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Interpretted languages:

Loops are very slow
Usually worth creating extra arrays to avoid explicit loops
People often call operations on arrays "vectorized", even if every operation is done in serial

Compiled languages:

Loops are fast.
Can choose whether to write a loop explicilty based on what's more intuitive for programmer and algorithm.
Using "vectorized" notation can unintentionally add unnecessary memory allocations...
- if you don't use broadcasting and fusing

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Generic functions in terms of abstract type

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Peer Code Review

Constructive suggestions for improving programming practices (1 point)
Specific, constructive suggestions for improving code readability/documentation (1 point)
Specific, constructive suggestions for improving tests and/or assertions (1 point)
Specific, constructive suggestions for improving code modularity/organization/maintainability (1 point)
Specific, constructive suggestions for improving code efficiency (1 point)
Finding any bugs (if code author confirms) (bonus points?)

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Implementation details for code efficiency

(assuming JIT languages)

Avoid unnecessary memory allocations
- Take advantage of fusing and broadcasting
- Use view (e.g., view(array,1:5,:)) instead of copying (array[1:5,:])
- Avoid many small allocations on heap (e.g., using StaticArrays.jl)
Avoid type instability
- Avoid untyped global variables
- Avoid containers (e.g., arrays) of abstract types
- Avoid abstract types for fields in structs
- Write type-stable functions
Organize code into small functions (see function barriers)
Avoid inefficient data structures (e.g., Dict when better choice avaliable)
Adding annotations that enable/allow compiler optimizations (e.g., @inbounds, @fastmath, @simd, @turbo), but only when appropriate
Avoid unnecessary use of strings or string interpolation
Write code so that it can be parallelized in the future (see later labs)

See Performance Tips for more details.

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When to start parallelizing?

Q: How do you strike the balance between:

optimizing the serial version of your code and
optimizing your parallelization?

A: The added cost of moving data between processors makes it important to avoid unnecessary data movement. One part of that is avoiding unnecessary memory allocations and using efficient data structures. If the algorithm is well suited to parallelization, then a memory efficient serial version is much more likely to get good performancfe when parallelized.

Q: Is it hard to tell when you should shift your focus to optimizing the other part?

A: Perhaps. Although, it gets easier with experience.

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Astro 528: High-Performance Scientific Computing for Astrophysics (Fall 2025)

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Containers of Abstract Types

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If you pass a data structure that's stored in the heap, then only a pointer (or something that acts like a pointer/reference) to that data is placed on the stack.

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According to the performance tips, it seems that using global variables leads to bad performance, and it is better to pass arguments to functions. When should one be using global variables then?

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What operations are expensive?

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I've been told to eliminate for loops wherever possible when writing Python/R/IDL code. In constrast, when writing Julia/C/C++/Fortran/Java for loops are not detrimental.

Why is this?

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ToC on side

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Types of elements in collections

Q: Does Julia automatically assume the whole array is of that type to optimize performance?

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Function barriers

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Helper Code

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Cost of common operations

Credit: ithare.com

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No Programming Interface

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For mathematical functions, results will differ from one processor to another. So I suggest you benchmark code yourself on the machine you plan to run on once you scale up.

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If you know your code is going to require for loops/nested for loops, is Julia just always going to be better than, for instance, Python?

Is there any case where the gains in optimization are marginal (especially for long runtimes)?

¤mime©text/html¬rootassigneeÀ²last_run_timestampËAÚE)àDž°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$1cf69f4d-04db-4c3a-897a-a1da9e46b88c¹depends_on_disabled_cellsÂ§runtimeÎ¦µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$db388c8a-ddb3-47a6-8ce0-586d9f9602b9Š¦queuedÂ¤logs§runningÂ¦output†¤bodyÚÏBenchmarkTools.Trial: 3564 samples with 1 evaluation. Range [90m([39m[36m[1mmin[22m[39m â€¦ [35mmax[39m[90m): [39m[36m[1m1.258 ms[22m[39m â€¦ [35m 18.012 ms[39m [90mâ”Š[39m GC [90m([39mmin â€¦ max[90m): [39m0.00% â€¦ 91.83% Time [90m([39m[34m[1mmedian[22m[39m[90m): [39m[34m[1m1.315 ms [22m[39m[90mâ”Š[39m GC [90m([39mmedian[90m): [39m0.00% Time [90m([39m[32m[1mmean[22m[39m Â± [32mÏƒ[39m[90m): [39m[32m[1m1.401 ms[22m[39m Â± [32m448.516 Î¼s[39m [90mâ”Š[39m GC [90m([39mmean Â± Ïƒ[90m): [39m4.45% Â± 9.89% [39mâ–ƒ[39mâ–†[39mâ–ˆ[34mâ–‡[39m[39mâ–ƒ[39m [39m [32m [39m[39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39mâ–‚[39mâ–ƒ[39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39mâ– [39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[34mâ–ˆ[39m[39mâ–ˆ[39mâ–ˆ[39mâ–‡[32mâ–…[39m[39mâ–ƒ[39mâ–[39mâ–ƒ[39mâ–…[39mâ–„[39mâ–ƒ[39mâ–ƒ[39mâ–„[39mâ–ƒ[39mâ–[39mâ–ƒ[39mâ–ƒ[39mâ–[39mâ–[39mâ–ƒ[39mâ–[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–„[39mâ–…[39mâ–…[39mâ–…[39mâ–ƒ[39mâ–[39mâ–[39mâ–[39mâ–ƒ[39mâ–„[39mâ–…[39mâ–[39mâ–„[39mâ–ƒ[39mâ–ƒ[39mâ–…[39mâ–…[39mâ–†[39mâ–†[39mâ–†[39mâ–…[39mâ–†[39mâ–‡[39mâ–†[39mâ–†[39mâ–‡[39mâ–†[39mâ–†[39mâ–‡[39mâ–…[39mâ–‡[39mâ–†[39m [39mâ–ˆ 1.26 ms[90m [39m[90mHistogram: [39m[90m[1mlog([22m[39m[90mfrequency[39m[90m[1m)[22m[39m[90m by time[39m 2.44 ms [0m[1m<[22m Memory estimate[90m: [39m[33m1.37 MiB[39m, allocs estimate[90m: [39m[33m73714[39m.¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE(þ[„°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$db388c8a-ddb3-47a6-8ce0-586d9f9602b9¹depends_on_disabled_cellsÂ§runtimeÏ©ý©µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$624e8936-de28-4e09-9a4e-3ef2f6c7d9b0Š¦queuedÂ¤logs§runningÂ¦output†¤body ¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE(öÒª°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$624e8936-de28-4e09-9a4e-3ef2f6c7d9b0¹depends_on_disabled_cellsÂ§runtimeÎ$ºnbµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$dfe5dcd7-9b62-4690-ac21-0930b3e4145cŠ¦queuedÂ¤logs§runningÂ¦output†¤bodyÚìBenchmarkTools.Trial: 10000 samples with 4 evaluations. Range [90m([39m[36m[1mmin[22m[39m â€¦ [35mmax[39m[90m): [39m[36m[1m 7.096 Î¼s[22m[39m â€¦ [35m948.589 Î¼s[39m [90mâ”Š[39m GC [90m([39mmin â€¦ max[90m): [39m 0.00% â€¦ 98.06% Time [90m([39m[34m[1mmedian[22m[39m[90m): [39m[34m[1m 9.945 Î¼s [22m[39m[90mâ”Š[39m GC [90m([39mmedian[90m): [39m 0.00% Time [90m([39m[32m[1mmean[22m[39m Â± [32mÏƒ[39m[90m): [39m[32m[1m13.059 Î¼s[22m[39m Â± [32m 20.403 Î¼s[39m [90mâ”Š[39m GC [90m([39mmean Â± Ïƒ[90m): [39m14.35% Â± 10.89% [39mâ–ˆ[39mâ–‡[34mâ–‡[39m[32mâ–†[39m[39mâ–‚[39mâ–[39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39mâ–‚[39mâ–[39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39mâ–‚ [39mâ–ˆ[39mâ–ˆ[34mâ–ˆ[39m[32mâ–ˆ[39m[39mâ–ˆ[39mâ–ˆ[39mâ–…[39mâ–ƒ[39mâ–[39mâ–ƒ[39mâ–ƒ[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–ƒ[39mâ–[39mâ–ƒ[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–†[39mâ–…[39mâ–ƒ[39mâ–ƒ[39mâ–ƒ[39mâ–„[39mâ–[39mâ–[39mâ–„[39mâ–„[39mâ–[39mâ–ƒ[39mâ–…[39mâ–„[39mâ–ƒ[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–„[39mâ–„[39mâ–†[39mâ–†[39mâ–†[39mâ–‡[39m [39mâ–ˆ 7.1 Î¼s[90m [39m[90mHistogram: [39m[90m[1mlog([22m[39m[90mfrequency[39m[90m[1m)[22m[39m[90m by time[39m 115 Î¼s [0m[1m<[22m Memory estimate[90m: [39m[33m128.09 KiB[39m, allocs estimate[90m: [39m[33m4[39m.¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE)½Y£°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$dfe5dcd7-9b62-4690-ac21-0930b3e4145c¹depends_on_disabled_cellsÂ§runtimeÏ¦ƒô5µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$208bf525-447d-4726-b67c-c3b968b415b8Š¦queuedÂ¤logs§runningÂ¦output†¤bodyÚË

Rubric for Serial version of Code

Code performs proposed tasks (1 point)
Comprehensive set of unit tests, at least one integration or regression test (1 point)
Code passes tests (1 point)
Student code uses a version control system effectively (1 point)
Repository includes many regular, small commits (1 point)
Documentation for functionsâ€™ purpose and design (1 point)
Comprehensive set of assertions (1 point)
Variable/function names consistent, distinctive & meaningful (1 point)
Useful & consistent code formatting & style (1 point)
Code is modular, rather than having chunks of same code copied and pasted (1 point)

¤mime©text/html¬rootassigneeÀ²last_run_timestampËAÚE(ì“Œa°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$208bf525-447d-4726-b67c-c3b968b415b8¹depends_on_disabled_cellsÂ§runtimeÎ¶+µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$c92d49d3-e8fc-4288-9ce2-3e617fc5c306Š¦queuedÂ¤logs§runningÂ¦output†¤body¶1.8369701987210297e-16¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE(ùþR°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$c92d49d3-e8fc-4288-9ce2-3e617fc5c306¹depends_on_disabled_cellsÂ§runtimeÍ.Lµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$aa767f81-4bcb-41b6-b141-85796a81d8fbŠ¦queuedÂ¤logs§runningÂ¦output†¤bodyÙW[33m[1mTest Broken[22m[39m Expression: my_model_stable_specific.(obs, param_true)¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE)Ç‚°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$aa767f81-4bcb-41b6-b141-85796a81d8fb¹depends_on_disabled_cellsÂ§runtimeÎÅÐ‹µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$b2ac3b2c-31c7-4e64-9009-47ac03e38afbŠ¦queuedÂ¤logs§runningÂ¦output†¤bodyÙr

Loops and "Vectorization"

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Making inner function type-stable

¤mime©text/html¬rootassigneeÀ²last_run_timestampËAÚE(ì•iˆ°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$495b281e-f4c9-4f55-bf5a-9a8d7f43044c¹depends_on_disabled_cellsÂ§runtimeÎÊMµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$be38f44f-9ce4-433a-84ef-782e5d8a4822Š¦queuedÂ¤logs§runningÂ¦output†¤body£0.0¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE(ùýRÛ°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$be38f44f-9ce4-433a-84ef-782e5d8a4822¹depends_on_disabled_cellsÂ§runtimeÍ-„µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$11e60eb5-980d-4d3d-8f09-03390584aaadŠ¦queuedÂ¤logs§runningÂ¦output†¤body ¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE) ØÞ/°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$11e60eb5-980d-4d3d-8f09-03390584aaad¹depends_on_disabled_cellsÂ§runtimeÎL#µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$957519f4-a669-472a-bc81-ecd0dcce9842Š¦queuedÂ¤logs§runningÂ¦output†¤bodyÚûBenchmarkTools.Trial: 10000 samples with 991 evaluations. Range [90m([39m[36m[1mmin[22m[39m â€¦ [35mmax[39m[90m): [39m[36m[1m 40.985 ns[22m[39m â€¦ [35m 22.722 Î¼s[39m [90mâ”Š[39m GC [90m([39mmin â€¦ max[90m): [39m 0.00% â€¦ 99.12% Time [90m([39m[34m[1mmedian[22m[39m[90m): [39m[34m[1m 68.246 ns [22m[39m[90mâ”Š[39m GC [90m([39mmedian[90m): [39m 0.00% Time [90m([39m[32m[1mmean[22m[39m Â± [32mÏƒ[39m[90m): [39m[32m[1m109.118 ns[22m[39m Â± [32m389.093 ns[39m [90mâ”Š[39m GC [90m([39mmean Â± Ïƒ[90m): [39m20.77% Â± 14.25% [39mâ–…[39mâ–…[39mâ–ˆ[34mâ–‡[39m[39mâ–…[39mâ–ƒ[39m [32m [39m[39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39mâ–‚[39mâ–ƒ[39mâ–‚[39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39mâ–‚ [39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[34mâ–ˆ[39m[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[32mâ–…[39m[39mâ–ƒ[39mâ–[39mâ–ƒ[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–ƒ[39mâ–[39mâ–ƒ[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–„[39mâ–[39mâ–[39mâ–[39mâ–ƒ[39mâ–ƒ[39mâ–[39mâ–„[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–‡[39mâ–…[39mâ–ƒ[39mâ–…[39mâ–…[39mâ–†[39mâ–…[39mâ–…[39mâ–…[39mâ–…[39mâ–…[39mâ–…[39mâ–…[39mâ–„[39mâ–„[39mâ–„[39mâ–„[39mâ–ƒ[39mâ–…[39mâ–†[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39m [39mâ–ˆ 41 ns[90m [39m[90mHistogram: [39m[90m[1mlog([22m[39m[90mfrequency[39m[90m[1m)[22m[39m[90m by time[39m 638 ns [0m[1m<[22m Memory estimate[90m: [39m[33m928 bytes[39m, allocs estimate[90m: [39m[33m2[39m.¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE)˜®£°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$957519f4-a669-472a-bc81-ecd0dcce9842¹depends_on_disabled_cellsÂ§runtimeÎ•žKÑµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$1b548d59-f18e-4cfc-9667-472c427d7cc2Š¦queuedÂ¤logs§runningÂ¦output†¤body ¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE(÷‘Ýn°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$1b548d59-f18e-4cfc-9667-472c427d7cc2¹depends_on_disabled_cellsÂ§runtimeÎ$ÑŸµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$cee02d24-1dcc-4c29-a322-0ddd12ab8180Š¦queuedÂ¤logs§runningÂ¦output†¤body ¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE)^ú°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$cee02d24-1dcc-4c29-a322-0ddd12ab8180¹depends_on_disabled_cellsÂ§runtimeÎým©µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$e1ec523b-3c2f-447d-8b71-063dc5955f45Š¦queuedÂ¤logs§runningÂ¦output†¤bodyÙh

Why would you want to do that?

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For small programs called many times, consider making a sysimage using PackageCompiler.jl to avoid compilation cost each time.

¤mime©text/html¬rootassigneeÀ²last_run_timestampËAÚE(ì–oT°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$279df4ae-a0e2-4838-8a9c-3ff82245935e¹depends_on_disabled_cellsÂ§runtimeÎA”µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$9ec9429d-c1f1-4845-a514-9c88b452071fŠ¦queuedÂ¤logs§runningÂ¦output†¤bodyÚ6 Full Width Mode ¤mime©text/html¬rootassigneeÀ²last_run_timestampËAÚE(÷)?°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$9ec9429d-c1f1-4845-a514-9c88b452071f¹depends_on_disabled_cellsÂ§runtimeÎJlµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$f3937141-49f4-49f2-8bcf-0f4e9c204d24Š¦queuedÂ¤logs‘ˆ¤lineÿ£msg’ÚMethodInstance for Main.var"workspace#3".func_with_type_instability(::Vector{Float64}, ::Int64) from func_with_type_instability([90mobs[39m, [90mparam[39m)[90m @[39m [90mMain.var"workspace#3"[39m [90m~/work/Notes-Fall2025/Notes-Fall2025/week5/[39m[90m[4mweek5.jl#==#fad14e46-21a4-41ea-8f3d-a747cdfe3a51:1[24m[39m Arguments #self#[36m::Core.Const(Main.var"workspace#3".func_with_type_instability)[39m obs[36m::Vector{Float64}[39m param[36m::Int64[39m Locals Ï‡Â²[91m[1m::Any[22m[39m pred[33m[1m::Union{Vector{Float64}, Vector{Int64}, Vector{Real}}[22m[39m Body[91m[1m::Any[22m[39m [90m1 â”€[39m %1 = Base.broadcasted(Main.var"workspace#3".my_model, obs, param)[36m::Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Nothing, typeof(Main.var"workspace#3".my_model), Tuple{Vector{Float64}, Int64}}[39m [90mâ”‚ [39m (pred = Base.materialize(%1)) [90mâ”‚ [39m %3 = pred[33m[1m::Union{Vector{Float64}, Vector{Int64}, Vector{Real}}[22m[39m [90mâ”‚ [39m %4 = Main.var"workspace#3".calc_Ï‡Â²(obs, %3)[91m[1m::Any[22m[39m [90mâ”‚ [39m (Ï‡Â² = %4) [90mâ””â”€â”€[39m return %4 ªtext/plain§cell_idÙ$f3937141-49f4-49f2-8bcf-0f4e9c204d24¦kwargs¢id´PlutoRunner_d1acb81e¤fileÙP/home/runner/.julia/packages/Pluto/CBqeh/src/runner/PlutoRunner/src/io/stdout.jl¥group¦stdout¥level®LogLevel(-555)§runningÂ¦output†¤body ¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE)2¬°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$f3937141-49f4-49f2-8bcf-0f4e9c204d24¹depends_on_disabled_cellsÂ§runtimeÎ¦6=¡µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$047835eb-6bcc-4f32-b991-5ccccbf34cb9Š¦queuedÂ¤logs§runningÂ¦output†¤body…¦prefix¤Real¨elements“’’£1.0ªtext/plain’’¡2ªtext/plain’’¡3ªtext/plain¤type¥Array¬prefix_short ¨objectid°dfb86ee7283adea9¤mimeÙ!application/vnd.pluto.tree+object¬rootassignee®array_of_reals²last_run_timestampËAÚE)`Ÿk°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$047835eb-6bcc-4f32-b991-5ccccbf34cb9¹depends_on_disabled_cellsÂ§runtimeÎ¼3µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$e1996c2f-5298-48c9-a29c-852bd37b54c4Š¦queuedÂ¤logs§runningÂ¦output†¤body ¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE)ÇbA°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$e1996c2f-5298-48c9-a29c-852bd37b54c4¹depends_on_disabled_cellsÂ§runtimeÎl³µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$59fbb599-c947-4a2a-a678-8e38a666660cŠ¦queuedÂ¤logs‘ˆ¤lineÿ£msg’Ù, 0.000001 seconds (1 allocation: 16 bytes) ªtext/plain§cell_idÙ$59fbb599-c947-4a2a-a678-8e38a666660c¦kwargs¢id´PlutoRunner_d1acb81e¤fileÙP/home/runner/.julia/packages/Pluto/CBqeh/src/runner/PlutoRunner/src/io/stdout.jl¥group¦stdout¥level®LogLevel(-555)§runningÂ¦output†¤body…¦prefix¿view(::Matrix{Float64}, :, 1): ¨elementsÜ’’§0.12307ªtext/plain’’¨0.368559ªtext/plain’’§2.27357ªtext/plain’’©-0.253736ªtext/plain’’¨-2.08108ªtext/plain’’¨-1.04544ªtext/plain’’©-0.416231ªtext/plain’’§0.14153ªtext/plain’ ’§1.21345ªtext/plain’ ’§1.06368ªtext/plain’’©-0.466929ªtext/plain’’¨0.125361ªtext/plain’ ’§1.00169ªtext/plain’’©0.0568795ªtext/plain’’¦2.2829ªtext/plain’’©-0.678769ªtext/plain’’§-0.4524ªtext/plain’’©-0.284222ªtext/plain’’©-0.347168ªtext/plain’’¨0.750999ªtext/plain¤more’[’¨0.750758ªtext/plain’\’©-0.182216ªtext/plain’]’©-0.392818ªtext/plain’^’©-0.623447ªtext/plain’_’¨0.297572ªtext/plain’`’§1.06335ªtext/plain’a’¨0.679394ªtext/plain’b’¨-1.29336ªtext/plain’c’§2.68771ªtext/plain’d’©-0.440474ªtext/plain¤type¥Array¬prefix_short¿view(::Matrix{Float64}, :, 1): ¨objectid°1c7acf235413e139¤mimeÙ!application/vnd.pluto.tree+object¬rootassignee²@time col_one_view²last_run_timestampËAÚE)ÔA°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$59fbb599-c947-4a2a-a678-8e38a666660c¹depends_on_disabled_cellsÂ§runtimeÎ’#µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$e80e73cc-fb81-4222-8fcd-a9c4aaf6326eŠ¦queuedÂ¤logs§runningÂ¦output†¤bodyÚÕBenchmarkTools.Trial: 10000 samples with 1 evaluation. Range [90m([39m[36m[1mmin[22m[39m â€¦ [35mmax[39m[90m): [39m[36m[1m12.874 Î¼s[22m[39m â€¦ [35m 3.274 ms[39m [90mâ”Š[39m GC [90m([39mmin â€¦ max[90m): [39m0.00% â€¦ 99.05% Time [90m([39m[34m[1mmedian[22m[39m[90m): [39m[34m[1m13.495 Î¼s [22m[39m[90mâ”Š[39m GC [90m([39mmedian[90m): [39m0.00% Time [90m([39m[32m[1mmean[22m[39m Â± [32mÏƒ[39m[90m): [39m[32m[1m19.275 Î¼s[22m[39m Â± [32m55.909 Î¼s[39m [90mâ”Š[39m GC [90m([39mmean Â± Ïƒ[90m): [39m8.06% Â± 3.62% [39mâ–ˆ[34mâ–…[39m[39mâ–[39m [39m [39m [39m [32m [39m[39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39mâ–[39mâ–[39mâ–‚[39mâ–[39mâ–[39m [39m [39m [39mâ– [39mâ–ˆ[34mâ–ˆ[39m[39mâ–ˆ[39mâ–ˆ[39mâ–‡[39mâ–‡[39mâ–…[32mâ–‡[39m[39mâ–‡[39mâ–†[39mâ–†[39mâ–ˆ[39mâ–ˆ[39mâ–†[39mâ–†[39mâ–†[39mâ–„[39mâ–„[39mâ–[39mâ–ƒ[39mâ–„[39mâ–„[39mâ–ƒ[39mâ–ƒ[39mâ–„[39mâ–„[39mâ–[39mâ–ƒ[39mâ–„[39mâ–„[39mâ–„[39mâ–„[39mâ–…[39mâ–…[39mâ–ƒ[39mâ–…[39mâ–[39mâ–„[39mâ–[39mâ–[39mâ–[39mâ–ƒ[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–‡[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–‡[39mâ–†[39m [39mâ–ˆ 12.9 Î¼s[90m [39m[90mHistogram: [39m[90m[1mlog([22m[39m[90mfrequency[39m[90m[1m)[22m[39m[90m by time[39m 66 Î¼s [0m[1m<[22m Memory estimate[90m: [39m[33m128.07 KiB[39m, allocs estimate[90m: [39m[33m3[39m.¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE(ÿõ§°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$e80e73cc-fb81-4222-8fcd-a9c4aaf6326e¹depends_on_disabled_cellsÂ§runtimeÏ}¶E»µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$8f4b3c77-e79f-457a-b9e9-9f30dd1f526aŠ¦queuedÂ¤logs§runningÂ¦output†¤bodyÙo

It can store an array of abstract types, but that can be quite inefficient.

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Writing functions that can take an unknown number of arguements

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How should we decide whether to inline a function or not?

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I thought [using many smaller functions] would take longer since the program needs to go somewhere else.

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Small functions that will be called many times (e.g., inside a loop) â†’ want to inline
Large functions or functions that will only be called a few times â†’ little benefit to inlining
Modern languages/compilers will typically decide for you based on some simple heuristics to guess the typical cost of executing the function.
You can provide a hint encouraging or discouraging the compiler from inlining code. (@inline or @noinline)

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Old Q&A

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When optimizing code, what typically has the most impact on decreasing run time?

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Inlining code

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Overloading Functions for each Type

¤mime©text/html¬rootassigneeÀ²last_run_timestampËAÚE(ì”7Ò°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$1969217c-24be-47e2-9853-b70cf4d5565d¹depends_on_disabled_cellsÂ§runtimeÎìûµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$20db6ae9-8c79-44d1-a3a7-0dadf1d0dc5aŠ¦queuedÂ¤logs§runningÂ¦output†¤bodyÙAfunc_without_type_instability_v2 (generic function with 1 method)¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE(ûUÊ*°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$20db6ae9-8c79-44d1-a3a7-0dadf1d0dc5a¹depends_on_disabled_cellsÂ§runtimeÎÈCµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$d0429b82-7e78-4a18-97bb-e34ba370e024Š¦queuedÂ¤logs§runningÂ¦output†¤bodyÚÛBenchmarkTools.Trial: 10000 samples with 4 evaluations. Range [90m([39m[36m[1mmin[22m[39m â€¦ [35mmax[39m[90m): [39m[36m[1m7.146 Î¼s[22m[39m â€¦ [35m236.249 Î¼s[39m [90mâ”Š[39m GC [90m([39mmin â€¦ max[90m): [39m0.00% â€¦ 83.64% Time [90m([39m[34m[1mmedian[22m[39m[90m): [39m[34m[1m7.797 Î¼s [22m[39m[90mâ”Š[39m GC [90m([39mmedian[90m): [39m0.00% Time [90m([39m[32m[1mmean[22m[39m Â± [32mÏƒ[39m[90m): [39m[32m[1m9.350 Î¼s[22m[39m Â± [32m 10.621 Î¼s[39m [90mâ”Š[39m GC [90m([39mmean Â± Ïƒ[90m): [39m8.71% Â± 7.77% [39mâ–ˆ[34mâ–‡[39m[39mâ–‡[39mâ–ƒ[39mâ–‚[32mâ–‚[39m[39mâ–‚[39mâ–‚[39mâ–[39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39mâ–[39m [39m [39m [39m [39m [39m [39m [39m [39mâ–‚ [39mâ–ˆ[34mâ–ˆ[39m[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[32mâ–ˆ[39m[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–‡[39mâ–‡[39mâ–‡[39mâ–†[39mâ–‡[39mâ–‡[39mâ–‡[39mâ–…[39mâ–…[39mâ–„[39mâ–„[39mâ–…[39mâ–[39mâ–[39mâ–ƒ[39mâ–ƒ[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–ƒ[39mâ–[39mâ–ƒ[39mâ–ƒ[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–…[39mâ–‡[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–†[39mâ–†[39mâ–…[39mâ–…[39mâ–†[39mâ–…[39m [39mâ–ˆ 7.15 Î¼s[90m [39m[90mHistogram: [39m[90m[1mlog([22m[39m[90mfrequency[39m[90m[1m)[22m[39m[90m by time[39m 32.9 Î¼s [0m[1m<[22m Memory estimate[90m: [39m[33m55.18 KiB[39m, allocs estimate[90m: [39m[33m21[39m.¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE(ùöRT°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$d0429b82-7e78-4a18-97bb-e34ba370e024¹depends_on_disabled_cellsÂ§runtimeÏ˜¯Žiµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$94223079-afab-4a6d-a126-068a4e94f52eŠ¦queuedÂ¤logs§runningÂ¦output†¤body ¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE(÷|E¦°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$94223079-afab-4a6d-a126-068a4e94f52e¹depends_on_disabled_cellsÂ§runtimeÎcµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$d3d085e6-67b5-4286-b66d-120720e1002dŠ¦queuedÂ¤logs§runningÂ¦output†¤bodyÚÇ

Preping for Code Review

Make it easy for your reviewer

Provide overview of what your code is doing in README.md
Where should they start?
What files should they focus on?
What files should they ignore?
Include an example of how to run/use code

Make it easy for you

As code starts getting larger, then

Move code out of notebooks and into .jl files, as functions mature.
Organize similar functions into .jl files in src directory
Use diretories like examples, test
If/when appropiate add more directories (e.g., data, deps, docs)

¤mime©text/html¬rootassigneeÀ²last_run_timestampËAÚE(ì–ç\°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$d3d085e6-67b5-4286-b66d-120720e1002d¹depends_on_disabled_cellsÂ§runtimeÎ•øµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$e7227a20-3d2d-4907-b9a6-422c0d4ab57aŠ¦queuedÂ¤logs§runningÂ¦output†¤bodyÙ*distance (generic function with 2 methods)¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE(÷™@d°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$e7227a20-3d2d-4907-b9a6-422c0d4ab57a¹depends_on_disabled_cellsÂ§runtimeÎ Êµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$348ee204-546f-46c5-bf5d-7d4a761002ecŠ¦queuedÂ¤logs§runningÂ¦output†¤bodyÙX

Optimizing Serial Code

¤mime©text/html¬rootassigneeÀ²last_run_timestampËAÚE(ì”™‰°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$348ee204-546f-46c5-bf5d-7d4a761002ec¹depends_on_disabled_cellsÂ§runtimeÎ²dµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$170f2bd0-bb5b-4e78-b92b-dfa8d47aded0Š¦queuedÂ¤logs§runningÂ¦output†¤bodyÚÙBenchmarkTools.Trial: 10000 samples with 1 evaluation. Range [90m([39m[36m[1mmin[22m[39m â€¦ [35mmax[39m[90m): [39m[36m[1m38.372 Î¼s[22m[39m â€¦ [35m 4.052 ms[39m [90mâ”Š[39m GC [90m([39mmin â€¦ max[90m): [39m0.00% â€¦ 98.14% Time [90m([39m[34m[1mmedian[22m[39m[90m): [39m[34m[1m38.862 Î¼s [22m[39m[90mâ”Š[39m GC [90m([39mmedian[90m): [39m0.00% Time [90m([39m[32m[1mmean[22m[39m Â± [32mÏƒ[39m[90m): [39m[32m[1m47.688 Î¼s[22m[39m Â± [32m77.323 Î¼s[39m [90mâ”Š[39m GC [90m([39mmean Â± Ïƒ[90m): [39m5.95% Â± 4.54% [34mâ–ˆ[39m[39mâ–ƒ[39mâ–[39mâ–[39m [39m [39m [39m [39m [32mâ–‚[39m[39mâ–[39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39mâ–‚[39mâ–‚[39mâ–‚[39mâ–‚[39m [39m [39m [39m [39m [39m [39m [39m [39m [39mâ– [34mâ–ˆ[39m[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–†[39mâ–‡[39mâ–‡[39mâ–…[32mâ–ˆ[39m[39mâ–ˆ[39mâ–‡[39mâ–ˆ[39mâ–ˆ[39mâ–‡[39mâ–‡[39mâ–†[39mâ–…[39mâ–„[39mâ–…[39mâ–ƒ[39mâ–…[39mâ–„[39mâ–[39mâ–„[39mâ–[39mâ–[39mâ–[39mâ–ƒ[39mâ–ƒ[39mâ–[39mâ–„[39mâ–[39mâ–ƒ[39mâ–[39mâ–[39mâ–[39mâ–„[39mâ–ƒ[39mâ–ƒ[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–ƒ[39mâ–[39mâ–‡[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–‡[39mâ–…[39mâ–…[39mâ–…[39mâ–†[39mâ–‡[39mâ–‡[39m [39mâ–ˆ 38.4 Î¼s[90m [39m[90mHistogram: [39m[90m[1mlog([22m[39m[90mfrequency[39m[90m[1m)[22m[39m[90m by time[39m 97.3 Î¼s [0m[1m<[22m Memory estimate[90m: [39m[33m128.07 KiB[39m, allocs estimate[90m: [39m[33m3[39m.¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE)Á°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$170f2bd0-bb5b-4e78-b92b-dfa8d47aded0¹depends_on_disabled_cellsÂ§runtimeÏ¾ƒçµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$a9cf77ec-434e-4477-a844-9f8b9199589fŠ¦queuedÂ¤logs§runningÂ¦output†¤body…¦prefix·Union{Missing, Float64}¨elements“’’£1.0ªtext/plain’’§missingªtext/plain’’£3.0ªtext/plain¤type¥Array¬prefix_short ¨objectid°8cbe156036c2c105¤mimeÙ!application/vnd.pluto.tree+object¬rootassignee¹array_of_float_or_missing²last_run_timestampËAÚE)~ß°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$a9cf77ec-434e-4477-a844-9f8b9199589f¹depends_on_disabled_cellsÂ§runtimeÍ6ßµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$781ef824-a235-46ce-accd-362f2e963550Š¦queuedÂ¤logs§runningÂ¦output†¤bodyÚ£BenchmarkTools.Trial: 471 samples with 1 evaluation. Range [90m([39m[36m[1mmin[22m[39m â€¦ [35mmax[39m[90m): [39m[36m[1m 8.678 ms[22m[39m â€¦ [35m132.052 ms[39m [90mâ”Š[39m GC [90m([39mmin â€¦ max[90m): [39m 0.00% â€¦ 93.20% Time [90m([39m[34m[1mmedian[22m[39m[90m): [39m[34m[1m10.373 ms [22m[39m[90mâ”Š[39m GC [90m([39mmedian[90m): [39m12.15% Time [90m([39m[32m[1mmean[22m[39m Â± [32mÏƒ[39m[90m): [39m[32m[1m10.595 ms[22m[39m Â± [32m 5.722 ms[39m [90mâ”Š[39m GC [90m([39mmean Â± Ïƒ[90m): [39m14.30% Â± 5.83% [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39mâ–‚[39mâ–‚[39mâ–„[39mâ–ƒ[39mâ–[39m [39m [39m [39m [39m [39m [39m [39m [34mâ–[39m[39mâ–[39mâ–‚[39mâ–„[39mâ–ˆ[32mâ–[39m[39m [39m [39mâ–[39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39mâ–‚[39mâ–[39mâ–‚[39mâ–‚[39mâ–‚[39mâ–ƒ[39mâ–‚[39mâ–‚[39mâ–[39mâ–ƒ[39mâ–[39mâ–[39mâ–[39mâ–‚[39mâ–ƒ[39mâ–‚[39mâ–ƒ[39mâ–‚[39mâ–ƒ[39mâ–„[39mâ–ƒ[39mâ–„[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–‡[39mâ–…[39mâ–„[39mâ–…[39mâ–„[39mâ–ˆ[39mâ–‡[34mâ–ˆ[39m[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[32mâ–ˆ[39m[39mâ–‡[39mâ–‡[39mâ–ˆ[39mâ–†[39mâ–„[39mâ–„[39mâ–‡[39mâ–„[39mâ–ƒ[39mâ–ƒ[39mâ–ƒ[39mâ–„[39mâ–ƒ[39mâ–„[39mâ–‚[39mâ–‚[39mâ–[39mâ–‚[39m [39mâ–„ 8.68 ms[90m Histogram: frequency by time[39m 11.5 ms [0m[1m<[22m Memory estimate[90m: [39m[33m61.04 MiB[39m, allocs estimate[90m: [39m[33m3[39m.¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE) °„Ç°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$781ef824-a235-46ce-accd-362f2e963550¹depends_on_disabled_cellsÂ§runtimeÏ¥{Hãµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$46cd3a5f-3358-4f21-91c7-82c544bc4353Š¦queuedÂ¤logs§runningÂ¦output†¤bodyÚB

Typically... yes.
Always... no. E.g., if runtime is dominated by time to read data from the internet/network/disk. Then, the cost of accessing the data the first time may be so large that the benefits of computing more efficiently are negligible.

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Yes!

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A: Easy answer... Never

Reality:

You're writing disposable code
You're working with some preexisting code that wasn't designed to do what you want and you want to try something quickly before implementing it well.
Other examples?

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> julia -h

  -O, --optimize={0,1,2*,3}     Set the optimization level
  --min-optlevel={0*,1,2,3}     Set a lower bound on the optimization level             
  -J, --sysimage <file>         Start up with the given system image file

  -t, --threads {auto|N[,auto|M]}    
  -p, --procs {N|auto}       

  -g, --debug-info=[{0,1*,2}]   Set the level of debug info generation  
  --check-bounds={yes|no|auto*} auto respects @inbounds declarations
  --math-mode={ieee|user*}      user respects `@fastmath` declarations

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Peer Review Logistics

Access
- I'll send you GitHub ID of peer reviewer(s)
- Make sure reviewer(s) can access your repo
  - If your project repo is private: Settings, Collaborators & Teams, Add people, Read, Add Selection.
  - Or make your project repo public: Settings, Change Visibility, plus multiple multiple steps to confirm.
- Make sure you can access repo to review
If using Jupyter notebooks, make sure to add Markdown version of code for getting feedback.

julia -e 'import Pkg; Pkg.add("Weave"); using Weave; convert_doc("NOTEBOOK_NAME.ipynb","NOTEBOOK_NAME.jmd")'

Review instructions
Provide most feedback via GitHub Issues

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Avoiding copying using views

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Type Instability

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When use global variables?

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What type of variables should always be passed to an inline function versus an external module (maybe large arrays/tables?) so they don't take up too much room on the stack?

¤mime©text/html¬rootassigneeÀ²last_run_timestampËAÚE)Ep°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$b556927c-ab72-41c5-9a3e-83756e40550a¹depends_on_disabled_cellsÂ§runtimeÎpµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$9e8cb539-5d69-4552-87e4-88fe61ab1fbeŠ¦queuedÂ¤logs§runningÂ¦output†¤bodyÙ&theta (generic function with 1 method)¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE(÷qø°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$9e8cb539-5d69-4552-87e4-88fe61ab1fbe¹depends_on_disabled_cellsÂ§runtimeÎ@0µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$fbd538a3-8ddc-4c3f-9748-35fa7b032809Š¦queuedÂ¤logs‘ˆ¤lineÿ£msg’ÚMethodInstance for Main.var"workspace#3".func_without_barriers(::Vector{Float64}, ::Int64) from func_without_barriers([90mobs[39m, [90mparam[39m)[90m @[39m [90mMain.var"workspace#3"[39m [90m~/work/Notes-Fall2025/Notes-Fall2025/week5/[39m[90m[4mweek5.jl#==#08d25c7e-907b-403d-b08d-27ca4efcd958:1[24m[39m Arguments #self#[36m::Core.Const(Main.var"workspace#3".func_without_barriers)[39m obs[36m::Vector{Float64}[39m param[36m::Int64[39m Locals Ï‡Â²[36m::Float64[39m n[36m::Int64[39m pred[33m[1m::Union{Vector{Float64}, Vector{Int64}}[22m[39m @_7[33m[1m::Union{Nothing, Tuple{Int64, Int64}}[22m[39m r#238[36m::UnitRange{Int64}[39m i#239[36m::Int64[39m n#240[36m::Int64[39m i#241[36m::Int64[39m val[36m::Float64[39m i[36m::Int64[39m Body[36m::Float64[39m [90m1 â”€â”€[39m Core.NewvarNode(:(Ï‡Â²)) [90mâ”‚ [39m Core.NewvarNode(:(n)) [90mâ”‚ [39m Core.NewvarNode(:(pred)) [90mâ”‚ [39m %4 = Main.var"workspace#3".:<[36m::Core.Const(<)[39m [90mâ”‚ [39m %5 = (%4)(param, 1)[36m::Bool[39m [90mâ””â”€â”€â”€[39m goto #3 if not %5 [90m2 â”€â”€[39m %7 = Base.broadcasted(Main.var"workspace#3".:*, param, obs)[36m::Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Nothing, typeof(*), Tuple{Int64, Vector{Float64}}}[39m [90mâ”‚ [39m (pred = Base.materialize(%7)) [90mâ””â”€â”€â”€[39m goto #4 [90m3 â”€â”€[39m %10 = Main.var"workspace#3".floor[36m::Core.Const(floor)[39m [90mâ”‚ [39m %11 = Main.var"workspace#3".Int64[36m::Core.Const(Int64)[39m [90mâ”‚ [39m %12 = Base.broadcasted(Main.var"workspace#3".:*, param, obs)[36m::Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Nothing, typeof(*), Tuple{Int64, Vector{Float64}}}[39m [90mâ”‚ [39m %13 = Base.broadcasted(%10, %11, %12)[36m::Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Nothing, typeof(floor), Tuple{Base.RefValue{Type{Int64}}, Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Nothing, typeof(*), Tuple{Int64, Vector{Float64}}}}}[39m [90mâ””â”€â”€â”€[39m (pred = Base.materialize(%13)) [90m4 â”„â”€[39m %15 = Main.var"workspace#3".length[36m::Core.Const(length)[39m [90mâ”‚ [39m (n = (%15)(obs)) [90mâ”‚ [39m %17 = Main.var"workspace#3".zero[36m::Core.Const(zero)[39m [90mâ”‚ [39m %18 = Main.var"workspace#3".promote_type[36m::Core.Const(promote_type)[39m [90mâ”‚ [39m %19 = Main.var"workspace#3".eltype[36m::Core.Const(eltype)[39m [90mâ”‚ [39m %20 = (%19)(obs)[36m::Core.Const(Float64)[39m [90mâ”‚ [39m %21 = Main.var"workspace#3".eltype[36m::Core.Const(eltype)[39m [90mâ”‚ [39m %22 = pred[33m[1m::Union{Vector{Float64}, Vector{Int64}}[22m[39m [90mâ”‚ [39m %23 = (%21)(%22)[33m[1m::Union{Type{Float64}, Type{Int64}}[22m[39m [90mâ”‚ [39m %24 = (%18)(%20, %23)[36m::Core.Const(Float64)[39m [90mâ”‚ [39m (Ï‡Â² = (%17)(%24)) [90mâ”‚ [39m %26 = n[36m::Int64[39m [90mâ”‚ [39m %27 = (1:%26)[36m::Core.PartialStruct(UnitRange{Int64}, Any[Core.Const(1), Int64])[39m [90mâ”‚ [39m (r#238 = %27) [90mâ”‚ [39m %29 = Base.simd_outer_range[36m::Core.Const(Base.SimdLoop.simd_outer_range)[39m [90mâ”‚ [39m %30 = r#238[36m::Core.PartialStruct(UnitRange{Int64}, Any[Core.Const(1), Int64])[39m [90mâ”‚ [39m %31 = (%29)(%30)[36m::Core.Const(0:0)[39m [90mâ”‚ [39m (@_7 = Base.iterate(%31)) [90mâ”‚ [39m %33 = @_7[36m::Core.Const((0, 0))[39m [90mâ”‚ [39m %34 = (%33 === nothing)[36m::Core.Const(false)[39m [90mâ”‚ [39m %35 = Base.not_int(%34)[36m::Core.Const(true)[39m [90mâ””â”€â”€â”€[39m goto #11 if not %35 [90m5 â”€â”€[39m %37 = @_7[36m::Core.Const((0, 0))[39m [90mâ”‚ [39m (i#239 = Core.getfield(%37, 1)) [90mâ”‚ [39m %39 = Core.getfield(%37, 2)[36m::Core.Const(0)[39m [90mâ”‚ [39m %40 = Base.simd_inner_length[36m::Core.Const(Base.SimdLoop.simd_inner_length)[39m [90mâ”‚ [39m %41 = r#238[36m::Core.PartialStruct(UnitRange{Int64}, Any[Core.Const(1), Int64])[39m [90mâ”‚ [39m %42 = i#239[36m::Core.Const(0)[39m [90mâ”‚ [39m %43 = (%40)(%41, %42)[36m::Int64[39m [90mâ”‚ [39m (n#240 = %43) [90mâ”‚ [39m %45 = Main.var"workspace#3".:<[36m::Core.Const(<)[39m [90mâ”‚ [39m %46 = Main.var"workspace#3".zero[36m::Core.Const(zero)[39m [90mâ”‚ [39m %47 = n#240[36m::Int64[39m [90mâ”‚ [39m %48 = (%46)(%47)[36m::Core.Const(0)[39m [90mâ”‚ [39m %49 = n#240[36m::Int64[39m [90mâ”‚ [39m %50 = (%45)(%48, %49)[36m::Bool[39m [90mâ””â”€â”€â”€[39m goto #9 if not %50 [90m6 â”€â”€[39m %52 = Main.var"workspace#3".zero[36m::Core.Const(zero)[39m [90mâ”‚ [39m %53 = n#240[36m::Int64[39m [90mâ”‚ [39m %54 = (%52)(%53)[36m::Core.Const(0)[39m [90mâ””â”€â”€â”€[39m (i#241 = %54) [90m7 â”„â”€[39m %56 = Main.var"workspace#3".:<[36m::Core.Const(<)[39m [90mâ”‚ [39m %57 = n#240[36m::Int64[39m [90mâ”‚ [39m %58 = (%56)(i#241, %57)[36m::Bool[39m [90mâ””â”€â”€â”€[39m goto #9 if not %58 [90m8 â”€â”€[39m %60 = Base.simd_index[36m::Core.Const(Base.SimdLoop.simd_index)[39m [90mâ”‚ [39m %61 = r#238[36m::Core.PartialStruct(UnitRange{Int64}, Any[Core.Const(1), Int64])[39m [90mâ”‚ [39m %62 = i#239[36m::Core.Const(0)[39m [90mâ”‚ [39m %63 = i#241[36m::Int64[39m [90mâ”‚ [39m (i = (%60)(%61, %62, %63)) [90mâ”‚ [39m nothing [90mâ”‚ [39m %66 = Main.var"workspace#3".:+[36m::Core.Const(+)[39m [90mâ”‚ [39m %67 = Ï‡Â²[36m::Float64[39m [90mâ”‚ [39m %68 = Main.var"workspace#3".:^[36m::Core.Const(^)[39m [90mâ”‚ [39m %69 = Main.var"workspace#3".:-[36m::Core.Const(-)[39m [90mâ”‚ [39m %70 = i[36m::Int64[39m [90mâ”‚ [39m %71 = Base.getindex(obs, %70)[36m::Float64[39m [90mâ”‚ [39m %72 = pred[33m[1m::Union{Vector{Float64}, Vector{Int64}}[22m[39m [90mâ”‚ [39m %73 = i[36m::Int64[39m [90mâ”‚ [39m %74 = Base.getindex(%72, %73)[33m[1m::Union{Float64, Int64}[22m[39m [90mâ”‚ [39m %75 = (%69)(%71, %74)[36m::Float64[39m [90mâ”‚ [39m %76 = Core.apply_type(Base.Val, 2)[36m::Core.Const(Val{2})[39m [90mâ”‚ [39m %77 = (%76)()[36m::Core.Const(Val{2}())[39m [90mâ”‚ [39m %78 = Base.literal_pow(%68, %75, %77)[36m::Float64[39m [90mâ”‚ [39m %79 = (%66)(%67, %78)[36m::Float64[39m [90mâ”‚ [39m (Ï‡Â² = %79) [90mâ”‚ [39m (val = %79) [90mâ”‚ [39m nothing [90mâ”‚ [39m val [90mâ”‚ [39m (i#241 = i#241 + 1) [90mâ”‚ [39m $(Expr(:loopinfo, Symbol("julia.simdloop"), nothing)) [90mâ””â”€â”€â”€[39m goto #7 [90m9 â”„â”€[39m (@_7 = Base.iterate(%31, %39)) [90mâ”‚ [39m %88 = @_7[36m::Core.Const(nothing)[39m [90mâ”‚ [39m %89 = (%88 === nothing)[36m::Core.Const(true)[39m [90mâ”‚ [39m %90 = Base.not_int(%89)[36m::Core.Const(false)[39m [90mâ””â”€â”€â”€[39m goto #11 if not %90 [90m10 â”€[39m Core.Const(:(goto %37)) [90m11 â”„[39m Main.var"workspace#3".nothing [90mâ”‚ [39m %94 = Ï‡Â²[36m::Float64[39m [90mâ””â”€â”€â”€[39m return %94 ªtext/plain§cell_idÙ$fbd538a3-8ddc-4c3f-9748-35fa7b032809¦kwargs¢id´PlutoRunner_d1acb81e¤fileÙP/home/runner/.julia/packages/Pluto/CBqeh/src/runner/PlutoRunner/src/io/stdout.jl¥group¦stdout¥level®LogLevel(-555)§runningÂ¦output†¤body ¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE)c2°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$fbd538a3-8ddc-4c3f-9748-35fa7b032809¹depends_on_disabled_cellsÂ§runtimeÎ'–Xµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$0f679916-5f87-45a3-996f-be3146a537a2Š¦queuedÂ¤logs§runningÂ¦output†¤bodyÙAfunc_without_type_instability_v3 (generic function with 1 method)¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE(ûbµî°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$0f679916-5f87-45a3-996f-be3146a537a2¹depends_on_disabled_cellsÂ§runtimeÎ·µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$252f394f-9d7d-41be-8cbf-ccb5558b83d1Š¦queuedÂ¤logs§runningÂ¦output†¤bodyÚ

How do we know where do we spend our time?

Q: How do we know where to focus our efforts based on the coding language we're using?

Profiling
Experience with common programming patterns
Knowing (enough about) how your language works under the hood

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Is it best to make sure that all cells of your array have the same data type?

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Making inner funciton type-stable & generic

¤mime©text/html¬rootassigneeÀ²last_run_timestampËAÚE(ì•ñ°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$8e3ba95e-7c10-4e95-95cb-a906259282fc¹depends_on_disabled_cellsÂ§runtimeÎÇ®µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$93beb233-81cc-47f8-89be-8164cc15d020Š¦queuedÂ¤logs§runningÂ¦output†¤bodyÙd

Containers of Concrete Types

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What's expensive?

¤mime©text/html¬rootassigneeÀ²last_run_timestampËAÚE(ì˜Ve°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$e6e22f60-4e6a-4160-ba06-42d469afb3f6¹depends_on_disabled_cellsÂ§runtimeÎ¿äµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$f5fe37e1-80b9-4853-84d6-82e56417a470Š¦queuedÂ¤logs§runningÂ¦output†¤bodyÙ3func_takes_varargs (generic function with 1 method)¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE)è’d°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$f5fe37e1-80b9-4853-84d6-82e56417a470¹depends_on_disabled_cellsÂ§runtimeÎA&µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$8f846ea8-9c6e-499b-bfd8-18bdbbd110f7Š¦queuedÂ¤logs§runningÂ¦output†¤bodyÚäBenchmarkTools.Trial: 10000 samples with 10 evaluations. Range [90m([39m[36m[1mmin[22m[39m â€¦ [35mmax[39m[90m): [39m[36m[1m1.321 Î¼s[22m[39m â€¦ [35m 4.371 Î¼s[39m [90mâ”Š[39m GC [90m([39mmin â€¦ max[90m): [39m0.00% â€¦ 0.00% Time [90m([39m[34m[1mmedian[22m[39m[90m): [39m[34m[1m1.633 Î¼s [22m[39m[90mâ”Š[39m GC [90m([39mmedian[90m): [39m0.00% Time [90m([39m[32m[1mmean[22m[39m Â± [32mÏƒ[39m[90m): [39m[32m[1m1.580 Î¼s[22m[39m Â± [32m233.944 ns[39m [90mâ”Š[39m GC [90m([39mmean Â± Ïƒ[90m): [39m0.00% Â± 0.00% [39mâ–ˆ[39mâ–†[39mâ–‚[39m [39m [39m [39mâ–‚[39m [39m [39m [39m [39m [39m [32m [39m[39mâ–…[34mâ–ˆ[39m[39mâ–†[39mâ–„[39mâ–‚[39m [39m [39m [39mâ–„[39mâ–…[39mâ–„[39mâ–‚[39m [39m [39m [39m [39mâ–ƒ[39mâ–‚[39m [39m [39m [39m [39m [39m [39mâ–[39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39mâ–‚ [39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–‡[39mâ–„[39mâ–„[39mâ–ˆ[39mâ–ˆ[39mâ–„[39mâ–[39mâ–[39mâ–[39mâ–ƒ[32mâ–…[39m[39mâ–ˆ[34mâ–ˆ[39m[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–‡[39mâ–†[39mâ–‡[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–…[39mâ–…[39mâ–‡[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–‡[39mâ–…[39mâ–[39mâ–ƒ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–…[39mâ–…[39mâ–„[39mâ–‡[39mâ–‡[39mâ–†[39mâ–„[39mâ–[39mâ–ƒ[39mâ–ƒ[39mâ–[39mâ–[39mâ–ƒ[39mâ–[39mâ–ƒ[39mâ–„[39mâ–[39mâ–„[39mâ–‡[39m [39mâ–ˆ 1.32 Î¼s[90m [39m[90mHistogram: [39m[90m[1mlog([22m[39m[90mfrequency[39m[90m[1m)[22m[39m[90m by time[39m 2.52 Î¼s [0m[1m<[22m Memory estimate[90m: [39m[33m928 bytes[39m, allocs estimate[90m: [39m[33m2[39m.¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE)ß¤Q°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$8f846ea8-9c6e-499b-bfd8-18bdbbd110f7¹depends_on_disabled_cellsÂ§runtimeÎŒ$'µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$21e3dc92-82c9-4486-8980-d5e6a012afecŠ¦queuedÂ¤logs‘ˆ¤lineÿ£msg’ƒ¨elements‘’’¡1ªtext/plain¤type¥Tuple¨objectid°5bca7c69703f9065Ù!application/vnd.pluto.tree+object§cell_idÙ$21e3dc92-82c9-4486-8980-d5e6a012afec¦kwargs¢id¹Main_workspace#2_32d8f177¤fileÙf/home/runner/work/Notes-Fall2025/Notes-Fall2025/week5/week5.jl#==#f5fe37e1-80b9-4853-84d6-82e56417a470¥group¥week5¥level¤Info§runningÂ¦output†¤body ¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE)õ:°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$21e3dc92-82c9-4486-8980-d5e6a012afec¹depends_on_disabled_cellsÂ§runtimeÎ §aµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$365c43af-37a3-4f0c-8e9e-d4003c47b6a3Š¦queuedÂ¤logs§runningÂ¦output†¤bodyÙ`

With Programming Interface

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Could you elaborate on the "..." operator that is used within functions and function arguments? How does this contribute to improved performance?

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How does Julia compile data into arrays efficiently if the array contains multiple different data types?

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Big picture steps to efficiency:

Use a compiled language
Use a strongly-typed language
Choose of algorithms wisely
Choose data types wisely
Avoid unnecessary memory allocations
Arrange memory accesses to reduce cache misses

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Why a Programming Interface?

¤mime©text/html¬rootassigneeÀ²last_run_timestampËAÚE(ì“îÌ°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$44c5243c-a044-4ed7-bf25-728b0291c14a¹depends_on_disabled_cellsÂ§runtimeÎµêµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$e7d4bc52-ee18-4d0b-8bab-591b688398feŠ¦queuedÂ¤logs§runningÂ¦output†¤bodyÚLò ¤mime©text/html¬rootassigneeÀ²last_run_timestampËAÚE(÷yØo°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$e7d4bc52-ee18-4d0b-8bab-591b688398fe¹depends_on_disabled_cellsÂ§runtimeÍ5bµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$b1557899-91c0-4f02-b486-e3c4f38d9218Š¦queuedÂ¤logs§runningÂ¦output†¤bodyÚôBenchmarkTools.Trial: 10000 samples with 294 evaluations. Range [90m([39m[36m[1mmin[22m[39m â€¦ [35mmax[39m[90m): [39m[36m[1m276.197 ns[22m[39m â€¦ [35m84.827 Î¼s[39m [90mâ”Š[39m GC [90m([39mmin â€¦ max[90m): [39m 0.00% â€¦ 99.06% Time [90m([39m[34m[1mmedian[22m[39m[90m): [39m[34m[1m278.633 ns [22m[39m[90mâ”Š[39m GC [90m([39mmedian[90m): [39m 0.00% Time [90m([39m[32m[1mmean[22m[39m Â± [32mÏƒ[39m[90m): [39m[32m[1m410.699 ns[22m[39m Â± [32m 1.459 Î¼s[39m [90mâ”Š[39m GC [90m([39mmean Â± Ïƒ[90m): [39m11.87% Â± 8.23% [34mâ–ˆ[39m[39mâ–ƒ[39m [39mâ–‚[39mâ–ƒ[39mâ–[39m [39m [39mâ–‚[39m [39m [39m [39m [39m [39m [39m [39m [32m [39m[39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39mâ–ƒ[39mâ–„[39mâ–„[39mâ–ƒ[39mâ–‚[39mâ–‚[39mâ–‚[39mâ–[39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39mâ– [34mâ–ˆ[39m[39mâ–ˆ[39mâ–‡[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–†[39mâ–‡[39mâ–ˆ[39mâ–‡[39mâ–…[39mâ–ƒ[39mâ–ƒ[39mâ–„[39mâ–ƒ[39mâ–[39mâ–[32mâ–[39m[39mâ–ƒ[39mâ–[39mâ–[39mâ–[39mâ–ƒ[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–ƒ[39mâ–ƒ[39mâ–[39mâ–[39mâ–ƒ[39mâ–„[39mâ–[39mâ–ƒ[39mâ–„[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–‡[39mâ–†[39mâ–…[39mâ–„[39mâ–„[39mâ–„[39mâ–[39mâ–„[39mâ–ƒ[39mâ–ƒ[39mâ–ƒ[39m [39mâ–ˆ 276 ns[90m [39m[90mHistogram: [39m[90m[1mlog([22m[39m[90mfrequency[39m[90m[1m)[22m[39m[90m by time[39m 758 ns [0m[1m<[22m Memory estimate[90m: [39m[33m928 bytes[39m, allocs estimate[90m: [39m[33m2[39m.¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE)Hã‚°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$b1557899-91c0-4f02-b486-e3c4f38d9218¹depends_on_disabled_cellsÂ§runtimeÎ£Ø\Dµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$e7b56266-5d70-451b-a448-6b6cfd85cab7Š¦queuedÂ¤logs‘ˆ¤lineÿ£msg’ƒ¨elements“’’¡1ªtext/plain’’¡2ªtext/plain’’¡3ªtext/plain¤type¥Tuple¨objectid°6e3572bbea69a4afÙ!application/vnd.pluto.tree+object§cell_idÙ$e7b56266-5d70-451b-a448-6b6cfd85cab7¦kwargs¢id¹Main_workspace#2_32d8f177¤fileÙf/home/runner/work/Notes-Fall2025/Notes-Fall2025/week5/week5.jl#==#f5fe37e1-80b9-4853-84d6-82e56417a470¥group¥week5¥level¤Info§runningÂ¦output†¤body ¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE)û`k°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$e7b56266-5d70-451b-a448-6b6cfd85cab7¹depends_on_disabled_cellsÂ§runtimeÎ‹Ãˆµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$a1992b28-16ab-456b-995d-1e40e423d70cŠ¦queuedÂ¤logs§runningÂ¦output†¤body ¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE(÷‘7ç°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$a1992b28-16ab-456b-995d-1e40e423d70c¹depends_on_disabled_cellsÂ§runtimeÎÏóµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$4b7b8ef8-e7c4-415b-a103-e109256e0210Š¦queuedÂ¤logs§runningÂ¦output†¤body£0.0¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE(ùýÊ*°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$4b7b8ef8-e7c4-415b-a103-e109256e0210¹depends_on_disabled_cellsÂ§runtimeÍ/Éµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$f658c638-8c9d-4828-ac15-ecd7d4650b13Š¦queuedÂ¤logs§runningÂ¦output†¤bodyÙn

Command-line Optimization options

¤mime©text/html¬rootassigneeÀ²last_run_timestampËAÚE(ì–;°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$f658c638-8c9d-4828-ac15-ecd7d4650b13¹depends_on_disabled_cellsÂ§runtimeÎ´úµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$d5cb70a8-079b-4fd5-851f-8742680ff515Š¦queuedÂ¤logs§runningÂ¦output†¤bodyÙ>func_without_type_instability (generic function with 1 method)¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE(ûGEª°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$d5cb70a8-079b-4fd5-851f-8742680ff515¹depends_on_disabled_cellsÂ§runtimeÎÏNµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$fad14e46-21a4-41ea-8f3d-a747cdfe3a51Š¦queuedÂ¤logs§runningÂ¦output†¤bodyÙ;func_with_type_instability (generic function with 1 method)¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE(û@×°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$fad14e46-21a4-41ea-8f3d-a747cdfe3a51¹depends_on_disabled_cellsÂ§runtimeÎ!Eµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$d6a2b578-88a4-4a82-bb20-641ccc60aa8dŠ¦queuedÂ¤logs§runningÂ¦output†¤bodyÙ´

There is a cost for calling a function.
But small functions are usually inlined, so as to avoid that cost.

¤mime©text/html¬rootassigneeÀ²last_run_timestampËAÚE(ì˜%ž°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$d6a2b578-88a4-4a82-bb20-641ccc60aa8d¹depends_on_disabled_cellsÂ§runtimeÎàÈµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$3fa48928-5311-49ec-83d2-cf4c45c7c579Š¦queuedÂ¤logs§runningÂ¦output†¤bodyÙŒ

Splat and variable number of function arguements

¤mime©text/html¬rootassigneeÀ²last_run_timestampËAÚE(ì˜Žó°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$3fa48928-5311-49ec-83d2-cf4c45c7c579¹depends_on_disabled_cellsÂ§runtimeÎ»oµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$04391eb3-daf0-4f20-b39e-33e626770e05Š¦queuedÂ¤logs§runningÂ¦output†¤bodyÚ×BenchmarkTools.Trial: 10000 samples with 3 evaluations. Range [90m([39m[36m[1mmin[22m[39m â€¦ [35mmax[39m[90m): [39m[36m[1m 5.964 Î¼s[22m[39m â€¦ [35m 1.276 ms[39m [90mâ”Š[39m GC [90m([39mmin â€¦ max[90m): [39m 0.00% â€¦ 98.48% Time [90m([39m[34m[1mmedian[22m[39m[90m): [39m[34m[1m 9.454 Î¼s [22m[39m[90mâ”Š[39m GC [90m([39mmedian[90m): [39m 0.00% Time [90m([39m[32m[1mmean[22m[39m Â± [32mÏƒ[39m[90m): [39m[32m[1m12.820 Î¼s[22m[39m Â± [32m24.087 Î¼s[39m [90mâ”Š[39m GC [90m([39mmean Â± Ïƒ[90m): [39m13.95% Â± 9.46% [39mâ–ˆ[39mâ–‡[34mâ–‡[39m[32mâ–…[39m[39mâ–ƒ[39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39mâ–[39mâ–ƒ[39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39mâ–‚ [39mâ–ˆ[39mâ–ˆ[34mâ–ˆ[39m[32mâ–ˆ[39m[39mâ–ˆ[39mâ–‡[39mâ–…[39mâ–[39mâ–[39mâ–„[39mâ–ƒ[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–ƒ[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–‡[39mâ–†[39mâ–„[39mâ–ƒ[39mâ–[39mâ–„[39mâ–[39mâ–[39mâ–[39mâ–ƒ[39mâ–ƒ[39mâ–„[39mâ–[39mâ–ƒ[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–„[39mâ–†[39m [39mâ–ˆ 5.96 Î¼s[90m [39m[90mHistogram: [39m[90m[1mlog([22m[39m[90mfrequency[39m[90m[1m)[22m[39m[90m by time[39m 139 Î¼s [0m[1m<[22m Memory estimate[90m: [39m[33m128.07 KiB[39m, allocs estimate[90m: [39m[33m3[39m.¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE)eÿë°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$04391eb3-daf0-4f20-b39e-33e626770e05¹depends_on_disabled_cellsÂ§runtimeÏ‹<ˆµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$953d09b8-d8d0-4e49-ae55-648f956aa248Š¦queuedÂ¤logs§runningÂ¦output†¤body£5.0¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE(ùü>p°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$953d09b8-d8d0-4e49-ae55-648f956aa248¹depends_on_disabled_cellsÂ§runtimeÍ¡Éµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$3e8c154a-3c22-49cc-accd-1076430268aeŠ¦queuedÂ¤logs§runningÂ¦output†¤bodyÙ8func_takes_varnamedargs (generic function with 1 method)¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE)8ã°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$3e8c154a-3c22-49cc-accd-1076430268ae¹depends_on_disabled_cellsÂ§runtimeÎ.Ð:µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$3ef73948-da0c-4afa-8a73-29c382b29bbdŠ¦queuedÂ¤logs§runningÂ¦output†¤bodyÚ×BenchmarkTools.Trial: 10000 samples with 1 evaluation. Range [90m([39m[36m[1mmin[22m[39m â€¦ [35mmax[39m[90m): [39m[36m[1m22.031 Î¼s[22m[39m â€¦ [35m 4.123 ms[39m [90mâ”Š[39m GC [90m([39mmin â€¦ max[90m): [39m0.00% â€¦ 98.99% Time [90m([39m[34m[1mmedian[22m[39m[90m): [39m[34m[1m22.452 Î¼s [22m[39m[90mâ”Š[39m GC [90m([39mmedian[90m): [39m0.00% Time [90m([39m[32m[1mmean[22m[39m Â± [32mÏƒ[39m[90m): [39m[32m[1m29.973 Î¼s[22m[39m Â± [32m60.341 Î¼s[39m [90mâ”Š[39m GC [90m([39mmean Â± Ïƒ[90m): [39m6.10% Â± 4.14% [34mâ–ˆ[39m[39mâ–ƒ[39mâ–[39m [39m [39m [39m [39m [32m [39m[39m [39mâ–[39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39mâ–[39mâ–‚[39mâ–ƒ[39mâ–‚[39mâ–[39m [39m [39m [39m [39m [39m [39m [39mâ– [34mâ–ˆ[39m[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–‡[39mâ–‡[39mâ–‡[39mâ–‡[32mâ–‡[39m[39mâ–ˆ[39mâ–ˆ[39mâ–‡[39mâ–†[39mâ–†[39mâ–†[39mâ–†[39mâ–„[39mâ–„[39mâ–…[39mâ–…[39mâ–„[39mâ–„[39mâ–[39mâ–„[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–ƒ[39mâ–[39mâ–[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–‡[39mâ–†[39mâ–†[39mâ–„[39mâ–„[39mâ–†[39m [39mâ–ˆ 22 Î¼s[90m [39m[90mHistogram: [39m[90m[1mlog([22m[39m[90mfrequency[39m[90m[1m)[22m[39m[90m by time[39m 78.8 Î¼s [0m[1m<[22m Memory estimate[90m: [39m[33m128.07 KiB[39m, allocs estimate[90m: [39m[33m3[39m.¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE)Á”d°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$3ef73948-da0c-4afa-8a73-29c382b29bbd¹depends_on_disabled_cellsÂ§runtimeÏ‰J+Hµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$15efacae-95a5-4607-8a38-76ee5f345235Š¦queuedÂ¤logs§runningÂ¦output†¤bodyÙ:

Popouri

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Announcements

¤mime©text/html¬rootassigneeÀ²last_run_timestampËAÚE(ì“²°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$9007f240-c88e-46c4-993d-fd6b93d8b18d¹depends_on_disabled_cellsÂ§runtimeÎ‚µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$b24a684b-b2d1-4d6a-9408-590feef3ba08Š¦queuedÂ¤logs§runningÂ¦output†¤bodyÙH

Abstract Types

¤mime©text/html¬rootassigneeÀ²last_run_timestampËAÚE(ì”q°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$b24a684b-b2d1-4d6a-9408-590feef3ba08¹depends_on_disabled_cellsÂ§runtimeÎ°µµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$282d2a07-5f63-4f3e-960e-b5ffcab6b9deŠ¦queuedÂ¤logs§runningÂ¦output†¤bodyÚ©BenchmarkTools.Trial: 463 samples with 1 evaluation. Range [90m([39m[36m[1mmin[22m[39m â€¦ [35mmax[39m[90m): [39m[36m[1m 8.975 ms[22m[39m â€¦ [35m141.024 ms[39m [90mâ”Š[39m GC [90m([39mmin â€¦ max[90m): [39m 0.00% â€¦ 92.57% Time [90m([39m[34m[1mmedian[22m[39m[90m): [39m[34m[1m10.501 ms [22m[39m[90mâ”Š[39m GC [90m([39mmedian[90m): [39m11.64% Time [90m([39m[32m[1mmean[22m[39m Â± [32mÏƒ[39m[90m): [39m[32m[1m10.793 ms[22m[39m Â± [32m 6.179 ms[39m [90mâ”Š[39m GC [90m([39mmean Â± Ïƒ[90m): [39m14.13% Â± 5.88% [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39mâ–[39mâ–‚[39m [39m [39mâ–[39mâ–[39m [39mâ–…[39m [39mâ–‚[39mâ–ƒ[34mâ–„[39m[39mâ–†[39mâ–ˆ[39mâ–…[39m [39mâ–…[39mâ–…[32mâ–ƒ[39m[39m [39mâ–‚[39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39mâ–ƒ[39mâ–„[39mâ–ƒ[39mâ–„[39mâ–ƒ[39mâ–ƒ[39mâ–ƒ[39mâ–ƒ[39mâ–[39mâ–[39mâ–ƒ[39mâ–ƒ[39mâ–ƒ[39mâ–[39mâ–ƒ[39mâ–…[39mâ–[39mâ–‡[39mâ–ˆ[39mâ–ˆ[39mâ–‡[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–†[39mâ–‡[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[34mâ–ˆ[39m[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[39mâ–ˆ[32mâ–ˆ[39m[39mâ–ˆ[39mâ–ˆ[39mâ–†[39mâ–‡[39mâ–†[39mâ–…[39mâ–„[39mâ–„[39mâ–ƒ[39mâ–ƒ[39mâ–ƒ[39mâ–„[39mâ–ƒ[39mâ–ƒ[39mâ–[39mâ–ƒ[39mâ–[39mâ–[39mâ–„[39m [39mâ–„ 8.97 ms[90m Histogram: frequency by time[39m 11.7 ms [0m[1m<[22m Memory estimate[90m: [39m[33m61.04 MiB[39m, allocs estimate[90m: [39m[33m3[39m.¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE)–²>°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$282d2a07-5f63-4f3e-960e-b5ffcab6b9de¹depends_on_disabled_cellsÂ§runtimeÏ²þ)µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$9ab94eea-4d57-4ef2-a73a-64e7c8b89222Š¦queuedÂ¤logs§runningÂ¦output†¤body³0.18237982380143794¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE)Døj°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$9ab94eea-4d57-4ef2-a73a-64e7c8b89222¹depends_on_disabled_cellsÂ§runtimeÎ.}(µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$5d599c10-f1d2-454e-ad85-0e092b6cae7eŠ¦queuedÂ¤logs‘ˆ¤lineÿ£msg’ÚMethodInstance for Main.var"workspace#3".func_without_type_instability(::Vector{Float64}, ::Int64) from func_without_type_instability([90mobs[39m, [90mparam[39m)[90m @[39m [90mMain.var"workspace#3"[39m [90m~/work/Notes-Fall2025/Notes-Fall2025/week5/[39m[90m[4mweek5.jl#==#d5cb70a8-079b-4fd5-851f-8742680ff515:1[24m[39m Arguments #self#[36m::Core.Const(Main.var"workspace#3".func_without_type_instability)[39m obs[36m::Vector{Float64}[39m param[36m::Int64[39m Locals Ï‡Â²[36m::Float64[39m pred[36m::Vector{Float64}[39m Body[36m::Float64[39m [90m1 â”€[39m %1 = Main.var"workspace#3".convert[36m::Core.Const(convert)[39m [90mâ”‚ [39m %2 = Main.var"workspace#3".Float64[36m::Core.Const(Float64)[39m [90mâ”‚ [39m %3 = Base.broadcasted(Main.var"workspace#3".my_model, obs, param)[36m::Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Nothing, typeof(Main.var"workspace#3".my_model), Tuple{Vector{Float64}, Int64}}[39m [90mâ”‚ [39m %4 = Base.broadcasted(%1, %2, %3)[36m::Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Nothing, typeof(convert), Tuple{Base.RefValue{Type{Float64}}, Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1}, Nothing, typeof(Main.var"workspace#3".my_model), Tuple{Vector{Float64}, Int64}}}}[39m [90mâ”‚ [39m (pred = Base.materialize(%4)) [90mâ”‚ [39m %6 = pred[36m::Vector{Float64}[39m [90mâ”‚ [39m %7 = Main.var"workspace#3".calc_Ï‡Â²(obs, %6)[36m::Float64[39m [90mâ”‚ [39m (Ï‡Â² = %7) [90mâ””â”€â”€[39m return %7 ªtext/plain§cell_idÙ$5d599c10-f1d2-454e-ad85-0e092b6cae7e¦kwargs¢id´PlutoRunner_d1acb81e¤fileÙP/home/runner/.julia/packages/Pluto/CBqeh/src/runner/PlutoRunner/src/io/stdout.jl¥group¦stdout¥level®LogLevel(-555)§runningÂ¦output†¤body ¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE)4ü¨°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$5d599c10-f1d2-454e-ad85-0e092b6cae7e¹depends_on_disabled_cellsÂ§runtimeÎ }ÿµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$4c3332a8-a5d1-43fb-887b-ac66dfa02de5Š¦queuedÂ¤logs§runningÂ¦output†¤bodyÙX

Programming Interfaces

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Class project

Review feedback on project proposals
Review project instructions and rubric on website
Can continue using repository from project proposal
Next step is the serial implementation, focusing on good practices that we've discussed/seen in labs
Serial code should be ready for peer code review by Oct 8
After this week's labs, will have everything you need to benchmark, profile and optimize the serial version of your code.
Sign up for project presentation schedule

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Passing array of data to function that expects distinct function arguments

¤mime©text/html¬rootassigneeÀ²last_run_timestampËAÚE(ì˜§°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$53863e96-0c11-484f-bfc9-23b52ca933de¹depends_on_disabled_cellsÂ§runtimeÎÈ1µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$ccb63eb8-1da0-48ce-ae51-c18c48509445Š¦queuedÂ¤logs§runningÂ¦output†¤bodyÙ;func_that_needs_parameters (generic function with 1 method)¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE)?=°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$ccb63eb8-1da0-48ce-ae51-c18c48509445¹depends_on_disabled_cellsÂ§runtimeÎ³’µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$0363149b-f34d-4120-81db-a655f18b908fŠ¦queuedÂ¤logs§runningÂ¦output†¤bodyÚ

Compiler Optimizations

Q: How does Julia go about auto-optimizing simple computation time sinks like loops, nested loop, functions called many times in a loop, etc.

Whole courses on optimizing compilers, but a few categories that come to mind:

Compilation
Static type inference
Inlining small functions
Dead code elimination
Unrolling small loops
Grouping operations for SIMD
...

Advanced optimizations that require additional help:

Precompiliation of functiosn to be used
Empirical branch prediction

¤mime©text/html¬rootassigneeÀ²last_run_timestampËAÚE(ì™ãÞ°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$0363149b-f34d-4120-81db-a655f18b908f¹depends_on_disabled_cellsÂ§runtimeÎz”µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$b8e117f5-b253-4208-a00e-7966978fb24bŠ¦queuedÂ¤logs§runningÂ¦output†¤bodyÙ)my_model (generic function with 1 method)¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE(û02#°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$b8e117f5-b253-4208-a00e-7966978fb24b¹depends_on_disabled_cellsÂ§runtimeÎ~Yµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$02002957-8644-40ca-99ef-86151769a5d9Š¦queuedÂ¤logs‘ˆ¤lineÿ£msg’Ù. 0.000002 seconds (2 allocations: 928 bytes) ªtext/plain§cell_idÙ$02002957-8644-40ca-99ef-86151769a5d9¦kwargs¢id´PlutoRunner_d1acb81e¤fileÙP/home/runner/.julia/packages/Pluto/CBqeh/src/runner/PlutoRunner/src/io/stdout.jl¥group¦stdout¥level®LogLevel(-555)§runningÂ¦output†¤body…¦prefix§Float64¨elementsÜ’’§0.12307ªtext/plain’’§1.01799ªtext/plain’’©-0.395052ªtext/plain’’¨0.824969ªtext/plain’’§-1.0832ªtext/plain’’¨0.139942ªtext/plain’’ª-0.0393634ªtext/plain’’¨0.848658ªtext/plain’ ’©-0.178521ªtext/plain’ ’¦1.7617ªtext/plain’’¨-1.15012ªtext/plain’’§3.27889ªtext/plain’ ’§1.39378ªtext/plain’’©-0.585879ªtext/plain’’¨0.528007ªtext/plain’’¨-1.61489ªtext/plain’’¨-1.56609ªtext/plain’’©-0.807679ªtext/plain’’§1.06054ªtext/plain’’©-0.358974ªtext/plain¤more’[’§-1.0875ªtext/plain’\’©-0.822131ªtext/plain’]’©-0.588678ªtext/plain’^’¨-0.84641ªtext/plain’_’§0.67201ªtext/plain’`’©-0.625109ªtext/plain’a’¨-1.20346ªtext/plain’b’§1.46734ªtext/plain’c’¨0.516096ªtext/plain’d’©0.0442022ªtext/plain¤type¥Array¬prefix_short ¨objectid°5db5f700787a2e87¤mimeÙ!application/vnd.pluto.tree+object¬rootassignee´@time row_one_copied²last_run_timestampËAÚE)¶Þ °persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$02002957-8644-40ca-99ef-86151769a5d9¹depends_on_disabled_cellsÂ§runtimeÎ«w{µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$12b8d696-0e7b-4814-9c73-22b7cf95fef4Š¦queuedÂ¤logs§runningÂ¦output†¤bodyÚBenchmarkTools.Trial: 60 samples with 1 evaluation. Range [90m([39m[36m[1mmin[22m[39m â€¦ [35mmax[39m[90m): [39m[36m[1m55.818 ms[22m[39m â€¦ [35m200.497 ms[39m [90mâ”Š[39m GC [90m([39mmin â€¦ max[90m): [39m 5.75% â€¦ 72.35% Time [90m([39m[34m[1mmedian[22m[39m[90m): [39m[34m[1m58.165 ms [22m[39m[90mâ”Š[39m GC [90m([39mmedian[90m): [39m 6.37% Time [90m([39m[32m[1mmean[22m[39m Â± [32mÏƒ[39m[90m): [39m[32m[1m83.423 ms[22m[39m Â± [32m 54.579 ms[39m [90mâ”Š[39m GC [90m([39mmean Â± Ïƒ[90m): [39m34.87% Â± 25.82% [39mâ–ˆ[34mâ–ƒ[39m[39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [32m [39m[39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39m [39mâ–ˆ[34mâ–ˆ[39m[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[32mâ–[39m[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–[39mâ–…[39mâ–„[39m [39mâ– 55.8 ms[90m Histogram: frequency by time[39m 200 ms [0m[1m<[22m Memory estimate[90m: [39m[33m366.23 MiB[39m, allocs estimate[90m: [39m[33m18[39m.¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÚE) ØŠ °persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$12b8d696-0e7b-4814-9c73-22b7cf95fef4¹depends_on_disabled_cellsÂ§runtimeÏÚÛÏÁµpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂÙ$9bf47a21-af6d-4c76-84d1-0b78635bae9aŠ¦queuedÂ¤logs§runningÂ¦output†¤bodyÙp

New Implementation, same interface

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Fusing broadcasted operations

¤mime©text/html¬rootassigneeÀ²last_run_timestampËAÚE(ì– R°persist_js_stateÂ·has_pluto_hook_featuresÂ§cell_idÙ$64d51527-1bd0-4010-b458-4dfa6f44610d¹depends_on_disabled_cellsÂ§runtimeÎº±µpublished_object_keys¸depends_on_skipped_cellsÂ§erroredÂ±cell_dependenciesÞÙ$bf497b24-72a7-4a2f-908e-c24922a5f3c8„´precedence_heuristic §cell_idÙ$bf497b24-72a7-4a2f-908e-c24922a5f3c8´downstream_cells_map¸my_model_stable_specific“Ù$aa767f81-4bcb-41b6-b141-85796a81d8fbÙ$cee02d24-1dcc-4c29-a322-0ddd12ab8180Ù$20db6ae9-8c79-44d1-a3a7-0dadf1d0dc5a²upstream_cells_map…¡<¡>¦isless§Float64¡*Ù$bdf99bf8-bb88-40d7-a8ec-84a99ab65ff3„´precedence_heuristic §cell_idÙ$bdf99bf8-bb88-40d7-a8ec-84a99ab65ff3´downstream_cells_map€²upstream_cells_map†£obs‘Ù$9303806b-a460-4ec2-9f71-252f43b34328°InteractiveUtils¾InteractiveUtils.code_warntype²func_with_barriers‘Ù$05d2780e-612c-4e86-93c4-f57734f49c74®@code_warntypeªparam_true‘Ù$9303806b-a460-4ec2-9f71-252f43b34328Ù$9d71d1b0-765d-48d7-a939-c951fc8caa67„´precedence_heuristic §cell_idÙ$9d71d1b0-765d-48d7-a939-c951fc8caa67´downstream_cells_map€²upstream_cells_map‚§@md_str¨getindexÙ$8a97f0bf-3ada-4503-98a5-7bdeca15edc4„´precedence_heuristic §cell_idÙ$8a97f0bf-3ada-4503-98a5-7bdeca15edc4´downstream_cells_mapªbig_matrix”Ù$02002957-8644-40ca-99ef-86151769a5d9Ù$426ccd5e-398b-4df7-a27d-cf7a578c658fÙ$18813a15-531f-4d74-a0f7-45a0574d6c1bÙ$59fbb599-c947-4a2a-a678-8e38a666660c²upstream_cells_map¥randnÙ$f9d3d93f-f1c4-4b3b-aa8a-097f2c8aaf68„´precedence_heuristic §cell_idÙ$f9d3d93f-f1c4-4b3b-aa8a-097f2c8aaf68´downstream_cells_map€²upstream_cells_map‚§@md_str¨getindexÙ$3738748d-7b3d-4015-bf71-0ffb9e28c43d„´precedence_heuristic §cell_idÙ$3738748d-7b3d-4015-bf71-0ffb9e28c43d´downstream_cells_map€²upstream_cells_map‚§@md_str¨getindexÙ$ac9b4f35-36fc-425b-a0a2-83fc32c62c7c„´precedence_heuristic §cell_idÙ$ac9b4f35-36fc-425b-a0a2-83fc32c62c7c´downstream_cells_map€²upstream_cells_map‚§@md_str¨getindexÙ$f13e442e-771f-4aab-b5f3-f08c4e72229c„´precedence_heuristic §cell_idÙ$f13e442e-771f-4aab-b5f3-f08c4e72229c´downstream_cells_map€²upstream_cells_map‚§@md_str¨getindexÙ$7b66fbe6-5f42-4619-a265-8d284d3dac8c„´precedence_heuristic §cell_idÙ$7b66fbe6-5f42-4619-a265-8d284d3dac8c´downstream_cells_map€²upstream_cells_map„¥Coord‘Ù$94223079-afab-4a6d-a126-068a4e94f52e¤sqrt¡^¡+Ù$cf5262da-1043-11ec-12fc-9916cc70070c„´precedence_heuristic §cell_idÙ$cf5262da-1043-11ec-12fc-9916cc70070c´downstream_cells_map€²upstream_cells_map‚§@md_str¨getindexÙ$2e32935f-c82f-434b-b0f5-01a4b15ddb80„´precedence_heuristic §cell_idÙ$2e32935f-c82f-434b-b0f5-01a4b15ddb80´downstream_cells_map€²upstream_cells_map‚§@md_str¨getindexÙ$46d264b6-73da-4790-92e4-988728c7e1df„´precedence_heuristic §cell_idÙ$46d264b6-73da-4790-92e4-988728c7e1df´downstream_cells_map€²upstream_cells_map‚§@md_str¨getindexÙ$3d06ed43-23c2-4c57-a1a5-e699713b9506„´precedence_heuristic 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[0m[1mResolving...[22m [90m===[39m [32m[1m Installed[22m[39m DiffRules â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.15.1 [32m[1m Installed[22m[39m DiffResults â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.1.0 [32m[1m Installed[22m[39m CommonSubexpressions â”€ v0.3.0 [32m[1m Installed[22m[39m OpenSpecFun_jll â”€â”€â”€â”€â”€â”€ v0.5.5+0 [32m[1m Installed[22m[39m ForwardDiff â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v0.10.36 [32m[1m Installed[22m[39m SpecialFunctions â”€â”€â”€â”€â”€ v2.3.1 [32m[1m Installed[22m[39m Preferences â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.4.0 [32m[1m Installed[22m[39m StaticArrays â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.6.3 [32m[1m Installed[22m[39m Revise â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v3.5.3 [32m[1m No Changes[22m[39m to `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sqxydbsfum/Project.toml` [32m[1m Updating[22m[39m `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sqxydbsfum/Manifest.toml` [90m[05823500] [39m[93mâ†‘ OpenLibm_jll v0.8.1+2 â‡’ v0.8.5+0[39m [0m[1mInstantiating...[22m [90m===[39m [0m[1mPrecompiling...[22m [90m===[39m Waiting for notebook process to start... Done. Starting precompilation... [92m[1mPrecompiling[22m[39m project... «ForwardDiffÚ [0m[1mResolving...[22m [90m===[39m [32m[1m Installed[22m[39m DiffRules â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.15.1 [32m[1m Installed[22m[39m DiffResults â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.1.0 [32m[1m Installed[22m[39m CommonSubexpressions â”€ v0.3.0 [32m[1m Installed[22m[39m OpenSpecFun_jll â”€â”€â”€â”€â”€â”€ v0.5.5+0 [32m[1m Installed[22m[39m ForwardDiff â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v0.10.36 [32m[1m Installed[22m[39m SpecialFunctions â”€â”€â”€â”€â”€ v2.3.1 [32m[1m Installed[22m[39m Preferences â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.4.0 [32m[1m Installed[22m[39m StaticArrays â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.6.3 [32m[1m Installed[22m[39m Revise â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v3.5.3 [32m[1m No Changes[22m[39m to `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sqxydbsfum/Project.toml` [32m[1m Updating[22m[39m `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sqxydbsfum/Manifest.toml` [90m[05823500] [39m[93mâ†‘ OpenLibm_jll v0.8.1+2 â‡’ v0.8.5+0[39m [0m[1mInstantiating...[22m [90m===[39m [0m[1mPrecompiling...[22m [90m===[39m Waiting for notebook process to start... Done. Starting precompilation... [92m[1mPrecompiling[22m[39m project... ªnbpkg_syncÚ [0m[1mResolving...[22m [90m===[39m [32m[1m Installed[22m[39m DiffRules â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.15.1 [32m[1m Installed[22m[39m DiffResults â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.1.0 [32m[1m Installed[22m[39m CommonSubexpressions â”€ v0.3.0 [32m[1m Installed[22m[39m OpenSpecFun_jll â”€â”€â”€â”€â”€â”€ v0.5.5+0 [32m[1m Installed[22m[39m ForwardDiff â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v0.10.36 [32m[1m Installed[22m[39m SpecialFunctions â”€â”€â”€â”€â”€ v2.3.1 [32m[1m Installed[22m[39m Preferences â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.4.0 [32m[1m Installed[22m[39m StaticArrays â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.6.3 [32m[1m Installed[22m[39m Revise â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v3.5.3 [32m[1m No Changes[22m[39m to `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sqxydbsfum/Project.toml` [32m[1m Updating[22m[39m `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sqxydbsfum/Manifest.toml` [90m[05823500] [39m[93mâ†‘ OpenLibm_jll v0.8.1+2 â‡’ v0.8.5+0[39m [0m[1mInstantiating...[22m [90m===[39m [0m[1mPrecompiling...[22m [90m===[39m Waiting for notebook process to start... Done. Starting precompilation... [92m[1mPrecompiling[22m[39m project... §PlutoUIÚ [0m[1mResolving...[22m [90m===[39m [32m[1m Installed[22m[39m DiffRules â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.15.1 [32m[1m Installed[22m[39m DiffResults â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.1.0 [32m[1m Installed[22m[39m CommonSubexpressions â”€ v0.3.0 [32m[1m Installed[22m[39m OpenSpecFun_jll â”€â”€â”€â”€â”€â”€ v0.5.5+0 [32m[1m Installed[22m[39m ForwardDiff â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v0.10.36 [32m[1m Installed[22m[39m SpecialFunctions â”€â”€â”€â”€â”€ v2.3.1 [32m[1m Installed[22m[39m Preferences â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.4.0 [32m[1m Installed[22m[39m StaticArrays â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.6.3 [32m[1m Installed[22m[39m Revise â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v3.5.3 [32m[1m No Changes[22m[39m to `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sqxydbsfum/Project.toml` [32m[1m Updating[22m[39m `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sqxydbsfum/Manifest.toml` [90m[05823500] [39m[93mâ†‘ OpenLibm_jll v0.8.1+2 â‡’ v0.8.5+0[39m [0m[1mInstantiating...[22m [90m===[39m [0m[1mPrecompiling...[22m [90m===[39m Waiting for notebook process to start... Done. Starting precompilation... [92m[1mPrecompiling[22m[39m project... ©PlutoTestÚ [0m[1mResolving...[22m [90m===[39m [32m[1m Installed[22m[39m DiffRules â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.15.1 [32m[1m Installed[22m[39m DiffResults â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.1.0 [32m[1m Installed[22m[39m CommonSubexpressions â”€ v0.3.0 [32m[1m Installed[22m[39m OpenSpecFun_jll â”€â”€â”€â”€â”€â”€ v0.5.5+0 [32m[1m Installed[22m[39m ForwardDiff â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v0.10.36 [32m[1m Installed[22m[39m SpecialFunctions â”€â”€â”€â”€â”€ v2.3.1 [32m[1m Installed[22m[39m Preferences â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.4.0 [32m[1m Installed[22m[39m StaticArrays â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.6.3 [32m[1m Installed[22m[39m Revise â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v3.5.3 [32m[1m No Changes[22m[39m to `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sqxydbsfum/Project.toml` [32m[1m Updating[22m[39m `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sqxydbsfum/Manifest.toml` [90m[05823500] [39m[93mâ†‘ OpenLibm_jll v0.8.1+2 â‡’ v0.8.5+0[39m [0m[1mInstantiating...[22m [90m===[39m [0m[1mPrecompiling...[22m [90m===[39m Waiting for notebook process to start... Done. Starting precompilation... [92m[1mPrecompiling[22m[39m project... ®BenchmarkToolsÚ [0m[1mResolving...[22m [90m===[39m [32m[1m Installed[22m[39m DiffRules â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.15.1 [32m[1m Installed[22m[39m DiffResults â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.1.0 [32m[1m Installed[22m[39m CommonSubexpressions â”€ v0.3.0 [32m[1m Installed[22m[39m OpenSpecFun_jll â”€â”€â”€â”€â”€â”€ v0.5.5+0 [32m[1m Installed[22m[39m ForwardDiff â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v0.10.36 [32m[1m Installed[22m[39m SpecialFunctions â”€â”€â”€â”€â”€ v2.3.1 [32m[1m Installed[22m[39m Preferences â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.4.0 [32m[1m Installed[22m[39m StaticArrays â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.6.3 [32m[1m Installed[22m[39m Revise â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v3.5.3 [32m[1m No Changes[22m[39m to `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sqxydbsfum/Project.toml` [32m[1m Updating[22m[39m `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sqxydbsfum/Manifest.toml` [90m[05823500] [39m[93mâ†‘ OpenLibm_jll v0.8.1+2 â‡’ v0.8.5+0[39m [0m[1mInstantiating...[22m [90m===[39m [0m[1mPrecompiling...[22m [90m===[39m Waiting for notebook process to start... Done. Starting precompilation... [92m[1mPrecompiling[22m[39m project... ²PlutoTeachingToolsÚ [0m[1mResolving...[22m [90m===[39m [32m[1m Installed[22m[39m DiffRules â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.15.1 [32m[1m Installed[22m[39m DiffResults â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.1.0 [32m[1m Installed[22m[39m CommonSubexpressions â”€ v0.3.0 [32m[1m Installed[22m[39m OpenSpecFun_jll â”€â”€â”€â”€â”€â”€ v0.5.5+0 [32m[1m Installed[22m[39m ForwardDiff â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v0.10.36 [32m[1m Installed[22m[39m SpecialFunctions â”€â”€â”€â”€â”€ v2.3.1 [32m[1m Installed[22m[39m Preferences â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.4.0 [32m[1m Installed[22m[39m StaticArrays â”€â”€â”€â”€â”€â”€â”€â”€â”€ v1.6.3 [32m[1m Installed[22m[39m Revise â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ v3.5.3 [32m[1m No Changes[22m[39m to `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sqxydbsfum/Project.toml` [32m[1m Updating[22m[39m `~/.julia/scratchspaces/c3e4b0f8-55cb-11ea-2926-15256bba5781/pkg_envs/env_sqxydbsfum/Manifest.toml` [90m[05823500] [39m[93mâ†‘ OpenLibm_jll v0.8.1+2 â‡’ v0.8.5+0[39m [0m[1mInstantiating...[22m [90m===[39m [0m[1mPrecompiling...[22m [90m===[39m Waiting for notebook process to start... Done. Starting precompilation... [92m[1mPrecompiling[22m[39m project... §enabledÃ·restart_recommended_msgÀ´restart_required_msgÀbusy_packages¶waiting_for_permissionÂÙ,waiting_for_permission_but_probably_disabledÂ«cell_inputsÞÙ$bf497b24-72a7-4a2f-908e-c24922a5f3c8„§cell_idÙ$bf497b24-72a7-4a2f-908e-c24922a5f3c8¤codeÙufunction my_model_stable_specific(x::Float64,slope::Float64) if x>1.0 return slope else return slope*x end end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$bdf99bf8-bb88-40d7-a8ec-84a99ab65ff3„§cell_idÙ$bdf99bf8-bb88-40d7-a8ec-84a99ab65ff3¤codeÙ1@code_warntype func_with_barriers(obs,param_true)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$9d71d1b0-765d-48d7-a939-c951fc8caa67„§cell_idÙ$9d71d1b0-765d-48d7-a939-c951fc8caa67¤codeÚ md""" **Interpretted languages:** + Loops are very slow + Usually worth creating extra arrays to avoid explicit loops + People often call operations on arrays "vectorized", even if every operation is done in serial **Compiled languages:** + Loops are fast. + Can choose whether to write a loop explicilty based on what's more intuitive for programmer and algorithm. + Using "vectorized" notation can unintentionally add unnecessary memory allocations... - if you don't use broadcasting and fusing """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$8a97f0bf-3ada-4503-98a5-7bdeca15edc4„§cell_idÙ$8a97f0bf-3ada-4503-98a5-7bdeca15edc4¤code¼big_matrix = randn(100,100);¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$f9d3d93f-f1c4-4b3b-aa8a-097f2c8aaf68„§cell_idÙ$f9d3d93f-f1c4-4b3b-aa8a-097f2c8aaf68¤codeÙ2md"## Generic functions in terms of abstract type"¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$3738748d-7b3d-4015-bf71-0ffb9e28c43d„§cell_idÙ$3738748d-7b3d-4015-bf71-0ffb9e28c43d¤codeÚmd""" ### Peer Code Review - Constructive suggestions for improving programming practices (1 point) - Specific, constructive suggestions for improving code readability/documentation (1 point) - Specific, constructive suggestions for improving tests and/or assertions (1 point) - Specific, constructive suggestions for improving code modularity/organization/maintainability (1 point) - Specific, constructive suggestions for improving code efficiency (1 point) - Finding any bugs (if code author confirms) (bonus points?) """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$ac9b4f35-36fc-425b-a0a2-83fc32c62c7c„§cell_idÙ$ac9b4f35-36fc-425b-a0a2-83fc32c62c7c¤codeÚ"md""" ### Implementation details for code efficiency #### (assuming JIT languages) - **Avoid unnecessary memory allocations** - Take advantage of *fusing* and *broadcasting* - Use `view` (e.g., `view(array,1:5,:)`) instead of copying (`array[1:5,:]`) - Avoid many small allocations on heap (e.g., using `StaticArrays.jl`) - **Avoid type instability** - Avoid untyped global variables - Avoid containers (e.g., arrays) of abstract types - Avoid abstract types for fields in `struct`s - Write type-stable functions - Organize code into small functions (see function barriers) - **Avoid inefficient data structures** (e.g., `Dict` when better choice avaliable) - Adding annotations that enable/allow compiler optimizations (e.g., `@inbounds`, `@fastmath`, `@simd`, `@turbo`), but *only* when appropriate - Avoid unnecessary use of strings or string interpolation - Write code so that it can be parallelized in the future (see later labs) See [Performance Tips](https://docs.julialang.org/en/v1/manual/performance-tips/) for more details. """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$f13e442e-771f-4aab-b5f3-f08c4e72229c„§cell_idÙ$f13e442e-771f-4aab-b5f3-f08c4e72229c¤codeÚ´md""" ## When to start parallelizing? **Q:** How do you strike the balance between: - optimizing the serial version of your code and - optimizing your parallelization? **A:** The added cost of moving data between processors makes it important to avoid unnecessary data movement. One part of that is avoiding unnecessary memory allocations and using efficient data structures. If the algorithm is well suited to parallelization, then a memory efficient serial version is much more likely to get good performancfe when parallelized. **Q:** Is it hard to tell when you should shift your focus to optimizing the other part? **A:** Perhaps. Although, it gets easier with experience. """ ¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$7b66fbe6-5f42-4619-a265-8d284d3dac8c„§cell_idÙ$7b66fbe6-5f42-4619-a265-8d284d3dac8c¤codeÙ>let pos = Coord(3,4) pos.x pos.y sqrt(pos.x^2+pos.y^2) end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$cf5262da-1043-11ec-12fc-9916cc70070c„§cell_idÙ$cf5262da-1043-11ec-12fc-9916cc70070c¤codeÙSmd"> Astro 528: High-Performance Scientific Computing for Astrophysics (Fall 2025)"¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$2e32935f-c82f-434b-b0f5-01a4b15ddb80„§cell_idÙ$2e32935f-c82f-434b-b0f5-01a4b15ddb80¤codeÙ#md"## Containers of Abstract Types"¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$46d264b6-73da-4790-92e4-988728c7e1df„§cell_idÙ$46d264b6-73da-4790-92e4-988728c7e1df¤codeÙ®md""" If you pass a data structure that's stored in the heap, then only a pointer (or something that acts like a pointer/reference) to that data is placed on the stack. """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$3d06ed43-23c2-4c57-a1a5-e699713b9506„§cell_idÙ$3d06ed43-23c2-4c57-a1a5-e699713b9506¤codeÙØblockquote(md""" According to the performance tips, it seems that using global variables leads to bad performance, and it is better to pass arguments to functions. When should one be using global variables then? """)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$248c85d4-bcac-40a4-9052-1f72a62422ed„§cell_idÙ$248c85d4-bcac-40a4-9052-1f72a62422ed¤code¿abstract type AbstractCoord end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$55af3d38-8956-4a22-8ca6-dbbb7de1b426„§cell_idÙ$55af3d38-8956-4a22-8ca6-dbbb7de1b426¤codeÙ integrate_f(x->sin(x)^2/Ï€,0,Ï€)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$c8a7838a-8f1a-4f33-a9de-48e60992d08b„§cell_idÙ$c8a7838a-8f1a-4f33-a9de-48e60992d08b¤codeÙYbegin vec_c1 = fill(c1,n) vec_c2 = fill(c2,n) @benchmark distance($vec_c1,$vec_c2) end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$fa1f963d-d674-442f-aa32-fcee86a8c058„§cell_idÙ$fa1f963d-d674-442f-aa32-fcee86a8c058¤codeÙ*md""" # What operations are expensive? """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$6985f2d5-6c71-4289-b655-ec06754f85c4„§cell_idÙ$6985f2d5-6c71-4289-b655-ec06754f85c4¤codeÙFstruct PolarCoord <: AbstractCoord r::Float64 theta::Float64 end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$c949701e-3399-44d8-9041-4dcb99c78cda„§cell_idÙ$c949701e-3399-44d8-9041-4dcb99c78cda¤codeÙÐblockquote(md"""I've been told to eliminate for loops wherever possible when writing Python/R/IDL code. In constrast, when writing Julia/C/C++/Fortran/Java `for` loops are not detrimental. Why is this?""")¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$ae709a34-9244-44ee-a004-381fc9b6cd0c„§cell_idÙ$ae709a34-9244-44ee-a004-381fc9b6cd0c¤codeÙ:md"ToC on side $(@bind toc_aside CheckBox(;default=true))"¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$ba8781e6-5c7e-4aaf-8ccd-da3fc6210ec5„§cell_idÙ$ba8781e6-5c7e-4aaf-8ccd-da3fc6210ec5¤codeÙ$func_takes_varargs([i for i in 1:3])¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$24a2ae54-a11d-42da-980c-1f4c78daf4b4„§cell_idÙ$24a2ae54-a11d-42da-980c-1f4c78daf4b4¤codeÙ1let pos = Coord(3,4) x(pos) y(pos) r(pos) end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$3ac9ad42-7bf1-4b36-9e0b-53f3f60796b1„§cell_idÙ$3ac9ad42-7bf1-4b36-9e0b-53f3f60796b1¤codeÙmd""" ## Types of elements in collections **Q:** Does Julia automatically assume the whole array is of that type to optimize performance? """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$c1628685-c357-436f-83dd-bf19bde24964„§cell_idÙ$c1628685-c357-436f-83dd-bf19bde24964¤code¾md""" ## Function barriers """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$d35aa76c-b4e6-45f8-a4e3-ba37d674db82„§cell_idÙ$d35aa76c-b4e6-45f8-a4e3-ba37d674db82¤code±md"# Helper Code"¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$fa116847-4bac-41e6-bd6e-e01c5c7234ae„§cell_idÙ$fa116847-4bac-41e6-bd6e-e01c5c7234ae¤codeÙþmd""" ### Cost of common operations $(RobustLocalResource("http://ithare.com/wp-content/uploads/part101_infographics_v08.png", "part101_infographics_v08.png")) - Credit: [ithare.com](http://ithare.com/wp-content/uploads/part101_infographics_v08.png) """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$96998f54-9f66-48fe-b808-559276667054„§cell_idÙ$96998f54-9f66-48fe-b808-559276667054¤codeÙ9f_fused_explicitly(x) = 3 .* x.^2 .+ 4 .* x .+ 7 .* x.^3;¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$f79de8d4-537e-421f-a66d-41bc79f8f12f„§cell_idÙ$f79de8d4-537e-421f-a66d-41bc79f8f12f¤code¿md"## No Programming Interface"¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$11c29d50-1975-48cc-b1c5-dd3814128e86„§cell_idÙ$11c29d50-1975-48cc-b1c5-dd3814128e86¤codeºf(x) = 3x.^2 + 4x + 7x.^3;¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$05d2780e-612c-4e86-93c4-f57734f49c74„§cell_idÙ$05d2780e-612c-4e86-93c4-f57734f49c74¤codeÙ”function func_with_barriers(obs, param) if param < 1 pred = param .* obs else pred = floor.(Int64,param .* obs) end calc_Ï‡Â²(obs, pred) end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$9122bdf0-c0b9-4966-8933-00a40562393a„§cell_idÙ$9122bdf0-c0b9-4966-8933-00a40562393a¤codeÙ»md""" For mathematical functions, results will differ from one processor to another. So I suggest you benchmark code yourself **on the machine you plan to run on once you scale up**. """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$1cf69f4d-04db-4c3a-897a-a1da9e46b88c„§cell_idÙ$1cf69f4d-04db-4c3a-897a-a1da9e46b88c¤codeÚblockquote(md""" If you know your code is going to require `for` loops/nested `for` loops, is Julia just always going to be better than, for instance, Python? Is there any case where the gains in optimization are marginal (especially for long runtimes)? """)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$db388c8a-ddb3-47a6-8ce0-586d9f9602b9„§cell_idÙ$db388c8a-ddb3-47a6-8ce0-586d9f9602b9¤codeÙ7@benchmark func_with_type_instability($obs,$param_true)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$624e8936-de28-4e09-9a4e-3ef2f6c7d9b0„§cell_idÙ$624e8936-de28-4e09-9a4e-3ef2f6c7d9b0¤codeÙ‚begin using PlutoUI, PlutoTest, PlutoTeachingTools using BenchmarkTools using ForwardDiff using StaticArrays #using Plots end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$dfe5dcd7-9b62-4690-ac21-0930b3e4145c„§cell_idÙ$dfe5dcd7-9b62-4690-ac21-0930b3e4145c¤codeÙ<@benchmark func_without_type_instability_v2($obs,param_true)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$208bf525-447d-4726-b67c-c3b968b415b8„§cell_idÙ$208bf525-447d-4726-b67c-c3b968b415b8¤codeÚmd""" ### Rubric for Serial version of Code - Code performs proposed tasks (1 point) - Comprehensive set of unit tests, at least one integration or regression test (1 point) - Code passes tests (1 point) - Student code uses a version control system effectively (1 point) - Repository includes many regular, small commits (1 point) - Documentation for functionsâ€™ purpose and design (1 point) - Comprehensive set of assertions (1 point) - Variable/function names consistent, distinctive & meaningful (1 point) - Useful & consistent code formatting & style (1 point) - Code is modular, rather than having chunks of same code copied and pasted (1 point) """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$c92d49d3-e8fc-4288-9ce2-3e617fc5c306„§cell_idÙ$c92d49d3-e8fc-4288-9ce2-3e617fc5c306¤code¯distance(c1,p1)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$aa767f81-4bcb-41b6-b141-85796a81d8fb„§cell_idÙ$aa767f81-4bcb-41b6-b141-85796a81d8fb¤codeÙ6@test_broken my_model_stable_specific.(obs,param_true)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$b2ac3b2c-31c7-4e64-9009-47ac03e38afb„§cell_idÙ$b2ac3b2c-31c7-4e64-9009-47ac03e38afb¤codeÙ%md""" # Loops and "Vectorization" """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$495b281e-f4c9-4f55-bf5a-9a8d7f43044c„§cell_idÙ$495b281e-f4c9-4f55-bf5a-9a8d7f43044c¤codeÙ/md""" ### Making inner function type-stable """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$be38f44f-9ce4-433a-84ef-782e5d8a4822„§cell_idÙ$be38f44f-9ce4-433a-84ef-782e5d8a4822¤code¯distance(c1,c1)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$11e60eb5-980d-4d3d-8f09-03390584aaad„§cell_idÙ$11e60eb5-980d-4d3d-8f09-03390584aaad¤codeÙ,f_fused_with_macro(x) = @. 3x^2 + 4x + 7x^3;¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$957519f4-a669-472a-bc81-ecd0dcce9842„§cell_idÙ$957519f4-a669-472a-bc81-ecd0dcce9842¤codeÙAlet n = 100; x = rand(n); y = rand(n); @benchmark ($x.*$y) end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$1b548d59-f18e-4cfc-9667-472c427d7cc2„§cell_idÙ$1b548d59-f18e-4cfc-9667-472c427d7cc2¤codeÚbegin x(p::CartesianCoord) = p.x y(p::CartesianCoord) = p.y r(p::CartesianCoord) = sqrt(x(p)^2+y(p)^2) theta(p::CartesianCoord) = atan(y(p),x(p)) x(p::PolarCoord) = p.r*cos(p.theta) y(p::PolarCoord) = p.r*sin(p.theta) r(p::PolarCoord) = p.r theta(p::PolarCoord) = p.theta end;¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$cee02d24-1dcc-4c29-a322-0ddd12ab8180„§cell_idÙ$cee02d24-1dcc-4c29-a322-0ddd12ab8180¤codeÙH@test_nowarn my_model_stable_specific.(obs,convert(Float64,param_true));¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$e1ec523b-3c2f-447d-8b71-063dc5955f45„§cell_idÙ$e1ec523b-3c2f-447d-8b71-063dc5955f45¤codeÙ,md""" ### Why would you want to do that? """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$279df4ae-a0e2-4838-8a9c-3ff82245935e„§cell_idÙ$279df4ae-a0e2-4838-8a9c-3ff82245935e¤codeÙÕmd""" For small programs called many times, consider making a **sysimage** using [PackageCompiler.jl](https://julialang.github.io/PackageCompiler.jl/stable/sysimages.html) to avoid compilation cost each time. """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$9ec9429d-c1f1-4845-a514-9c88b452071f„§cell_idÙ$9ec9429d-c1f1-4845-a514-9c88b452071f¤code¯WidthOverDocs()¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$f3937141-49f4-49f2-8bcf-0f4e9c204d24„§cell_idÙ$f3937141-49f4-49f2-8bcf-0f4e9c204d24¤codeÙ9@code_warntype func_with_type_instability(obs,param_true)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$047835eb-6bcc-4f32-b991-5ccccbf34cb9„§cell_idÙ$047835eb-6bcc-4f32-b991-5ccccbf34cb9¤codeÙ array_of_reals = Real[1.0, 2, 3]¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$e1996c2f-5298-48c9-a29c-852bd37b54c4„§cell_idÙ$e1996c2f-5298-48c9-a29c-852bd37b54c4¤code¹bigvector = rand(8*10^6);¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$59fbb599-c947-4a2a-a678-8e38a666660c„§cell_idÙ$59fbb599-c947-4a2a-a678-8e38a666660c¤codeÙ)@time col_one_view = view(big_matrix,:,1)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$e80e73cc-fb81-4222-8fcd-a9c4aaf6326e„§cell_idÙ$e80e73cc-fb81-4222-8fcd-a9c4aaf6326e¤codeÙ:@benchmark func_without_type_instability($obs,$param_true)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$8f4b3c77-e79f-457a-b9e9-9f30dd1f526a„§cell_idÙ$8f4b3c77-e79f-457a-b9e9-9f30dd1f526a¤codeÙOmd"It can store an array of abstract types, but that can be quite inefficient."¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$79783bcb-fe34-4c9d-af08-7a82c851beec„§cell_idÙ$79783bcb-fe34-4c9d-af08-7a82c851beec¤codeÙMmd""" ### Writing functions that can take an unknown number of arguements """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$18813a15-531f-4d74-a0f7-45a0574d6c1b„§cell_idÙ$18813a15-531f-4d74-a0f7-45a0574d6c1b¤codeÙ'@time col_one_copied = big_matrix[:,:1]¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$d58ee47e-10df-4d8c-aad3-ae755a5024e4„§cell_idÙ$d58ee47e-10df-4d8c-aad3-ae755a5024e4¤code¡ ¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$b243656e-2eec-4650-adbe-5ca8a712d5d6„§cell_idÙ$b243656e-2eec-4650-adbe-5ca8a712d5d6¤codeÙOblockquote(md""" How should we decide whether to inline a function or not? """)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$bd011001-07cb-4f74-9c69-8f91945e2cbf„§cell_idÙ$bd011001-07cb-4f74-9c69-8f91945e2cbf¤codeÙblockquote(md""" I thought [using many smaller functions] would take longer since the program needs to go somewhere else. """)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$77e28f2e-d53a-4dd7-938e-5d95bac81db1„§cell_idÙ$77e28f2e-d53a-4dd7-938e-5d95bac81db1¤code¿array_of_float64s = [1.0, 2, 3]¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$64fc3013-09e3-4f95-a3f4-20138125e71b„§cell_idÙ$64fc3013-09e3-4f95-a3f4-20138125e71b¤codeÚÌmd""" - Small functions that will be called many times (e.g., inside a loop) â†’ want to inline - Large functions or functions that will only be called a few times â†’ little benefit to inlining - Modern languages/compilers will typically decide for you based on some simple heuristics to guess the typical cost of executing the function. - You can provide a **hint** encouraging or discouraging the compiler from inlining code. (`@inline` or `@noinline`) """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$b7c23b8b-aaca-41b0-8397-ad2300eeda50„§cell_idÙ$b7c23b8b-aaca-41b0-8397-ad2300eeda50¤code³md""" # Old Q&A """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$fd3c57f9-1f47-4e3e-91ee-b05911f992ee„§cell_idÙ$fd3c57f9-1f47-4e3e-91ee-b05911f992ee¤codeÙfblockquote(md""" When optimizing code, what typically has the most impact on decreasing run time? """)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$31debff2-3667-4631-bff5-e95cf107ae9a„§cell_idÙ$31debff2-3667-4631-bff5-e95cf107ae9a¤codeÙ!array_of_anys = [1.0, 2, "three"]¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$783e926f-91a2-4ded-a21b-ae27fa3bc4d8„§cell_idÙ$783e926f-91a2-4ded-a21b-ae27fa3bc4d8¤codeÙûfunction calc_Ï‡Â²(obs::AbstractVector, pred::AbstractVector) @assert length(obs) == length(pred) n = length(obs) Ï‡Â² = zero(promote_type(eltype(obs),eltype(pred))) @simd for i in 1:n @inbounds Ï‡Â² += (obs[i]-pred[i])^2 end return Ï‡Â² end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$d6147ce2-b3ec-45f0-ba90-2c453a719548„§cell_idÙ$d6147ce2-b3ec-45f0-ba90-2c453a719548¤codeºmd""" ## Inlining code """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$1969217c-24be-47e2-9853-b70cf4d5565d„§cell_idÙ$1969217c-24be-47e2-9853-b70cf4d5565d¤codeÙ*md"## Overloading Functions for each Type"¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$20db6ae9-8c79-44d1-a3a7-0dadf1d0dc5a„§cell_idÙ$20db6ae9-8c79-44d1-a3a7-0dadf1d0dc5a¤codeÙ”function func_without_type_instability_v2(obs, param) pred = my_model_stable_specific.(obs,convert(Float64,param)) Ï‡Â² = calc_Ï‡Â²(obs, pred) end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$d0429b82-7e78-4a18-97bb-e34ba370e024„§cell_idÙ$d0429b82-7e78-4a18-97bb-e34ba370e024¤codeÙØbegin n = 1000 vec_abs_c1 = Vector{AbstractCoord}(undef,n) vec_abs_c2 = Vector{AbstractCoord}(undef,n) for i in 1:n vec_abs_c1[i] = c1 vec_abs_c2[i] = c2 end @benchmark distance($vec_abs_c1,$vec_abs_c2) end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$94223079-afab-4a6d-a126-068a4e94f52e„§cell_idÙ$94223079-afab-4a6d-a126-068a4e94f52e¤codeÙ+struct Coord x::Float64 y::Float64 end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$d3d085e6-67b5-4286-b66d-120720e1002d„§cell_idÙ$d3d085e6-67b5-4286-b66d-120720e1002d¤codeÚCmd""" # Preping for Code Review ## Make it easy for your reviewer - Provide overview of what your code is doing in README.md - Where should they start? - What files should they focus on? - What files should they ignore? - Include an example of how to run/use code ## Make it easy for you As code starts getting larger, then - Move code out of notebooks and into `.jl` files, as functions mature. - Organize similar functions into `.jl` files in `src` directory - Use diretories like `examples`, `test` - If/when appropiate add more directories (e.g., `data`, `deps`, `docs`) """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$e7227a20-3d2d-4907-b9a6-422c0d4ab57a„§cell_idÙ$e7227a20-3d2d-4907-b9a6-422c0d4ab57a¤codeÙˆfunction distance(a::Array{AbstractCoord}, b::Array{AbstractCoord}) dx = x.(a)-x.(b) dy = y.(a)-y.(b) sqrt.(dx.^2 .+ dy.^2) end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$348ee204-546f-46c5-bf5d-7d4a761002ec„§cell_idÙ$348ee204-546f-46c5-bf5d-7d4a761002ec¤codeÙ"md""" # Optimizing Serial Code """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$170f2bd0-bb5b-4e78-b92b-dfa8d47aded0„§cell_idÙ$170f2bd0-bb5b-4e78-b92b-dfa8d47aded0¤codeÙ2@benchmark func_without_barriers($obs,$param_true)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$a9cf77ec-434e-4477-a844-9f8b9199589f„§cell_idÙ$a9cf77ec-434e-4477-a844-9f8b9199589f¤codeÙ-array_of_float_or_missing = [1.0, missing, 3]¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$781ef824-a235-46ce-accd-362f2e963550„§cell_idÙ$781ef824-a235-46ce-accd-362f2e963550¤codeÙ)@benchmark f_fused_explicitly($bigvector)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$46cd3a5f-3358-4f21-91c7-82c544bc4353„§cell_idÙ$46cd3a5f-3358-4f21-91c7-82c544bc4353¤codeÚmd""" - Typically... yes. - Always... no. E.g., if runtime is dominated by time to read data from the internet/network/disk. Then, the cost of accessing the data the first time may be so large that the benefits of computing more efficiently are negligible. """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$73b01b03-2016-4253-8f95-e0bdb3bca5f4„§cell_idÙ$73b01b03-2016-4253-8f95-e0bdb3bca5f4¤code¬md"**Yes!**"¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$5c5f9760-695f-4fa2-b4a6-8a878ab97ea6„§cell_idÙ$5c5f9760-695f-4fa2-b4a6-8a878ab97ea6¤codeÙúmd""" **A:** Easy answer... Never Reality: - You're writing disposable code - You're working with some preexisting code that wasn't designed to do what you want and you want to try something quickly before implementing it well. - Other examples? """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$e04666f8-801b-4973-9b9e-807abc5199b7„§cell_idÙ$e04666f8-801b-4973-9b9e-807abc5199b7¤codeÙ function distance(a::Array{T1},b::Array{T2}) where { T1<:AbstractCoord, T2<:AbstractCoord} dx = x.(a)-x.(b) dy = y.(a)-y.(b) sqrt.(dx.^2 .+ dy.^2) end;¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$08d25c7e-907b-403d-b08d-27ca4efcd958„§cell_idÙ$08d25c7e-907b-403d-b08d-27ca4efcd958¤codeÚfunction func_without_barriers(obs, param) if param < 1 pred = param .* obs else pred = floor.(Int64,param .* obs) end n = length(obs) Ï‡Â² = zero(promote_type(eltype(obs),eltype(pred))) @simd for i in 1:n @inbounds Ï‡Â² += (obs[i]-pred[i])^2 end return Ï‡Â² end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$d2e1b3c3-3a81-44cd-a57b-fd9c29badce4„§cell_idÙ$d2e1b3c3-3a81-44cd-a57b-fd9c29badce4¤codeÚmd""" ```shell > julia -h -O, --optimize={0,1,2*,3} Set the optimization level --min-optlevel={0*,1,2,3} Set a lower bound on the optimization level -J, --sysimage Start up with the given system image file -t, --threads {auto|N[,auto|M]} -p, --procs {N|auto} -g, --debug-info=[{0,1*,2}] Set the level of debug info generation --check-bounds={yes|no|auto*} auto respects @inbounds declarations --math-mode={ieee|user*} user respects `@fastmath` declarations ``` """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$dc23159c-95ca-466d-9cbe-23bb0448d134„§cell_idÙ$dc23159c-95ca-466d-9cbe-23bb0448d134¤codeÚ0md""" ## Peer Review Logistics - Access - I'll send you GitHub ID of peer reviewer(s) - Make sure reviewer(s) can access your repo + If your project repo is private: `Settings`, `Collaborators & Teams`, `Add people`, `Read`, `Add Selection`. + Or make your project repo public: `Settings`, `Change Visibility`, plus multiple multiple steps to confirm. - Make sure you can access repo to review - If using Jupyter notebooks, make sure to add Markdown version of code for getting feedback. ```julia julia -e 'import Pkg; Pkg.add("Weave"); using Weave; convert_doc("NOTEBOOK_NAME.ipynb","NOTEBOOK_NAME.jmd")' ``` - [Review instructions](https://psuastro528.github.io/Fall2025/project/code_reviews/how_to/) - Provide most feedback via [GitHub Issues](https://guides.github.com/features/issues/) """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$404c0658-ae86-457a-adc3-4ef69bb43ac8„§cell_idÙ$404c0658-ae86-457a-adc3-4ef69bb43ac8¤codeÙ”function integrate_f(f::Function, a::Real, b::Real; n::Integer = 100, kwargs...) x = range(a,stop=b, length=n) sum(f.(x; kwargs...)) * (b-a)/n end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$3bf761b6-132b-43fa-aa41-b2e73ddce94b„§cell_idÙ$3bf761b6-132b-43fa-aa41-b2e73ddce94b¤codeÙ(md""" # Avoiding copying using views """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$b7fbdc93-4c8b-4222-98e3-62fa7e726e2f„§cell_idÙ$b7fbdc93-4c8b-4222-98e3-62fa7e726e2f¤code¼md""" # Type Instability """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$febc6f64-0d39-4206-8475-e6324973284f„§cell_idÙ$febc6f64-0d39-4206-8475-e6324973284f¤codeÙ(md""" ### When use global variables? """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$b556927c-ab72-41c5-9a3e-83756e40550a„§cell_idÙ$b556927c-ab72-41c5-9a3e-83756e40550a¤codeÙ½blockquote(md"What type of variables should always be passed to an inline function versus an external module (maybe large arrays/tables?) so they don't take up too much room on the stack?")¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$9e8cb539-5d69-4552-87e4-88fe61ab1fbe„§cell_idÙ$9e8cb539-5d69-4552-87e4-88fe61ab1fbe¤codeÙqbegin x(p::Coord) = p.x y(p::Coord) = p.y r(p::Coord) = sqrt(p.x^2+p.y^2) theta(p::Coord) = atan(p.y,p.x) end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$fbd538a3-8ddc-4c3f-9748-35fa7b032809„§cell_idÙ$fbd538a3-8ddc-4c3f-9748-35fa7b032809¤codeÙ4@code_warntype func_without_barriers(obs,param_true)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$0f679916-5f87-45a3-996f-be3146a537a2„§cell_idÙ$0f679916-5f87-45a3-996f-be3146a537a2¤codeÙzfunction func_without_type_instability_v3(obs, param) pred = my_model_stable.(obs,param) Ï‡Â² = calc_Ï‡Â²(obs, pred) end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$252f394f-9d7d-41be-8cbf-ccb5558b83d1„§cell_idÙ$252f394f-9d7d-41be-8cbf-ccb5558b83d1¤codeÚmd""" ## How do we know where do we spend our time? **Q:** How do we know where to focus our efforts based on the coding language we're using? - Profiling - Experience with common programming patterns - Knowing (enough about) how your language works under the hood """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$7e466eb6-9b5f-4e9f-90e2-be11fb66d557„§cell_idÙ$7e466eb6-9b5f-4e9f-90e2-be11fb66d557¤code¯distance(c1,p2)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$288d3aaf-ee71-44f5-aefb-4b7b787c7caa„§cell_idÙ$288d3aaf-ee71-44f5-aefb-4b7b787c7caa¤codeÙbblockquote(md"""Is it best to make sure that all cells of your array have the same data type? """)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$8446120e-5bac-4b8e-bc86-836f773f79a0„§cell_idÙ$8446120e-5bac-4b8e-bc86-836f773f79a0¤codeÙ6let pos_xy = [rand(), rand() ] atan(pos_xy...) end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$c16a95ce-2926-4d99-a907-71c95f32c042„§cell_idÙ$c16a95ce-2926-4d99-a907-71c95f32c042¤codeÙNbegin c1 = CartesianCoord(0,3) c2 = CartesianCoord(4,0) distance(c1,c2) end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$8e3ba95e-7c10-4e95-95cb-a906259282fc„§cell_idÙ$8e3ba95e-7c10-4e95-95cb-a906259282fc¤codeÙ:md""" ### Making inner funciton type-stable & generic """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$93beb233-81cc-47f8-89be-8164cc15d020„§cell_idÙ$93beb233-81cc-47f8-89be-8164cc15d020¤codeÙ#md"## Containers of Concrete Types"¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$e6e22f60-4e6a-4160-ba06-42d469afb3f6„§cell_idÙ$e6e22f60-4e6a-4160-ba06-42d469afb3f6¤code¾md""" ## What's expensive? """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$f5fe37e1-80b9-4853-84d6-82e56417a470„§cell_idÙ$f5fe37e1-80b9-4853-84d6-82e56417a470¤codeÙ.function func_takes_varargs(x...) @info x end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$8f846ea8-9c6e-499b-bfd8-18bdbbd110f7„§cell_idÙ$8f846ea8-9c6e-499b-bfd8-18bdbbd110f7¤codeÙFlet n = 100; x = rand(n); y = rand(n); @benchmark atan.($x,$y) end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$21e3dc92-82c9-4486-8980-d5e6a012afec„§cell_idÙ$21e3dc92-82c9-4486-8980-d5e6a012afec¤codeµfunc_takes_varargs(1)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$365c43af-37a3-4f0c-8e9e-d4003c47b6a3„§cell_idÙ$365c43af-37a3-4f0c-8e9e-d4003c47b6a3¤codeÙ!md"## With Programming Interface"¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$9850f52c-7209-4ba0-9298-942d68947b9e„§cell_idÙ$9850f52c-7209-4ba0-9298-942d68947b9e¤codeÙ§blockquote(md""" Could you elaborate on the "..." operator that is used within functions and function arguments? How does this contribute to improved performance? """)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$1fd8655d-8065-4945-acef-7774ed882d51„§cell_idÙ$1fd8655d-8065-4945-acef-7774ed882d51¤codeÙ½begin struct CoordAlt r::Float64 theta::Float64 end x(p::CoordAlt) = p.r*cos(p.theta) y(p::CoordAlt) = p.r*sin(p.theta) r(p::CoordAlt) = p.r theta(p::CoordAlt) = p.theta end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$0913de40-9fa0-44db-9b2c-9bd93db31790„§cell_idÙ$0913de40-9fa0-44db-9b2c-9bd93db31790¤codeÙ„function distance( a::AbstractCoord, b::AbstractCoord ) dx = x(a) - x(b) dy = y(a) - y(b) sqrt( dx^2 + dy^2 ) end;¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$28b53ea4-5bdc-4ac2-b83e-bcb8f0a6416c„§cell_idÙ$28b53ea4-5bdc-4ac2-b83e-bcb8f0a6416c¤codeÙ}blockquote(md""" How does Julia compile data into arrays efficiently if the array contains multiple different data types?""")¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$9303806b-a460-4ec2-9f71-252f43b34328„§cell_idÙ$9303806b-a460-4ec2-9f71-252f43b34328¤codeÙšbegin x_in = rand(16*1024) param_true = 2 obs = my_model.(x_in, param_true) .+ 0.01 .* randn(length(x_in)) func_without_barriers(obs, param_true) end;¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$9e8035cd-c5ba-47c7-8567-1279e666c4fc„§cell_idÙ$9e8035cd-c5ba-47c7-8567-1279e666c4fc¤codeÙ$func_takes_varnamedargs(;a="a", b=2)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$426ccd5e-398b-4df7-a27d-cf7a578c658f„§cell_idÙ$426ccd5e-398b-4df7-a27d-cf7a578c658f¤codeÙ)@time row_one_view = view(big_matrix,1,:)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$82883c5d-db3d-4293-bf74-a6e36552a125„§cell_idÙ$82883c5d-db3d-4293-bf74-a6e36552a125¤codeÙ¥function my_model_stable(x,slope) out_type = promote_type(typeof(x),typeof(slope)) if x>one(slope) return convert(out_type,slope) else return slope*x end end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$c6460feb-67f0-4028-8b05-e195a8c2bd41„§cell_idÙ$c6460feb-67f0-4028-8b05-e195a8c2bd41¤codeÙùmd""" ### Big picture steps to efficiency: - Use a compiled language - Use a strongly-typed language - Choose of algorithms wisely - Choose data types wisely - Avoid unnecessary memory allocations - Arrange memory accesses to reduce cache misses """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$44c5243c-a044-4ed7-bf25-728b0291c14a„§cell_idÙ$44c5243c-a044-4ed7-bf25-728b0291c14a¤codeÙ#md"## Why a Programming Interface?"¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$e7d4bc52-ee18-4d0b-8bab-591b688398fe„§cell_idÙ$e7d4bc52-ee18-4d0b-8bab-591b688398fe¤codeÙ TableOfContents(aside=toc_aside)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$b1557899-91c0-4f02-b486-e3c4f38d9218„§cell_idÙ$b1557899-91c0-4f02-b486-e3c4f38d9218¤codeÙ7let n = 100; x = rand(n); @benchmark sqrt.($x); end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$e7b56266-5d70-451b-a448-6b6cfd85cab7„§cell_idÙ$e7b56266-5d70-451b-a448-6b6cfd85cab7¤code¹func_takes_varargs(1,2,3)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$a1992b28-16ab-456b-995d-1e40e423d70c„§cell_idÙ$a1992b28-16ab-456b-995d-1e40e423d70c¤codeÙFstruct CartesianCoord <: AbstractCoord x::Float64 y::Float64 end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$4b7b8ef8-e7c4-415b-a103-e109256e0210„§cell_idÙ$4b7b8ef8-e7c4-415b-a103-e109256e0210¤code¯distance(p1,p1)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$f658c638-8c9d-4828-ac15-ecd7d4650b13„§cell_idÙ$f658c638-8c9d-4828-ac15-ecd7d4650b13¤codeÙ-md""" # Command-line Optimization options """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$d5cb70a8-079b-4fd5-851f-8742680ff515„§cell_idÙ$d5cb70a8-079b-4fd5-851f-8742680ff515¤codeÙ‚function func_without_type_instability(obs, param) pred = convert.(Float64,my_model.(obs,param)) Ï‡Â² = calc_Ï‡Â²(obs, pred) end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$fad14e46-21a4-41ea-8f3d-a747cdfe3a51„§cell_idÙ$fad14e46-21a4-41ea-8f3d-a747cdfe3a51¤codeÙmfunction func_with_type_instability(obs, param) pred = my_model.(obs,param) Ï‡Â² = calc_Ï‡Â²(obs, pred) end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$d6a2b578-88a4-4a82-bb20-641ccc60aa8d„§cell_idÙ$d6a2b578-88a4-4a82-bb20-641ccc60aa8d¤codeÙxmd""" - There is a cost for calling a function. - But small functions are usually inlined, so as to avoid that cost. """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$3fa48928-5311-49ec-83d2-cf4c45c7c579„§cell_idÙ$3fa48928-5311-49ec-83d2-cf4c45c7c579¤codeÙ=md""" ## Splat and variable number of function arguements """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$04391eb3-daf0-4f20-b39e-33e626770e05„§cell_idÙ$04391eb3-daf0-4f20-b39e-33e626770e05¤codeÙ=@benchmark func_without_type_instability_v3($obs,$param_true)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$953d09b8-d8d0-4e49-ae55-648f956aa248„§cell_idÙ$953d09b8-d8d0-4e49-ae55-648f956aa248¤codeÙdbegin p1 = PolarCoord( r(c1), theta(c1) ) p2 = PolarCoord( r(c2), theta(c2) ) distance(p1,p2) end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$3e8c154a-3c22-49cc-accd-1076430268ae„§cell_idÙ$3e8c154a-3c22-49cc-accd-1076430268ae¤codeÙ4function func_takes_varnamedargs(;x...) @info x end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$3ef73948-da0c-4afa-8a73-29c382b29bbd„§cell_idÙ$3ef73948-da0c-4afa-8a73-29c382b29bbd¤codeÙ/@benchmark func_with_barriers($obs,$param_true)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$15efacae-95a5-4607-8a38-76ee5f345235„§cell_idÙ$15efacae-95a5-4607-8a38-76ee5f345235¤code´md""" ## Popouri """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$9007f240-c88e-46c4-993d-fd6b93d8b18d„§cell_idÙ$9007f240-c88e-46c4-993d-fd6b93d8b18d¤code¹md""" # Announcements """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$b24a684b-b2d1-4d6a-9408-590feef3ba08„§cell_idÙ$b24a684b-b2d1-4d6a-9408-590feef3ba08¤codeµmd"## Abstract Types"¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$282d2a07-5f63-4f3e-960e-b5ffcab6b9de„§cell_idÙ$282d2a07-5f63-4f3e-960e-b5ffcab6b9de¤codeÙ)@benchmark f_fused_with_macro($bigvector)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$9ab94eea-4d57-4ef2-a73a-64e7c8b89222„§cell_idÙ$9ab94eea-4d57-4ef2-a73a-64e7c8b89222¤codeÙ2integrate_f(func_that_needs_parameters,0,Ï€; Î¸=4)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$5d599c10-f1d2-454e-ad85-0e092b6cae7e„§cell_idÙ$5d599c10-f1d2-454e-ad85-0e092b6cae7e¤codeÙ<@code_warntype func_without_type_instability(obs,param_true)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$4c3332a8-a5d1-43fb-887b-ac66dfa02de5„§cell_idÙ$4c3332a8-a5d1-43fb-887b-ac66dfa02de5¤code¼md"# Programming Interfaces"¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$31476473-d619-404c-a1c1-b32c1b8c5930„§cell_idÙ$31476473-d619-404c-a1c1-b32c1b8c5930¤codeÚimd""" # Class project - Review feedback on project proposals - Review [project instructions and rubric](https://psuastro528.github.io/Fall2025/project/) on website - Can continue using repository from project proposal - Next step is the serial implementation, focusing on good practices that we've discussed/seen in labs - Serial code should be ready for peer code review by **Oct 8** - After this week's labs, will have everything you need to benchmark, profile and optimize the serial version of your code. - Sign up for [project presentation schedule](https://github.com/PsuAstro528/PresentationsSchedule2025) """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$53863e96-0c11-484f-bfc9-23b52ca933de„§cell_idÙ$53863e96-0c11-484f-bfc9-23b52ca933de¤codeÙXmd""" ### Passing array of data to function that expects distinct function arguments """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$ccb63eb8-1da0-48ce-ae51-c18c48509445„§cell_idÙ$ccb63eb8-1da0-48ce-ae51-c18c48509445¤codeÙJfunction func_that_needs_parameters(x::Real; Î¸::Real) sin(x/Î¸)^2/Ï€ end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$0363149b-f34d-4120-81db-a655f18b908f„§cell_idÙ$0363149b-f34d-4120-81db-a655f18b908f¤codeÚmd""" ## Compiler Optimizations **Q:** How does Julia go about auto-optimizing simple computation time sinks like loops, nested loop, functions called many times in a loop, etc. Whole courses on optimizing compilers, but a few categories that come to mind: - Compilation - Static type inference - Inlining small functions - Dead code elimination - Unrolling small loops - Grouping operations for SIMD - ... Advanced optimizations that require additional help: - Precompiliation of functiosn to be used - Empirical branch prediction """¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$b8e117f5-b253-4208-a00e-7966978fb24b„§cell_idÙ$b8e117f5-b253-4208-a00e-7966978fb24b¤codeÙQfunction my_model(x,slope) if x>1 return slope else return slope*x end end¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$02002957-8644-40ca-99ef-86151769a5d9„§cell_idÙ$02002957-8644-40ca-99ef-86151769a5d9¤codeÙ&@time row_one_copied = big_matrix[1,:]¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$12b8d696-0e7b-4814-9c73-22b7cf95fef4„§cell_idÙ$12b8d696-0e7b-4814-9c73-22b7cf95fef4¤code¸@benchmark f($bigvector)¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÂÙ$9bf47a21-af6d-4c76-84d1-0b78635bae9a„§cell_idÙ$9bf47a21-af6d-4c76-84d1-0b78635bae9a¤codeÙ)md"## New Implementation, same interface"¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃÙ$64d51527-1bd0-4010-b458-4dfa6f44610d„§cell_idÙ$64d51527-1bd0-4010-b458-4dfa6f44610d¤codeÙ%md"### Fusing broadcasted operations"¨metadataƒ©show_logsÃ¨disabledÂ®skip_as_scriptÂ«code_foldedÃ«notebook_idÙ$e76e6978-bfd9-11f0-1d27-c1e0c10829f4«in_temp_dirÂ¨metadata€