conditional test in D-Fns

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Re: conditional test in D-Fns

Postby Veli-Matti on Thu Aug 18, 2022 8:40 am

Had some spare time, and tried to find different ways to solve the problem.
      foo1←(((2|⊢)×1+3×⊢)+(~2|⊢)×0.5×⊢) 
foo2←(6÷⍨¯1+⊢)@(2|⊢)(1+3×⊢)
foo3←{(b×1+3×⍵)+⍵×0.5×~b←2|⍵}
foo4←{2÷⍨@(⍸~b)⊢(1+3×⊢)@(⍸b←2|⍵)⊢⍵}
foo5←{(⊂⍋⍋b)⌷(0.5×(~b)/⍵),1+3×⍵/⍨b←2|⍵}
foo6←{b←2|v←⍵ ⋄ v[⍸b]←1+3×b/v ⋄ v[⍸~b]←0.5×(~b)/v ⋄ v}
foo7←{2|⍵:1+3×⍵ ⋄ ⍵÷2}¨
foo8←{b←2|⍵ ⋄ (~b){2÷⍨⍣⍺⊢⍵}¨b{(1+3×⊢)⍣⍺⊢⍵}¨⍵}
w←1e5?1e6
]runtime -c "foo1 w" "foo2 w" "foo3 w" "foo4 w" "foo5 w" "foo6 w" "foo7 w" "foo8 w"

foo1 w → 5.8E¯4 | 0%
foo2 w → 7.3E¯4 | +25%
foo3 w → 8.9E¯4 | +54%
foo4 w → 1.0E¯3 | +81% ⎕
foo5 w → 1.5E¯3 | +154% ⎕
foo6 w → 1.7E¯3 | +190% ⎕
foo7 w → 2.0E¯2 | +3345% ⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕
foo8 w → 7.2E¯2 | +12363% ⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕

-wm
Veli-Matti
 
Posts: 91
Joined: Sat Nov 28, 2009 3:12 pm

Re: conditional test in D-Fns

Postby paulmansour on Thu Aug 18, 2022 3:39 pm

Try a 3d array and watch everything change:

Code: Select all
 w←100 100 10⍴100000?1000000

]runtime -c "foo1 w" "foo2 w" "foo3 w" "foo4 w"  "foo7 w" "foo8 w" "foo9 w"
                                                                     
  foo1 w → 3.6E¯4 |      0%                                         
  foo2 w → 4.3E¯3 |  +1091% ⎕⎕⎕                                     
  foo3 w → 2.5E¯4 |    -31%                                         
  foo4 w → 8.1E¯3 |  +2143% ⎕⎕⎕⎕⎕                                   
  foo7 w → 1.6E¯2 |  +4469% ⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕                               
  foo8 w → 6.6E¯2 | +18334% ⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕
  foo9 w → 3.1E¯3 |   +750% ⎕⎕   


foo5 and foo6 omitted as they don't work on high rank arrays and one addition:

Code: Select all
foo9←{⊃(⊂⍤¯1)(2|⍵)⊖↑(⍵÷2)(1+3×⍵)}
paulmansour
 
Posts: 399
Joined: Fri Oct 03, 2008 4:14 pm

Re: conditional test in D-Fns

Postby Veli-Matti on Fri Aug 19, 2022 6:12 am

Hi Paul, what a nice surprise!

I _thought_ that the original problem was meant for simple vectors, but you are right, higher ranks should be taken into account as well.

A couple of other possible (but not necessarily effective) algorithms:
      foo10←{b←2|⍵ ⋄ (~b){2÷⍨⍣⍺⊢⍵}¨b{(1+3×⊢)⍣⍺⊢⍵}¨⍵}
foo11←{(⍴⍵)⍴1↑(2|⍵)⊖(⍵÷2),[0.1]1+3×⍵}

It's funny how some simple problems can have so many different approaches.

-wm (looking forward to Olhão)
Veli-Matti
 
Posts: 91
Joined: Sat Nov 28, 2009 3:12 pm

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