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+--------+-------------------------+-------------------------+--------+--------+
|00000000| 00 08 6d 69 6e 69 6d 69 | 7a 65 00 00 00 00 00 00 |..minimi|ze......|
|00000010| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000020| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000030| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000040| 00 54 45 58 54 4d 50 61 | 64 00 00 00 00 00 00 00 |.TEXTMPa|d.......|
|00000050| 00 00 00 00 00 0d 3d 00 | 00 01 8e ad 91 af bb ad |......=.|........|
|00000060| 91 af bb 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000070| 00 00 00 00 00 00 00 00 | 00 00 81 81 8a 3d 00 00 |........|.....=..|
|00000080| 2d 2d 20 50 65 72 66 6f | 72 6d 20 6d 75 6c 74 69 |-- Perfo|rm multi|
|00000090| 64 69 6d 65 6e 73 69 6f | 6e 61 6c 20 66 75 6e 63 |dimensio|nal func|
|000000a0| 74 69 6f 6e 20 6d 69 6e | 69 6d 69 7a 61 74 69 6f |tion min|imizatio|
|000000b0| 6e 2e 0d 7e 20 54 68 65 | 20 75 73 65 72 20 6d 75 |n..~ The| user mu|
|000000c0| 73 74 20 73 75 70 70 6c | 79 3a 0d 0d 22 66 28 70 |st suppl|y:.."f(p|
|000000d0| 61 72 6d 73 29 22 20 20 | 54 68 65 20 66 75 6e 63 |arms)"  |The func|
|000000e0| 74 69 6f 6e 20 74 6f 20 | 62 65 20 6d 69 6e 69 6d |tion to |be minim|
|000000f0| 69 7a 65 64 20 77 68 65 | 72 65 0d 20 20 20 20 20 |ized whe|re.     |
|00000100| 20 20 20 20 20 20 20 22 | 70 61 72 6d 73 22 20 69 |       "|parms" i|
|00000110| 73 20 61 6e 20 61 72 72 | 61 79 20 6f 66 20 70 61 |s an arr|ay of pa|
|00000120| 72 61 6d 65 74 65 72 73 | 2e 0d 22 67 75 65 73 73 |rameters|.."guess|
|00000130| 22 20 20 20 20 20 41 6e | 20 61 72 72 61 79 20 20 |"     An| array  |
|00000140| 6f 66 20 69 6e 69 74 69 | 61 6c 20 70 61 72 61 6d |of initi|al param|
|00000150| 65 74 65 72 20 76 61 6c | 75 65 73 2e 0d 22 64 65 |eter val|ues.."de|
|00000160| 6c 74 61 73 22 20 20 20 | 20 49 6e 69 74 69 61 6c |ltas"   | Initial|
|00000170| 20 73 74 65 70 20 73 69 | 7a 65 20 66 6f 72 20 74 | step si|ze for t|
|00000180| 68 65 20 70 61 72 61 6d | 65 74 65 72 73 2e 0d 20 |he param|eters.. |
|00000190| 20 20 20 20 20 20 20 20 | 20 20 20 49 66 20 74 68 |        |   If th|
|000001a0| 65 20 70 61 72 61 6d 65 | 74 65 72 73 20 68 61 76 |e parame|ters hav|
|000001b0| 65 20 64 69 66 66 65 72 | 65 6e 74 0d 20 20 20 20 |e differ|ent.    |
|000001c0| 20 20 20 20 20 20 20 20 | 73 63 61 6c 65 20 73 69 |        |scale si|
|000001d0| 7a 65 73 2c 20 22 64 65 | 6c 74 61 73 22 20 73 68 |zes, "de|ltas" sh|
|000001e0| 6f 75 6c 64 20 64 65 66 | 69 6e 65 20 61 6e 0d 20 |ould def|ine an. |
|000001f0| 20 20 20 20 20 20 20 20 | 20 20 20 61 72 72 61 79 |        |   array|
|00000200| 20 77 69 74 68 20 61 20 | 73 74 65 70 20 73 69 7a | with a |step siz|
|00000210| 65 20 66 6f 72 20 65 61 | 63 68 2c 0d 20 20 20 20 |e for ea|ch,.    |
|00000220| 20 20 20 20 20 20 20 20 | 6f 74 68 65 72 77 69 73 |        |otherwis|
|00000230| 65 20 61 20 73 63 61 6c | 61 72 20 63 61 6e 20 62 |e a scal|ar can b|
|00000240| 65 20 75 73 65 64 2e 0d | 22 74 6f 6c 22 20 20 20 |e used..|"tol"   |
|00000250| 20 20 20 20 54 68 65 20 | 74 65 72 6d 69 6e 61 74 |    The |terminat|
|00000260| 69 6f 6e 20 63 72 69 74 | 65 72 69 61 20 62 61 73 |ion crit|eria bas|
|00000270| 65 64 20 6f 6e 20 74 68 | 65 0d 20 20 20 20 20 20 |ed on th|e.      |
|00000280| 20 20 20 20 20 20 61 6d | 6f 75 6e 74 20 6f 66 20 |      am|ount of |
|00000290| 63 68 61 6e 67 65 20 69 | 6e 20 70 61 72 61 6d 65 |change i|n parame|
|000002a0| 74 65 72 20 76 61 6c 75 | 65 73 2e 0d 20 20 20 20 |ter valu|es..    |
|000002b0| 20 20 20 20 20 20 20 20 | 41 20 74 6f 6c 20 6f 66 |        |A tol of|
|000002c0| 20 31 2e 30 65 2d 36 20 | 67 69 76 65 73 20 61 62 | 1.0e-6 |gives ab|
|000002d0| 6f 75 74 20 33 20 64 69 | 67 69 74 0d 20 20 20 20 |out 3 di|git.    |
|000002e0| 20 20 20 20 20 20 20 20 | 61 63 63 75 72 61 63 79 |        |accuracy|
|000002f0| 2e 0d 0d 54 68 65 20 72 | 6f 75 74 69 6e 65 20 22 |...The r|outine "|
|00000300| 6d 69 6e 69 6d 69 7a 65 | 22 20 73 74 65 70 73 20 |minimize|" steps |
|00000310| 75 6e 74 69 6c 20 61 20 | 6d 69 6e 69 6d 75 6d 20 |until a |minimum |
|00000320| 69 73 20 66 6f 75 6e 64 | 2e 0d 41 66 74 65 72 20 |is found|..After |
|00000330| 6d 69 6e 69 6d 69 7a 65 | 20 69 73 20 72 75 6e 20 |minimize| is run |
|00000340| 74 68 65 20 66 6f 6c 6c | 6f 77 69 6e 67 20 67 6c |the foll|owing gl|
|00000350| 6f 62 61 6c 73 20 61 72 | 65 20 73 65 74 3a 0d 0d |obals ar|e set:..|
|00000360| 22 6d 69 6e 70 22 20 20 | 54 68 65 20 73 6f 6c 75 |"minp"  |The solu|
|00000370| 74 69 6f 6e 20 70 61 72 | 61 6d 65 74 65 72 20 61 |tion par|ameter a|
|00000380| 72 72 61 79 0d 22 70 22 | 20 20 20 20 20 54 68 65 |rray."p"|     The|
|00000390| 20 66 69 6e 61 6c 20 73 | 69 6d 70 6c 65 78 20 76 | final s|implex v|
|000003a0| 65 72 74 69 63 65 73 0d | 22 79 22 20 20 20 20 20 |ertices.|"y"     |
|000003b0| 54 68 65 20 66 75 6e 63 | 74 69 6f 6e 20 76 61 6c |The func|tion val|
|000003c0| 75 65 73 20 61 74 20 65 | 61 63 68 20 76 65 72 74 |ues at e|ach vert|
|000003d0| 65 78 0d 0d 7e 0d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |ex..~.--|--------|
|000003e0| 2d 2d 20 45 78 61 6d 70 | 6c 65 20 2d 2d 2d 2d 2d |-- Examp|le -----|
|000003f0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 0d |--------|-------.|
|00000400| 2d 2d 20 66 69 74 20 61 | 20 63 75 72 76 65 20 74 |-- fit a| curve t|
|00000410| 6f 20 64 61 74 61 20 62 | 79 20 6d 69 6e 69 6d 69 |o data b|y minimi|
|00000420| 7a 69 6e 67 20 74 68 65 | 20 73 75 6d 20 6f 66 20 |zing the| sum of |
|00000430| 74 68 65 20 73 71 75 61 | 72 65 20 6f 66 20 74 68 |the squa|re of th|
|00000440| 65 20 64 69 66 66 65 72 | 65 6e 63 65 73 20 62 65 |e differ|ences be|
|00000450| 74 77 65 65 6e 20 64 61 | 74 61 20 61 6e 64 20 66 |tween da|ta and f|
|00000460| 69 74 2e 0d 0d 66 69 74 | 28 61 2c 78 29 20 3d 20 |it...fit|(a,x) = |
|00000470| 61 5b 31 5d 2b 61 5b 32 | 5d 2a 63 6f 73 28 61 5b |a[1]+a[2|]*cos(a[|
|00000480| 33 5d 2a 78 29 0d 0d 64 | 61 74 61 3d 72 65 61 64 |3]*x)..d|ata=read|
|00000490| 28 78 79 64 61 74 61 29 | 3b 20 78 78 5b 69 5d 3d |(xydata)|; xx[i]=|
|000004a0| 64 61 74 61 5b 69 2c 31 | 5d 3b 20 79 79 5b 69 5d |data[i,1|]; yy[i]|
|000004b0| 3d 64 61 74 61 5b 69 2c | 32 5d 20 0d 0d 65 72 72 |=data[i,|2] ..err|
|000004c0| 28 61 29 20 3d 20 73 75 | 6d 28 28 66 69 74 28 61 |(a) = su|m((fit(a|
|000004d0| 2c 78 78 5b 6a 5d 29 2d | 79 79 5b 6a 5d 29 5e 32 |,xx[j])-|yy[j])^2|
|000004e0| 2c 6a 2c 31 2c 63 6f 75 | 6e 74 28 64 61 74 61 29 |,j,1,cou|nt(data)|
|000004f0| 29 0d 0d 2d 2d 20 73 65 | 74 20 75 70 20 67 6c 6f |)..-- se|t up glo|
|00000500| 62 61 6c 73 20 66 6f 72 | 20 6d 69 6e 69 6d 69 7a |bals for| minimiz|
|00000510| 65 0d 66 28 61 29 20 3d | 20 65 72 72 28 61 29 0d |e.f(a) =| err(a).|
|00000520| 67 75 65 73 73 20 3d 20 | 7b 38 30 2c 2d 37 35 2c |guess = |{80,-75,|
|00000530| 31 7d 0d 64 65 6c 74 61 | 73 20 3d 20 2e 35 0d 74 |1}.delta|s = .5.t|
|00000540| 6f 6c 20 3d 20 31 65 2d | 35 0d 0d 70 6c 6f 74 20 |ol = 1e-|5..plot |
|00000550| 64 61 74 61 0d 0d 6d 69 | 6e 69 6d 69 7a 65 3a 3b |data..mi|nimize:;|
|00000560| 20 20 20 20 6d 69 6e 70 | 3a 7b 38 30 2e 32 2c 2d |    minp|:{80.2,-|
|00000570| 37 33 2e 34 2c 30 2e 38 | 39 35 7d 0d 70 6c 6f 74 |73.4,0.8|95}.plot|
|00000580| 20 66 69 74 28 6d 69 6e | 70 2c 58 29 0d 0d 2d 2d | fit(min|p,X)..--|
|00000590| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 20 6d 69 6e 69 6d 69 |--------|- minimi|
|000005a0| 7a 61 74 69 6f 6e 20 72 | 6f 75 74 69 6e 65 73 20 |zation r|outines |
|000005b0| 2d 2d 2d 2d 2d 2d 2d 0d | 2d 2d 20 54 68 65 73 65 |-------.|-- These|
|000005c0| 20 72 6f 75 74 69 6e 65 | 73 20 75 73 65 20 74 68 | routine|s use th|
|000005d0| 65 20 22 64 6f 77 6e 68 | 69 6c 6c 20 73 69 6d 70 |e "downh|ill simp|
|000005e0| 6c 65 78 20 6d 65 74 68 | 6f 64 22 2e 20 41 20 73 |lex meth|od". A s|
|000005f0| 69 6d 70 6c 65 78 20 69 | 73 20 61 20 4e 20 64 69 |implex i|s a N di|
|00000600| 6d 65 6e 73 69 6f 6e 61 | 6c 20 67 65 6f 6d 65 74 |mensiona|l geomet|
|00000610| 72 69 63 61 6c 20 66 69 | 67 75 72 65 20 77 69 74 |rical fi|gure wit|
|00000620| 68 20 4e 2b 31 20 76 65 | 72 74 69 63 65 73 2e 20 |h N+1 ve|rtices. |
|00000630| 54 68 65 20 61 6c 67 6f | 72 69 74 68 69 6d 20 65 |The algo|rithim e|
|00000640| 76 61 6c 75 61 74 65 73 | 20 74 68 65 20 66 75 6e |valuates| the fun|
|00000650| 63 74 69 6f 6e 20 61 74 | 20 65 61 63 68 20 76 65 |ction at| each ve|
|00000660| 72 74 65 78 20 61 6e 64 | 20 73 74 65 70 73 20 74 |rtex and| steps t|
|00000670| 68 65 20 73 69 6d 70 6c | 65 78 20 74 6f 77 61 72 |he simpl|ex towar|
|00000680| 64 20 74 68 65 20 6d 69 | 6e 69 6d 75 6d 20 62 79 |d the mi|nimum by|
|00000690| 3a 20 31 29 20 72 65 66 | 6c 65 63 74 69 6e 67 20 |: 1) ref|lecting |
|000006a0| 61 20 76 65 72 74 65 78 | 20 61 77 61 79 20 66 72 |a vertex| away fr|
|000006b0| 6f 6d 20 74 68 65 20 66 | 75 6e 63 74 69 6f 6e 27 |om the f|unction'|
|000006c0| 73 20 68 69 67 68 65 73 | 74 20 70 6f 69 6e 74 2e |s highes|t point.|
|000006d0| 20 32 29 20 72 65 66 6c | 65 63 74 69 6f 6e 20 61 | 2) refl|ection a|
|000006e0| 6e 64 20 65 78 70 61 6e | 73 69 6f 6e 20 61 77 61 |nd expan|sion awa|
|000006f0| 79 20 66 72 6f 6d 20 74 | 68 65 20 68 69 67 68 65 |y from t|he highe|
|00000700| 73 74 20 70 6f 69 6e 74 | 2e 20 33 29 20 63 6f 6e |st point|. 3) con|
|00000710| 74 72 61 63 74 69 6f 6e | 20 61 77 61 79 20 66 72 |traction| away fr|
|00000720| 6f 6d 20 74 68 65 20 68 | 69 67 68 65 73 74 20 70 |om the h|ighest p|
|00000730| 6f 69 6e 74 2e 20 34 29 | 20 63 6f 6e 74 72 61 63 |oint. 4)| contrac|
|00000740| 74 69 6f 6e 20 69 6e 20 | 61 6c 6c 20 64 69 6d 65 |tion in |all dime|
|00000750| 6e 73 69 6f 6e 73 20 74 | 6f 77 61 72 64 20 74 68 |nsions t|oward th|
|00000760| 65 20 6c 6f 77 65 73 74 | 20 70 6f 69 6e 74 2e 0d |e lowest| point..|
|00000770| 0d 2d 2d 20 73 74 65 70 | 20 75 6e 74 69 6c 20 70 |.-- step| until p|
|00000780| 61 72 61 6d 65 74 65 72 | 73 20 63 68 61 6e 67 65 |arameter|s change|
|00000790| 20 62 79 20 6c 65 73 73 | 20 74 68 61 6e 20 74 6f | by less| than to|
|000007a0| 6c 0d 6d 69 6e 69 6d 69 | 7a 65 20 3d 20 69 6e 69 |l.minimi|ze = ini|
|000007b0| 74 2c 0d 20 20 20 20 20 | 20 20 20 20 20 20 73 74 |t,.     |      st|
|000007c0| 65 70 2c 0d 20 20 20 20 | 20 20 20 20 20 20 20 73 |ep,.    |       s|
|000007d0| 74 65 70 20 77 68 69 6c | 65 20 70 63 68 61 6e 67 |tep whil|e pchang|
|000007e0| 65 20 3e 20 74 6f 6c 2c | 0d 20 20 20 20 20 20 20 |e > tol,|.       |
|000007f0| 20 20 20 20 6d 69 6e 70 | 3a 3d 70 73 75 6d 2f 6d |    minp|:=psum/m|
|00000800| 0d 0d 70 63 68 61 6e 67 | 65 20 3d 20 73 75 6d 28 |..pchang|e = sum(|
|00000810| 28 61 62 73 28 70 5b 6c | 6f 77 65 73 74 5d 2d 70 |(abs(p[l|owest]-p|
|00000820| 5b 68 69 67 68 65 73 74 | 5d 29 2f 0d 20 20 20 20 |[highest|])/.    |
|00000830| 20 20 20 20 20 20 20 28 | 61 62 73 28 70 5b 6c 6f |       (|abs(p[lo|
|00000840| 77 65 73 74 5d 29 2b 61 | 62 73 28 70 5b 68 69 67 |west])+a|bs(p[hig|
|00000850| 68 65 73 74 5d 29 29 29 | 5b 69 69 5d 2c 69 69 2c |hest])))|[ii],ii,|
|00000860| 0d 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 31 |.       |       1|
|00000870| 2c 6e 29 0d 0d 2d 2d 20 | 6d 6f 76 65 20 73 69 6d |,n)..-- |move sim|
|00000880| 70 6c 65 78 20 6f 6e 65 | 20 73 74 65 70 0d 73 74 |plex one| step.st|
|00000890| 65 70 20 3d 20 20 72 61 | 6e 6b 2c 0d 20 74 72 79 |ep =  ra|nk,. try|
|000008a0| 28 2d 61 6c 70 68 61 29 | 2c 20 20 20 20 20 20 20 |(-alpha)|,       |
|000008b0| 20 20 20 20 20 20 20 20 | 20 2d 2d 20 72 65 66 6c |        | -- refl|
|000008c0| 65 63 74 20 66 72 6f 6d | 20 68 69 67 68 65 73 74 |ect from| highest|
|000008d0| 0d 20 74 72 79 28 67 61 | 6d 6d 61 29 20 77 68 65 |. try(ga|mma) whe|
|000008e0| 6e 20 79 74 72 79 20 b2 | 20 79 5b 6c 6f 77 65 73 |n ytry .| y[lowes|
|000008f0| 74 5d 2c 20 2d 2d 20 6b | 65 65 70 20 67 6f 69 6e |t], -- k|eep goin|
|00000900| 67 0d 20 28 79 73 61 76 | 65 3a 3d 79 5b 68 69 67 |g. (ysav|e:=y[hig|
|00000910| 68 65 73 74 5d 2c 0d 20 | 20 74 72 79 28 62 65 74 |hest],. | try(bet|
|00000920| 61 29 2c 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |a),     |        |
|00000930| 20 20 20 20 2d 2d 20 63 | 6f 6e 74 72 61 63 74 20 |    -- c|ontract |
|00000940| 66 72 6f 6d 20 68 69 67 | 68 65 73 74 0d 20 20 73 |from hig|hest.  s|
|00000950| 68 72 69 6e 6b 20 77 68 | 65 6e 20 79 74 72 79 20 |hrink wh|en ytry |
|00000960| b3 20 79 73 61 76 65 29 | 20 77 68 65 6e 20 79 74 |. ysave)| when yt|
|00000970| 72 79 20 b3 20 79 5b 68 | 69 67 68 5d 0d 0d 2d 2d |ry . y[h|igh]..--|
|00000980| 20 66 69 6e 64 20 6c 6f | 77 65 73 74 2c 20 68 69 | find lo|west, hi|
|00000990| 67 68 65 73 74 20 61 6e | 64 20 6e 65 78 74 20 68 |ghest an|d next h|
|000009a0| 69 67 68 65 73 74 20 76 | 65 72 74 65 78 0d 72 61 |ighest v|ertex.ra|
|000009b0| 6e 6b 20 3d 20 6c 6f 77 | 65 73 74 3a 3d 31 2c 68 |nk = low|est:=1,h|
|000009c0| 69 67 68 3a 3d 31 2c 68 | 69 67 68 65 73 74 3a 3d |igh:=1,h|ighest:=|
|000009d0| 32 2c 69 3a 3d 31 2c 0d | 20 20 20 28 6c 6f 77 65 |2,i:=1,.|   (lowe|
|000009e0| 73 74 3a 3d 69 20 77 68 | 65 6e 20 79 5b 69 5d 3c |st:=i wh|en y[i]<|
|000009f0| 79 5b 6c 6f 77 65 73 74 | 5d 2c 2c 0d 20 20 20 20 |y[lowest|],,.    |
|00000a00| 28 68 69 67 68 3a 3d 68 | 69 67 68 65 73 74 2c 68 |(high:=h|ighest,h|
|00000a10| 69 67 68 65 73 74 3a 3d | 69 29 20 77 68 65 6e 20 |ighest:=|i) when |
|00000a20| 79 5b 69 5d 3e 79 5b 68 | 69 67 68 65 73 74 5d 2c |y[i]>y[h|ighest],|
|00000a30| 2c 0d 20 20 20 20 68 69 | 67 68 3a 3d 69 20 77 68 |,.    hi|gh:=i wh|
|00000a40| 65 6e 20 79 5b 69 5d 3e | 79 5b 68 69 67 68 5d 20 |en y[i]>|y[high] |
|00000a50| 61 6e 64 20 69 20 ad 20 | 68 69 67 68 65 73 74 2c |and i . |highest,|
|00000a60| 2c 0d 20 20 20 20 69 3a | 3d 69 2b 31 29 20 77 68 |,.    i:|=i+1) wh|
|00000a70| 69 6c 65 20 69 b2 6d 0d | 0d 2d 2d 20 6d 6f 76 65 |ile i.m.|.-- move|
|00000a80| 20 68 69 67 68 65 73 74 | 20 76 65 72 74 65 78 20 | highest| vertex |
|00000a90| 74 68 72 6f 75 67 68 20 | 66 61 63 65 20 62 79 20 |through |face by |
|00000aa0| 66 61 63 0d 74 72 79 28 | 66 61 63 29 20 3d 20 70 |fac.try(|fac) = p|
|00000ab0| 74 72 79 3a 3d 70 73 75 | 6d 2a 28 31 2d 66 61 63 |try:=psu|m*(1-fac|
|00000ac0| 29 2f 6e 2d 0d 20 20 20 | 20 20 20 20 20 20 20 20 |)/n-.   |        |
|00000ad0| 20 20 20 20 20 20 20 70 | 5b 68 69 67 68 65 73 74 |       p|[highest|
|00000ae0| 5d 2a 28 28 31 2d 66 61 | 63 29 2f 6e 2d 66 61 63 |]*((1-fa|c)/n-fac|
|00000af0| 29 2c 0d 20 20 20 20 79 | 74 72 79 3a 3d 66 28 70 |),.    y|try:=f(p|
|00000b00| 74 72 79 29 2c 0d 20 20 | 20 20 28 79 5b 68 69 67 |try),.  |  (y[hig|
|00000b10| 68 65 73 74 5d 3a 3d 79 | 74 72 79 2c 0d 20 20 20 |hest]:=y|try,.   |
|00000b20| 20 20 70 73 75 6d 3a 3d | 70 73 75 6d 2b 70 74 72 |  psum:=|psum+ptr|
|00000b30| 79 2d 70 5b 68 69 67 68 | 65 73 74 5d 2c 0d 20 20 |y-p[high|est],.  |
|00000b40| 20 20 20 70 3a 3d 72 65 | 70 6c 61 63 65 28 70 2c |   p:=re|place(p,|
|00000b50| 68 69 67 68 65 73 74 2c | 70 74 72 79 29 29 20 77 |highest,|ptry)) w|
|00000b60| 68 65 6e 20 79 74 72 79 | 3c 79 5b 68 69 67 68 65 |hen ytry|<y[highe|
|00000b70| 73 74 5d 0d 0d 2d 2d 20 | 73 68 72 69 6e 6b 20 65 |st]..-- |shrink e|
|00000b80| 6e 74 69 72 65 20 73 69 | 6d 70 6c 65 78 0d 73 68 |ntire si|mplex.sh|
|00000b90| 72 69 6e 6b 70 28 6b 29 | 5b 6a 5d 20 3d 20 2e 35 |rinkp(k)|[j] = .5|
|00000ba0| 2a 28 70 5b 6b 2c 6a 5d | 2b 70 5b 6c 6f 77 65 73 |*(p[k,j]|+p[lowes|
|00000bb0| 74 2c 6a 5d 29 20 64 69 | 6d 5b 6e 5d 0d 73 68 72 |t,j]) di|m[n].shr|
|00000bc0| 69 6e 6b 20 3d 20 6b 6b | 3a 3d 31 2c 20 20 20 20 |ink = kk|:=1,    |
|00000bd0| 20 20 0d 20 20 28 28 70 | 73 75 6d 3a 3d 73 68 72 |  .  ((p|sum:=shr|
|00000be0| 69 6e 6b 70 28 6b 6b 29 | 2c 0d 20 20 20 20 70 3a |inkp(kk)|,.    p:|
|00000bf0| 3d 72 65 70 6c 61 63 65 | 28 70 2c 6b 6b 2c 70 73 |=replace|(p,kk,ps|
|00000c00| 75 6d 29 29 20 77 68 65 | 6e 20 6b 6b ad 6c 6f 77 |um)) whe|n kk.low|
|00000c10| 65 73 74 2c 2c 0d 20 20 | 20 20 6b 6b 3a 3d 6b 6b |est,,.  |  kk:=kk|
|00000c20| 2b 31 20 29 20 77 68 69 | 6c 65 20 6b 6b b2 6d 2c |+1 ) whi|le kk.m,|
|00000c30| 0d 20 20 79 3a 3d 66 70 | 0d 0d 2d 2d 20 64 65 66 |.  y:=fp|..-- def|
|00000c40| 69 6e 65 20 66 69 6e 69 | 74 65 20 61 72 72 61 79 |ine fini|te array|
|00000c50| 73 20 73 6f 20 74 68 65 | 79 20 63 61 6e 20 62 65 |s so the|y can be|
|00000c60| 20 61 73 73 69 67 6e 65 | 64 0d 73 75 6d 70 5b 6a | assigne|d.sump[j|
|00000c70| 5d 20 3d 20 73 75 6d 28 | 70 5b 69 69 2c 6a 5d 2c |] = sum(|p[ii,j],|
|00000c80| 69 69 2c 31 2c 6d 29 20 | 64 69 6d 5b 6e 5d 0d 69 |ii,1,m) |dim[n].i|
|00000c90| 6e 69 74 70 5b 69 2c 6a | 5d 3d 20 67 75 65 73 73 |nitp[i,j|]= guess|
|00000ca0| 5b 6a 5d 2b 28 64 65 6c | 74 61 73 5b 6a 5d 20 77 |[j]+(del|tas[j] w|
|00000cb0| 68 65 6e 20 69 3d 6a 2c | 30 29 20 64 69 6d 5b 6d |hen i=j,|0) dim[m|
|00000cc0| 2c 6e 5d 0d 66 70 5b 69 | 5d 3d 66 28 70 5b 69 5d |,n].fp[i|]=f(p[i]|
|00000cd0| 29 20 64 69 6d 5b 6d 5d | 0d 0d 69 6e 69 74 20 3d |) dim[m]|..init =|
|00000ce0| 20 6e 3a 3d 63 6f 75 6e | 74 28 67 75 65 73 73 29 | n:=coun|t(guess)|
|00000cf0| 2c 20 6d 3a 3d 6e 2b 31 | 2c 0d 20 20 20 20 20 20 |, m:=n+1|,.      |
|00000d00| 20 70 3a 3d 69 6e 69 74 | 70 2c 0d 20 20 20 20 20 | p:=init|p,.     |
|00000d10| 20 20 70 73 75 6d 3a 3d | 73 75 6d 70 2c 0d 20 20 |  psum:=|sump,.  |
|00000d20| 20 20 20 20 20 79 3a 3d | 66 70 0d 0d 72 65 70 6c |     y:=|fp..repl|
|00000d30| 61 63 65 28 61 72 72 61 | 79 2c 69 6e 64 65 78 2c |ace(arra|y,index,|
|00000d40| 6e 65 77 76 61 6c 29 5b | 69 5d 20 3d 20 6e 65 77 |newval)[|i] = new|
|00000d50| 76 61 6c 20 77 68 65 6e | 20 69 3d 69 6e 64 65 78 |val when| i=index|
|00000d60| 2c 0d 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |,.      |        |
|00000d70| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
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+--------+-------------------------+-------------------------+--------+--------+