abrudz

Sort←{⎕ML←1                             ⍝ Total array ordering (TAO) comparison.

    acmp←{                              ⍝ array comparison.
        ≡/⍵:¯1                          ⍝ match: equal.
        ~≡/⍴∘⍴¨⍵:∇ xrnk ⍵               ⍝ ranks differ: reshape with 1-axes.
        ⊃⊃⍷/⍵:1                         ⍝ prefixes precede their continuations.
        ⊃⊃⍷/⌽⍵:0                        ⍝ continuations follow their prefixes.
        ~≡/⍴¨⍵:∇ xshp ⍵                 ⍝ shapes differ: stretch with fills.
        0=×/⍴⊃⍵:∇⊃¨⍵                    ⍝ null: comparison of proto items.
        ~⍵≡⊃¨⍵:∇ halves,¨⍵              ⍝ non-atomic: item-wise comparison.

abrudz

 Eigen←{⎕IO ⎕ML←1                             ⍝ Eigen values⍪vectors
                                             ⍝ graeme@dyadic.com
     dsyev←{                                 ⍝ real symmetric:
         args←'dsyev_'assoc↓⍉↑⌽{             ⍝ associate external fn.
             ⍵,⊂' <T1 ' 'V'}{                ⍝ JOBZ
             ⍵,⊂' <T1 ' 'L'}{                ⍝ UPLO
             ⍵,⊂' <I4 'n}{                   ⍝ N
             ⍵,⊂' =F8[] '(,mat)}{            ⍝ A
             ⍵,⊂' <I4 'n}{                   ⍝ LDA
             ⍵,⊂' >F8[] 'n}{                 ⍝ W

abrudz

    ∇ vv←Eigen mat;vecs;vals;code;n
      n←≢mat
     
      :If Real mat
          :If (Sym mat)∧2≠n ⍝ symmetric
              (vals vecs code)←Dsyev mat
     
          :Else ⍝ general
              (vals vecs code)←Dgeev mat
          :EndIf

abrudz

cmp←{  ⍝ compare basic arrays, results in ¯1 (⍺ precedes ⍵), 0 (⍺ is identical to ⍵), or 1 (⍺ follows ⍵)

⍝ DEFINITION:
⍝            ┌
⍝            │ ¯1 if ⍺ strictly precedes ⍵
⍝ ⍺ cmp ⍵  = │  0 if ⍺ exactly matches   ⍵
⍝            │  1 if ⍺ strictly follows  ⍵
⍝            └

⍝ AXIOMS:

abrudz

abrudz

abrudz

;(_=>{
let hc={'<':'&lt;','&':'&amp;',"'":'&apos;','"':'&quot;'},he=x=>x.replace(/[<&'"]/g,c=>hc[c]) //html chars and escape fn
,tcs='<-←xx×/\\×:-÷*O⍟[-⌹-]⌹OO○77⌈FF⌈ll⌊LL⌊|_⊥TT⊤-|⊣|-⊢=/≠L-≠<=≤<_≤>=≥>_≥==≡=_≡/_≢L=≢vv∨^^∧^~⍲v~⍱^|↑v|↓((⊂cc⊂(_⊆))⊃[|⌷|]⌷A|⍋V|⍒ii⍳i_⍸ee∊e_⍷'+
'uu∪UU∪nn∩/-⌿\\-⍀,-⍪rr⍴pp⍴O|⌽O-⊖O\\⍉::¨""¨~:⍨~"⍨*:⍣*"⍣oo∘o:⍤o"⍤[\'⍞\']⍞[]⎕[:⍠:]⍠[=⌸=]⌸[<⌺>]⌺o_⍎oT⍕o-⍕<>⋄on⍝->→aa⍺ww⍵VV∇--¯0~⍬'+
'^-∆^=⍙[?⍰?]⍰:V⍢∇"⍢||∥ox¤)_⊇_)⊇O:⍥O"⍥V~⍫\'\'`'
,lbs=['←←\nASSIGN',' ','++\nconjugate\nplus','--\nnegate\nminus','××\ndirection\ntimes','÷÷\nreciprocal\ndivide','**\nexponential\npower','⍟⍟\nnatural logarithm\nlogarithm',
'⌹⌹\nmatrix inverse\nmatrix divide','○○\npi times\ncircular','!!\nfactorial\nbinomial','??\nroll\ndeal',' ','||\nmagnitude\nresidue',
'⌈⌈\nceiling\nmaximum','⌊⌊\nfloor\nminimum','⊥⊥\ndecode','⊤⊤\nencode','⊣⊣\nsame\nleft','⊢⊢\nsame\nright',' ','==\nequal','≠≠\nnot equal',
'≤≤\nless than or equal to','<<\nless than','>>\ngreater than','≥≥\ngreater than or equal to','≡≡\ndepth\nmatch','≢≢\ntally\nnot matc

abrudz

 P7S←{
     ⍝ Implement recursive topological sort
     Segs←#.U.Segs
     Trim←#.U.Trim
     data←⍉⊃¨@2⍉' 'Segs¨Trim↑'->'∘Segs¨⍵
     results←¯1⍴⍨≢data
     ToBin←(16⍴2)∘⊤
     FromBin←2∘⊥
     NOT←=
     AND←∧

abrudz

Post Link,Score,AnswerCount,ClosedDate
"{
  ""id"": 108170,
  ""title"": ""Totally Cubular""
}","17","0",""
"{
  ""id"": 101222,
  ""title"": ""Hexasweep (part 1): The Solver""
}","15","0",""
"{

abrudz

Background

While the yearly get-togethers are called user meetings (previously known as conferences), I found that the social setting allowed Dyalog's staff to discuss and develop ideas in a way that would not happen in the office setting of Bramley.

I had a vague idea about an operator that would ease working with value tolerances and ranges. During our ride up Mount Etna, I by chance had the pleasure of sitting next to Geoff Streeter. We started discussing some things, and before long I had my laptop out and we were prototyping a new operator.

I discussed my idea with Nick Nickolov, who told me that being a fan of ⎕CT←0, he has considered ≈ to denote tolerant equality. I think we then naturally would want ≉, and ≲, and