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```@meta | ||
CurrentModule = BLASBenchmarks | ||
``` | ||
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# Memory Required for Large Matrices | ||
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These tables show how much memory is required for four matrices of the given size and type. (We need four matrices: `A`, `B`, `C1`, and `C2`.) | ||
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## Float64 | ||
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| Matrix Size | Memory | | ||
| ----------- | ------ | | ||
| 1k by 1k | 0.03 GiB | | ||
| 2k by 2k | 0.12 GiB | | ||
| 3k by 3k | 0.27 GiB | | ||
| 4k by 4k | 0.48 GiB | | ||
| 5k by 5k | 0.75 GiB | | ||
| 6k by 6k | 1.07 GiB | | ||
| 7k by 7k | 1.46 GiB | | ||
| 8k by 8k | 1.91 GiB | | ||
| 9k by 9k | 2.41 GiB | | ||
| 10k by 10k | 2.98 GiB | | ||
| 11k by 11k | 3.61 GiB | | ||
| 12k by 12k | 4.29 GiB | | ||
| 13k by 13k | 5.04 GiB | | ||
| 14k by 14k | 5.84 GiB | | ||
| 15k by 15k | 6.71 GiB | | ||
| 16k by 16k | 7.63 GiB | | ||
| 17k by 17k | 8.61 GiB | | ||
| 18k by 18k | 9.66 GiB | | ||
| 19k by 19k | 10.76 GiB | | ||
| 20k by 20k | 11.92 GiB | | ||
| 30k by 30k | 26.82 GiB | | ||
| 40k by 40k | 47.68 GiB | | ||
| 50k by 50k | 74.51 GiB | | ||
| 60k by 60k | 107.29 GiB | | ||
| 70k by 70k | 146.03 GiB | | ||
| 80k by 80k | 190.73 GiB | | ||
| 90k by 90k | 241.4 GiB | | ||
| 100k by 100k | 298.02 GiB | | ||
|
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## Float32 | ||
|
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| Matrix Size | Memory | | ||
| ----------- | ------ | | ||
| 1k by 1k | 0.01 GiB | | ||
| 2k by 2k | 0.06 GiB | | ||
| 3k by 3k | 0.13 GiB | | ||
| 4k by 4k | 0.24 GiB | | ||
| 5k by 5k | 0.37 GiB | | ||
| 6k by 6k | 0.54 GiB | | ||
| 7k by 7k | 0.73 GiB | | ||
| 8k by 8k | 0.95 GiB | | ||
| 9k by 9k | 1.21 GiB | | ||
| 10k by 10k | 1.49 GiB | | ||
| 11k by 11k | 1.8 GiB | | ||
| 12k by 12k | 2.15 GiB | | ||
| 13k by 13k | 2.52 GiB | | ||
| 14k by 14k | 2.92 GiB | | ||
| 15k by 15k | 3.35 GiB | | ||
| 16k by 16k | 3.81 GiB | | ||
| 17k by 17k | 4.31 GiB | | ||
| 18k by 18k | 4.83 GiB | | ||
| 19k by 19k | 5.38 GiB | | ||
| 20k by 20k | 5.96 GiB | | ||
| 30k by 30k | 13.41 GiB | | ||
| 40k by 40k | 23.84 GiB | | ||
| 50k by 50k | 37.25 GiB | | ||
| 60k by 60k | 53.64 GiB | | ||
| 70k by 70k | 73.02 GiB | | ||
| 80k by 80k | 95.37 GiB | | ||
| 90k by 90k | 120.7 GiB | | ||
| 100k by 100k | 149.01 GiB | | ||
|
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## Int64 | ||
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| Matrix Size | Memory | | ||
| ----------- | ------ | | ||
| 1k by 1k | 0.03 GiB | | ||
| 2k by 2k | 0.12 GiB | | ||
| 3k by 3k | 0.27 GiB | | ||
| 4k by 4k | 0.48 GiB | | ||
| 5k by 5k | 0.75 GiB | | ||
| 6k by 6k | 1.07 GiB | | ||
| 7k by 7k | 1.46 GiB | | ||
| 8k by 8k | 1.91 GiB | | ||
| 9k by 9k | 2.41 GiB | | ||
| 10k by 10k | 2.98 GiB | | ||
| 11k by 11k | 3.61 GiB | | ||
| 12k by 12k | 4.29 GiB | | ||
| 13k by 13k | 5.04 GiB | | ||
| 14k by 14k | 5.84 GiB | | ||
| 15k by 15k | 6.71 GiB | | ||
| 16k by 16k | 7.63 GiB | | ||
| 17k by 17k | 8.61 GiB | | ||
| 18k by 18k | 9.66 GiB | | ||
| 19k by 19k | 10.76 GiB | | ||
| 20k by 20k | 11.92 GiB | | ||
| 30k by 30k | 26.82 GiB | | ||
| 40k by 40k | 47.68 GiB | | ||
| 50k by 50k | 74.51 GiB | | ||
| 60k by 60k | 107.29 GiB | | ||
| 70k by 70k | 146.03 GiB | | ||
| 80k by 80k | 190.73 GiB | | ||
| 90k by 90k | 241.4 GiB | | ||
| 100k by 100k | 298.02 GiB | | ||
|
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## Int32 | ||
|
||
| Matrix Size | Memory | | ||
| ----------- | ------ | | ||
| 1k by 1k | 0.01 GiB | | ||
| 2k by 2k | 0.06 GiB | | ||
| 3k by 3k | 0.13 GiB | | ||
| 4k by 4k | 0.24 GiB | | ||
| 5k by 5k | 0.37 GiB | | ||
| 6k by 6k | 0.54 GiB | | ||
| 7k by 7k | 0.73 GiB | | ||
| 8k by 8k | 0.95 GiB | | ||
| 9k by 9k | 1.21 GiB | | ||
| 10k by 10k | 1.49 GiB | | ||
| 11k by 11k | 1.8 GiB | | ||
| 12k by 12k | 2.15 GiB | | ||
| 13k by 13k | 2.52 GiB | | ||
| 14k by 14k | 2.92 GiB | | ||
| 15k by 15k | 3.35 GiB | | ||
| 16k by 16k | 3.81 GiB | | ||
| 17k by 17k | 4.31 GiB | | ||
| 18k by 18k | 4.83 GiB | | ||
| 19k by 19k | 5.38 GiB | | ||
| 20k by 20k | 5.96 GiB | | ||
| 30k by 30k | 13.41 GiB | | ||
| 40k by 40k | 23.84 GiB | | ||
| 50k by 50k | 37.25 GiB | | ||
| 60k by 60k | 53.64 GiB | | ||
| 70k by 70k | 73.02 GiB | | ||
| 80k by 80k | 95.37 GiB | | ||
| 90k by 90k | 120.7 GiB | | ||
| 100k by 100k | 149.01 GiB | | ||
|
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## Generating These Tables | ||
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```julia | ||
mem_req(s, T) = 4s^2*sizeof(T) / (1 << 30) | ||
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function print_table(::Type{T}, Ns = nothing) where {T} | ||
println("| Matrix Size | Memory |") | ||
println("| ----------- | ------ |") | ||
if Ns isa Nothing | ||
_Ns = sort(unique(vcat(collect(1:1:20), collect(20:10:100)))) | ||
else | ||
_Ns = Ns | ||
end | ||
for N in _Ns | ||
mem = mem_req(N * 1_000, T) | ||
m = round(mem; digits = 2) | ||
println("| $(N)k by $(N)k | $(m) GiB |") | ||
end | ||
return nothing | ||
end | ||
``` |
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