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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 01 00 00 00 00 00 00 |.TEXTMPa|d.......|
|00000050| 00 00 00 00 00 0d 40 00 | 00 01 56 aa 05 d7 34 aa |......@.|..V...4.|
|00000060| 05 d7 34 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |..4.....|........|
|00000070| 00 00 00 00 00 00 00 00 | 00 00 81 81 21 da 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 33 20 | 67 69 76 65 73 20 61 62 | 1.0e-3 |gives ab|
|000002d0| 6f 75 74 20 32 20 64 69 | 67 69 74 0d 20 20 20 20 |out 2 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 | 33 0d 0d 70 6c 6f 74 20 |ol = 1e-|3..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 33 2e 38 37 32 |    minp|:{83.872|
|00000570| 2c 2d 37 37 2e 30 35 33 | 2c 30 2e 38 36 39 7d 0d |,-77.053|,0.869}.|
|00000580| 0d 70 6c 6f 74 20 66 69 | 74 28 6d 69 6e 70 2c 58 |.plot fi|t(minp,X|
|00000590| 29 0d 0d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 20 6d |)..-----|------ m|
|000005a0| 69 6e 69 6d 69 7a 61 74 | 69 6f 6e 20 72 6f 75 74 |inimizat|ion rout|
|000005b0| 69 6e 65 73 20 2d 2d 2d | 2d 2d 2d 2d 0d 2d 2d 20 |ines ---|----.-- |
|000005c0| 54 68 65 73 65 20 72 6f | 75 74 69 6e 65 73 20 75 |These ro|utines u|
|000005d0| 73 65 20 74 68 65 20 22 | 64 6f 77 6e 68 69 6c 6c |se the "|downhill|
|000005e0| 20 73 69 6d 70 6c 65 78 | 20 6d 65 74 68 6f 64 22 | simplex| method"|
|000005f0| 2e 20 41 20 73 69 6d 70 | 6c 65 78 20 69 73 20 61 |. A simp|lex is a|
|00000600| 20 4e 20 64 69 6d 65 6e | 73 69 6f 6e 61 6c 20 67 | N dimen|sional g|
|00000610| 65 6f 6d 65 74 72 69 63 | 61 6c 20 66 69 67 75 72 |eometric|al figur|
|00000620| 65 20 77 69 74 68 20 4e | 2b 31 20 76 65 72 74 69 |e with N|+1 verti|
|00000630| 63 65 73 2e 20 54 68 65 | 20 61 6c 67 6f 72 69 74 |ces. The| algorit|
|00000640| 68 69 6d 20 65 76 61 6c | 75 61 74 65 73 20 74 68 |him eval|uates th|
|00000650| 65 20 66 75 6e 63 74 69 | 6f 6e 20 61 74 20 65 61 |e functi|on at ea|
|00000660| 63 68 20 76 65 72 74 65 | 78 20 61 6e 64 20 73 74 |ch verte|x and st|
|00000670| 65 70 73 20 74 68 65 20 | 73 69 6d 70 6c 65 78 20 |eps the |simplex |
|00000680| 74 6f 77 61 72 64 20 74 | 68 65 20 6d 69 6e 69 6d |toward t|he minim|
|00000690| 75 6d 20 62 79 3a 20 31 | 29 20 72 65 66 6c 65 63 |um by: 1|) reflec|
|000006a0| 74 69 6e 67 20 61 20 76 | 65 72 74 65 78 20 61 77 |ting a v|ertex aw|
|000006b0| 61 79 20 66 72 6f 6d 20 | 74 68 65 20 66 75 6e 63 |ay from |the func|
|000006c0| 74 69 6f 6e 27 73 20 68 | 69 67 68 65 73 74 20 70 |tion's h|ighest p|
|000006d0| 6f 69 6e 74 2e 20 32 29 | 20 72 65 66 6c 65 63 74 |oint. 2)| reflect|
|000006e0| 69 6f 6e 20 61 6e 64 20 | 65 78 70 61 6e 73 69 6f |ion and |expansio|
|000006f0| 6e 20 61 77 61 79 20 66 | 72 6f 6d 20 74 68 65 20 |n away f|rom the |
|00000700| 68 69 67 68 65 73 74 20 | 70 6f 69 6e 74 2e 20 33 |highest |point. 3|
|00000710| 29 20 63 6f 6e 74 72 61 | 63 74 69 6f 6e 20 61 77 |) contra|ction aw|
|00000720| 61 79 20 66 72 6f 6d 20 | 74 68 65 20 68 69 67 68 |ay from |the high|
|00000730| 65 73 74 20 70 6f 69 6e | 74 2e 20 34 29 20 63 6f |est poin|t. 4) co|
|00000740| 6e 74 72 61 63 74 69 6f | 6e 20 69 6e 20 61 6c 6c |ntractio|n in all|
|00000750| 20 64 69 6d 65 6e 73 69 | 6f 6e 73 20 74 6f 77 61 | dimensi|ons towa|
|00000760| 72 64 20 74 68 65 20 6c | 6f 77 65 73 74 20 70 6f |rd the l|owest po|
|00000770| 69 6e 74 2e 0d 0d 2d 2d | 20 73 74 65 70 20 75 6e |int...--| step un|
|00000780| 74 69 6c 20 70 61 72 61 | 6d 65 74 65 72 73 20 63 |til para|meters c|
|00000790| 68 61 6e 67 65 20 62 79 | 20 6c 65 73 73 20 74 68 |hange by| less th|
|000007a0| 61 6e 20 74 6f 6c 0d 6d | 69 6e 69 6d 69 7a 65 20 |an tol.m|inimize |
|000007b0| 3d 20 69 6e 69 74 2c 0d | 20 20 20 20 20 20 20 20 |= init,.|        |
|000007c0| 20 20 20 73 74 65 70 2c | 0d 20 20 20 20 20 20 20 |   step,|.       |
|000007d0| 20 20 20 20 73 74 65 70 | 20 77 68 69 6c 65 20 70 |    step| while p|
|000007e0| 63 68 61 6e 67 65 20 3e | 20 74 6f 6c 2c 0d 20 20 |change >| tol,.  |
|000007f0| 20 20 20 20 20 20 20 20 | 20 6d 69 6e 70 3a 3d 70 |        | minp:=p|
|00000800| 73 75 6d 2f 6d 0d 0d 70 | 63 68 61 6e 67 65 20 3d |sum/m..p|change =|
|00000810| 20 73 75 6d 28 28 61 62 | 73 28 70 5b 6c 6f 77 65 | sum((ab|s(p[lowe|
|00000820| 73 74 5d 2d 70 5b 68 69 | 67 68 65 73 74 5d 29 2f |st]-p[hi|ghest])/|
|00000830| 0d 20 20 20 20 20 20 20 | 20 20 20 20 28 61 62 73 |.       |    (abs|
|00000840| 28 70 5b 6c 6f 77 65 73 | 74 5d 29 2b 61 62 73 28 |(p[lowes|t])+abs(|
|00000850| 70 5b 68 69 67 68 65 73 | 74 5d 29 29 29 5b 69 69 |p[highes|t])))[ii|
|00000860| 5d 2c 69 69 2c 0d 20 20 | 20 20 20 20 20 20 20 20 |],ii,.  |        |
|00000870| 20 20 20 20 31 2c 6e 29 | 0d 0d 2d 2d 20 6d 6f 76 |    1,n)|..-- mov|
|00000880| 65 20 73 69 6d 70 6c 65 | 78 20 6f 6e 65 20 73 74 |e simple|x one st|
|00000890| 65 70 0d 73 74 65 70 20 | 3d 20 20 72 61 6e 6b 2c |ep.step |=  rank,|
|000008a0| 0d 20 74 72 79 28 2d 61 | 6c 70 68 61 29 2c 20 20 |. try(-a|lpha),  |
|000008b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 2d 2d |        |      --|
|000008c0| 20 72 65 66 6c 65 63 74 | 20 66 72 6f 6d 20 68 69 | reflect| from hi|
|000008d0| 67 68 65 73 74 0d 20 74 | 72 79 28 67 61 6d 6d 61 |ghest. t|ry(gamma|
|000008e0| 29 20 77 68 65 6e 20 79 | 74 72 79 20 b2 20 79 5b |) when y|try . y[|
|000008f0| 6c 6f 77 65 73 74 5d 2c | 2c 20 2d 2d 20 6b 65 65 |lowest],|, -- kee|
|00000900| 70 20 67 6f 69 6e 67 0d | 20 28 79 73 61 76 65 3a |p going.| (ysave:|
|00000910| 3d 79 5b 68 69 67 65 73 | 74 5d 2c 0d 20 20 74 72 |=y[higes|t],.  tr|
|00000920| 79 28 62 65 74 61 29 2c | 20 20 20 20 20 20 20 20 |y(beta),|        |
|00000930| 20 20 20 20 20 20 20 20 | 20 2d 2d 20 63 6f 6e 74 |        | -- cont|
|00000940| 72 61 63 74 20 66 72 6f | 6d 20 68 69 67 68 65 73 |ract fro|m highes|
|00000950| 74 0d 20 20 73 68 72 69 | 6e 6b 20 77 68 65 6e 20 |t.  shri|nk when |
|00000960| 79 74 72 79 20 b3 20 79 | 73 61 76 65 29 20 77 68 |ytry . y|save) wh|
|00000970| 65 6e 20 79 74 72 79 20 | b3 20 79 5b 68 69 67 68 |en ytry |. y[high|
|00000980| 5d 0d 0d 2d 2d 20 66 69 | 6e 64 20 6c 6f 77 65 73 |]..-- fi|nd lowes|
|00000990| 74 2c 20 68 69 67 68 65 | 73 74 20 61 6e 64 20 6e |t, highe|st and n|
|000009a0| 65 78 74 20 68 69 67 68 | 65 73 74 20 76 65 72 74 |ext high|est vert|
|000009b0| 65 78 0d 72 61 6e 6b 20 | 3d 20 6c 6f 77 65 73 74 |ex.rank |= lowest|
|000009c0| 3a 3d 31 2c 68 69 67 68 | 3a 3d 31 2c 68 69 67 68 |:=1,high|:=1,high|
|000009d0| 65 73 74 3a 3d 32 2c 69 | 3a 3d 31 2c 0d 20 20 20 |est:=2,i|:=1,.   |
|000009e0| 28 6c 6f 77 65 73 74 3a | 3d 69 20 77 68 65 6e 20 |(lowest:|=i when |
|000009f0| 79 5b 69 5d 3c 79 5b 6c | 6f 77 65 73 74 5d 2c 2c |y[i]<y[l|owest],,|
|00000a00| 0d 20 20 20 20 28 68 69 | 67 68 3a 3d 68 69 67 68 |.    (hi|gh:=high|
|00000a10| 65 73 74 2c 68 69 67 68 | 65 73 74 3a 3d 69 29 20 |est,high|est:=i) |
|00000a20| 77 68 65 6e 20 79 5b 69 | 5d 3e 79 5b 68 69 67 68 |when y[i|]>y[high|
|00000a30| 65 73 74 5d 2c 2c 0d 20 | 20 20 20 68 69 67 68 3a |est],,. |   high:|
|00000a40| 3d 69 20 77 68 65 6e 20 | 79 5b 69 5d 3e 79 5b 68 |=i when |y[i]>y[h|
|00000a50| 69 67 68 5d 20 61 6e 64 | 20 69 20 ad 20 68 69 67 |igh] and| i . hig|
|00000a60| 68 65 73 74 2c 2c 0d 20 | 20 20 20 69 3a 3d 69 2b |hest,,. |   i:=i+|
|00000a70| 31 29 20 77 68 69 6c 65 | 20 69 b2 6d 0d 0d 2d 2d |1) while| i.m..--|
|00000a80| 20 6d 6f 76 65 20 68 69 | 67 68 65 73 74 20 76 65 | move hi|ghest ve|
|00000a90| 72 74 65 78 20 74 68 72 | 6f 75 67 68 20 66 61 63 |rtex thr|ough fac|
|00000aa0| 65 20 62 79 20 66 61 63 | 0d 74 72 79 28 66 61 63 |e by fac|.try(fac|
|00000ab0| 29 20 3d 20 70 74 72 79 | 3a 3d 70 73 75 6d 2a 28 |) = ptry|:=psum*(|
|00000ac0| 31 2d 66 61 63 29 2f 6e | 2d 0d 20 20 20 20 20 20 |1-fac)/n|-.      |
|00000ad0| 20 20 20 20 20 20 20 20 | 20 20 20 20 70 5b 68 69 |        |    p[hi|
|00000ae0| 67 68 65 73 74 5d 2a 28 | 28 31 2d 66 61 63 29 2f |ghest]*(|(1-fac)/|
|00000af0| 6e 2d 66 61 63 29 2c 0d | 20 20 20 20 79 74 72 79 |n-fac),.|    ytry|
|00000b00| 3a 3d 66 28 70 74 72 79 | 29 2c 0d 20 20 20 20 28 |:=f(ptry|),.    (|
|00000b10| 79 5b 68 69 67 68 65 73 | 74 5d 3a 3d 79 74 72 79 |y[highes|t]:=ytry|
|00000b20| 2c 0d 20 20 20 20 20 70 | 73 75 6d 3a 3d 70 73 75 |,.     p|sum:=psu|
|00000b30| 6d 2b 70 74 72 79 2d 70 | 5b 68 69 67 68 65 73 74 |m+ptry-p|[highest|
|00000b40| 5d 2c 0d 20 20 20 20 20 | 70 3a 3d 72 65 70 6c 61 |],.     |p:=repla|
|00000b50| 63 65 28 70 2c 68 69 67 | 68 65 73 74 2c 70 74 72 |ce(p,hig|hest,ptr|
|00000b60| 79 29 29 20 77 68 65 6e | 20 79 74 72 79 3c 79 5b |y)) when| ytry<y[|
|00000b70| 68 69 67 68 65 73 74 5d | 0d 0d 2d 2d 20 73 68 72 |highest]|..-- shr|
|00000b80| 69 6e 6b 20 65 6e 74 69 | 72 65 20 73 69 6d 70 6c |ink enti|re simpl|
|00000b90| 65 78 0d 73 68 72 69 6e | 6b 70 28 6b 29 5b 6a 5d |ex.shrin|kp(k)[j]|
|00000ba0| 20 3d 20 2e 35 2a 28 70 | 5b 6b 2c 6a 5d 2b 70 5b | = .5*(p|[k,j]+p[|
|00000bb0| 6c 6f 77 65 73 74 2c 6a | 5d 29 20 64 69 6d 5b 6e |lowest,j|]) dim[n|
|00000bc0| 5d 0d 73 68 72 69 6e 6b | 20 3d 20 6b 6b 3a 3d 31 |].shrink| = kk:=1|
|00000bd0| 2c 20 20 20 20 20 20 0d | 20 20 28 28 70 73 75 6d |,      .|  ((psum|
|00000be0| 3a 3d 73 68 72 69 6e 6b | 70 28 6b 6b 29 2c 0d 20 |:=shrink|p(kk),. |
|00000bf0| 20 20 20 70 3a 3d 72 65 | 70 6c 61 63 65 28 70 2c |   p:=re|place(p,|
|00000c00| 6b 6b 2c 70 73 75 6d 29 | 2c 0d 20 20 20 20 6b 6b |kk,psum)|,.    kk|
|00000c10| 3a 3d 6b 6b 2b 31 29 20 | 77 68 65 6e 20 6b 6b ad |:=kk+1) |when kk.|
|00000c20| 6c 6f 77 65 73 74 29 20 | 77 68 69 6c 65 20 6b 6b |lowest) |while kk|
|00000c30| b2 6d 2c 0d 20 20 79 3a | 3d 66 70 0d 0d 2d 2d 20 |.m,.  y:|=fp..-- |
|00000c40| 64 65 66 69 6e 65 20 66 | 69 6e 69 74 65 20 61 72 |define f|inite ar|
|00000c50| 72 61 79 73 20 73 6f 20 | 74 68 65 79 20 63 61 6e |rays so |they can|
|00000c60| 20 62 65 20 61 73 73 69 | 67 6e 65 64 0d 73 75 6d | be assi|gned.sum|
|00000c70| 70 5b 6a 5d 20 3d 20 73 | 75 6d 28 70 5b 69 69 2c |p[j] = s|um(p[ii,|
|00000c80| 6a 5d 2c 69 69 2c 31 2c | 6d 29 20 64 69 6d 5b 6e |j],ii,1,|m) dim[n|
|00000c90| 5d 0d 69 6e 69 74 70 5b | 69 2c 6a 5d 3d 20 67 75 |].initp[|i,j]= gu|
|00000ca0| 65 73 73 5b 6a 5d 2b 28 | 64 65 6c 74 61 73 5b 6a |ess[j]+(|deltas[j|
|00000cb0| 5d 20 77 68 65 6e 20 69 | 3d 6a 2c 30 29 20 64 69 |] when i|=j,0) di|
|00000cc0| 6d 5b 6d 2c 6e 5d 0d 66 | 70 5b 69 5d 3d 66 28 70 |m[m,n].f|p[i]=f(p|
|00000cd0| 5b 69 5d 29 20 64 69 6d | 5b 6d 5d 0d 0d 69 6e 69 |[i]) dim|[m]..ini|
|00000ce0| 74 20 3d 20 6e 3a 3d 63 | 6f 75 6e 74 28 67 75 65 |t = n:=c|ount(gue|
|00000cf0| 73 73 29 2c 20 6d 3a 3d | 6e 2b 31 2c 0d 20 20 20 |ss), m:=|n+1,.   |
|00000d00| 20 20 20 20 70 3a 3d 69 | 6e 69 74 70 2c 0d 20 20 |    p:=i|nitp,.  |
|00000d10| 20 20 20 20 20 70 73 75 | 6d 3a 3d 73 75 6d 70 2c |     psu|m:=sump,|
|00000d20| 0d 20 20 20 20 20 20 20 | 79 3a 3d 66 70 0d 0d 72 |.       |y:=fp..r|
|00000d30| 65 70 6c 61 63 65 28 61 | 72 72 61 79 2c 69 6e 64 |eplace(a|rray,ind|
|00000d40| 65 78 2c 6e 65 77 76 61 | 6c 29 5b 69 5d 20 3d 20 |ex,newva|l)[i] = |
|00000d50| 6e 65 77 76 61 6c 20 77 | 68 65 6e 20 69 3d 69 6e |newval w|hen i=in|
|00000d60| 64 65 78 2c 0d 20 20 20 | 20 20 20 20 20 20 20 20 |dex,.   |        |
|00000d70| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00000d80| 20 20 20 20 20 20 61 72 | 72 61 79 5b 69 5d 0d 0d |      ar|ray[i]..|
|00000d90| 2d 2d 20 74 75 6e 65 61 | 62 6c 65 20 63 6f 6e 73 |-- tunea|ble cons|
|00000da0| 74 61 6e 74 73 0d 61 6c | 70 68 61 3d 31 3b 20 62 |tants.al|pha=1; b|
|00000db0| 65 74 61 3d 2e 35 3b 20 | 67 61 6d 6d 61 3d 32 0d |eta=.5; |gamma=2.|
|00000dc0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000dd0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000de0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000df0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000e00| 00 00 01 00 00 00 01 24 | 00 00 00 24 00 00 00 32 |.......$|...$...2|
|00000e10| 30 28 00 0a d0 68 00 08 | b0 41 62 02 30 01 31 40 |0(...h..|.Ab.0.1@|
|00000e20| 00 08 d0 a8 00 04 20 50 | a0 24 20 5f 4e 75 4e 5e |...... P|.$ _NuN^|
|00000e30| 08 6d 69 6e 69 6d 69 7a | 65 00 02 00 00 00 54 45 |.minimiz|e.....TE|
|00000e40| 58 54 4d 50 61 64 01 00 | 00 34 00 40 00 00 00 00 |XTMPad..|.4.@....|
|00000e50| 00 00 54 45 58 54 4d 50 | 61 64 01 00 00 34 00 40 |..TEXTMP|ad...4.@|
|00000e60| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000e70| 00 00 a8 4a 08 e4 00 00 | 0d 40 00 00 01 56 67 5c |...J....|.@...Vg\|
|00000e80| 6a 16 04 00 00 cc 67 54 | 6a 06 52 00 6a 1e 60 50 |j.....gT|j.R.j.`P|
|00000e90| 04 00 00 32 67 26 60 48 | 04 00 00 1f 67 42 6a 06 |...2g&`H|....gBj.|
|00000ea0| 52 00 6a 28 60 3a 55 00 | 6a 36 60 30 2f 0c 3f 3c |R.j(`:U.|j6`0/.?<|
|00000eb0| 28 29 4e ba ff 88 28 40 | 5c 8f 60 24 2f 0c 3f 3c |()N...(@|\.`$/.?<|
|00000ec0| 5b 5d 4e ba ff 78 28 40 | 5c 8f 60 14 2f 0c 3f 3c |[]N..x(@|\.`./.?<|
|00000ed0| 7b 7d 4e ba ff 68 28 40 | 5c 8f 60 04 28 6d a7 e2 |{}N..h(@|\.`.(m..|
|00000ee0| 52 8c b9 ed a7 e2 65 00 | ff 72 20 0c 4c df 10 80 |R.....e.|.r .L...|
|00000ef0| 4e 5e 4e 75 4e 56 ff f8 | 48 e7 1f 38 42 a7 a9 24 |N^NuNV..|H..8B..$|
|00000f00| 00 00 00 20 00 00 00 03 | 00 02 3f f9 8e fa 35 12 |... ....|..?...5.|
|00000f10| 94 e9 c8 ae 01 55 01 2d | 00 03 00 28 00 a2 01 2b |.....U.-|...(...+|
|00000f20| 01 57 00 2a 00 00 01 00 | 00 00 01 24 00 00 00 24 |.W.*....|...$...$|
|00000f30| 00 00 00 32 00 25 f4 e4 | 07 5a 00 00 00 1c 00 32 |...2.%..|.Z.....2|
|00000f40| 00 00 50 52 65 66 00 00 | 00 0a 00 80 ff ff 00 00 |..PRef..|........|
|00000f50| 00 00 00 25 f3 f8 00 00 | 00 00 00 00 00 00 00 00 |...%....|........|
|00000f60| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000f70| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
+--------+-------------------------+-------------------------+--------+--------+