In-place versions of mttkrp and khatrirao

[dahong67]

Fixes #42

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 100.00%. Comparing base (940a3a4) to head (85a8ed3).

Additional details and impacted files

@@            Coverage Diff            @@
##            master       #43   +/-   ##
=========================================
  Coverage   100.00%   100.00%           
=========================================
  Files            8         8           
  Lines          220       240   +20     
=========================================
+ Hits           220       240   +20     

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[dahong67]

Using khatrirao! in-place of khatrirao in mttkrp! results in more memory use for intermediate modes in some cases, as shown in the following benchmark. Reason is that we have some calls to khatrirao! with a single matrix - before this was essentially a no-op but now we make a new copy. Consider, e.g., the following lines when n == 2:

GCPDecompositions.jl/src/kernels.jl

Lines 54 to 56 in 2bbf6f1

	# Inner multiplication: left side
	buffer_kr_inner = similar(U[1], prod(I[1:n-1]), r)
	khatrirao!(buffer_kr_inner, U[reverse(1:n-1)]...)

Benchmark Report for GCPDecompositions

Job Properties

• Time of benchmarks:
  • Target: 3 Mar 2024 - 20:58
  • Baseline: 3 Mar 2024 - 20:59
• Package commits:
  • Target: 2bbf6f
  • Baseline: 38648a
• Julia commits:
  • Target: bed2cd
  • Baseline: bed2cd
• Julia command flags:
  • Target: None
  • Baseline: None
• Environment variables:
  • Target: GCP_BENCHMARK_SUITES => mttkrp
  • Baseline: GCP_BENCHMARK_SUITES => mttkrp

Results

A ratio greater than 1.0 denotes a possible regression (marked with ❌), while a ratio less
than 1.0 denotes a possible improvement (marked with ✅). Only significant results - results
that indicate possible regressions or improvements - are shown below (thus, an empty table means that all
benchmark results remained invariant between builds).

ID	time ratio	memory ratio
["mttkrp", "size=(100, 100, 100), rank=10, mode=2"]	1.00 (5%)	1.02 (1%) ❌
["mttkrp", "size=(100, 100, 100), rank=100, mode=2"]	1.00 (5%)	1.02 (1%) ❌
["mttkrp", "size=(100, 100, 100), rank=150, mode=1"]	0.95 (5%) ✅	1.00 (1%)
["mttkrp", "size=(100, 100, 100), rank=150, mode=2"]	0.92 (5%) ✅	1.02 (1%) ❌
["mttkrp", "size=(100, 100, 100), rank=200, mode=2"]	0.99 (5%)	1.02 (1%) ❌
["mttkrp", "size=(100, 100, 100), rank=250, mode=1"]	1.06 (5%) ❌	1.00 (1%)
["mttkrp", "size=(100, 100, 100), rank=250, mode=2"]	0.96 (5%)	1.02 (1%) ❌
["mttkrp", "size=(100, 100, 100), rank=300, mode=2"]	0.96 (5%)	1.02 (1%) ❌
["mttkrp", "size=(100, 100, 100), rank=50, mode=2"]	0.98 (5%)	1.02 (1%) ❌
["mttkrp", "size=(1000, 100, 30), rank=10, mode=2"]	1.08 (5%) ❌	1.33 (1%) ❌
["mttkrp", "size=(1000, 100, 30), rank=100, mode=2"]	1.02 (5%)	1.33 (1%) ❌
["mttkrp", "size=(1000, 100, 30), rank=200, mode=2"]	1.01 (5%)	1.33 (1%) ❌
["mttkrp", "size=(1000, 100, 30), rank=300, mode=2"]	1.02 (5%)	1.33 (1%) ❌
["mttkrp", "size=(150, 150, 150), rank=10, mode=2"]	1.00 (5%)	1.01 (1%) ❌
["mttkrp", "size=(150, 150, 150), rank=100, mode=2"]	0.99 (5%)	1.01 (1%) ❌
["mttkrp", "size=(150, 150, 150), rank=150, mode=2"]	1.00 (5%)	1.01 (1%) ❌
["mttkrp", "size=(150, 150, 150), rank=200, mode=2"]	1.00 (5%)	1.01 (1%) ❌
["mttkrp", "size=(150, 150, 150), rank=250, mode=2"]	0.99 (5%)	1.01 (1%) ❌
["mttkrp", "size=(150, 150, 150), rank=300, mode=2"]	1.02 (5%)	1.01 (1%) ❌
["mttkrp", "size=(150, 150, 150), rank=50, mode=2"]	1.06 (5%) ❌	1.01 (1%) ❌
["mttkrp", "size=(200, 200, 200), rank=10, mode=1"]	0.93 (5%) ✅	1.00 (1%)
["mttkrp", "size=(200, 200, 200), rank=10, mode=2"]	0.98 (5%)	1.01 (1%) ❌
["mttkrp", "size=(30, 100, 1000), rank=10, mode=2"]	1.03 (5%)	1.33 (1%) ❌
["mttkrp", "size=(30, 100, 1000), rank=100, mode=1"]	1.09 (5%) ❌	1.00 (1%)
["mttkrp", "size=(30, 100, 1000), rank=100, mode=2"]	1.00 (5%)	1.33 (1%) ❌
["mttkrp", "size=(30, 100, 1000), rank=200, mode=1"]	1.11 (5%) ❌	1.00 (1%)
["mttkrp", "size=(30, 100, 1000), rank=200, mode=2"]	1.01 (5%)	1.33 (1%) ❌
["mttkrp", "size=(30, 100, 1000), rank=300, mode=2"]	1.02 (5%)	1.32 (1%) ❌
["mttkrp", "size=(50, 50, 50), rank=10, mode=2"]	1.06 (5%) ❌	1.04 (1%) ❌
["mttkrp", "size=(50, 50, 50), rank=100, mode=2"]	0.93 (5%) ✅	1.04 (1%) ❌
["mttkrp", "size=(50, 50, 50), rank=150, mode=2"]	0.93 (5%) ✅	1.04 (1%) ❌
["mttkrp", "size=(50, 50, 50), rank=200, mode=2"]	0.93 (5%) ✅	1.04 (1%) ❌
["mttkrp", "size=(50, 50, 50), rank=250, mode=2"]	0.91 (5%) ✅	1.04 (1%) ❌
["mttkrp", "size=(50, 50, 50), rank=300, mode=2"]	0.91 (5%) ✅	1.04 (1%) ❌
["mttkrp", "size=(50, 50, 50), rank=50, mode=2"]	0.94 (5%) ✅	1.04 (1%) ❌

Benchmark Group List

Here's a list of all the benchmark groups executed by this job:

• ["mttkrp"]

Julia versioninfo

Target

Julia Version 1.9.3
Commit bed2cd540a1 (2023-08-24 14:43 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (arm64-apple-darwin22.4.0)
  uname: Darwin 23.2.0 Darwin Kernel Version 23.2.0: Wed Nov 15 21:53:18 PST 2023; root:xnu-10002.61.3~2/RELEASE_ARM64_T6000 arm64 arm
  CPU: Apple M1 Max: 
                 speed         user         nice          sys         idle          irq
       #1-10  2400 MHz    1482743 s          0 s     567725 s   20188677 s          0 s
  Memory: 64.0 GB (36831.0625 MB free)
  Uptime: 488287.0 sec
  Load Avg:  5.26708984375  2.78662109375  2.3720703125
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-14.0.6 (ORCJIT, apple-m1)
  Threads: 1 on 8 virtual cores

Baseline

Julia Version 1.9.3
Commit bed2cd540a1 (2023-08-24 14:43 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (arm64-apple-darwin22.4.0)
  uname: Darwin 23.2.0 Darwin Kernel Version 23.2.0: Wed Nov 15 21:53:18 PST 2023; root:xnu-10002.61.3~2/RELEASE_ARM64_T6000 arm64 arm
  CPU: Apple M1 Max: 
                 speed         user         nice          sys         idle          irq
       #1-10  2400 MHz    1484453 s          0 s     568304 s   20189652 s          0 s
  Memory: 64.0 GB (36949.71875 MB free)
  Uptime: 488320.0 sec
  Load Avg:  5.80224609375  3.189453125  2.5341796875
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-14.0.6 (ORCJIT, apple-m1)
  Threads: 1 on 8 virtual cores

MTTKRP benchmark plots

Runtime vs. size (for square tensors)

Below are plots showing the runtime in miliseconds of MTTKRP as a function of the size of the square tensor, for varying ranks and modes:

	ndims = 3, rank = 10, mode = 1	ndims = 3, rank = 10, mode = 2	ndims = 3, rank = 10, mode = 3	ndims = 3, rank = 50, mode = 1	ndims = 3, rank = 50, mode = 2	ndims = 3, rank = 50, mode = 3	ndims = 3, rank = 100, mode = 1	ndims = 3, rank = 100, mode = 2	ndims = 3, rank = 100, mode = 3	ndims = 3, rank = 150, mode = 1	ndims = 3, rank = 150, mode = 2	ndims = 3, rank = 150, mode = 3	ndims = 3, rank = 200, mode = 1	ndims = 3, rank = 200, mode = 2	ndims = 3, rank = 200, mode = 3	ndims = 3, rank = 250, mode = 1	ndims = 3, rank = 250, mode = 2	ndims = 3, rank = 250, mode = 3	ndims = 3, rank = 300, mode = 1	ndims = 3, rank = 300, mode = 2	ndims = 3, rank = 300, mode = 3
Target	ndims = 3, rank = 10, mode = 1 ┌──────────────────────────────┐ 4 │ .│ │ : │ │ .' │ │ .' │ Time (ms) │ .' │ │ : │ │ ..' │ │ .' │ │ ....' │ 0 │ ..''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 10, mode = 2 ┌──────────────────────────────┐ 2 │ │ │ .│ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ .' │ │ .' │ │ ...' │ 0 │ ..'''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 10, mode = 3 ┌──────────────────────────────┐ 3 │ .│ │ .'│ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ .' │ │ .'' │ │ ..''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 50, mode = 1 ┌──────────────────────────────┐ 10 │ .│ │ .' │ │ .' │ │ .' │ Time (ms) │ .' │ │ : │ │ .'' │ │ ..' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 50, mode = 2 ┌──────────────────────────────┐ 20 │ │ │ │ │ │ │ .. │ Time (ms) │ : '. │ │ .' '.. │ │ .' '│ │ .' │ │ : │ 0 │ ........: │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 50, mode = 3 ┌──────────────────────────────┐ 10 │ │ │ .'│ │ .' │ │ .' │ Time (ms) │ : │ │ .' │ │ ..' │ │ .' │ │ ...'' │ 0 │ .'''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 100, mode = 1 ┌──────────────────────────────┐ 20 │ │ │ │ │ │ │ .│ Time (ms) │ ..' │ │ .' │ │ .' │ │ ..'' │ │ ...'' │ 0 │ ..'''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 100, mode = 2 ┌──────────────────────────────┐ 20 │ │ │ │ │ │ │ │ Time (ms) │ .''│ │ .' │ │ .' │ │ .' │ │ ..'' │ 0 │ ......'''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 100, mode = 3 ┌──────────────────────────────┐ 20 │ │ │ │ │ │ │ .│ Time (ms) │ .'' │ │ .' │ │ .' │ │ ..'' │ │ ...'' │ 0 │ ..'''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 150, mode = 1 ┌──────────────────────────────┐ 20 │ │ │ .'│ │ .' │ │ : │ Time (ms) │ .' │ │ .: │ │ .' │ │ .'' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 150, mode = 2 ┌──────────────────────────────┐ 20 │ │ │ │ │ .│ │ .' │ Time (ms) │ .' │ │ .' │ │ .: │ │ ..'' │ │ ...'' │ 0 │ ..''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 150, mode = 3 ┌──────────────────────────────┐ 20 │ │ │ .'│ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ .' │ │ .'' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 200, mode = 1 ┌──────────────────────────────┐ 30 │ │ │ │ │ .│ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ ..' │ │ ...'' │ 0 │ ..''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 200, mode = 2 ┌──────────────────────────────┐ 20 │ .│ │ .'│ │ .' │ │ .' │ Time (ms) │ .' │ │ .: │ │ ..' │ │ .' │ │ ..''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 200, mode = 3 ┌──────────────────────────────┐ 30 │ │ │ │ │ .│ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ ..' │ │ ...'' │ 0 │ ..''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 250, mode = 1 ┌──────────────────────────────┐ 30 │ .│ │ .'│ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ .'' │ │ ..' │ │ ...'' │ 0 │ .'' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 250, mode = 2 ┌──────────────────────────────┐ 30 │ │ │ │ │ .│ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ .'' │ │ ..''' │ 0 │ ..''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 250, mode = 3 ┌──────────────────────────────┐ 30 │ .│ │ .'│ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ .' │ │ ..''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 300, mode = 1 ┌──────────────────────────────┐ 40 │ │ │ .│ │ : │ │ .' │ Time (ms) │ .' │ │ .' │ │ .'' │ │ ..' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 300, mode = 2 ┌──────────────────────────────┐ 30 │ .│ │ .' │ │ .' │ │ .' │ Time (ms) │ .... .' │ │ .' '''' │ │ : │ │ .' │ │ : │ 0 │ .' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 300, mode = 3 ┌──────────────────────────────┐ 40 │ │ │ │ │ .'│ │ .' │ Time (ms) │ .' │ │ .' │ │ .'' │ │ ..' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size
Baseline	ndims = 3, rank = 10, mode = 1 ┌──────────────────────────────┐ 4 │ │ │ .'│ │ : │ │ .' │ Time (ms) │ : │ │ .' │ │ .' │ │ .'' │ │ ...' │ 0 │ ..'''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 10, mode = 2 ┌──────────────────────────────┐ 2 │ │ │ .'│ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ .' │ │ .' │ │ ..: │ 0 │ ..'''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 10, mode = 3 ┌──────────────────────────────┐ 3 │ :│ │ .' │ │ : │ │ .' │ Time (ms) │ : │ │ .: │ │ .' │ │ .'' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 50, mode = 1 ┌──────────────────────────────┐ 10 │ .│ │ .'│ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ .' │ │ ...''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 50, mode = 2 ┌──────────────────────────────┐ 20 │ │ │ │ │ │ │ .. │ Time (ms) │ : '. │ │ .' ''. │ │ .' '│ │ .' │ │ : │ 0 │ ........: │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 50, mode = 3 ┌──────────────────────────────┐ 9 │ .│ │ .' │ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ .' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 100, mode = 1 ┌──────────────────────────────┐ 20 │ │ │ │ │ │ │ ..│ Time (ms) │ .' │ │ .' │ │ ..' │ │ ..' │ │ ...'' │ 0 │ ..'''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 100, mode = 2 ┌──────────────────────────────┐ 20 │ │ │ │ │ .. │ │ : ''.. │ Time (ms) │ .' ''│ │ .' │ │ .' │ │ .' │ │ .' │ 0 │ ......''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 100, mode = 3 ┌──────────────────────────────┐ 20 │ │ │ │ │ │ │ .│ Time (ms) │ .'' │ │ .' │ │ .' │ │ ..'' │ │ ....' │ 0 │ ..'''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 150, mode = 1 ┌──────────────────────────────┐ 20 │ .│ │ .'│ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ .' │ │ .'' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 150, mode = 2 ┌──────────────────────────────┐ 20 │ │ │ │ │ .│ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ ..' │ │ ..''' │ 0 │ ..''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 150, mode = 3 ┌──────────────────────────────┐ 20 │ │ │ .'│ │ .' │ │ : │ Time (ms) │ .' │ │ .: │ │ .' │ │ .'' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 200, mode = 1 ┌──────────────────────────────┐ 30 │ │ │ │ │ .│ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ ..' │ │ ...'' │ 0 │ ..''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 200, mode = 2 ┌──────────────────────────────┐ 20 │ │ │ .'│ │ .' │ │ : │ Time (ms) │ .' │ │ .' │ │ ..' │ │ .' │ │ ..''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 200, mode = 3 ┌──────────────────────────────┐ 30 │ │ │ │ │ .│ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ ..' │ │ ....' │ 0 │ ..''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 250, mode = 1 ┌──────────────────────────────┐ 30 │ │ │ .'│ │ .' │ │ : │ Time (ms) │ .' │ │ .' │ │ ..' │ │ .' │ │ ..''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 250, mode = 2 ┌──────────────────────────────┐ 30 │ │ │ │ │ ...'''''│ │ : │ Time (ms) │ .' │ │ .' │ │ : │ │ .' │ │ ...'' │ 0 │ ..'' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 250, mode = 3 ┌──────────────────────────────┐ 30 │ .│ │ .'│ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ .' │ │ .'' │ │ ..''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 300, mode = 1 ┌──────────────────────────────┐ 40 │ │ │ .│ │ .' │ │ : │ Time (ms) │ .' │ │ .' │ │ .'' │ │ ..' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 300, mode = 2 ┌──────────────────────────────┐ 40 │ .│ │ : │ │ .' │ │ .' │ Time (ms) │ .' │ │ : │ │ .: │ │ ..'' │ │ ..''' │ 0 │ ..''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 300, mode = 3 ┌──────────────────────────────┐ 40 │ │ │ .│ │ .' │ │ : │ Time (ms) │ .' │ │ .' │ │ ..' │ │ ..' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size

Runtime vs. rank

Below are plots showing the runtime in miliseconds of MTTKRP as a function of the size of the rank, for varying sizes and modes:

	size = (30, 100, 1000), mode = 1	size = (30, 100, 1000), mode = 2	size = (30, 100, 1000), mode = 3	size = (50, 50, 50), mode = 1	size = (50, 50, 50), mode = 2	size = (50, 50, 50), mode = 3	size = (100, 100, 100), mode = 1	size = (100, 100, 100), mode = 2	size = (100, 100, 100), mode = 3	size = (150, 150, 150), mode = 1	size = (150, 150, 150), mode = 2	size = (150, 150, 150), mode = 3	size = (200, 200, 200), mode = 1	size = (200, 200, 200), mode = 2	size = (200, 200, 200), mode = 3	size = (1000, 100, 30), mode = 1	size = (1000, 100, 30), mode = 2	size = (1000, 100, 30), mode = 3
Target	size = (30, 100, 1000), mode = 1 ┌──────────────────────────────┐ 50 │ .│ │ ..''│ │ ..'' │ │ ..'' │ Time (ms) │ ..' │ │ .'' │ │ .'' │ │ .'' │ │ .'' │ 0 │ '' │ └──────────────────────────────┘ 0 300 Rank	size = (30, 100, 1000), mode = 2 ┌──────────────────────────────┐ 8 │ │ │ .'│ │ .'' │ │ .'' │ Time (ms) │ ...'' │ │ ..'' │ │ .''' │ │ ..'' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (30, 100, 1000), mode = 3 ┌──────────────────────────────┐ 8 │ .│ │ .''│ │ .'' │ │ ..'' │ Time (ms) │ ..'' │ │ ..'' │ │ ..'' │ │ ..' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (50, 50, 50), mode = 1 ┌──────────────────────────────┐ 2 │ │ │ │ │ │ │ ...''│ Time (ms) │ ..'' │ │ ..'' │ │ ..''' │ │ ...'' │ │ .''' │ 0 │ '' │ └──────────────────────────────┘ 0 300 Rank	size = (50, 50, 50), mode = 2 ┌──────────────────────────────┐ 1 │ .│ │ .'' │ │ ..'' │ │ ..' │ Time (ms) │ .'' │ │ ..'' │ │ ..' │ │ ..'' │ │ ..' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (50, 50, 50), mode = 3 ┌──────────────────────────────┐ 2 │ │ │ │ │ .│ │ ..'│ Time (ms) │ ....'' │ │ ...'' │ │ ..'' │ │ ..''' │ │ .''' │ 0 │ '' │ └──────────────────────────────┘ 0 300 Rank	size = (100, 100, 100), mode = 1 ┌──────────────────────────────┐ 7 │ ..:│ │ .'' │ │ .' │ │ ..' │ Time (ms) │ .'' │ │ ..'' │ │ ..'' │ │ .'' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (100, 100, 100), mode = 2 ┌──────────────────────────────┐ 20 │ │ │ │ │ .│ │ .'│ Time (ms) │ .' │ │ .' │ │ .' │ │ ....: │ │ ..'''''' │ 0 │ .......''''' │ └──────────────────────────────┘ 0 300 Rank	size = (100, 100, 100), mode = 3 ┌──────────────────────────────┐ 7 │ .:│ │ ..' │ │ ..' │ │ .'' │ Time (ms) │ ..'' │ │ ..' │ │ ..' │ │ ..'' │ │ ..' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (150, 150, 150), mode = 1 ┌──────────────────────────────┐ 20 │ │ │ .'│ │ ..'' │ │ ..' │ Time (ms) │ ..'' │ │ ..'' │ │ ..'' │ │ ..'' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (150, 150, 150), mode = 2 ┌──────────────────────────────┐ 20 │ │ │ │ │ .│ │ . ..''│ Time (ms) │ :'. ..'' │ │ .' : ...'' │ │ : '. ...'' │ │ : ''' │ │ .' │ 0 │ : │ └──────────────────────────────┘ 0 300 Rank	size = (150, 150, 150), mode = 3 ┌──────────────────────────────┐ 20 │ │ │ .'│ │ .'' │ │ ..'' │ Time (ms) │ ..'' │ │ ..'' │ │ ..'' │ │ ..'' │ │ ..' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (200, 200, 200), mode = 1 ┌──────────────────────────────┐ 40 │ │ │ :│ │ ..'' │ │ ..'' │ Time (ms) │ ..'' │ │ ..'' │ │ ..'' │ │ .''' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (200, 200, 200), mode = 2 ┌──────────────────────────────┐ 30 │ :│ │ ..' │ │ ..' │ │ ..' │ Time (ms) │ ..'' │ │ ...''' │ │ ..' │ │ .' │ │ ..' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (200, 200, 200), mode = 3 ┌──────────────────────────────┐ 40 │ │ │ .│ │ .'' │ │ ..'' │ Time (ms) │ ..'' │ │ ...'' │ │ ..'' │ │ ..'' │ │ ..' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (1000, 100, 30), mode = 1 ┌──────────────────────────────┐ 8 │ .│ │ ..' │ │ .' │ │ .'' │ Time (ms) │ ..''' │ │ ..'' │ │ ..'' │ │ .'' │ │ ..'' │ 0 │ │ └──────────────────────────────┘ 0 300 Rank	size = (1000, 100, 30), mode = 2 ┌──────────────────────────────┐ 20 │ │ │ │ │ │ │ . │ Time (ms) │ .' ''. │ │ : '. │ │ .' '.. ...:│ │ : '..'''' │ │ .' │ 0 │ : │ └──────────────────────────────┘ 0 300 Rank	size = (1000, 100, 30), mode = 3 ┌──────────────────────────────┐ 50 │ .│ │ ..''│ │ ..' │ │ ..'' │ Time (ms) │ .'' │ │ ..'' │ │ .'' │ │ .'' │ │ .'' │ 0 │ '' │ └──────────────────────────────┘ 0 300 Rank
Baseline	size = (30, 100, 1000), mode = 1 ┌──────────────────────────────┐ 50 │ │ │ ..'│ │ ..'' │ │ ..' │ Time (ms) │ ..'' │ │ .'' │ │ ..'' │ │ ..'' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (30, 100, 1000), mode = 2 ┌──────────────────────────────┐ 7 │ .'│ │ .'' │ │ ..' │ │ ..' │ Time (ms) │ ..'' │ │ ..'' │ │ ..'' │ │ ..' │ │ ..' │ 0 │ │ └──────────────────────────────┘ 0 300 Rank	size = (30, 100, 1000), mode = 3 ┌──────────────────────────────┐ 9 │ │ │ .'│ │ ..'' │ │ ..' │ Time (ms) │ ..' │ │ ..'' │ │ ..'' │ │ ..'' │ │ ..'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (50, 50, 50), mode = 1 ┌──────────────────────────────┐ 2 │ │ │ │ │ │ │ ...'''│ Time (ms) │ ..' │ │ ..'' │ │ ...''' │ │ ...'' │ │ .'' │ 0 │ '' │ └──────────────────────────────┘ 0 300 Rank	size = (50, 50, 50), mode = 2 ┌──────────────────────────────┐ 1.1 │ .│ │ ..' │ │ .'' │ │ ..'' │ Time (ms) │ ..' │ │ .'' │ │ ..'' │ │ .'' │ │ .'' │ 0 │ '' │ └──────────────────────────────┘ 0 300 Rank	size = (50, 50, 50), mode = 3 ┌──────────────────────────────┐ 2 │ │ │ │ │ │ │ ..'│ Time (ms) │ ....' │ │ ..''' │ │ ...'' │ │ ...''' │ │ .'' │ 0 │ '' │ └──────────────────────────────┘ 0 300 Rank	size = (100, 100, 100), mode = 1 ┌──────────────────────────────┐ 7 │ .│ │ ..' │ │ ..'' │ │ .'' │ Time (ms) │ ..'' │ │ ..' │ │ ..'' │ │ .'' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (100, 100, 100), mode = 2 ┌──────────────────────────────┐ 7 │ .│ │ .''│ │ ..' │ │ ..' │ Time (ms) │ ...' │ │ .'' │ │ .' │ │ .' │ │ ...''' │ 0 │ .''' │ └──────────────────────────────┘ 0 300 Rank	size = (100, 100, 100), mode = 3 ┌──────────────────────────────┐ 7 │ :│ │ .'' │ │ .'' │ │ ..'' │ Time (ms) │ ..'' │ │ ..' │ │ ..' │ │ ..'' │ │ ..' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (150, 150, 150), mode = 1 ┌──────────────────────────────┐ 20 │ │ │ .'│ │ .'' │ │ ..'' │ Time (ms) │ ..'' │ │ ..'' │ │ ..'' │ │ ..'' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (150, 150, 150), mode = 2 ┌──────────────────────────────┐ 30 │ │ │ │ │ .. │ │ .''. │ Time (ms) │ .' '. │ │ ..''': : '│ │ : '. .: │ │ : '..''' │ │ : │ 0 │ : │ └──────────────────────────────┘ 0 300 Rank	size = (150, 150, 150), mode = 3 ┌──────────────────────────────┐ 20 │ │ │ .:│ │ ..' │ │ ..'' │ Time (ms) │ ..'' │ │ ..'' │ │ ..'' │ │ ..'' │ │ ..' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (200, 200, 200), mode = 1 ┌──────────────────────────────┐ 40 │ │ │ :│ │ .'' │ │ ..'' │ Time (ms) │ ...'' │ │ ..'' │ │ ..'' │ │ .''' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (200, 200, 200), mode = 2 ┌──────────────────────────────┐ 40 │ .│ │ .'│ │ : │ │ .' │ Time (ms) │ ..'' │ │ ...'' │ │ ..''' │ │ ..''' │ │ ..'' │ 0 │ .' │ └──────────────────────────────┘ 0 300 Rank	size = (200, 200, 200), mode = 3 ┌──────────────────────────────┐ 40 │ │ │ :│ │ .'' │ │ ..'' │ Time (ms) │ ..'' │ │ ...'' │ │ ..'' │ │ ..'' │ │ ..' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (1000, 100, 30), mode = 1 ┌──────────────────────────────┐ 8 │ .│ │ .' │ │ .'' │ │ .'' │ Time (ms) │ ...'' │ │ ..'' │ │ ..'' │ │ .'' │ │ ..'' │ 0 │ │ └──────────────────────────────┘ 0 300 Rank	size = (1000, 100, 30), mode = 2 ┌──────────────────────────────┐ 7 │ .'│ │ .'' │ │ ..' │ │ ..' │ Time (ms) │ ..'' │ │ ...'' │ │ ..' │ │ ..' │ │ ..' │ 0 │ │ └──────────────────────────────┘ 0 300 Rank	size = (1000, 100, 30), mode = 3 ┌──────────────────────────────┐ 50 │ .│ │ .'' │ │ .'' │ │ ..'' │ Time (ms) │ .'' │ │ ..'' │ │ .'' │ │ .'' │ │ .'' │ 0 │ '' │ └──────────────────────────────┘ 0 300 Rank

Runtime vs. mode

Below are plots showing the runtime in miliseconds of MTTKRP as a function of the mode, for varying sizes and ranks:

	size = (30, 100, 1000), rank = 10	size = (30, 100, 1000), rank = 100	size = (30, 100, 1000), rank = 200	size = (30, 100, 1000), rank = 300	size = (50, 50, 50), rank = 10	size = (50, 50, 50), rank = 50	size = (50, 50, 50), rank = 100	size = (50, 50, 50), rank = 150	size = (50, 50, 50), rank = 200	size = (50, 50, 50), rank = 250	size = (50, 50, 50), rank = 300	size = (100, 100, 100), rank = 10	size = (100, 100, 100), rank = 50	size = (100, 100, 100), rank = 100	size = (100, 100, 100), rank = 150	size = (100, 100, 100), rank = 200	size = (100, 100, 100), rank = 250	size = (100, 100, 100), rank = 300	size = (150, 150, 150), rank = 10	size = (150, 150, 150), rank = 50	size = (150, 150, 150), rank = 100	size = (150, 150, 150), rank = 150	size = (150, 150, 150), rank = 200	size = (150, 150, 150), rank = 250	size = (150, 150, 150), rank = 300	size = (200, 200, 200), rank = 10	size = (200, 200, 200), rank = 50	size = (200, 200, 200), rank = 100	size = (200, 200, 200), rank = 150	size = (200, 200, 200), rank = 200	size = (200, 200, 200), rank = 250	size = (200, 200, 200), rank = 300	size = (1000, 100, 30), rank = 10	size = (1000, 100, 30), rank = 100	size = (1000, 100, 30), rank = 200	size = (1000, 100, 30), rank = 300
Target	size = (30, 100, 1000), rank = 10 ┌ ┐ ┬┐ ╷ mode 1 │├──────────┤ ┴┘ ╵ ┌┐ ╷ mode 2 ┤├──────┤ └┘ ╵ ┐ ╷ mode 3 ├──┤ ┘ ╵ └ ┘ 0 2.5 5 Time (ms)	size = (30, 100, 1000), rank = 100 ┌ ┐ ┐ ╷ mode 1 ├─────────────────────┤ ┘ ╵ ╷ mode 2 ┤ ╵ ╷ mode 3 ┤ ╵ └ ┘ 0 55 110 Time (ms)	size = (30, 100, 1000), rank = 200 ┌ ┐ ┬╷ mode 1 │┤ ┴╵ ┐╷ mode 2 ├┤ ┘╵ ┐╷ mode 3 ├┤ ┘╵ └ ┘ 0 20 40 Time (ms)	size = (30, 100, 1000), rank = 300 ┌ ┐ ┬╷ mode 1 │┤ ┴╵ ┬┐ ╷ mode 2 │├─────┤ ┴┘ ╵ ┐╷ mode 3 ├┤ ┘╵ └ ┘ 0 25 50 Time (ms)	size = (50, 50, 50), rank = 10 ┌ ┐ ┬┐ ╷ mode 1 │├─────┤ ┴┘ ╵ ┬┐ ╷ mode 2 │├───────┤ ┴┘ ╵ ┬┐ ╷ mode 3 │├────────┤ ┴┘ ╵ └ ┘ 0 0.1 0.2 Time (ms)	size = (50, 50, 50), rank = 50 ┌ ┐ ┐ ╷ mode 1 ├───┤ ┘ ╵ ┌┐ ╷ mode 2 ┤├─────┤ └┘ ╵ ┌┐ ╷ mode 3 ┤├──┤ └┘ ╵ └ ┘ 0.1 0.3 0.5 Time (ms)	size = (50, 50, 50), rank = 100 ┌ ┐ ┬─┐ ╷ mode 1 │ ├──┤ ┴─┘ ╵ ┬┐ ╷ mode 2 │├────┤ ┴┘ ╵ ┐ ╷ mode 3 ├───┤ ┘ ╵ └ ┘ 0.3 0.45 0.6 Time (ms)	size = (50, 50, 50), rank = 150 ┌ ┐ ┬┐ ╷ mode 1 │├─┤ ┴┘ ╵ ┬┐ ╷ mode 2 │├──────┤ ┴┘ ╵ ╷┐ ╷ mode 3 ├├───────┤ ╵┘ ╵ └ ┘ 0.4 0.65 0.9 Time (ms)	size = (50, 50, 50), rank = 200 ┌ ┐ ┬┐ ╷ mode 1 │├──┤ ┴┘ ╵ ╷┬──┐ ╷ mode 2 ├│ ├─────┤ ╵┴──┘ ╵ ╷┐ ╷ mode 3 ├├─────┤ ╵┘ ╵ └ ┘ 0.6 0.85 1.1 Time (ms)	size = (50, 50, 50), rank = 250 ┌ ┐ ╷┬┐ ╷ mode 1 ├│├─┤ ╵┴┘ ╵ ┌┬┐ ╷ mode 2 ┤│├─┤ └┴┘ ╵ ┌┐ ╷ mode 3 ┤├──┤ └┘ ╵ └ ┘ 0.7 1 1.3 Time (ms)	size = (50, 50, 50), rank = 300 ┌ ┐ ┌┐ ╷ mode 1 ┤├───┤ └┘ ╵ ┬┐ ╷ mode 2 │├─┤ ┴┘ ╵ ╷┐ ╷ mode 3 ├├──┤ ╵┘ ╵ └ ┘ 0.9 1.2 1.5 Time (ms)	size = (100, 100, 100), rank = 10 ┌ ┐ ╷┐ ╷ mode 1 ├├───────────┤ ╵┘ ╵ ┐ ╷ mode 2 ├─────┤ ┘ ╵ ┬┐ ╷ mode 3 │├───┤ ┴┘ ╵ └ ┘ 0.2 0.55 0.9 Time (ms)	size = (100, 100, 100), rank = 50 ┌ ┐ ┬┐ ╷ mode 1 │├─┤ ┴┘ ╵ ┐ ╷ mode 2 ├───┤ ┘ ╵ ┬┐ ╷ mode 3 │├───┤ ┴┘ ╵ └ ┘ 0.7 1.25 1.8 Time (ms)	size = (100, 100, 100), rank = 100 ┌ ┐ ╷┐ ╷ mode 1 ├├─┤ ╵┘ ╵ ┐ ╷ mode 2 ├─┤ ┘ ╵ ┐ ╷ mode 3 ├──┤ ┘ ╵ └ ┘ 1 2 3 Time (ms)	size = (100, 100, 100), rank = 150 ┌ ┐ ╷ mode 1 ┤ ╵ ╷┐ ╷ mode 2 ├├─────────────────────────┤ ╵┘ ╵ ┬╷ mode 3 │┤ ┴╵ └ ┘ 2 7.5 13 Time (ms)	size = (100, 100, 100), rank = 200 ┌ ┐ ╷ ┐ ╷ mode 1 ├─├─┤ ╵ ┘ ╵ ╷ ┌┐ ╷ mode 2 ├──┤├──┤ ╵ └┘ ╵ ╷ ┌┬─┐ ╷ mode 3 ├──┤│ ├─┤ ╵ └┴─┘ ╵ └ ┘ 3.7 4.25 4.8 Time (ms)	size = (100, 100, 100), rank = 250 ┌ ┐ ╷┬─┐ ╷ mode 1 ├│ ├─┤ ╵┴─┘ ╵ ┐ ╷ mode 2 ├──────────────┤ ┘ ╵ ┬╷ mode 3 │┤ ┴╵ └ ┘ 0 10 20 Time (ms)	size = (100, 100, 100), rank = 300 ┌ ┐ ╷ mode 1 ┤ ╵ ┌──────────────╷ mode 2 ┤ ┤ └──────────────╵ ╷ mode 3 ┤ ╵ └ ┘ 0 10 20 Time (ms)	size = (150, 150, 150), rank = 10 ┌ ┐ ╷ mode 1 ┤ ╵ ┐ ╷ mode 2 ├─────────────────────────┤ ┘ ╵ ╷ mode 3 ┤ ╵ └ ┘ 0 100 200 Time (ms)	size = (150, 150, 150), rank = 50 ┌ ┐ ╷╷ mode 1 ├┤ ╵╵ ╷ ┌╷ mode 2 ├───────────────────────────┤┤ ╵ └╵ ╷ mode 3 ┤ ╵ └ ┘ 3 8 13 Time (ms)	size = (150, 150, 150), rank = 100 ┌ ┐ ╷ mode 1 ┤ ╵ ┬──────────────╷ mode 2 │ ┤ ┴──────────────╵ ╷ mode 3 ┤ ╵ └ ┘ 0 10 20 Time (ms)	size = (150, 150, 150), rank = 150 ┌ ┐ ╷ mode 1 ┤ ╵ ┐ ╷ mode 2 ├──────────────┤ ┘ ╵ ╷ mode 3 ┤ ╵ └ ┘ 0 10 20 Time (ms)	size = (150, 150, 150), rank = 200 ┌ ┐ ╷┌┬┐╷ mode 1 ├┤│├┤ ╵└┴┘╵ ┌┐╷ mode 2 ┤├┤ └┘╵ ┐ ╷ mode 3 ├─┤ ┘ ╵ └ ┘ 9 11 13 Time (ms)	size = (150, 150, 150), rank = 250 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ╷┬────────────────────────┐╷ mode 2 ├│ ├┤ ╵┴────────────────────────┘╵ ┐╷ mode 3 ├┤ ┘╵ └ ┘ 11 16.5 22 Time (ms)	size = (150, 150, 150), rank = 300 ┌ ┐ ╷ mode 1 ┤ ╵ ┬──────┐ ╷ mode 2 │ ├────────────┤ ┴──────┘ ╵ ┐ ╷ mode 3 ├─┤ ┘ ╵ └ ┘ 10 30 50 Time (ms)	size = (200, 200, 200), rank = 10 ┌ ┐ ╷┌┬┐╷ mode 1 ├┤│├┤ ╵└┴┘╵ ╷┐╷ mode 2 ├├┤ ╵┘╵ ┐╷ mode 3 ├┤ ┘╵ └ ┘ 1 2.5 4 Time (ms)	size = (200, 200, 200), rank = 50 ┌ ┐ ╷ mode 1 ┤ ╵ ┬──────────────┐╷ mode 2 │ ├┤ ┴──────────────┘╵ ┌╷ mode 3 ┤┤ └╵ └ ┘ 0 10 20 Time (ms)	size = (200, 200, 200), rank = 100 ┌ ┐ ┌╷ mode 1 ┤┤ └╵ ┌──┬──────────┐ ╷ mode 2 ┤ │ ├──────────────┤ └──┴──────────┘ ╵ ╷╷ mode 3 ├┤ ╵╵ └ ┘ 10 20 30 Time (ms)	size = (200, 200, 200), rank = 150 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┬──────────────╷ mode 2 │ ┤ ┴──────────────╵ ┐╷ mode 3 ├┤ ┘╵ └ ┘ 10 20 30 Time (ms)	size = (200, 200, 200), rank = 200 ┌ ┐ ╷ mode 1 ┤ ╵ ┬─────╷ mode 2 │ ┤ ┴─────╵ ╷┬────┐ ╷ mode 3 ├│ ├──────────┤ ╵┴────┘ ╵ └ ┘ 10 35 60 Time (ms)	size = (200, 200, 200), rank = 250 ┌ ┐ ┬─┐╷ mode 1 │ ├┤ ┴─┘╵ ╷┌─╷ mode 2 ├┤ ┤ ╵└─╵ ┬┐╷ mode 3 │├┤ ┴┘╵ └ ┘ 22 25.5 29 Time (ms)	size = (200, 200, 200), rank = 300 ┌ ┐ ╷┐╷ mode 1 ├├┤ ╵┘╵ ┌┐ ╷ mode 2 ┤├─────────────────────────┤ └┘ ╵ ┬┐ ╷ mode 3 │├──┤ ┴┘ ╵ └ ┘ 28 33.5 39 Time (ms)	size = (1000, 100, 30), rank = 10 ┌ ┐ ┌┬──────┐ ╷ mode 1 ┤│ ├───┤ └┴──────┘ ╵ ┐ ╷ mode 2 ├───┤ ┘ ╵ ┬┐ ╷ mode 3 │├───┤ ┴┘ ╵ └ ┘ 0 2 4 Time (ms)	size = (1000, 100, 30), rank = 100 ┌ ┐ ┐ ╷ mode 1 ├─┤ ┘ ╵ ┌─────────┐ ╷ mode 2 ┤ ├────────────┤ └─────────┘ ╵ ┌╷ mode 3 ┤┤ └╵ └ ┘ 0 15 30 Time (ms)	size = (1000, 100, 30), rank = 200 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┐╷ mode 2 ├┤ ┘╵ ╷ mode 3 ┤ ╵ └ ┘ 0 20 40 Time (ms)	size = (1000, 100, 30), rank = 300 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┐╷ mode 2 ├┤ ┘╵ ┌┐╷ mode 3 ┤├┤ └┘╵ └ ┘ 0 25 50 Time (ms)
Baseline	size = (30, 100, 1000), rank = 10 ┌ ┐ ┌──────┬─┐ ╷ mode 1 ┤ │ ├─────┤ └──────┴─┘ ╵ ┐ ╷ mode 2 ├────┤ ┘ ╵ ┐ ╷ mode 3 ├─┤ ┘ ╵ └ ┘ 0 3.5 7 Time (ms)	size = (30, 100, 1000), rank = 100 ┌ ┐ ╷┐ ╷ mode 1 ├├───────────────────────┤ ╵┘ ╵ ╷ mode 2 ┤ ╵ ╷ mode 3 ┤ ╵ └ ┘ 0 45 90 Time (ms)	size = (30, 100, 1000), rank = 200 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┐╷ mode 2 ├┤ ┘╵ ┬──────┐ ╷ mode 3 │ ├────────────┤ ┴──────┘ ╵ └ ┘ 0 20 40 Time (ms)	size = (30, 100, 1000), rank = 300 ┌ ┐ ╷┬╷ mode 1 ├│┤ ╵┴╵ ┐╷ mode 2 ├┤ ┘╵ ╷ mode 3 ┤ ╵ └ ┘ 0 25 50 Time (ms)	size = (50, 50, 50), rank = 10 ┌ ┐ ┌┬─┐ ╷ mode 1 ┤│ ├───┤ └┴─┘ ╵ ╷┐ ╷ mode 2 ├├────────┤ ╵┘ ╵ ┐ ╷ mode 3 ├─────┤ ┘ ╵ └ ┘ 0 0.1 0.2 Time (ms)	size = (50, 50, 50), rank = 50 ┌ ┐ ┬┐ ╷ mode 1 │├───┤ ┴┘ ╵ ╷┐ ╷ mode 2 ├├─────┤ ╵┘ ╵ ╷┐ ╷ mode 3 ├├────┤ ╵┘ ╵ └ ┘ 0.2 0.35 0.5 Time (ms)	size = (50, 50, 50), rank = 100 ┌ ┐ ╷┌┬┐ ╷ mode 1 ├┤│├──┤ ╵└┴┘ ╵ ┌┐ ╷ mode 2 ┤├─────┤ └┘ ╵ ┐ ╷ mode 3 ├─┤ ┘ ╵ └ ┘ 0.3 0.5 0.7 Time (ms)	size = (50, 50, 50), rank = 150 ┌ ┐ ╷┬┐ ╷ mode 1 ├│├──┤ ╵┴┘ ╵ ┌┬┐ ╷ mode 2 ┤│├──┤ └┴┘ ╵ ╷┬┐ ╷ mode 3 ├│├──┤ ╵┴┘ ╵ └ ┘ 0.5 0.7 0.9 Time (ms)	size = (50, 50, 50), rank = 200 ┌ ┐ ┌┐╷ mode 1 ┤├┤ └┘╵ ┬┐ ╷ mode 2 │├───┤ ┴┘ ╵ ╷┬─┐ ╷ mode 3 ├│ ├───┤ ╵┴─┘ ╵ └ ┘ 0.6 0.85 1.1 Time (ms)	size = (50, 50, 50), rank = 250 ┌ ┐ ╷ ┌┐ ╷ mode 1 ├───┤├─┤ ╵ └┘ ╵ ┬───┐╷ mode 2 │ ├┤ ┴───┘╵ ┌┬┐ ╷ mode 3 ┤│├───┤ └┴┘ ╵ └ ┘ 0.8 1.1 1.4 Time (ms)	size = (50, 50, 50), rank = 300 ┌ ┐ ╷┬─┐ ╷ mode 1 ├│ ├──┤ ╵┴─┘ ╵ ┬┐ ╷ mode 2 │├──┤ ┴┘ ╵ ╷┐ ╷ mode 3 ├├──┤ ╵┘ ╵ └ ┘ 1 1.3 1.6 Time (ms)	size = (100, 100, 100), rank = 10 ┌ ┐ ┐ ╷ mode 1 ├───────────┤ ┘ ╵ ┐ ╷ mode 2 ├─────┤ ┘ ╵ ╷┐ ╷ mode 3 ├├───┤ ╵┘ ╵ └ ┘ 0.2 0.55 0.9 Time (ms)	size = (100, 100, 100), rank = 50 ┌ ┐ ╷┐ ╷ mode 1 ├├───┤ ╵┘ ╵ ┐ ╷ mode 2 ├──┤ ┘ ╵ ┬┐ ╷ mode 3 │├──┤ ┴┘ ╵ └ ┘ 0.8 1.3 1.8 Time (ms)	size = (100, 100, 100), rank = 100 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┐ ╷ mode 2 ├─┤ ┘ ╵ ┐ ╷ mode 3 ├──┤ ┘ ╵ └ ┘ 1 2 3 Time (ms)	size = (100, 100, 100), rank = 150 ┌ ┐ ╷ mode 1 ┤ ╵ ┬──────────────╷ mode 2 │ ┤ ┴──────────────╵ ┐╷ mode 3 ├┤ ┘╵ └ ┘ 0 10 20 Time (ms)	size = (100, 100, 100), rank = 200 ┌ ┐ ╷ mode 1 ┤ ╵ ┐ ╷ mode 2 ├──────────────┤ ┘ ╵ ╷ mode 3 ┤ ╵ └ ┘ 0 10 20 Time (ms)	size = (100, 100, 100), rank = 250 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ╷┬┐ ╷ mode 2 ├│├─────────────────────────┤ ╵┴┘ ╵ ┐╷ mode 3 ├┤ ┘╵ └ ┘ 4 9.5 15 Time (ms)	size = (100, 100, 100), rank = 300 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┌┬─────────────╷ mode 2 ┤│ ┤ └┴─────────────╵ ┬┐ ╷ mode 3 │├────────────────┤ ┴┘ ╵ └ ┘ 0 10 20 Time (ms)	size = (150, 150, 150), rank = 10 ┌ ┐ ╷ mode 1 ┤ ╵ ┐ ╷ mode 2 ├────────────────────┤ ┘ ╵ ╷ mode 3 ┤ ╵ └ ┘ 0 100 200 Time (ms)	size = (150, 150, 150), rank = 50 ┌ ┐ ╷╷ mode 1 ├┤ ╵╵ ┌─────────────┐╷ mode 2 ┤ ├┤ └─────────────┘╵ ╷ mode 3 ┤ ╵ └ ┘ 0 10 20 Time (ms)	size = (150, 150, 150), rank = 100 ┌ ┐ ┬╷ mode 1 │┤ ┴╵ ╷ ┬╷ mode 2 ├─────────────│┤ ╵ ┴╵ ╷ mode 3 ┤ ╵ └ ┘ 0 10 20 Time (ms)	size = (150, 150, 150), rank = 150 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┬──────────────╷ mode 2 │ ┤ ┴──────────────╵ ╷ mode 3 ┤ ╵ └ ┘ 0 10 20 Time (ms)	size = (150, 150, 150), rank = 200 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┬─────────────┐╷ mode 2 │ ├┤ ┴─────────────┘╵ ┬╷ mode 3 │┤ ┴╵ └ ┘ 0 10 20 Time (ms)	size = (150, 150, 150), rank = 250 ┌ ┐ ╷ mode 1 ┤ ╵ ╷┌──────────────╷ mode 2 ├┤ ┤ ╵└──────────────╵ ┐╷ mode 3 ├┤ ┘╵ └ ┘ 10 20 30 Time (ms)	size = (150, 150, 150), rank = 300 ┌ ┐ ┌┐╷ mode 1 ┤├┤ └┘╵ ┬┐ ╷ mode 2 │├─────────────┤ ┴┘ ╵ ┬╷ mode 3 │┤ ┴╵ └ ┘ 10 20 30 Time (ms)	size = (200, 200, 200), rank = 10 ┌ ┐ ╷┐ ╷ mode 1 ├├─┤ ╵┘ ╵ ┐╷ mode 2 ├┤ ┘╵ ┐╷ mode 3 ├┤ ┘╵ └ ┘ 1 2.5 4 Time (ms)	size = (200, 200, 200), rank = 50 ┌ ┐ ╷ mode 1 ┤ ╵ ┌┬─────────────╷ mode 2 ┤│ ┤ └┴─────────────╵ ╷ mode 3 ┤ ╵ └ ┘ 0 10 20 Time (ms)	size = (200, 200, 200), rank = 100 ┌ ┐ ╷ mode 1 ┤ ╵ ┬─────────────┐╷ mode 2 │ ├┤ ┴─────────────┘╵ ╷ mode 3 ┤ ╵ └ ┘ 10 20 30 Time (ms)	size = (200, 200, 200), rank = 150 ┌ ┐ ╷┐╷ mode 1 ├├┤ ╵┘╵ ┬──────────────╷ mode 2 │ ┤ ┴──────────────╵ ╷ mode 3 ┤ ╵ └ ┘ 10 20 30 Time (ms)	size = (200, 200, 200), rank = 200 ┌ ┐ ╷┬┐╷ mode 1 ├│├┤ ╵┴┘╵ ┌┐╷ mode 2 ┤├┤ └┘╵ ╷┐ ╷ mode 3 ├├─┤ ╵┘ ╵ └ ┘ 18 20.5 23 Time (ms)	size = (200, 200, 200), rank = 250 ┌ ┐ ┌╷ mode 1 ┤┤ └╵ ┬──────────────┐╷ mode 2 │ ├┤ ┴──────────────┘╵ ┌╷ mode 3 ┤┤ └╵ └ ┘ 20 30 40 Time (ms)	size = (200, 200, 200), rank = 300 ┌ ┐ ┌┐╷ mode 1 ┤├┤ └┘╵ ┌─────────────┬╷ mode 2 ┤ │┤ └─────────────┴╵ ┌╷ mode 3 ┤┤ └╵ └ ┘ 20 30 40 Time (ms)	size = (1000, 100, 30), rank = 10 ┌ ┐ ┬┐ ╷ mode 1 │├─────────┤ ┴┘ ╵ ╷┐ ╷ mode 2 ├├──┤ ╵┘ ╵ ┬─┐ ╷ mode 3 │ ├─┤ ┴─┘ ╵ └ ┘ 0 2 4 Time (ms)	size = (1000, 100, 30), rank = 100 ┌ ┐ ┐ ╷ mode 1 ├─┤ ┘ ╵ ┬┐ ╷ mode 2 │├───────────────────┤ ┴┘ ╵ ┬╷ mode 3 │┤ ┴╵ └ ┘ 0 10 20 Time (ms)	size = (1000, 100, 30), rank = 200 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┐╷ mode 2 ├┤ ┘╵ ╷┐╷ mode 3 ├├┤ ╵┘╵ └ ┘ 0 20 40 Time (ms)	size = (1000, 100, 30), rank = 300 ┌ ┐ ┬╷ mode 1 │┤ ┴╵ ╷ mode 2 ┤ ╵ ╷╷ mode 3 ├┤ ╵╵ └ ┘ 0 25 50 Time (ms)

[dahong67]

After handling the special case of a Khatri-Rao product with only one matrix, we recover the earlier performance.

Benchmark Report for GCPDecompositions

Job Properties

• Time of benchmarks:
  • Target: 3 Mar 2024 - 21:23
  • Baseline: 3 Mar 2024 - 21:23
• Package commits:
  • Target: 140154
  • Baseline: 38648a
• Julia commits:
  • Target: bed2cd
  • Baseline: bed2cd
• Julia command flags:
  • Target: None
  • Baseline: None
• Environment variables:
  • Target: GCP_BENCHMARK_SUITES => mttkrp
  • Baseline: GCP_BENCHMARK_SUITES => mttkrp

Results

A ratio greater than 1.0 denotes a possible regression (marked with ❌), while a ratio less
than 1.0 denotes a possible improvement (marked with ✅). Only significant results - results
that indicate possible regressions or improvements - are shown below (thus, an empty table means that all
benchmark results remained invariant between builds).

ID	time ratio	memory ratio
["mttkrp", "size=(100, 100, 100), rank=150, mode=2"]	1.08 (5%) ❌	1.00 (1%)
["mttkrp", "size=(100, 100, 100), rank=250, mode=3"]	1.07 (5%) ❌	1.00 (1%)
["mttkrp", "size=(1000, 100, 30), rank=10, mode=3"]	0.93 (5%) ✅	1.00 (1%)
["mttkrp", "size=(1000, 100, 30), rank=100, mode=3"]	0.93 (5%) ✅	1.00 (1%)
["mttkrp", "size=(150, 150, 150), rank=10, mode=1"]	0.94 (5%) ✅	1.00 (1%)
["mttkrp", "size=(200, 200, 200), rank=50, mode=1"]	0.95 (5%) ✅	1.00 (1%)
["mttkrp", "size=(200, 200, 200), rank=50, mode=2"]	0.43 (5%) ✅	1.00 (1%)
["mttkrp", "size=(30, 100, 1000), rank=100, mode=1"]	0.94 (5%) ✅	1.00 (1%)
["mttkrp", "size=(50, 50, 50), rank=10, mode=2"]	1.13 (5%) ❌	1.00 (1%)
["mttkrp", "size=(50, 50, 50), rank=100, mode=3"]	0.95 (5%) ✅	1.00 (1%)
["mttkrp", "size=(50, 50, 50), rank=50, mode=2"]	1.06 (5%) ❌	1.00 (1%)

Benchmark Group List

Here's a list of all the benchmark groups executed by this job:

• ["mttkrp"]

Julia versioninfo

Target

Julia Version 1.9.3
Commit bed2cd540a1 (2023-08-24 14:43 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (arm64-apple-darwin22.4.0)
  uname: Darwin 23.2.0 Darwin Kernel Version 23.2.0: Wed Nov 15 21:53:18 PST 2023; root:xnu-10002.61.3~2/RELEASE_ARM64_T6000 arm64 arm
  CPU: Apple M1 Max: 
                 speed         user         nice          sys         idle          irq
       #1-10  2400 MHz    1499358 s          0 s     574884 s   20313069 s          0 s
  Memory: 64.0 GB (35929.046875 MB free)
  Uptime: 489776.0 sec
  Load Avg:  6.3447265625  4.35791015625  3.13671875
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-14.0.6 (ORCJIT, apple-m1)
  Threads: 1 on 8 virtual cores

Baseline

Julia Version 1.9.3
Commit bed2cd540a1 (2023-08-24 14:43 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (arm64-apple-darwin22.4.0)
  uname: Darwin 23.2.0 Darwin Kernel Version 23.2.0: Wed Nov 15 21:53:18 PST 2023; root:xnu-10002.61.3~2/RELEASE_ARM64_T6000 arm64 arm
  CPU: Apple M1 Max: 
                 speed         user         nice          sys         idle          irq
       #1-10  2400 MHz    1500949 s          0 s     575574 s   20314036 s          0 s
  Memory: 64.0 GB (36006.421875 MB free)
  Uptime: 489809.0 sec
  Load Avg:  6.70654296875  4.61376953125  3.27001953125
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-14.0.6 (ORCJIT, apple-m1)
  Threads: 1 on 8 virtual cores

MTTKRP benchmark plots

Runtime vs. size (for square tensors)

Below are plots showing the runtime in miliseconds of MTTKRP as a function of the size of the square tensor, for varying ranks and modes:

	ndims = 3, rank = 10, mode = 1	ndims = 3, rank = 10, mode = 2	ndims = 3, rank = 10, mode = 3	ndims = 3, rank = 50, mode = 1	ndims = 3, rank = 50, mode = 2	ndims = 3, rank = 50, mode = 3	ndims = 3, rank = 100, mode = 1	ndims = 3, rank = 100, mode = 2	ndims = 3, rank = 100, mode = 3	ndims = 3, rank = 150, mode = 1	ndims = 3, rank = 150, mode = 2	ndims = 3, rank = 150, mode = 3	ndims = 3, rank = 200, mode = 1	ndims = 3, rank = 200, mode = 2	ndims = 3, rank = 200, mode = 3	ndims = 3, rank = 250, mode = 1	ndims = 3, rank = 250, mode = 2	ndims = 3, rank = 250, mode = 3	ndims = 3, rank = 300, mode = 1	ndims = 3, rank = 300, mode = 2	ndims = 3, rank = 300, mode = 3
Target	ndims = 3, rank = 10, mode = 1 ┌──────────────────────────────┐ 4 │ │ │ :│ │ .' │ │ .' │ Time (ms) │ : │ │ .' │ │ ..' │ │ .' │ │ ....' │ 0 │ ..''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 10, mode = 2 ┌──────────────────────────────┐ 2 │ │ │ .'│ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ .' │ │ .' │ │ ..: │ 0 │ .''''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 10, mode = 3 ┌──────────────────────────────┐ 3 │ .│ │ : │ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ .' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 50, mode = 1 ┌──────────────────────────────┐ 9 │ .'│ │ .' │ │ .' │ │ : │ Time (ms) │ .' │ │ .' │ │ .'' │ │ .' │ │ ..''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 50, mode = 2 ┌──────────────────────────────┐ 20 │ │ │ .│ │ .'│ │ .' │ Time (ms) │ .' │ │ : │ │ : │ │ : │ │ ...: │ 0 │ .........''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 50, mode = 3 ┌──────────────────────────────┐ 9 │ .│ │ : │ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ .' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 100, mode = 1 ┌──────────────────────────────┐ 20 │ │ │ │ │ │ │ .│ Time (ms) │ ..' │ │ .' │ │ .' │ │ ..'' │ │ ....' │ 0 │ ..'''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 100, mode = 2 ┌──────────────────────────────┐ 30 │ │ │ │ │ │ │ :│ Time (ms) │ .' │ │ : │ │ .' │ │ : │ │ ...' │ 0 │ .........''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 100, mode = 3 ┌──────────────────────────────┐ 20 │ │ │ │ │ │ │ .│ Time (ms) │ ..' │ │ .' │ │ .' │ │ ..'' │ │ ....' │ 0 │ ..'''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 150, mode = 1 ┌──────────────────────────────┐ 20 │ │ │ .'│ │ .' │ │ : │ Time (ms) │ .' │ │ .: │ │ .' │ │ .'' │ │ ..''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 150, mode = 2 ┌──────────────────────────────┐ 20 │ │ │ │ │ .│ │ .'. .' │ Time (ms) │ .' '.. .' │ │ : '. .' │ │ : ' │ │ .' │ │ .' │ 0 │ .' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 150, mode = 3 ┌──────────────────────────────┐ 20 │ │ │ .'│ │ .' │ │ : │ Time (ms) │ .' │ │ .: │ │ .' │ │ .'' │ │ ..''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 200, mode = 1 ┌──────────────────────────────┐ 30 │ │ │ │ │ .│ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ ..' │ │ ....' │ 0 │ ..''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 200, mode = 2 ┌──────────────────────────────┐ 20 │ .│ │ .'│ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ .'' │ │ ..' │ │ ...'' │ 0 │ .'' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 200, mode = 3 ┌──────────────────────────────┐ 30 │ │ │ │ │ .│ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ ..' │ │ ...'' │ 0 │ ..''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 250, mode = 1 ┌──────────────────────────────┐ 30 │ │ │ .'│ │ .' │ │ : │ Time (ms) │ .' │ │ .' │ │ .' │ │ .'' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 250, mode = 2 ┌──────────────────────────────┐ 40 │ │ │ │ │ .''│ │ ..' │ Time (ms) │ .' │ │ .' │ │ .' │ │ .' │ │ ..: │ 0 │ ..'''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 250, mode = 3 ┌──────────────────────────────┐ 30 │ │ │ .'│ │ .' │ │ : │ Time (ms) │ .' │ │ .' │ │ ..' │ │ .' │ │ ..''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 300, mode = 1 ┌──────────────────────────────┐ 40 │ │ │ .│ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ ..' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 300, mode = 2 ┌──────────────────────────────┐ 30 │ .│ │ .' │ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ .'' │ │ ..' │ │ ..''' │ 0 │ .'' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 300, mode = 3 ┌──────────────────────────────┐ 40 │ │ │ .│ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ .' │ │ .'' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size
Baseline	ndims = 3, rank = 10, mode = 1 ┌──────────────────────────────┐ 4 │ :│ │ .' │ │ : │ │ .' │ Time (ms) │ : │ │ .: │ │ .' │ │ .' │ │ ....' │ 0 │ ..''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 10, mode = 2 ┌──────────────────────────────┐ 2 │ │ │ .'│ │ .' │ │ ..' │ Time (ms) │ .' │ │ .' │ │ .' │ │ .' │ │ ..: │ 0 │ ..'''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 10, mode = 3 ┌──────────────────────────────┐ 3 │ .│ │ : │ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ .' │ │ ..''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 50, mode = 1 ┌──────────────────────────────┐ 10 │ .│ │ .' │ │ .' │ │ .' │ Time (ms) │ .' │ │ : │ │ .'' │ │ ..' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 50, mode = 2 ┌──────────────────────────────┐ 20 │ │ │ .│ │ ..'' │ │ .'' │ Time (ms) │ : │ │ .' │ │ .' │ │ .' │ │ : │ 0 │ ........: │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 50, mode = 3 ┌──────────────────────────────┐ 9 │ .│ │ .' │ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ .' │ │ ..''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 100, mode = 1 ┌──────────────────────────────┐ 20 │ │ │ │ │ │ │ .'│ Time (ms) │ .' │ │ .' │ │ .' │ │ ..'' │ │ ...'' │ 0 │ ..'''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 100, mode = 2 ┌──────────────────────────────┐ 20 │ │ │ │ │ │ │ │ Time (ms) │ .│ │ ..' │ │ .' │ │ .:' │ │ ..'' │ 0 │ ......'''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 100, mode = 3 ┌──────────────────────────────┐ 20 │ │ │ │ │ │ │ .│ Time (ms) │ .'' │ │ .' │ │ .' │ │ ..'' │ │ ...'' │ 0 │ ..'''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 150, mode = 1 ┌──────────────────────────────┐ 20 │ │ │ .'│ │ .' │ │ : │ Time (ms) │ .' │ │ .: │ │ .' │ │ .'' │ │ ..''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 150, mode = 2 ┌──────────────────────────────┐ 30 │ │ │ │ │ :│ │ .' │ Time (ms) │ .' │ │ ... : │ │ .' ''.. .' │ │ .' ':' │ │ .' │ 0 │ .' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 150, mode = 3 ┌──────────────────────────────┐ 20 │ │ │ .'│ │ .' │ │ : │ Time (ms) │ .' │ │ .: │ │ .' │ │ ..' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 200, mode = 1 ┌──────────────────────────────┐ 30 │ │ │ │ │ .│ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ .'' │ │ ...'' │ 0 │ ..''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 200, mode = 2 ┌──────────────────────────────┐ 20 │ │ │ .'│ │ .' │ │ : │ Time (ms) │ .' │ │ .' │ │ .'' │ │ ..' │ │ ..''' │ 0 │ .'' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 200, mode = 3 ┌──────────────────────────────┐ 30 │ │ │ │ │ .│ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ ..' │ │ ....' │ 0 │ ..''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 250, mode = 1 ┌──────────────────────────────┐ 30 │ .│ │ : │ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ .' │ │ ..''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 250, mode = 2 ┌──────────────────────────────┐ 30 │ │ │ │ │ .....'''│ │ .' │ Time (ms) │ .' │ │ .' │ │ : │ │ .' │ │ ...'' │ 0 │ ..'' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 250, mode = 3 ┌──────────────────────────────┐ 30 │ │ │ .'│ │ .' │ │ : │ Time (ms) │ .' │ │ .' │ │ .' │ │ .'' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 300, mode = 1 ┌──────────────────────────────┐ 40 │ │ │ :│ │ .' │ │ .' │ Time (ms) │ : │ │ .' │ │ .'' │ │ ..' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 300, mode = 2 ┌──────────────────────────────┐ 30 │ .│ │ : │ │ .' │ │ .' │ Time (ms) │ ..... .' │ │ .' ''' │ │ : │ │ .' │ │ : │ 0 │ .' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 300, mode = 3 ┌──────────────────────────────┐ 40 │ │ │ .│ │ : │ │ .' │ Time (ms) │ .' │ │ .' │ │ .'' │ │ ..' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size

Runtime vs. rank

Below are plots showing the runtime in miliseconds of MTTKRP as a function of the size of the rank, for varying sizes and modes:

	size = (30, 100, 1000), mode = 1	size = (30, 100, 1000), mode = 2	size = (30, 100, 1000), mode = 3	size = (50, 50, 50), mode = 1	size = (50, 50, 50), mode = 2	size = (50, 50, 50), mode = 3	size = (100, 100, 100), mode = 1	size = (100, 100, 100), mode = 2	size = (100, 100, 100), mode = 3	size = (150, 150, 150), mode = 1	size = (150, 150, 150), mode = 2	size = (150, 150, 150), mode = 3	size = (200, 200, 200), mode = 1	size = (200, 200, 200), mode = 2	size = (200, 200, 200), mode = 3	size = (1000, 100, 30), mode = 1	size = (1000, 100, 30), mode = 2	size = (1000, 100, 30), mode = 3
Target	size = (30, 100, 1000), mode = 1 ┌──────────────────────────────┐ 50 │ .│ │ ..'│ │ ..'' │ │ ..' │ Time (ms) │ .'' │ │ ..'' │ │ .'' │ │ ..'' │ │ .'' │ 0 │ '' │ └──────────────────────────────┘ 0 300 Rank	size = (30, 100, 1000), mode = 2 ┌──────────────────────────────┐ 7 │ .'│ │ .'' │ │ ..' │ │ ..' │ Time (ms) │ ..'' │ │ ..'' │ │ ..'' │ │ ..' │ │ ..' │ 0 │ │ └──────────────────────────────┘ 0 300 Rank	size = (30, 100, 1000), mode = 3 ┌──────────────────────────────┐ 8 │ .│ │ .''│ │ .'' │ │ .'' │ Time (ms) │ ..'' │ │ ..''' │ │ ..'' │ │ ..' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (50, 50, 50), mode = 1 ┌──────────────────────────────┐ 2 │ │ │ │ │ │ │ ...''│ Time (ms) │ ..'' │ │ ...'' │ │ ..'' │ │ ..''' │ │ .''' │ 0 │ '' │ └──────────────────────────────┘ 0 300 Rank	size = (50, 50, 50), mode = 2 ┌──────────────────────────────┐ 1.1 │ :│ │ ..'' │ │ ..' │ │ .'' │ Time (ms) │ ..'' │ │ ..' │ │ .'' │ │ ..'' │ │ ..' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (50, 50, 50), mode = 3 ┌──────────────────────────────┐ 2 │ │ │ │ │ │ │ ..''│ Time (ms) │ ..'' │ │ ..''' │ │ ..''' │ │ ...'' │ │ .''' │ 0 │ '' │ └──────────────────────────────┘ 0 300 Rank	size = (100, 100, 100), mode = 1 ┌──────────────────────────────┐ 7 │ .│ │ .' │ │ ..'' │ │ ..'' │ Time (ms) │ ..'' │ │ ..' │ │ ..' │ │ .''' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (100, 100, 100), mode = 2 ┌──────────────────────────────┐ 20 │ │ │ │ │ │ │ .: │ Time (ms) │ .' : │ │ .' : │ │ : : .│ │ : '.....'''' │ │ : │ 0 │ ......'''' │ └──────────────────────────────┘ 0 300 Rank	size = (100, 100, 100), mode = 3 ┌──────────────────────────────┐ 7 │ :│ │ .'' │ │ ..'' │ │ ..' │ Time (ms) │ ..'' │ │ ..' │ │ ..' │ │ ..'' │ │ ..' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (150, 150, 150), mode = 1 ┌──────────────────────────────┐ 20 │ │ │ .:│ │ ..' │ │ ..'' │ Time (ms) │ ..'' │ │ ..'' │ │ ..'' │ │ .''' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (150, 150, 150), mode = 2 ┌──────────────────────────────┐ 30 │ │ │ │ │ . │ │ .' '. │ Time (ms) │ .' '.│ │ : '│ │ .: │ │ ...'''' │ │ ....''' │ 0 │ .''' │ └──────────────────────────────┘ 0 300 Rank	size = (150, 150, 150), mode = 3 ┌──────────────────────────────┐ 20 │ .'│ │ .' │ │ : │ │ ..'' │ Time (ms) │ ..'' │ │ ..'' │ │ ..'' │ │ ..'' │ │ ..' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (200, 200, 200), mode = 1 ┌──────────────────────────────┐ 40 │ │ │ :│ │ .'' │ │ ..'' │ Time (ms) │ ..''' │ │ ..'' │ │ ..'' │ │ ..'' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (200, 200, 200), mode = 2 ┌──────────────────────────────┐ 40 │ │ │ .. │ │ .' ''.│ │ : │ Time (ms) │ . .' │ │ ...'' ''. ..'' │ │ : ''' │ │ : │ │ : │ 0 │ : │ └──────────────────────────────┘ 0 300 Rank	size = (200, 200, 200), mode = 3 ┌──────────────────────────────┐ 40 │ │ │ :│ │ .'' │ │ ..'' │ Time (ms) │ ..''' │ │ ..'' │ │ ...' │ │ ..'' │ │ ..' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (1000, 100, 30), mode = 1 ┌──────────────────────────────┐ 8 │ .│ │ .''│ │ .'' │ │ .'' │ Time (ms) │ ...'' │ │ ...'' │ │ ..' │ │ ..'' │ │ ..' │ 0 │ │ └──────────────────────────────┘ 0 300 Rank	size = (1000, 100, 30), mode = 2 ┌──────────────────────────────┐ 7 │ .'│ │ .'' │ │ ..' │ │ ..' │ Time (ms) │ ..'' │ │ ..'' │ │ ..'' │ │ ..' │ │ ..' │ 0 │ │ └──────────────────────────────┘ 0 300 Rank	size = (1000, 100, 30), mode = 3 ┌──────────────────────────────┐ 50 │ .│ │ .'' │ │ .'' │ │ ..'' │ Time (ms) │ ..' │ │ .'' │ │ ..'' │ │ ..' │ │ .'' │ 0 │ '' │ └──────────────────────────────┘ 0 300 Rank
Baseline	size = (30, 100, 1000), mode = 1 ┌──────────────────────────────┐ 50 │ :│ │ .'' │ │ .'' │ │ ..'' │ Time (ms) │ ..' │ │ ..'' │ │ ..' │ │ .'' │ │ .'' │ 0 │ '' │ └──────────────────────────────┘ 0 300 Rank	size = (30, 100, 1000), mode = 2 ┌──────────────────────────────┐ 8 │ │ │ .'│ │ .'' │ │ .'' │ Time (ms) │ ..'' │ │ ..''' │ │ ..'' │ │ ..'' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (30, 100, 1000), mode = 3 ┌──────────────────────────────┐ 8 │ .│ │ .''│ │ .'' │ │ .'' │ Time (ms) │ ...'' │ │ ..'' │ │ ..'' │ │ ..' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (50, 50, 50), mode = 1 ┌──────────────────────────────┐ 2 │ │ │ │ │ │ │ .'''''│ Time (ms) │ .'' │ │ ..'' │ │ ...'' │ │ ...''' │ │ .'' │ 0 │ '' │ └──────────────────────────────┘ 0 300 Rank	size = (50, 50, 50), mode = 2 ┌──────────────────────────────┐ 1.1 │ :│ │ ..' │ │ ..' │ │ .'' │ Time (ms) │ ..'' │ │ ..' │ │ ..'' │ │ .'' │ │ .'' │ 0 │ '' │ └──────────────────────────────┘ 0 300 Rank	size = (50, 50, 50), mode = 3 ┌──────────────────────────────┐ 2 │ │ │ │ │ .│ │ ..''│ Time (ms) │ ..'' │ │ ..''' │ │ ..''' │ │ ..''' │ │ ..'' │ 0 │ '' │ └──────────────────────────────┘ 0 300 Rank	size = (100, 100, 100), mode = 1 ┌──────────────────────────────┐ 7 │ .│ │ ..' │ │ ..'' │ │ .'' │ Time (ms) │ ..'' │ │ .'' │ │ ..'' │ │ .'' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (100, 100, 100), mode = 2 ┌──────────────────────────────┐ 20 │ │ │ │ │ :│ │ .. : │ Time (ms) │ .''. : │ │ .' '. : │ │ : '. : │ │ : '.....'' │ │ : │ 0 │ .......''' │ └──────────────────────────────┘ 0 300 Rank	size = (100, 100, 100), mode = 3 ┌──────────────────────────────┐ 7 │ :│ │ .' │ │ ..' │ │ ..''' │ Time (ms) │ ..' │ │ ..'' │ │ ..' │ │ .''' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (150, 150, 150), mode = 1 ┌──────────────────────────────┐ 20 │ │ │ .'│ │ .'' │ │ ..'' │ Time (ms) │ ..'' │ │ ..'' │ │ ..'' │ │ ..'' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (150, 150, 150), mode = 2 ┌──────────────────────────────┐ 30 │ │ │ │ │ . │ │ .' '. │ Time (ms) │ .' '.│ │ . : '│ │ :'. .: │ │ : '. ....''' │ │ : ''' │ 0 │ : │ └──────────────────────────────┘ 0 300 Rank	size = (150, 150, 150), mode = 3 ┌──────────────────────────────┐ 20 │ │ │ .'│ │ .'' │ │ ..'' │ Time (ms) │ ..'' │ │ ..'' │ │ ..'' │ │ ..'' │ │ ..' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (200, 200, 200), mode = 1 ┌──────────────────────────────┐ 40 │ .│ │ .'│ │ .'' │ │ .'' │ Time (ms) │ ..'' │ │ ...'' │ │ ..'' │ │ .''' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (200, 200, 200), mode = 2 ┌──────────────────────────────┐ 30 │ .│ │ .. ..' │ │ .' '. ..' │ │ .' ''..' │ Time (ms) │ .'. .' │ │ .' '. .' │ │ : '' │ │ : │ │ : │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (200, 200, 200), mode = 3 ┌──────────────────────────────┐ 40 │ │ │ :│ │ .'' │ │ ..'' │ Time (ms) │ ..'' │ │ ...'' │ │ ..'' │ │ ..'' │ │ ..' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (1000, 100, 30), mode = 1 ┌──────────────────────────────┐ 8 │ .│ │ .''│ │ .'' │ │ .'' │ Time (ms) │ ..''' │ │ ..'' │ │ ..'' │ │ ..'' │ │ ..' │ 0 │ │ └──────────────────────────────┘ 0 300 Rank	size = (1000, 100, 30), mode = 2 ┌──────────────────────────────┐ 8 │ │ │ .:│ │ .'' │ │ .'' │ Time (ms) │ ..'' │ │ ..''' │ │ .''' │ │ ..'' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (1000, 100, 30), mode = 3 ┌──────────────────────────────┐ 50 │ .:│ │ ..' │ │ ..' │ │ ..' │ Time (ms) │ .'' │ │ ..'' │ │ ..' │ │ .'' │ │ .'' │ 0 │ '' │ └──────────────────────────────┘ 0 300 Rank

Runtime vs. mode

Below are plots showing the runtime in miliseconds of MTTKRP as a function of the mode, for varying sizes and ranks:

	size = (30, 100, 1000), rank = 10	size = (30, 100, 1000), rank = 100	size = (30, 100, 1000), rank = 200	size = (30, 100, 1000), rank = 300	size = (50, 50, 50), rank = 10	size = (50, 50, 50), rank = 50	size = (50, 50, 50), rank = 100	size = (50, 50, 50), rank = 150	size = (50, 50, 50), rank = 200	size = (50, 50, 50), rank = 250	size = (50, 50, 50), rank = 300	size = (100, 100, 100), rank = 10	size = (100, 100, 100), rank = 50	size = (100, 100, 100), rank = 100	size = (100, 100, 100), rank = 150	size = (100, 100, 100), rank = 200	size = (100, 100, 100), rank = 250	size = (100, 100, 100), rank = 300	size = (150, 150, 150), rank = 10	size = (150, 150, 150), rank = 50	size = (150, 150, 150), rank = 100	size = (150, 150, 150), rank = 150	size = (150, 150, 150), rank = 200	size = (150, 150, 150), rank = 250	size = (150, 150, 150), rank = 300	size = (200, 200, 200), rank = 10	size = (200, 200, 200), rank = 50	size = (200, 200, 200), rank = 100	size = (200, 200, 200), rank = 150	size = (200, 200, 200), rank = 200	size = (200, 200, 200), rank = 250	size = (200, 200, 200), rank = 300	size = (1000, 100, 30), rank = 10	size = (1000, 100, 30), rank = 100	size = (1000, 100, 30), rank = 200	size = (1000, 100, 30), rank = 300
Target	size = (30, 100, 1000), rank = 10 ┌ ┐ ┬┐ ╷ mode 1 │├────────┤ ┴┘ ╵ ┐ ╷ mode 2 ├─────┤ ┘ ╵ ┐ ╷ mode 3 ├─┤ ┘ ╵ └ ┘ 0 3 6 Time (ms)	size = (30, 100, 1000), rank = 100 ┌ ┐ ┐ ╷ mode 1 ├───────────────────────┤ ┘ ╵ ╷ mode 2 ┤ ╵ ╷ mode 3 ┤ ╵ └ ┘ 0 45 90 Time (ms)	size = (30, 100, 1000), rank = 200 ┌ ┐ ╷ mode 1 ┤ ╵ ┐╷ mode 2 ├┤ ┘╵ ╷ mode 3 ┤ ╵ └ ┘ 0 20 40 Time (ms)	size = (30, 100, 1000), rank = 300 ┌ ┐ ╷ mode 1 ┤ ╵ ┐╷ mode 2 ├┤ ┘╵ ┐╷ mode 3 ├┤ ┘╵ └ ┘ 0 25 50 Time (ms)	size = (50, 50, 50), rank = 10 ┌ ┐ ╷┐ ╷ mode 1 ├├──────────┤ ╵┘ ╵ ╷┐ ╷ mode 2 ├├────────────┤ ╵┘ ╵ ┌┬┐ ╷ mode 3 ┤│├──┤ └┴┘ ╵ └ ┘ 0 0.15 0.3 Time (ms)	size = (50, 50, 50), rank = 50 ┌ ┐ ╷┐ ╷ mode 1 ├├────┤ ╵┘ ╵ ┌┐ ╷ mode 2 ┤├─────┤ └┘ ╵ ┌┐ ╷ mode 3 ┤├──────┤ └┘ ╵ └ ┘ 0.2 0.35 0.5 Time (ms)	size = (50, 50, 50), rank = 100 ┌ ┐ ╷┌┐ ╷ mode 1 ├┤├───┤ ╵└┘ ╵ ╷┌┬┐ ╷ mode 2 ├┤│├─────┤ ╵└┴┘ ╵ ┌┐ ╷ mode 3 ┤├─────┤ └┘ ╵ └ ┘ 0.3 0.45 0.6 Time (ms)	size = (50, 50, 50), rank = 150 ┌ ┐ ┐ ╷ mode 1 ├──────┤ ┘ ╵ ┌┬┐ ╷ mode 2 ┤│├───┤ └┴┘ ╵ ╷┬───┐ ╷ mode 3 ├│ ├────┤ ╵┴───┘ ╵ └ ┘ 0.5 0.7 0.9 Time (ms)	size = (50, 50, 50), rank = 200 ┌ ┐ ╷ ┬┐ ╷ mode 1 ├─│├───┤ ╵ ┴┘ ╵ ┐ ╷ mode 2 ├───┤ ┘ ╵ ┌┐ ╷ mode 3 ┤├───┤ └┘ ╵ └ ┘ 0.7 0.9 1.1 Time (ms)	size = (50, 50, 50), rank = 250 ┌ ┐ ╷ ┌┐ ╷ mode 1 ├─┤├──┤ ╵ └┘ ╵ ┬┐ ╷ mode 2 │├───┤ ┴┘ ╵ ┌┬─┐ ╷ mode 3 ┤│ ├───┤ └┴─┘ ╵ └ ┘ 0.8 1.1 1.4 Time (ms)	size = (50, 50, 50), rank = 300 ┌ ┐ ╷┬┐ ╷ mode 1 ├│├──────┤ ╵┴┘ ╵ ┬┐ ╷ mode 2 │├─┤ ┴┘ ╵ ┌┐ ╷ mode 3 ┤├────┤ └┘ ╵ └ ┘ 1 1.3 1.6 Time (ms)	size = (100, 100, 100), rank = 10 ┌ ┐ ┐ ╷ mode 1 ├────────────┤ ┘ ╵ ┌┐ ╷ mode 2 ┤├─────┤ └┘ ╵ ╷┐ ╷ mode 3 ├├───┤ ╵┘ ╵ └ ┘ 0.2 0.55 0.9 Time (ms)	size = (100, 100, 100), rank = 50 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┐╷ mode 2 ├┤ ┘╵ ┐ ╷ mode 3 ├────────────────────┤ ┘ ╵ └ ┘ 0 3 6 Time (ms)	size = (100, 100, 100), rank = 100 ┌ ┐ ┐ ╷ mode 1 ├──┤ ┘ ╵ ┐ ╷ mode 2 ├─┤ ┘ ╵ ┐ ╷ mode 3 ├──┤ ┘ ╵ └ ┘ 1 2 3 Time (ms)	size = (100, 100, 100), rank = 150 ┌ ┐ ╷ mode 1 ┤ ╵ ╷ ╷ mode 2 ├─────────────────────────┤ ╵ ╵ ┌┐ ╷ mode 3 ┤├──────────────────────┤ └┘ ╵ └ ┘ 3 8.5 14 Time (ms)	size = (100, 100, 100), rank = 200 ┌ ┐ ┌╷ mode 1 ┤┤ └╵ ┬──────────────╷ mode 2 │ ┤ ┴──────────────╵ ╷ mode 3 ┤ ╵ └ ┘ 0 10 20 Time (ms)	size = (100, 100, 100), rank = 250 ┌ ┐ ╷ mode 1 ┤ ╵ ┬─────────────────────────╷ mode 2 │ ┤ ┴─────────────────────────╵ ┌╷ mode 3 ┤┤ └╵ └ ┘ 5 10.5 16 Time (ms)	size = (100, 100, 100), rank = 300 ┌ ┐ ╷ mode 1 ┤ ╵ ┬──────────────╷ mode 2 │ ┤ ┴──────────────╵ ╷ mode 3 ┤ ╵ └ ┘ 0 10 20 Time (ms)	size = (150, 150, 150), rank = 10 ┌ ┐ ╷ mode 1 ┤ ╵ ┬┐ ╷ mode 2 │├───────────────────┤ ┴┘ ╵ ╷ mode 3 ┤ ╵ └ ┘ 0 100 200 Time (ms)	size = (150, 150, 150), rank = 50 ┌ ┐ ┌┐╷ mode 1 ┤├┤ └┘╵ ╷┐ ╷ mode 2 ├├─┤ ╵┘ ╵ ╷┐ ╷ mode 3 ├├─┤ ╵┘ ╵ └ ┘ 2 3.5 5 Time (ms)	size = (150, 150, 150), rank = 100 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┬────────────────────────────╷ mode 2 │ ┤ ┴────────────────────────────╵ ┐╷ mode 3 ├┤ ┘╵ └ ┘ 5 10 15 Time (ms)	size = (150, 150, 150), rank = 150 ┌ ┐ ┬╷ mode 1 │┤ ┴╵ ┬───┐ ╷ mode 2 │ ├──────────┤ ┴───┘ ╵ ╷ mode 3 ┤ ╵ └ ┘ 0 10 20 Time (ms)	size = (150, 150, 150), rank = 200 ┌ ┐ ┬╷ mode 1 │┤ ┴╵ ┐ ╷ mode 2 ├──────────────────────────┤ ┘ ╵ ┬╷ mode 3 │┤ ┴╵ └ ┘ 9 14.5 20 Time (ms)	size = (150, 150, 150), rank = 250 ┌ ┐ ╷ mode 1 ┤ ╵ ┌─────────────────────────┐╷ mode 2 ┤ ├┤ └─────────────────────────┘╵ ┬─────┐ ╷ mode 3 │ ├────────┤ ┴─────┘ ╵ └ ┘ 11 16.5 22 Time (ms)	size = (150, 150, 150), rank = 300 ┌ ┐ ╷╷ mode 1 ├┤ ╵╵ ╷┬─────┐ ╷ mode 2 ├│ ├──┤ ╵┴─────┘ ╵ ┌┬──┐ ╷ mode 3 ┤│ ├───────────────────┤ └┴──┘ ╵ └ ┘ 10 35 60 Time (ms)	size = (200, 200, 200), rank = 10 ┌ ┐ ╷┬┐ ╷ mode 1 ├│├─┤ ╵┴┘ ╵ ┐╷ mode 2 ├┤ ┘╵ ┐ ╷ mode 3 ├─┤ ┘ ╵ └ ┘ 1 2.5 4 Time (ms)	size = (200, 200, 200), rank = 50 ┌ ┐ ╷ mode 1 ┤ ╵ ┌────────┐ ╷ mode 2 ┤ ├─────────┤ └────────┘ ╵ ╷ mode 3 ┤ ╵ └ ┘ 0 15 30 Time (ms)	size = (200, 200, 200), rank = 100 ┌ ┐ ┌╷ mode 1 ┤┤ └╵ ╷ ┌╷ mode 2 ├─────────────┤┤ ╵ └╵ ┐╷ mode 3 ├┤ ┘╵ └ ┘ 10 20 30 Time (ms)	size = (200, 200, 200), rank = 150 ┌ ┐ ╷┐╷ mode 1 ├├┤ ╵┘╵ ┬──────────────────────────╷ mode 2 │ ┤ ┴──────────────────────────╵ ┐╷ mode 3 ├┤ ┘╵ └ ┘ 14 19.5 25 Time (ms)	size = (200, 200, 200), rank = 200 ┌ ┐ ┌┐╷ mode 1 ┤├┤ └┘╵ ┐ ╷ mode 2 ├──────────────┤ ┘ ╵ ┌─┐ ╷ mode 3 ┤ ├──┤ └─┘ ╵ └ ┘ 10 20 30 Time (ms)	size = (200, 200, 200), rank = 250 ┌ ┐ ┬─┐╷ mode 1 │ ├┤ ┴─┘╵ ╷ ┌┬┐╷ mode 2 ├───────────────────────┤│├┤ ╵ └┴┘╵ ┬┐ ╷ mode 3 │├─┤ ┴┘ ╵ └ ┘ 23 28.5 34 Time (ms)	size = (200, 200, 200), rank = 300 ┌ ┐ ┬┐ ╷ mode 1 │├─┤ ┴┘ ╵ ┬─────────────┐╷ mode 2 │ ├┤ ┴─────────────┘╵ ┬┐ ╷ mode 3 │├─┤ ┴┘ ╵ └ ┘ 20 30 40 Time (ms)	size = (1000, 100, 30), rank = 10 ┌ ┐ ┐ ╷ mode 1 ├───────────┤ ┘ ╵ ┐ ╷ mode 2 ├──┤ ┘ ╵ ╷┌┐ ╷ mode 3 ├┤├───┤ ╵└┘ ╵ └ ┘ 0 2 4 Time (ms)	size = (1000, 100, 30), rank = 100 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┐ ╷ mode 2 ├──────────────────────┤ ┘ ╵ ╷╷ mode 3 ├┤ ╵╵ └ ┘ 0 15 30 Time (ms)	size = (1000, 100, 30), rank = 200 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┐╷ mode 2 ├┤ ┘╵ ┌╷ mode 3 ┤┤ └╵ └ ┘ 0 20 40 Time (ms)	size = (1000, 100, 30), rank = 300 ┌ ┐ ╷ mode 1 ┤ ╵ ┐╷ mode 2 ├┤ ┘╵ ┌┐ ╷ mode 3 ┤├─┤ └┘ ╵ └ ┘ 0 30 60 Time (ms)
Baseline	size = (30, 100, 1000), rank = 10 ┌ ┐ ┐ ╷ mode 1 ├───────┤ ┘ ╵ ╷┐ ╷ mode 2 ├├─────┤ ╵┘ ╵ ┐ ╷ mode 3 ├──┤ ┘ ╵ └ ┘ 0 2.5 5 Time (ms)	size = (30, 100, 1000), rank = 100 ┌ ┐ ┐ ╷ mode 1 ├─────────────────────┤ ┘ ╵ ╷ mode 2 ┤ ╵ ╷ mode 3 ┤ ╵ └ ┘ 0 50 100 Time (ms)	size = (30, 100, 1000), rank = 200 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┐╷ mode 2 ├┤ ┘╵ ╷ mode 3 ┤ ╵ └ ┘ 0 20 40 Time (ms)	size = (30, 100, 1000), rank = 300 ┌ ┐ ┌╷ mode 1 ┤┤ └╵ ┐╷ mode 2 ├┤ ┘╵ ┐╷ mode 3 ├┤ ┘╵ └ ┘ 0 25 50 Time (ms)	size = (50, 50, 50), rank = 10 ┌ ┐ ┐ ╷ mode 1 ├─────┤ ┘ ╵ ┌┐ ╷ mode 2 ┤├──────────────┤ └┘ ╵ ┐ ╷ mode 3 ├──────┤ ┘ ╵ └ ┘ 0 0.1 0.2 Time (ms)	size = (50, 50, 50), rank = 50 ┌ ┐ ╷┐ ╷ mode 1 ├├────┤ ╵┘ ╵ ┌┐ ╷ mode 2 ┤├─────┤ └┘ ╵ ╷┐ ╷ mode 3 ├├───────┤ ╵┘ ╵ └ ┘ 0.2 0.35 0.5 Time (ms)	size = (50, 50, 50), rank = 100 ┌ ┐ ┬┐ ╷ mode 1 │├──┤ ┴┘ ╵ ┌┐ ╷ mode 2 ┤├────┤ └┘ ╵ ╷┐ ╷ mode 3 ├├───┤ ╵┘ ╵ └ ┘ 0.3 0.45 0.6 Time (ms)	size = (50, 50, 50), rank = 150 ┌ ┐ ┬┐ ╷ mode 1 │├─────┤ ┴┘ ╵ ┐ ╷ mode 2 ├──────┤ ┘ ╵ ╷┬┐ ╷ mode 3 ├│├─────┤ ╵┴┘ ╵ └ ┘ 0.5 0.7 0.9 Time (ms)	size = (50, 50, 50), rank = 200 ┌ ┐ ┌─┐╷ mode 1 ┤ ├┤ └─┘╵ ┐ ╷ mode 2 ├─────┤ ┘ ╵ ┐ ╷ mode 3 ├─────┤ ┘ ╵ └ ┘ 0.6 0.85 1.1 Time (ms)	size = (50, 50, 50), rank = 250 ┌ ┐ ╷ ┌───┐ ╷ mode 1 ├──┤ ├─┤ ╵ └───┘ ╵ ┌┬┐ ╷ mode 2 ┤│├─┤ └┴┘ ╵ ╷┬┐ ╷ mode 3 ├│├───┤ ╵┴┘ ╵ └ ┘ 0.8 1.1 1.4 Time (ms)	size = (50, 50, 50), rank = 300 ┌ ┐ ╷ ┬──┐ ╷ mode 1 ├─│ ├─┤ ╵ ┴──┘ ╵ ╷┐ ╷ mode 2 ├├───┤ ╵┘ ╵ ┌┬┐ ╷ mode 3 ┤│├──┤ └┴┘ ╵ └ ┘ 1 1.25 1.5 Time (ms)	size = (100, 100, 100), rank = 10 ┌ ┐ ┌┐ ╷ mode 1 ┤├───────────┤ └┘ ╵ ┐ ╷ mode 2 ├──────┤ ┘ ╵ ╷┐ ╷ mode 3 ├├────┤ ╵┘ ╵ └ ┘ 0.2 0.55 0.9 Time (ms)	size = (100, 100, 100), rank = 50 ┌ ┐ ┐ ╷ mode 1 ├─┤ ┘ ╵ ┐ ╷ mode 2 ├─┤ ┘ ╵ ┬┐ ╷ mode 3 │├─────┤ ┴┘ ╵ └ ┘ 0 1.5 3 Time (ms)	size = (100, 100, 100), rank = 100 ┌ ┐ ┐ ╷ mode 1 ├──┤ ┘ ╵ ┐ ╷ mode 2 ├─┤ ┘ ╵ ┬┐╷ mode 3 │├┤ ┴┘╵ └ ┘ 1 2 3 Time (ms)	size = (100, 100, 100), rank = 150 ┌ ┐ ╷ mode 1 ┤ ╵ ╷ ┐ ╷ mode 2 ├───────├─────────────┤ ╵ ┘ ╵ ╷ mode 3 ┤ ╵ └ ┘ 0 20 40 Time (ms)	size = (100, 100, 100), rank = 200 ┌ ┐ ╷┌─┬──┐╷ mode 1 ├┤ │ ├┤ ╵└─┴──┘╵ ╷ ┌─┐╷ mode 2 ├─┤ ├┤ ╵ └─┘╵ ┌┐ ╷ mode 3 ┤├─────┤ └┘ ╵ └ ┘ 4 4.35 4.7 Time (ms)	size = (100, 100, 100), rank = 250 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┬───────────────────────────┐╷ mode 2 │ ├┤ ┴───────────────────────────┘╵ ╷ mode 3 ┤ ╵ └ ┘ 5 10 15 Time (ms)	size = (100, 100, 100), rank = 300 ┌ ┐ ╷ mode 1 ┤ ╵ ┌──────────────╷ mode 2 ┤ ┤ └──────────────╵ ┐╷ mode 3 ├┤ ┘╵ └ ┘ 0 10 20 Time (ms)	size = (150, 150, 150), rank = 10 ┌ ┐ ╷ mode 1 ┤ ╵ ┐ ╷ mode 2 ├────────────────────┤ ┘ ╵ ╷ mode 3 ┤ ╵ └ ┘ 0 100 200 Time (ms)	size = (150, 150, 150), rank = 50 ┌ ┐ ╷ mode 1 ┤ ╵ ┌─────────────┬╷ mode 2 ┤ │┤ └─────────────┴╵ ╷ mode 3 ┤ ╵ └ ┘ 0 10 20 Time (ms)	size = (150, 150, 150), rank = 100 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┐ ╷ mode 2 ├────────────────────────────┤ ┘ ╵ ┬╷ mode 3 │┤ ┴╵ └ ┘ 5 10 15 Time (ms)	size = (150, 150, 150), rank = 150 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┐ ╷ mode 2 ├─────────────────────────┤ ┘ ╵ ┐ ╷ mode 3 ├───┤ ┘ ╵ └ ┘ 7 12.5 18 Time (ms)	size = (150, 150, 150), rank = 200 ┌ ┐ ╷┬┐╷ mode 1 ├│├┤ ╵┴┘╵ ╷ ┐ ╷ mode 2 ├─├─┤ ╵ ┘ ╵ ┬─┐ ╷ mode 3 │ ├─┤ ┴─┘ ╵ └ ┘ 9 11 13 Time (ms)	size = (150, 150, 150), rank = 250 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┌─────────────┐╷ mode 2 ┤ ├┤ └─────────────┘╵ ┬╷ mode 3 │┤ ┴╵ └ ┘ 10 20 30 Time (ms)	size = (150, 150, 150), rank = 300 ┌ ┐ ┌┐╷ mode 1 ┤├┤ └┘╵ ┐ ╷ mode 2 ├──────────────────────────┤ ┘ ╵ ┌╷ mode 3 ┤┤ └╵ └ ┘ 14 19.5 25 Time (ms)	size = (200, 200, 200), rank = 10 ┌ ┐ ╷┌─╷ mode 1 ├┤ ┤ ╵└─╵ ┐╷ mode 2 ├┤ ┘╵ ┐╷ mode 3 ├┤ ┘╵ └ ┘ 1 2.5 4 Time (ms)	size = (200, 200, 200), rank = 50 ┌ ┐ ┬╷ mode 1 │┤ ┴╵ ╷ ╷ mode 2 ├─┤ ╵ ╵ ╷ mode 3 ┤ ╵ └ ┘ 8 12.5 17 Time (ms)	size = (200, 200, 200), rank = 100 ┌ ┐ ┌┐ ╷ mode 1 ┤├──────┤ └┘ ╵ ╷┌┬╷ mode 2 ├┤│┤ ╵└┴╵ ┌┐ ╷ mode 3 ┤├─┤ └┘ ╵ └ ┘ 10 12.5 15 Time (ms)	size = (200, 200, 200), rank = 150 ┌ ┐ ╷ mode 1 ┤ ╵ ╷ ┬┐ ╷ mode 2 ├────────│├───────┤ ╵ ┴┘ ╵ ╷ mode 3 ┤ ╵ └ ┘ 10 25 40 Time (ms)	size = (200, 200, 200), rank = 200 ┌ ┐ ╷ mode 1 ┤ ╵ ╷┐ ╷ mode 2 ├├──────────────┤ ╵┘ ╵ ┬─╷ mode 3 │ ┤ ┴─╵ └ ┘ 10 20 30 Time (ms)	size = (200, 200, 200), rank = 250 ┌ ┐ ╷┐╷ mode 1 ├├┤ ╵┘╵ ╷┬─────────────┐╷ mode 2 ├│ ├┤ ╵┴─────────────┘╵ ┐╷ mode 3 ├┤ ┘╵ └ ┘ 20 30 40 Time (ms)	size = (200, 200, 200), rank = 300 ┌ ┐ ┌─┬─┐ ╷ mode 1 ┤ │ ├───────┤ └─┴─┘ ╵ ┐╷ mode 2 ├┤ ┘╵ ┐╷ mode 3 ├┤ ┘╵ └ ┘ 20 35 50 Time (ms)	size = (1000, 100, 30), rank = 10 ┌ ┐ ┬┐ ╷ mode 1 │├────────┤ ┴┘ ╵ ┐ ╷ mode 2 ├──┤ ┘ ╵ ┬─┐ ╷ mode 3 │ ├─┤ ┴─┘ ╵ └ ┘ 0 2 4 Time (ms)	size = (1000, 100, 30), rank = 100 ┌ ┐ ┬┐╷ mode 1 │├┤ ┴┘╵ ┬──────────────┐ ╷ mode 2 │ ├─────┤ ┴──────────────┘ ╵ ┐╷ mode 3 ├┤ ┘╵ └ ┘ 0 10 20 Time (ms)	size = (1000, 100, 30), rank = 200 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┐╷ mode 2 ├┤ ┘╵ ╷ mode 3 ┤ ╵ └ ┘ 0 20 40 Time (ms)	size = (1000, 100, 30), rank = 300 ┌ ┐ ╷ mode 1 ┤ ╵ ╷╷ mode 2 ├┤ ╵╵ ┬┐╷ mode 3 │├┤ ┴┘╵ └ ┘ 0 30 60 Time (ms)

[dahong67]

As desired, with new in-place methods, mttkrp has similar performance as before.

Benchmark Report for GCPDecompositions

Job Properties

• Time of benchmarks:
  • Target: 3 Mar 2024 - 23:54
  • Baseline: 3 Mar 2024 - 23:54
• Package commits:
  • Target: 85a8ed
  • Baseline: 38648a
• Julia commits:
  • Target: bed2cd
  • Baseline: bed2cd
• Julia command flags:
  • Target: None
  • Baseline: None
• Environment variables:
  • Target: GCP_BENCHMARK_SUITES => mttkrp
  • Baseline: GCP_BENCHMARK_SUITES => mttkrp

Results

A ratio greater than 1.0 denotes a possible regression (marked with ❌), while a ratio less
than 1.0 denotes a possible improvement (marked with ✅). Only significant results - results
that indicate possible regressions or improvements - are shown below (thus, an empty table means that all
benchmark results remained invariant between builds).

ID	time ratio	memory ratio
["mttkrp", "size=(100, 100, 100), rank=200, mode=2"]	0.92 (5%) ✅	0.99 (1%)
["mttkrp", "size=(100, 100, 100), rank=200, mode=3"]	1.07 (5%) ❌	1.00 (1%)
["mttkrp", "size=(1000, 100, 30), rank=10, mode=1"]	1.17 (5%) ❌	0.99 (1%)
["mttkrp", "size=(1000, 100, 30), rank=10, mode=2"]	0.94 (5%) ✅	0.98 (1%) ✅
["mttkrp", "size=(1000, 100, 30), rank=100, mode=2"]	0.99 (5%)	0.98 (1%) ✅
["mttkrp", "size=(1000, 100, 30), rank=200, mode=2"]	0.97 (5%)	0.98 (1%) ✅
["mttkrp", "size=(1000, 100, 30), rank=300, mode=1"]	1.06 (5%) ❌	1.00 (1%)
["mttkrp", "size=(1000, 100, 30), rank=300, mode=2"]	0.98 (5%)	0.98 (1%) ✅
["mttkrp", "size=(200, 200, 200), rank=10, mode=1"]	1.12 (5%) ❌	1.00 (1%)
["mttkrp", "size=(200, 200, 200), rank=10, mode=3"]	0.95 (5%) ✅	1.00 (1%)
["mttkrp", "size=(30, 100, 1000), rank=10, mode=2"]	1.02 (5%)	0.98 (1%) ✅
["mttkrp", "size=(30, 100, 1000), rank=100, mode=1"]	1.07 (5%) ❌	1.00 (1%)
["mttkrp", "size=(30, 100, 1000), rank=100, mode=2"]	0.97 (5%)	0.98 (1%) ✅
["mttkrp", "size=(30, 100, 1000), rank=200, mode=2"]	0.97 (5%)	0.98 (1%) ✅
["mttkrp", "size=(30, 100, 1000), rank=300, mode=1"]	0.94 (5%) ✅	1.00 (1%)
["mttkrp", "size=(30, 100, 1000), rank=300, mode=2"]	0.97 (5%)	0.98 (1%) ✅
["mttkrp", "size=(50, 50, 50), rank=10, mode=2"]	0.97 (5%)	0.97 (1%) ✅
["mttkrp", "size=(50, 50, 50), rank=100, mode=2"]	0.90 (5%) ✅	0.98 (1%) ✅
["mttkrp", "size=(50, 50, 50), rank=150, mode=2"]	0.91 (5%) ✅	0.98 (1%) ✅
["mttkrp", "size=(50, 50, 50), rank=200, mode=2"]	0.89 (5%) ✅	0.98 (1%) ✅
["mttkrp", "size=(50, 50, 50), rank=250, mode=2"]	0.86 (5%) ✅	0.98 (1%) ✅
["mttkrp", "size=(50, 50, 50), rank=300, mode=2"]	0.87 (5%) ✅	0.98 (1%) ✅
["mttkrp", "size=(50, 50, 50), rank=50, mode=2"]	0.86 (5%) ✅	0.98 (1%) ✅

Benchmark Group List

Here's a list of all the benchmark groups executed by this job:

• ["mttkrp"]

Julia versioninfo

Target

Julia Version 1.9.3
Commit bed2cd540a1 (2023-08-24 14:43 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (arm64-apple-darwin22.4.0)
  uname: Darwin 23.2.0 Darwin Kernel Version 23.2.0: Wed Nov 15 21:53:18 PST 2023; root:xnu-10002.61.3~2/RELEASE_ARM64_T6000 arm64 arm
  CPU: Apple M1 Max: 
                 speed         user         nice          sys         idle          irq
       #1-10  2400 MHz    1588339 s          0 s     606505 s   21093654 s          0 s
  Memory: 64.0 GB (33643.921875 MB free)
  Uptime: 498837.0 sec
  Load Avg:  5.25634765625  3.19482421875  3.0380859375
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-14.0.6 (ORCJIT, apple-m1)
  Threads: 1 on 8 virtual cores

Baseline

Julia Version 1.9.3
Commit bed2cd540a1 (2023-08-24 14:43 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (arm64-apple-darwin22.4.0)
  uname: Darwin 23.2.0 Darwin Kernel Version 23.2.0: Wed Nov 15 21:53:18 PST 2023; root:xnu-10002.61.3~2/RELEASE_ARM64_T6000 arm64 arm
  CPU: Apple M1 Max: 
                 speed         user         nice          sys         idle          irq
       #1-10  2400 MHz    1589686 s          0 s     607606 s   21094507 s          0 s
  Memory: 64.0 GB (33974.0625 MB free)
  Uptime: 498871.0 sec
  Load Avg:  6.8251953125  3.79345703125  3.26025390625
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-14.0.6 (ORCJIT, apple-m1)
  Threads: 1 on 8 virtual cores

MTTKRP benchmark plots

Runtime vs. size (for square tensors)

Below are plots showing the runtime in miliseconds of MTTKRP as a function of the size of the square tensor, for varying ranks and modes:

	ndims = 3, rank = 10, mode = 1	ndims = 3, rank = 10, mode = 2	ndims = 3, rank = 10, mode = 3	ndims = 3, rank = 50, mode = 1	ndims = 3, rank = 50, mode = 2	ndims = 3, rank = 50, mode = 3	ndims = 3, rank = 100, mode = 1	ndims = 3, rank = 100, mode = 2	ndims = 3, rank = 100, mode = 3	ndims = 3, rank = 150, mode = 1	ndims = 3, rank = 150, mode = 2	ndims = 3, rank = 150, mode = 3	ndims = 3, rank = 200, mode = 1	ndims = 3, rank = 200, mode = 2	ndims = 3, rank = 200, mode = 3	ndims = 3, rank = 250, mode = 1	ndims = 3, rank = 250, mode = 2	ndims = 3, rank = 250, mode = 3	ndims = 3, rank = 300, mode = 1	ndims = 3, rank = 300, mode = 2	ndims = 3, rank = 300, mode = 3
Target	ndims = 3, rank = 10, mode = 1 ┌──────────────────────────────┐ 4 │ .'│ │ .' │ │ : │ │ .' │ Time (ms) │ : │ │ : │ │ .'' │ │ .' │ │ ....' │ 0 │ .'''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 10, mode = 2 ┌──────────────────────────────┐ 2 │ │ │ .'│ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ .' │ │ .' │ │ ...' │ 0 │ ..'''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 10, mode = 3 ┌──────────────────────────────┐ 3 │ .│ │ : │ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ .' │ │ .'' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 50, mode = 1 ┌──────────────────────────────┐ 10 │ .│ │ .' │ │ .' │ │ .' │ Time (ms) │ .' │ │ : │ │ .'' │ │ .' │ │ ...''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 50, mode = 2 ┌──────────────────────────────┐ 7 │ .│ │ : │ │ .' │ │ .' │ Time (ms) │ .' │ │ .'' │ │ .' │ │ .' │ │ .: │ 0 │ ..''''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 50, mode = 3 ┌──────────────────────────────┐ 9 │ .│ │ : │ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ .' │ │ .'' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 100, mode = 1 ┌──────────────────────────────┐ 20 │ │ │ │ │ │ │ ..│ Time (ms) │ .' │ │ .' │ │ .' │ │ ..'' │ │ ....' │ 0 │ ..'''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 100, mode = 2 ┌──────────────────────────────┐ 20 │ │ │ │ │ │ │ │ Time (ms) │ .│ │ .'' │ │ ..' │ │ ..' │ │ ..' │ 0 │ ......'''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 100, mode = 3 ┌──────────────────────────────┐ 20 │ │ │ │ │ │ │ .│ Time (ms) │ ..' │ │ .' │ │ .' │ │ ..'' │ │ ...'' │ 0 │ ..'''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 150, mode = 1 ┌──────────────────────────────┐ 20 │ │ │ .'│ │ .' │ │ : │ Time (ms) │ .' │ │ .' │ │ .' │ │ .'' │ │ ..''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 150, mode = 2 ┌──────────────────────────────┐ 20 │ │ │ │ │ │ │ .'│ Time (ms) │ ..' │ │ .' │ │ .: │ │ ..'' │ │ ...'' │ 0 │ ..''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 150, mode = 3 ┌──────────────────────────────┐ 20 │ │ │ .'│ │ .' │ │ .' │ Time (ms) │ .' │ │ .: │ │ .' │ │ .'' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 200, mode = 1 ┌──────────────────────────────┐ 30 │ │ │ │ │ .│ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ ..' │ │ ...'' │ 0 │ ..''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 200, mode = 2 ┌──────────────────────────────┐ 20 │ .│ │ .'│ │ .' │ │ .' │ Time (ms) │ .' │ │ .: │ │ .' │ │ .'' │ │ ..''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 200, mode = 3 ┌──────────────────────────────┐ 30 │ │ │ │ │ .│ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ .'' │ │ ...''' │ 0 │ ..'' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 250, mode = 1 ┌──────────────────────────────┐ 30 │ │ │ .'│ │ .' │ │ : │ Time (ms) │ .' │ │ .' │ │ .' │ │ .'' │ │ ..''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 250, mode = 2 ┌──────────────────────────────┐ 30 │ │ │ │ │ .│ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ .'' │ │ ..''' │ 0 │ ..''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 250, mode = 3 ┌──────────────────────────────┐ 30 │ │ │ .'│ │ .' │ │ : │ Time (ms) │ .' │ │ .' │ │ ..' │ │ .' │ │ ..''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 300, mode = 1 ┌──────────────────────────────┐ 40 │ │ │ .│ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ .'' │ │ ..' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 300, mode = 2 ┌──────────────────────────────┐ 30 │ .│ │ : │ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ .' │ │ ..''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 300, mode = 3 ┌──────────────────────────────┐ 40 │ │ │ .│ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ ..' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size
Baseline	ndims = 3, rank = 10, mode = 1 ┌──────────────────────────────┐ 4 │ │ │ .'│ │ .' │ │ .' │ Time (ms) │ .' │ │ .: │ │ .' │ │ .' │ │ ....' │ 0 │ ..''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 10, mode = 2 ┌──────────────────────────────┐ 2 │ │ │ .'│ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ .' │ │ .' │ │ ..: │ 0 │ ..'''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 10, mode = 3 ┌──────────────────────────────┐ 3 │ :│ │ .' │ │ : │ │ .' │ Time (ms) │ : │ │ .' │ │ .' │ │ .'' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 50, mode = 1 ┌──────────────────────────────┐ 10 │ .│ │ .'│ │ .' │ │ .' │ Time (ms) │ .' │ │ .: │ │ .' │ │ ..' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 50, mode = 2 ┌──────────────────────────────┐ 20 │ │ │ .│ │ ...'' │ │ :' │ Time (ms) │ : │ │ .' │ │ .' │ │ .' │ │ : │ 0 │ ........: │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 50, mode = 3 ┌──────────────────────────────┐ 9 │ .│ │ .' │ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ .' │ │ .'' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 100, mode = 1 ┌──────────────────────────────┐ 20 │ │ │ │ │ │ │ .'│ Time (ms) │ .' │ │ .' │ │ .' │ │ ..'' │ │ ...'' │ 0 │ ..'''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 100, mode = 2 ┌──────────────────────────────┐ 20 │ │ │ │ │ .. │ │ : '''...│ Time (ms) │ : │ │ .' │ │ .' │ │ .' │ │ .' │ 0 │ ......''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 100, mode = 3 ┌──────────────────────────────┐ 20 │ │ │ │ │ │ │ .│ Time (ms) │ .' │ │ .'' │ │ .' │ │ ..'' │ │ ....' │ 0 │ ..'''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 150, mode = 1 ┌──────────────────────────────┐ 20 │ .│ │ .'│ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ .' │ │ .'' │ │ ..''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 150, mode = 2 ┌──────────────────────────────┐ 20 │ │ │ ... │ │ : '''..│ │ .' │ Time (ms) │ .' │ │ .' │ │ .' │ │ .' │ │ ..'' │ 0 │ ..''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 150, mode = 3 ┌──────────────────────────────┐ 20 │ │ │ .'│ │ .' │ │ : │ Time (ms) │ .' │ │ .: │ │ .' │ │ .'' │ │ ..''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 200, mode = 1 ┌──────────────────────────────┐ 30 │ │ │ │ │ .│ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ ..' │ │ ...'' │ 0 │ ..''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 200, mode = 2 ┌──────────────────────────────┐ 20 │ .│ │ .'│ │ .' │ │ :''.. .' │ Time (ms) │ : '.. .' │ │ : ' │ │ .' │ │ .' │ │ .' │ 0 │ .' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 200, mode = 3 ┌──────────────────────────────┐ 30 │ │ │ │ │ .│ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ ..' │ │ ....' │ 0 │ ..''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 250, mode = 1 ┌──────────────────────────────┐ 30 │ .│ │ .'│ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ ..' │ │ .' │ │ ..''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 250, mode = 2 ┌──────────────────────────────┐ 30 │ │ │ │ │ .│ │ .' │ Time (ms) │ .' │ │ .' │ │ .'' │ │ ..'' │ │ ...'' │ 0 │ ..'' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 250, mode = 3 ┌──────────────────────────────┐ 30 │ │ │ .'│ │ .' │ │ : │ Time (ms) │ .' │ │ .' │ │ ..' │ │ .' │ │ ..''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 300, mode = 1 ┌──────────────────────────────┐ 40 │ │ │ .│ │ .' │ │ .' │ Time (ms) │ .' │ │ .' │ │ .'' │ │ ..' │ │ ...'' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 300, mode = 2 ┌──────────────────────────────┐ 30 │ │ │ .'│ │ .' │ │ : │ Time (ms) │ .' │ │ .' │ │ .'' │ │ .' │ │ ..''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size	ndims = 3, rank = 300, mode = 3 ┌──────────────────────────────┐ 40 │ │ │ .│ │ .' │ │ : │ Time (ms) │ .' │ │ .' │ │ ..' │ │ .' │ │ ...''' │ 0 │ .''' │ └──────────────────────────────┘ 0 200 Size

Runtime vs. rank

Below are plots showing the runtime in miliseconds of MTTKRP as a function of the size of the rank, for varying sizes and modes:

	size = (30, 100, 1000), mode = 1	size = (30, 100, 1000), mode = 2	size = (30, 100, 1000), mode = 3	size = (50, 50, 50), mode = 1	size = (50, 50, 50), mode = 2	size = (50, 50, 50), mode = 3	size = (100, 100, 100), mode = 1	size = (100, 100, 100), mode = 2	size = (100, 100, 100), mode = 3	size = (150, 150, 150), mode = 1	size = (150, 150, 150), mode = 2	size = (150, 150, 150), mode = 3	size = (200, 200, 200), mode = 1	size = (200, 200, 200), mode = 2	size = (200, 200, 200), mode = 3	size = (1000, 100, 30), mode = 1	size = (1000, 100, 30), mode = 2	size = (1000, 100, 30), mode = 3
Target	size = (30, 100, 1000), mode = 1 ┌──────────────────────────────┐ 50 │ .│ │ ..'│ │ ..'' │ │ ..'' │ Time (ms) │ ..' │ │ ..'' │ │ ..' │ │ .'' │ │ .'' │ 0 │ '' │ └──────────────────────────────┘ 0 300 Rank	size = (30, 100, 1000), mode = 2 ┌──────────────────────────────┐ 7 │ .:│ │ .' │ │ .'' │ │ .'' │ Time (ms) │ ...'' │ │ ..'' │ │ .'' │ │ ..'' │ │ ..' │ 0 │ │ └──────────────────────────────┘ 0 300 Rank	size = (30, 100, 1000), mode = 3 ┌──────────────────────────────┐ 9 │ .│ │ .'│ │ .'' │ │ ..' │ Time (ms) │ ..' │ │ ..''' │ │ ..'' │ │ ..'' │ │ ..'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (50, 50, 50), mode = 1 ┌──────────────────────────────┐ 2 │ │ │ │ │ │ │ ...'│ Time (ms) │ ..''' │ │ ..''' │ │ ...'' │ │ ...'' │ │ ..'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (50, 50, 50), mode = 2 ┌──────────────────────────────┐ 1 │ :│ │ .' │ │ .'' │ │ ..'' │ Time (ms) │ ..'' │ │ ..' │ │ ..'' │ │ ..' │ │ ..'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (50, 50, 50), mode = 3 ┌──────────────────────────────┐ 2 │ │ │ │ │ .│ │ ..''│ Time (ms) │ ..''' │ │ ..'' │ │ ...'' │ │ ...''' │ │ .'' │ 0 │ '' │ └──────────────────────────────┘ 0 300 Rank	size = (100, 100, 100), mode = 1 ┌──────────────────────────────┐ 7 │ :│ │ .'' │ │ ..'' │ │ .'' │ Time (ms) │ ..'' │ │ ..' │ │ ..' │ │ .''' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (100, 100, 100), mode = 2 ┌──────────────────────────────┐ 6 │ .:│ │ ..' │ │ ..' │ │ ..' │ Time (ms) │ ..''' │ │ : │ │ .' │ │ : │ │ ...''' │ 0 │ .'' │ └──────────────────────────────┘ 0 300 Rank	size = (100, 100, 100), mode = 3 ┌──────────────────────────────┐ 7 │ :│ │ .'' │ │ ...''' │ │ .' │ Time (ms) │ .' │ │ ..'' │ │ ..'' │ │ ..' │ │ ..' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (150, 150, 150), mode = 1 ┌──────────────────────────────┐ 20 │ │ │ .'│ │ ..' │ │ ..'' │ Time (ms) │ ..'' │ │ ..'' │ │ ..'' │ │ ..'' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (150, 150, 150), mode = 2 ┌──────────────────────────────┐ 20 │ │ │ │ │ .│ │ ..''│ Time (ms) │ ..'' │ │ ...'' │ │ ...'' │ │ ..''' │ │ ..'' │ 0 │ .' │ └──────────────────────────────┘ 0 300 Rank	size = (150, 150, 150), mode = 3 ┌──────────────────────────────┐ 20 │ │ │ .:│ │ .'' │ │ ..'' │ Time (ms) │ ..'' │ │ ..'' │ │ ..'' │ │ ..'' │ │ ..' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (200, 200, 200), mode = 1 ┌──────────────────────────────┐ 40 │ │ │ :│ │ .'' │ │ ..'' │ Time (ms) │ ...'' │ │ ..'' │ │ ..'' │ │ ..''' │ │ .' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (200, 200, 200), mode = 2 ┌──────────────────────────────┐ 30 │ .│ │ .' │ │ ..' │ │ ..'' │ Time (ms) │ ..'' │ │ ..'' │ │ ..'' │ │ ..' │ │ ..' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (200, 200, 200), mode = 3 ┌──────────────────────────────┐ 40 │ │ │ :│ │ .'' │ │ ..'' │ Time (ms) │ ..'' │ │ ..'' │ │ ..''' │ │ ..'' │ │ ..' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (1000, 100, 30), mode = 1 ┌──────────────────────────────┐ 9 │ :│ │ .' │ │ .' │ │ .'' │ Time (ms) │ ..' │ │ ...'' │ │ ...'' │ │ ..'' │ │ ..'' │ 0 │ │ └──────────────────────────────┘ 0 300 Rank	size = (1000, 100, 30), mode = 2 ┌──────────────────────────────┐ 7 │ .:│ │ ..' │ │ .' │ │ ..'' │ Time (ms) │ ...'' │ │ .''' │ │ .'' │ │ .'' │ │ ..' │ 0 │ │ └──────────────────────────────┘ 0 300 Rank	size = (1000, 100, 30), mode = 3 ┌──────────────────────────────┐ 50 │ .│ │ .'' │ │ ..'' │ │ .'' │ Time (ms) │ ..'' │ │ ..' │ │ .'' │ │ .'' │ │ .'' │ 0 │ '' │ └──────────────────────────────┘ 0 300 Rank
Baseline	size = (30, 100, 1000), mode = 1 ┌──────────────────────────────┐ 50 │ :│ │ .'' │ │ ..'' │ │ ..' │ Time (ms) │ ..' │ │ .'' │ │ ..'' │ │ ..' │ │ .'' │ 0 │ '' │ └──────────────────────────────┘ 0 300 Rank	size = (30, 100, 1000), mode = 2 ┌──────────────────────────────┐ 8 │ │ │ .:│ │ .'' │ │ .'' │ Time (ms) │ ..'' │ │ ..''' │ │ ..'' │ │ ..'' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (30, 100, 1000), mode = 3 ┌──────────────────────────────┐ 8 │ .│ │ ..'│ │ .'' │ │ .'' │ Time (ms) │ ...'' │ │ ..'' │ │ ..'' │ │ ..' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (50, 50, 50), mode = 1 ┌──────────────────────────────┐ 2 │ │ │ │ │ .│ │ ...''│ Time (ms) │ ...'' │ │ ..' │ │ ..''' │ │ ..''' │ │ ..'' │ 0 │ '' │ └──────────────────────────────┘ 0 300 Rank	size = (50, 50, 50), mode = 2 ┌──────────────────────────────┐ 1.1 │ :│ │ .'' │ │ .'' │ │ ..'' │ Time (ms) │ ..' │ │ .'' │ │ ..'' │ │ .'' │ │ .'' │ 0 │ '' │ └──────────────────────────────┘ 0 300 Rank	size = (50, 50, 50), mode = 3 ┌──────────────────────────────┐ 2 │ │ │ │ │ .│ │ ..''│ Time (ms) │ ..'' │ │ ..''' │ │ ..''' │ │ ...''' │ │ .'' │ 0 │ '' │ └──────────────────────────────┘ 0 300 Rank	size = (100, 100, 100), mode = 1 ┌──────────────────────────────┐ 7 │ .:│ │ .' │ │ ..'' │ │ .'' │ Time (ms) │ ..'' │ │ .'' │ │ ..'' │ │ .'' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (100, 100, 100), mode = 2 ┌──────────────────────────────┐ 20 │ │ │ │ │ │ │ :: │ Time (ms) │ : : │ │ : : │ │ : '. │ │ : ''''''│ │ ...' │ 0 │ ......''''' │ └──────────────────────────────┘ 0 300 Rank	size = (100, 100, 100), mode = 3 ┌──────────────────────────────┐ 7 │ .│ │ ..'' │ │ .' │ │ ..'' │ Time (ms) │ ..'' │ │ ..' │ │ ..' │ │ ..'' │ │ ..' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (150, 150, 150), mode = 1 ┌──────────────────────────────┐ 20 │ │ │ .'│ │ ..'' │ │ ..' │ Time (ms) │ ..'' │ │ ..'' │ │ ..'' │ │ .''' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (150, 150, 150), mode = 2 ┌──────────────────────────────┐ 20 │ │ │ .. │ │ ...''' '. .│ │ :''' '. .'' │ Time (ms) │ .' : ..'' │ │ : ''' │ │ : │ │ .' │ │ : │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (150, 150, 150), mode = 3 ┌──────────────────────────────┐ 20 │ │ │ .:│ │ ..' │ │ .'' │ Time (ms) │ ...'' │ │ ..'' │ │ ..'' │ │ ..'' │ │ ..' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (200, 200, 200), mode = 1 ┌──────────────────────────────┐ 40 │ │ │ :│ │ ..'' │ │ ..' │ Time (ms) │ ..'' │ │ ..''' │ │ ..'' │ │ .''' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (200, 200, 200), mode = 2 ┌──────────────────────────────┐ 30 │ .│ │ ..' │ │ .'' │ │ ..' │ Time (ms) │ .'. ..'' │ │ .' ''.....'' │ │ : │ │ : │ │ : │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (200, 200, 200), mode = 3 ┌──────────────────────────────┐ 40 │ │ │ :│ │ .'' │ │ ..'' │ Time (ms) │ ..'' │ │ ..''' │ │ ..'' │ │ ..'' │ │ ..' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (1000, 100, 30), mode = 1 ┌──────────────────────────────┐ 8 │ .│ │ .''│ │ .'' │ │ .'' │ Time (ms) │ ..''' │ │ ...'' │ │ .'' │ │ .'' │ │ .'' │ 0 │ ' │ └──────────────────────────────┘ 0 300 Rank	size = (1000, 100, 30), mode = 2 ┌──────────────────────────────┐ 7 │ .'│ │ .'' │ │ .'' │ │ ..' │ Time (ms) │ ..'' │ │ ..''' │ │ ..' │ │ ..' │ │ ..' │ 0 │ │ └──────────────────────────────┘ 0 300 Rank	size = (1000, 100, 30), mode = 3 ┌──────────────────────────────┐ 50 │ .│ │ .'' │ │ ..'' │ │ ..' │ Time (ms) │ ..'' │ │ ..' │ │ .'' │ │ .'' │ │ .'' │ 0 │ '' │ └──────────────────────────────┘ 0 300 Rank

Runtime vs. mode

Below are plots showing the runtime in miliseconds of MTTKRP as a function of the mode, for varying sizes and ranks:

	size = (30, 100, 1000), rank = 10	size = (30, 100, 1000), rank = 100	size = (30, 100, 1000), rank = 200	size = (30, 100, 1000), rank = 300	size = (50, 50, 50), rank = 10	size = (50, 50, 50), rank = 50	size = (50, 50, 50), rank = 100	size = (50, 50, 50), rank = 150	size = (50, 50, 50), rank = 200	size = (50, 50, 50), rank = 250	size = (50, 50, 50), rank = 300	size = (100, 100, 100), rank = 10	size = (100, 100, 100), rank = 50	size = (100, 100, 100), rank = 100	size = (100, 100, 100), rank = 150	size = (100, 100, 100), rank = 200	size = (100, 100, 100), rank = 250	size = (100, 100, 100), rank = 300	size = (150, 150, 150), rank = 10	size = (150, 150, 150), rank = 50	size = (150, 150, 150), rank = 100	size = (150, 150, 150), rank = 150	size = (150, 150, 150), rank = 200	size = (150, 150, 150), rank = 250	size = (150, 150, 150), rank = 300	size = (200, 200, 200), rank = 10	size = (200, 200, 200), rank = 50	size = (200, 200, 200), rank = 100	size = (200, 200, 200), rank = 150	size = (200, 200, 200), rank = 200	size = (200, 200, 200), rank = 250	size = (200, 200, 200), rank = 300	size = (1000, 100, 30), rank = 10	size = (1000, 100, 30), rank = 100	size = (1000, 100, 30), rank = 200	size = (1000, 100, 30), rank = 300
Target	size = (30, 100, 1000), rank = 10 ┌ ┐ ╷┐ ╷ mode 1 ├├──┤ ╵┘ ╵ ┐╷ mode 2 ├┤ ┘╵ ┬┐ ╷ mode 3 │├──┤ ┴┘ ╵ └ ┘ 0 2 4 Time (ms)	size = (30, 100, 1000), rank = 100 ┌ ┐ ┐ ╷ mode 1 ├────────────┤ ┘ ╵ ╷ mode 2 ┤ ╵ ╷ mode 3 ┤ ╵ └ ┘ 0 100 200 Time (ms)	size = (30, 100, 1000), rank = 200 ┌ ┐ ╷┐╷ mode 1 ├├┤ ╵┘╵ ╷ mode 2 ┤ ╵ ╷ mode 3 ┤ ╵ └ ┘ 0 20 40 Time (ms)	size = (30, 100, 1000), rank = 300 ┌ ┐ ╷┐╷ mode 1 ├├┤ ╵┘╵ ┐╷ mode 2 ├┤ ┘╵ ╷╷ mode 3 ├┤ ╵╵ └ ┘ 0 25 50 Time (ms)	size = (50, 50, 50), rank = 10 ┌ ┐ ┌┬┐ ╷ mode 1 ┤│├─────┤ └┴┘ ╵ ┐ ╷ mode 2 ├────────┤ ┘ ╵ ┌┐ ╷ mode 3 ┤├──┤ └┘ ╵ └ ┘ 0 0.15 0.3 Time (ms)	size = (50, 50, 50), rank = 50 ┌ ┐ ┐ ╷ mode 1 ├────────────────────────┤ ┘ ╵ ╷ mode 2 ┤ ╵ ╷ mode 3 ┤ ╵ └ ┘ 0 3 6 Time (ms)	size = (50, 50, 50), rank = 100 ┌ ┐ ╷┐ ╷ mode 1 ├├─┤ ╵┘ ╵ ┐ ╷ mode 2 ├───┤ ┘ ╵ ╷┬┐ ╷ mode 3 ├│├───┤ ╵┴┘ ╵ └ ┘ 0.3 0.5 0.7 Time (ms)	size = (50, 50, 50), rank = 150 ┌ ┐ ╷┬┐ ╷ mode 1 ├│├──┤ ╵┴┘ ╵ ┌┐ ╷ mode 2 ┤├─┤ └┘ ╵ ┬┐ ╷ mode 3 │├──┤ ┴┘ ╵ └ ┘ 0.4 0.65 0.9 Time (ms)	size = (50, 50, 50), rank = 200 ┌ ┐ ╷┌┬┐ ╷ mode 1 ├┤│├────┤ ╵└┴┘ ╵ ┐ ╷ mode 2 ├─┤ ┘ ╵ ╷┬─┐ ╷ mode 3 ├│ ├───┤ ╵┴─┘ ╵ └ ┘ 0.6 0.85 1.1 Time (ms)	size = (50, 50, 50), rank = 250 ┌ ┐ ╷┌─┐ ╷ mode 1 ├┤ ├──┤ ╵└─┘ ╵ ┌┐ ╷ mode 2 ┤├──┤ └┘ ╵ ┌┐ ╷ mode 3 ┤├──┤ └┘ ╵ └ ┘ 0.7 1 1.3 Time (ms)	size = (50, 50, 50), rank = 300 ┌ ┐ ╷┐ ╷ mode 1 ├├────┤ ╵┘ ╵ ╷┌┬────┐ ╷ mode 2 ├┤│ ├──────────────┤ ╵└┴────┘ ╵ ╷┬┐ ╷ mode 3 ├│├──┤ ╵┴┘ ╵ └ ┘ 0.9 1.25 1.6 Time (ms)	size = (100, 100, 100), rank = 10 ┌ ┐ ╷┐ ╷ mode 1 ├├───────────┤ ╵┘ ╵ ╷┬┐ ╷ mode 2 ├│├────┤ ╵┴┘ ╵ ┐ ╷ mode 3 ├────┤ ┘ ╵ └ ┘ 0.2 0.5 0.8 Time (ms)	size = (100, 100, 100), rank = 50 ┌ ┐ ┬┐ ╷ mode 1 │├───┤ ┴┘ ╵ ┌┐ ╷ mode 2 ┤├──┤ └┘ ╵ ┬┐ ╷ mode 3 │├──┤ ┴┘ ╵ └ ┘ 0.7 1.25 1.8 Time (ms)	size = (100, 100, 100), rank = 100 ┌ ┐ ┬╷ mode 1 │┤ ┴╵ ┐ ╷ mode 2 ├─┤ ┘ ╵ ┬┐╷ mode 3 │├┤ ┴┘╵ └ ┘ 1 2 3 Time (ms)	size = (100, 100, 100), rank = 150 ┌ ┐ ╷ mode 1 ┤ ╵ ┐ ╷ mode 2 ├──────────────┤ ┘ ╵ ╷ mode 3 ┤ ╵ └ ┘ 0 10 20 Time (ms)	size = (100, 100, 100), rank = 200 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┬─────────────────────────┐╷ mode 2 │ ├┤ ┴─────────────────────────┘╵ ╷┬─┐╷ mode 3 ├│ ├┤ ╵┴─┘╵ └ ┘ 3 8.5 14 Time (ms)	size = (100, 100, 100), rank = 250 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┬┐ ╷ mode 2 │├─────────────────────────┤ ┴┘ ╵ ┬╷ mode 3 │┤ ┴╵ └ ┘ 4 9.5 15 Time (ms)	size = (100, 100, 100), rank = 300 ┌ ┐ ┌╷ mode 1 ┤┤ └╵ ╷┐ ╷ mode 2 ├├─────────────────────────┤ ╵┘ ╵ ┌╷ mode 3 ┤┤ └╵ └ ┘ 5 10.5 16 Time (ms)	size = (150, 150, 150), rank = 10 ┌ ┐ ╷ mode 1 ┤ ╵ ┐ ╷ mode 2 ├────────────────────────┤ ┘ ╵ ╷ mode 3 ┤ ╵ └ ┘ 0 250 500 Time (ms)	size = (150, 150, 150), rank = 50 ┌ ┐ ╷╷ mode 1 ├┤ ╵╵ ┬───────────────────────────┐╷ mode 2 │ ├┤ ┴───────────────────────────┘╵ ╷ mode 3 ┤ ╵ └ ┘ 3 8 13 Time (ms)	size = (150, 150, 150), rank = 100 ┌ ┐ ╷ mode 1 ┤ ╵ ┬─┐ ╷ mode 2 │ ├───┤ ┴─┘ ╵ ┐ ╷ mode 3 ├────────────────┤ ┘ ╵ └ ┘ 0 10 20 Time (ms)	size = (150, 150, 150), rank = 150 ┌ ┐ ┌┬┐╷ mode 1 ┤│├┤ └┴┘╵ ╷┐ ╷ mode 2 ├├─┤ ╵┘ ╵ ┐ ╷ mode 3 ├─┤ ┘ ╵ └ ┘ 7 8.5 10 Time (ms)	size = (150, 150, 150), rank = 200 ┌ ┐ ┬╷ mode 1 │┤ ┴╵ ╷ ╷ mode 2 ├─┤ ╵ ╵ ┬┐╷ mode 3 │├┤ ┴┘╵ └ ┘ 8 10.5 13 Time (ms)	size = (150, 150, 150), rank = 250 ┌ ┐ ╷╷ mode 1 ├┤ ╵╵ ┐ ╷ mode 2 ├─────────────────────────┤ ┘ ╵ ┬╷ mode 3 │┤ ┴╵ └ ┘ 11 16.5 22 Time (ms)	size = (150, 150, 150), rank = 300 ┌ ┐ ┐ ╷ mode 1 ├───────────────────────┤ ┘ ╵ ┌┐ ╷ mode 2 ┤├────┤ └┘ ╵ ┐╷ mode 3 ├┤ ┘╵ └ ┘ 10 35 60 Time (ms)	size = (200, 200, 200), rank = 10 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┐╷ mode 2 ├┤ ┘╵ ╷╷ mode 3 ├┤ ╵╵ └ ┘ 1 3 5 Time (ms)	size = (200, 200, 200), rank = 50 ┌ ┐ ╷ mode 1 ┤ ╵ ╷╷ mode 2 ├┤ ╵╵ ┐ ╷ mode 3 ├───────────────┤ ┘ ╵ └ ┘ 0 15 30 Time (ms)	size = (200, 200, 200), rank = 100 ┌ ┐ ╷ mode 1 ┤ ╵ ┬──────────────╷ mode 2 │ ┤ ┴──────────────╵ ╷ mode 3 ┤ ╵ └ ┘ 10 20 30 Time (ms)	size = (200, 200, 200), rank = 150 ┌ ┐ ╷┬┐ ╷ mode 1 ├│├─┤ ╵┴┘ ╵ ┬╷ mode 2 │┤ ┴╵ ┬╷ mode 3 │┤ ┴╵ └ ┘ 14 16.5 19 Time (ms)	size = (200, 200, 200), rank = 200 ┌ ┐ ╷╷ mode 1 ├┤ ╵╵ ┬─────╷ mode 2 │ ┤ ┴─────╵ ┬──────┐ ╷ mode 3 │ ├──────────┤ ┴──────┘ ╵ └ ┘ 10 35 60 Time (ms)	size = (200, 200, 200), rank = 250 ┌ ┐ ┌╷ mode 1 ┤┤ └╵ ┬╷ mode 2 │┤ ┴╵ ┌┐╷ mode 3 ┤├┤ └┘╵ └ ┘ 22 25 28 Time (ms)	size = (200, 200, 200), rank = 300 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┬┐ ╷ mode 2 │├───────────────┤ ┴┘ ╵ ┬╷ mode 3 │┤ ┴╵ └ ┘ 20 35 50 Time (ms)	size = (1000, 100, 30), rank = 10 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┐ ╷ mode 2 ├─┤ ┘ ╵ ┌┐ ╷ mode 3 ┤├──┤ └┘ ╵ └ ┘ 0 2 4 Time (ms)	size = (1000, 100, 30), rank = 100 ┌ ┐ ┬╷ mode 1 │┤ ┴╵ ┌┬───┐ ╷ mode 2 ┤│ ├─────────┤ └┴───┘ ╵ ╷ mode 3 ┤ ╵ └ ┘ 0 10 20 Time (ms)	size = (1000, 100, 30), rank = 200 ┌ ┐ ╷ mode 1 ┤ ╵ ┐╷ mode 2 ├┤ ┘╵ ┬─╷ mode 3 │ ┤ ┴─╵ └ ┘ 0 20 40 Time (ms)	size = (1000, 100, 30), rank = 300 ┌ ┐ ┐ ╷ mode 1 ├─┤ ┘ ╵ ╷ mode 2 ┤ ╵ ╷ mode 3 ┤ ╵ └ ┘ 0 25 50 Time (ms)
Baseline	size = (30, 100, 1000), rank = 10 ┌ ┐ ┌┐ ╷ mode 1 ┤├────────┤ └┘ ╵ ┐ ╷ mode 2 ├─────┤ ┘ ╵ ┐ ╷ mode 3 ├─┤ ┘ ╵ └ ┘ 0 3 6 Time (ms)	size = (30, 100, 1000), rank = 100 ┌ ┐ ┌┐ ╷ mode 1 ┤├───────────────────────┤ └┘ ╵ ╷ mode 2 ┤ ╵ ╷ mode 3 ┤ ╵ └ ┘ 0 45 90 Time (ms)	size = (30, 100, 1000), rank = 200 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┐╷ mode 2 ├┤ ┘╵ ╷ mode 3 ┤ ╵ └ ┘ 0 20 40 Time (ms)	size = (30, 100, 1000), rank = 300 ┌ ┐ ┌┐╷ mode 1 ┤├┤ └┘╵ ┐ ╷ mode 2 ├─────┤ ┘ ╵ ┐╷ mode 3 ├┤ ┘╵ └ ┘ 0 25 50 Time (ms)	size = (50, 50, 50), rank = 10 ┌ ┐ ┐ ╷ mode 1 ├──────┤ ┘ ╵ ┌┐ ╷ mode 2 ┤├───────────────┤ └┘ ╵ ┬┐ ╷ mode 3 │├───────┤ ┴┘ ╵ └ ┘ 0 0.1 0.2 Time (ms)	size = (50, 50, 50), rank = 50 ┌ ┐ ╷┐ ╷ mode 1 ├├────┤ ╵┘ ╵ ┐ ╷ mode 2 ├─────┤ ┘ ╵ ╷┐ ╷ mode 3 ├├───┤ ╵┘ ╵ └ ┘ 0.2 0.35 0.5 Time (ms)	size = (50, 50, 50), rank = 100 ┌ ┐ ╷┌┬─┐ ╷ mode 1 ├┤│ ├─┤ ╵└┴─┘ ╵ ┐ ╷ mode 2 ├────┤ ┘ ╵ ┌┐ ╷ mode 3 ┤├─────┤ └┘ ╵ └ ┘ 0.3 0.5 0.7 Time (ms)	size = (50, 50, 50), rank = 150 ┌ ┐ ┌─┐ ╷ mode 1 ┤ ├───┤ └─┘ ╵ ╷┌┬┐ ╷ mode 2 ├┤│├───┤ ╵└┴┘ ╵ ╷┬┐ ╷ mode 3 ├│├────┤ ╵┴┘ ╵ └ ┘ 0.5 0.7 0.9 Time (ms)	size = (50, 50, 50), rank = 200 ┌ ┐ ┬┐ ╷ mode 1 │├──┤ ┴┘ ╵ ┬┐ ╷ mode 2 │├────┤ ┴┘ ╵ ╷┐ ╷ mode 3 ├├────┤ ╵┘ ╵ └ ┘ 0.6 0.85 1.1 Time (ms)	size = (50, 50, 50), rank = 250 ┌ ┐ ╷ ┬┐ ╷ mode 1 ├───│├──┤ ╵ ┴┘ ╵ ┌┐ ╷ mode 2 ┤├─────┤ └┘ ╵ ╷┬┐ ╷ mode 3 ├│├───────┤ ╵┴┘ ╵ └ ┘ 0.8 1.05 1.3 Time (ms)	size = (50, 50, 50), rank = 300 ┌ ┐ ╷ ┌┬┐ ╷ mode 1 ├─┤│├──┤ ╵ └┴┘ ╵ ┌┐ ╷ mode 2 ┤├──┤ └┘ ╵ ┌┬┐ ╷ mode 3 ┤│├───┤ └┴┘ ╵ └ ┘ 1 1.3 1.6 Time (ms)	size = (100, 100, 100), rank = 10 ┌ ┐ ╷┬┐ ╷ mode 1 ├│├───────┤ ╵┴┘ ╵ ┬┐ ╷ mode 2 │├─────┤ ┴┘ ╵ ╷┐ ╷ mode 3 ├├────┤ ╵┘ ╵ └ ┘ 0.2 0.5 0.8 Time (ms)	size = (100, 100, 100), rank = 50 ┌ ┐ ╷┐ ╷ mode 1 ├├──┤ ╵┘ ╵ ┐ ╷ mode 2 ├──┤ ┘ ╵ ┬┐ ╷ mode 3 │├─┤ ┴┘ ╵ └ ┘ 0.8 1.3 1.8 Time (ms)	size = (100, 100, 100), rank = 100 ┌ ┐ ┐ ╷ mode 1 ├─┤ ┘ ╵ ┐ ╷ mode 2 ├─┤ ┘ ╵ ┌┐ ╷ mode 3 ┤├─┤ └┘ ╵ └ ┘ 1 2 3 Time (ms)	size = (100, 100, 100), rank = 150 ┌ ┐ ╷┬────┐╷ mode 1 ├│ ├┤ ╵┴────┘╵ ╷┌───┬─┐ ╷ mode 2 ├┤ │ ├──┤ ╵└───┴─┘ ╵ ╷┌┬──┐╷ mode 3 ├┤│ ├┤ ╵└┴──┘╵ └ ┘ 3 3.45 3.9 Time (ms)	size = (100, 100, 100), rank = 200 ┌ ┐ ╷╷ mode 1 ├┤ ╵╵ ┌─────────────────────────╷ mode 2 ┤ ┤ └─────────────────────────╵ ╷ mode 3 ┤ ╵ └ ┘ 4 9.5 15 Time (ms)	size = (100, 100, 100), rank = 250 ┌ ┐ ╷┬┐╷ mode 1 ├│├┤ ╵┴┘╵ ╷ ┌─────┬─────╷ mode 2 ├─┤ │ ┤ ╵ └─────┴─────╵ ╷┌┬─┐╷ mode 3 ├┤│ ├┤ ╵└┴─┘╵ └ ┘ 4.9 5.3 5.7 Time (ms)	size = (100, 100, 100), rank = 300 ┌ ┐ ╷ mode 1 ┤ ╵ ┐ ╷ mode 2 ├──────────────────────────┤ ┘ ╵ ┐╷ mode 3 ├┤ ┘╵ └ ┘ 5 10.5 16 Time (ms)	size = (150, 150, 150), rank = 10 ┌ ┐ ╷ mode 1 ┤ ╵ ┬┐ ╷ mode 2 │├────────────────────┤ ┴┘ ╵ ╷ mode 3 ┤ ╵ └ ┘ 0 100 200 Time (ms)	size = (150, 150, 150), rank = 50 ┌ ┐ ╷ mode 1 ┤ ╵ ╷ ╷ mode 2 ├──────────────┤ ╵ ╵ ┬╷ mode 3 │┤ ┴╵ └ ┘ 0 10 20 Time (ms)	size = (150, 150, 150), rank = 100 ┌ ┐ ╷ mode 1 ┤ ╵ ┌─────────┐ ╷ mode 2 ┤ ├────────┤ └─────────┘ ╵ ┌╷ mode 3 ┤┤ └╵ └ ┘ 0 15 30 Time (ms)	size = (150, 150, 150), rank = 150 ┌ ┐ ╷ mode 1 ┤ ╵ ┌─────────────────────────┬╷ mode 2 ┤ │┤ └─────────────────────────┴╵ ┬╷ mode 3 │┤ ┴╵ └ ┘ 7 12.5 18 Time (ms)	size = (150, 150, 150), rank = 200 ┌ ┐ ╷┌─┐╷ mode 1 ├┤ ├┤ ╵└─┘╵ ╷ ┐ ╷ mode 2 ├─├──┤ ╵ ┘ ╵ ╷┐╷ mode 3 ├├┤ ╵┘╵ └ ┘ 9 10.5 12 Time (ms)	size = (150, 150, 150), rank = 250 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┬─────────────────────────╷ mode 2 │ ┤ ┴─────────────────────────╵ ╷╷ mode 3 ├┤ ╵╵ └ ┘ 11 16.5 22 Time (ms)	size = (150, 150, 150), rank = 300 ┌ ┐ ╷┬╷ mode 1 ├│┤ ╵┴╵ ┬─────────────────────────╷ mode 2 │ ┤ ┴─────────────────────────╵ ┐╷ mode 3 ├┤ ┘╵ └ ┘ 14 19.5 25 Time (ms)	size = (200, 200, 200), rank = 10 ┌ ┐ ┐ ╷ mode 1 ├─┤ ┘ ╵ ┐╷ mode 2 ├┤ ┘╵ ┐╷ mode 3 ├┤ ┘╵ └ ┘ 1 2.5 4 Time (ms)	size = (200, 200, 200), rank = 50 ┌ ┐ ┌┐╷ mode 1 ┤├┤ └┘╵ ╷┌─────────────────────────╷ mode 2 ├┤ ┤ ╵└─────────────────────────╵ ╷╷ mode 3 ├┤ ╵╵ └ ┘ 6 11.5 17 Time (ms)	size = (200, 200, 200), rank = 100 ┌ ┐ ╷┬──╷ mode 1 ├│ ┤ ╵┴──╵ ┌┬────────┐ ╷ mode 2 ┤│ ├──────────────┤ └┴────────┘ ╵ ╷ mode 3 ┤ ╵ └ ┘ 10 25 40 Time (ms)	size = (200, 200, 200), rank = 150 ┌ ┐ ╷╷ mode 1 ├┤ ╵╵ ┌┐ ╷ mode 2 ┤├─────────────┤ └┘ ╵ ╷ mode 3 ┤ ╵ └ ┘ 10 20 30 Time (ms)	size = (200, 200, 200), rank = 200 ┌ ┐ ┬╷ mode 1 │┤ ┴╵ ┌┬─────────────┐╷ mode 2 ┤│ ├┤ └┴─────────────┘╵ ┬─┐ ╷ mode 3 │ ├─────┤ ┴─┘ ╵ └ ┘ 10 20 30 Time (ms)	size = (200, 200, 200), rank = 250 ┌ ┐ ┬─┐ ╷ mode 1 │ ├───────────────┤ ┴─┘ ╵ ╷┌┬───┐ ╷ mode 2 ├┤│ ├────┤ ╵└┴───┘ ╵ ╷ mode 3 ┤ ╵ └ ┘ 20 40 60 Time (ms)	size = (200, 200, 200), rank = 300 ┌ ┐ ┌┐╷ mode 1 ┤├┤ └┘╵ ┬─────────────┐╷ mode 2 │ ├┤ ┴─────────────┘╵ ┬┐╷ mode 3 │├┤ ┴┘╵ └ ┘ 20 30 40 Time (ms)	size = (1000, 100, 30), rank = 10 ┌ ┐ ┐ ╷ mode 1 ├──────────┤ ┘ ╵ ┐ ╷ mode 2 ├──┤ ┘ ╵ ┬┐ ╷ mode 3 │├──┤ ┴┘ ╵ └ ┘ 0 2 4 Time (ms)	size = (1000, 100, 30), rank = 100 ┌ ┐ ╷┐ ╷ mode 1 ├├─┤ ╵┘ ╵ ┬───────────────┐ ╷ mode 2 │ ├────┤ ┴───────────────┘ ╵ ┌┐╷ mode 3 ┤├┤ └┘╵ └ ┘ 0 10 20 Time (ms)	size = (1000, 100, 30), rank = 200 ┌ ┐ ┐╷ mode 1 ├┤ ┘╵ ┐╷ mode 2 ├┤ ┘╵ ┬╷ mode 3 │┤ ┴╵ └ ┘ 0 20 40 Time (ms)	size = (1000, 100, 30), rank = 300 ┌ ┐ ┬╷ mode 1 │┤ ┴╵ ╷ mode 2 ┤ ╵ ╷ mode 3 ┤ ╵ └ ┘ 0 25 50 Time (ms)

[dahong67]

And yields benefits for gcp, especially in terms of memory use.

Benchmark Report for GCPDecompositions

Job Properties

• Time of benchmarks:
  • Target: 4 Mar 2024 - 00:01
  • Baseline: 4 Mar 2024 - 00:03
• Package commits:
  • Target: 85a8ed
  • Baseline: 38648a
• Julia commits:
  • Target: bed2cd
  • Baseline: bed2cd
• Julia command flags:
  • Target: None
  • Baseline: None
• Environment variables:
  • Target: GCP_BENCHMARK_SUITES => gcp
  • Baseline: GCP_BENCHMARK_SUITES => gcp

Results

A ratio greater than 1.0 denotes a possible regression (marked with ❌), while a ratio less
than 1.0 denotes a possible improvement (marked with ✅). Only significant results - results
that indicate possible regressions or improvements - are shown below (thus, an empty table means that all
benchmark results remained invariant between builds).

ID	time ratio	memory ratio
["gcp", "bernoulliOdds-size(X)=(15, 20, 25), rank(X)=1"]	0.95 (5%)	0.96 (1%) ✅
["gcp", "bernoulliOdds-size(X)=(15, 20, 25), rank(X)=2"]	1.14 (5%) ❌	1.18 (1%) ❌
["gcp", "bernoulliOdds-size(X)=(30, 40, 50), rank(X)=1"]	0.96 (5%)	0.95 (1%) ✅
["gcp", "bernoulliOdds-size(X)=(30, 40, 50), rank(X)=2"]	0.92 (5%) ✅	0.94 (1%) ✅
["gcp", "gamma-size(X)=(15, 20, 25), rank(X)=2"]	0.95 (5%)	0.98 (1%) ✅
["gcp", "gamma-size(X)=(30, 40, 50), rank(X)=1"]	1.04 (5%)	1.05 (1%) ❌
["gcp", "gamma-size(X)=(30, 40, 50), rank(X)=2"]	0.95 (5%)	0.96 (1%) ✅
["gcp", "least-squares-size(X)=(15, 20, 25), rank(X)=1"]	0.64 (5%) ✅	0.42 (1%) ✅
["gcp", "least-squares-size(X)=(15, 20, 25), rank(X)=2"]	0.68 (5%) ✅	0.35 (1%) ✅
["gcp", "least-squares-size(X)=(30, 40, 50), rank(X)=1"]	0.88 (5%) ✅	0.55 (1%) ✅
["gcp", "least-squares-size(X)=(30, 40, 50), rank(X)=2"]	0.89 (5%) ✅	0.41 (1%) ✅
["gcp", "poisson-size(X)=(30, 40, 50), rank(X)=1"]	0.97 (5%)	0.99 (1%) ✅
["gcp", "poisson-size(X)=(30, 40, 50), rank(X)=2"]	0.97 (5%)	0.97 (1%) ✅

Benchmark Group List

Here's a list of all the benchmark groups executed by this job:

• ["gcp"]

Julia versioninfo

Target

Julia Version 1.9.3
Commit bed2cd540a1 (2023-08-24 14:43 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (arm64-apple-darwin22.4.0)
  uname: Darwin 23.2.0 Darwin Kernel Version 23.2.0: Wed Nov 15 21:53:18 PST 2023; root:xnu-10002.61.3~2/RELEASE_ARM64_T6000 arm64 arm
  CPU: Apple M1 Max: 
                 speed         user         nice          sys         idle          irq
       #1-10  2400 MHz    1592886 s          0 s     608959 s   21131960 s          0 s
  Memory: 64.0 GB (36595.609375 MB free)
  Uptime: 499293.0 sec
  Load Avg:  2.35498046875  2.36669921875  2.69384765625
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-14.0.6 (ORCJIT, apple-m1)
  Threads: 1 on 8 virtual cores

Baseline

Julia Version 1.9.3
Commit bed2cd540a1 (2023-08-24 14:43 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (arm64-apple-darwin22.4.0)
  uname: Darwin 23.2.0 Darwin Kernel Version 23.2.0: Wed Nov 15 21:53:18 PST 2023; root:xnu-10002.61.3~2/RELEASE_ARM64_T6000 arm64 arm
  CPU: Apple M1 Max: 
                 speed         user         nice          sys         idle          irq
       #1-10  2400 MHz    1594429 s          0 s     609486 s   21139488 s          0 s
  Memory: 64.0 GB (36540.078125 MB free)
  Uptime: 499390.0 sec
  Load Avg:  2.14990234375  2.32861328125  2.64208984375
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-14.0.6 (ORCJIT, apple-m1)
  Threads: 1 on 8 virtual cores

[dahong67]

All tests pass, except on nightly (which is likely due to the other issues). Merged!