Added contiguous check and fortran_contiguous check to dot method.

[naitoh]

I wrote patch for improve the performance of the a.dot(b.transpose). (See https://github.com/ruby-numo/numo-narray/issues/95 for details.)

This patch requires https://github.com/ruby-numo/numo-narray/pull/116 .

Benchmarke code (numo-linalg 0.2.0 : this pull request version)

$ numo_linalg_fp32.yaml
contexts:
  - gems: { numo-linalg: 0.1.3 }
    require: false
    prelude: |
      require 'numo/linalg'
  - gems: { numo-linalg: 0.2.0 }
    require: false
    prelude: |
      require 'numo/linalg'

loop_count: 1000
prelude: |
  X = 1000
  Y = 784
  YY = Y + 1
  a = Numo::SFloat.new(X, Y).seq(0)
  b = Numo::SFloat.new(X, Y).seq(0).transpose
  c = b.dup
  d = Numo::SFloat.new(X, YY).seq(0)[true,1..-1]           # contiguous? => false, transpose? => false
  e = Numo::SFloat.new(X, YY).seq(0)[true,1..-1].transpose # contiguous? => false, transpose? => false
  f = e.dup
  sleep 30

benchmark:
  'a.dot(b.transpose)     : view     (contiguous? => false, transpose?  => true) ' : a.dot(b)
  'a.dot(b.transpose.dup) : not view (contiguous? => true)                       ' : a.dot(c)
  'a.dot(d.transpose)     : view     (contiguous? => false, transpose?  => false)' : a.dot(e)
  'a.dot(f.transpose.dup) : not view (contiguous? => true)                       ' : a.dot(f)

Benchmarked Result (numo-linalg 0.2.0 : this pull request version)

$ ruby -v
ruby 2.5.3p105 (2018-10-18 revision 65156) [x86_64-linux]
$ gem install benchmark_driver
$ benchmark-driver  numo_linalg_fp32.yaml 
Calculating -------------------------------------
                                                                               numo-linalg 0.1.3  numo-linalg 0.2.0 
a.dot(b.transpose)     : view     (contiguous? => false, transpose?  => true)             40.131             60.995 i/s -      1.000k times in 24.918112s 16.394857s
a.dot(b.transpose.dup) : not view (contiguous? => true)                                   60.657             60.348 i/s -      1.000k times in 16.486182s 16.570423s
a.dot(d.transpose)     : view     (contiguous? => false, transpose?  => false)            37.098             51.162 i/s -      1.000k times in 26.955645s 19.545771s
a.dot(f.transpose.dup) : not view (contiguous? => true)                                   60.031             59.439 i/s -      1.000k times in 16.658179s 16.824028s

Comparison:
             a.dot(b.transpose)     : view     (contiguous? => false, transpose?  => true) 
                                                             numo-linalg 0.2.0:        61.0 i/s 
                                                             numo-linalg 0.1.3:        40.1 i/s - 1.52x  slower

             a.dot(b.transpose.dup) : not view (contiguous? => true)                       
                                                             numo-linalg 0.1.3:        60.7 i/s 
                                                             numo-linalg 0.2.0:        60.3 i/s - 1.01x  slower

             a.dot(d.transpose)     : view     (contiguous? => false, transpose?  => false)
                                                             numo-linalg 0.2.0:        51.2 i/s 
                                                             numo-linalg 0.1.3:        37.1 i/s - 1.38x  slower

             a.dot(f.transpose.dup) : not view (contiguous? => true)                       
                                                             numo-linalg 0.1.3:        60.0 i/s 
                                                             numo-linalg 0.2.0:        59.4 i/s - 1.01x  slower

[naitoh]

Benchmarke Updated. (transpose? => f_contiguous?)

Benchmark code (numo-linalg 0.2.0 : this pull request version)

$ cat numo_linalg_fp32.yaml
contexts:
  - gems: { numo-linalg: 0.1.3 }
    require: false
    prelude: |
      require 'numo/linalg'
  - gems: { numo-linalg: 0.2.0 }
    require: false
    prelude: |
      require 'numo/linalg'

loop_count: 1000
prelude: |
  X = 1000
  Y = 784
  YY = Y + 1
  a = Numo::SFloat.new(X, Y).seq(0)
  b = Numo::SFloat.new(X, Y).seq(0).transpose
  c = b.dup
  d = Numo::SFloat.new(X, YY).seq(0)[true,1..-1]           # contiguous? => false, f_contiguous? => false
  e = Numo::SFloat.new(X, YY).seq(0)[true,1..-1].transpose # contiguous? => false, f_contiguous? => false
  f = e.dup
  sleep 30

benchmark:
  'a.dot(b.transpose)     : view     (contiguous? => false, f_contiguous?  => true) ' : a.dot(b)
  'a.dot(b.transpose.dup) : not view (contiguous? => true)                          ' : a.dot(c)
  'a.dot(d.transpose)     : view     (contiguous? => false, f_contiguous?  => false)' : a.dot(e)
  'a.dot(f.transpose.dup) : not view (contiguous? => true)                          ' : a.dot(f)

Benchmarked Result (numo-linalg 0.2.0 : this pull request version)

$ benchmark-driver numo_linalg_fp32.yaml 
Calculating -------------------------------------
                                                                                  numo-linalg 0.1.3  numo-linalg 0.2.0 
a.dot(b.transpose)     : view     (contiguous? => false, f_contiguous?  => true)             38.316             59.741 i/s -      1.000k times in 26.098845s 16.739011s
a.dot(b.transpose.dup) : not view (contiguous? => true)                                      58.714             57.679 i/s -      1.000k times in 17.031678s 17.337227s
a.dot(d.transpose)     : view     (contiguous? => false, f_contiguous?  => false)            36.577             48.925 i/s -      1.000k times in 27.339320s 20.439631s
a.dot(f.transpose.dup) : not view (contiguous? => true)                                      56.454             57.231 i/s -      1.000k times in 17.713388s 17.472999s

Comparison:
             a.dot(b.transpose)     : view     (contiguous? => false, f_contiguous?  => true) 
                                                                numo-linalg 0.2.0:        59.7 i/s 
                                                                numo-linalg 0.1.3:        38.3 i/s - 1.56x  slower

             a.dot(b.transpose.dup) : not view (contiguous? => true)                          
                                                                numo-linalg 0.1.3:        58.7 i/s 
                                                                numo-linalg 0.2.0:        57.7 i/s - 1.02x  slower

             a.dot(d.transpose)     : view     (contiguous? => false, f_contiguous?  => false)
                                                                numo-linalg 0.2.0:        48.9 i/s 
                                                                numo-linalg 0.1.3:        36.6 i/s - 1.34x  slower

             a.dot(f.transpose.dup) : not view (contiguous? => true)                          
                                                                numo-linalg 0.2.0:        57.2 i/s 
                                                                numo-linalg 0.1.3:        56.5 i/s - 1.01x  slower

[naitoh]

I changed the name of the method I am using. (f_contiguous? => fortran_contiguous?)

[naitoh]

Thanks!