Improve src/matrixlu.jl to optimize arrlu

[terasakisatoshi]

This PR updates src/matrixlu.jl to optimize arrlu.

Here is a benchmark script:

using Random

using BenchmarkTools
import TensorCrossInterpolation as TCI

begin
	struct CallableMatrix{T} <: Function
		A::Matrix{T}
	end

	function (c::CallableMatrix)(i, j)
		c.A[i, j]
	end
end

begin
	@benchmark TCI.arrlu(Float64, CallableMatrix(A), size(A), [1], [1]) setup=begin
		A = rand(10, 10)
	end samples=100
end

On main branch:

               _
   _       _ _(_)_     |  Documentation: https://docs.julialang.org
  (_)     | (_) (_)    |
   _ _   _| |_  __ _   |  Type "?" for help, "]?" for Pkg help.
  | | | | | | |/ _` |  |
  | | |_| | | | (_| |  |  Version 1.11.1 (2024-10-16)
 _/ |\__'_|_|_|\__'_|  |  Official https://julialang.org/ release
|__/                   |

julia> versioninfo()
Julia Version 1.11.1
Commit 8f5b7ca12ad (2024-10-16 10:53 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (x86_64-apple-darwin22.4.0)
  CPU: 16 × Intel(R) Core(TM) i9-9980HK CPU @ 2.40GHz
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, skylake)
Threads: 1 default, 0 interactive, 1 GC (on 16 virtual cores)
Environment:
  JULIA_PROJECT = @.
  JULIA_PKG_USE_CLI_GIT = true
  JULIA_EDITOR = subl

julia> using Random

julia> using BenchmarkTools

julia> import TensorCrossInterpolation as TCI

julia> begin
               struct CallableMatrix{T} <: Function
                       A::Matrix{T}
               end

               function (c::CallableMatrix)(i, j)
                       c.A[i, j]
               end
       end

julia> begin
               @benchmark TCI.arrlu(Float64, CallableMatrix(A), size(A), [1], [1]) setup=begin
                       A = rand(10, 10)
               end samples=100
       end

BenchmarkTools.Trial: 100 samples with 1 evaluation.
 Range (min … max):  45.684 μs … 90.908 μs  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     56.826 μs              ┊ GC (median):    0.00%
 Time  (mean ± σ):   57.139 μs ±  6.828 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

        ▂        ▄ █   ▆ ▂  ▂ ▂▄  ▄                            
  ▄▆▄▆▄▄██▄▆▆▁▄▄▆█▆█▆▆▄█▄█▄▆████▆▆█▄▁█▄▄▄▁▆▄▄▆▄▁▄▁▁▁▁▁▄▁▁▁▁▁▄ ▄
  45.7 μs         Histogram: frequency by time        74.3 μs <

 Memory estimate: 118.83 KiB, allocs estimate: 1934.

julia> 

This PR

               _
   _       _ _(_)_     |  Documentation: https://docs.julialang.org
  (_)     | (_) (_)    |
   _ _   _| |_  __ _   |  Type "?" for help, "]?" for Pkg help.
  | | | | | | |/ _` |  |
  | | |_| | | | (_| |  |  Version 1.11.1 (2024-10-16)
 _/ |\__'_|_|_|\__'_|  |  Official https://julialang.org/ release
|__/                   |

julia> versioninfo()
Julia Version 1.11.1
Commit 8f5b7ca12ad (2024-10-16 10:53 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (x86_64-apple-darwin22.4.0)
  CPU: 16 × Intel(R) Core(TM) i9-9980HK CPU @ 2.40GHz
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, skylake)
Threads: 1 default, 0 interactive, 1 GC (on 16 virtual cores)
Environment:
  JULIA_PROJECT = @.
  JULIA_PKG_USE_CLI_GIT = true
  JULIA_EDITOR = subl

julia> using Random

julia> using BenchmarkTools

julia> import TensorCrossInterpolation as TCI

julia> begin
               struct CallableMatrix{T} <: Function
                       A::Matrix{T}
               end

               function (c::CallableMatrix)(i, j)
                       c.A[i, j]
               end
       end

julia> begin
               @benchmark TCI.arrlu(Float64, CallableMatrix(A), size(A), [1], [1]) setup=begin
                       A = rand(10, 10)
               end samples=100
       end

BenchmarkTools.Trial: 100 samples with 1 evaluation.
 Range (min … max):  18.551 μs … 44.954 μs  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     22.490 μs              ┊ GC (median):    0.00%
 Time  (mean ± σ):   22.753 μs ±  3.648 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

  ▂▁  ▁█▁▄▅ █▄▅▂                                               
  ██▃▅█████▆█████▅▃█▆▁▁▁▃▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▃ ▃
  18.6 μs         Histogram: frequency by time        42.9 μs <

 Memory estimate: 29.77 KiB, allocs estimate: 294.

julia>