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/ Ian & Stuart's Australian Mac 1993 September / September 93.iso / Archives / Applications / Calculators / NumberCrunch 1.41 / Number Crunch II Demo / Library Routines / All Library Routines
MacBinary  |  1992-10-18  |  155.6 KB  |  [Ndc2/NCII]
open in: MacOS 8.1     |     Win98     |     DOS

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This file was processed as: MacBinary (archive/macBinary).

ConfidenceProgramDetectionMatch TypeSupport
10% dexvert MacBinary (archive/macBinary) fallback Supported
100% file MacBinary II, inited, Thu Sep 3 18:24:31 1992, modified Sun Oct 18 07:47:59 1992, creator 'NCII', type 'Ndc2', 55898 bytes "All Library Routines" DIY-Thermocam raw data (Lepton 3.x), scale 0-0, spot sensor temperature 0.000000, unit celsius, color scheme 0, calibration: offset 10635122040493960690137589106325061632.000000, slope 10393912610528979221508331143168.000000, at 0xdada 103255 bytes resource DIY-Thermocam raw data (Lepton 3.x), scale 0-0, spot sensor temperature 0.000000, unit celsius, color scheme 0, calibration: offset 10635122040493960690137589106325061632.000000, slope 10393912610528979221508331143168.000000 default (weak)
99% file data default
66% TrID raw Group 3 FAX bitmap default (weak)
33% TrID MacBinary 2 default (weak)
100% siegfried fmt/1762 MacBinary (II) default
100% lsar MacBinary default


id metadata
keyvalue
macFileType[Ndc2]
macFileCreator[NCII]


hex view
+--------+-------------------------+-------------------------+--------+--------+
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|00000010| 75 74 69 6e 65 73 00 00 | 00 00 00 00 00 00 00 00 |utines..|........|
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|00000030| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
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|000008a0| 69 7a 65 41 73 49 66 52 | 65 61 6c 28 7a 29 20 74 |izeAsIfR|eal(z) t|
|000008b0| 68 65 6e 20 62 65 65 70 | 0d 2e 20 20 20 65 6e 64 |hen beep|..   end|
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|00000a60| 20 20 20 4f 75 74 70 75 | 74 3a 0d 2e 20 23 20 20 |   Outpu|t:.. #  |
|00000a70| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00000a80| 20 20 20 42 65 73 73 65 | 6c 20 3d 20 6a 5f 6c 28 |   Besse|l = j_l(|
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|00000b20| 73 65 6c 20 3d 20 22 45 | 52 52 4f 52 3a 20 4c 20 |sel = "E|RROR: L |
|00000b30| 6d 75 73 74 20 62 65 20 | 3e 30 20 69 6e 20 42 65 |must be |>0 in Be|
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|00000bf0| 20 00 00 7c 00 00 00 02 | 00 7d 95 20 00 00 01 da | ..|....|.}. ....|
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|00000c10| 00 00 00 00 20 00 00 7c | 00 00 00 02 00 7d 95 20 |.... ..||.....}. |
|00000c20| 00 00 01 da 00 91 48 ee | 05 00 7d 84 20 00 00 00 |......H.|..}. ...|
|00000c30| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 3f |........|.......?|
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|00000cf0| 65 6e 64 72 65 28 4a 2c | 20 78 29 20 20 23 20 52 |endre(J,| x)  # R|
|00000d00| 65 74 75 72 6e 73 20 50 | 5b 6c 2c 31 c9 73 69 7a |eturns P|[l,1.siz|
|00000d10| 65 28 78 29 5d 20 3d 20 | 50 5f 6c 28 78 29 20 66 |e(x)] = |P_l(x) f|
|00000d20| 6f 72 20 6c 3d 31 c9 4a | 2e 20 0d 2e 20 20 20 76 |or l=1.J|. ..   v|
|00000d30| 61 72 20 50 7a 2c 20 6e | 0d 2e 20 20 20 23 20 20 |ar Pz, n|..   #  |
|00000d40| 49 6e 70 75 74 3a 20 20 | 20 78 20 3d 20 61 72 72 |Input:  | x = arr|
|00000d50| 61 79 20 6f 66 20 70 6f | 69 6e 74 73 20 74 6f 20 |ay of po|ints to |
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|00000d70| 65 20 70 6f 6c 79 6e 6f | 6d 69 61 6c 73 20 6f 6e |e polyno|mials on|
|00000d80| 2e 0d 2e 20 20 20 23 20 | 20 20 20 20 20 20 20 20 |...   # |        |
|00000d90| 20 20 20 20 4a 20 3d 20 | 70 6f 73 69 74 69 76 65 |    J = |positive|
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|00000db0| 20 20 23 20 20 4f 75 74 | 70 75 74 3a 20 43 61 6c |  #  Out|put: Cal|
|00000dc0| 63 4c 65 67 65 6e 64 72 | 65 20 3d 20 50 5b 31 c9 |cLegendr|e = P[1.|
|00000dd0| 4a 2c 20 31 c9 73 69 7a | 65 28 78 29 5d 20 77 69 |J, 1.siz|e(x)] wi|
|00000de0| 74 68 0d 2e 20 20 20 23 | 20 20 20 20 20 20 20 20 |th..   #|        |
|00000df0| 20 20 20 20 20 20 50 5b | 6a 2c 5d 20 3d 20 6f 6e |      P[|j,] = on|
|00000e00| 65 20 6f 66 20 74 68 65 | 20 70 6f 6c 79 6e 6f 6d |e of the| polynom|
|00000e10| 69 61 6c 73 20 3d 20 50 | 5f 6a 28 78 29 0d 2e 20 |ials = P|_j(x).. |
|00000e20| 20 20 23 20 4e 4f 54 45 | 20 74 68 61 74 20 68 65 |  # NOTE| that he|
|00000e30| 72 65 20 74 68 65 20 6c | 6f 77 65 73 74 20 70 6f |re the l|owest po|
|00000e40| 73 73 69 62 6c 65 20 4a | 20 69 73 20 31 2c 20 72 |ssible J| is 1, r|
|00000e50| 61 74 68 65 72 20 74 68 | 61 6e 20 30 20 0d 2e 20 |ather th|an 0 .. |
|00000e60| 20 20 23 20 61 73 20 69 | 73 20 73 6f 6d 65 74 69 |  # as i|s someti|
|00000e70| 6d 65 73 20 64 6f 6e 65 | 2e 20 54 68 75 73 20 50 |mes done|. Thus P|
|00000e80| 5f 6a 20 69 73 20 61 20 | 28 6a 2d 31 29 27 74 68 |_j is a |(j-1)'th|
|00000e90| 20 6f 72 64 65 72 20 70 | 6f 6c 79 6e 6f 6d 69 61 | order p|olynomia|
|00000ea0| 6c 20 69 6e 20 78 2e 0d | 2e 20 20 20 62 65 67 69 |l in x..|.   begi|
|00000eb0| 6e 0d 2e 20 20 20 20 20 | 50 7a 5b 31 c9 4a 2c 20 |n..     |Pz[1.J, |
|00000ec0| 31 c9 73 69 7a 65 28 78 | 29 5d 20 3d 20 30 20 20 |1.size(x|)] = 0  |
|00000ed0| 23 20 72 65 73 65 72 76 | 65 20 73 70 61 63 65 0d |# reserv|e space.|
|00000ee0| 2e 20 20 20 20 20 50 7a | 5b 31 2c 5d 20 3d 20 31 |.     Pz|[1,] = 1|
|00000ef0| 3b 0d 2e 20 20 20 20 20 | 69 66 20 4a 3e 31 20 74 |;..     |if J>1 t|
|00000f00| 68 65 6e 0d 2e 20 20 20 | 20 20 62 65 67 69 6e 0d |hen..   |  begin.|
|00000f10| 2e 20 20 20 20 20 20 20 | 50 7a 5b 32 2c 5d 20 3d |.       |Pz[2,] =|
|00000f20| 20 78 0d 2e 20 20 20 20 | 20 20 20 66 6f 72 20 6e | x..    |   for n|
|00000f30| 3d 20 32 c9 28 4a 2d 31 | 29 20 64 6f 20 50 7a 5b |= 2.(J-1|) do Pz[|
|00000f40| 6e 2b 31 2c 5d 20 3d 20 | 31 2f 28 6e 2b 31 29 20 |n+1,] = |1/(n+1) |
|00000f50| 7b 20 28 32 6e 2b 31 29 | 2a 78 2a 50 7a 5b 6e 2c |{ (2n+1)|*x*Pz[n,|
|00000f60| 5d 20 2d 20 6e 2a 50 7a | 5b 6e 2d 31 2c 5d 20 7d |] - n*Pz|[n-1,] }|
|00000f70| 0d 2e 20 20 20 20 20 65 | 6e 64 0d 2e 20 20 20 20 |..     e|nd..    |
|00000f80| 20 43 61 6c 63 4c 65 67 | 65 6e 64 72 65 20 3d 20 | CalcLeg|endre = |
|00000f90| 50 7a 0d 2e 20 20 20 65 | 6e 64 00 00 00 02 01 4a |Pz..   e|nd.....J|
|00000fa0| 1f 9c 00 95 01 20 40 80 | 9a 0a 00 7d 94 d8 00 7e |..... @.|...}...~|
|00000fb0| 7b f4 00 95 59 ff 00 00 | ff ff 00 00 00 00 20 00 |{...Y...|...... .|
|00000fc0| 00 7c 01 78 1f 9c 00 95 | 01 20 40 80 9a 0a 00 7d |.|.x....|. @....}|
|00000fd0| 94 d8 00 7e 7b f4 00 95 | 59 ff 00 00 ff ff 00 00 |...~{...|Y.......|
|00000fe0| 00 00 20 00 00 7c 00 00 | 00 02 02 50 7a f4 00 95 |.. ..|..|...Pz...|
|00000ff0| 59 ff 00 00 ff ff 00 00 | 00 00 20 00 00 7c 00 00 |Y.......|.. ..|..|
|00001000| 00 02 00 7d 94 f0 00 00 | 02 bc 00 91 48 ee 01 6e |...}....|....H..n|
|00001010| 7a f4 00 95 59 ff 00 00 | ff ff 00 00 00 00 20 00 |z...Y...|...... .|
|00001020| 00 7c 00 00 00 02 00 7d | 94 f0 00 00 02 bc 00 91 |.|.....}|........|
|00001030| 48 ee 10 00 7d 94 b0 00 | 00 00 00 00 00 00 00 00 |H...}...|........|
|00001040| 00 00 00 00 00 00 7d 94 | b4 00 00 00 00 00 7d 94 |......}.|......}.|
|00001050| a8 00 7d 94 ac 01 99 01 | d6 00 00 01 de 00 00 00 |..}.....|........|
|00001060| 00 00 00 00 00 00 7d 94 | 98 36 00 00 00 00 00 00 |......}.|.6......|
|00001070| 00 00 00 00 00 00 00 10 | 43 68 69 53 71 50 72 6f |........|ChiSqPro|
|00001080| 62 61 62 69 6c 69 74 79 | 7d 94 b4 00 95 1f 9c 00 |bability|}.......|
|00001090| 95 01 30 40 80 9a 0a 00 | 7d 94 ac 00 00 01 de 20 |..0@....|}...... |
|000010a0| 20 66 75 6e 63 74 69 6f | 6e 20 43 68 69 53 71 50 | functio|n ChiSqP|
|000010b0| 72 6f 62 61 62 69 6c 69 | 74 79 28 43 68 69 53 71 |robabili|ty(ChiSq|
|000010c0| 2c 4e 75 29 20 20 23 20 | 52 65 74 75 72 6e 73 20 |,Nu)  # |Returns |
|000010d0| 70 72 6f 62 2e 20 6f 66 | 20 43 68 69 53 71 61 75 |prob. of| ChiSqau|
|000010e0| 72 65 64 20 66 69 74 2e | 0d 2e 20 20 23 20 49 6e |red fit.|..  # In|
|000010f0| 70 75 74 3a 20 43 68 69 | 53 71 20 3d 20 73 75 6d |put: Chi|Sq = sum|
|00001100| 20 5b 28 79 44 61 74 61 | 5b 31 c9 4e 5d 2d 79 4d | [(yData|[1.N]-yM|
|00001110| 6f 64 65 6c 28 78 44 61 | 74 61 29 29 2f 73 69 67 |odel(xDa|ta))/sig|
|00001120| 6d 61 5d 5e 32 0d 2e 20 | 20 23 20 20 20 20 20 20 |ma]^2.. | #      |
|00001130| 20 20 20 20 4e 75 20 3d | 20 4e 20 64 61 74 61 20 |    Nu =| N data |
|00001140| 70 6f 69 6e 74 73 20 2d | 20 4a 20 6d 6f 64 65 6c |points -| J model|
|00001150| 20 70 61 72 61 6d 73 20 | 3d 20 64 65 67 72 65 65 | params |= degree|
|00001160| 73 20 6f 66 20 66 72 65 | 65 64 6f 6d 0d 2e 20 20 |s of fre|edom..  |
|00001170| 23 20 4f 75 74 70 75 74 | 3a 20 43 68 69 53 71 50 |# Output|: ChiSqP|
|00001180| 72 6f 62 61 62 69 6c 69 | 74 79 20 3d 20 70 72 6f |robabili|ty = pro|
|00001190| 62 20 6f 66 20 61 20 66 | 69 74 20 74 68 69 73 20 |b of a f|it this |
|000011a0| 62 61 64 20 62 65 69 6e | 67 20 64 75 65 0d 2e 20 |bad bein|g due.. |
|000011b0| 20 23 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | #      |        |
|000011c0| 74 6f 20 47 61 75 73 73 | 69 61 6e 20 6e 6f 72 6d |to Gauss|ian norm|
|000011d0| 61 6c 20 65 72 72 6f 72 | 73 20 77 69 74 68 20 73 |al error|s with s|
|000011e0| 74 6e 64 2e 20 64 65 76 | 2e 20 53 69 67 6d 61 5b |tnd. dev|. Sigma[|
|000011f0| 31 c9 4e 5d 2e 0d 2e 20 | 20 23 20 20 20 20 20 28 |1.N]... | #     (|
|00001200| 43 68 69 53 71 50 72 6f | 62 61 62 69 6c 69 74 69 |ChiSqPro|babiliti|
|00001210| 74 79 20 3c 3c 20 31 20 | 6d 65 61 6e 73 20 74 68 |ty << 1 |means th|
|00001220| 65 20 66 69 74 20 69 73 | 20 62 61 64 2e 29 0d 2e |e fit is| bad.)..|
|00001230| 20 20 62 65 67 69 6e 0d | 2e 20 20 20 20 20 20 43 |  begin.|.      C|
|00001240| 68 69 53 71 50 72 6f 62 | 61 62 69 6c 69 74 79 20 |hiSqProb|ability |
|00001250| 3d 20 31 20 2d 20 49 6e | 63 6f 6d 70 6c 65 74 65 |= 1 - In|complete|
|00001260| 47 61 6d 6d 61 28 4e 75 | 2f 32 2c 20 43 68 69 53 |Gamma(Nu|/2, ChiS|
|00001270| 71 2f 32 29 3b 0d 2e 20 | 20 20 65 6e 64 00 00 00 |q/2);.. |  end...|
|00001280| 02 05 43 68 69 53 71 01 | 20 40 80 9a 0a 00 7d 94 |..ChiSq.| @....}.|
|00001290| ac 00 7e 7b f4 00 95 59 | ff 00 00 ff ff 00 00 00 |..~{...Y|........|
|000012a0| 00 20 00 00 7c 02 4e 75 | 69 53 71 01 20 40 80 9a |. ..|.Nu|iSq. @..|
|000012b0| 0a 00 7d 94 ac 00 7e 7b | f4 00 95 59 ff 00 00 ff |..}...~{|...Y....|
|000012c0| ff 00 00 00 00 20 00 00 | 7c 00 00 00 00 0f 00 7d |..... ..||......}|
|000012d0| 94 8c 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000012e0| 00 7d 94 90 00 00 00 00 | 00 7d 94 84 00 7d 94 88 |.}......|.}...}..|
|000012f0| 00 00 00 0b 00 00 00 0b | 00 00 00 00 00 00 00 00 |........|........|
|00001300| 0a 43 6f 6d 6d 75 74 61 | 74 6f 72 e2 00 7d 94 90 |.Commuta|tor..}..|
|00001310| 00 7d 94 90 00 95 1f 9c | 00 95 01 40 40 80 9a 0a |.}......|...@@...|
|00001320| 00 7d 94 88 00 00 00 0b | 20 20 61 a5 62 20 2d 20 |.}......|  a.b - |
|00001330| 62 a5 61 00 00 00 02 01 | 61 1f 9c 00 95 01 30 40 |b.a.....|a.....0@|
|00001340| 80 9a 0a 00 7d 94 88 00 | 7e 7b f4 00 95 59 ff 00 |....}...|~{...Y..|
|00001350| 00 ff ff 00 00 00 00 20 | 00 00 7c 01 62 1f 9c 00 |....... |..|.b...|
|00001360| 95 01 30 40 80 9a 0a 00 | 7d 94 88 00 7e 7b f4 00 |..0@....|}...~{..|
|00001370| 95 59 ff 00 00 ff ff 00 | 00 00 00 20 00 00 7c 10 |.Y......|... ..|.|
|00001380| 00 7d 94 70 00 00 00 00 | 00 00 00 00 00 00 00 00 |.}.p....|........|
|00001390| 00 00 00 7d 94 74 00 00 | 00 00 00 7d 94 68 00 7d |...}.t..|...}.h.}|
|000013a0| 94 6c 00 4b 00 5d 00 00 | 00 65 00 00 00 00 00 00 |.l.K.]..|.e......|
|000013b0| 00 00 00 7d 94 5c 35 00 | 00 00 00 00 00 00 00 00 |...}.\5.|........|
|000013c0| 00 00 00 00 10 43 6f 6e | 76 65 72 74 54 6f 43 6f |.....Con|vertToCo|
|000013d0| 6d 70 6c 65 78 7d 94 74 | 00 95 1f 9c 00 95 01 30 |mplex}.t|.......0|
|000013e0| 40 80 9a 0a 00 7d 94 6c | 00 00 00 65 20 70 72 6f |@....}.l|...e pro|
|000013f0| 67 72 61 6d 20 43 6f 6e | 76 65 72 74 54 6f 43 6f |gram Con|vertToCo|
|00001400| 6d 70 6c 65 78 28 78 29 | 20 23 20 43 6f 6e 76 65 |mplex(x)| # Conve|
|00001410| 72 74 73 20 78 20 74 6f | 20 61 20 63 6f 6d 70 6c |rts x to| a compl|
|00001420| 65 78 20 71 75 61 6e 74 | 69 74 79 2e 0d 2e 20 20 |ex quant|ity...  |
|00001430| 20 62 65 67 69 6e 0d 2e | 20 20 20 20 20 78 20 20 | begin..|     x  |
|00001440| 3d 20 28 78 2b 69 29 2d | 69 0d 2e 20 20 20 65 6e |= (x+i)-|i..   en|
|00001450| 64 00 00 00 01 01 78 1f | 9c 00 95 01 20 40 80 9a |d.....x.|.... @..|
|00001460| 0a 00 7d 94 6c 00 7e 7b | f4 00 95 59 ff 00 00 ff |..}.l.~{|...Y....|
|00001470| ff 00 00 00 00 20 00 00 | 7c 00 00 00 00 0c 00 7d |..... ..||......}|
|00001480| 94 50 01 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |.P......|........|
|00001490| 11 00 00 00 00 00 03 63 | 6f 73 00 91 48 ee 00 00 |.......c|os..H...|
|000014a0| 00 00 00 00 ff ff 00 00 | 00 00 00 95 01 42 00 91 |........|.....B..|
|000014b0| ff 28 00 95 01 31 00 00 | 00 01 12 00 7d 94 48 01 |.(...1..|....}.H.|
|000014c0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000014d0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000014e0| 00 00 00 00 00 00 00 00 | 06 00 7d 94 44 04 63 6f |........|..}.D.co|
|000014f0| 75 6c 00 00 05 00 7d 94 | 48 00 7d 94 74 03 63 6f |ul....}.|H.}.t.co|
|00001500| 73 00 91 48 ee 00 00 00 | 00 00 00 ff ff 00 00 00 |s..H....|........|
|00001510| 00 00 00 00 3c 3f ff 80 | 00 00 00 00 00 00 00 00 |....<?..|........|
|00001520| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00001530| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00001540| 00 00 00 00 00 00 00 3f | ff 80 00 00 00 00 00 00 |.......?|........|
|00001550| 00 10 00 7d 94 3c 00 00 | 00 00 00 00 00 00 00 00 |...}.<..|........|
|00001560| 00 00 00 00 00 7d 94 40 | 00 00 00 00 00 7d 94 34 |.....}.@|.....}.4|
|00001570| 00 7d 94 38 00 a9 02 12 | 00 00 02 1b 00 00 00 00 |.}.8....|........|
|00001580| 00 00 00 00 00 7d 94 24 | 36 00 00 00 00 00 00 00 |.....}.$|6.......|
|00001590| 00 00 00 00 00 00 07 43 | 72 6f 73 73 33 44 00 7d |.......C|ross3D.}|
|000015a0| c9 e2 00 7d 94 40 00 7d | 94 40 00 95 1f 9c 00 95 |...}.@.}|.@......|
|000015b0| 01 30 40 80 9a 0a 00 7d | 94 38 00 00 02 1b 66 75 |.0@....}|.8....fu|
|000015c0| 6e 63 74 69 6f 6e 20 43 | 72 6f 73 73 33 44 28 58 |nction C|ross3D(X|
|000015d0| 2c 59 29 20 20 23 20 52 | 65 74 75 72 6e 73 20 74 |,Y)  # R|eturns t|
|000015e0| 68 65 20 33 44 20 63 72 | 6f 73 73 20 70 72 6f 64 |he 3D cr|oss prod|
|000015f0| 75 63 74 20 6f 66 20 74 | 77 6f 20 33 44 20 76 65 |uct of t|wo 3D ve|
|00001600| 63 74 6f 72 73 20 78 2c | 79 2e 0d 2e 20 20 20 76 |ctors x,|y...   v|
|00001610| 61 72 20 5a 0d 2e 20 20 | 20 23 20 20 49 6e 70 75 |ar Z..  | #  Inpu|
|00001620| 74 3a 20 20 20 58 2c 59 | 5b 31 c9 33 5d 20 33 2d |t:   X,Y|[1.3] 3-|
|00001630| 44 20 76 65 63 74 6f 72 | 73 0d 2e 20 20 20 23 20 |D vector|s..   # |
|00001640| 20 4f 75 74 70 75 74 3a | 20 43 72 6f 73 73 33 44 | Output:| Cross3D|
|00001650| 20 3d 20 58 20 63 72 6f | 73 73 20 59 0d 2e 20 20 | = X cro|ss Y..  |
|00001660| 20 62 65 67 69 6e 0d 2e | 20 20 20 20 20 20 69 66 | begin..|      if|
|00001670| 20 73 69 7a 65 28 78 29 | 20 3c 3e 20 33 20 74 68 | size(x)| <> 3 th|
|00001680| 65 6e 0d 2e 20 20 20 20 | 20 20 20 20 43 72 6f 73 |en..    |    Cros|
|00001690| 73 33 44 20 3d 20 22 20 | 45 52 52 4f 52 3a 20 58 |s3D = " |ERROR: X|
|000016a0| 20 6d 75 73 74 20 62 65 | 20 61 20 33 44 20 76 65 | must be| a 3D ve|
|000016b0| 63 74 6f 72 20 66 6f 72 | 20 43 72 6f 73 73 33 44 |ctor for| Cross3D|
|000016c0| 22 0d 2e 20 20 20 20 20 | 20 65 6c 73 65 20 69 66 |"..     | else if|
|000016d0| 20 73 69 7a 65 28 79 29 | 20 3c 3e 20 33 20 74 68 | size(y)| <> 3 th|
|000016e0| 65 6e 0d 2e 20 20 20 20 | 20 20 20 20 20 43 72 6f |en..    |     Cro|
|000016f0| 73 73 33 44 20 3d 20 22 | 20 45 52 52 4f 52 3a 20 |ss3D = "| ERROR: |
|00001700| 59 20 6d 75 73 74 20 62 | 65 20 61 20 33 44 20 76 |Y must b|e a 3D v|
|00001710| 65 63 74 6f 72 20 66 6f | 72 20 43 72 6f 73 73 33 |ector fo|r Cross3|
|00001720| 44 22 0d 2e 20 20 20 20 | 20 20 65 6c 73 65 0d 2e |D"..    |  else..|
|00001730| 20 20 20 20 20 20 62 65 | 67 69 6e 0d 2e 20 20 20 |      be|gin..   |
|00001740| 20 20 20 20 20 7a 5b 31 | 5d 20 3d 20 78 5b 32 5d |     z[1|] = x[2]|
|00001750| 20 79 5b 33 5d 20 2d 20 | 78 5b 33 5d 20 79 5b 32 | y[3] - |x[3] y[2|
|00001760| 5d 3b 0d 2e 20 20 20 20 | 20 20 20 20 7a 5b 32 5d |];..    |    z[2]|
|00001770| 20 3d 20 78 5b 33 5d 20 | 79 5b 31 5d 20 2d 20 78 | = x[3] |y[1] - x|
|00001780| 5b 31 5d 20 79 5b 33 5d | 3b 0d 2e 20 20 20 20 20 |[1] y[3]|;..     |
|00001790| 20 20 20 7a 5b 33 5d 20 | 3d 20 78 5b 31 5d 20 79 |   z[3] |= x[1] y|
|000017a0| 5b 32 5d 20 2d 20 78 5b | 32 5d 20 79 5b 31 5d 3b |[2] - x[|2] y[1];|
|000017b0| 0d 2e 20 20 20 20 20 20 | 20 20 43 72 6f 73 73 33 |..      |  Cross3|
|000017c0| 44 20 3d 20 7a 0d 2e 20 | 20 20 20 20 20 65 6e 64 |D = z.. |     end|
|000017d0| 0d 2e 20 20 20 20 65 6e | 64 00 00 00 02 01 58 1f |..    en|d.....X.|
|000017e0| 9c 00 95 01 20 40 80 9a | 0a 00 7d 94 38 00 7e 7b |.... @..|..}.8.~{|
|000017f0| f4 00 95 59 ff 00 00 ff | ff 00 00 00 00 20 00 00 |...Y....|..... ..|
|00001800| 7c 01 59 1f 9c 00 95 01 | 20 40 80 9a 0a 00 7d 94 ||.Y.....| @....}.|
|00001810| 38 00 7e 7b f4 00 95 59 | ff 00 00 ff ff 00 00 00 |8.~{...Y|........|
|00001820| 00 20 00 00 7c 00 00 00 | 01 01 5a 7b f4 00 95 59 |. ..|...|..Z{...Y|
|00001830| ff 00 00 ff ff 00 00 00 | 00 20 00 00 7c 00 00 00 |........|. ..|...|
|00001840| 02 00 7d 94 40 00 00 02 | 1b 00 91 48 ee 12 00 7d |..}.@...|...H...}|
|00001850| 94 14 01 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00001860| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00001870| 00 00 00 00 00 00 00 00 | 00 00 00 05 00 7d 94 10 |........|.....}..|
|00001880| 04 64 65 67 4b 00 00 05 | 00 7d 94 14 00 7d 94 40 |.degK...|.}...}.@|
|00001890| 00 00 02 1b 00 91 48 ee | 00 00 00 01 00 00 ff ff |......H.|........|
|000018a0| 00 00 00 00 00 00 00 32 | 3f ff 80 00 00 00 00 00 |.......2|?.......|
|000018b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000018c0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000018d0| 3f ff 80 00 00 00 00 00 | 00 00 0c 00 7d 94 08 01 |?.......|....}...|
|000018e0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 22 00 00 |........|....."..|
|000018f0| 00 00 00 06 44 65 6c 65 | 74 65 7c 00 7c f5 2c 00 |....Dele|te|.|.,.|
|00001900| 7d 94 18 00 00 00 32 00 | 95 01 42 00 91 ff 28 00 |}.....2.|..B...(.|
|00001910| 95 01 31 00 00 00 01 10 | 00 7d 94 00 00 00 00 00 |..1.....|.}......|
|00001920| 00 00 00 00 00 00 00 00 | 00 00 00 7d 94 04 00 00 |........|...}....|
|00001930| 00 00 00 7d 93 f8 00 7d | 93 fc 00 e7 02 88 00 00 |...}...}|........|
|00001940| 02 90 00 00 00 00 00 00 | 00 00 00 7d 93 ec 36 00 |........|...}..6.|
|00001950| 00 00 00 00 00 00 00 00 | 00 00 00 00 0b 44 65 74 |........|.....Det|
|00001960| 65 72 6d 69 6e 61 6e 74 | 00 7d 94 04 00 7d 94 04 |erminant|.}...}..|
|00001970| 00 95 1f 9c 00 95 01 30 | 40 80 9a 0a 00 7d 93 fc |.......0|@....}..|
|00001980| 00 00 02 90 20 20 66 75 | 6e 63 74 69 6f 6e 20 44 |....  fu|nction D|
|00001990| 65 74 65 72 6d 69 6e 61 | 6e 74 28 41 29 20 20 23 |etermina|nt(A)  #|
|000019a0| 20 52 65 74 75 72 6e 73 | 20 74 68 65 20 64 65 74 | Returns| the det|
|000019b0| 65 72 6d 69 6e 61 6e 74 | 20 6f 66 20 74 68 65 20 |erminant| of the |
|000019c0| 6d 61 74 72 69 78 20 41 | 2e 0d 2e 20 20 20 76 61 |matrix A|...   va|
|000019d0| 72 20 64 2c 6e 2c 20 61 | 6e 73 2c 20 74 65 6d 70 |r d,n, a|ns, temp|
|000019e0| 2c 20 65 72 72 0d 2e 20 | 20 23 20 20 49 6e 70 75 |, err.. | #  Inpu|
|000019f0| 74 3a 20 0d 2e 20 20 23 | 20 20 20 20 20 20 20 20 |t: ..  #|        |
|00001a00| 20 20 20 20 20 20 41 5b | 31 c9 6e 2c 31 c9 6e 5d |      A[|1.n,1.n]|
|00001a10| 20 3d 20 73 71 75 61 72 | 65 2c 20 72 65 61 6c 20 | = squar|e, real |
|00001a20| 6d 61 74 72 69 78 0d 2e | 20 20 23 20 20 4f 75 70 |matrix..|  #  Oup|
|00001a30| 75 74 3a 20 0d 2e 20 20 | 23 20 20 20 20 20 20 20 |ut: ..  |#       |
|00001a40| 20 20 20 20 20 20 20 44 | 65 74 65 72 6d 69 6e 61 |       D|etermina|
|00001a50| 6e 74 20 3d 20 72 65 61 | 6c 20 6e 75 6d 62 65 72 |nt = rea|l number|
|00001a60| 0d 2e 20 20 20 62 65 67 | 69 6e 0d 2e 20 20 20 64 |..   beg|in..   d|
|00001a70| 3d 64 69 6d 65 6e 73 69 | 6f 6e 28 61 29 0d 2e 20 |=dimensi|on(a).. |
|00001a80| 20 20 69 66 20 73 69 7a | 65 28 64 29 3c 3e 32 20 |  if siz|e(d)<>2 |
|00001a90| 74 68 65 6e 20 0d 2e 20 | 20 20 20 20 20 70 72 69 |then .. |     pri|
|00001aa0| 6e 74 28 27 a5 a5 20 45 | 52 52 4f 52 20 3a 20 6e |nt('.. E|RROR : n|
|00001ab0| 6f 74 20 61 20 6d 61 74 | 72 69 78 2e 27 29 0d 2e |ot a mat|rix.')..|
|00001ac0| 20 20 20 65 6c 73 65 20 | 69 66 20 64 5b 31 5d 3c |   else |if d[1]<|
|00001ad0| 3e 64 5b 32 5d 20 74 68 | 65 6e 20 0d 2e 20 20 20 |>d[2] th|en ..   |
|00001ae0| 20 20 20 70 72 69 6e 74 | 28 27 a5 a5 20 45 52 52 |   print|('.. ERR|
|00001af0| 4f 52 20 3a 20 6e 6f 74 | 20 61 20 73 71 75 61 72 |OR : not| a squar|
|00001b00| 65 20 6d 61 74 72 69 78 | 2e 27 29 0d 2e 20 20 20 |e matrix|.')..   |
|00001b10| 65 6c 73 65 0d 2e 20 20 | 20 20 20 62 65 67 69 6e |else..  |   begin|
|00001b20| 0d 2e 20 20 20 20 20 20 | 20 6e 20 3d 20 64 5b 31 |..      | n = d[1|
|00001b30| 5d 3b 0d 2e 20 20 20 20 | 20 20 20 74 65 6d 70 3d |];..    |   temp=|
|00001b40| 61 0d 2e 20 20 20 20 20 | 20 20 78 44 45 54 45 52 |a..     |  xDETER|
|00001b50| 4d 49 4e 41 4e 54 28 6e | 2c 74 65 6d 70 2c 61 6e |MINANT(n|,temp,an|
|00001b60| 73 2c 65 72 72 29 0d 2e | 20 20 20 20 20 20 20 69 |s,err)..|       i|
|00001b70| 66 20 65 72 72 3c 3e 30 | 20 74 68 65 6e 20 0d 2e |f err<>0| then ..|
|00001b80| 20 20 20 20 20 20 20 20 | 20 20 20 44 65 74 65 72 |        |   Deter|
|00001b90| 6d 69 6e 61 6e 74 20 3d | 20 22 45 52 52 4f 52 20 |minant =| "ERROR |
|00001ba0| 69 6e 20 78 44 45 54 45 | 52 4d 49 4e 41 4e 54 2c |in xDETE|RMINANT,|
|00001bb0| 20 6d 61 74 72 69 78 20 | 6d 75 73 74 20 62 65 20 | matrix |must be |
|00001bc0| 73 6d 61 6c 6c 65 72 20 | 74 68 61 6e 20 31 30 30 |smaller |than 100|
|00001bd0| 30 78 31 30 30 30 22 0d | 2e 20 20 20 20 20 20 20 |0x1000".|.       |
|00001be0| 65 6c 73 65 0d 2e 20 20 | 20 20 20 20 20 20 20 20 |else..  |        |
|00001bf0| 20 44 65 74 65 72 6d 69 | 6e 61 6e 74 20 3d 20 61 | Determi|nant = a|
|00001c00| 6e 73 0d 2e 20 20 20 20 | 20 65 6e 64 0d 2e 20 20 |ns..    | end..  |
|00001c10| 20 65 6e 64 00 00 00 01 | 01 41 1f 9c 00 95 01 20 | end....|.A..... |
|00001c20| 40 80 9a 0a 00 7d 93 fc | 00 7e 7b f4 00 95 59 ff |@....}..|.~{...Y.|
|00001c30| 00 00 ff ff 00 00 00 00 | 20 00 00 7c 00 00 00 05 |........| ..|....|
|00001c40| 01 64 7b f4 00 95 59 ff | 00 00 ff ff 00 00 00 00 |.d{...Y.|........|
|00001c50| 20 00 00 7c 00 00 00 01 | 00 7d 94 04 00 00 02 90 | ..|....|.}......|
|00001c60| 00 91 48 ee 01 6e 7b f4 | 00 95 59 ff 00 00 ff ff |..H..n{.|..Y.....|
|00001c70| 00 00 00 00 20 00 00 7c | 00 00 00 01 00 7d 94 04 |.... ..||.....}..|
|00001c80| 00 00 02 90 00 91 48 ee | 03 61 6e 73 00 95 59 ff |......H.|.ans..Y.|
|00001c90| 00 00 ff ff 00 00 00 00 | 20 00 00 7c 00 00 00 01 |........| ..|....|
|00001ca0| 00 7d 94 04 00 00 02 90 | 00 91 48 ee 04 74 65 6d |.}......|..H..tem|
|00001cb0| 70 95 59 ff 00 00 ff ff | 00 00 00 00 20 00 00 7c |p.Y.....|.... ..||
|00001cc0| 00 00 00 01 00 7d 94 04 | 00 00 02 90 00 91 48 ee |.....}..|......H.|
|00001cd0| 03 65 72 72 70 95 59 ff | 00 00 ff ff 00 00 00 00 |.errp.Y.|........|
|00001ce0| 20 00 00 7c 00 00 00 01 | 00 7d 94 04 00 00 02 90 | ..|....|.}......|
|00001cf0| 00 91 48 ee 0f 00 7d 93 | bc 00 00 00 00 00 00 00 |..H...}.|........|
|00001d00| 00 00 00 00 00 00 00 00 | 7d 93 c0 00 00 00 00 00 |........|}.......|
|00001d10| 7d 93 b4 00 7d 93 b8 00 | 00 00 39 00 00 00 39 00 |}...}...|..9...9.|
|00001d20| 00 00 00 00 00 00 00 0d | 44 69 66 66 65 72 65 6e |........|Differen|
|00001d30| 74 69 61 74 65 93 c0 00 | 7d 93 c0 00 95 1f 9c 00 |tiate...|}.......|
|00001d40| 95 01 40 40 80 9a 0a 00 | 7d 93 b8 00 00 00 39 20 |..@@....|}.....9 |
|00001d50| 20 5b 20 66 28 78 2b 64 | 78 2f 32 29 20 2d 20 66 | [ f(x+d|x/2) - f|
|00001d60| 28 78 2d 64 78 2f 32 29 | 20 5d 2f 64 78 20 20 23 |(x-dx/2)| ]/dx  #|
|00001d70| 20 52 65 74 75 72 6e 73 | 20 64 66 2f 64 78 20 61 | Returns| df/dx a|
|00001d80| 74 20 78 5b 31 c9 4e 5d | 00 00 00 03 01 66 1f 9c |t x[1.N]|.....f..|
|00001d90| 00 95 01 30 40 80 9a 0a | 00 7d 93 b8 00 7e 7b f4 |...0@...|.}...~{.|
|00001da0| 00 95 59 ff 00 00 ff ff | 00 00 00 00 20 00 00 7c |..Y.....|.... ..||
|00001db0| 01 78 1f 9c 00 95 01 30 | 40 80 9a 0a 00 7d 93 b8 |.x.....0|@....}..|
|00001dc0| 00 7e 7b f4 00 95 59 ff | 00 00 ff ff 00 00 00 00 |.~{...Y.|........|
|00001dd0| 20 00 00 7c 02 64 78 9c | 00 95 01 30 40 80 9a 0a | ..|.dx.|...0@...|
|00001de0| 00 7d 93 b8 00 7e 7b f4 | 00 95 59 ff 00 00 ff ff |.}...~{.|..Y.....|
|00001df0| 00 00 00 00 20 00 00 7c | 10 00 7d 93 9c 00 00 00 |.... ..||..}.....|
|00001e00| 00 00 00 00 00 00 00 00 | 00 00 00 00 7d 93 a0 00 |........|....}...|
|00001e10| 00 00 00 00 7d 93 94 00 | 7d 93 98 00 e6 01 6d 00 |....}...|}.....m.|
|00001e20| 00 01 75 00 00 00 00 00 | 00 00 00 00 7d 93 84 36 |..u.....|....}..6|
|00001e30| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 12 44 69 |........|......Di|
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|00001e50| a0 00 95 1f 9c 00 95 01 | 30 40 80 9a 0a 00 7d 93 |........|0@....}.|
|00001e60| 98 00 00 01 75 20 20 66 | 75 6e 63 74 69 6f 6e 20 |....u  f|unction |
|00001e70| 44 69 66 66 65 72 65 6e | 74 69 61 74 65 41 72 72 |Differen|tiateArr|
|00001e80| 61 79 28 79 2c 78 29 20 | 20 23 20 52 65 74 75 72 |ay(y,x) | # Retur|
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|00001ea0| c9 6e 5d 20 61 74 20 78 | 5b 31 c9 6e 5d 2e 0d 2e |.n] at x|[1.n]...|
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|00001ed0| 3a 0d 2e 20 23 20 20 20 | 20 20 20 20 20 20 20 20 |:.. #   |        |
|00001ee0| 20 20 20 20 20 20 20 20 | 20 20 78 2c 20 79 20 3d |        |  x, y =|
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|00001f00| 4f 75 74 70 75 74 3a 0d | 2e 20 23 20 20 20 20 20 |Output:.|. #     |
|00001f10| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001f20| 44 69 66 66 65 72 65 6e | 74 69 61 74 65 41 72 72 |Differen|tiateArr|
|00001f30| 61 79 20 3d 20 64 79 2f | 64 78 20 61 72 72 61 79 |ay = dy/|dx array|
|00001f40| 0d 2e 20 20 20 62 65 67 | 69 6e 0d 2e 20 20 20 20 |..   beg|in..    |
|00001f50| 20 64 79 32 3d 79 3b 20 | 61 6e 73 3d 79 20 20 23 | dy2=y; |ans=y  #|
|00001f60| 20 72 65 73 65 72 76 65 | 20 73 74 6f 72 61 67 65 | reserve| storage|
|00001f70| 20 73 70 61 63 65 2e 0d | 2e 20 20 20 20 20 6e 20 | space..|.     n |
|00001f80| 3d 20 73 69 7a 65 28 79 | 29 0d 2e 20 20 20 20 20 |= size(y|)..     |
|00001f90| 78 44 49 46 46 45 52 45 | 4e 54 49 41 54 45 5f 41 |xDIFFERE|NTIATE_A|
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|00001fc0| 65 6e 74 69 61 74 65 41 | 72 72 61 79 20 3d 20 61 |entiateA|rray = a|
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|00001fe0| 1f 9c 00 95 01 20 40 80 | 9a 0a 00 7d 93 98 00 7e |..... @.|...}...~|
|00001ff0| 7b f4 00 95 59 ff 00 00 | ff ff 00 00 00 00 20 00 |{...Y...|...... .|
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|00002020| 00 00 20 00 00 7c 00 00 | 00 03 01 6e 7b f4 00 95 |.. ..|..|...n{...|
|00002030| 59 ff 00 00 ff ff 00 00 | 00 00 20 00 00 7c 00 00 |Y.......|.. ..|..|
|00002040| 00 02 00 7d 93 a0 00 00 | 01 75 00 91 48 ee 03 64 |...}....|.u..H..d|
|00002050| 79 32 00 95 59 ff 00 00 | ff ff 00 00 00 00 20 00 |y2..Y...|...... .|
|00002060| 00 7c 00 00 00 02 00 7d | 93 a0 00 00 01 75 00 91 |.|.....}|.....u..|
|00002070| 48 ee 03 61 6e 73 00 95 | 59 ff 00 00 ff ff 00 00 |H..ans..|Y.......|
|00002080| 00 00 20 00 00 7c 00 00 | 00 02 00 7d 93 a0 00 00 |.. ..|..|...}....|
|00002090| 01 75 00 91 48 ee 0c 00 | 7d 93 6c 01 00 00 00 00 |.u..H...|}.l.....|
|000020a0| 00 00 00 00 00 00 00 00 | 00 42 00 00 00 00 00 09 |........|.B......|
|000020b0| 44 69 6d 65 6e 73 69 6f | 6e 00 03 00 00 ff ff 00 |Dimensio|n.......|
|000020c0| 00 00 00 00 95 01 42 00 | 91 ff 28 00 95 01 31 00 |......B.|..(...1.|
|000020d0| 00 00 01 04 00 7d 93 64 | 01 00 00 00 00 00 00 00 |.....}.d|........|
|000020e0| 00 00 00 00 00 00 3b 00 | 02 44 6f 6d 65 6e 73 69 |......;.|.Domensi|
|000020f0| 6f 6e 00 03 00 00 ff ff | 00 00 00 00 00 95 01 42 |on......|.......B|
|00002100| 00 91 ff 28 00 95 01 31 | 00 00 00 01 12 00 7d 93 |...(...1|......}.|
|00002110| 5c 01 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |\.......|........|
|00002120| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00002130| 00 00 00 00 00 00 00 00 | 00 00 08 00 7d 93 58 07 |........|....}.X.|
|00002140| 64 6f 6c 6c 61 72 73 00 | 7d 93 5c 00 7d 93 a0 02 |dollars.|}.\.}...|
|00002150| 44 6f 6d 65 6e 73 69 6f | 6e 00 03 00 00 ff ff 00 |Domensio|n.......|
|00002160| 00 00 00 00 00 00 50 3f | ff 80 00 00 00 00 00 00 |......P?|........|
|00002170| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00002180| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00002190| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000021a0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 3f ff 80 |........|.....?..|
|000021b0| 00 00 00 00 00 00 00 10 | 00 7d 93 50 00 00 00 00 |........|.}.P....|
|000021c0| 00 00 00 00 00 00 00 00 | 00 00 00 7d 93 54 00 00 |........|...}.T..|
|000021d0| 00 00 00 7d 93 48 00 7d | 93 4c 01 28 03 83 00 00 |...}.H.}|.L.(....|
|000021e0| 03 8c 00 00 00 00 00 00 | 00 00 00 7d 93 34 35 00 |........|...}.45.|
|000021f0| 00 00 00 00 00 00 00 00 | 00 00 00 00 06 45 69 67 |........|.....Eig|
|00002200| 65 6e 73 05 00 7d c9 e2 | 00 7d 93 54 00 7d 93 54 |ens..}..|.}.T.}.T|
|00002210| 00 95 1f 9c 00 95 01 30 | 40 80 9a 0a 00 7d 93 4c |.......0|@....}.L|
|00002220| 00 00 03 8c 20 70 72 6f | 67 72 61 6d 20 45 69 67 |.... pro|gram Eig|
|00002230| 65 6e 73 28 74 68 65 4d | 61 74 2c 74 68 65 45 69 |ens(theM|at,theEi|
|00002240| 67 73 2c 74 68 65 56 65 | 63 73 29 20 23 20 46 69 |gs,theVe|cs) # Fi|
|00002250| 6e 64 73 20 74 68 65 45 | 69 67 73 2c 74 68 65 56 |nds theE|igs,theV|
|00002260| 65 63 73 20 66 72 6f 6d | 20 74 68 65 4d 61 74 2e |ecs from| theMat.|
|00002270| 0d 2e 20 20 20 76 61 72 | 20 72 6d 2c 69 6d 2c 65 |..   var| rm,im,e|
|00002280| 72 2c 65 69 2c 76 72 2c | 76 69 2c 69 2c 6e 2c 64 |r,ei,vr,|vi,i,n,d|
|00002290| 2c 20 65 72 72 2c 20 77 | 31 2c 77 32 2c 77 33 0d |, err, w|1,w2,w3.|
|000022a0| 2e 20 20 23 20 49 6e 70 | 75 74 20 3a 20 20 20 0d |.  # Inp|ut :   .|
|000022b0| 2e 20 20 23 20 20 20 20 | 74 68 65 4d 61 74 5b 31 |.  #    |theMat[1|
|000022c0| c9 4e 2c 20 31 c9 4e 5d | 20 20 72 65 61 6c 20 6f |.N, 1.N]|  real o|
|000022d0| 72 20 63 6f 6d 70 6c 65 | 78 0d 2e 20 20 23 20 4f |r comple|x..  # O|
|000022e0| 75 74 70 75 74 3a 0d 2e | 20 20 23 20 20 20 20 20 |utput:..|  #     |
|000022f0| 74 68 65 45 69 67 73 5b | 31 c9 4e 5d 20 0d 2e 20 |theEigs[|1.N] .. |
|00002300| 20 23 20 20 20 20 20 74 | 68 65 56 65 63 73 5b 31 | #     t|heVecs[1|
|00002310| c9 4e 2c 31 c9 4e 5d 20 | 63 6f 6d 70 6c 65 78 20 |.N,1.N] |complex |
|00002320| 20 20 0d 2e 20 20 23 20 | 20 20 20 20 45 72 72 3a |  ..  # |    Err:|
|00002330| 20 20 30 20 66 6f 72 20 | 6e 6f 20 65 72 72 6f 72 |  0 for |no error|
|00002340| 2e 0d 2e 20 20 20 62 65 | 67 69 6e 0d 2e 20 20 20 |...   be|gin..   |
|00002350| 64 3d 64 69 6d 65 6e 73 | 69 6f 6e 28 74 68 65 4d |d=dimens|ion(theM|
|00002360| 61 74 29 0d 2e 20 20 20 | 69 66 20 73 69 7a 65 28 |at)..   |if size(|
|00002370| 64 29 3c 3e 32 20 74 68 | 65 6e 20 0d 2e 20 20 20 |d)<>2 th|en ..   |
|00002380| 20 20 20 50 72 69 6e 74 | 28 22 23 20 a5 a5 20 45 |   Print|("# .. E|
|00002390| 52 52 4f 52 20 3a 20 6e | 6f 74 20 61 20 6d 61 74 |RROR : n|ot a mat|
|000023a0| 72 69 78 2e 22 29 0d 2e | 20 20 20 65 6c 73 65 20 |rix.")..|   else |
|000023b0| 69 66 20 64 5b 31 5d 3c | 3e 64 5b 32 5d 20 74 68 |if d[1]<|>d[2] th|
|000023c0| 65 6e 20 0d 2e 20 20 20 | 20 20 20 50 72 69 6e 74 |en ..   |   Print|
|000023d0| 28 22 23 20 a5 a5 20 45 | 52 52 4f 52 20 3a 20 6e |("# .. E|RROR : n|
|000023e0| 6f 74 20 61 20 73 71 75 | 61 72 65 20 6d 61 74 72 |ot a squ|are matr|
|000023f0| 69 78 2e 22 29 0d 2e 20 | 20 20 65 6c 73 65 0d 2e |ix.").. |  else..|
|00002400| 20 20 20 20 20 20 20 62 | 65 67 69 6e 0d 2e 20 20 |       b|egin..  |
|00002410| 20 20 20 20 20 69 20 3d | 20 73 71 72 74 28 2d 31 |     i =| sqrt(-1|
|00002420| 29 20 23 20 6a 75 73 74 | 20 69 6e 20 63 61 73 65 |) # just| in case|
|00002430| 20 67 6c 6f 62 61 6c 20 | 22 69 22 20 69 73 20 64 | global |"i" is d|
|00002440| 69 66 66 65 72 65 6e 74 | 2e 0d 2e 20 20 20 20 20 |ifferent|...     |
|00002450| 20 20 6e 20 3d 20 64 5b | 31 5d 3b 0d 2e 20 20 20 |  n = d[|1];..   |
|00002460| 20 20 20 20 77 31 3d 31 | c9 6e 3b 20 20 77 32 3d |    w1=1|.n;  w2=|
|00002470| 77 31 3b 20 77 33 3d 77 | 31 3b 0d 2e 20 20 20 20 |w1; w3=w|1;..    |
|00002480| 20 20 20 72 6d 20 3d 20 | 72 65 61 6c 28 74 68 65 |   rm = |real(the|
|00002490| 4d 61 74 29 0d 2e 20 20 | 20 20 20 20 20 69 6d 20 |Mat)..  |     im |
|000024a0| 3d 20 69 6d 61 67 69 6e | 61 72 79 28 74 68 65 4d |= imagin|ary(theM|
|000024b0| 61 74 29 0d 2e 20 20 20 | 20 20 20 20 65 72 3d 31 |at)..   |    er=1|
|000024c0| c9 6e 3b 20 65 69 20 3d | 20 65 72 3b 20 76 72 3d |.n; ei =| er; vr=|
|000024d0| 72 6d 3b 76 69 3d 72 6d | 3b 20 65 72 72 3d 30 3b |rm;vi=rm|; err=0;|
|000024e0| 0d 2e 20 20 20 20 20 20 | 20 78 43 4f 4d 50 4c 45 |..      | xCOMPLE|
|000024f0| 58 5f 45 49 47 5f 53 50 | 4c 49 54 28 6e 2c 72 6d |X_EIG_SP|LIT(n,rm|
|00002500| 2c 69 6d 2c 65 72 2c 65 | 69 2c 76 72 2c 76 69 2c |,im,er,e|i,vr,vi,|
|00002510| 20 77 31 2c 77 32 2c 77 | 33 2c 20 78 45 49 47 32 | w1,w2,w|3, xEIG2|
|00002520| 2c 65 72 72 29 0d 2e 20 | 20 20 20 20 20 20 20 69 |,err).. |       i|
|00002530| 66 20 65 72 72 3c 3e 30 | 20 74 68 65 6e 20 50 72 |f err<>0| then Pr|
|00002540| 69 6e 74 28 22 23 20 a5 | a5 20 45 52 52 4f 52 20 |int("# .|. ERROR |
|00002550| 69 6e 20 45 69 67 65 6e | 73 20 3d 20 22 2b 65 72 |in Eigen|s = "+er|
|00002560| 72 29 0d 2e 20 20 20 20 | 20 20 20 20 74 68 65 45 |r)..    |    theE|
|00002570| 69 67 73 20 3d 20 65 72 | 20 2b 20 69 2a 65 69 0d |igs = er| + i*ei.|
|00002580| 2e 20 20 20 20 20 20 20 | 20 74 68 65 56 65 63 73 |.       | theVecs|
|00002590| 20 3d 20 76 72 2b 69 2a | 76 69 0d 2e 20 20 20 20 | = vr+i*|vi..    |
|000025a0| 20 20 20 20 65 6e 64 0d | 2e 20 20 20 20 65 6e 64 |    end.|.    end|
|000025b0| 00 00 00 03 06 74 68 65 | 4d 61 74 20 40 80 9a 0a |.....the|Mat @...|
|000025c0| 00 7d 93 4c 00 7e 7b f4 | 00 95 59 ff 00 00 ff ff |.}.L.~{.|..Y.....|
|000025d0| 00 00 00 00 20 00 00 7c | 07 74 68 65 45 69 67 73 |.... ..||.theEigs|
|000025e0| 40 80 9a 0a 00 7d 93 4c | 00 7e 7b f4 00 95 59 ff |@....}.L|.~{...Y.|
|000025f0| 00 00 ff ff 00 00 00 00 | 20 00 00 7c 07 74 68 65 |........| ..|.the|
|00002600| 56 65 63 73 40 80 9a 0a | 00 7d 93 4c 00 7e 7b f4 |Vecs@...|.}.L.~{.|
|00002610| 00 95 59 ff 00 00 ff ff | 00 00 00 00 20 00 00 7c |..Y.....|.... ..||
|00002620| 00 00 00 0d 02 72 6d f4 | 00 95 59 ff 00 00 ff ff |.....rm.|..Y.....|
|00002630| 00 00 00 00 20 00 00 7c | 00 00 00 03 00 7d 93 54 |.... ..||.....}.T|
|00002640| 00 00 03 8c 00 91 48 ee | 02 69 6d f4 00 95 59 ff |......H.|.im...Y.|
|00002650| 00 00 ff ff 00 00 00 00 | 20 00 00 7c 00 00 00 03 |........| ..|....|
|00002660| 00 7d 93 54 00 00 03 8c | 00 91 48 ee 02 65 72 f4 |.}.T....|..H..er.|
|00002670| 00 95 59 ff 00 00 ff ff | 00 00 00 00 20 00 00 7c |..Y.....|.... ..||
|00002680| 00 00 00 03 00 7d 93 54 | 00 00 03 8c 00 91 48 ee |.....}.T|......H.|
|00002690| 02 65 69 f4 00 95 59 ff | 00 00 ff ff 00 00 00 00 |.ei...Y.|........|
|000026a0| 20 00 00 7c 00 00 00 03 | 00 7d 93 54 00 00 03 8c | ..|....|.}.T....|
|000026b0| 00 91 48 ee 02 76 72 f4 | 00 95 59 ff 00 00 ff ff |..H..vr.|..Y.....|
|000026c0| 00 00 00 00 20 00 00 7c | 00 00 00 03 00 7d 93 54 |.... ..||.....}.T|
|000026d0| 00 00 03 8c 00 91 48 ee | 02 76 69 f4 00 95 59 ff |......H.|.vi...Y.|
|000026e0| 00 00 ff ff 00 00 00 00 | 20 00 00 7c 00 00 00 03 |........| ..|....|
|000026f0| 00 7d 93 54 00 00 03 8c | 00 91 48 ee 01 69 69 f4 |.}.T....|..H..ii.|
|00002700| 00 95 59 ff 00 00 ff ff | 00 00 00 00 20 00 00 7c |..Y.....|.... ..||
|00002710| 00 00 00 03 00 7d 93 54 | 00 00 03 8c 00 91 48 ee |.....}.T|......H.|
|00002720| 01 6e 69 f4 00 95 59 ff | 00 00 ff ff 00 00 00 00 |.ni...Y.|........|
|00002730| 20 00 00 7c 00 00 00 03 | 00 7d 93 54 00 00 03 8c | ..|....|.}.T....|
|00002740| 00 91 48 ee 01 64 69 f4 | 00 95 59 ff 00 00 ff ff |..H..di.|..Y.....|
|00002750| 00 00 00 00 20 00 00 7c | 00 00 00 03 00 7d 93 54 |.... ..||.....}.T|
|00002760| 00 00 03 8c 00 91 48 ee | 03 65 72 72 00 95 59 ff |......H.|.err..Y.|
|00002770| 00 00 ff ff 00 00 00 00 | 20 00 00 7c 00 00 00 03 |........| ..|....|
|00002780| 00 7d 93 54 00 00 03 8c | 00 91 48 ee 02 77 31 72 |.}.T....|..H..w1r|
|00002790| 00 95 59 ff 00 00 ff ff | 00 00 00 00 20 00 00 7c |..Y.....|.... ..||
|000027a0| 00 00 00 03 00 7d 93 54 | 00 00 03 8c 00 91 48 ee |.....}.T|......H.|
|000027b0| 02 77 32 72 00 95 59 ff | 00 00 ff ff 00 00 00 00 |.w2r..Y.|........|
|000027c0| 20 00 00 7c 00 00 00 03 | 00 7d 93 54 00 00 03 8c | ..|....|.}.T....|
|000027d0| 00 91 48 ee 02 77 33 72 | 00 95 59 ff 00 00 ff ff |..H..w3r|..Y.....|
|000027e0| 00 00 00 00 20 00 00 7c | 00 00 00 03 00 7d 93 54 |.... ..||.....}.T|
|000027f0| 00 00 03 8c 00 91 48 ee | 04 00 7d 92 f4 01 00 00 |......H.|..}.....|
|00002800| 00 00 00 00 00 00 00 00 | 00 00 00 3f 00 04 45 6c |........|...?..El|
|00002810| 73 65 91 48 ee 00 00 00 | 0d 00 00 ff ff 00 00 00 |se.H....|........|
|00002820| 00 00 95 01 42 00 91 ff | 28 00 95 01 31 00 00 00 |....B...|(...1...|
|00002830| 01 04 00 7d 92 ec 01 00 | 00 00 00 00 00 00 00 00 |...}....|........|
|00002840| 00 00 00 00 39 00 03 45 | 6e 64 65 91 48 ee 00 00 |....9..E|nde.H...|
|00002850| 00 0d 00 00 ff ff 00 00 | 00 00 00 95 01 42 00 91 |........|.....B..|
|00002860| ff 28 00 95 01 31 00 00 | 00 01 10 00 7d 92 e4 00 |.(...1..|....}...|
|00002870| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 7d 92 |........|......}.|
|00002880| e8 00 00 00 00 00 7d 92 | dc 00 7d 92 e0 00 da 01 |......}.|..}.....|
|00002890| 5b 00 00 01 65 00 00 00 | 00 00 00 00 00 00 7d 92 |[...e...|......}.|
|000028a0| d0 36 00 00 00 00 00 00 | 00 00 00 00 00 00 00 0d |.6......|........|
|000028b0| 45 72 72 6f 72 46 75 6e | 63 74 69 6f 6e 92 e8 00 |ErrorFun|ction...|
|000028c0| 7d 92 e8 00 95 1f 9c 00 | 95 01 30 40 80 9a 0a 00 |}.......|..0@....|
|000028d0| 7d 92 e0 00 00 01 65 20 | 20 66 75 6e 63 74 69 6f |}.....e | functio|
|000028e0| 6e 20 45 72 72 6f 72 46 | 75 6e 63 74 69 6f 6e 28 |n ErrorF|unction(|
|000028f0| 78 29 20 20 23 20 52 65 | 74 75 72 6e 20 65 72 66 |x)  # Re|turn erf|
|00002900| 28 78 29 2e 0d 2e 20 20 | 20 23 20 20 20 20 49 6e |(x)...  | #    In|
|00002910| 70 75 74 3a 20 20 78 20 | 3d 20 6e 75 6d 62 65 72 |put:  x |= number|
|00002920| 20 6f 72 20 61 72 72 61 | 79 0d 2e 20 20 20 23 20 | or arra|y..   # |
|00002930| 20 20 20 4f 75 74 70 75 | 74 20 20 45 72 72 6f 72 |   Outpu|t  Error|
|00002940| 46 75 6e 63 74 69 6f 6e | 20 3d 20 65 72 66 28 78 |Function| = erf(x|
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|00002960| 72 61 79 0d 2e 20 20 20 | 23 20 20 20 20 20 20 20 |ray..   |#       |
|00002970| 20 20 20 20 20 20 20 20 | 20 20 20 20 3d 20 32 2f |        |    = 2/|
|00002980| 73 71 72 74 28 b9 29 20 | 69 6e 74 65 67 72 61 6c |sqrt(.) |integral|
|00002990| 20 30 2d 3e 78 20 7b 20 | 65 78 70 28 2d 74 5e 32 | 0->x { |exp(-t^2|
|000029a0| 29 20 64 74 20 7d 0d 2e | 20 20 20 62 65 67 69 6e |) dt }..|   begin|
|000029b0| 0d 2e 20 20 20 20 20 69 | 66 20 78 3c 30 20 74 68 |..     i|f x<0 th|
|000029c0| 65 6e 0d 2e 20 20 20 20 | 20 20 20 45 72 72 6f 72 |en..    |   Error|
|000029d0| 46 75 6e 63 74 69 6f 6e | 20 3d 20 2d 49 6e 63 6f |Function| = -Inco|
|000029e0| 6d 70 6c 65 74 65 47 61 | 6d 6d 61 28 30 2e 35 2c |mpleteGa|mma(0.5,|
|000029f0| 20 78 5e 32 29 0d 2e 20 | 20 20 20 20 65 6c 73 65 | x^2).. |    else|
|00002a00| 0d 2e 20 20 20 20 20 20 | 20 45 72 72 6f 72 46 75 |..      | ErrorFu|
|00002a10| 6e 63 74 69 6f 6e 20 3d | 20 49 6e 63 6f 6d 70 6c |nction =| Incompl|
|00002a20| 65 74 65 47 61 6d 6d 61 | 28 30 2e 35 2c 20 78 5e |eteGamma|(0.5, x^|
|00002a30| 32 29 0d 2e 20 20 20 20 | 20 65 6e 64 00 00 00 01 |2)..    | end....|
|00002a40| 01 78 1f 9c 00 95 01 20 | 40 80 9a 0a 00 7d 92 e0 |.x..... |@....}..|
|00002a50| 00 7e 7b f4 00 95 59 ff | 00 00 ff ff 00 00 00 00 |.~{...Y.|........|
|00002a60| 20 00 00 7c 00 00 00 00 | 10 00 7d 92 b4 00 00 00 | ..|....|..}.....|
|00002a70| 00 00 00 00 00 00 00 00 | 00 00 00 00 7d 92 b8 00 |........|....}...|
|00002a80| 00 00 00 00 7d 92 ac 00 | 7d 92 b0 00 45 00 71 00 |....}...|}...E.q.|
|00002a90| 00 00 79 00 00 00 00 00 | 00 00 00 00 7d 92 a0 36 |..y.....|....}..6|
|00002aa0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 06 45 78 |........|......Ex|
|00002ab0| 69 73 74 73 05 00 7d c9 | e2 00 7d 92 b8 00 7d 92 |ists..}.|..}...}.|
|00002ac0| b8 00 95 1f 9c 00 95 01 | 30 40 80 9a 0a 00 7d 92 |........|0@....}.|
|00002ad0| b0 00 00 00 79 20 20 66 | 75 6e 63 74 69 6f 6e 20 |....y  f|unction |
|00002ae0| 45 78 69 73 74 73 28 4f | 62 6a 29 20 23 20 52 65 |Exists(O|bj) # Re|
|00002af0| 74 75 72 6e 20 31 20 69 | 66 20 4f 62 6a 20 65 78 |turn 1 i|f Obj ex|
|00002b00| 69 73 74 73 2c 20 30 20 | 69 66 20 6e 6f 74 2e 0d |ists, 0 |if not..|
|00002b10| 2e 20 20 20 62 65 67 69 | 6e 0d 2e 20 20 20 20 20 |.   begi|n..     |
|00002b20| 69 66 20 4f 62 6a 3d 4f | 62 6a 20 74 68 65 6e 20 |if Obj=O|bj then |
|00002b30| 45 78 69 73 74 73 3d 31 | 20 65 6c 73 65 20 45 78 |Exists=1| else Ex|
|00002b40| 69 73 74 73 3d 30 0d 2e | 20 20 20 65 6e 64 00 00 |ists=0..|   end..|
|00002b50| 00 01 03 4f 62 6a 00 95 | 01 20 40 80 9a 0a 00 7d |...Obj..|. @....}|
|00002b60| 92 b0 00 7e 7b f4 00 95 | 59 ff 00 00 ff ff 00 00 |...~{...|Y.......|
|00002b70| 00 00 20 00 00 7c 00 00 | 00 00 0c 00 7d 92 94 01 |.. ..|..|....}...|
|00002b80| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 13 00 00 |........|........|
|00002b90| 00 00 00 03 65 78 70 00 | 91 48 ee 00 00 00 00 00 |....exp.|.H......|
|00002ba0| 00 ff ff 00 00 00 00 00 | 95 01 42 00 91 ff 28 00 |........|..B...(.|
|00002bb0| 95 01 31 00 00 00 01 10 | 00 7d 92 8c 00 00 00 00 |..1.....|.}......|
|00002bc0| 00 00 00 00 00 00 00 00 | 00 00 00 7d 92 90 00 00 |........|...}....|
|00002bd0| 00 00 00 7d 92 84 00 7d | 92 88 00 e3 01 c3 00 00 |...}...}|........|
|00002be0| 01 cb 00 00 00 00 00 00 | 00 00 00 7d 92 78 36 00 |........|...}.x6.|
|00002bf0| 00 00 00 00 00 00 00 00 | 00 00 00 00 03 46 46 54 |........|.....FFT|
|00002c00| 00 00 00 05 00 7d c9 e2 | 00 7d 92 90 00 7d 92 90 |.....}..|.}...}..|
|00002c10| 00 95 1f 9c 00 95 01 30 | 40 80 9a 0a 00 7d 92 88 |.......0|@....}..|
|00002c20| 00 00 01 cb 20 20 66 75 | 6e 63 74 69 6f 6e 20 46 |....  fu|nction F|
|00002c30| 46 54 28 43 78 29 20 20 | 23 20 20 52 65 74 75 72 |FT(Cx)  |#  Retur|
|00002c40| 6e 73 20 74 68 65 20 64 | 69 73 63 72 65 74 65 20 |ns the d|iscrete |
|00002c50| 66 6f 75 72 69 65 72 20 | 74 72 61 6e 73 66 6f 72 |fourier |transfor|
|00002c60| 6d 20 6f 66 20 43 78 2e | 0d 2e 20 20 20 76 61 72 |m of Cx.|..   var|
|00002c70| 20 6e 2c 20 43 6b 2c 20 | 65 72 72 0d 2e 20 23 20 | n, Ck, |err.. # |
|00002c80| 20 20 49 6e 70 75 74 3a | 20 20 20 20 20 43 78 20 |  Input:|     Cx |
|00002c90| 3d 20 72 65 61 6c 20 6f | 72 20 63 6f 6d 70 6c 65 |= real o|r comple|
|00002ca0| 78 20 61 72 72 61 79 2c | 20 32 5e 4e 20 70 6f 69 |x array,| 2^N poi|
|00002cb0| 6e 74 73 2e 0d 2e 20 23 | 20 20 20 4f 75 74 70 75 |nts... #|   Outpu|
|00002cc0| 74 3a 20 20 20 46 46 54 | 20 3d 20 63 6f 6d 70 6c |t:   FFT| = compl|
|00002cd0| 65 78 20 61 72 72 61 79 | 20 3d 20 64 69 73 63 72 |ex array| = discr|
|00002ce0| 65 74 65 20 66 6f 75 72 | 69 65 72 20 74 72 61 6e |ete four|ier tran|
|00002cf0| 73 66 6f 72 6d 20 6f 66 | 20 43 78 2e 0d 2e 20 20 |sform of| Cx...  |
|00002d00| 20 62 65 67 69 6e 0d 2e | 20 20 20 20 20 43 6b 20 | begin..|     Ck |
|00002d10| 3d 20 43 78 0d 2e 20 20 | 20 20 20 6e 20 3d 20 73 |= Cx..  |   n = s|
|00002d20| 69 7a 65 28 43 6b 29 0d | 2e 20 20 20 20 20 78 46 |ize(Ck).|.     xF|
|00002d30| 46 54 28 6e 2c 2d 31 2c | 43 6b 2c 45 72 72 29 0d |FT(n,-1,|Ck,Err).|
|00002d40| 2e 20 20 20 20 20 69 66 | 20 45 72 72 3c 3e 30 20 |.     if| Err<>0 |
|00002d50| 74 68 65 6e 0d 2e 20 20 | 20 20 20 20 20 62 65 67 |then..  |     beg|
|00002d60| 69 6e 20 0d 2e 20 20 20 | 20 20 20 20 20 20 70 72 |in ..   |      pr|
|00002d70| 69 6e 74 28 22 20 a5 a5 | 20 45 52 52 4f 52 20 69 |int(" ..| ERROR i|
|00002d80| 6e 20 78 46 46 54 2c 20 | 65 72 72 3d 22 2b 45 72 |n xFFT, |err="+Er|
|00002d90| 72 29 0d 2e 20 20 20 20 | 20 20 20 20 20 46 46 54 |r)..    |     FFT|
|00002da0| 20 3d 20 30 2f 30 20 20 | 23 20 77 68 69 63 68 20 | = 0/0  |# which |
|00002db0| 69 73 20 22 4e 6f 74 20 | 61 20 6e 75 6d 62 65 72 |is "Not |a number|
|00002dc0| 22 0d 2e 20 20 20 20 20 | 20 20 65 6e 64 0d 2e 20 |"..     |  end.. |
|00002dd0| 20 20 20 20 65 6c 73 65 | 0d 2e 20 20 20 20 20 46 |    else|..     F|
|00002de0| 46 54 20 3d 20 43 6b 0d | 2e 20 20 20 65 6e 64 00 |FT = Ck.|.   end.|
|00002df0| 00 00 01 02 43 78 9c 00 | 95 01 20 40 80 9a 0a 00 |....Cx..|.. @....|
|00002e00| 7d 92 88 00 7e 7b f4 00 | 95 59 ff 00 00 ff ff 00 |}...~{..|.Y......|
|00002e10| 00 00 00 20 00 00 7c 00 | 00 00 03 01 6e 7b f4 00 |... ..|.|....n{..|
|00002e20| 95 59 ff 00 00 ff ff 00 | 00 00 00 20 00 00 7c 00 |.Y......|... ..|.|
|00002e30| 00 00 01 00 7d 92 90 00 | 00 01 cb 00 91 48 ee 02 |....}...|.....H..|
|00002e40| 43 6b f4 00 95 59 ff 00 | 00 ff ff 00 00 00 00 20 |Ck...Y..|....... |
|00002e50| 00 00 7c 00 00 00 01 00 | 7d 92 90 00 00 01 cb 00 |..|.....|}.......|
|00002e60| 91 48 ee 03 65 72 72 00 | 95 59 ff 00 00 ff ff 00 |.H..err.|.Y......|
|00002e70| 00 00 00 20 00 00 7c 00 | 00 00 01 00 7d 92 90 00 |... ..|.|....}...|
|00002e80| 00 01 cb 00 91 48 ee 0c | 00 7d 92 60 01 00 00 00 |.....H..|.}.`....|
|00002e90| 00 00 00 00 00 00 00 00 | 00 00 45 00 00 00 00 00 |........|..E.....|
|00002ea0| 0a 46 69 72 73 74 49 6e | 64 65 78 03 00 00 ff ff |.FirstIn|dex.....|
|00002eb0| 00 00 00 00 00 95 01 42 | 00 91 ff 28 00 95 01 31 |.......B|...(...1|
|00002ec0| 00 00 00 01 10 00 7d 92 | 58 00 00 00 00 00 00 00 |......}.|X.......|
|00002ed0| 00 00 00 00 00 00 00 00 | 7d 92 5c 00 00 00 00 00 |........|}.\.....|
|00002ee0| 7d 92 50 00 7d 92 54 02 | 8f 05 a7 00 00 05 af 00 |}.P.}.T.|........|
|00002ef0| 00 00 00 00 00 00 00 00 | 7d 92 30 35 00 00 00 00 |........|}.05....|
|00002f00| 00 00 00 00 00 00 00 00 | 00 0b 46 69 74 4c 65 67 |........|..FitLeg|
|00002f10| 65 6e 64 72 65 00 7d 92 | 5c 00 7d 92 5c 00 95 1f |endre.}.|\.}.\...|
|00002f20| 9c 00 95 01 30 40 80 9a | 0a 00 7d 92 54 00 00 05 |....0@..|..}.T...|
|00002f30| af 20 70 72 6f 67 72 61 | 6d 20 46 69 74 4c 65 67 |. progra|m FitLeg|
|00002f40| 65 6e 64 72 65 28 78 44 | 61 74 61 2c 79 44 61 74 |endre(xD|ata,yDat|
|00002f50| 61 2c 53 69 67 6d 61 2c | 20 4a 2c 41 2c 20 20 50 |a,Sigma,| J,A,  P|
|00002f60| 72 6f 62 29 20 23 46 69 | 6e 64 20 41 5b 31 c9 4a |rob) #Fi|nd A[1.J|
|00002f70| 5d 20 73 75 63 68 20 74 | 68 61 74 20 47 28 78 29 |] such t|hat G(x)|
|00002f80| 20 3d 20 41 5b 6a 5d 20 | a5 ca 50 5f 6a 28 78 29 | = A[j] |..P_j(x)|
|00002f90| 20 66 69 74 73 20 79 44 | 61 74 61 5b 31 c9 4e 5d | fits yD|ata[1.N]|
|00002fa0| 2e 0d 2e 20 20 20 76 61 | 72 20 4e 2c 6e 6e 2c 6a |...   va|r N,nn,j|
|00002fb0| 6a 2c 41 76 61 72 2c 77 | 31 2c 77 32 2c 77 33 2c |j,Avar,w|1,w2,w3,|
|00002fc0| 43 68 69 53 71 2c 20 65 | 72 72 0d 2e 20 20 23 20 |ChiSq, e|rr..  # |
|00002fd0| 20 49 6e 70 75 74 73 3a | 0d 2e 20 20 23 20 20 20 | Inputs:|..  #   |
|00002fe0| 20 20 78 44 61 74 61 5b | 31 c9 4e 5d 2c 20 79 44 |  xData[|1.N], yD|
|00002ff0| 61 74 61 5b 31 c9 4e 5d | 20 20 20 64 61 74 61 20 |ata[1.N]|   data |
|00003000| 70 6f 69 6e 74 73 2c 0d | 2e 20 20 23 20 20 20 20 |points,.|.  #    |
|00003010| 20 53 69 67 6d 61 20 20 | 28 72 65 61 6c 20 6f 72 | Sigma  |(real or|
|00003020| 20 61 72 72 61 79 29 20 | 3d 20 79 44 61 74 61 20 | array) |= yData |
|00003030| 65 72 72 6f 72 73 2c 20 | 0d 2e 20 20 23 20 20 20 |errors, |..  #   |
|00003040| 20 20 4a 20 3d 20 6e 75 | 6d 62 65 72 20 6f 66 20 |  J = nu|mber of |
|00003050| 70 61 72 61 6d 65 74 65 | 72 73 20 41 5b 6a 5d 20 |paramete|rs A[j] |
|00003060| 74 6f 20 66 69 74 2c 20 | 0d 2e 20 20 23 20 20 20 |to fit, |..  #   |
|00003070| 20 20 20 20 20 20 28 20 | 77 69 74 68 20 67 28 78 |      ( |with g(x|
|00003080| 29 20 3d 20 41 5b 31 5d | 20 50 5f 31 28 78 29 20 |) = A[1]| P_1(x) |
|00003090| 2b 20 41 5b 32 5d 20 50 | 5f 32 28 78 29 20 2b 20 |+ A[2] P|_2(x) + |
|000030a0| 20 c9 20 2b 20 41 5b 4a | 5d 20 50 5f 6a 28 78 29 | . + A[J|] P_j(x)|
|000030b0| 20 20 29 0d 2e 20 20 23 | 20 4f 75 74 70 75 74 73 |  )..  #| Outputs|
|000030c0| 3a 0d 2e 20 20 23 20 20 | 20 20 20 41 5b 31 c9 4a |:..  #  |   A[1.J|
|000030d0| 5d 20 3d 20 62 65 73 74 | 20 66 69 74 20 63 6f 65 |] = best| fit coe|
|000030e0| 66 66 69 63 69 65 6e 74 | 73 2c 0d 2e 20 20 23 20 |fficient|s,..  # |
|000030f0| 20 20 20 20 50 72 6f 62 | 20 3d 20 70 72 6f 62 61 |    Prob| = proba|
|00003100| 62 69 6c 69 74 79 20 6f | 66 20 74 68 69 73 20 66 |bility o|f this f|
|00003110| 69 74 20 6d 61 74 63 68 | 69 6e 67 20 64 61 74 61 |it match|ing data|
|00003120| 20 77 69 74 68 20 67 69 | 76 65 6e 20 53 69 67 6d | with gi|ven Sigm|
|00003130| 61 2e 0d 2e 20 20 23 20 | 0d 2e 20 20 23 20 4e 6f |a...  # |..  # No|
|00003140| 74 65 20 74 68 61 74 20 | 68 65 72 65 20 74 68 65 |te that |here the|
|00003150| 20 4c 65 67 65 6e 64 72 | 65 20 70 6f 6c 79 73 2e | Legendr|e polys.|
|00003160| 20 61 72 65 20 50 5f 6a | 20 77 69 74 68 20 6a 3d | are P_j| with j=|
|00003170| 31 2c 32 2c 33 2c c9 2c | 0d 2e 20 20 23 20 20 20 |1,2,3,.,|..  #   |
|00003180| 20 20 20 4e 4f 54 20 6a | 3d 30 2c 31 2c 32 2c c9 |   NOT j|=0,1,2,.|
|00003190| 20 61 73 20 69 73 20 74 | 68 65 20 63 6f 6e 76 65 | as is t|he conve|
|000031a0| 6e 74 69 6f 6e 20 73 6f | 6d 65 74 69 6d 65 73 2e |ntion so|metimes.|
|000031b0| 0d 2e 20 20 23 0d 2e 20 | 20 20 62 65 67 69 6e 0d |..  #.. |  begin.|
|000031c0| 2e 20 20 20 20 20 6a 6a | 3d 31 c9 4a 3b 0d 2e 20 |.     jj|=1.J;.. |
|000031d0| 20 20 20 20 4e 20 3d 20 | 73 69 7a 65 28 78 44 61 |    N = |size(xDa|
|000031e0| 74 61 29 3b 20 20 20 20 | 20 20 20 20 20 23 20 6e |ta);    |     # n|
|000031f0| 75 6d 62 65 72 20 6f 66 | 20 64 61 74 61 20 70 6f |umber of| data po|
|00003200| 69 6e 74 73 2e 0d 2e 20 | 20 20 20 20 6e 6e 20 3d |ints... |    nn =|
|00003210| 20 31 c9 4e 0d 2e 20 20 | 20 20 20 69 66 20 73 69 | 1.N..  |   if si|
|00003220| 7a 65 28 53 69 67 6d 61 | 29 3d 31 20 74 68 65 6e |ze(Sigma|)=1 then|
|00003230| 0d 2e 20 20 20 20 20 20 | 20 53 69 67 6d 61 5b 6e |..      | Sigma[n|
|00003240| 6e 5d 3d 53 69 67 6d 61 | 20 20 20 20 20 23 20 6d |n]=Sigma|     # m|
|00003250| 61 6b 65 20 73 75 72 65 | 20 73 69 67 6d 61 20 69 |ake sure| sigma i|
|00003260| 73 20 61 6e 20 61 72 72 | 61 79 0d 2e 20 20 20 20 |s an arr|ay..    |
|00003270| 20 69 66 20 73 69 7a 65 | 28 53 69 67 6d 61 29 3c | if size|(Sigma)<|
|00003280| 3e 4e 20 74 68 65 6e 0d | 2e 20 20 20 20 20 20 20 |>N then.|.       |
|00003290| 20 20 50 72 69 6e 74 28 | 22 45 52 52 4f 52 3a 20 |  Print(|"ERROR: |
|000032a0| 78 44 61 74 61 2c 20 53 | 69 67 6d 61 20 6e 6f 74 |xData, S|igma not|
|000032b0| 20 73 61 6d 65 20 73 69 | 7a 65 22 29 0d 2e 20 20 | same si|ze")..  |
|000032c0| 20 20 20 65 6c 73 65 20 | 69 66 20 73 69 7a 65 28 |   else |if size(|
|000032d0| 79 44 61 74 61 29 3c 3e | 4e 20 74 68 65 6e 20 0d |yData)<>|N then .|
|000032e0| 2e 20 20 20 20 20 20 20 | 20 20 50 72 69 6e 74 28 |.       |  Print(|
|000032f0| 22 20 45 52 52 4f 52 3a | 20 78 44 61 74 61 2c 79 |" ERROR:| xData,y|
|00003300| 44 61 74 61 20 6e 6f 74 | 20 73 61 6d 65 20 73 69 |Data not| same si|
|00003310| 7a 65 22 29 0d 2e 20 20 | 20 20 20 65 6c 73 65 20 |ze")..  |   else |
|00003320| 0d 2e 20 20 20 20 20 20 | 20 62 65 67 69 6e 0d 2e |..      | begin..|
|00003330| 20 20 20 20 20 20 20 41 | 76 61 72 5b 6a 6a 2c 6a |       A|var[jj,j|
|00003340| 6a 5d 3d 30 3b 20 20 20 | 20 20 20 20 20 20 20 20 |j]=0;   |        |
|00003350| 20 23 20 20 20 61 6e 64 | 20 63 6f 2d 76 61 72 69 | #   and| co-vari|
|00003360| 61 6e 63 65 20 61 72 72 | 61 79 2e 0d 2e 20 20 20 |ance arr|ay...   |
|00003370| 20 20 20 20 77 31 5b 6e | 6e 2c 6a 6a 5d 20 3d 20 |    w1[n|n,jj] = |
|00003380| 30 3b 20 20 20 20 20 20 | 20 20 20 20 20 20 23 20 |0;      |      # |
|00003390| 77 6f 72 6b 20 73 70 61 | 63 65 0d 2e 20 20 20 20 |work spa|ce..    |
|000033a0| 20 20 20 77 32 5b 6a 6a | 2c 6a 6a 5d 20 3d 20 30 |   w2[jj|,jj] = 0|
|000033b0| 3b 0d 2e 20 20 20 20 20 | 20 20 77 33 5b 6a 6a 5d |;..     |  w3[jj]|
|000033c0| 20 3d 20 30 3b 0d 2e 20 | 20 20 20 20 20 20 43 68 | = 0;.. |      Ch|
|000033d0| 69 53 71 20 3d 20 30 3b | 20 65 72 72 3d 30 3b 0d |iSq = 0;| err=0;.|
|000033e0| 2e 20 20 20 20 20 20 20 | 41 5b 6a 6a 5d 20 3d 20 |.       |A[jj] = |
|000033f0| 30 3b 0d 2e 20 20 20 20 | 20 20 20 78 46 49 54 5f |0;..    |   xFIT_|
|00003400| 46 55 4e 43 53 28 78 42 | 41 53 49 53 5f 4c 45 47 |FUNCS(xB|ASIS_LEG|
|00003410| 45 4e 44 52 45 2c 20 4e | 2c 78 44 61 74 61 2c 79 |ENDRE, N|,xData,y|
|00003420| 44 61 74 61 2c 53 69 67 | 6d 61 2c 20 4a 2c 41 2c |Data,Sig|ma, J,A,|
|00003430| 41 76 61 72 2c 20 77 31 | 2c 77 32 2c 77 33 2c 20 |Avar, w1|,w2,w3, |
|00003440| 43 68 69 53 71 2c 20 65 | 72 72 29 0d 2e 20 20 20 |ChiSq, e|rr)..   |
|00003450| 20 20 20 20 69 66 20 65 | 72 72 3c 3e 30 20 74 68 |    if e|rr<>0 th|
|00003460| 65 6e 20 50 72 69 6e 74 | 28 22 20 45 52 52 4f 52 |en Print|(" ERROR|
|00003470| 20 69 6e 20 78 46 49 54 | 5f 46 55 4e 43 53 20 3d | in xFIT|_FUNCS =|
|00003480| 20 22 2b 65 72 72 29 0d | 2e 20 20 20 20 20 20 20 | "+err).|.       |
|00003490| 50 72 6f 62 20 3d 20 43 | 68 69 53 71 50 72 6f 62 |Prob = C|hiSqProb|
|000034a0| 61 62 69 6c 69 74 79 28 | 20 43 68 69 53 71 2c 20 |ability(| ChiSq, |
|000034b0| 4a 29 20 20 20 23 20 73 | 65 65 20 62 65 6c 6f 77 |J)   # s|ee below|
|000034c0| 2e 0d 2e 20 20 20 20 20 | 20 20 65 6e 64 20 20 23 |...     |  end  #|
|000034d0| 20 6f 66 20 65 6c 73 65 | 0d 2e 20 20 20 65 6e 64 | of else|..   end|
|000034e0| 00 00 00 06 05 78 44 61 | 74 61 01 20 40 80 9a 0a |.....xDa|ta. @...|
|000034f0| 00 7d 92 54 00 7e 7b f4 | 00 95 59 ff 00 00 ff ff |.}.T.~{.|..Y.....|
|00003500| 00 00 00 00 20 00 00 7c | 05 79 44 61 74 61 01 20 |.... ..||.yData. |
|00003510| 40 80 9a 0a 00 7d 92 54 | 00 7e 7b f4 00 95 59 ff |@....}.T|.~{...Y.|
|00003520| 00 00 ff ff 00 00 00 00 | 20 00 00 7c 05 53 69 67 |........| ..|.Sig|
|00003530| 6d 61 01 20 40 80 9a 0a | 00 7d 92 54 00 7e 7b f4 |ma. @...|.}.T.~{.|
|00003540| 00 95 59 ff 00 00 ff ff | 00 00 00 00 20 00 00 7c |..Y.....|.... ..||
|00003550| 01 4a 69 67 6d 61 01 20 | 40 80 9a 0a 00 7d 92 54 |.Jigma. |@....}.T|
|00003560| 00 7e 7b f4 00 95 59 ff | 00 00 ff ff 00 00 00 00 |.~{...Y.|........|
|00003570| 20 00 00 7c 01 41 69 67 | 6d 61 01 20 40 80 9a 0a | ..|.Aig|ma. @...|
|00003580| 00 7d 92 54 00 7e 7b f4 | 00 95 59 ff 00 00 ff ff |.}.T.~{.|..Y.....|
|00003590| 00 00 00 00 20 00 00 7c | 04 50 72 6f 62 61 01 20 |.... ..||.Proba. |
|000035a0| 40 80 9a 0a 00 7d 92 54 | 00 7e 7b f4 00 95 59 ff |@....}.T|.~{...Y.|
|000035b0| 00 00 ff ff 00 00 00 00 | 20 00 00 7c 00 00 00 09 |........| ..|....|
|000035c0| 01 4e 7b f4 00 95 59 ff | 00 00 ff ff 00 00 00 00 |.N{...Y.|........|
|000035d0| 20 00 00 7c 00 00 00 06 | 00 7d 92 5c 00 00 05 af | ..|....|.}.\....|
|000035e0| 00 91 48 ee 02 6e 6e f4 | 00 95 59 ff 00 00 ff ff |..H..nn.|..Y.....|
|000035f0| 00 00 00 00 20 00 00 7c | 00 00 00 06 00 7d 92 5c |.... ..||.....}.\|
|00003600| 00 00 05 af 00 91 48 ee | 02 6a 6a f4 00 95 59 ff |......H.|.jj...Y.|
|00003610| 00 00 ff ff 00 00 00 00 | 20 00 00 7c 00 00 00 06 |........| ..|....|
|00003620| 00 7d 92 5c 00 00 05 af | 00 91 48 ee 04 41 76 61 |.}.\....|..H..Ava|
|00003630| 72 95 59 ff 00 00 ff ff | 00 00 00 00 20 00 00 7c |r.Y.....|.... ..||
|00003640| 00 00 00 06 00 7d 92 5c | 00 00 05 af 00 91 48 ee |.....}.\|......H.|
|00003650| 02 77 31 61 72 95 59 ff | 00 00 ff ff 00 00 00 00 |.w1ar.Y.|........|
|00003660| 20 00 00 7c 00 00 00 06 | 00 7d 92 5c 00 00 05 af | ..|....|.}.\....|
|00003670| 00 91 48 ee 02 77 32 61 | 72 95 59 ff 00 00 ff ff |..H..w2a|r.Y.....|
|00003680| 00 00 00 00 20 00 00 7c | 00 00 00 06 00 7d 92 5c |.... ..||.....}.\|
|00003690| 00 00 05 af 00 91 48 ee | 02 77 33 61 72 95 59 ff |......H.|.w3ar.Y.|
|000036a0| 00 00 ff ff 00 00 00 00 | 20 00 00 7c 00 00 00 06 |........| ..|....|
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|000036d0| 00 00 00 06 00 7d 92 5c | 00 00 05 af 00 91 48 ee |.....}.\|......H.|
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|000036f0| 20 00 00 7c 00 00 00 06 | 00 7d 92 5c 00 00 05 af | ..|....|.}.\....|
|00003700| 00 91 48 ee 10 00 7d 92 | 00 00 00 00 00 00 00 00 |..H...}.|........|
|00003710| 00 00 00 00 00 00 00 00 | 7d 92 04 00 00 00 00 00 |........|}.......|
|00003720| 7d 91 f8 00 7d 91 fc 01 | e8 05 76 00 00 05 7e 00 |}...}...|..v...~.|
|00003730| 00 00 00 00 00 00 00 00 | 7d 91 d8 35 00 00 00 00 |........|}..5....|
|00003740| 00 00 00 00 00 00 00 00 | 00 07 46 69 74 4c 69 6e |........|..FitLin|
|00003750| 65 00 7d c9 e2 00 7d 92 | 04 00 7d 92 04 00 95 1f |e.}...}.|..}.....|
|00003760| 9c 00 95 01 30 40 80 9a | 0a 00 7d 91 fc 00 00 05 |....0@..|..}.....|
|00003770| 7e 20 70 72 6f 67 72 61 | 6d 20 46 69 74 4c 69 6e |~ progra|m FitLin|
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|00003790| 2c 42 2c 20 72 2c 45 72 | 72 6f 72 45 73 74 69 6d |,B, r,Er|rorEstim|
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|000037b0| 6f 72 20 79 3d 41 20 78 | 20 2b 20 62 0d 2e 20 20 |or y=A x| + b..  |
|000037c0| 20 76 61 72 20 4e 2c 4a | 2c 6a 6a 2c 6e 6e 2c 53 | var N,J|,jj,nn,S|
|000037d0| 69 67 6d 61 2c 43 2c 43 | 76 61 72 2c 77 31 2c 77 |igma,C,C|var,w1,w|
|000037e0| 32 2c 77 33 2c 43 68 69 | 53 71 2c 20 65 72 72 0d |2,w3,Chi|Sq, err.|
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|00003800| 0d 2e 20 23 20 20 20 20 | 20 20 20 78 44 61 74 61 |.. #    |   xData|
|00003810| 5b 31 c9 6e 5d 2c 20 79 | 44 61 74 61 5b 31 c9 6e |[1.n], y|Data[1.n|
|00003820| 5d 0d 2e 20 23 20 20 4f | 75 74 70 75 74 73 3a 0d |].. #  O|utputs:.|
|00003830| 2e 20 23 20 20 20 20 20 | 20 20 41 20 3d 20 73 6c |. #     |  A = sl|
|00003840| 6f 70 65 2c 20 20 42 20 | 3d 20 69 6e 74 65 72 63 |ope,  B |= interc|
|00003850| 65 70 74 20 6f 66 20 62 | 65 73 74 20 66 69 74 20 |ept of b|est fit |
|00003860| 6c 69 6e 65 20 20 20 20 | 79 20 3d 20 41 20 78 20 |line    |y = A x |
|00003870| 2b 20 62 0d 2e 20 23 20 | 20 20 20 20 20 20 72 20 |+ b.. # |      r |
|00003880| 3d 20 63 6f 72 72 65 6c | 61 74 69 6f 6e 20 63 6f |= correl|ation co|
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|000038a0| 3c 3d 31 2e 20 20 0d 2e | 20 23 20 20 20 20 20 20 |<=1.  ..| #      |
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|00003900| 20 20 20 20 20 20 20 45 | 72 72 6f 72 45 73 74 69 |       E|rrorEsti|
|00003910| 6d 61 74 65 20 3d 20 61 | 70 70 72 6f 78 69 6d 61 |mate = a|pproxima|
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|00003930| 74 61 20 61 73 73 75 6d | 69 6e 67 20 66 69 74 20 |ta assum|ing fit |
|00003940| 74 6f 20 6c 69 6e 65 20 | 69 73 20 4f 4b 2e 0d 2e |to line |is OK...|
|00003950| 20 20 20 62 65 67 69 6e | 0d 2e 20 20 20 20 20 4a |   begin|..     J|
|00003960| 20 3d 20 32 3b 20 20 20 | 20 20 20 20 20 20 20 20 | = 2;   |        |
|00003970| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 23 20 6e |        |     # n|
|00003980| 75 6d 62 65 72 20 6f 66 | 20 63 6f 65 66 66 69 65 |umber of| coeffie|
|00003990| 6e 74 73 20 74 6f 20 66 | 69 6e 65 0d 2e 20 20 20 |nts to f|ine..   |
|000039a0| 20 20 6a 6a 3d 31 c9 4a | 3b 0d 2e 20 20 20 20 20 |  jj=1.J|;..     |
|000039b0| 4e 20 3d 20 73 69 7a 65 | 28 78 44 61 74 61 29 3b |N = size|(xData);|
|000039c0| 20 20 20 20 20 20 20 20 | 20 23 20 6e 75 6d 62 65 |        | # numbe|
|000039d0| 72 20 6f 66 20 64 61 74 | 61 20 70 6f 69 6e 74 73 |r of dat|a points|
|000039e0| 2e 0d 2e 20 20 20 20 20 | 6e 6e 20 3d 20 31 c9 4e |...     |nn = 1.N|
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|00003a10| 2e 20 20 20 20 20 20 20 | 20 20 50 72 69 6e 74 28 |.       |  Print(|
|00003a20| 22 20 45 52 52 4f 52 3a | 20 78 44 61 74 61 2c 79 |" ERROR:| xData,y|
|00003a30| 44 61 74 61 20 6e 6f 74 | 20 73 61 6d 65 20 73 69 |Data not| same si|
|00003a40| 7a 65 22 29 0d 2e 20 20 | 20 20 20 65 6c 73 65 20 |ze")..  |   else |
|00003a50| 0d 2e 20 20 20 20 20 20 | 20 62 65 67 69 6e 0d 2e |..      | begin..|
|00003a60| 20 20 20 20 20 20 20 43 | 5b 6a 6a 5d 20 3d 20 30 |       C|[jj] = 0|
|00003a70| 3b 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |;       |        |
|00003a80| 20 20 20 20 23 20 73 70 | 61 63 65 20 66 6f 72 20 |    # sp|ace for |
|00003a90| 63 6f 65 66 66 69 63 69 | 65 6e 74 73 0d 2e 20 20 |coeffici|ents..  |
|00003aa0| 20 20 20 20 20 43 76 61 | 72 5b 6a 6a 2c 6a 6a 5d |     Cva|r[jj,jj]|
|00003ab0| 3d 30 3b 20 20 20 20 20 | 20 20 20 20 20 20 20 23 |=0;     |       #|
|00003ac0| 20 20 20 61 6e 64 20 63 | 6f 2d 76 61 72 69 61 6e |   and c|o-varian|
|00003ad0| 63 65 20 61 72 72 61 79 | 2e 0d 2e 20 20 20 20 20 |ce array|...     |
|00003ae0| 20 20 77 31 5b 6e 6e 2c | 6a 6a 5d 20 3d 20 30 3b |  w1[nn,|jj] = 0;|
|00003af0| 20 20 20 20 20 20 20 20 | 20 20 20 20 23 20 77 6f |        |    # wo|
|00003b00| 72 6b 20 73 70 61 63 65 | 0d 2e 20 20 20 20 20 20 |rk space|..      |
|00003b10| 20 77 32 5b 6a 6a 2c 6a | 6a 5d 20 3d 20 30 3b 0d | w2[jj,j|j] = 0;.|
|00003b20| 2e 20 20 20 20 20 20 20 | 77 33 5b 6a 6a 5d 20 3d |.       |w3[jj] =|
|00003b30| 20 30 3b 0d 2e 20 20 20 | 20 20 20 20 43 68 69 53 | 0;..   |    ChiS|
|00003b40| 71 20 3d 20 30 3b 20 65 | 72 72 3d 30 3b 0d 2e 20 |q = 0; e|rr=0;.. |
|00003b50| 20 20 20 20 20 20 53 69 | 67 6d 61 5b 6e 6e 5d 20 |      Si|gma[nn] |
|00003b60| 3d 20 31 3b 20 20 20 20 | 20 20 20 20 20 20 20 23 |= 1;    |       #|
|00003b70| 20 61 73 73 75 6d 65 20 | 75 6e 69 66 6f 72 6d 20 | assume |uniform |
|00003b80| 79 20 75 6e 63 65 72 74 | 61 69 6e 74 69 65 73 0d |y uncert|ainties.|
|00003b90| 2e 20 20 20 20 20 20 20 | 78 46 49 54 5f 46 55 4e |.       |xFIT_FUN|
|00003ba0| 43 53 28 78 42 41 53 49 | 53 5f 50 4f 4c 59 2c 20 |CS(xBASI|S_POLY, |
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|00003bc0| 67 6d 61 2c 20 4a 2c 43 | 2c 43 76 61 72 2c 20 77 |gma, J,C|,Cvar, w|
|00003bd0| 31 2c 77 32 2c 77 33 2c | 20 43 68 69 53 71 2c 20 |1,w2,w3,| ChiSq, |
|00003be0| 65 72 72 29 0d 2e 20 20 | 20 20 20 20 20 69 66 20 |err)..  |     if |
|00003bf0| 65 72 72 3c 3e 30 20 74 | 68 65 6e 20 50 72 69 6e |err<>0 t|hen Prin|
|00003c00| 74 28 22 20 45 52 52 4f | 52 20 69 6e 20 78 46 49 |t(" ERRO|R in xFI|
|00003c10| 54 5f 46 55 4e 43 53 20 | 3d 20 22 2b 65 72 72 29 |T_FUNCS |= "+err)|
|00003c20| 0d 2e 20 20 20 20 20 20 | 20 41 20 3d 20 43 28 32 |..      | A = C(2|
|00003c30| 29 3b 20 20 42 3d 43 28 | 31 29 3b 20 20 20 20 20 |);  B=C(|1);     |
|00003c40| 23 20 72 65 74 75 72 6e | 20 63 6f 65 66 66 69 63 |# return| coeffic|
|00003c50| 69 65 6e 74 73 20 0d 2e | 20 20 20 20 20 20 20 72 |ients ..|       r|
|00003c60| 20 3d 20 2d 43 76 61 72 | 28 31 2c 32 29 2f 73 71 | = -Cvar|(1,2)/sq|
|00003c70| 72 74 28 20 43 76 61 72 | 28 31 2c 31 29 2a 43 76 |rt( Cvar|(1,1)*Cv|
|00003c80| 61 72 28 32 2c 32 29 20 | 29 20 20 20 23 20 61 6e |ar(2,2) |)   # an|
|00003c90| 64 20 63 6f 72 72 65 6c | 61 74 69 6f 6e 20 63 6f |d correl|ation co|
|00003ca0| 65 66 66 20 72 2e 0d 2e | 20 20 20 20 20 20 20 45 |eff r...|       E|
|00003cb0| 72 72 6f 72 45 73 74 69 | 6d 61 74 65 20 3d 20 73 |rrorEsti|mate = s|
|00003cc0| 71 72 74 28 43 68 69 53 | 71 2f 28 4e 2d 4a 29 29 |qrt(ChiS|q/(N-J))|
|00003cd0| 0d 2e 20 20 20 20 20 20 | 20 65 6e 64 20 20 23 20 |..      | end  # |
|00003ce0| 6f 66 20 65 6c 73 65 0d | 2e 20 20 20 65 6e 64 00 |of else.|.   end.|
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|00003d00| 7d 91 fc 00 7e 7b f4 00 | 95 59 ff 00 00 ff ff 00 |}...~{..|.Y......|
|00003d10| 00 00 00 20 00 00 7c 05 | 79 44 61 74 61 01 20 40 |... ..|.|yData. @|
|00003d20| 80 9a 0a 00 7d 91 fc 00 | 7e 7b f4 00 95 59 ff 00 |....}...|~{...Y..|
|00003d30| 00 ff ff 00 00 00 00 20 | 00 00 7c 01 41 44 61 74 |....... |..|.ADat|
|00003d40| 61 01 20 40 80 9a 0a 00 | 7d 91 fc 00 7e 7b f4 00 |a. @....|}...~{..|
|00003d50| 95 59 ff 00 00 ff ff 00 | 00 00 00 20 00 00 7c 01 |.Y......|... ..|.|
|00003d60| 42 44 61 74 61 01 20 40 | 80 9a 0a 00 7d 91 fc 00 |BData. @|....}...|
|00003d70| 7e 7b f4 00 95 59 ff 00 | 00 ff ff 00 00 00 00 20 |~{...Y..|....... |
|00003d80| 00 00 7c 01 72 44 61 74 | 61 01 20 40 80 9a 0a 00 |..|.rDat|a. @....|
|00003d90| 7d 91 fc 00 7e 7b f4 00 | 95 59 ff 00 00 ff ff 00 |}...~{..|.Y......|
|00003da0| 00 00 00 20 00 00 7c 0d | 45 72 72 6f 72 45 73 74 |... ..|.|ErrorEst|
|00003db0| 69 6d 61 74 65 91 fc 00 | 7e 7b f4 00 95 59 ff 00 |imate...|~{...Y..|
|00003dc0| 00 ff ff 00 00 00 00 20 | 00 00 7c 00 00 00 0c 01 |....... |..|.....|
|00003dd0| 4e 7b f4 00 95 59 ff 00 | 00 ff ff 00 00 00 00 20 |N{...Y..|....... |
|00003de0| 00 00 7c 00 00 00 06 00 | 7d 92 04 00 00 05 7e 00 |..|.....|}.....~.|
|00003df0| 91 48 ee 01 4a 7b f4 00 | 95 59 ff 00 00 ff ff 00 |.H..J{..|.Y......|
|00003e00| 00 00 00 20 00 00 7c 00 | 00 00 06 00 7d 92 04 00 |... ..|.|....}...|
|00003e10| 00 05 7e 00 91 48 ee 02 | 6a 6a f4 00 95 59 ff 00 |..~..H..|jj...Y..|
|00003e20| 00 ff ff 00 00 00 00 20 | 00 00 7c 00 00 00 06 00 |....... |..|.....|
|00003e30| 7d 92 04 00 00 05 7e 00 | 91 48 ee 02 6e 6e f4 00 |}.....~.|.H..nn..|
|00003e40| 95 59 ff 00 00 ff ff 00 | 00 00 00 20 00 00 7c 00 |.Y......|... ..|.|
|00003e50| 00 00 06 00 7d 92 04 00 | 00 05 7e 00 91 48 ee 05 |....}...|..~..H..|
|00003e60| 53 69 67 6d 61 59 ff 00 | 00 ff ff 00 00 00 00 20 |SigmaY..|....... |
|00003e70| 00 00 7c 00 00 00 06 00 | 7d 92 04 00 00 05 7e 00 |..|.....|}.....~.|
|00003e80| 91 48 ee 01 43 69 67 6d | 61 59 ff 00 00 ff ff 00 |.H..Cigm|aY......|
|00003e90| 00 00 00 20 00 00 7c 00 | 00 00 06 00 7d 92 04 00 |... ..|.|....}...|
|00003ea0| 00 05 7e 00 91 48 ee 04 | 43 76 61 72 61 59 ff 00 |..~..H..|CvaraY..|
|00003eb0| 00 ff ff 00 00 00 00 20 | 00 00 7c 00 00 00 06 00 |....... |..|.....|
|00003ec0| 7d 92 04 00 00 05 7e 00 | 91 48 ee 02 77 31 61 72 |}.....~.|.H..w1ar|
|00003ed0| 61 59 ff 00 00 ff ff 00 | 00 00 00 20 00 00 7c 00 |aY......|... ..|.|
|00003ee0| 00 00 06 00 7d 92 04 00 | 00 05 7e 00 91 48 ee 02 |....}...|..~..H..|
|00003ef0| 77 32 61 72 61 59 ff 00 | 00 ff ff 00 00 00 00 20 |w2araY..|....... |
|00003f00| 00 00 7c 00 00 00 06 00 | 7d 92 04 00 00 05 7e 00 |..|.....|}.....~.|
|00003f10| 91 48 ee 02 77 33 61 72 | 61 59 ff 00 00 ff ff 00 |.H..w3ar|aY......|
|00003f20| 00 00 00 20 00 00 7c 00 | 00 00 06 00 7d 92 04 00 |... ..|.|....}...|
|00003f30| 00 05 7e 00 91 48 ee 05 | 43 68 69 53 71 59 ff 00 |..~..H..|ChiSqY..|
|00003f40| 00 ff ff 00 00 00 00 20 | 00 00 7c 00 00 00 06 00 |....... |..|.....|
|00003f50| 7d 92 04 00 00 05 7e 00 | 91 48 ee 03 65 72 72 53 |}.....~.|.H..errS|
|00003f60| 71 59 ff 00 00 ff ff 00 | 00 00 00 20 00 00 7c 00 |qY......|... ..|.|
|00003f70| 00 00 06 00 7d 92 04 00 | 00 05 7e 00 91 48 ee 10 |....}...|..~..H..|
|00003f80| 00 7d 91 8c 00 00 00 00 | 00 00 00 00 00 00 00 00 |.}......|........|
|00003f90| 00 00 00 7d 91 90 00 00 | 00 00 00 7d 91 84 00 7d |...}....|...}...}|
|00003fa0| 91 88 02 04 05 18 00 00 | 05 20 00 00 00 00 00 00 |........|. ......|
|00003fb0| 00 00 00 7d 91 64 35 00 | 00 00 00 00 00 00 00 00 |...}.d5.|........|
|00003fc0| 00 00 00 00 07 46 69 74 | 50 6f 6c 79 00 7d c9 e2 |.....Fit|Poly.}..|
|00003fd0| 00 7d 91 90 00 7d 91 90 | 00 95 1f 9c 00 95 01 30 |.}...}..|.......0|
|00003fe0| 40 80 9a 0a 00 7d 91 88 | 00 00 05 20 20 70 72 6f |@....}..|...  pro|
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|00004010| 4a 2c 41 2c 20 20 50 72 | 6f 62 29 20 23 46 69 6e |J,A,  Pr|ob) #Fin|
|00004020| 64 20 41 20 74 6f 20 66 | 69 74 20 78 2c 79 44 61 |d A to f|it x,yDa|
|00004030| 74 61 5b 31 c9 4e 5d 20 | 77 69 74 68 20 47 28 78 |ta[1.N] |with G(x|
|00004040| 29 3d 41 5b 31 5d 2b 41 | 5b 32 5d 78 2b c9 2b 41 |)=A[1]+A|[2]x+.+A|
|00004050| 5b 4a 5d 20 78 5e 28 4a | 2d 31 29 2e 20 0d 2e 20 |[J] x^(J|-1). .. |
|00004060| 20 20 76 61 72 20 4e 2c | 6e 6e 2c 6a 6a 2c 41 76 |  var N,|nn,jj,Av|
|00004070| 61 72 2c 77 31 2c 77 32 | 2c 77 33 2c 43 68 69 53 |ar,w1,w2|,w3,ChiS|
|00004080| 71 2c 20 65 72 72 0d 2e | 20 23 20 49 6e 70 75 74 |q, err..| # Input|
|00004090| 73 3a 20 0d 2e 20 23 20 | 20 20 20 20 78 44 61 74 |s: .. # |    xDat|
|000040a0| 61 2c 20 79 44 61 74 61 | 2c 20 53 69 67 6d 61 20 |a, yData|, Sigma |
|000040b0| 3d 20 79 44 61 74 61 20 | 65 72 72 6f 72 73 2c 20 |= yData |errors, |
|000040c0| 0d 2e 20 23 20 20 20 20 | 20 4a 20 3d 20 6e 75 6d |.. #    | J = num|
|000040d0| 62 65 72 20 6f 66 20 70 | 61 72 61 6d 65 74 65 72 |ber of p|arameter|
|000040e0| 73 20 41 5b 6a 5d 20 74 | 6f 20 66 69 74 2c 20 0d |s A[j] t|o fit, .|
|000040f0| 2e 20 23 20 20 20 20 20 | 20 20 20 20 20 28 20 77 |. #     |     ( w|
|00004100| 69 74 68 20 6d 6f 64 65 | 6c 20 47 28 78 29 20 3d |ith mode|l G(x) =|
|00004110| 20 41 5b 31 5d 20 2b 20 | 41 5b 32 5d 20 78 20 2b | A[1] + |A[2] x +|
|00004120| 20 61 5b 33 5d 20 78 5e | 32 20 2b 20 c9 20 2b 20 | a[3] x^|2 + . + |
|00004130| 61 5b 4a 5d 20 78 5e 28 | 4a 2d 31 29 20 20 29 0d |a[J] x^(|J-1)  ).|
|00004140| 2e 20 23 20 4f 75 74 70 | 75 74 73 3a 0d 2e 20 23 |. # Outp|uts:.. #|
|00004150| 20 20 20 20 20 41 5b 31 | c9 4a 5d 20 3d 20 62 65 |     A[1|.J] = be|
|00004160| 73 74 20 66 69 74 20 63 | 6f 65 66 66 69 63 69 65 |st fit c|oefficie|
|00004170| 6e 74 73 2c 0d 2e 20 23 | 20 20 20 20 20 50 72 6f |nts,.. #|     Pro|
|00004180| 62 20 3d 20 70 72 6f 62 | 61 62 69 6c 69 74 79 20 |b = prob|ability |
|00004190| 74 68 61 74 20 61 20 66 | 69 74 20 74 68 69 73 20 |that a f|it this |
|000041a0| 62 61 64 20 63 6f 75 6c | 64 20 62 65 20 6e 6f 72 |bad coul|d be nor|
|000041b0| 6d 61 6c 20 65 72 72 6f | 72 73 20 77 69 74 68 0d |mal erro|rs with.|
|000041c0| 2e 20 23 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. #     |        |
|000041d0| 20 20 20 73 74 6e 64 2e | 20 64 65 76 73 2e 20 53 |   stnd.| devs. S|
|000041e0| 69 67 6d 61 2e 0d 2e 20 | 20 20 62 65 67 69 6e 0d |igma... |  begin.|
|000041f0| 2e 20 20 20 20 20 6a 6a | 3d 31 c9 4a 3b 0d 2e 20 |.     jj|=1.J;.. |
|00004200| 20 20 20 20 4e 20 3d 20 | 73 69 7a 65 28 78 44 61 |    N = |size(xDa|
|00004210| 74 61 29 3b 20 20 20 20 | 20 20 20 20 20 23 20 6e |ta);    |     # n|
|00004220| 75 6d 62 65 72 20 6f 66 | 20 64 61 74 61 20 70 6f |umber of| data po|
|00004230| 69 6e 74 73 2e 0d 2e 20 | 20 20 20 20 6e 6e 20 3d |ints... |    nn =|
|00004240| 20 31 c9 4e 0d 2e 20 20 | 20 20 20 69 66 20 73 69 | 1.N..  |   if si|
|00004250| 7a 65 28 53 69 67 6d 61 | 29 3d 31 20 74 68 65 6e |ze(Sigma|)=1 then|
|00004260| 0d 2e 20 20 20 20 20 20 | 20 53 69 67 6d 61 5b 6e |..      | Sigma[n|
|00004270| 6e 5d 3d 53 69 67 6d 61 | 20 20 20 20 20 23 20 6d |n]=Sigma|     # m|
|00004280| 61 6b 65 20 73 75 72 65 | 20 73 69 67 6d 61 20 69 |ake sure| sigma i|
|00004290| 73 20 61 6e 20 61 72 72 | 61 79 0d 2e 20 20 20 20 |s an arr|ay..    |
|000042a0| 20 69 66 20 73 69 7a 65 | 28 53 69 67 6d 61 29 3c | if size|(Sigma)<|
|000042b0| 3e 4e 20 74 68 65 6e 0d | 2e 20 20 20 20 20 20 20 |>N then.|.       |
|000042c0| 20 20 50 72 69 6e 74 28 | 22 45 52 52 4f 52 3a 20 |  Print(|"ERROR: |
|000042d0| 78 44 61 74 61 2c 20 53 | 69 67 6d 61 20 6e 6f 74 |xData, S|igma not|
|000042e0| 20 73 61 6d 65 20 73 69 | 7a 65 22 29 0d 2e 20 20 | same si|ze")..  |
|000042f0| 20 20 20 65 6c 73 65 20 | 69 66 20 73 69 7a 65 28 |   else |if size(|
|00004300| 79 44 61 74 61 29 3c 3e | 4e 20 74 68 65 6e 20 0d |yData)<>|N then .|
|00004310| 2e 20 20 20 20 20 20 20 | 20 20 50 72 69 6e 74 28 |.       |  Print(|
|00004320| 22 20 45 52 52 4f 52 3a | 20 78 44 61 74 61 2c 79 |" ERROR:| xData,y|
|00004330| 44 61 74 61 20 6e 6f 74 | 20 73 61 6d 65 20 73 69 |Data not| same si|
|00004340| 7a 65 22 29 0d 2e 20 20 | 20 20 20 65 6c 73 65 20 |ze")..  |   else |
|00004350| 0d 2e 20 20 20 20 20 20 | 20 62 65 67 69 6e 0d 2e |..      | begin..|
|00004360| 20 20 20 20 20 20 20 41 | 5b 6a 6a 5d 20 3d 20 30 |       A|[jj] = 0|
|00004370| 3b 0d 2e 20 20 20 20 20 | 20 20 41 76 61 72 5b 6a |;..     |  Avar[j|
|00004380| 6a 2c 6a 6a 5d 3d 30 3b | 20 20 20 20 20 20 20 20 |j,jj]=0;|        |
|00004390| 20 20 20 20 23 20 20 20 | 61 6e 64 20 63 6f 2d 76 |    #   |and co-v|
|000043a0| 61 72 69 61 6e 63 65 20 | 61 72 72 61 79 2e 0d 2e |ariance |array...|
|000043b0| 20 20 20 20 20 20 20 77 | 31 5b 6e 6e 2c 6a 6a 5d |       w|1[nn,jj]|
|000043c0| 20 3d 20 30 3b 20 20 20 | 20 20 20 20 20 20 20 20 | = 0;   |        |
|000043d0| 20 23 20 77 6f 72 6b 20 | 73 70 61 63 65 0d 2e 20 | # work |space.. |
|000043e0| 20 20 20 20 20 20 77 32 | 5b 6a 6a 2c 6a 6a 5d 20 |      w2|[jj,jj] |
|000043f0| 3d 20 30 3b 0d 2e 20 20 | 20 20 20 20 20 77 33 5b |= 0;..  |     w3[|
|00004400| 6a 6a 5d 20 3d 20 30 3b | 0d 2e 20 20 20 20 20 20 |jj] = 0;|..      |
|00004410| 20 43 68 69 53 71 20 3d | 20 30 3b 20 65 72 72 3d | ChiSq =| 0; err=|
|00004420| 30 3b 0d 2e 20 20 20 20 | 20 20 20 78 46 49 54 5f |0;..    |   xFIT_|
|00004430| 46 55 4e 43 53 28 78 42 | 41 53 49 53 5f 50 4f 4c |FUNCS(xB|ASIS_POL|
|00004440| 59 2c 20 4e 2c 78 44 61 | 74 61 2c 79 44 61 74 61 |Y, N,xDa|ta,yData|
|00004450| 2c 53 69 67 6d 61 2c 20 | 4a 2c 41 2c 41 76 61 72 |,Sigma, |J,A,Avar|
|00004460| 2c 20 77 31 2c 77 32 2c | 77 33 2c 20 43 68 69 53 |, w1,w2,|w3, ChiS|
|00004470| 71 2c 20 65 72 72 29 0d | 2e 20 20 20 20 20 20 20 |q, err).|.       |
|00004480| 69 66 20 65 72 72 3c 3e | 30 20 74 68 65 6e 20 50 |if err<>|0 then P|
|00004490| 72 69 6e 74 28 22 20 45 | 52 52 4f 52 20 69 6e 20 |rint(" E|RROR in |
|000044a0| 78 46 49 54 5f 46 55 4e | 43 53 20 3d 20 22 2b 65 |xFIT_FUN|CS = "+e|
|000044b0| 72 72 29 0d 2e 20 20 20 | 20 20 20 20 50 72 6f 62 |rr)..   |    Prob|
|000044c0| 20 3d 20 43 68 69 53 71 | 50 72 6f 62 61 62 69 6c | = ChiSq|Probabil|
|000044d0| 69 74 79 28 20 43 68 69 | 53 71 2c 20 4a 29 20 20 |ity( Chi|Sq, J)  |
|000044e0| 20 23 20 73 65 65 20 62 | 65 6c 6f 77 2e 0d 2e 20 | # see b|elow... |
|000044f0| 20 20 20 20 20 20 65 6e | 64 20 20 23 20 6f 66 20 |      en|d  # of |
|00004500| 65 6c 73 65 0d 2e 20 20 | 20 65 6e 64 00 00 00 06 |else..  | end....|
|00004510| 05 78 44 61 74 61 01 20 | 40 80 9a 0a 00 7d 91 88 |.xData. |@....}..|
|00004520| 00 7e 7b f4 00 95 59 ff | 00 00 ff ff 00 00 00 00 |.~{...Y.|........|
|00004530| 20 00 00 7c 05 79 44 61 | 74 61 01 20 40 80 9a 0a | ..|.yDa|ta. @...|
|00004540| 00 7d 91 88 00 7e 7b f4 | 00 95 59 ff 00 00 ff ff |.}...~{.|..Y.....|
|00004550| 00 00 00 00 20 00 00 7c | 05 53 69 67 6d 61 01 20 |.... ..||.Sigma. |
|00004560| 40 80 9a 0a 00 7d 91 88 | 00 7e 7b f4 00 95 59 ff |@....}..|.~{...Y.|
|00004570| 00 00 ff ff 00 00 00 00 | 20 00 00 7c 01 4a 69 67 |........| ..|.Jig|
|00004580| 6d 61 01 20 40 80 9a 0a | 00 7d 91 88 00 7e 7b f4 |ma. @...|.}...~{.|
|00004590| 00 95 59 ff 00 00 ff ff | 00 00 00 00 20 00 00 7c |..Y.....|.... ..||
|000045a0| 01 41 69 67 6d 61 01 20 | 40 80 9a 0a 00 7d 91 88 |.Aigma. |@....}..|
|000045b0| 00 7e 7b f4 00 95 59 ff | 00 00 ff ff 00 00 00 00 |.~{...Y.|........|
|000045c0| 20 00 00 7c 04 50 72 6f | 62 61 01 20 40 80 9a 0a | ..|.Pro|ba. @...|
|000045d0| 00 7d 91 88 00 7e 7b f4 | 00 95 59 ff 00 00 ff ff |.}...~{.|..Y.....|
|000045e0| 00 00 00 00 20 00 00 7c | 00 00 00 09 01 4e 7b f4 |.... ..||.....N{.|
|000045f0| 00 95 59 ff 00 00 ff ff | 00 00 00 00 20 00 00 7c |..Y.....|.... ..||
|00004600| 00 00 00 06 00 7d 91 90 | 00 00 05 20 00 91 48 ee |.....}..|... ..H.|
|00004610| 02 6e 6e f4 00 95 59 ff | 00 00 ff ff 00 00 00 00 |.nn...Y.|........|
|00004620| 20 00 00 7c 00 00 00 06 | 00 7d 91 90 00 00 05 20 | ..|....|.}..... |
|00004630| 00 91 48 ee 02 6a 6a f4 | 00 95 59 ff 00 00 ff ff |..H..jj.|..Y.....|
|00004640| 00 00 00 00 20 00 00 7c | 00 00 00 06 00 7d 91 90 |.... ..||.....}..|
|00004650| 00 00 05 20 00 91 48 ee | 04 41 76 61 72 95 59 ff |... ..H.|.Avar.Y.|
|00004660| 00 00 ff ff 00 00 00 00 | 20 00 00 7c 00 00 00 06 |........| ..|....|
|00004670| 00 7d 91 90 00 00 05 20 | 00 91 48 ee 02 77 31 61 |.}..... |..H..w1a|
|00004680| 72 95 59 ff 00 00 ff ff | 00 00 00 00 20 00 00 7c |r.Y.....|.... ..||
|00004690| 00 00 00 06 00 7d 91 90 | 00 00 05 20 00 91 48 ee |.....}..|... ..H.|
|000046a0| 02 77 32 61 72 95 59 ff | 00 00 ff ff 00 00 00 00 |.w2ar.Y.|........|
|000046b0| 20 00 00 7c 00 00 00 06 | 00 7d 91 90 00 00 05 20 | ..|....|.}..... |
|000046c0| 00 91 48 ee 02 77 33 61 | 72 95 59 ff 00 00 ff ff |..H..w3a|r.Y.....|
|000046d0| 00 00 00 00 20 00 00 7c | 00 00 00 06 00 7d 91 90 |.... ..||.....}..|
|000046e0| 00 00 05 20 00 91 48 ee | 05 43 68 69 53 71 59 ff |... ..H.|.ChiSqY.|
|000046f0| 00 00 ff ff 00 00 00 00 | 20 00 00 7c 00 00 00 06 |........| ..|....|
|00004700| 00 7d 91 90 00 00 05 20 | 00 91 48 ee 03 65 72 72 |.}..... |..H..err|
|00004710| 53 71 59 ff 00 00 ff ff | 00 00 00 00 20 00 00 7c |SqY.....|.... ..||
|00004720| 00 00 00 06 00 7d 91 90 | 00 00 05 20 00 91 48 ee |.....}..|... ..H.|
|00004730| 10 00 7d 91 34 00 00 00 | 00 00 00 00 00 00 00 00 |..}.4...|........|
|00004740| 00 00 00 00 7d 91 38 00 | 00 00 00 00 7d 91 2c 00 |....}.8.|....}.,.|
|00004750| 7d 91 30 02 c9 05 da 00 | 00 05 e2 00 00 00 00 00 |}.0.....|........|
|00004760| 00 00 00 00 7d 91 08 35 | 00 00 00 00 00 00 00 00 |....}..5|........|
|00004770| 00 00 00 00 00 07 46 69 | 74 55 73 65 72 00 7d c9 |......Fi|tUser.}.|
|00004780| e2 00 7d 91 38 00 7d 91 | 38 00 95 1f 9c 00 95 01 |..}.8.}.|8.......|
|00004790| 30 40 80 9a 0a 00 7d 91 | 30 00 00 05 e2 20 70 72 |0@....}.|0.... pr|
|000047a0| 6f 67 72 61 6d 20 46 69 | 74 55 73 65 72 28 78 44 |ogram Fi|tUser(xD|
|000047b0| 61 74 61 2c 79 44 61 74 | 61 2c 53 69 67 6d 61 2c |ata,yDat|a,Sigma,|
|000047c0| 20 4a 2c 41 2c 20 20 50 | 72 6f 62 2c 20 42 61 73 | J,A,  P|rob, Bas|
|000047d0| 69 73 55 73 65 72 29 20 | 23 20 46 69 74 73 20 79 |isUser) |# Fits y|
|000047e0| 44 61 74 61 20 74 6f 20 | 61 20 73 75 6d 20 6f 66 |Data to |a sum of|
|000047f0| 20 75 73 65 72 20 73 75 | 70 70 6c 69 65 64 20 62 | user su|pplied b|
|00004800| 61 73 69 73 20 66 75 6e | 63 74 69 6f 6e 73 2e 0d |asis fun|ctions..|
|00004810| 2e 20 20 20 76 61 72 20 | 4e 2c 6e 6e 2c 6a 6a 2c |.   var |N,nn,jj,|
|00004820| 41 76 61 72 2c 77 31 2c | 77 32 2c 77 33 2c 43 68 |Avar,w1,|w2,w3,Ch|
|00004830| 69 53 71 2c 20 65 72 72 | 0d 2e 20 23 20 20 49 6e |iSq, err|.. #  In|
|00004840| 70 75 74 3a 20 20 0d 2e | 20 23 20 20 20 20 20 20 |put:  ..| #      |
|00004850| 20 20 20 20 20 20 42 61 | 73 69 73 55 73 65 72 20 |      Ba|sisUser |
|00004860| 20 20 20 20 3d 20 20 70 | 72 6f 67 72 61 6d 20 74 |    =  p|rogram t|
|00004870| 6f 20 63 61 6c 63 75 6c | 61 74 65 20 74 68 65 20 |o calcul|ate the |
|00004880| 62 61 73 69 73 2c 20 46 | 5f 6a 28 78 29 2c 0d 2e |basis, F|_j(x),..|
|00004890| 20 23 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | #      |        |
|000048a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000048b0| 20 20 6c 69 6b 65 20 53 | 61 6d 70 6c 65 42 61 73 |  like S|ampleBas|
|000048c0| 69 73 55 73 65 72 20 6f | 72 20 78 42 41 53 49 5f |isUser o|r xBASI_|
|000048d0| 50 4f 4c 59 2e 0d 2e 20 | 23 20 20 20 20 20 20 20 |POLY... |#       |
|000048e0| 20 20 20 20 20 78 44 61 | 74 61 5b 31 c9 4e 5d 2c |     xDa|ta[1.N],|
|000048f0| 20 79 44 61 74 61 5b 31 | c9 4e 5d 20 3d 20 64 61 | yData[1|.N] = da|
|00004900| 74 61 20 70 6f 69 6e 74 | 73 20 0d 2e 20 23 20 20 |ta point|s .. #  |
|00004910| 20 20 20 20 20 20 20 20 | 20 20 53 69 67 6d 61 20 |        |  Sigma |
|00004920| 28 72 65 61 6c 20 6f 72 | 20 61 72 72 61 79 29 20 |(real or| array) |
|00004930| 3d 20 75 6e 63 65 72 74 | 61 69 6e 74 69 65 73 20 |= uncert|ainties |
|00004940| 69 6e 20 79 44 61 74 61 | 0d 2e 20 23 20 20 20 20 |in yData|.. #    |
|00004950| 20 20 20 20 20 20 20 20 | 4a 20 3d 20 6e 75 6d 62 |        |J = numb|
|00004960| 65 72 20 6f 66 20 41 5b | 31 c9 4a 5d 20 70 61 72 |er of A[|1.J] par|
|00004970| 61 6d 65 74 65 72 73 20 | 69 6e 20 62 61 73 69 73 |ameters |in basis|
|00004980| 0d 2e 20 23 20 20 4f 75 | 74 70 75 74 3a 0d 2e 20 |.. #  Ou|tput:.. |
|00004990| 23 20 20 20 20 20 20 20 | 20 20 20 20 20 41 5b 31 |#       |     A[1|
|000049a0| c9 4a 5d 20 62 65 73 74 | 2d 66 69 74 20 70 61 72 |.J] best|-fit par|
|000049b0| 61 6d 65 74 65 72 73 2c | 20 20 73 75 63 68 20 74 |ameters,|  such t|
|000049c0| 68 61 74 0d 2e 20 23 20 | 20 20 20 20 20 20 20 20 |hat.. # |        |
|000049d0| 20 20 20 20 20 20 20 20 | 20 47 28 78 29 20 3d 20 |        | G(x) = |
|000049e0| 73 75 6d 20 6f 76 65 72 | 20 69 3d 31 c9 4a 20 7b |sum over| i=1.J {|
|000049f0| 20 41 5b 69 5d 20 46 5f | 69 28 78 29 20 7d 20 66 | A[i] F_|i(x) } f|
|00004a00| 69 74 73 20 79 44 61 74 | 61 2e 0d 2e 20 23 20 20 |its yDat|a... #  |
|00004a10| 20 20 20 20 20 20 20 20 | 20 20 50 72 6f 62 20 3d |        |  Prob =|
|00004a20| 20 70 72 6f 62 61 62 69 | 6c 69 74 79 20 74 68 61 | probabi|lity tha|
|00004a30| 74 20 74 68 65 20 70 6f | 6f 72 6e 65 73 73 20 6f |t the po|orness o|
|00004a40| 66 20 74 68 65 20 66 69 | 74 20 69 73 20 64 75 65 |f the fi|t is due|
|00004a50| 20 74 6f 20 63 68 61 6e | 63 65 2e 0d 2e 20 20 20 | to chan|ce...   |
|00004a60| 62 65 67 69 6e 0d 2e 20 | 20 20 20 20 6a 6a 3d 31 |begin.. |    jj=1|
|00004a70| c9 4a 3b 0d 2e 20 20 20 | 20 20 4e 20 3d 20 73 69 |.J;..   |  N = si|
|00004a80| 7a 65 28 78 44 61 74 61 | 29 3b 20 20 20 20 20 20 |ze(xData|);      |
|00004a90| 20 20 20 23 20 6e 75 6d | 62 65 72 20 6f 66 20 64 |   # num|ber of d|
|00004aa0| 61 74 61 20 70 6f 69 6e | 74 73 2e 0d 2e 20 20 20 |ata poin|ts...   |
|00004ab0| 20 20 6e 6e 20 3d 20 31 | c9 4e 0d 2e 20 20 20 20 |  nn = 1|.N..    |
|00004ac0| 20 69 66 20 73 69 7a 65 | 28 53 69 67 6d 61 29 3d | if size|(Sigma)=|
|00004ad0| 31 20 74 68 65 6e 0d 2e | 20 20 20 20 20 20 20 53 |1 then..|       S|
|00004ae0| 69 67 6d 61 5b 6e 6e 5d | 3d 53 69 67 6d 61 20 20 |igma[nn]|=Sigma  |
|00004af0| 20 20 20 23 20 6d 61 6b | 65 20 73 75 72 65 20 73 |   # mak|e sure s|
|00004b00| 69 67 6d 61 20 69 73 20 | 61 6e 20 61 72 72 61 79 |igma is |an array|
|00004b10| 0d 2e 20 20 20 20 20 69 | 66 20 73 69 7a 65 28 53 |..     i|f size(S|
|00004b20| 69 67 6d 61 29 3c 3e 4e | 20 74 68 65 6e 0d 2e 20 |igma)<>N| then.. |
|00004b30| 20 20 20 20 20 20 20 20 | 50 72 69 6e 74 28 22 45 |        |Print("E|
|00004b40| 52 52 4f 52 3a 20 78 44 | 61 74 61 2c 20 53 69 67 |RROR: xD|ata, Sig|
|00004b50| 6d 61 20 6e 6f 74 20 73 | 61 6d 65 20 73 69 7a 65 |ma not s|ame size|
|00004b60| 22 29 0d 2e 20 20 20 20 | 20 65 6c 73 65 20 69 66 |")..    | else if|
|00004b70| 20 73 69 7a 65 28 79 44 | 61 74 61 29 3c 3e 4e 20 | size(yD|ata)<>N |
|00004b80| 74 68 65 6e 20 0d 2e 20 | 20 20 20 20 20 20 20 20 |then .. |        |
|00004b90| 50 72 69 6e 74 28 22 20 | 45 52 52 4f 52 3a 20 78 |Print(" |ERROR: x|
|00004ba0| 44 61 74 61 2c 79 44 61 | 74 61 20 6e 6f 74 20 73 |Data,yDa|ta not s|
|00004bb0| 61 6d 65 20 73 69 7a 65 | 22 29 0d 2e 20 20 20 20 |ame size|")..    |
|00004bc0| 20 65 6c 73 65 20 0d 2e | 20 20 20 20 20 20 20 62 | else ..|       b|
|00004bd0| 65 67 69 6e 0d 2e 20 20 | 20 20 20 20 20 41 76 61 |egin..  |     Ava|
|00004be0| 72 5b 6a 6a 2c 6a 6a 5d | 3d 30 3b 20 20 20 20 20 |r[jj,jj]|=0;     |
|00004bf0| 20 20 20 20 20 20 20 23 | 20 20 20 61 6e 64 20 63 |       #|   and c|
|00004c00| 6f 2d 76 61 72 69 61 6e | 63 65 20 61 72 72 61 79 |o-varian|ce array|
|00004c10| 2e 0d 2e 20 20 20 20 20 | 20 20 77 31 5b 6e 6e 2c |...     |  w1[nn,|
|00004c20| 6a 6a 5d 20 3d 20 30 3b | 20 20 20 20 20 20 20 20 |jj] = 0;|        |
|00004c30| 20 20 20 20 23 20 77 6f | 72 6b 20 73 70 61 63 65 |    # wo|rk space|
|00004c40| 0d 2e 20 20 20 20 20 20 | 20 77 32 5b 6a 6a 2c 6a |..      | w2[jj,j|
|00004c50| 6a 5d 20 3d 20 30 3b 0d | 2e 20 20 20 20 20 20 20 |j] = 0;.|.       |
|00004c60| 77 33 5b 6a 6a 5d 20 3d | 20 30 3b 0d 2e 20 20 20 |w3[jj] =| 0;..   |
|00004c70| 20 20 20 20 43 68 69 53 | 71 20 3d 20 30 3b 20 65 |    ChiS|q = 0; e|
|00004c80| 72 72 3d 30 3b 0d 2e 20 | 20 20 20 20 20 20 41 5b |rr=0;.. |      A[|
|00004c90| 6a 6a 5d 20 3d 20 30 3b | 0d 2e 20 20 20 20 20 20 |jj] = 0;|..      |
|00004ca0| 20 78 46 49 54 5f 46 55 | 4e 43 53 28 42 61 73 69 | xFIT_FU|NCS(Basi|
|00004cb0| 73 55 73 65 72 2c 20 4e | 2c 78 44 61 74 61 2c 79 |sUser, N|,xData,y|
|00004cc0| 44 61 74 61 2c 53 69 67 | 6d 61 2c 20 4a 2c 41 2c |Data,Sig|ma, J,A,|
|00004cd0| 41 76 61 72 2c 20 77 31 | 2c 77 32 2c 77 33 2c 20 |Avar, w1|,w2,w3, |
|00004ce0| 43 68 69 53 71 2c 20 65 | 72 72 29 0d 2e 20 20 20 |ChiSq, e|rr)..   |
|00004cf0| 20 20 20 20 69 66 20 65 | 72 72 3c 3e 30 20 74 68 |    if e|rr<>0 th|
|00004d00| 65 6e 20 50 72 69 6e 74 | 28 22 45 52 52 4f 52 20 |en Print|("ERROR |
|00004d10| 69 6e 20 78 46 49 54 5f | 46 55 4e 43 53 20 3d 20 |in xFIT_|FUNCS = |
|00004d20| 22 2b 65 72 72 29 0d 2e | 20 20 20 20 20 20 20 50 |"+err)..|       P|
|00004d30| 72 6f 62 20 3d 20 43 68 | 69 53 71 50 72 6f 62 61 |rob = Ch|iSqProba|
|00004d40| 62 69 6c 69 74 79 28 20 | 43 68 69 53 71 2c 20 4a |bility( |ChiSq, J|
|00004d50| 29 20 20 20 23 20 73 65 | 65 20 62 65 6c 6f 77 2e |)   # se|e below.|
|00004d60| 0d 2e 20 20 20 20 20 20 | 20 65 6e 64 20 20 23 20 |..      | end  # |
|00004d70| 6f 66 20 65 6c 73 65 0d | 2e 20 20 20 65 6e 64 00 |of else.|.   end.|
|00004d80| 00 00 07 05 78 44 61 74 | 61 01 20 40 80 9a 0a 00 |....xDat|a. @....|
|00004d90| 7d 91 30 00 7e 7b f4 00 | 95 59 ff 00 00 ff ff 00 |}.0.~{..|.Y......|
|00004da0| 00 00 00 20 00 00 7c 05 | 79 44 61 74 61 01 20 40 |... ..|.|yData. @|
|00004db0| 80 9a 0a 00 7d 91 30 00 | 7e 7b f4 00 95 59 ff 00 |....}.0.|~{...Y..|
|00004dc0| 00 ff ff 00 00 00 00 20 | 00 00 7c 05 53 69 67 6d |....... |..|.Sigm|
|00004dd0| 61 01 20 40 80 9a 0a 00 | 7d 91 30 00 7e 7b f4 00 |a. @....|}.0.~{..|
|00004de0| 95 59 ff 00 00 ff ff 00 | 00 00 00 20 00 00 7c 01 |.Y......|... ..|.|
|00004df0| 4a 69 67 6d 61 01 20 40 | 80 9a 0a 00 7d 91 30 00 |Jigma. @|....}.0.|
|00004e00| 7e 7b f4 00 95 59 ff 00 | 00 ff ff 00 00 00 00 20 |~{...Y..|....... |
|00004e10| 00 00 7c 01 41 69 67 6d | 61 01 20 40 80 9a 0a 00 |..|.Aigm|a. @....|
|00004e20| 7d 91 30 00 7e 7b f4 00 | 95 59 ff 00 00 ff ff 00 |}.0.~{..|.Y......|
|00004e30| 00 00 00 20 00 00 7c 04 | 50 72 6f 62 61 01 20 40 |... ..|.|Proba. @|
|00004e40| 80 9a 0a 00 7d 91 30 00 | 7e 7b f4 00 95 59 ff 00 |....}.0.|~{...Y..|
|00004e50| 00 ff ff 00 00 00 00 20 | 00 00 7c 09 42 61 73 69 |....... |..|.Basi|
|00004e60| 73 55 73 65 72 9a 0a 00 | 7d 91 30 00 7e 7b f4 00 |sUser...|}.0.~{..|
|00004e70| 95 59 ff 00 00 ff ff 00 | 00 00 00 20 00 00 7c 00 |.Y......|... ..|.|
|00004e80| 00 00 09 01 4e 7b f4 00 | 95 59 ff 00 00 ff ff 00 |....N{..|.Y......|
|00004e90| 00 00 00 20 00 00 7c 00 | 00 00 07 00 7d 91 38 00 |... ..|.|....}.8.|
|00004ea0| 00 05 e2 00 91 48 ee 02 | 6e 6e f4 00 95 59 ff 00 |.....H..|nn...Y..|
|00004eb0| 00 ff ff 00 00 00 00 20 | 00 00 7c 00 00 00 07 00 |....... |..|.....|
|00004ec0| 7d 91 38 00 00 05 e2 00 | 91 48 ee 02 6a 6a f4 00 |}.8.....|.H..jj..|
|00004ed0| 95 59 ff 00 00 ff ff 00 | 00 00 00 20 00 00 7c 00 |.Y......|... ..|.|
|00004ee0| 00 00 07 00 7d 91 38 00 | 00 05 e2 00 91 48 ee 04 |....}.8.|.....H..|
|00004ef0| 41 76 61 72 95 59 ff 00 | 00 ff ff 00 00 00 00 20 |Avar.Y..|....... |
|00004f00| 00 00 7c 00 00 00 07 00 | 7d 91 38 00 00 05 e2 00 |..|.....|}.8.....|
|00004f10| 91 48 ee 02 77 31 61 72 | 95 59 ff 00 00 ff ff 00 |.H..w1ar|.Y......|
|00004f20| 00 00 00 20 00 00 7c 00 | 00 00 07 00 7d 91 38 00 |... ..|.|....}.8.|
|00004f30| 00 05 e2 00 91 48 ee 02 | 77 32 61 72 95 59 ff 00 |.....H..|w2ar.Y..|
|00004f40| 00 ff ff 00 00 00 00 20 | 00 00 7c 00 00 00 07 00 |....... |..|.....|
|00004f50| 7d 91 38 00 00 05 e2 00 | 91 48 ee 02 77 33 61 72 |}.8.....|.H..w3ar|
|00004f60| 95 59 ff 00 00 ff ff 00 | 00 00 00 20 00 00 7c 00 |.Y......|... ..|.|
|00004f70| 00 00 07 00 7d 91 38 00 | 00 05 e2 00 91 48 ee 05 |....}.8.|.....H..|
|00004f80| 43 68 69 53 71 59 ff 00 | 00 ff ff 00 00 00 00 20 |ChiSqY..|....... |
|00004f90| 00 00 7c 00 00 00 07 00 | 7d 91 38 00 00 05 e2 00 |..|.....|}.8.....|
|00004fa0| 91 48 ee 03 65 72 72 53 | 71 59 ff 00 00 ff ff 00 |.H..errS|qY......|
|00004fb0| 00 00 00 20 00 00 7c 00 | 00 00 07 00 7d 91 38 00 |... ..|.|....}.8.|
|00004fc0| 00 05 e2 00 91 48 ee 0f | 00 7d 90 d8 00 00 00 00 |.....H..|.}......|
|00004fd0| 00 00 00 00 00 00 00 00 | 00 00 00 7d 90 dc 00 00 |........|...}....|
|00004fe0| 00 00 00 7d 90 d0 00 7d | 90 d4 00 00 00 31 00 00 |...}...}|.....1..|
|00004ff0| 00 31 00 00 00 00 00 00 | 00 00 0b 46 69 78 52 6f |.1......|...FixRo|
|00005000| 75 6e 64 4f 66 66 00 7d | 90 dc 00 7d 90 dc 00 95 |undOff.}|...}....|
|00005010| 1f 9c 00 95 01 40 40 80 | 9a 0a 00 7d 90 d4 00 00 |.....@@.|...}....|
|00005020| 00 31 20 20 28 78 2b 31 | 29 2d 31 20 23 20 52 65 |.1  (x+1|)-1 # Re|
|00005030| 74 75 72 6e 73 20 78 20 | 72 6f 75 6e 64 65 64 20 |turns x |rounded |
|00005040| 6f 66 66 20 74 6f 20 61 | 62 6f 75 74 20 31 65 2d |off to a|bout 1e-|
|00005050| 31 39 2e 00 00 00 01 01 | 78 1f 9c 00 95 01 30 40 |19......|x.....0@|
|00005060| 80 9a 0a 00 7d 90 d4 00 | 7e 7b f4 00 95 59 ff 00 |....}...|~{...Y..|
|00005070| 00 ff ff 00 00 00 00 20 | 00 00 7c 04 00 7d 90 c0 |....... |..|..}..|
|00005080| 01 00 00 00 00 00 00 00 | 00 00 00 00 00 00 3a 00 |........|......:.|
|00005090| 03 46 6f 72 20 00 00 7c | 00 00 00 01 00 7d 90 dc |.For ..||.....}..|
|000050a0| 00 00 00 31 00 95 01 42 | 00 91 ff 28 00 95 01 31 |...1...B|...(...1|
|000050b0| 00 00 00 01 0f 00 7d 90 | b8 00 00 00 00 00 00 00 |......}.|........|
|000050c0| 00 00 00 00 00 00 00 00 | 7d 90 bc 00 00 00 00 00 |........|}.......|
|000050d0| 7d 90 b0 00 7d 90 b4 00 | 00 00 32 00 00 00 32 00 |}...}...|..2...2.|
|000050e0| 00 00 00 00 00 00 00 0e | 46 72 61 63 74 69 6f 6e |........|Fraction|
|000050f0| 61 6c 50 61 72 74 bc 00 | 7d 90 bc 00 95 1f 9c 00 |alPart..|}.......|
|00005100| 95 01 40 40 80 9a 0a 00 | 7d 90 b4 00 00 00 32 20 |..@@....|}.....2 |
|00005110| 20 78 20 2d 20 54 72 75 | 6e 63 61 74 65 28 78 29 | x - Tru|ncate(x)|
|00005120| 23 20 52 65 74 75 72 6e | 73 20 66 72 61 63 74 69 |# Return|s fracti|
|00005130| 6f 6e 61 6c 20 70 61 72 | 74 20 6f 66 20 78 3e 30 |onal par|t of x>0|
|00005140| 2e 00 00 00 01 01 78 1f | 9c 00 95 01 30 40 80 9a |......x.|....0@..|
|00005150| 0a 00 7d 90 b4 00 7e 7b | f4 00 95 59 ff 00 00 ff |..}...~{|...Y....|
|00005160| ff 00 00 00 00 20 00 00 | 7c 04 00 7d 90 90 01 00 |..... ..||..}....|
|00005170| 00 00 00 00 00 00 00 00 | 00 00 00 00 36 00 08 46 |........|....6..F|
|00005180| 75 6e 63 74 69 6f 6e 00 | 00 01 00 7d 90 bc 00 00 |unction.|...}....|
|00005190| 00 32 00 95 01 42 00 91 | ff 28 00 95 01 31 00 00 |.2...B..|.(...1..|
|000051a0| 00 01 10 00 7d 90 88 00 | 00 00 00 00 00 00 00 00 |....}...|........|
|000051b0| 00 00 00 00 00 00 7d 90 | 8c 00 00 00 00 00 7d 90 |......}.|......}.|
|000051c0| 80 00 7d 90 84 00 ec 01 | 45 00 00 01 4d 00 00 00 |..}.....|E...M...|
|000051d0| 00 00 00 00 00 00 7d 90 | 74 36 00 00 00 00 00 00 |......}.|t6......|
|000051e0| 00 00 00 00 00 00 00 05 | 47 61 6d 6d 61 00 05 00 |........|Gamma...|
|000051f0| 7d c9 e2 00 7d 90 8c 00 | 7d 90 8c 00 95 1f 9c 00 |}...}...|}.......|
|00005200| 95 01 30 40 80 9a 0a 00 | 7d 90 84 00 00 01 4d 66 |..0@....|}.....Mf|
|00005210| 75 6e 63 74 69 6f 6e 20 | 47 61 6d 6d 61 28 78 29 |unction |Gamma(x)|
|00005220| 20 23 20 52 65 74 75 72 | 6e 73 20 20 69 6e 74 65 | # Retur|ns  inte|
|00005230| 67 72 61 6c 20 30 2d 3e | b0 20 7b 20 65 78 70 28 |gral 0->|. { exp(|
|00005240| 2d 74 29 20 74 5e 28 78 | 2d 31 29 20 64 74 20 2e |-t) t^(x|-1) dt .|
|00005250| 0d 2e 20 20 20 76 61 72 | 20 6e 2c 79 0d 2e 20 23 |..   var| n,y.. #|
|00005260| 20 20 20 49 6e 70 75 74 | 3a 20 20 20 20 20 78 20 |   Input|:     x |
|00005270| 3d 20 6e 75 6d 62 65 72 | 20 6f 72 20 61 72 72 61 |= number| or arra|
|00005280| 79 0d 2e 20 23 20 20 20 | 4f 75 74 70 75 74 3a 20 |y.. #   |Output: |
|00005290| 20 20 47 61 6d 6d 61 28 | 78 29 20 3d 20 6e 75 6d |  Gamma(|x) = num|
|000052a0| 62 65 72 20 6f 72 20 61 | 72 72 61 79 20 3d 20 47 |ber or a|rray = G|
|000052b0| 28 78 29 0d 2e 20 23 20 | 20 20 20 20 20 20 20 20 |(x).. # |        |
|000052c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 3d 20 69 6e |        |    = in|
|000052d0| 74 65 67 72 61 6c 20 30 | 2d 3e b0 20 7b 20 65 78 |tegral 0|->. { ex|
|000052e0| 70 28 2d 74 29 20 74 5e | 28 78 2d 31 29 20 64 74 |p(-t) t^|(x-1) dt|
|000052f0| 0d 2e 20 20 20 62 65 67 | 69 6e 0d 2e 20 20 20 20 |..   beg|in..    |
|00005300| 20 6e 20 3d 20 73 69 7a | 65 28 78 29 0d 2e 20 20 | n = siz|e(x)..  |
|00005310| 20 20 20 79 20 3d 20 78 | 20 23 20 73 61 76 65 20 |   y = x| # save |
|00005320| 73 70 61 63 65 20 66 6f | 72 20 61 6e 73 77 65 72 |space fo|r answer|
|00005330| 0d 2e 20 20 20 20 20 78 | 47 41 4d 4d 41 28 6e 2c |..     x|GAMMA(n,|
|00005340| 78 2c 79 29 0d 2e 20 20 | 20 20 20 47 61 6d 6d 61 |x,y)..  |   Gamma|
|00005350| 20 3d 20 79 0d 2e 20 20 | 20 65 6e 64 00 00 00 01 | = y..  | end....|
|00005360| 01 78 1f 9c 00 95 01 20 | 40 80 9a 0a 00 7d 90 84 |.x..... |@....}..|
|00005370| 00 7e 7b f4 00 95 59 ff | 00 00 ff ff 00 00 00 00 |.~{...Y.|........|
|00005380| 20 00 00 7c 00 00 00 02 | 01 6e 7b f4 00 95 59 ff | ..|....|.n{...Y.|
|00005390| 00 00 ff ff 00 00 00 00 | 20 00 00 7c 00 00 00 01 |........| ..|....|
|000053a0| 00 7d 90 8c 00 00 01 4d | 00 91 48 ee 01 79 7b f4 |.}.....M|..H..y{.|
|000053b0| 00 95 59 ff 00 00 ff ff | 00 00 00 00 20 00 00 7c |..Y.....|.... ..||
|000053c0| 00 00 00 01 00 7d 90 8c | 00 00 01 4d 00 91 48 ee |.....}..|...M..H.|
|000053d0| 0f 00 7d 90 60 00 00 00 | 00 00 00 00 00 00 00 00 |..}.`...|........|
|000053e0| 00 00 00 00 7d 90 64 00 | 00 00 00 00 7d 90 58 00 |....}.d.|....}.X.|
|000053f0| 7d 90 5c 00 00 00 2c 00 | 00 00 2c 00 00 00 00 00 |}.\...,.|..,.....|
|00005400| 00 00 00 08 47 61 75 73 | 73 69 61 6e 7d c9 e2 00 |....Gaus|sian}...|
|00005410| 7d 90 64 00 7d 90 64 00 | 95 1f 9c 00 95 01 40 40 |}.d.}.d.|......@@|
|00005420| 80 9a 0a 00 7d 90 5c 00 | 00 00 2c 20 31 2f 73 71 |....}.\.|.., 1/sq|
|00005430| 72 74 28 32 b9 73 69 67 | 6d 61 5e 32 29 20 65 78 |rt(2.sig|ma^2) ex|
|00005440| 70 28 2d 30 2e 35 7b 28 | 78 2d 78 30 29 2f 73 69 |p(-0.5{(|x-x0)/si|
|00005450| 67 6d 61 7d 5e 32 29 00 | 00 00 03 01 78 1f 9c 00 |gma}^2).|....x...|
|00005460| 95 01 30 40 80 9a 0a 00 | 7d 90 5c 00 7e 7b f4 00 |..0@....|}.\.~{..|
|00005470| 95 59 ff 00 00 ff ff 00 | 00 00 00 20 00 00 7c 02 |.Y......|... ..|.|
|00005480| 78 30 9c 00 95 01 30 40 | 80 9a 0a 00 7d 90 5c 00 |x0....0@|....}.\.|
|00005490| 7e 7b f4 00 95 59 ff 00 | 00 ff ff 00 00 00 00 20 |~{...Y..|....... |
|000054a0| 00 00 7c 05 73 69 67 6d | 61 01 30 40 80 9a 0a 00 |..|.sigm|a.0@....|
|000054b0| 7d 90 5c 00 7e 7b f4 00 | 95 59 ff 00 00 ff ff 00 |}.\.~{..|.Y......|
|000054c0| 00 00 00 20 00 00 7c 10 | 00 7d 90 40 00 00 00 00 |... ..|.|.}.@....|
|000054d0| 00 00 00 00 00 00 00 00 | 00 00 00 7d 90 44 00 00 |........|...}.D..|
|000054e0| 00 00 00 7d 90 38 00 7d | 90 3c 00 cb 01 2a 00 00 |...}.8.}|.<...*..|
|000054f0| 01 32 00 00 00 00 00 00 | 00 00 00 7d 90 2c 36 00 |.2......|...}.,6.|
|00005500| 00 00 00 00 00 00 00 00 | 00 00 00 00 0d 47 61 75 |........|.....Gau|
|00005510| 73 73 69 61 6e 4e 6f 69 | 73 65 90 44 00 7d 90 44 |ssianNoi|se.D.}.D|
|00005520| 00 95 1f 9c 00 95 01 30 | 40 80 9a 0a 00 7d 90 3c |.......0|@....}.<|
|00005530| 00 00 01 32 20 20 66 75 | 6e 63 74 69 6f 6e 20 47 |...2  fu|nction G|
|00005540| 61 75 73 73 69 61 6e 4e | 6f 69 73 65 28 4e 29 20 |aussianN|oise(N) |
|00005550| 23 20 52 65 74 75 72 6e | 73 20 61 72 72 61 79 20 |# Return|s array |
|00005560| 6f 66 20 67 61 75 73 73 | 69 61 6e 20 6e 6f 69 73 |of gauss|ian nois|
|00005570| 65 2c 20 73 69 67 6d 61 | 3d 31 2e 0d 2e 20 20 20 |e, sigma|=1...   |
|00005580| 76 61 72 20 78 2c 79 0d | 2e 20 23 20 20 49 6e 70 |var x,y.|. #  Inp|
|00005590| 75 74 3a 20 20 20 4e 20 | 3d 20 70 6f 73 69 74 69 |ut:   N |= positi|
|000055a0| 76 65 20 69 6e 74 65 67 | 65 72 0d 2e 20 23 20 20 |ve integ|er.. #  |
|000055b0| 4f 75 74 70 75 74 3a 20 | 20 20 47 61 75 73 73 69 |Output: |  Gaussi|
|000055c0| 61 6e 4e 6f 69 73 65 20 | 3d 20 47 5b 31 c9 6e 5d |anNoise |= G[1.n]|
|000055d0| 20 3d 20 61 72 72 61 79 | 20 6f 66 20 30 20 6d 65 | = array| of 0 me|
|000055e0| 61 6e 2c 20 73 69 67 6d | 61 3d 31 20 72 61 6e 64 |an, sigm|a=1 rand|
|000055f0| 6f 6d 73 2e 0d 2e 20 20 | 20 62 65 67 69 6e 0d 2e |oms...  | begin..|
|00005600| 20 20 20 20 20 78 20 3d | 20 52 61 6e 64 6f 6d 41 |     x =| RandomA|
|00005610| 72 72 61 79 28 6e 29 0d | 2e 20 20 20 20 20 79 20 |rray(n).|.     y |
|00005620| 3d 20 52 61 6e 64 6f 6d | 41 72 72 61 79 28 6e 29 |= Random|Array(n)|
|00005630| 0d 2e 20 20 20 20 20 47 | 61 75 73 73 69 61 6e 4e |..     G|aussianN|
|00005640| 6f 69 73 65 20 3d 20 73 | 71 72 74 28 2d 32 20 6c |oise = s|qrt(-2 l|
|00005650| 6e 28 78 29 29 20 73 69 | 6e 28 32 b9 79 29 0d 2e |n(x)) si|n(2.y)..|
|00005660| 20 20 20 65 6e 64 00 00 | 00 01 01 4e 1f 9c 00 95 |   end..|...N....|
|00005670| 01 20 40 80 9a 0a 00 7d | 90 3c 00 7e 7b f4 00 95 |. @....}|.<.~{...|
|00005680| 59 ff 00 00 ff ff 00 00 | 00 00 20 00 00 7c 00 00 |Y.......|.. ..|..|
|00005690| 00 02 01 78 7b f4 00 95 | 59 ff 00 00 ff ff 00 00 |...x{...|Y.......|
|000056a0| 00 00 20 00 00 7c 00 00 | 00 01 00 7d 90 44 00 00 |.. ..|..|...}.D..|
|000056b0| 01 32 00 91 48 ee 01 79 | 7b f4 00 95 59 ff 00 00 |.2..H..y|{...Y...|
|000056c0| ff ff 00 00 00 00 20 00 | 00 7c 00 00 00 01 00 7d |...... .|.|.....}|
|000056d0| 90 44 00 00 01 32 00 91 | 48 ee 0f 00 7d 90 18 00 |.D...2..|H...}...|
|000056e0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 7d 90 |........|......}.|
|000056f0| 1c 00 00 00 00 00 7d 90 | 10 00 7d 90 14 00 00 00 |......}.|..}.....|
|00005700| 14 00 00 00 14 00 00 00 | 00 00 00 00 00 09 48 65 |........|......He|
|00005710| 72 6d 69 74 69 61 6e c9 | e2 00 7d 90 1c 00 7d 90 |rmitian.|..}...}.|
|00005720| 1c 00 95 1f 9c 00 95 01 | 40 40 80 9a 0a 00 7d 90 |........|@@....}.|
|00005730| 14 00 00 00 14 20 20 54 | 72 61 6e 73 70 6f 73 65 |.....  T|ranspose|
|00005740| 28 74 68 65 4d 61 74 a0 | 29 00 00 00 01 06 74 68 |(theMat.|).....th|
|00005750| 65 4d 61 74 30 40 80 9a | 0a 00 7d 90 14 00 7e 7b |eMat0@..|..}...~{|
|00005760| f4 00 95 59 ff 00 00 ff | ff 00 00 00 00 20 00 00 |...Y....|..... ..|
|00005770| 7c 06 00 7d 90 00 00 00 | 00 00 00 00 00 00 00 00 ||..}....|........|
|00005780| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00005790| 00 00 3f ff 80 00 00 00 | 00 00 00 00 00 00 00 00 |..?.....|........|
|000057a0| 01 69 00 00 20 00 00 7c | 00 00 00 01 00 7d 90 1c |.i.. ..||.....}..|
|000057b0| 00 00 00 14 00 95 01 42 | 00 91 ff 28 00 95 01 31 |.......B|...(...1|
|000057c0| 00 00 00 01 10 00 7d 8f | f8 00 00 00 00 00 00 00 |......}.|........|
|000057d0| 00 00 00 00 00 00 00 00 | 7d 8f fc 00 00 00 00 00 |........|}.......|
|000057e0| 7d 8f f0 00 7d 8f f4 00 | ce 01 78 00 00 01 80 00 |}...}...|..x.....|
|000057f0| 00 00 00 00 00 00 00 00 | 7d 8f e4 36 00 00 00 00 |........|}..6....|
|00005800| 00 00 00 00 00 00 00 00 | 00 08 49 64 65 6e 74 69 |........|..Identi|
|00005810| 74 79 7d c9 e2 00 7d 8f | fc 00 7d 8f fc 00 95 1f |ty}...}.|..}.....|
|00005820| 9c 00 95 01 30 40 80 9a | 0a 00 7d 8f f4 00 00 01 |....0@..|..}.....|
|00005830| 80 20 20 66 75 6e 63 74 | 69 6f 6e 20 49 64 65 6e |.  funct|ion Iden|
|00005840| 74 69 74 79 28 4e 29 20 | 20 20 23 20 72 65 74 75 |tity(N) |  # retu|
|00005850| 72 6e 73 20 4e 78 4e 20 | 69 64 65 6e 74 69 74 79 |rns NxN |identity|
|00005860| 20 6d 61 74 72 69 78 2e | 0d 2e 20 20 20 76 61 72 | matrix.|..   var|
|00005870| 20 61 6e 73 2c 72 61 6e | 67 65 0d 2e 20 23 20 20 | ans,ran|ge.. #  |
|00005880| 49 6e 70 75 74 3a 20 70 | 6f 73 69 74 69 76 65 20 |Input: p|ositive |
|00005890| 69 6e 74 65 67 65 72 20 | 4e 0d 2e 20 23 20 20 4f |integer |N.. #  O|
|000058a0| 75 74 70 75 74 3a 20 49 | 64 65 6e 74 69 74 79 20 |utput: I|dentity |
|000058b0| 3d 20 42 5b 31 c9 4e 2c | 31 c9 4e 5d 20 77 69 74 |= B[1.N,|1.N] wit|
|000058c0| 68 20 42 5b 69 2c 6a 5d | 20 3d 20 30 20 69 66 20 |h B[i,j]| = 0 if |
|000058d0| 69 3c 3e 6a 3b 20 20 3d | 20 31 20 69 66 20 69 3d |i<>j;  =| 1 if i=|
|000058e0| 6a 2e 0d 2e 20 20 20 76 | 61 72 20 61 6e 73 2c 72 |j...   v|ar ans,r|
|000058f0| 61 6e 67 65 0d 2e 20 20 | 20 62 65 67 69 6e 0d 2e |ange..  | begin..|
|00005900| 20 20 20 20 20 72 61 6e | 67 65 3d 31 c9 4e 3b 0d |     ran|ge=1.N;.|
|00005910| 2e 20 20 20 20 20 61 6e | 73 5b 72 61 6e 67 65 2c |.     an|s[range,|
|00005920| 72 61 6e 67 65 5d 20 3d | 20 30 3b 20 23 20 20 20 |range] =| 0; #   |
|00005930| 54 68 69 73 20 73 65 74 | 73 20 65 6e 74 69 72 65 |This set|s entire|
|00005940| 20 61 72 72 61 79 20 74 | 6f 20 30 2e 0d 2e 20 20 | array t|o 0...  |
|00005950| 20 20 20 66 6f 72 20 72 | 61 6e 67 65 20 64 6f 20 |   for r|ange do |
|00005960| 61 6e 73 5b 72 61 6e 67 | 65 2c 72 61 6e 67 65 5d |ans[rang|e,range]|
|00005970| 3d 31 3b 20 20 20 23 20 | 57 68 69 6c 65 20 74 68 |=1;   # |While th|
|00005980| 69 73 20 73 65 74 73 20 | 64 69 61 67 6f 6e 61 6c |is sets |diagonal|
|00005990| 20 74 6f 20 31 2e 0d 2e | 20 20 20 20 20 49 64 65 | to 1...|     Ide|
|000059a0| 6e 74 69 74 79 3d 61 6e | 73 0d 2e 20 20 20 65 6e |ntity=an|s..   en|
|000059b0| 64 00 00 00 01 01 4e 1f | 9c 00 95 01 20 40 80 9a |d.....N.|.... @..|
|000059c0| 0a 00 7d 8f f4 00 7e 7b | f4 00 95 59 ff 00 00 ff |..}...~{|...Y....|
|000059d0| ff 00 00 00 00 20 00 00 | 7c 00 00 00 02 03 61 6e |..... ..||.....an|
|000059e0| 73 00 95 59 ff 00 00 ff | ff 00 00 00 00 20 00 00 |s..Y....|..... ..|
|000059f0| 7c 00 00 00 01 00 7d 8f | fc 00 00 01 80 00 91 48 ||.....}.|.......H|
|00005a00| ee 05 72 61 6e 67 65 59 | ff 00 00 ff ff 00 00 00 |..rangeY|........|
|00005a10| 00 20 00 00 7c 00 00 00 | 01 00 7d 8f fc 00 00 01 |. ..|...|..}.....|
|00005a20| 80 00 91 48 ee 04 00 7d | 8f d0 01 00 00 00 00 00 |...H...}|........|
|00005a30| 00 00 00 00 00 00 00 00 | 3d 00 02 49 66 80 00 91 |........|=..If...|
|00005a40| 48 ee 00 00 00 02 00 00 | ff ff 00 00 00 00 00 95 |H.......|........|
|00005a50| 01 42 00 91 ff 28 00 95 | 01 31 00 00 00 01 0c 00 |.B...(..|.1......|
|00005a60| 7d 8f c8 01 00 00 00 00 | 00 00 00 00 00 00 00 00 |}.......|........|
|00005a70| 00 1f 00 00 00 00 00 09 | 49 6d 61 67 69 6e 61 72 |........|Imaginar|
|00005a80| 79 00 02 00 00 ff ff 00 | 00 00 00 00 95 01 42 00 |y.......|......B.|
|00005a90| 91 ff 28 00 95 01 31 00 | 00 00 01 10 00 7d 8f c0 |..(...1.|.....}..|
|00005aa0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 7d |........|.......}|
|00005ab0| 8f c4 00 00 00 00 00 7d | 8f b8 00 7d 8f bc 01 65 |.......}|...}...e|
|00005ac0| 02 95 00 00 02 9d 00 00 | 00 00 00 00 00 00 00 7d |........|.......}|
|00005ad0| 8f a8 36 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |..6.....|........|
|00005ae0| 0f 49 6e 63 6f 6d 70 6c | 65 74 65 47 61 6d 6d 61 |.Incompl|eteGamma|
|00005af0| 00 7d 8f c4 00 95 1f 9c | 00 95 01 30 40 80 9a 0a |.}......|...0@...|
|00005b00| 00 7d 8f bc 00 00 02 9d | 66 75 6e 63 74 69 6f 6e |.}......|function|
|00005b10| 20 49 6e 63 6f 6d 70 6c | 65 74 65 47 61 6d 6d 61 | Incompl|eteGamma|
|00005b20| 28 61 2c 78 29 20 20 23 | 20 52 65 74 75 72 6e 73 |(a,x)  #| Returns|
|00005b30| 20 50 28 61 2c 78 29 3d | 20 31 2f 67 61 6d 6d 61 | P(a,x)=| 1/gamma|
|00005b40| 28 78 29 20 20 69 6e 74 | 65 67 72 61 6c 20 30 2d |(x)  int|egral 0-|
|00005b50| 3e 78 20 7b 20 65 78 70 | 28 2d 74 29 20 74 5e 28 |>x { exp|(-t) t^(|
|00005b60| 61 2d 31 29 20 64 74 20 | 7d 0d 2e 20 20 20 76 61 |a-1) dt |}..   va|
|00005b70| 72 20 6e 2c 79 2c 20 65 | 72 72 0d 2e 20 23 20 20 |r n,y, e|rr.. #  |
|00005b80| 20 20 20 49 6e 70 75 74 | 3a 20 20 20 20 20 61 20 |   Input|:     a |
|00005b90| 3d 20 6e 75 6d 62 65 72 | 20 3e 20 30 0d 2e 20 23 |= number| > 0.. #|
|00005ba0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00005bb0| 20 20 20 78 20 3d 20 6e | 75 6d 62 65 72 20 6f 72 |   x = n|umber or|
|00005bc0| 20 61 72 72 61 79 0d 2e | 20 23 20 20 20 20 20 4f | array..| #     O|
|00005bd0| 75 74 70 75 74 3a 0d 2e | 20 23 20 20 20 20 20 20 |utput:..| #      |
|00005be0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 49 6e 63 |        |     Inc|
|00005bf0| 6f 6d 70 6c 65 74 65 47 | 61 6d 6d 61 20 3d 20 50 |ompleteG|amma = P|
|00005c00| 28 61 2c 78 29 20 3d 20 | 6e 75 6d 62 65 72 20 6f |(a,x) = |number o|
|00005c10| 72 20 61 72 72 61 79 0d | 2e 20 23 20 20 20 20 20 |r array.|. #     |
|00005c20| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00005c30| 3d 20 31 2f 67 61 6d 6d | 61 28 78 29 20 20 69 6e |= 1/gamm|a(x)  in|
|00005c40| 74 65 67 72 61 6c 20 30 | 2d 3e 78 20 7b 20 65 78 |tegral 0|->x { ex|
|00005c50| 70 28 2d 74 29 20 74 5e | 28 61 2d 31 29 20 64 74 |p(-t) t^|(a-1) dt|
|00005c60| 20 7d 0d 2e 20 20 20 62 | 65 67 69 6e 0d 2e 20 20 | }..   b|egin..  |
|00005c70| 20 20 20 6e 3d 73 69 7a | 65 28 78 29 0d 2e 20 20 |   n=siz|e(x)..  |
|00005c80| 20 20 20 79 3d 78 20 20 | 23 20 73 61 76 65 20 73 |   y=x  |# save s|
|00005c90| 70 61 63 65 20 66 6f 72 | 20 61 6e 73 77 65 72 0d |pace for| answer.|
|00005ca0| 2e 20 20 20 20 20 78 49 | 4e 43 4f 4d 50 4c 45 54 |.     xI|NCOMPLET|
|00005cb0| 45 5f 47 41 4d 4d 41 28 | 6e 2c 61 2c 78 2c 79 2c |E_GAMMA(|n,a,x,y,|
|00005cc0| 65 72 72 29 0d 2e 20 20 | 20 20 20 69 66 20 65 72 |err)..  |   if er|
|00005cd0| 72 3d 30 20 74 68 65 6e | 0d 2e 20 20 20 20 20 20 |r=0 then|..      |
|00005ce0| 20 49 6e 63 6f 6d 70 6c | 65 74 65 47 61 6d 6d 61 | Incompl|eteGamma|
|00005cf0| 20 3d 20 79 0d 2e 20 20 | 20 20 20 65 6c 73 65 20 | = y..  |   else |
|00005d00| 69 66 20 2d 32 20 74 68 | 65 6e 0d 2e 20 20 20 20 |if -2 th|en..    |
|00005d10| 20 20 20 49 6e 63 6f 6d | 70 6c 65 74 65 47 61 6d |   Incom|pleteGam|
|00005d20| 6d 61 20 3d 20 22 20 45 | 52 52 4f 52 20 69 6e 20 |ma = " E|RROR in |
|00005d30| 78 49 4e 43 4f 4d 50 4c | 45 54 45 5f 47 41 4d 4d |xINCOMPL|ETE_GAMM|
|00005d40| 41 2c 20 78 3c 30 20 22 | 0d 2e 20 20 20 20 20 65 |A, x<0 "|..     e|
|00005d50| 6c 73 65 0d 2e 20 20 20 | 20 20 20 20 49 6e 63 6f |lse..   |    Inco|
|00005d60| 6d 70 6c 65 74 65 47 61 | 6d 6d 61 20 3d 20 22 20 |mpleteGa|mma = " |
|00005d70| 45 52 52 4f 52 20 69 6e | 20 78 49 4e 43 4f 4d 50 |ERROR in| xINCOMP|
|00005d80| 4c 45 54 45 5f 47 41 4d | 4d 41 2c 20 64 69 64 20 |LETE_GAM|MA, did |
|00005d90| 6e 6f 74 20 63 6f 6e 76 | 65 72 67 65 22 0d 2e 20 |not conv|erge".. |
|00005da0| 20 20 65 6e 64 00 00 00 | 02 01 61 1f 9c 00 95 01 |  end...|..a.....|
|00005db0| 20 40 80 9a 0a 00 7d 8f | bc 00 7e 7b f4 00 95 59 | @....}.|..~{...Y|
|00005dc0| ff 00 00 ff ff 00 00 00 | 00 20 00 00 7c 01 78 1f |........|. ..|.x.|
|00005dd0| 9c 00 95 01 20 40 80 9a | 0a 00 7d 8f bc 00 7e 7b |.... @..|..}...~{|
|00005de0| f4 00 95 59 ff 00 00 ff | ff 00 00 00 00 20 00 00 |...Y....|..... ..|
|00005df0| 7c 00 00 00 03 01 6e 7b | f4 00 95 59 ff 00 00 ff ||.....n{|...Y....|
|00005e00| ff 00 00 00 00 20 00 00 | 7c 00 00 00 02 00 7d 8f |..... ..||.....}.|
|00005e10| c4 00 00 02 9d 00 91 48 | ee 01 79 7b f4 00 95 59 |.......H|..y{...Y|
|00005e20| ff 00 00 ff ff 00 00 00 | 00 20 00 00 7c 00 00 00 |........|. ..|...|
|00005e30| 02 00 7d 8f c4 00 00 02 | 9d 00 91 48 ee 03 65 72 |..}.....|...H..er|
|00005e40| 72 00 95 59 ff 00 00 ff | ff 00 00 00 00 20 00 00 |r..Y....|..... ..|
|00005e50| 7c 00 00 00 02 00 7d 8f | c4 00 00 02 9d 00 91 48 ||.....}.|.......H|
|00005e60| ee 10 00 7d 8f 80 00 00 | 00 00 00 00 00 00 00 00 |...}....|........|
|00005e70| 00 00 00 00 00 7d 8f 84 | 00 00 00 00 00 7d 8f 78 |.....}..|.....}.x|
|00005e80| 00 7d 8f 7c 00 ba 01 16 | 00 00 01 1e 00 00 00 00 |.}.|....|........|
|00005e90| 00 00 00 00 00 7d 8f 6c | 35 00 00 00 00 00 00 00 |.....}.l|5.......|
|00005ea0| 00 00 00 00 00 00 0a 49 | 6e 69 74 52 61 6e 64 6f |.......I|nitRando|
|00005eb0| 6d e2 00 7d 8f 84 00 7d | 8f 84 00 95 1f 9c 00 95 |m..}...}|........|
|00005ec0| 01 30 40 80 9a 0a 00 7d | 8f 7c 00 00 01 1e 20 70 |.0@....}|.|.... p|
|00005ed0| 72 6f 67 72 61 6d 20 49 | 6e 69 74 52 61 6e 64 6f |rogram I|nitRando|
|00005ee0| 6d 28 73 65 65 64 29 20 | 20 23 20 49 6e 74 69 74 |m(seed) | # Intit|
|00005ef0| 69 61 6c 69 7a 65 73 20 | 61 6c 6c 20 72 61 6e 64 |ializes |all rand|
|00005f00| 6f 6d 20 72 6f 75 74 69 | 6e 65 73 3b 20 73 65 65 |om routi|nes; see|
|00005f10| 64 20 7e 20 31 2e 30 20 | 2e 20 0d 2e 20 20 20 76 |d ~ 1.0 |. ..   v|
|00005f20| 61 72 20 78 0d 2e 20 20 | 20 23 20 20 49 6e 70 75 |ar x..  | #  Inpu|
|00005f30| 74 3a 20 20 73 65 65 64 | 20 3d 20 72 65 61 6c 20 |t:  seed| = real |
|00005f40| 72 61 6e 64 6f 6d 20 6e | 75 6d 62 65 72 20 7e 20 |random n|umber ~ |
|00005f50| 31 2e 30 0d 2e 20 20 20 | 23 20 20 4f 75 74 70 75 |1.0..   |#  Outpu|
|00005f60| 74 3a 20 20 6e 6f 6e 65 | 2e 20 20 53 65 74 73 20 |t:  none|.  Sets |
|00005f70| 75 70 20 52 61 6e 64 53 | 74 6f 72 65 2e 0d 2e 20 |up RandS|tore... |
|00005f80| 20 20 62 65 67 69 6e 0d | 2e 20 20 20 20 20 52 61 |  begin.|.     Ra|
|00005f90| 6e 64 53 74 6f 72 65 5b | 31 c9 31 30 30 5d 20 3d |ndStore[|1.100] =|
|00005fa0| 20 30 0d 2e 20 20 20 20 | 20 78 5b 31 c9 32 5d 20 | 0..    | x[1.2] |
|00005fb0| 3d 20 30 0d 2e 20 20 20 | 20 20 78 52 41 4e 44 4f |= 0..   |  xRANDO|
|00005fc0| 4d 28 2d 33 31 34 31 35 | 39 2a 73 65 65 64 2c 20 |M(-31415|9*seed, |
|00005fd0| 73 69 7a 65 28 78 29 2c | 78 2c 52 61 6e 64 53 74 |size(x),|x,RandSt|
|00005fe0| 6f 72 65 29 0d 2e 20 20 | 20 65 6e 64 00 00 00 01 |ore)..  | end....|
|00005ff0| 04 73 65 65 64 95 01 20 | 40 80 9a 0a 00 7d 8f 7c |.seed.. |@....}.||
|00006000| 00 7e 7b f4 00 95 59 ff | 00 00 ff ff 00 00 00 00 |.~{...Y.|........|
|00006010| 20 00 00 7c 00 00 00 01 | 01 78 7b f4 00 95 59 ff | ..|....|.x{...Y.|
|00006020| 00 00 ff ff 00 00 00 00 | 20 00 00 7c 00 00 00 01 |........| ..|....|
|00006030| 00 7d 8f 84 00 00 01 1e | 00 91 48 ee 0c 00 7d 8f |.}......|..H...}.|
|00006040| 5c 01 00 00 00 00 00 00 | 00 00 00 00 00 00 00 1d |\.......|........|
|00006050| 00 00 00 00 00 03 69 6e | 74 00 91 48 ee 00 00 00 |......in|t..H....|
|00006060| 01 00 00 ff ff 00 00 00 | 00 00 95 01 42 00 91 ff |........|....B...|
|00006070| 28 00 95 01 31 00 00 00 | 01 10 00 7d 8f 54 00 00 |(...1...|...}.T..|
|00006080| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 7d 8f 58 |........|.....}.X|
|00006090| 00 00 00 00 00 7d 8f 4c | 00 7d 8f 50 01 2d 02 85 |.....}.L|.}.P.-..|
|000060a0| 00 00 02 8d 00 00 00 00 | 00 00 00 00 00 7d 8f 38 |........|.....}.8|
|000060b0| 36 00 00 00 00 00 00 00 | 00 00 00 00 00 00 09 49 |6.......|.......I|
|000060c0| 6e 74 65 67 72 61 74 65 | c9 e2 00 7d 8f 58 00 7d |ntegrate|...}.X.}|
|000060d0| 8f 58 00 95 1f 9c 00 95 | 01 30 40 80 9a 0a 00 7d |.X......|.0@....}|
|000060e0| 8f 50 00 00 02 8d 20 20 | 66 75 6e 63 74 69 6f 6e |.P....  |function|
|000060f0| 20 49 6e 74 65 67 72 61 | 74 65 28 66 2c 61 2c 62 | Integra|te(f,a,b|
|00006100| 29 20 23 20 52 65 74 75 | 72 6e 73 20 64 65 66 69 |) # Retu|rns defi|
|00006110| 6e 69 74 65 20 69 6e 74 | 65 67 72 61 6c 20 6f 66 |nite int|egral of|
|00006120| 20 66 28 78 29 20 64 78 | 20 66 72 6f 6d 20 78 3d | f(x) dx| from x=|
|00006130| 61 20 74 6f 20 62 2e 0d | 2e 20 20 20 76 61 72 20 |a to b..|.   var |
|00006140| 74 6f 6c 2c 20 61 6e 73 | 2c 20 65 72 72 0d 2e 20 |tol, ans|, err.. |
|00006150| 23 20 20 20 49 6e 70 75 | 74 3a 0d 2e 20 23 20 20 |#   Inpu|t:.. #  |
|00006160| 20 20 20 20 20 20 20 20 | 20 20 20 4e 43 49 49 20 |        |   NCII |
|00006170| 75 73 65 72 20 66 75 6e | 63 74 69 6f 6e 20 66 0d |user fun|ction f.|
|00006180| 2e 20 23 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. #     |        |
|00006190| 61 2c 20 62 20 3d 20 6e | 75 6d 62 65 72 73 20 66 |a, b = n|umbers f|
|000061a0| 6f 72 20 6c 65 66 74 2c | 20 72 69 67 68 74 20 6f |or left,| right o|
|000061b0| 66 20 69 6e 74 65 67 72 | 61 74 69 6f 6e 20 72 61 |f integr|ation ra|
|000061c0| 6e 67 65 0d 2e 20 23 20 | 20 20 4f 75 74 70 75 74 |nge.. # |  Output|
|000061d0| 3a 0d 2e 20 23 20 20 20 | 20 20 20 20 20 20 20 20 |:.. #   |        |
|000061e0| 20 20 49 6e 74 65 67 72 | 61 74 65 20 3d 20 69 6e |  Integr|ate = in|
|000061f0| 74 65 67 72 61 6c 20 6f | 66 20 66 20 66 72 6f 6d |tegral o|f f from|
|00006200| 20 61 20 74 6f 20 62 2c | 20 61 20 6e 75 6d 62 65 | a to b,| a numbe|
|00006210| 72 2e 0d 2e 20 20 20 62 | 65 67 69 6e 20 20 20 20 |r...   b|egin    |
|00006220| 23 20 66 69 72 73 74 2c | 20 72 65 6e 61 6d 65 20 |# first,| rename |
|00006230| 74 68 65 20 66 75 6e 63 | 74 69 6f 6e 20 66 28 78 |the func|tion f(x|
|00006240| 29 2e 0d 2e 20 20 20 20 | 20 7a 7a 46 5f 49 6e 74 |)...    | zzF_Int|
|00006250| 65 67 72 61 6c 5f 5f 20 | 3d 20 66 0d 2e 20 20 20 |egral__ |= f..   |
|00006260| 20 20 74 6f 6c 20 3d 20 | 31 65 2d 38 20 20 23 20 |  tol = |1e-8  # |
|00006270| 67 6f 69 6e 67 20 74 6f | 6f 20 68 69 67 68 20 77 |going to|o high w|
|00006280| 69 6c 6c 20 64 65 6d 61 | 6e 64 20 76 65 72 79 20 |ill dema|nd very |
|00006290| 6c 61 72 67 65 20 61 72 | 72 61 79 73 20 69 6e 20 |large ar|rays in |
|000062a0| 53 75 6d 46 0d 2e 20 20 | 20 20 20 78 49 4e 54 45 |SumF..  |   xINTE|
|000062b0| 47 52 41 54 45 28 7a 7a | 46 75 6e 63 46 6f 72 49 |GRATE(zz|FuncForI|
|000062c0| 6e 74 65 67 72 61 74 65 | 5f 5f 2c 20 61 2c 20 62 |ntegrate|__, a, b|
|000062d0| 2c 20 74 6f 6c 2c 20 61 | 6e 73 2c 20 65 72 72 29 |, tol, a|ns, err)|
|000062e0| 0d 2e 20 20 20 20 20 69 | 66 20 65 72 72 3c 3e 30 |..     i|f err<>0|
|000062f0| 20 74 68 65 6e 20 0d 2e | 20 20 20 20 20 20 20 20 | then ..|        |
|00006300| 62 65 67 69 6e 0d 2e 20 | 20 20 20 20 20 20 20 20 |begin.. |        |
|00006310| 20 62 65 65 70 3b 0d 2e | 20 20 20 20 20 20 20 20 | beep;..|        |
|00006320| 20 20 50 72 69 6e 74 28 | 22 20 49 6e 74 65 67 72 |  Print(|" Integr|
|00006330| 61 74 65 20 64 69 64 20 | 6e 6f 74 20 63 6f 6e 76 |ate did |not conv|
|00006340| 65 72 67 65 20 22 29 3b | 0d 2e 20 20 20 20 20 20 |erge ");|..      |
|00006350| 20 20 65 6e 64 0d 2e 20 | 20 20 20 20 49 6e 74 65 |  end.. |    Inte|
|00006360| 67 72 61 74 65 20 3d 20 | 61 6e 73 0d 2e 20 20 20 |grate = |ans..   |
|00006370| 65 6e 64 00 00 00 03 01 | 66 1f 9c 00 95 01 20 40 |end.....|f..... @|
|00006380| 80 9a 0a 00 7d 8f 50 00 | 7e 7b f4 00 95 59 ff 00 |....}.P.|~{...Y..|
|00006390| 00 ff ff 00 00 00 00 20 | 00 00 7c 01 61 1f 9c 00 |....... |..|.a...|
|000063a0| 95 01 20 40 80 9a 0a 00 | 7d 8f 50 00 7e 7b f4 00 |.. @....|}.P.~{..|
|000063b0| 95 59 ff 00 00 ff ff 00 | 00 00 00 20 00 00 7c 01 |.Y......|... ..|.|
|000063c0| 62 1f 9c 00 95 01 20 40 | 80 9a 0a 00 7d 8f 50 00 |b..... @|....}.P.|
|000063d0| 7e 7b f4 00 95 59 ff 00 | 00 ff ff 00 00 00 00 20 |~{...Y..|....... |
|000063e0| 00 00 7c 00 00 00 03 03 | 74 6f 6c 00 95 59 ff 00 |..|.....|tol..Y..|
|000063f0| 00 ff ff 00 00 00 00 20 | 00 00 7c 00 00 00 03 00 |....... |..|.....|
+--------+-------------------------+-------------------------+--------+--------+
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