 0 0 0 0 0;
        0 0 1 -1 0 0 0 0 0 0;
        0 0 0 1 -1 0 0 0 0 0;
        0 0 0 0 1 -1 0 0 0 0;
        0 0 0 0 0 1 -1 0 0 0;
        0 0 0 0 0 0 1 -1 0 0;
        0 0 0 0 0 0 0 1 -1 0;
        ];

x0 = [1.0,0,0,0,0,0,0,0,0,0]
saveat = 0:0.01:5

function fun(dx,x,p,t)
    dx[1,:] .= 0
    dx[2:9,:] .= mat1*x + mat2*x
    dx[10,:] .= 2*(x[end-1] - x[end])
end

prob = ODEProblem(fun,x0,(0.0,5.0))
sys = modelingtoolkitize(prob)
fastprob = ODEProblem(sys,x0,(0.0,5.0),jac=true)

# Explicit RK Methods
@btime sol = solve(fastprob,Tsit5()) # 16.700 μs (245 allocations: 40.28 KiB)
@btime sol = solve(fastprob,BS3()) # 19.800 μs (231 allocations: 33.70 KiB)
@btime sol = solve(fastprob,Vern7()) # 18.400 μs (266 allocations: 49.62 KiB)

# Stabilized-Explicit RK Methods
@btime sol = solve(fastprob,ROCK2()) # 173.300 μs (831 allocations: 159.59 KiB)
@btime sol = solve(fastprob,ROCK4()) # 237.100 μs (1958 allocations: 191.64 KiB)

# Implicit and Semi-Implicit Methods
@btime sol = solve(fastprob,Rosenbrock23()) # 83.200 μs (541 allocations: 53.50 KiB)
@btime sol = solve(fastprob,TRBDF2()) # 72.400 μs (297 allocations: 31.72 KiB)
@btime sol = solve(fastprob,KenCarp47()) # 110.500 μs (444 allocations: 33.02 KiB)

sparseprob = ODEProblem(sys,x0,(0.0,5.0),jac=true,sparse=true)
@btime sol = solve(sparseprob,Rosenbrock23()) # 670.000 μs (3505 allocations: 1.22 MiB)
@btime sol = solve(sparseprob,TRBDF2()) # 254.000 μs (1332 allocations: 414.91 KiB)
@btime sol = solve(sparseprob,KenCarp47()) # 346.400 μs (1757 allocations: 525.05 KiB)

using Setfield, LinearAlgebra
f = fastprob.f
newf = @set f.jac_prototype = Tridiagonal(sparseprob.f.jac_prototype)
newf = @set newf.sparsity = Tridiagonal(sparseprob.f.sparsity)
tridiagprob = ODEProblem(newf,x0,(0.0,5.0))
@btime sol = solve(tridiagprob,Rosenbrock23()) # 188.000 μs (556 allocations: 66.19 KiB)
@btime sol = solve(tridiagprob,TRBDF2()) # 87.800 μs (338 allocations: 40.31 KiB)
@btime sol = solve(tridiagprob,KenCarp47()) # 133.400 μs (482 allocations: 42.16 KiB)

```

I’m not sure why but I observe time in ms and not in microseconds as posted by @ChrisRackauckas on SE.

```julia
  2.847 ms (34957 allocations: 2.63 MiB)
  2.985 ms (31647 allocations: 1.73 MiB)
  3.721 ms (46812 allocations: 5.47 MiB)
  22.349 ms (268252 allocations: 10.67 MiB)
  5.789 ms (80043 allocations: 3.01 MiB)
  78.085 ms (605234 allocations: 20.99 MiB)
  25.611 ms (217583 allocations: 7.47 MiB)
  33.834 ms (288531 allocations: 10.52 MiB)
  74.903 ms (597849 allocations: 20.82 MiB)
  25.356 ms (210161 allocations: 7.29 MiB)
  34.504 ms (281243 allocations: 10.33 MiB)
  11.809 ms (156756 allocations: 4.92 MiB)
  7.047 ms (72883 allocations: 2.52 MiB)
  9.795 ms (103225 allocations: 4.15 MiB)

```

Could someone help me in understanding why it takes ms and not microseconds when I run the code ?

Thanks so much

---

<div class="post-metadata">

**Author:** ![Oscar\_Smith](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/oscar_smith/32/25343_2.png) [@Oscar\_Smith](https://discourse.julialang.org/u/Oscar_Smith)\
**Post date:** [May 25, 2021, 2:31pm UTC](https://discourse.julialang.org/t/specifying-ode-solver-options-to-speed-up-compute-time/61784/2 "2021-05-25T14:31:43Z")

</div>

The big thing that will slow this down is that you aren’t taking advantage of the structure of your matrices (and they are non-`const` globals). If you use `BandedMatrices` for `mat1` and `mat2`, and make them `const` it should be a massive improvement.

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [May 25, 2021, 2:38pm UTC](https://discourse.julialang.org/t/specifying-ode-solver-options-to-speed-up-compute-time/61784/3 "2021-05-25T14:38:00Z")

</div>

Julia v1.6.1? What happens if you run it in the REPL?

---

<div class="post-metadata">

**Author:** ![Deepa](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/deepa/32/23385_2.png) [@Deepa](https://discourse.julialang.org/u/Deepa)\
**Post date:** [May 25, 2021, 2:40pm UTC](https://discourse.julialang.org/t/specifying-ode-solver-options-to-speed-up-compute-time/61784/4 "2021-05-25T14:40:18Z")

</div>

Hi @Oscar_Smith , Thanks for the suggestion. Since the compute time reported in  
in microseconds ( the link shared above) was without the use of `BandedMatrices `, I wasn’t sure why I am not able to observe the same compute time reported by @ChrisRackauckas.

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [May 25, 2021, 2:45pm UTC](https://discourse.julialang.org/t/specifying-ode-solver-options-to-speed-up-compute-time/61784/5 "2021-05-25T14:45:19Z")

</div>

> [@Oscar\_Smith](#):
>
> The big thing that will slow this down is that you aren’t taking advantage of the structure of your matrices (and they are non- `const` globals). If you use `BandedMatrices` for `mat1` and `mat2` , and make them `const` it should be a massive improvement.

That’s not needed because it’s already further optimizing beyond that using the `modelingtoolkitize` to fully scalarize it.

---

<div class="post-metadata">

**Author:** ![Deepa](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/deepa/32/23385_2.png) [@Deepa](https://discourse.julialang.org/u/Deepa)\
**Post date:** [May 25, 2021, 2:45pm UTC](https://discourse.julialang.org/t/specifying-ode-solver-options-to-speed-up-compute-time/61784/6 "2021-05-25T14:45:36Z")

</div>

Yes , I’m using Julia 1.6.1. I’m sorry, I’m really new to Julia and I couldn’t figure out what REPL means. If you don’t mind, could you please direct me to a tutorial on how to run via REPL?

I think you meant the terminal window of the julia executable. I’ll give it a try. Thank you

---

<div class="post-metadata">

**Author:** ![Deepa](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/deepa/32/23385_2.png) [@Deepa](https://discourse.julialang.org/u/Deepa)\
**Post date:** [May 25, 2021, 4:09pm UTC](https://discourse.julialang.org/t/specifying-ode-solver-options-to-speed-up-compute-time/61784/7 "2021-05-25T16:09:09Z")

</div>

in REPL, should I do julia file.jl?

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [May 25, 2021, 5:33pm UTC](https://discourse.julialang.org/t/specifying-ode-solver-options-to-speed-up-compute-time/61784/8 "2021-05-25T17:33:50Z")

</div>

I’m not doing anything special. I’m just doing it the standard way in Juno.

![running](https://global.discourse-cdn.com/julialang/original/3X/8/7/879d3d245f8073b87d81e1a3ed0070a19468031f.gif)

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [May 25, 2021, 5:34pm UTC](https://discourse.julialang.org/t/specifying-ode-solver-options-to-speed-up-compute-time/61784/9 "2021-05-25T17:34:22Z")

</div>

Can you share `versioninfo()` @Deepa ?

---

<div class="post-metadata">

**Author:** ![Deepa](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/deepa/32/23385_2.png) [@Deepa](https://discourse.julialang.org/u/Deepa)\
**Post date:** [May 26, 2021, 9:41am UTC](https://discourse.julialang.org/t/specifying-ode-solver-options-to-speed-up-compute-time/61784/10 "2021-05-26T09:41:52Z")

</div>

@ChrisRackauckas Please find the version info below

```julia
Julia Version 1.6.1
Commit 6aaedecc44 (2021-04-23 05:59 UTC)
Platform Info:
  OS: Windows (x86_64-w64-mingw32)
  CPU: Intel(R) Core(TM) i7-7500U CPU @ 2.70GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-11.0.1 (ORCJIT, skylake)

```

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [May 26, 2021, 10:33am UTC](https://discourse.julialang.org/t/specifying-ode-solver-options-to-speed-up-compute-time/61784/11 "2021-05-26T10:33:29Z")

</div>

@Elrod are you able to reproduce this one? I wonder if there’s some weird thing FastBroadcast.jl does to some chips.

---

<div class="post-metadata">

**Author:** ![Elrod](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/elrod/32/22461_2.png) [@Elrod](https://discourse.julialang.org/u/Elrod)\
**Post date:** [May 26, 2021, 11:00am UTC](https://discourse.julialang.org/t/specifying-ode-solver-options-to-speed-up-compute-time/61784/12 "2021-05-26T11:00:07Z")

</div>

> [@ChrisRackauckas](#):
>
> @Elrod are you able to reproduce this one?

No.

```julia
julia> using DifferentialEquations, BenchmarkHistograms

julia> mat1=[
              1 -2 1 0 0 0 0 0 0 0;
              0 1 -2 1 0 0 0 0 0 0;
              0 0 1 -2 1 0 0 0 0 0;
              0 0 0 1 -2 1 0 0 0 0;
              0 0 0 0 1 -2 1 0 0 0;
              0 0 0 0 0 1 -2 1 0 0;
              0 0 0 0 0 0 1 -2 1 0;
              0 0 0 0 0 0 0 1 -2 1;
              ];

julia> mat2 = [
               1 -1 0 0 0 0 0 0 0 0;
               0 1 -1 0 0 0 0 0 0 0;
               0 0 1 -1 0 0 0 0 0 0;
               0 0 0 1 -1 0 0 0 0 0;
               0 0 0 0 1 -1 0 0 0 0;
               0 0 0 0 0 1 -1 0 0 0;
               0 0 0 0 0 0 1 -1 0 0;
               0 0 0 0 0 0 0 1 -1 0;
               ];

julia> x0 = [1.0,0,0,0,0,0,0,0,0,0];

julia> saveat = 0:0.01:5;

julia> function fun(dx,x,p,t)
           dx[1,:] .= 0
           dx[2:9,:] .= mat1*x + mat2*x
           dx[10,:] .= 2*(x[end-1] - x[end])
       end
fun (generic function with 1 method)

julia> prob = ODEProblem(fun,x0,(0.0,5.0));

julia> sys = modelingtoolkitize(prob);

julia> fastprob = ODEProblem(sys,x0,(0.0,5.0),jac=true);

julia> # Explicit RK Methods
       @benchmark sol = solve($fastprob,Tsit5()) # 16.700 μs (245 allocations: 40.28 KiB)
samples: 10000; evals/sample: 1; memory estimate: 39.20 KiB; allocs estimate: 244
ns

 (14200.0 - 15900.0 ] ██████████████████████████████ 5365
 (15900.0 - 17600.0 ] █▍245
 (17600.0 - 19400.0 ] ▌68
 (19400.0 - 21100.0 ] ██344
 (21100.0 - 22800.0 ] █████████▋1700
 (22800.0 - 24500.0 ] ████████▌1518
 (24500.0 - 26200.0 ] ██▉513
 (26200.0 - 27900.0 ] █▏181
 (27900.0 - 29600.0 ] ▍48
 (29600.0 - 31300.0 ] ▏2
 (31300.0 - 33000.0 ] ▏2
 (33000.0 - 34700.0 ] ▏2
 (34700.0 - 36400.0 ] ▏1
 (36400.0 - 38100.0 ] ▏1
 (38100.0 - 4.4385e6] ▏10

                  Counts

min: 14.226 μs (0.00% GC); mean: 20.654 μs (10.28% GC); median: 15.399 μs (0.00% GC); max: 4.438 ms (99.04% GC).

julia> @benchmark sol = solve($fastprob,BS3()) # 19.800 μs (231 allocations: 33.70 KiB)
samples: 10000; evals/sample: 1; memory estimate: 33.03 KiB; allocs estimate: 230
ns

 (17900.0 - 19600.0 ] ██████████████████████████████ 5474
 (19600.0 - 21200.0 ] █▊305
 (21200.0 - 22800.0 ] ▌86
 (22800.0 - 24400.0 ] █████████▏1661
 (24400.0 - 26100.0 ] █████████▎1680
 (26100.0 - 27700.0 ] ██▉518
 (27700.0 - 29300.0 ] ▉144
 (29300.0 - 31000.0 ] ▌88
 (31000.0 - 32600.0 ] ▎30
 (32600.0 - 34200.0 ] ▏1
 (34200.0 - 35900.0 ] 0
 (35900.0 - 37500.0 ] 0
 (37500.0 - 39100.0 ] 0
 (39100.0 - 40700.0 ] ▏3
 (40700.0 - 4.8166e6] ▏10

                  Counts

min: 17.927 μs (0.00% GC); mean: 23.190 μs (7.90% GC); median: 18.893 μs (0.00% GC); max: 4.817 ms (99.08% GC).

julia> @benchmark sol = solve($fastprob,Vern7()) # 18.400 μs (266 allocations: 49.62 KiB)
samples: 10000; evals/sample: 1; memory estimate: 47.36 KiB; allocs estimate: 265
ns

 (15800.0 - 18200.0 ] ██████████████████████████████6001
 (18200.0 - 20700.0 ] █▊341
 (20700.0 - 23100.0 ] ▍63
 (23100.0 - 25600.0 ] ██████▌1280
 (25600.0 - 28000.0 ] █████████▏1824
 (28000.0 - 30500.0 ] █▉360
 (30500.0 - 32900.0 ] ▋102
 (32900.0 - 35400.0 ] ▏11
 (35400.0 - 37800.0 ] 0
 (37800.0 - 40300.0 ] 0
 (40300.0 - 42700.0 ] ▏4
 (42700.0 - 45200.0 ] ▏3
 (45200.0 - 47600.0 ] 0
 (47600.0 - 50100.0 ] ▏1
 (50100.0 - 3.9094e6] ▏10

                  Counts

min: 15.794 μs (0.00% GC); mean: 22.292 μs (8.35% GC); median: 17.203 μs (0.00% GC); max: 3.909 ms (98.93% GC).

julia> # Stabilized-Explicit RK Methods
       @benchmark sol = solve($fastprob,ROCK2()) # 173.300 μs (831 allocations: 159.59 KiB)
samples: 10000; evals/sample: 1; memory estimate: 158.97 KiB; allocs estimate: 830
ns

 (160000.0 - 390000.0] ██████████████████████████████ 9980
 (390000.0 - 620000.0] ▏1
 (620000.0 - 840000.0] 0
 (840000.0 - 1.07e6 ] 0
 (1.07e6 - 1.3e6 ] 0
 (1.3e6 - 1.52e6 ] 0
 (1.52e6 - 1.75e6 ] 0
 (1.75e6 - 1.98e6 ] 0
 (1.98e6 - 2.2e6 ] 0
 (2.2e6 - 2.43e6 ] 0
 (2.43e6 - 2.66e6 ] 0
 (2.66e6 - 2.88e6 ] 0
 (2.88e6 - 3.11e6 ] 0
 (3.11e6 - 3.34e6 ] ▏9
 (3.34e6 - 3.85e6 ] ▏10

                  Counts

min: 161.643 μs (0.00% GC); mean: 175.670 μs (3.43% GC); median: 166.189 μs (0.00% GC); max: 3.846 ms (94.05% GC).

julia> @benchmark sol = solve($fastprob,ROCK4()) # 237.100 μs (1958 allocations: 191.64 KiB)
samples: 10000; evals/sample: 1; memory estimate: 191.62 KiB; allocs estimate: 1958
ns

 (200000.0 - 690000.0] ██████████████████████████████ 9977
 (690000.0 - 1.17e6 ] 0
 (1.17e6 - 1.66e6 ] 0
 (1.66e6 - 2.14e6 ] 0
 (2.14e6 - 2.63e6 ] 0
 (2.63e6 - 3.11e6 ] 0
 (3.11e6 - 3.6e6 ] 0
 (3.6e6 - 4.08e6 ] 0
 (4.08e6 - 4.57e6 ] 0
 (4.57e6 - 5.06e6 ] 0
 (5.06e6 - 5.54e6 ] 0
 (5.54e6 - 6.03e6 ] 0
 (6.03e6 - 6.51e6 ] 0
 (6.51e6 - 7.0e6 ] 0
 (7.0e6 - 7.48e6 ] ▏23

                  Counts

min: 199.522 μs (0.00% GC); mean: 220.741 μs (7.10% GC); median: 203.291 μs (0.00% GC); max: 7.485 ms (96.29% GC).

julia> # Implicit and Semi-Implicit Methods
       @benchmark sol = solve($fastprob,Rosenbrock23()) # 83.200 μs (541 allocations: 53.50 KiB)
samples: 10000; evals/sample: 1; memory estimate: 52.97 KiB; allocs estimate: 541
ns

 (79100.0 - 82100.0 ] ██████████████████████████████ 5525
 (82100.0 - 85000.0 ] ██████▎1138
 (85000.0 - 87900.0 ] ███▏555
 (87900.0 - 90800.0 ] █████████▍1715
 (90800.0 - 93800.0 ] ███▉696
 (93800.0 - 96700.0 ] █▍236
 (96700.0 - 99600.0 ] ▍49
 (99600.0 - 102500.0] ▎25
 (102500.0 - 105500.0] ▏17
 (105500.0 - 108400.0] ▏8
 (108400.0 - 111300.0] ▏5
 (111300.0 - 114200.0] ▏7
 (114200.0 - 117200.0] ▏4
 (117200.0 - 120100.0] ▏10
 (120100.0 - 6.349e6 ] ▏10

                  Counts

min: 79.133 μs (0.00% GC); mean: 87.742 μs (4.07% GC); median: 81.390 μs (0.00% GC); max: 6.349 ms (97.74% GC).

julia> @benchmark sol = solve($fastprob,TRBDF2()) # 72.400 μs (297 allocations: 31.72 KiB)
samples: 10000; evals/sample: 1; memory estimate: 30.98 KiB; allocs estimate: 295
ns

 (66400.0 - 68100.0 ] ██████████████████████████████ 4508
 (68100.0 - 69700.0 ] ████████▊1301
 (69700.0 - 71300.0 ] ███▉570
 (71300.0 - 72900.0 ] ████████▊1312
 (72900.0 - 74600.0 ] █████████1349
 (74600.0 - 76200.0 ] ████586
 (76200.0 - 77800.0 ] █▎185
 (77800.0 - 79400.0 ] ▊96
 (79400.0 - 81100.0 ] ▌58
 (81100.0 - 82700.0 ] ▏17
 (82700.0 - 84300.0 ] ▏4
 (84300.0 - 85900.0 ] ▏1
 (85900.0 - 87600.0 ] 0
 (87600.0 - 89200.0 ] ▏3
 (89200.0 - 6.4517e6] ▏10

                  Counts

min: 66.446 μs (0.00% GC); mean: 72.016 μs (2.59% GC); median: 68.454 μs (0.00% GC); max: 6.452 ms (98.48% GC).

julia> @benchmark sol = solve($fastprob,KenCarp47()) # 110.500 μs (444 allocations: 33.02 KiB)
samples: 10000; evals/sample: 1; memory estimate: 32.28 KiB; allocs estimate: 442
ns

 (93800.0 - 95400.0 ] ██████████████████████████████ 3879
 (95400.0 - 97100.0 ] ██████████████████▌2383
 (97100.0 - 98700.0 ] ██████▏786
 (98700.0 - 100300.0] ██████▌829
 (100300.0 - 101900.0] ████████▍1069
 (101900.0 - 103500.0] ████▊614
 (103500.0 - 105100.0] █▊220
 (105100.0 - 106700.0] ▊94
 (106700.0 - 108300.0] ▌63
 (108300.0 - 109900.0] ▎32
 (109900.0 - 111500.0] ▏14
 (111500.0 - 113100.0] ▏4
 (113100.0 - 114800.0] ▏1
 (114800.0 - 116400.0] ▏2
 (116400.0 - 6.5823e6] ▏10

                  Counts

min: 93.838 μs (0.00% GC); mean: 98.714 μs (1.29% GC); median: 95.878 μs (0.00% GC); max: 6.582 ms (97.31% GC).

julia> sparseprob = ODEProblem(sys,x0,(0.0,5.0),jac=true,sparse=true);

julia> @benchmark sol = solve($sparseprob,Rosenbrock23()) # 670.000 μs (3505 allocations: 1.22 MiB)
samples: 10000; evals/sample: 1; memory estimate: 60.00 KiB; allocs estimate: 576
ns

 (82100.0 - 85000.0 ] ██████████████████████████████5107
 (85000.0 - 87900.0 ] ███████▊1318
 (87900.0 - 90900.0 ] ███▏512
 (90900.0 - 93800.0 ] ████▋779
 (93800.0 - 96700.0 ] ████████▌1429
 (96700.0 - 99700.0 ] ███▍560
 (99700.0 - 102600.0] █▏177
 (102600.0 - 105500.0] ▍48
 (105500.0 - 108500.0] ▏16
 (108500.0 - 111400.0] ▏13
 (111400.0 - 114300.0] ▏13
 (114300.0 - 117300.0] ▏7
 (117300.0 - 120200.0] ▏5
 (120200.0 - 123100.0] ▏6
 (123100.0 - 6.7211e6] ▏10

                  Counts

min: 82.072 μs (0.00% GC); mean: 91.952 μs (4.12% GC); median: 84.918 μs (0.00% GC); max: 6.721 ms (97.90% GC).

julia> @benchmark sol = solve($sparseprob,TRBDF2()) # 254.000 μs (1332 allocations: 414.91 KiB)
samples: 10000; evals/sample: 1; memory estimate: 38.38 KiB; allocs estimate: 332
ns

 (69200.0 - 71000.0 ] ██████████████████████████████ 3557
 (71000.0 - 72900.0 ] ██████████████████▊2215
 (72900.0 - 74700.0 ] ████▌525
 (74700.0 - 76500.0 ] ██████▍743
 (76500.0 - 78400.0 ] ██████████▊1264
 (78400.0 - 80200.0 ] ████████▊1027
 (80200.0 - 82000.0 ] ███▎381
 (82000.0 - 83900.0 ] █▌165
 (83900.0 - 85700.0 ] ▋74
 (85700.0 - 87500.0 ] ▎20
 (87500.0 - 89400.0 ] ▏9
 (89400.0 - 91200.0 ] ▏1
 (91200.0 - 93000.0 ] ▏3
 (93000.0 - 94900.0 ] ▏6
 (94900.0 - 6.7441e6] ▏10

                  Counts

min: 69.216 μs (0.00% GC); mean: 76.484 μs (3.37% GC); median: 71.754 μs (0.00% GC); max: 6.744 ms (98.18% GC).

julia> @benchmark sol = solve($sparseprob,KenCarp47()) # 346.400 μs (1757 allocations: 525.05 KiB)
samples: 10000; evals/sample: 1; memory estimate: 39.67 KiB; allocs estimate: 479
ns

 (97300.0 - 99100.0 ] █████████████████████▊2522
 (99100.0 - 100900.0] ██████████████████████████████ 3480
 (100900.0 - 102700.0] ████████▏932
 (102700.0 - 104600.0] █████▉673
 (104600.0 - 106400.0] ███████▉903
 (106400.0 - 108200.0] ███████▏826
 (108200.0 - 110000.0] ███▍391
 (110000.0 - 111900.0] █▍148
 (111900.0 - 113700.0] ▋64
 (113700.0 - 115500.0] ▎28
 (115500.0 - 117300.0] ▎16
 (117300.0 - 119200.0] ▏4
 (119200.0 - 121000.0] 0
 (121000.0 - 122800.0] ▏3
 (122800.0 - 6.9148e6] ▏10

                  Counts

min: 97.279 μs (0.00% GC); mean: 104.418 μs (2.50% GC); median: 100.061 μs (0.00% GC); max: 6.915 ms (97.43% GC).

julia> using Setfield, LinearAlgebra

julia> f = fastprob.f;

julia> newf = @set f.jac_prototype = Tridiagonal(sparseprob.f.jac_prototype);

julia> newf = @set newf.sparsity = Tridiagonal(sparseprob.f.sparsity);

julia> tridiagprob = ODEProblem(newf,x0,(0.0,5.0));

julia> @benchmark sol = solve($tridiagprob,Rosenbrock23()) # 188.000 μs (556 allocations: 66.19 KiB)
samples: 10000; evals/sample: 1; memory estimate: 60.91 KiB; allocs estimate: 501
ns

 (93000.0 - 95600.0 ] ██████████████████████████████ 4781
 (95600.0 - 98100.0 ] ████████▊1394
 (98100.0 - 100700.0] ███▏494
 (100700.0 - 103200.0] █155
 (103200.0 - 105800.0] ██████▌1019
 (105800.0 - 108300.0] ████████▋1355
 (108300.0 - 110900.0] ███▊581
 (110900.0 - 113400.0] █▏167
 (113400.0 - 116000.0] ▎29
 (116000.0 - 118500.0] ▏6
 (118500.0 - 121100.0] ▏2
 (121100.0 - 123600.0] ▏4
 (123600.0 - 126200.0] 0
 (126200.0 - 128700.0] ▏3
 (128700.0 - 6.8546e6] ▏10

                  Counts

min: 93.010 μs (0.00% GC); mean: 103.109 μs (3.80% GC); median: 95.750 μs (0.00% GC); max: 6.855 ms (98.14% GC).

julia> @benchmark sol = solve($tridiagprob,TRBDF2()) # 87.800 μs (338 allocations: 40.31 KiB)
samples: 10000; evals/sample: 1; memory estimate: 37.61 KiB; allocs estimate: 317
ns

 (54300.0 - 55900.0 ] ██████████████████████████████4345
 (55900.0 - 57600.0 ] ██████████1434
 (57600.0 - 59300.0 ] ██▎315
 (59300.0 - 61000.0 ] ███▉548
 (61000.0 - 62700.0 ] █████████▊1411
 (62700.0 - 64400.0 ] ████████1148
 (64400.0 - 66000.0 ] ███▏449
 (66000.0 - 67700.0 ] █▍188
 (67700.0 - 69400.0 ] ▊96
 (69400.0 - 71100.0 ] ▍37
 (71100.0 - 72800.0 ] ▏12
 (72800.0 - 74500.0 ] ▏3
 (74500.0 - 76100.0 ] 0
 (76100.0 - 77800.0 ] ▏4
 (77800.0 - 6.9987e6] ▏10

                  Counts

min: 54.263 μs (0.00% GC); mean: 61.268 μs (4.35% GC); median: 56.349 μs (0.00% GC); max: 6.999 ms (98.13% GC).

julia> @benchmark sol = solve($tridiagprob,KenCarp47()) # 133.400 μs (482 allocations: 42.16 KiB)
samples: 10000; evals/sample: 1; memory estimate: 39.14 KiB; allocs estimate: 457
ns

 (80500.0 - 82500.0 ] ██████████████████████████████ 4414
 (82500.0 - 84500.0 ] █████████████▌1977
 (84500.0 - 86500.0 ] ███▉558
 (86500.0 - 88500.0 ] █████▉856
 (88500.0 - 90500.0 ] ████████▏1185
 (90500.0 - 92500.0 ] ████▎619
 (92500.0 - 94600.0 ] █▊246
 (94600.0 - 96600.0 ] ▋89
 (96600.0 - 98600.0 ] ▎34
 (98600.0 - 100600.0] ▏5
 (100600.0 - 102600.0] ▏2
 (102600.0 - 104600.0] ▏2
 (104600.0 - 106600.0] 0
 (106600.0 - 108600.0] ▏3
 (108600.0 - 7.0086e6] ▏10

                  Counts

min: 80.466 μs (0.00% GC); mean: 87.458 μs (3.05% GC); median: 82.759 μs (0.00% GC); max: 7.009 ms (97.91% GC).

```

> [@ChrisRackauckas](#):
>
> I wonder if there’s some weird thing FastBroadcast.jl does to some chips.

The other issue reporting a regression used a Skylake-X Xeon CPU, which is more or less the same as mine. Two possible causes there:

1. Their config was dual socket, mine is single socket. Maybe there’s an issue with multi-socket systems.
2. Starting in Julia 1.6 (with LLVM \>=10, 1.6 ships with LLVM 11, 1.5 with LLVM 9), LLVM will use 256-bit vectors on AVX512 systems (note: LoopVectorization will continue to use 512-bit vectors). I override this by default (starting Julia with `-C"native,-prefer-256-bit"` to turn off the preference for 256-bit). I did try running the benchmarks with the default settings. This caused around a 5% hit to performance, nothing like the one [reported in that issue](https://github.com/SciML/OrdinaryDiffEq.jl/issues/1422) so I didn’t bring it up there as it couldn’t explain the reported \<1.6 v 1.6 discrepency.

But neither of these are the case with Deepa’s skylake CPU (single socket, no AVX512).

FastBroadcast.jl just relies on LLVM to optimize loops, just like base broadcasting and the old `@..`, but should be easier on LLVM.

I think someone experiencing bad performance should profile, looking for anything taking a lot more time in 1.6 than in \<1.6, and report with that example.

---

<div class="post-metadata">

**Author:** ![ptoche](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ptoche/32/23554_2.png) [@ptoche](https://discourse.julialang.org/u/ptoche)\
**Post date:** [May 26, 2021, 11:09am UTC](https://discourse.julialang.org/t/specifying-ode-solver-options-to-speed-up-compute-time/61784/13 "2021-05-26T11:09:22Z")

</div>

Out of curiosity I ran the code on my 2017 MacBook Pro and found times comparable to Chris’s.

23.593 μs (267 allocations: 40.45 KiB)  
28.850 μs (278 allocations: 34.07 KiB)  
28.965 μs (284 allocations: 49.77 KiB)

234.572 μs (1020 allocations: 161.07 KiB)  
327.884 μs (1986 allocations: 191.86 KiB)

123.919 μs (637 allocations: 54.28 KiB)  
108.163 μs (467 allocations: 33.05 KiB)  
147.139 μs (669 allocations: 34.77 KiB)

130.978 μs (671 allocations: 60.78 KiB)  
117.362 μs (503 allocations: 39.83 KiB)  
155.347 μs (705 allocations: 41.55 KiB)

164.535 μs (596 allocations: 61.69 KiB)  
102.793 μs (488 allocations: 39.06 KiB)  
145.441 μs (683 allocations: 41.02 KiB)

Julia Version 1.6.1  
Commit 6aaedecc44 (2021-04-23 05:59 UTC)  
Platform Info:  
OS: macOS (x86\_64-apple-darwin18.7.0)  
CPU: Intel(R) Core™ i7-4870HQ CPU @ 2.50GHz  
WORD\_SIZE: 64  
LIBM: libopenlibm  
LLVM: libLLVM-11.0.1 (ORCJIT, haswell)  
Environment:  
JULIA\_NUM\_THREADS = 4

```
# https://scicomp.stackexchange.com/questions/37440/specifying-ode-solver-options-to-speed-up-compute-time

using DifferentialEquations, BenchmarkTools

mat1=[
       1 -2 1 0 0 0 0 0 0 0;
       0 1 -2 1 0 0 0 0 0 0;
       0 0 1 -2 1 0 0 0 0 0;
       0 0 0 1 -2 1 0 0 0 0;
       0 0 0 0 1 -2 1 0 0 0;
       0 0 0 0 0 1 -2 1 0 0;
       0 0 0 0 0 0 1 -2 1 0;
       0 0 0 0 0 0 0 1 -2 1;
       ];

mat2 = [
        1 -1 0 0 0 0 0 0 0 0;
        0 1 -1 0 0 0 0 0 0 0;
        0 0 1 -1 0 0 0 0 0 0;
        0 0 0 1 -1 0 0 0 0 0;
        0 0 0 0 1 -1 0 0 0 0;
        0 0 0 0 0 1 -1 0 0 0;
        0 0 0 0 0 0 1 -1 0 0;
        0 0 0 0 0 0 0 1 -1 0;
        ];

x0 = [1.0,0,0,0,0,0,0,0,0,0]
saveat = 0:0.01:5

function fun(dx,x,p,t)
    dx[1,:] .= 0
    dx[2:9,:] .= mat1*x + mat2*x
    dx[10,:] .= 2*(x[end-1] - x[end])
end

prob = ODEProblem(fun,x0,(0.0,5.0))
sys = modelingtoolkitize(prob)
fastprob = ODEProblem(sys,x0,(0.0,5.0),jac=true)

# Explicit RK Methods
@btime sol = solve(fastprob,Tsit5()) # 16.700 μs (245 allocations: 40.28 KiB)
@btime sol = solve(fastprob,BS3()) # 19.800 μs (231 allocations: 33.70 KiB)
@btime sol = solve(fastprob,Vern7()) # 18.400 μs (266 allocations: 49.62 KiB)

# Stabilized-Explicit RK Methods
@btime sol = solve(fastprob,ROCK2()) # 173.300 μs (831 allocations: 159.59 KiB)
@btime sol = solve(fastprob,ROCK4()) # 237.100 μs (1958 allocations: 191.64 KiB)

# Implicit and Semi-Implicit Methods
@btime sol = solve(fastprob,Rosenbrock23()) # 83.200 μs (541 allocations: 53.50 KiB)
@btime sol = solve(fastprob,TRBDF2()) # 72.400 μs (297 allocations: 31.72 KiB)
@btime sol = solve(fastprob,KenCarp47()) # 110.500 μs (444 allocations: 33.02 KiB)

sparseprob = ODEProblem(sys,x0,(0.0,5.0),jac=true,sparse=true)
@btime sol = solve(sparseprob,Rosenbrock23()) # 670.000 μs (3505 allocations: 1.22 MiB)
@btime sol = solve(sparseprob,TRBDF2()) # 254.000 μs (1332 allocations: 414.91 KiB)
@btime sol = solve(sparseprob,KenCarp47()) # 346.400 μs (1757 allocations: 525.05 KiB)

using Setfield, LinearAlgebra
f = fastprob.f
newf = @set f.jac_prototype = Tridiagonal(sparseprob.f.jac_prototype)
newf = @set newf.sparsity = Tridiagonal(sparseprob.f.sparsity)
tridiagprob = ODEProblem(newf,x0,(0.0,5.0))
@btime sol = solve(tridiagprob,Rosenbrock23()) # 188.000 μs (556 allocations: 66.19 KiB)
@btime sol = solve(tridiagprob,TRBDF2()) # 87.800 μs (338 allocations: 40.31 KiB)
@btime sol = solve(tridiagprob,KenCarp47()) # 133.400 μs (482 allocations: 42.16 KiB)

versioninfo()

```

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [May 26, 2021, 11:10am UTC](https://discourse.julialang.org/t/specifying-ode-solver-options-to-speed-up-compute-time/61784/14 "2021-05-26T11:10:36Z")

</div>

It would be good to have a few other people run it too, see if we can find a pattern in the CPUs or something.

---

<div class="post-metadata">

**Author:** ![Elrod](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/elrod/32/22461_2.png) [@Elrod](https://discourse.julialang.org/u/Elrod)\
**Post date:** [May 26, 2021, 12:01pm UTC](https://discourse.julialang.org/t/specifying-ode-solver-options-to-speed-up-compute-time/61784/15 "2021-05-26T12:01:26Z")

</div>

And also `Base.JLOptions()`, to make sure there aren’t any weird settings?

---

<div class="post-metadata">

**Author:** ![Deepa](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/deepa/32/23385_2.png) [@Deepa](https://discourse.julialang.org/u/Deepa)\
**Post date:** [May 26, 2021, 2:26pm UTC](https://discourse.julialang.org/t/specifying-ode-solver-options-to-speed-up-compute-time/61784/16 "2021-05-26T14:26:07Z")

</div>

Hi @ChrisRackauckas ,

I tried the same code in Juno and I observe the following

```julia
19.200 μs (245 allocations: 40.27 KiB)
  24.100 μs (231 allocations: 33.69 KiB)
  22.100 μs (266 allocations: 49.61 KiB)
  204.200 μs (831 allocations: 159.58 KiB)
  277.700 μs (1958 allocations: 191.62 KiB)
  5.259 ms (10836 allocations: 301.75 KiB)
  1.501 ms (3144 allocations: 100.36 KiB)
  1.985 ms (4167 allocations: 122.78 KiB)
  5.275 ms (10870 allocations: 308.25 KiB)
  1.515 ms (3180 allocations: 107.14 KiB)
  1.998 ms (4203 allocations: 129.56 KiB)
  127.900 μs (502 allocations: 60.94 KiB)
  72.500 μs (318 allocations: 37.72 KiB)
  107.700 μs (458 allocations: 39.25 KiB)

```

I still observe ms for `Implicit and Semi-Implicit Methods` and while running `sparseprob` . The other runtimes are more or less close to what was posted by you.

---

<div class="post-metadata">

**Author:** ![BLI](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bli/32/37206_2.png) [@BLI](https://discourse.julialang.org/u/BLI)\
**Post date:** [May 26, 2021, 3:05pm UTC](https://discourse.julialang.org/t/specifying-ode-solver-options-to-speed-up-compute-time/61784/17 "2021-05-26T15:05:40Z")

</div>

I ran the code on my home computer set-up (16GB RAM):

```julia
Julia Version 1.6.0
Commit f9720dc2eb (2021-03-24 12:55 UTC)
Platform Info:
  OS: Windows (x86_64-w64-mingw32)
  CPU: Intel(R) Core(TM) i9-9900T CPU @ 2.10GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-11.0.1 (ORCJIT, skylake)

```

The results are (REPL):

```julia
julia> # Explicit RK Methods
julia> @btime sol = solve(fastprob,Tsit5()); # 16.700 μs (245 allocations: 40.28 KiB)
  16.100 μs (245 allocations: 40.28 KiB)
julia> @btime sol = solve(fastprob,BS3()); # 19.800 μs (231 allocations: 33.70 KiB)
  20.200 μs (231 allocations: 33.70 KiB)
julia> @btime sol = solve(fastprob,Vern7()); # 18.400 μs (266 allocations: 49.62 KiB)
  18.100 μs (266 allocations: 49.62 KiB)

julia> # Stabilized-Explicit RK Methods
julia> @btime sol = solve(fastprob,ROCK2()); # 173.300 μs (831 allocations: 159.59 KiB)
  170.200 μs (831 allocations: 159.59 KiB)
julia> @btime sol = solve(fastprob,ROCK4()); # 237.100 μs (1958 allocations: 191.64 KiB)
  212.100 μs (1958 allocations: 191.64 KiB)

julia> # Implicit and Semi-Implicit Methods
julia> @btime sol = solve(fastprob,Rosenbrock23()); # 83.200 μs (541 allocations: 53.50 KiB)
  82.100 μs (543 allocations: 53.55 KiB)
julia> @btime sol = solve(fastprob,TRBDF2()); # 72.400 μs (297 allocations: 31.72 KiB)
  69.100 μs (297 allocations: 31.72 KiB)
julia> @btime sol = solve(fastprob,KenCarp47()); # 110.500 μs (444 allocations: 33.02 KiB)
  98.600 μs (444 allocations: 33.02 KiB)

julia> # Sparse problems
julia> @btime sol = solve(sparseprob,Rosenbrock23()); # 670.000 μs (3505 allocations: 1.22 MiB)
  86.900 μs (577 allocations: 60.05 KiB)
julia> @btime sol = solve(sparseprob,TRBDF2()); # 254.000 μs (1332 allocations: 414.91 KiB)
  76.200 μs (333 allocations: 38.50 KiB)
julia> @btime sol = solve(sparseprob,KenCarp47()); # 346.400 μs (1757 allocations: 525.05 KiB)
  100.800 μs (480 allocations: 39.80 KiB)

julia> # Tridiagonal problems 
julia> @btime sol = solve(tridiagprob,Rosenbrock23()); # 188.000 μs (556 allocations: 66.19 KiB)
  108.900 μs (502 allocations: 60.95 KiB)
julia> @btime sol = solve(tridiagprob,TRBDF2()); # 87.800 μs (338 allocations: 40.31 KiB)
  61.900 μs (318 allocations: 37.73 KiB)
julia> @btime sol = solve(tridiagprob,KenCarp47()); # 133.400 μs (482 allocations: 42.16
  88.000 μs (458 allocations: 39.27 KiB)

```

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [May 26, 2021, 3:39pm UTC](https://discourse.julialang.org/t/specifying-ode-solver-options-to-speed-up-compute-time/61784/18 "2021-05-26T15:39:17Z")

</div>

So the issue is PyCharm? Can you share what `Base.JLOptions()` gives from PyCharm?

---

<div class="post-metadata">

**Author:** ![Deepa](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/deepa/32/23385_2.png) [@Deepa](https://discourse.julialang.org/u/Deepa)\
**Post date:** [May 26, 2021, 4:45pm UTC](https://discourse.julialang.org/t/specifying-ode-solver-options-to-speed-up-compute-time/61784/19 "2021-05-26T16:45:03Z")

</div>

@ChrisRackauckas Sure, I post what Base.JLOptions() gives soon. I’m facing some issue in opening REPL in PyCharm.

Also, in Juno I’m not sure why Implicit and Semi-Implicit Methods take long time for my run.

---

<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [May 26, 2021, 6:23pm UTC](https://discourse.julialang.org/t/specifying-ode-solver-options-to-speed-up-compute-time/61784/20 "2021-05-26T18:23:51Z")

</div>

Are your BLAS threads one or something?

[Next page](https://discourse.julialang.org/t/specifying-ode-solver-options-to-speed-up-compute-time/61784.md?page=2)