DOP853 & DOPRI5 Julia Performance

perf_results.txt

== problem A3 in DETEST ==

testing method ode23
elapsed time: 0.078190123 seconds (12007840 bytes allocated)
*  number of steps: 307
*  minimal step: 0.017235477520255074
*  maximal step: 0.13251841619057103
*  maximal deviation from known solution: 0.00024150339666606513

testing method ode23_bs
elapsed time: 0.033126906 seconds (9628320 bytes allocated)
*  number of steps: 309
*  minimal step: 0.03031894300476523
*  maximal step: 0.13334865621622605
*  maximal deviation from known solution: 0.0002443491465573544

testing method ode45_dp
elapsed time: 0.00598708 seconds (1163120 bytes allocated)
*  number of steps: 52
*  minimal step: 0.1490770803541963
*  maximal step: 0.5277942154551631
*  maximal deviation from known solution: 1.4358013599391484e-5

testing method ode45_fb
elapsed time: 0.006219132 seconds (1255360 bytes allocated)
*  number of steps: 57
*  minimal step: 0.2
*  maximal step: 0.6019190640348882
*  maximal deviation from known solution: 0.0002961599011430671

testing method ode45_ck
elapsed time: 0.005484652 seconds (1071120 bytes allocated)
*  number of steps: 50
*  minimal step: 0.2
*  maximal step: 0.6412708946634034
*  maximal deviation from known solution: 0.00015482199542482533

testing method ode78_fb
elapsed time: 0.003243284 seconds (642960 bytes allocated)
*  number of steps: 26
*  minimal step: 0.06587922665555013
*  maximal step: 1.04220819385041
*  maximal deviation from known solution: 1.1710040641155217e-5

testing method dop853
elapsed time: 0.001676933 seconds (805040 bytes allocated)
*  number of steps: 28
*  minimal step: 0.10018506139785896
*  maximal step: 1.0589836354734983
*  maximal deviation from known solution: 1.2285766426423095e-6

testing method dopri5
elapsed time: 0.002445262 seconds (1112880 bytes allocated)
*  number of steps: 74
*  minimal step: 0.02519328211186309
*  maximal step: 0.35855999952947926
*  maximal deviation from known solution: 4.9140511206857695e-6


== problem B5 in DETEST ==

testing method ode23
elapsed time: 0.047458819 seconds (15729200 bytes allocated)
*  number of steps: 238
*  minimal step: 1.7235477520255075e-5
*  maximal step: 0.13058852624067363


testing method ode23_bs
elapsed time: 0.024245292 seconds (10955760 bytes allocated)
*  number of steps: 172
*  minimal step: 0.0007839590484195469
*  maximal step: 0.18195874962695058


testing method ode45_dp
elapsed time: 0.007087988 seconds (3670320 bytes allocated)
*  number of steps: 34
*  minimal step: 0.12
*  maximal step: 0.5079142619984776


testing method ode45_fb
elapsed time: 0.006479896 seconds (3475760 bytes allocated)
*  number of steps: 36
*  minimal step: 0.12
*  maximal step: 0.5526493932284717


testing method ode45_ck
elapsed time: 0.005299039 seconds (2588080 bytes allocated)
*  number of steps: 28
*  minimal step: 0.12
*  maximal step: 0.5484556191795456


testing method ode78_fb
elapsed time: 0.007544782 seconds (5003920 bytes allocated)
*  number of steps: 16
*  minimal step: 0.12
*  maximal step: 1.1468526118328999


testing method dop853
elapsed time: 0.000937938 seconds (528800 bytes allocated)
*  number of steps: 20
*  minimal step: 0.018298673543277744
*  maximal step: 0.8704990979433624


testing method dopri5
elapsed time: 0.001778931 seconds (885840 bytes allocated)
*  number of steps: 57
*  minimal step: 0.01083038817429916
*  maximal step: 0.31293498238215633



== problem Gravity in DETEST ==

testing method ode23
elapsed time: 0.980828097 seconds (697802080 bytes allocated)
*  number of steps: 3458
*  minimal step: 1.7969148347567307
*  maximal step: 39.060781983490415


testing method ode23_bs
elapsed time: 0.308633596 seconds (202950000 bytes allocated)
*  number of steps: 1609
*  minimal step: 24.995537551425514
*  maximal step: 58.10734867301653


testing method ode45_dp
elapsed time: 0.074177714 seconds (41533040 bytes allocated)
*  number of steps: 304
*  minimal step: 232.63351497167605
*  maximal step: 296.21785556010127


testing method ode45_fb
elapsed time: 0.070920731 seconds (38245520 bytes allocated)
*  number of steps: 334
*  minimal step: 199.5495023339754
*  maximal step: 269.976061169953


testing method ode45_ck
elapsed time: 0.050533567 seconds (26644400 bytes allocated)
*  number of steps: 240
*  minimal step: 283.0622840151336
*  maximal step: 378.1776419570051


testing method ode78_fb
elapsed time: 0.068507682 seconds (45735280 bytes allocated)
*  number of steps: 141
*  minimal step: 196.05248933298572
*  maximal step: 635.4255672809013


testing method dop853
elapsed time: 0.007405494 seconds (3998880 bytes allocated)
*  number of steps: 142
*  minimal step: 0.17736658104116593
*  maximal step: 654.7270685115654


testing method dopri5
elapsed time: 0.031609513 seconds (8225360 bytes allocated)
*  number of steps: 502
*  minimal step: 0.06283402366619872
*  maximal step: 190.75680832781927

results.txt

Julia Version 0.3.0-prerelease+4017
Commit 56da98a (2014-07-02 12:18 UTC)
Platform Info:
  System: Darwin (x86_64-apple-darwin13.3.0)
  CPU: Intel(R) Core(TM) i5-2557M CPU @ 1.70GHz
  WORD_SIZE: 64
  BLAS: libopenblas (USE64BITINT DYNAMIC_ARCH NO_AFFINITY)
  LAPACK: libopenblas
  LIBM: libm
================================================================================

Final results and solver statistics.

DOP853
======
-1814.0158065395183
-3707.990103971951
5153.002179414949
6.511993554724289
-4.229010818589299
-0.7439840760122736

			Fortran	Julia
Func. calls		170	170
Steps taken		14	14
Accepted		14	14
Rejected		0	0

DOPRI5
======
-1813.9287959004837
-3708.0448704225864
5152.990477446107
6.512026718045747
-4.2289470209802875
-0.7440742421532821

			Fortran	Julia
Func. calls		230	230
Steps taken		38	38
Accepted		36	36
Rejected		2	2
================================================================================

Comparison of results for all solver steps.

DOP853
======
1: OK
2: OK
3: OK
4: OK
5: OK
6: OK
7: OK
8: OK
9: OK
10: OK
11: OK
12: OK
13: OK
14: OK
15: OK

DOPRI5
======
1: OK
2: OK
3: OK
4: OK
5: OK
6: OK
7: OK
8: OK
9: OK
10: OK
11: OK
12: OK
13: OK
14: OK
15: OK
16: OK
17: OK
18: OK
19: OK
20: OK
21: OK
22: OK
23: OK
24: OK
25: OK
26: OK
27: OK
28: OK
29: OK
30: OK
31: OK
32: OK
33: OK
34: OK
35: OK
36: OK
37: OK
================================================================================

Timing of a single run and memory allocations.

DOP853
======
High-Level runtime:	8.0463e-5 seconds
High-Level memory:	59928 bytes
Low-Level time:		4.796e-5 seconds
Low-Level memory:	5256 bytes

DOPRI5
======
High-Level runtime:	0.000102152 seconds
High-Level memory:	82776 bytes
Low-Level time:		4.2687e-5 seconds
Low-Level memory:	8904 bytes
================================================================================

Averaged time over N runs.

10000 runs

DOP853
======
High-Level runtime:	0.00010592087599999955 seconds per loop
Low-Level runtime:	2.8295204100000006e-5 seconds per loop
Gfortran:		2.5700000000000018e-5 seconds per loop.
Gfortran (-Ofast):	9.900000000000007e-6 seconds per loop.


DOPRI5
======
High-Level runtime:	0.00022080424379999997 seconds per loop
Low-Level runtime:	6.378757010000009e-5 seconds per loop
Gfortran:		6.330000000000005e-5 seconds per loop
Gfortran (-Ofast):	2.840000000000002e-5 seconds per loop

================================================================================