| 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. |
| Eigen←{⎕IO ⎕ML←1 ⍝ Eigen values⍪vectors | |
| ⍝ [email protected] | |
| 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 |
| ∇ 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 |
| 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: |
| ;(_=>{ | |
| let hc={'<':'<','&':'&',"'":''','"':'"'},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 |
| 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←∧ |
| Post Link,Score,AnswerCount,ClosedDate | |
| "{ | |
| ""id"": 108170, | |
| ""title"": ""Totally Cubular"" | |
| }","17","0","" | |
| "{ | |
| ""id"": 101222, | |
| ""title"": ""Hexasweep (part 1): The Solver"" | |
| }","15","0","" | |
| "{ |
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