home *** CD-ROM | disk | FTP | other *** search
view JSON data
|
view as text
|
open on a Mac
|
open on a PC
This file was processed as: SHell self-extracting ARchive
(archive/shar).
You can browse this item here: part01
| Confidence | Program | Detection | Match Type | Support
|
|---|
| 100%
| dexvert
| SHell self-extracting ARchive (archive/shar)
| magic
| Supported |
| 1%
| dexvert
| Text File (text/txt)
| fallback
| Supported |
| 100%
| file
| ASCII text
| default
| |
| 100%
| checkBytes
| Printable ASCII
| default
| |
| 100%
| perlTextCheck
| Likely Text (Perl)
| default
| |
| 100%
| siegfried
| fmt/329 Shell Archive Format
| default
| |
| 100%
| detectItEasy
| Format: plain text[LF]
| default (weak)
|
|
hex view+--------+-------------------------+-------------------------+--------+--------+
|00000000| 4e 65 77 73 67 72 6f 75 | 70 73 3a 20 63 6f 6d 70 |Newsgrou|ps: comp|
|00000010| 2e 73 6f 75 72 63 65 73 | 2e 6d 69 73 63 0a 46 72 |.sources|.misc.Fr|
|00000020| 6f 6d 3a 20 72 6f 62 65 | 72 74 40 61 6d 2e 64 73 |om: robe|rt@am.ds|
|00000030| 69 72 2e 67 6f 76 74 2e | 6e 7a 20 28 52 6f 62 65 |ir.govt.|nz (Robe|
|00000040| 72 74 20 44 61 76 69 65 | 73 29 0a 53 75 62 6a 65 |rt Davie|s).Subje|
|00000050| 63 74 3a 20 20 76 32 36 | 69 30 38 37 3a 20 20 6e |ct: v26|i087: n|
|00000060| 65 77 6d 61 74 30 34 20 | 2d 20 41 20 6d 61 74 72 |ewmat04 |- A matr|
|00000070| 69 78 20 70 61 63 6b 61 | 67 65 20 69 6e 20 43 2b |ix packa|ge in C+|
|00000080| 2b 2c 20 50 61 72 74 30 | 31 2f 30 35 0a 4d 65 73 |+, Part0|1/05.Mes|
|00000090| 73 61 67 65 2d 49 44 3a | 20 3c 63 73 6d 2d 76 32 |sage-ID:| <csm-v2|
|000000a0| 36 69 30 38 37 3d 6e 65 | 77 6d 61 74 30 34 2e 31 |6i087=ne|wmat04.1|
|000000b0| 34 34 39 33 34 40 73 70 | 61 72 6b 79 2e 49 4d 44 |44934@sp|arky.IMD|
|000000c0| 2e 53 74 65 72 6c 69 6e | 67 2e 43 4f 4d 3e 0a 58 |.Sterlin|g.COM>.X|
|000000d0| 2d 4d 64 34 2d 53 69 67 | 6e 61 74 75 72 65 3a 20 |-Md4-Sig|nature: |
|000000e0| 35 30 66 63 30 38 62 66 | 39 33 35 63 61 39 39 38 |50fc08bf|935ca998|
|000000f0| 39 65 66 38 66 37 63 30 | 32 61 31 62 31 62 64 36 |9ef8f7c0|2a1b1bd6|
|00000100| 0a 44 61 74 65 3a 20 53 | 61 74 2c 20 33 30 20 4e |.Date: S|at, 30 N|
|00000110| 6f 76 20 31 39 39 31 20 | 32 30 3a 35 32 3a 30 33 |ov 1991 |20:52:03|
|00000120| 20 47 4d 54 0a 41 70 70 | 72 6f 76 65 64 3a 20 6b | GMT.App|roved: k|
|00000130| 65 6e 74 40 73 70 61 72 | 6b 79 2e 69 6d 64 2e 73 |ent@spar|ky.imd.s|
|00000140| 74 65 72 6c 69 6e 67 2e | 63 6f 6d 0a 0a 53 75 62 |terling.|com..Sub|
|00000150| 6d 69 74 74 65 64 2d 62 | 79 3a 20 72 6f 62 65 72 |mitted-b|y: rober|
|00000160| 74 40 61 6d 2e 64 73 69 | 72 2e 67 6f 76 74 2e 6e |t@am.dsi|r.govt.n|
|00000170| 7a 20 28 52 6f 62 65 72 | 74 20 44 61 76 69 65 73 |z (Rober|t Davies|
|00000180| 29 0a 50 6f 73 74 69 6e | 67 2d 6e 75 6d 62 65 72 |).Postin|g-number|
|00000190| 3a 20 56 6f 6c 75 6d 65 | 20 32 36 2c 20 49 73 73 |: Volume| 26, Iss|
|000001a0| 75 65 20 38 37 0a 41 72 | 63 68 69 76 65 2d 6e 61 |ue 87.Ar|chive-na|
|000001b0| 6d 65 3a 20 6e 65 77 6d | 61 74 30 34 2f 70 61 72 |me: newm|at04/par|
|000001c0| 74 30 31 0a 45 6e 76 69 | 72 6f 6e 6d 65 6e 74 3a |t01.Envi|ronment:|
|000001d0| 20 43 2b 2b 0a 53 75 70 | 65 72 73 65 64 65 73 3a | C++.Sup|ersedes:|
|000001e0| 20 6e 65 77 6d 61 74 30 | 32 3a 20 56 6f 6c 75 6d | newmat0|2: Volum|
|000001f0| 65 20 32 31 2c 20 49 73 | 73 75 65 20 34 39 2d 35 |e 21, Is|sue 49-5|
|00000200| 32 0a 0a 41 6e 20 65 78 | 70 65 72 69 6d 65 6e 74 |2..An ex|periment|
|00000210| 61 6c 20 6d 61 74 72 69 | 78 20 70 61 63 6b 61 67 |al matri|x packag|
|00000220| 65 20 69 6e 20 43 2b 2b | 2e 20 20 49 74 20 73 75 |e in C++|. It su|
|00000230| 70 70 6f 72 74 73 20 6d | 61 74 72 69 78 20 74 79 |pports m|atrix ty|
|00000240| 70 65 73 3a 20 0a 4d 61 | 74 72 69 78 2c 20 55 70 |pes: .Ma|trix, Up|
|00000250| 70 65 72 54 72 69 61 6e | 67 75 6c 61 72 4d 61 74 |perTrian|gularMat|
|00000260| 72 69 78 2c 20 4c 6f 77 | 65 72 54 72 69 61 6e 67 |rix, Low|erTriang|
|00000270| 75 6c 61 72 4d 61 74 72 | 69 78 2c 20 44 69 61 67 |ularMatr|ix, Diag|
|00000280| 6f 6e 61 6c 4d 61 74 72 | 69 78 2c 20 0a 53 79 6d |onalMatr|ix, .Sym|
|00000290| 6d 65 74 72 69 63 4d 61 | 74 72 69 78 2c 20 52 6f |metricMa|trix, Ro|
|000002a0| 77 56 65 63 74 6f 72 2c | 20 43 6f 6c 75 6d 6e 56 |wVector,| ColumnV|
|000002b0| 65 63 74 6f 72 2e 20 4f | 6e 6c 79 20 6f 6e 65 20 |ector. O|nly one |
|000002c0| 65 6c 65 6d 65 6e 74 20 | 74 79 70 65 20 28 66 6c |element |type (fl|
|000002d0| 6f 61 74 20 0a 6f 72 20 | 64 6f 75 62 6c 65 29 20 |oat .or |double) |
|000002e0| 69 73 20 73 75 70 70 6f | 72 74 65 64 2e 0a 0a 54 |is suppo|rted...T|
|000002f0| 68 65 20 70 61 63 6b 61 | 67 65 20 69 6e 63 6c 75 |he packa|ge inclu|
|00000300| 64 65 73 20 74 68 65 20 | 6f 70 65 72 61 74 69 6f |des the |operatio|
|00000310| 6e 73 20 2a 2c 20 2b 2c | 20 2d 2c 20 28 64 65 66 |ns *, +,| -, (def|
|00000320| 69 6e 65 64 20 61 73 20 | 6f 70 65 72 61 74 6f 72 |ined as |operator|
|00000330| 73 29 0a 69 6e 76 65 72 | 73 65 2c 20 74 72 61 6e |s).inver|se, tran|
|00000340| 73 70 6f 73 65 2c 20 63 | 6f 6e 76 65 72 73 69 6f |spose, c|onversio|
|00000350| 6e 20 62 65 74 77 65 65 | 6e 20 74 79 70 65 73 2c |n betwee|n types,|
|00000360| 20 73 75 62 6d 61 74 72 | 69 78 2c 20 64 65 74 65 | submatr|ix, dete|
|00000370| 72 6d 69 6e 61 6e 74 2c | 0a 43 68 6f 6c 65 73 6b |rminant,|.Cholesk|
|00000380| 79 20 64 65 63 6f 6d 70 | 6f 73 69 74 69 6f 6e 2c |y decomp|osition,|
|00000390| 20 48 6f 75 73 65 68 6f | 6c 64 65 72 20 74 72 69 | Househo|lder tri|
|000003a0| 61 6e 67 75 6c 61 72 69 | 73 61 74 69 6f 6e 2c 20 |angulari|sation, |
|000003b0| 73 69 6e 67 75 6c 61 72 | 20 76 61 6c 75 65 0a 64 |singular| value.d|
|000003c0| 65 63 6f 6d 70 6f 73 69 | 74 69 6f 6e 2c 20 65 69 |ecomposi|tion, ei|
|000003d0| 67 65 6e 76 61 6c 75 65 | 73 20 6f 66 20 61 20 73 |genvalue|s of a s|
|000003e0| 79 6d 6d 65 74 72 69 63 | 20 6d 61 74 72 69 78 2c |ymmetric| matrix,|
|000003f0| 20 73 6f 72 74 69 6e 67 | 2c 20 66 61 73 74 20 66 | sorting|, fast f|
|00000400| 6f 75 72 69 65 72 0a 74 | 72 61 6e 73 66 6f 72 6d |ourier.t|ransform|
|00000410| 2c 20 70 72 69 6e 74 69 | 6e 67 20 61 6e 64 20 61 |, printi|ng and a|
|00000420| 6e 20 69 6e 74 65 72 66 | 61 63 65 20 77 69 74 68 |n interf|ace with|
|00000430| 20 22 4e 75 6d 65 72 69 | 63 61 6c 20 52 65 63 69 | "Numeri|cal Reci|
|00000440| 70 65 73 20 69 6e 20 43 | 22 2e 0a 0a 49 74 20 69 |pes in C|"...It i|
|00000450| 73 20 69 6e 74 65 6e 64 | 65 64 20 66 6f 72 20 6d |s intend|ed for m|
|00000460| 61 74 72 69 63 65 73 20 | 69 6e 20 74 68 65 20 72 |atrices |in the r|
|00000470| 61 6e 67 65 20 34 20 78 | 20 34 20 74 6f 20 61 62 |ange 4 x| 4 to ab|
|00000480| 6f 75 74 20 39 30 20 78 | 20 39 30 20 28 31 32 35 |out 90 x| 90 (125|
|00000490| 0a 78 20 31 32 35 20 66 | 6f 72 20 74 72 69 61 6e |.x 125 f|or trian|
|000004a0| 67 75 6c 61 72 20 6d 61 | 74 72 69 63 65 73 29 2e |gular ma|trices).|
|000004b0| 0a 2d 2d 2d 0a 23 21 20 | 2f 62 69 6e 2f 73 68 0a |.---.#! |/bin/sh.|
|000004c0| 23 20 54 68 69 73 20 69 | 73 20 61 20 73 68 65 6c |# This i|s a shel|
|000004d0| 6c 20 61 72 63 68 69 76 | 65 2e 20 20 52 65 6d 6f |l archiv|e. Remo|
|000004e0| 76 65 20 61 6e 79 74 68 | 69 6e 67 20 62 65 66 6f |ve anyth|ing befo|
|000004f0| 72 65 20 74 68 69 73 20 | 6c 69 6e 65 2c 20 74 68 |re this |line, th|
|00000500| 65 6e 20 75 6e 70 61 63 | 6b 0a 23 20 69 74 20 62 |en unpac|k.# it b|
|00000510| 79 20 73 61 76 69 6e 67 | 20 69 74 20 69 6e 74 6f |y saving| it into|
|00000520| 20 61 20 66 69 6c 65 20 | 61 6e 64 20 74 79 70 69 | a file |and typi|
|00000530| 6e 67 20 22 73 68 20 66 | 69 6c 65 22 2e 20 20 54 |ng "sh f|ile". T|
|00000540| 6f 20 6f 76 65 72 77 72 | 69 74 65 20 65 78 69 73 |o overwr|ite exis|
|00000550| 74 69 6e 67 0a 23 20 66 | 69 6c 65 73 2c 20 74 79 |ting.# f|iles, ty|
|00000560| 70 65 20 22 73 68 20 66 | 69 6c 65 20 2d 63 22 2e |pe "sh f|ile -c".|
|00000570| 20 20 59 6f 75 20 63 61 | 6e 20 61 6c 73 6f 20 66 | You ca|n also f|
|00000580| 65 65 64 20 74 68 69 73 | 20 61 73 20 73 74 61 6e |eed this| as stan|
|00000590| 64 61 72 64 20 69 6e 70 | 75 74 20 76 69 61 0a 23 |dard inp|ut via.#|
|000005a0| 20 75 6e 73 68 61 72 2c | 20 6f 72 20 62 79 20 74 | unshar,| or by t|
|000005b0| 79 70 69 6e 67 20 22 73 | 68 20 3c 66 69 6c 65 22 |yping "s|h <file"|
|000005c0| 2c 20 65 2e 67 2e 2e 20 | 20 49 66 20 74 68 69 73 |, e.g.. | If this|
|000005d0| 20 61 72 63 68 69 76 65 | 20 69 73 20 63 6f 6d 70 | archive| is comp|
|000005e0| 6c 65 74 65 2c 20 79 6f | 75 0a 23 20 77 69 6c 6c |lete, yo|u.# will|
|000005f0| 20 73 65 65 20 74 68 65 | 20 66 6f 6c 6c 6f 77 69 | see the| followi|
|00000600| 6e 67 20 6d 65 73 73 61 | 67 65 20 61 74 20 74 68 |ng messa|ge at th|
|00000610| 65 20 65 6e 64 3a 0a 23 | 09 09 22 45 6e 64 20 6f |e end:.#|.."End o|
|00000620| 66 20 73 68 65 6c 6c 20 | 61 72 63 68 69 76 65 2e |f shell |archive.|
|00000630| 22 0a 23 20 43 6f 6e 74 | 65 6e 74 73 3a 20 20 6e |".# Cont|ents: n|
|00000640| 65 77 6d 61 74 2e 74 78 | 74 0a 23 20 57 72 61 70 |ewmat.tx|t.# Wrap|
|00000650| 70 65 64 20 62 79 20 72 | 6f 62 65 72 74 40 6b 65 |ped by r|obert@ke|
|00000660| 61 20 6f 6e 20 53 61 74 | 20 4e 6f 76 20 33 30 20 |a on Sat| Nov 30 |
|00000670| 31 38 3a 32 34 3a 30 33 | 20 31 39 39 31 0a 50 41 |18:24:03| 1991.PA|
|00000680| 54 48 3d 2f 62 69 6e 3a | 2f 75 73 72 2f 62 69 6e |TH=/bin:|/usr/bin|
|00000690| 3a 2f 75 73 72 2f 75 63 | 62 20 3b 20 65 78 70 6f |:/usr/uc|b ; expo|
|000006a0| 72 74 20 50 41 54 48 0a | 69 66 20 74 65 73 74 20 |rt PATH.|if test |
|000006b0| 2d 66 20 27 6e 65 77 6d | 61 74 2e 74 78 74 27 20 |-f 'newm|at.txt' |
|000006c0| 2d 61 20 22 24 7b 31 7d | 22 20 21 3d 20 22 2d 63 |-a "${1}|" != "-c|
|000006d0| 22 20 3b 20 74 68 65 6e | 20 0a 20 20 65 63 68 6f |" ; then| . echo|
|000006e0| 20 73 68 61 72 3a 20 57 | 69 6c 6c 20 6e 6f 74 20 | shar: W|ill not |
|000006f0| 63 6c 6f 62 62 65 72 20 | 65 78 69 73 74 69 6e 67 |clobber |existing|
|00000700| 20 66 69 6c 65 20 5c 22 | 27 6e 65 77 6d 61 74 2e | file \"|'newmat.|
|00000710| 74 78 74 27 5c 22 0a 65 | 6c 73 65 0a 65 63 68 6f |txt'\".e|lse.echo|
|00000720| 20 73 68 61 72 3a 20 45 | 78 74 72 61 63 74 69 6e | shar: E|xtractin|
|00000730| 67 20 5c 22 27 6e 65 77 | 6d 61 74 2e 74 78 74 27 |g \"'new|mat.txt'|
|00000740| 5c 22 20 5c 28 35 33 34 | 37 35 20 63 68 61 72 61 |\" \(534|75 chara|
|00000750| 63 74 65 72 73 5c 29 0a | 73 65 64 20 22 73 2f 5e |cters\).|sed "s/^|
|00000760| 58 2f 2f 22 20 3e 27 6e | 65 77 6d 61 74 2e 74 78 |X//" >'n|ewmat.tx|
|00000770| 74 27 20 3c 3c 27 45 4e | 44 5f 4f 46 5f 46 49 4c |t' <<'EN|D_OF_FIL|
|00000780| 45 27 0a 58 2f 2f 24 24 | 20 6e 65 77 6d 61 74 2e |E'.X//$$| newmat.|
|00000790| 74 78 74 20 20 20 20 20 | 20 20 20 20 20 20 20 44 |txt | D|
|000007a0| 6f 63 75 6d 65 6e 74 61 | 74 69 6f 6e 20 66 69 6c |ocumenta|tion fil|
|000007b0| 65 0a 58 0a 58 0a 58 20 | 20 20 44 6f 63 75 6d 65 |e.X.X.X | Docume|
|000007c0| 6e 74 61 74 69 6f 6e 20 | 66 6f 72 20 6e 65 77 6d |ntation |for newm|
|000007d0| 61 74 30 33 2c 20 61 6e | 20 65 78 70 65 72 69 6d |at03, an| experim|
|000007e0| 65 6e 74 61 6c 20 6d 61 | 74 72 69 78 20 70 61 63 |ental ma|trix pac|
|000007f0| 6b 61 67 65 20 69 6e 20 | 43 2b 2b 2e 0a 58 20 20 |kage in |C++..X |
|00000800| 20 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d | =======|========|
|00000810| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |========|========|
|00000820| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |========|========|
|00000830| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |========|========|
|00000840| 3d 3d 3d 0a 58 0a 58 0a | 58 4d 41 54 52 49 58 20 |===.X.X.|XMATRIX |
|00000850| 50 41 43 4b 41 47 45 20 | 20 20 20 20 20 20 20 20 |PACKAGE | |
|00000860| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000870| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000880| 20 20 32 35 20 4e 6f 76 | 65 6d 62 65 72 2c 20 31 | 25 Nov|ember, 1|
|00000890| 39 39 31 0a 58 0a 58 43 | 6f 70 79 72 69 67 68 74 |991.X.XC|opyright|
|000008a0| 20 28 43 29 20 31 39 39 | 31 3a 20 52 20 42 20 44 | (C) 199|1: R B D|
|000008b0| 61 76 69 65 73 20 61 6e | 64 20 44 53 49 52 0a 58 |avies an|d DSIR.X|
|000008c0| 0a 58 50 65 72 6d 69 73 | 73 69 6f 6e 20 69 73 20 |.XPermis|sion is |
|000008d0| 67 72 61 6e 74 65 64 20 | 74 6f 20 75 73 65 20 62 |granted |to use b|
|000008e0| 75 74 20 6e 6f 74 20 74 | 6f 20 73 65 6c 6c 2e 0a |ut not t|o sell..|
|000008f0| 58 0a 58 0a 58 43 6f 6e | 74 65 6e 74 73 0a 58 3d |X.X.XCon|tents.X=|
|00000900| 3d 3d 3d 3d 3d 3d 3d 0a | 58 0a 58 47 65 6e 65 72 |=======.|X.XGener|
|00000910| 61 6c 20 64 65 73 63 72 | 69 70 74 69 6f 6e 0a 58 |al descr|iption.X|
|00000920| 49 73 20 74 68 69 73 20 | 74 68 65 20 70 61 63 6b |Is this |the pack|
|00000930| 61 67 65 20 79 6f 75 20 | 6e 65 65 64 3f 0a 58 43 |age you |need?.XC|
|00000940| 68 61 6e 67 65 73 0a 58 | 57 68 65 72 65 20 79 6f |hanges.X|Where yo|
|00000950| 75 20 63 61 6e 20 67 65 | 74 20 61 20 63 6f 70 79 |u can ge|t a copy|
|00000960| 20 6f 66 20 74 68 69 73 | 20 70 61 63 6b 61 67 65 | of this| package|
|00000970| 0a 58 43 6f 6d 70 69 6c | 65 72 20 70 65 72 66 6f |.XCompil|er perfo|
|00000980| 72 6d 61 6e 63 65 0a 58 | 45 78 61 6d 70 6c 65 0a |rmance.X|Example.|
|00000990| 58 44 65 74 61 69 6c 65 | 64 20 64 6f 63 75 6d 65 |XDetaile|d docume|
|000009a0| 6e 74 61 74 69 6f 6e 0a | 58 20 20 20 43 75 73 74 |ntation.|X Cust|
|000009b0| 6f 6d 69 73 69 6e 67 0a | 58 20 20 20 43 6f 6e 73 |omising.|X Cons|
|000009c0| 74 72 75 63 74 6f 72 73 | 0a 58 20 20 20 45 6c 65 |tructors|.X Ele|
|000009d0| 6d 65 6e 74 73 20 6f 66 | 20 6d 61 74 72 69 63 65 |ments of| matrice|
|000009e0| 73 0a 58 20 20 20 4d 61 | 74 72 69 78 20 63 6f 70 |s.X Ma|trix cop|
|000009f0| 79 0a 58 20 20 20 55 6e | 61 72 79 20 6f 70 65 72 |y.X Un|ary oper|
|00000a00| 61 74 6f 72 73 0a 58 20 | 20 20 42 69 6e 61 72 79 |ators.X | Binary|
|00000a10| 20 6f 70 65 72 61 74 6f | 72 73 0a 58 20 20 20 43 | operato|rs.X C|
|00000a20| 6f 6d 62 69 6e 61 74 69 | 6f 6e 20 6f 66 20 61 20 |ombinati|on of a |
|00000a30| 6d 61 74 72 69 78 20 61 | 6e 64 20 73 63 61 6c 61 |matrix a|nd scala|
|00000a40| 72 0a 58 20 20 20 53 63 | 61 6c 61 72 20 66 75 6e |r.X Sc|alar fun|
|00000a50| 63 74 69 6f 6e 73 20 6f | 66 20 6d 61 74 72 69 63 |ctions o|f matric|
|00000a60| 65 73 0a 58 20 20 20 53 | 75 62 6d 61 74 72 69 78 |es.X S|ubmatrix|
|00000a70| 20 6f 70 65 72 61 74 69 | 6f 6e 73 0a 58 20 20 20 | operati|ons.X |
|00000a80| 43 68 61 6e 67 65 20 64 | 69 6d 65 6e 73 69 6f 6e |Change d|imension|
|00000a90| 73 0a 58 20 20 20 43 68 | 61 6e 67 65 20 74 79 70 |s.X Ch|ange typ|
|00000aa0| 65 0a 58 20 20 20 4d 75 | 6c 74 69 70 6c 65 20 6d |e.X Mu|ltiple m|
|00000ab0| 61 74 72 69 78 20 73 6f | 6c 76 65 0a 58 20 20 20 |atrix so|lve.X |
|00000ac0| 4d 65 6d 6f 72 79 20 6d | 61 6e 61 67 65 6d 65 6e |Memory m|anagemen|
|00000ad0| 74 0a 58 20 20 20 4f 75 | 74 70 75 74 0a 58 20 20 |t.X Ou|tput.X |
|00000ae0| 20 41 63 63 65 73 73 69 | 6e 67 20 6d 61 74 72 69 | Accessi|ng matri|
|00000af0| 63 65 73 20 6f 66 20 75 | 6e 73 70 65 63 69 66 69 |ces of u|nspecifi|
|00000b00| 65 64 20 74 79 70 65 0a | 58 20 20 20 43 68 6f 6c |ed type.|X Chol|
|00000b10| 65 73 6b 79 20 64 65 63 | 6f 6d 70 6f 73 69 74 69 |esky dec|ompositi|
|00000b20| 6f 6e 0a 58 20 20 20 48 | 6f 75 73 65 68 6f 6c 64 |on.X H|ousehold|
|00000b30| 65 72 20 74 72 69 61 6e | 67 75 6c 61 72 69 73 61 |er trian|gularisa|
|00000b40| 74 69 6f 6e 0a 58 20 20 | 20 53 69 6e 67 75 6c 61 |tion.X | Singula|
|00000b50| 72 20 56 61 6c 75 65 20 | 44 65 63 6f 6d 70 6f 73 |r Value |Decompos|
|00000b60| 69 74 69 6f 6e 0a 58 20 | 20 20 45 69 67 65 6e 76 |ition.X | Eigenv|
|00000b70| 61 6c 75 65 73 0a 58 20 | 20 20 53 6f 72 74 69 6e |alues.X | Sortin|
|00000b80| 67 0a 58 20 20 20 46 61 | 73 74 20 46 6f 75 72 69 |g.X Fa|st Fouri|
|00000b90| 65 72 20 54 72 61 6e 73 | 66 6f 72 6d 0a 58 20 20 |er Trans|form.X |
|00000ba0| 20 49 6e 74 65 72 66 61 | 63 65 20 74 6f 20 4e 75 | Interfa|ce to Nu|
|00000bb0| 6d 65 72 69 63 61 6c 20 | 52 65 63 69 70 65 73 20 |merical |Recipes |
|00000bc0| 69 6e 20 43 0a 58 4c 69 | 73 74 20 6f 66 20 66 69 |in C.XLi|st of fi|
|00000bd0| 6c 65 73 0a 58 4e 6f 74 | 65 73 20 6f 6e 20 74 68 |les.XNot|es on th|
|00000be0| 65 20 64 65 73 69 67 6e | 20 6f 66 20 74 68 65 20 |e design| of the |
|00000bf0| 70 61 63 6b 61 67 65 0a | 58 20 20 20 57 68 61 74 |package.|X What|
|00000c00| 20 74 68 69 73 20 69 73 | 20 70 61 63 6b 61 67 65 | this is| package|
|00000c10| 20 66 6f 72 0a 58 20 20 | 20 57 68 61 74 20 73 69 | for.X | What si|
|00000c20| 7a 65 20 6f 66 20 6d 61 | 74 72 69 63 65 73 3f 0a |ze of ma|trices?.|
|00000c30| 58 20 20 20 41 6c 6c 6f | 77 20 6d 61 74 72 69 78 |X Allo|w matrix|
|00000c40| 20 65 78 70 72 65 73 73 | 69 6f 6e 73 3f 0a 58 20 | express|ions?.X |
|00000c50| 20 20 57 68 69 63 68 20 | 6d 61 74 72 69 78 20 74 | Which |matrix t|
|00000c60| 79 70 65 73 3f 0a 58 20 | 20 20 57 68 61 74 20 65 |ypes?.X | What e|
|00000c70| 6c 65 6d 65 6e 74 20 74 | 79 70 65 73 3f 0a 58 20 |lement t|ypes?.X |
|00000c80| 20 20 4e 61 6d 69 6e 67 | 20 63 6f 6e 76 65 6e 74 | Naming| convent|
|00000c90| 69 6f 6e 0a 58 20 20 20 | 52 6f 77 20 61 6e 64 20 |ion.X |Row and |
|00000ca0| 43 6f 6c 75 6d 6e 20 69 | 6e 64 65 78 20 72 61 6e |Column i|ndex ran|
|00000cb0| 67 65 73 0a 58 20 20 20 | 53 74 72 75 63 74 75 72 |ges.X |Structur|
|00000cc0| 65 20 6f 66 20 6d 61 74 | 72 69 78 20 6f 62 6a 65 |e of mat|rix obje|
|00000cd0| 63 74 73 0a 58 20 20 20 | 44 61 74 61 20 73 74 6f |cts.X |Data sto|
|00000ce0| 72 61 67 65 20 2d 20 6f | 6e 65 20 62 6c 6f 63 6b |rage - o|ne block|
|00000cf0| 20 6f 72 20 73 65 76 65 | 72 61 6c 0a 58 20 20 20 | or seve|ral.X |
|00000d00| 44 61 74 61 20 73 74 6f | 72 61 67 65 20 2d 20 62 |Data sto|rage - b|
|00000d10| 79 20 72 6f 77 20 6f 72 | 20 62 79 20 63 6f 6c 75 |y row or| by colu|
|00000d20| 6d 6e 20 6f 72 20 6f 74 | 68 65 72 0a 58 20 20 20 |mn or ot|her.X |
|00000d30| 53 74 6f 72 61 67 65 20 | 6f 66 20 73 79 6d 6d 65 |Storage |of symme|
|00000d40| 74 72 69 63 20 6d 61 74 | 72 69 63 65 73 0a 58 20 |tric mat|rices.X |
|00000d50| 20 20 45 6c 65 6d 65 6e | 74 20 61 63 63 65 73 73 | Elemen|t access|
|00000d60| 20 2d 20 6d 65 74 68 6f | 64 20 61 6e 64 20 63 68 | - metho|d and ch|
|00000d70| 65 63 6b 69 6e 67 0a 58 | 20 20 20 55 73 65 20 69 |ecking.X| Use i|
|00000d80| 74 65 72 61 74 6f 72 73 | 3f 0a 58 20 20 20 4d 65 |terators|?.X Me|
|00000d90| 6d 6f 72 79 20 6d 61 6e | 61 67 65 6d 65 6e 74 20 |mory man|agement |
|00000da0| 2d 20 72 65 66 65 72 65 | 6e 63 65 20 63 6f 75 6e |- refere|nce coun|
|00000db0| 74 69 6e 67 20 6f 72 20 | 73 74 61 74 75 73 20 76 |ting or |status v|
|00000dc0| 61 72 69 61 62 6c 65 3f | 0a 58 20 20 20 45 76 61 |ariable?|.X Eva|
|00000dd0| 6c 75 61 74 69 6f 6e 20 | 6f 66 20 65 78 70 72 65 |luation |of expre|
|00000de0| 73 73 69 6f 6e 73 20 2d | 20 75 73 65 20 74 77 6f |ssions -| use two|
|00000df0| 20 73 74 61 67 65 20 6d | 65 74 68 6f 64 3f 0a 58 | stage m|ethod?.X|
|00000e00| 20 20 20 48 6f 77 20 74 | 6f 20 6f 76 65 72 63 6f | How t|o overco|
|00000e10| 6d 65 20 61 6e 20 65 78 | 70 6c 6f 73 69 6f 6e 20 |me an ex|plosion |
|00000e20| 69 6e 20 6e 75 6d 62 65 | 72 20 6f 66 20 6f 70 65 |in numbe|r of ope|
|00000e30| 72 61 74 69 6f 6e 73 0a | 58 20 20 20 55 73 69 6e |rations.|X Usin|
|00000e40| 67 20 63 6f 6e 73 74 0a | 58 20 20 20 41 20 63 61 |g const.|X A ca|
|00000e50| 6c 63 75 6c 75 73 20 6f | 66 20 6d 61 74 72 69 78 |lculus o|f matrix|
|00000e60| 20 74 79 70 65 73 0a 58 | 20 20 20 45 72 72 6f 72 | types.X| Error|
|00000e70| 20 68 61 6e 64 6c 69 6e | 67 0a 58 20 20 20 42 61 | handlin|g.X Ba|
|00000e80| 6e 64 20 61 6e 64 20 73 | 70 61 72 73 65 20 6d 61 |nd and s|parse ma|
|00000e90| 74 72 69 63 65 73 0a 58 | 50 72 6f 62 6c 65 6d 20 |trices.X|Problem |
|00000ea0| 72 65 70 6f 72 74 20 66 | 6f 72 6d 0a 58 0a 58 0a |report f|orm.X.X.|
|00000eb0| 58 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |X-------|--------|
|00000ec0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000ed0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000ee0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000ef0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 0a 58 0a 58 |--------|----.X.X|
|00000f00| 0a 58 47 65 6e 65 72 61 | 6c 20 64 65 73 63 72 69 |.XGenera|l descri|
|00000f10| 70 74 69 6f 6e 0a 58 3d | 3d 3d 3d 3d 3d 3d 3d 3d |ption.X=|========|
|00000f20| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 0a 58 0a 58 54 68 |========|==.X.XTh|
|00000f30| 65 20 70 61 63 6b 61 67 | 65 20 69 73 20 69 6e 74 |e packag|e is int|
|00000f40| 65 6e 74 65 64 20 66 6f | 72 20 73 63 69 65 6e 74 |ented fo|r scient|
|00000f50| 69 73 74 73 20 61 6e 64 | 20 65 6e 67 69 6e 65 65 |ists and| enginee|
|00000f60| 72 73 20 77 68 6f 20 6e | 65 65 64 20 74 6f 0a 58 |rs who n|eed to.X|
|00000f70| 6d 61 6e 69 70 75 6c 61 | 74 65 20 61 20 76 61 72 |manipula|te a var|
|00000f80| 69 65 74 79 20 6f 66 20 | 74 79 70 65 73 20 6f 66 |iety of |types of|
|00000f90| 20 6d 61 74 72 69 63 65 | 73 20 75 73 69 6e 67 20 | matrice|s using |
|00000fa0| 73 74 61 6e 64 61 72 64 | 20 6d 61 74 72 69 78 0a |standard| matrix.|
|00000fb0| 58 6f 70 65 72 61 74 69 | 6f 6e 73 2e 20 45 6d 70 |Xoperati|ons. Emp|
|00000fc0| 68 61 73 69 73 20 69 73 | 20 6f 6e 20 74 68 65 20 |hasis is| on the |
|00000fd0| 6b 69 6e 64 20 6f 66 20 | 6f 70 65 72 61 74 69 6f |kind of |operatio|
|00000fe0| 6e 73 20 6e 65 65 64 65 | 64 20 69 6e 20 73 74 61 |ns neede|d in sta|
|00000ff0| 74 69 73 74 69 63 61 6c | 0a 58 63 61 6c 63 75 6c |tistical|.Xcalcul|
|00001000| 61 74 69 6f 6e 73 20 73 | 75 63 68 20 61 73 20 6c |ations s|uch as l|
|00001010| 65 61 73 74 20 73 71 75 | 61 72 65 73 2c 20 6c 69 |east squ|ares, li|
|00001020| 6e 65 61 72 20 65 71 75 | 61 74 69 6f 6e 20 73 6f |near equ|ation so|
|00001030| 6c 76 65 20 61 6e 64 0a | 58 65 69 67 65 6e 76 61 |lve and.|Xeigenva|
|00001040| 6c 75 65 73 2e 0a 58 0a | 58 49 74 20 73 75 70 70 |lues..X.|XIt supp|
|00001050| 6f 72 74 73 20 6d 61 74 | 72 69 78 20 74 79 70 65 |orts mat|rix type|
|00001060| 73 0a 58 0a 58 20 20 20 | 20 4d 61 74 72 69 78 20 |s.X.X | Matrix |
|00001070| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001080| 20 20 20 20 20 20 28 72 | 65 63 74 61 6e 67 75 6c | (r|ectangul|
|00001090| 61 72 20 6d 61 74 72 69 | 78 29 0a 58 20 20 20 20 |ar matri|x).X |
|000010a0| 6e 72 69 63 4d 61 74 72 | 69 78 20 20 20 20 20 20 |nricMatr|ix |
|000010b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 28 76 61 | | (va|
|000010c0| 72 69 61 6e 74 20 6f 66 | 20 72 65 63 74 61 6e 67 |riant of| rectang|
|000010d0| 75 6c 61 72 20 6d 61 74 | 72 69 78 29 0a 58 20 20 |ular mat|rix).X |
|000010e0| 20 20 55 70 70 65 72 54 | 72 69 61 6e 67 75 6c 61 | UpperT|riangula|
|000010f0| 72 4d 61 74 72 69 78 0a | 58 20 20 20 20 4c 6f 77 |rMatrix.|X Low|
|00001100| 65 72 54 72 69 61 6e 67 | 75 6c 61 72 4d 61 74 72 |erTriang|ularMatr|
|00001110| 69 78 0a 58 20 20 20 20 | 44 69 61 67 6f 6e 61 6c |ix.X |Diagonal|
|00001120| 4d 61 74 72 69 78 0a 58 | 20 20 20 20 53 79 6d 6d |Matrix.X| Symm|
|00001130| 65 74 72 69 63 4d 61 74 | 72 69 78 0a 58 20 20 20 |etricMat|rix.X |
|00001140| 20 52 6f 77 56 65 63 74 | 6f 72 20 20 20 20 20 20 | RowVect|or |
|00001150| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 28 64 | | (d|
|00001160| 65 72 69 76 65 64 20 66 | 72 6f 6d 20 4d 61 74 72 |erived f|rom Matr|
|00001170| 69 78 29 0a 58 20 20 20 | 20 43 6f 6c 75 6d 6e 56 |ix).X | ColumnV|
|00001180| 65 63 74 6f 72 20 20 20 | 20 20 20 20 20 20 20 20 |ector | |
|00001190| 20 20 20 20 20 20 28 64 | 65 72 69 76 65 64 20 66 | (d|erived f|
|000011a0| 72 6f 6d 20 4d 61 74 72 | 69 78 29 2e 0a 58 0a 58 |rom Matr|ix)..X.X|
|000011b0| 4f 6e 6c 79 20 6f 6e 65 | 20 65 6c 65 6d 65 6e 74 |Only one| element|
|000011c0| 20 74 79 70 65 20 28 66 | 6c 6f 61 74 20 6f 72 20 | type (f|loat or |
|000011d0| 64 6f 75 62 6c 65 29 20 | 69 73 20 73 75 70 70 6f |double) |is suppo|
|000011e0| 72 74 65 64 2e 0a 58 0a | 58 54 68 65 20 70 61 63 |rted..X.|XThe pac|
|000011f0| 6b 61 67 65 20 69 6e 63 | 6c 75 64 65 73 20 74 68 |kage inc|ludes th|
|00001200| 65 20 6f 70 65 72 61 74 | 69 6f 6e 73 20 2a 2c 20 |e operat|ions *, |
|00001210| 2b 2c 20 2d 2c 20 69 6e | 76 65 72 73 65 2c 20 74 |+, -, in|verse, t|
|00001220| 72 61 6e 73 70 6f 73 65 | 2c 0a 58 63 6f 6e 76 65 |ranspose|,.Xconve|
|00001230| 72 73 69 6f 6e 20 62 65 | 74 77 65 65 6e 20 74 79 |rsion be|tween ty|
|00001240| 70 65 73 2c 20 73 75 62 | 6d 61 74 72 69 78 2c 20 |pes, sub|matrix, |
|00001250| 64 65 74 65 72 6d 69 6e | 61 6e 74 2c 20 43 68 6f |determin|ant, Cho|
|00001260| 6c 65 73 6b 79 0a 58 64 | 65 63 6f 6d 70 6f 73 69 |lesky.Xd|ecomposi|
|00001270| 74 69 6f 6e 2c 20 48 6f | 75 73 65 68 6f 6c 64 65 |tion, Ho|useholde|
|00001280| 72 20 74 72 69 61 6e 67 | 75 6c 61 72 69 73 61 74 |r triang|ularisat|
|00001290| 69 6f 6e 2c 20 73 69 6e | 67 75 6c 61 72 20 76 61 |ion, sin|gular va|
|000012a0| 6c 75 65 0a 58 64 65 63 | 6f 6d 70 6f 73 69 74 69 |lue.Xdec|ompositi|
|000012b0| 6f 6e 2c 20 65 69 67 65 | 6e 76 61 6c 75 65 73 20 |on, eige|nvalues |
|000012c0| 6f 66 20 61 20 73 79 6d | 6d 65 74 72 69 63 20 6d |of a sym|metric m|
|000012d0| 61 74 72 69 78 2c 20 73 | 6f 72 74 69 6e 67 2c 20 |atrix, s|orting, |
|000012e0| 66 61 73 74 20 66 6f 75 | 72 69 65 72 0a 58 74 72 |fast fou|rier.Xtr|
|000012f0| 61 6e 73 66 6f 72 6d 2c | 20 70 72 69 6e 74 69 6e |ansform,| printin|
|00001300| 67 20 61 6e 64 20 61 6e | 20 69 6e 74 65 72 66 61 |g and an| interfa|
|00001310| 63 65 20 77 69 74 68 20 | 22 4e 75 6d 65 72 69 63 |ce with |"Numeric|
|00001320| 61 6c 20 52 65 63 69 70 | 65 73 20 69 6e 20 43 22 |al Recip|es in C"|
|00001330| 2e 0a 58 0a 58 49 74 20 | 69 73 20 69 6e 74 65 6e |..X.XIt |is inten|
|00001340| 64 65 64 20 66 6f 72 20 | 6d 61 74 72 69 63 65 73 |ded for |matrices|
|00001350| 20 69 6e 20 74 68 65 20 | 72 61 6e 67 65 20 34 20 | in the |range 4 |
|00001360| 78 20 34 20 74 6f 20 61 | 62 6f 75 74 20 39 30 20 |x 4 to a|bout 90 |
|00001370| 78 20 39 30 20 28 31 32 | 35 20 78 0a 58 31 32 35 |x 90 (12|5 x.X125|
|00001380| 20 66 6f 72 20 74 72 69 | 61 6e 67 75 6c 61 72 20 | for tri|angular |
|00001390| 6d 61 74 72 69 63 65 73 | 29 2e 20 54 68 65 20 75 |matrices|). The u|
|000013a0| 70 70 65 72 20 6c 69 6d | 69 74 20 69 73 20 69 6d |pper lim|it is im|
|000013b0| 70 6f 73 65 64 20 62 79 | 20 74 68 65 20 6d 61 78 |posed by| the max|
|000013c0| 69 6d 75 6d 0a 58 6e 75 | 6d 62 65 72 20 6f 66 20 |imum.Xnu|mber of |
|000013d0| 65 6c 65 6d 65 6e 74 73 | 20 74 68 61 74 20 63 61 |elements| that ca|
|000013e0| 6e 20 62 65 20 63 6f 6e | 74 61 69 6e 65 64 20 69 |n be con|tained i|
|000013f0| 6e 20 61 20 73 69 6e 67 | 6c 65 20 61 72 72 61 79 |n a sing|le array|
|00001400| 20 28 38 31 39 32 20 64 | 6f 75 62 6c 65 73 0a 58 | (8192 d|oubles.X|
|00001410| 69 6e 20 73 6f 6d 65 20 | 6d 61 63 68 69 6e 65 73 |in some |machines|
|00001420| 29 2e 0a 58 0a 58 41 20 | 74 77 6f 2d 73 74 61 67 |)..X.XA |two-stag|
|00001430| 65 20 61 70 70 72 6f 61 | 63 68 20 74 6f 20 65 76 |e approa|ch to ev|
|00001440| 61 6c 75 61 74 69 6e 67 | 20 6d 61 74 72 69 78 20 |aluating| matrix |
|00001450| 65 78 70 72 65 73 73 69 | 6f 6e 73 20 69 73 20 75 |expressi|ons is u|
|00001460| 73 65 64 20 74 6f 20 69 | 6d 70 72 6f 76 65 0a 58 |sed to i|mprove.X|
|00001470| 65 66 66 69 63 69 65 6e | 63 79 20 61 6e 64 20 72 |efficien|cy and r|
|00001480| 65 64 75 63 65 20 75 73 | 65 20 6f 66 20 74 65 6d |educe us|e of tem|
|00001490| 70 6f 72 61 72 79 20 73 | 74 6f 72 61 67 65 2e 0a |porary s|torage..|
|000014a0| 58 0a 58 54 68 65 20 70 | 61 63 6b 61 67 65 20 69 |X.XThe p|ackage i|
|000014b0| 73 20 64 65 73 69 67 6e | 65 64 20 66 6f 72 20 76 |s design|ed for v|
|000014c0| 65 72 73 69 6f 6e 20 32 | 20 6f 66 20 43 2b 2b 2e |ersion 2| of C++.|
|000014d0| 20 49 74 20 77 6f 72 6b | 73 20 77 69 74 68 20 54 | It work|s with T|
|000014e0| 75 72 62 6f 20 43 2b 2b | 2c 0a 58 42 6f 72 6c 61 |urbo C++|,.XBorla|
|000014f0| 6e 64 20 43 2b 2b 2c 20 | 47 6c 6f 63 6b 65 6e 73 |nd C++, |Glockens|
|00001500| 70 69 65 6c 20 43 2b 2b | 20 28 32 2e 30 30 61 29 |piel C++| (2.00a)|
|00001510| 20 6f 6e 20 61 20 50 43 | 20 61 6e 64 20 41 54 26 | on a PC| and AT&|
|00001520| 54 20 43 2b 2b 20 28 32 | 2e 30 29 20 61 6e 64 20 |T C++ (2|.0) and |
|00001530| 47 6e 75 0a 58 43 2b 2b | 20 6f 6e 20 61 20 53 75 |Gnu.XC++| on a Su|
|00001540| 6e 2e 20 49 74 20 77 6f | 72 6b 73 20 77 69 74 68 |n. It wo|rks with|
|00001550| 20 73 6f 6d 65 20 70 72 | 6f 62 6c 65 6d 73 20 77 | some pr|oblems w|
|00001560| 69 74 68 20 5a 6f 72 74 | 65 63 68 20 43 2b 2b 20 |ith Zort|ech C++ |
|00001570| 28 76 65 72 73 69 6f 6e | 20 32 29 2e 0a 58 0a 58 |(version| 2)..X.X|
|00001580| 0a 58 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |.X------|--------|
|00001590| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000015a0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000015b0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000015c0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 0a 58 0a |--------|-----.X.|
|000015d0| 58 0a 58 49 73 20 74 68 | 69 73 20 74 68 65 20 70 |X.XIs th|is the p|
|000015e0| 61 63 6b 61 67 65 20 79 | 6f 75 20 6e 65 65 64 3f |ackage y|ou need?|
|000015f0| 0a 58 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |.X======|========|
|00001600| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 0a |========|=======.|
|00001610| 58 0a 58 44 6f 20 79 6f | 75 0a 58 0a 58 31 2e 20 |X.XDo yo|u.X.X1. |
|00001620| 20 20 6e 65 65 64 20 6d | 61 74 72 69 78 20 6f 70 | need m|atrix op|
|00001630| 65 72 61 74 6f 72 73 20 | 73 75 63 68 20 61 73 20 |erators |such as |
|00001640| 2a 20 61 6e 64 20 2b 20 | 64 65 66 69 6e 65 64 20 |* and + |defined |
|00001650| 61 73 20 6f 70 65 72 61 | 74 6f 72 73 20 73 6f 20 |as opera|tors so |
|00001660| 79 6f 75 0a 58 20 20 20 | 20 20 63 61 6e 20 77 72 |you.X | can wr|
|00001670| 69 74 65 20 74 68 69 6e | 67 73 20 6c 69 6b 65 0a |ite thin|gs like.|
|00001680| 58 0a 58 20 20 20 20 20 | 20 20 20 58 20 20 3d 20 |X.X | X = |
|00001690| 41 20 2a 20 28 42 20 2b | 20 43 29 3b 0a 58 0a 58 |A * (B +| C);.X.X|
|000016a0| 32 2e 20 20 20 6e 65 65 | 64 20 61 20 76 61 72 69 |2. nee|d a vari|
|000016b0| 65 74 79 20 6f 66 20 74 | 79 70 65 73 20 6f 66 20 |ety of t|ypes of |
|000016c0| 6d 61 74 72 69 63 65 73 | 0a 58 0a 58 33 2e 20 20 |matrices|.X.X3. |
|000016d0| 20 6e 65 65 64 20 6f 6e | 6c 79 20 6f 6e 65 20 65 | need on|ly one e|
|000016e0| 6c 65 6d 65 6e 74 20 74 | 79 70 65 20 28 66 6c 6f |lement t|ype (flo|
|000016f0| 61 74 20 6f 72 20 64 6f | 75 62 6c 65 29 0a 58 0a |at or do|uble).X.|
|00001700| 58 34 2e 20 20 20 77 6f | 72 6b 20 77 69 74 68 20 |X4. wo|rk with |
|00001710| 6d 61 74 72 69 63 65 73 | 20 69 6e 20 74 68 65 20 |matrices| in the |
|00001720| 72 61 6e 67 65 20 34 78 | 34 20 74 6f 20 39 30 78 |range 4x|4 to 90x|
|00001730| 39 30 0a 58 0a 58 35 2e | 20 20 20 74 6f 6c 65 72 |90.X.X5.| toler|
|00001740| 61 74 65 20 61 20 6c 61 | 72 67 65 20 61 6e 64 20 |ate a la|rge and |
|00001750| 63 6f 6d 70 6c 65 78 20 | 70 61 63 6b 61 67 65 0a |complex |package.|
|00001760| 58 0a 58 0a 58 54 68 65 | 6e 20 6d 61 79 62 65 20 |X.X.XThe|n maybe |
|00001770| 74 68 69 73 20 69 73 20 | 74 68 65 20 72 69 67 68 |this is |the righ|
|00001780| 74 20 70 61 63 6b 61 67 | 65 20 66 6f 72 20 79 6f |t packag|e for yo|
|00001790| 75 2e 20 0a 58 0a 58 49 | 66 20 79 6f 75 20 64 6f |u. .X.XI|f you do|
|000017a0| 6e 27 74 20 6e 65 65 64 | 20 28 31 29 20 74 68 65 |n't need| (1) the|
|000017b0| 6e 20 74 68 65 72 65 20 | 6d 61 79 20 62 65 20 62 |n there |may be b|
|000017c0| 65 74 74 65 72 20 6f 70 | 74 69 6f 6e 73 2e 20 4c |etter op|tions. L|
|000017d0| 69 6b 65 77 69 73 65 20 | 69 66 20 79 6f 75 0a 58 |ikewise |if you.X|
|000017e0| 64 6f 6e 27 74 20 6e 65 | 65 64 20 28 32 29 20 74 |don't ne|ed (2) t|
|000017f0| 68 65 72 65 20 6d 61 79 | 20 62 65 20 62 65 74 74 |here may| be bett|
|00001800| 65 72 20 6f 70 74 69 6f | 6e 73 2e 20 49 66 20 79 |er optio|ns. If y|
|00001810| 6f 75 20 72 65 71 75 69 | 72 65 20 22 6e 6f 74 20 |ou requi|re "not |
|00001820| 28 35 29 22 0a 58 74 68 | 65 6e 20 74 68 69 73 20 |(5)".Xth|en this |
|00001830| 69 73 20 6e 6f 74 20 74 | 68 65 20 70 61 63 6b 61 |is not t|he packa|
|00001840| 67 65 20 66 6f 72 20 79 | 6f 75 2e 0a 58 0a 58 0a |ge for y|ou..X.X.|
|00001850| 58 49 66 20 79 6f 75 20 | 6e 65 65 64 20 28 32 29 |XIf you |need (2)|
|00001860| 20 61 6e 64 20 22 6e 6f | 74 20 28 33 29 22 20 61 | and "no|t (3)" a|
|00001870| 6e 64 20 68 61 76 65 20 | 73 6f 6d 65 20 73 70 61 |nd have |some spa|
|00001880| 72 65 20 6d 6f 6e 65 79 | 2c 20 74 68 65 6e 20 6d |re money|, then m|
|00001890| 61 79 62 65 20 79 6f 75 | 0a 58 73 68 6f 75 6c 64 |aybe you|.Xshould|
|000018a0| 20 6c 6f 6f 6b 20 61 74 | 20 4d 2b 2b 20 66 72 6f | look at| M++ fro|
|000018b0| 6d 20 44 79 61 64 20 6f | 72 20 74 68 65 20 52 6f |m Dyad o|r the Ro|
|000018c0| 67 75 65 20 57 61 76 65 | 20 6d 61 74 72 69 78 20 |gue Wave| matrix |
|000018d0| 70 61 63 6b 61 67 65 2e | 0a 58 0a 58 0a 58 2d 2d |package.|.X.X.X--|
|000018e0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000018f0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001900| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001910| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001920| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 0a 58 0a 58 0a 58 43 |--------|-.X.X.XC|
|00001930| 68 61 6e 67 65 73 0a 58 | 3d 3d 3d 3d 3d 3d 3d 0a |hanges.X|=======.|
|00001940| 58 0a 58 4e 65 77 6d 61 | 74 30 33 20 2d 20 4e 6f |X.XNewma|t03 - No|
|00001950| 76 65 6d 62 65 72 20 31 | 39 39 31 3a 0a 58 0a 58 |vember 1|991:.X.X|
|00001960| 43 6f 6c 20 61 6e 64 20 | 43 6f 6c 73 20 62 65 63 |Col and |Cols bec|
|00001970| 6f 6d 65 20 43 6f 6c 75 | 6d 6e 20 61 6e 64 20 43 |ome Colu|mn and C|
|00001980| 6f 6c 75 6d 6e 73 2e 20 | 41 64 64 65 64 20 53 6f |olumns. |Added So|
|00001990| 72 74 2c 20 53 56 44 2c | 20 4a 61 63 6f 62 69 2c |rt, SVD,| Jacobi,|
|000019a0| 0a 58 45 69 67 65 6e 76 | 61 6c 75 65 73 2c 20 46 |.XEigenv|alues, F|
|000019b0| 46 54 2c 20 72 65 61 6c | 20 63 6f 6e 76 65 72 73 |FT, real| convers|
|000019c0| 69 6f 6e 20 6f 66 20 31 | 78 31 20 6d 61 74 72 69 |ion of 1|x1 matri|
|000019d0| 78 2c 20 22 4e 75 6d 65 | 72 69 63 61 6c 20 52 65 |x, "Nume|rical Re|
|000019e0| 63 69 70 65 73 20 69 6e | 0a 58 43 22 20 69 6e 74 |cipes in|.XC" int|
|000019f0| 65 72 66 61 63 65 2c 20 | 6f 75 74 70 75 74 20 6f |erface, |output o|
|00001a00| 70 65 72 61 74 69 6f 6e | 73 2c 20 76 61 72 69 6f |peration|s, vario|
|00001a10| 75 73 20 73 63 61 6c 61 | 72 20 66 75 6e 63 74 69 |us scala|r functi|
|00001a20| 6f 6e 73 2e 20 49 6d 70 | 72 6f 76 65 64 0a 58 72 |ons. Imp|roved.Xr|
|00001a30| 65 74 75 72 6e 20 66 72 | 6f 6d 20 66 75 6e 63 74 |eturn fr|om funct|
|00001a40| 69 6f 6e 73 2e 20 52 65 | 6f 72 67 61 6e 69 73 65 |ions. Re|organise|
|00001a50| 64 20 73 65 74 74 69 6e | 67 20 6f 70 74 69 6f 6e |d settin|g option|
|00001a60| 73 20 69 6e 20 22 69 6e | 63 6c 75 64 65 2e 68 78 |s in "in|clude.hx|
|00001a70| 78 22 2e 0a 58 0a 58 0a | 58 4e 65 77 6d 61 74 30 |x"..X.X.|XNewmat0|
|00001a80| 32 20 2d 20 4a 75 6c 79 | 20 31 39 39 31 3a 0a 58 |2 - July| 1991:.X|
|00001a90| 0a 58 56 65 72 73 69 6f | 6e 20 77 69 74 68 20 6d |.XVersio|n with m|
|00001aa0| 61 74 72 69 78 20 72 6f | 77 2f 63 6f 6c 75 6d 6e |atrix ro|w/column|
|00001ab0| 20 6f 70 65 72 61 74 69 | 6f 6e 73 20 61 6e 64 20 | operati|ons and |
|00001ac0| 6e 75 6d 65 72 6f 75 73 | 20 61 64 64 69 74 69 6f |numerous| additio|
|00001ad0| 6e 61 6c 0a 58 66 75 6e | 63 74 69 6f 6e 73 2e 0a |nal.Xfun|ctions..|
|00001ae0| 58 0a 58 0a 58 4d 61 74 | 72 69 78 20 2d 20 4f 63 |X.X.XMat|rix - Oc|
|00001af0| 74 6f 62 65 72 20 31 39 | 39 30 3a 0a 58 0a 58 45 |tober 19|90:.X.XE|
|00001b00| 61 72 6c 79 20 76 65 72 | 73 69 6f 6e 20 6f 66 20 |arly ver|sion of |
|00001b10| 70 61 63 6b 61 67 65 2e | 0a 58 0a 58 0a 58 2d 2d |package.|.X.X.X--|
|00001b20| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001b30| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001b40| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001b50| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001b60| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 0a 58 0a 58 0a 58 48 |--------|-.X.X.XH|
|00001b70| 6f 77 20 74 6f 20 67 65 | 74 20 61 20 63 6f 70 79 |ow to ge|t a copy|
|00001b80| 20 6f 66 20 74 68 69 73 | 20 70 61 63 6b 61 67 65 | of this| package|
|00001b90| 0a 58 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |.X======|========|
|00001ba0| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |========|========|
|00001bb0| 3d 3d 3d 0a 58 0a 58 49 | 20 61 6d 20 70 75 74 74 |===.X.XI| am putt|
|00001bc0| 69 6e 67 20 63 6f 70 69 | 65 73 20 6f 6e 20 43 6f |ing copi|es on Co|
|00001bd0| 6d 70 75 73 65 72 76 65 | 20 28 42 6f 72 6c 61 6e |mpuserve| (Borlan|
|00001be0| 64 20 6c 69 62 72 61 72 | 79 2c 20 7a 69 70 20 66 |d librar|y, zip f|
|00001bf0| 6f 72 6d 61 74 29 2c 0a | 58 53 49 4d 54 45 4c 32 |ormat),.|XSIMTEL2|
|00001c00| 30 20 28 4d 73 44 6f 73 | 20 6c 69 62 72 61 72 79 |0 (MsDos| library|
|00001c10| 2c 20 7a 69 70 20 66 6f | 72 6d 61 74 29 2c 20 63 |, zip fo|rmat), c|
|00001c20| 6f 6d 70 2e 73 6f 75 72 | 63 65 73 2e 6d 69 73 63 |omp.sour|ces.misc|
|00001c30| 20 6f 6e 20 49 6e 74 65 | 72 6e 65 74 0a 58 28 73 | on Inte|rnet.X(s|
|00001c40| 68 61 72 20 66 6f 72 6d | 61 74 29 2c 20 61 6e 64 |har form|at), and|
|00001c50| 20 6f 6e 20 74 68 65 20 | 4d 73 44 6f 73 20 70 72 | on the |MsDos pr|
|00001c60| 6f 67 72 61 6d 20 6c 69 | 62 72 61 72 79 20 61 74 |ogram li|brary at|
|00001c70| 20 56 69 63 74 6f 72 69 | 61 20 55 6e 69 76 65 72 | Victori|a Univer|
|00001c80| 73 69 74 79 2c 0a 58 57 | 65 6c 6c 69 6e 67 74 6f |sity,.XW|ellingto|
|00001c90| 6e 2e 0a 58 0a 58 0a 58 | 2d 2d 2d 2d 2d 2d 2d 2d |n..X.X.X|--------|
|00001ca0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001cb0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001cc0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001cd0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00001ce0| 2d 2d 2d 0a 58 0a 58 0a | 58 43 6f 6d 70 69 6c 65 |---.X.X.|XCompile|
|00001cf0| 72 20 70 65 72 66 6f 72 | 6d 61 6e 63 65 0a 58 3d |r perfor|mance.X=|
|00001d00| 3d 3d 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |========|========|
|00001d10| 3d 3d 3d 0a 58 0a 58 49 | 20 68 61 76 65 20 74 65 |===.X.XI| have te|
|00001d20| 73 74 65 64 20 74 68 69 | 73 20 70 61 63 6b 61 67 |sted thi|s packag|
|00001d30| 65 20 6f 6e 20 61 20 6e | 75 6d 62 65 72 20 6f 66 |e on a n|umber of|
|00001d40| 20 63 6f 6d 70 69 6c 65 | 72 73 2e 20 48 65 72 65 | compile|rs. Here|
|00001d50| 20 61 72 65 20 74 68 65 | 0a 58 6c 65 76 65 6c 73 | are the|.Xlevels|
|00001d60| 20 6f 66 20 73 75 63 63 | 65 73 73 20 77 69 74 68 | of succ|ess with|
|00001d70| 20 74 68 69 73 20 70 61 | 63 6b 61 67 65 2e 20 49 | this pa|ckage. I|
|00001d80| 6e 20 6d 6f 73 74 20 63 | 61 73 65 73 20 49 20 68 |n most c|ases I h|
|00001d90| 61 76 65 20 63 68 6f 73 | 65 6e 20 63 6f 64 65 0a |ave chos|en code.|
|00001da0| 58 74 68 61 74 20 77 6f | 72 6b 73 20 75 6e 64 65 |Xthat wo|rks unde|
|00001db0| 72 20 61 6c 6c 20 74 68 | 65 20 63 6f 6d 70 69 6c |r all th|e compil|
|00001dc0| 65 72 73 20 49 20 68 61 | 76 65 20 61 63 63 65 73 |ers I ha|ve acces|
|00001dd0| 73 20 74 6f 2c 20 62 75 | 74 20 49 20 68 61 76 65 |s to, bu|t I have|
|00001de0| 20 68 61 64 20 74 6f 0a | 58 69 6e 63 6c 75 64 65 | had to.|Xinclude|
|00001df0| 20 73 6f 6d 65 20 73 70 | 65 63 69 66 69 63 20 77 | some sp|ecific w|
|00001e00| 6f 72 6b 2d 61 72 6f 75 | 6e 64 73 20 66 6f 72 20 |ork-arou|nds for |
|00001e10| 73 6f 6d 65 20 63 6f 6d | 70 69 6c 65 72 73 2e 20 |some com|pilers. |
|00001e20| 46 6f 72 20 74 68 65 20 | 4d 73 44 6f 73 0a 58 76 |For the |MsDos.Xv|
|00001e30| 65 72 73 69 6f 6e 73 2c | 20 49 20 61 6d 20 75 73 |ersions,| I am us|
|00001e40| 69 6e 67 20 61 20 33 38 | 36 2f 33 38 37 73 78 20 |ing a 38|6/387sx |
|00001e50| 63 6f 6d 70 75 74 65 72 | 20 72 75 6e 6e 69 6e 67 |computer| running|
|00001e60| 20 4d 73 44 6f 73 20 35 | 2c 20 65 78 63 65 70 74 | MsDos 5|, except|
|00001e70| 20 74 68 61 74 0a 58 54 | 75 72 62 6f 20 69 73 20 | that.XT|urbo is |
|00001e80| 6f 6e 20 61 6e 20 6f 6c | 64 20 58 54 2e 20 54 68 |on an ol|d XT. Th|
|00001e90| 65 20 75 6e 69 78 20 76 | 65 72 73 69 6f 6e 73 20 |e unix v|ersions |
|00001ea0| 61 72 65 20 6f 6e 20 61 | 20 53 75 6e 20 53 70 61 |are on a| Sun Spa|
|00001eb0| 72 63 20 73 74 61 74 69 | 6f 6e 2e 0a 58 0a 58 41 |rc stati|on..X.XA|
|00001ec0| 20 73 65 72 69 65 73 20 | 6f 66 20 23 64 65 66 69 | series |of #defi|
|00001ed0| 6e 65 73 20 61 74 20 74 | 68 65 20 62 65 67 69 6e |nes at t|he begin|
|00001ee0| 6e 69 6e 67 20 6f 66 20 | 22 69 6e 63 6c 75 64 65 |ning of |"include|
|00001ef0| 2e 68 78 78 22 20 63 75 | 73 74 6f 6d 69 73 65 73 |.hxx" cu|stomises|
|00001f00| 20 74 68 65 0a 58 70 61 | 63 6b 61 67 65 20 66 6f | the.Xpa|ckage fo|
|00001f10| 72 20 74 68 65 20 63 6f | 6d 70 69 6c 65 72 20 79 |r the co|mpiler y|
|00001f20| 6f 75 20 61 72 65 20 75 | 73 69 6e 67 2e 20 54 75 |ou are u|sing. Tu|
|00001f30| 72 62 6f 2c 20 42 6f 72 | 6c 61 6e 64 20 61 6e 64 |rbo, Bor|land and|
|00001f40| 20 5a 6f 72 74 65 63 68 | 20 61 72 65 0a 58 72 65 | Zortech| are.Xre|
|00001f50| 63 6f 67 6e 69 73 65 64 | 20 61 75 74 6f 6d 61 74 |cognised| automat|
|00001f60| 69 63 61 6c 6c 79 2c 20 | 6f 74 68 65 72 77 69 73 |ically, |otherwis|
|00001f70| 65 20 79 6f 75 20 68 61 | 76 65 20 74 6f 20 73 65 |e you ha|ve to se|
|00001f80| 74 20 74 68 65 20 61 70 | 70 72 6f 70 72 69 61 74 |t the ap|propriat|
|00001f90| 65 0a 58 23 64 65 66 69 | 6e 65 20 73 74 61 74 65 |e.X#defi|ne state|
|00001fa0| 6d 65 6e 74 2e 0a 58 0a | 58 54 68 65 20 63 6f 6d |ment..X.|XThe com|
|00001fb0| 70 69 6c 65 72 73 20 61 | 72 65 20 6c 6f 6f 6b 69 |pilers a|re looki|
|00001fc0| 6e 67 20 61 20 62 69 74 | 20 6f 6c 64 20 6e 6f 77 |ng a bit| old now|
|00001fd0| 2e 20 49 20 64 6f 20 69 | 6e 74 65 6e 64 20 74 6f |. I do i|ntend to|
|00001fe0| 20 74 65 73 74 20 74 68 | 65 20 70 61 63 6b 61 67 | test th|e packag|
|00001ff0| 65 0a 58 61 67 61 69 6e | 73 74 20 6e 65 77 65 72 |e.Xagain|st newer|
|00002000| 20 76 65 72 73 69 6f 6e | 73 20 61 73 20 74 68 65 | version|s as the|
|00002010| 79 20 62 65 63 6f 6d 65 | 20 61 76 61 69 6c 61 62 |y become| availab|
|00002020| 6c 65 2e 0a 58 0a 58 42 | 6f 72 6c 61 6e 64 20 43 |le..X.XB|orland C|
|00002030| 2b 2b 20 32 2e 30 3a 20 | 52 65 63 65 6e 74 6c 79 |++ 2.0: |Recently|
|00002040| 2c 20 74 68 69 73 20 68 | 61 73 20 62 65 65 6e 20 |, this h|as been |
|00002050| 6d 79 20 6d 61 69 6e 20 | 64 65 76 65 6c 6f 70 6d |my main |developm|
|00002060| 65 6e 74 20 70 6c 61 74 | 66 6f 72 6d 2c 0a 58 73 |ent plat|form,.Xs|
|00002070| 6f 20 6e 61 74 75 72 61 | 6c 6c 79 20 61 6c 6d 6f |o natura|lly almo|
|00002080| 73 74 20 65 76 65 72 79 | 74 68 69 6e 67 20 77 6f |st every|thing wo|
|00002090| 72 6b 73 20 77 69 74 68 | 20 74 68 69 73 20 63 6f |rks with| this co|
|000020a0| 6d 70 69 6c 65 72 2e 20 | 54 68 65 20 6c 69 62 72 |mpiler. |The libr|
|000020b0| 61 72 79 0a 58 6d 61 6e | 61 67 65 72 20 22 74 6c |ary.Xman|ager "tl|
|000020c0| 69 62 22 20 66 61 69 6c | 73 20 62 75 74 20 79 6f |ib" fail|s but yo|
|000020d0| 75 20 63 61 6e 20 75 73 | 65 20 22 7a 6f 72 6c 69 |u can us|e "zorli|
|000020e0| 62 22 20 66 72 6f 6d 20 | 5a 6f 72 74 65 63 68 20 |b" from |Zortech |
|000020f0| 69 6e 73 74 65 61 64 2e | 0a 58 53 6f 6d 65 74 69 |instead.|.XSometi|
|00002100| 6d 65 73 20 42 6f 72 6c | 61 6e 64 20 63 72 61 73 |mes Borl|and cras|
|00002110| 68 65 73 20 64 75 72 69 | 6e 67 20 61 20 63 6f 6d |hes duri|ng a com|
|00002120| 70 69 6c 65 72 20 6f 72 | 20 6d 69 73 2d 63 6f 6d |piler or| mis-com|
|00002130| 70 69 6c 65 73 2e 20 59 | 6f 75 20 6a 75 73 74 0a |piles. Y|ou just.|
|00002140| 58 68 61 76 65 20 74 6f | 20 72 65 62 6f 6f 74 20 |Xhave to| reboot |
|00002150| 61 6e 64 20 63 6f 6e 74 | 69 6e 75 65 20 74 68 65 |and cont|inue the|
|00002160| 20 63 6f 6d 70 69 6c 65 | 2e 0a 58 0a 58 54 75 72 | compile|..X.XTur|
|00002170| 62 6f 20 43 2b 2b 20 28 | 3f 20 76 65 72 73 69 6f |bo C++ (|? versio|
|00002180| 6e 29 3a 20 41 6c 6d 6f | 73 74 20 77 6f 72 6b 73 |n): Almo|st works|
|00002190| 20 4f 4b 2e 20 4d 79 20 | 72 61 74 68 65 72 20 65 | OK. My |rather e|
|000021a0| 6c 64 65 72 6c 79 20 76 | 65 72 73 69 6f 6e 20 64 |lderly v|ersion d|
|000021b0| 6f 65 73 0a 58 73 68 6f | 77 20 61 20 70 72 6f 62 |oes.Xsho|w a prob|
|000021c0| 6c 65 6d 2e 20 50 72 6f | 62 61 62 6c 79 20 6e 6f |lem. Pro|bably no|
|000021d0| 74 20 77 6f 72 74 68 20 | 74 72 61 63 6b 69 6e 67 |t worth |tracking|
|000021e0| 20 64 6f 77 6e 20 2d 20 | 62 75 79 20 61 20 6e 65 | down - |buy a ne|
|000021f0| 77 65 72 20 76 65 72 73 | 69 6f 6e 2e 0a 58 48 61 |wer vers|ion..XHa|
|00002200| 76 65 6e 27 74 20 74 72 | 69 65 64 20 74 68 65 20 |ven't tr|ied the |
|00002210| 6c 69 6e 6b 65 72 2e 0a | 58 0a 58 5a 6f 72 74 65 |linker..|X.XZorte|
|00002220| 63 68 20 43 2b 2b 20 32 | 2e 31 32 3a 20 22 63 6f |ch C++ 2|.12: "co|
|00002230| 6e 73 74 22 20 64 6f 65 | 73 6e 27 74 20 77 6f 72 |nst" doe|sn't wor|
|00002240| 6b 20 63 6f 72 72 65 63 | 74 6c 79 20 77 69 74 68 |k correc|tly with|
|00002250| 20 74 68 69 73 20 63 6f | 6d 70 69 6c 65 72 2c 20 | this co|mpiler, |
|00002260| 73 6f 0a 58 74 68 65 20 | 70 61 63 6b 61 67 65 20 |so.Xthe |package |
|00002270| 73 6b 69 70 73 20 61 6c | 6c 20 6f 66 20 74 68 65 |skips al|l of the|
|00002280| 20 73 74 61 74 65 6d 65 | 6e 74 73 20 5a 6f 72 74 | stateme|nts Zort|
|00002290| 65 63 68 20 63 61 6e 27 | 74 20 68 61 6e 64 6c 65 |ech can'|t handle|
|000022a0| 2e 20 49 66 20 79 6f 75 | 20 61 72 65 0a 58 75 73 |. If you| are.Xus|
|000022b0| 69 6e 67 20 61 20 6c 61 | 74 65 72 20 76 65 72 73 |ing a la|ter vers|
|000022c0| 69 6f 6e 20 6f 66 20 5a | 6f 72 74 65 63 68 20 79 |ion of Z|ortech y|
|000022d0| 6f 75 20 63 6f 75 6c 64 | 20 70 72 6f 62 61 62 6c |ou could| probabl|
|000022e0| 79 20 72 65 2d 61 63 74 | 69 76 61 74 65 20 74 68 |y re-act|ivate th|
|000022f0| 65 73 65 0a 58 73 74 61 | 74 65 6d 65 6e 74 73 2e |ese.Xsta|tements.|
|00002300| 20 5a 6f 72 74 65 63 68 | 20 6c 65 61 76 65 73 20 | Zortech| leaves |
|00002310| 72 75 62 62 69 73 68 20 | 6f 6e 20 74 68 65 20 68 |rubbish |on the h|
|00002320| 65 61 70 2e 20 49 20 64 | 6f 6e 27 74 20 6b 6e 6f |eap. I d|on't kno|
|00002330| 77 20 77 68 65 74 68 65 | 72 0a 58 74 68 69 73 20 |w whethe|r.Xthis |
|00002340| 69 73 20 6d 79 20 70 72 | 6f 67 72 61 6d 6d 69 6e |is my pr|ogrammin|
|00002350| 67 20 65 72 72 6f 72 20 | 6f 72 20 61 20 5a 6f 72 |g error |or a Zor|
|00002360| 74 65 63 68 20 65 72 72 | 6f 72 2e 20 49 74 20 77 |tech err|or. It w|
|00002370| 6f 72 6b 73 20 62 65 74 | 74 65 72 20 77 68 65 6e |orks bet|ter when|
|00002380| 0a 58 6f 6e 65 20 64 6f | 65 73 6e 27 74 20 6f 70 |.Xone do|esn't op|
|00002390| 74 69 6d 69 73 65 20 62 | 75 74 20 74 68 65 72 65 |timise b|ut there|
|000023a0| 20 73 74 69 6c 6c 20 61 | 72 65 20 70 72 6f 62 6c | still a|re probl|
|000023b0| 65 6d 73 2e 20 54 68 65 | 20 6e 72 69 63 20 72 6f |ems. The| nric ro|
|000023c0| 75 74 69 6e 65 73 0a 58 | 64 6f 6e 27 74 20 77 6f |utines.X|don't wo|
|000023d0| 72 6b 2e 20 5a 6f 72 74 | 65 63 68 20 64 6f 65 73 |rk. Zort|ech does|
|000023e0| 20 6e 6f 74 20 73 75 70 | 70 6f 72 74 20 49 4f 20 | not sup|port IO |
|000023f0| 6d 61 6e 69 70 75 6c 61 | 74 6f 72 73 2e 0a 58 0a |manipula|tors..X.|
|00002400| 58 47 6c 6f 63 6b 65 6e | 73 70 69 65 6c 20 43 2b |XGlocken|spiel C+|
|00002410| 2b 20 28 32 2e 30 30 61 | 20 66 6f 72 20 4d 73 44 |+ (2.00a| for MsD|
|00002420| 6f 73 20 6c 6f 61 64 69 | 6e 67 20 69 6e 74 6f 20 |os loadi|ng into |
|00002430| 4d 69 63 72 6f 73 6f 66 | 74 20 43 20 35 2e 31 29 |Microsof|t C 5.1)|
|00002440| 3a 20 49 0a 58 68 61 76 | 65 6e 27 74 20 74 65 73 |: I.Xhav|en't tes|
|00002450| 74 65 64 20 74 68 65 20 | 6c 61 74 65 73 74 20 76 |ted the |latest v|
|00002460| 65 72 73 69 6f 6e 20 6f | 66 20 6d 79 20 70 61 63 |ersion o|f my pac|
|00002470| 6b 61 67 65 20 77 69 74 | 68 20 47 6c 6f 63 6b 65 |kage wit|h Glocke|
|00002480| 6e 73 70 69 65 6c 2e 20 | 49 20 68 61 64 0a 58 74 |nspiel. |I had.Xt|
|00002490| 6f 20 23 64 65 66 69 6e | 65 20 74 68 65 20 6d 61 |o #defin|e the ma|
|000024a0| 74 72 69 78 20 6e 61 6d | 65 73 20 74 6f 20 73 68 |trix nam|es to sh|
|000024b0| 6f 72 74 65 72 20 6e 61 | 6d 65 73 20 74 6f 20 61 |orter na|mes to a|
|000024c0| 76 6f 69 64 20 61 6d 62 | 69 67 75 69 74 69 65 73 |void amb|iguities|
|000024d0| 20 61 6e 64 0a 58 68 61 | 64 20 71 75 69 74 65 20 | and.Xha|d quite |
|000024e0| 61 20 62 69 74 20 6f 66 | 20 64 69 66 66 69 63 75 |a bit of| difficu|
|000024f0| 6c 74 79 20 73 74 6f 70 | 70 69 6e 67 20 74 68 65 |lty stop|ping the|
|00002500| 20 63 6f 6d 70 69 6c 65 | 73 20 66 72 6f 6d 20 72 | compile|s from r|
|00002510| 75 6e 6e 69 6e 67 20 6f | 75 74 20 6f 66 0a 58 73 |unning o|ut of.Xs|
|00002520| 70 61 63 65 20 61 6e 64 | 20 6e 6f 74 20 65 78 63 |pace and| not exc|
|00002530| 65 65 64 69 6e 67 20 4d | 69 63 72 6f 73 6f 66 74 |eeding M|icrosoft|
|00002540| 27 73 20 62 6c 6f 63 6b | 20 6e 65 73 74 69 6e 67 |'s block| nesting|
|00002550| 20 6c 69 6d 69 74 2e 20 | 41 20 63 6f 75 70 6c 65 | limit. |A couple|
|00002560| 20 6f 66 20 6d 79 0a 58 | 74 65 73 74 20 73 74 61 | of my.X|test sta|
|00002570| 74 65 6d 65 6e 74 73 20 | 70 72 6f 64 75 63 65 64 |tements |produced|
|00002580| 20 73 74 61 74 65 6d 65 | 6e 74 73 20 74 6f 6f 20 | stateme|nts too |
|00002590| 63 6f 6d 70 6c 65 78 20 | 66 6f 72 20 4d 69 63 72 |complex |for Micr|
|000025a0| 6f 73 6f 66 74 2c 20 62 | 75 74 0a 58 62 61 73 69 |osoft, b|ut.Xbasi|
|000025b0| 63 61 6c 6c 79 20 74 68 | 65 20 70 61 63 6b 61 67 |cally th|e packag|
|000025c0| 65 20 77 6f 72 6b 65 64 | 2e 20 54 68 69 73 20 77 |e worked|. This w|
|000025d0| 61 73 20 6d 79 20 6f 72 | 69 67 69 6e 61 6c 20 64 |as my or|iginal d|
|000025e0| 65 76 65 6c 6f 70 6d 65 | 6e 74 20 70 6c 61 74 66 |evelopme|nt platf|
|000025f0| 6f 72 6d 0a 58 61 6e 64 | 20 49 20 73 74 69 6c 6c |orm.Xand| I still|
|00002600| 20 75 73 65 20 2e 63 78 | 78 20 61 6e 64 20 2e 68 | use .cx|x and .h|
|00002610| 78 78 20 61 73 20 6d 79 | 20 66 69 6c 65 20 6e 61 |xx as my| file na|
|00002620| 6d 65 20 65 78 74 65 6e | 73 69 6f 6e 73 2e 20 48 |me exten|sions. H|
|00002630| 6f 77 65 76 65 72 2c 0a | 58 47 6c 6f 63 6b 65 6e |owever,.|XGlocken|
|00002640| 73 70 69 65 6c 20 69 73 | 20 6e 6f 20 6c 6f 6e 67 |spiel is| no long|
|00002650| 65 72 20 63 6f 6d 70 65 | 74 69 74 69 76 65 20 66 |er compe|titive f|
|00002660| 6f 72 20 4d 73 44 6f 73 | 20 61 6e 64 20 49 20 61 |or MsDos| and I a|
|00002670| 6d 20 6e 6f 74 20 75 70 | 64 61 74 69 6e 67 20 6d |m not up|dating m|
|00002680| 79 0a 58 63 6f 70 79 20 | 6f 66 20 74 68 65 20 63 |y.Xcopy |of the c|
|00002690| 6f 6d 70 69 6c 65 72 2e | 0a 58 0a 58 53 75 6e 20 |ompiler.|.X.XSun |
|000026a0| 41 54 26 54 20 43 2b 2b | 20 32 2e 30 30 3a 20 54 |AT&T C++| 2.00: T|
|000026b0| 68 69 73 20 77 6f 72 6b | 73 20 66 69 6e 65 2e 20 |his work|s fine. |
|000026c0| 45 78 63 65 70 74 20 61 | 67 67 72 65 67 61 74 65 |Except a|ggregate|
|000026d0| 73 20 61 72 65 20 6e 6f | 74 20 73 75 70 70 6f 72 |s are no|t suppor|
|000026e0| 74 65 64 2e 0a 58 0a 58 | 47 6e 75 20 47 2b 2b 20 |ted..X.X|Gnu G++ |
|000026f0| 31 2e 33 37 2e 31 3a 20 | 54 68 69 73 20 6d 6f 73 |1.37.1: |This mos|
|00002700| 74 6c 79 20 77 6f 72 6b | 73 2e 20 59 6f 75 20 64 |tly work|s. You d|
|00002710| 6f 6e 27 74 20 73 65 65 | 6d 20 74 6f 20 62 65 20 |on't see|m to be |
|00002720| 61 62 6c 65 20 74 6f 20 | 75 73 65 0a 58 65 78 70 |able to |use.Xexp|
|00002730| 72 65 73 73 69 6f 6e 73 | 20 6c 69 6b 65 20 4d 61 |ressions| like Ma|
|00002740| 74 72 69 78 28 58 2a 59 | 29 20 69 6e 20 74 68 65 |trix(X*Y|) in the|
|00002750| 20 6d 69 64 64 6c 65 20 | 6f 66 20 61 6e 20 65 78 | middle |of an ex|
|00002760| 70 72 65 73 73 69 6f 6e | 20 61 6e 64 0a 58 28 4d |pression| and.X(M|
|00002770| 61 74 72 69 78 29 28 58 | 2a 59 29 20 69 73 20 75 |atrix)(X|*Y) is u|
|00002780| 6e 72 65 6c 69 61 62 6c | 65 2e 20 47 6e 75 20 64 |nreliabl|e. Gnu d|
|00002790| 6f 65 73 20 6e 6f 74 20 | 73 75 70 70 6f 72 74 20 |oes not |support |
|000027a0| 49 4f 20 6d 61 6e 69 70 | 75 6c 61 74 6f 72 73 2e |IO manip|ulators.|
|000027b0| 20 47 6e 75 0a 58 6c 65 | 61 76 65 73 20 72 75 62 | Gnu.Xle|aves rub|
|000027c0| 62 69 73 68 20 6f 6e 20 | 74 68 65 20 68 65 61 70 |bish on |the heap|
|000027d0| 2e 20 54 68 69 73 20 69 | 73 20 66 72 6f 6d 20 6f |. This i|s from o|
|000027e0| 75 74 70 75 74 20 73 74 | 61 74 65 6d 65 6e 74 73 |utput st|atements|
|000027f0| 20 61 6e 64 20 6e 6f 74 | 20 6d 79 0a 58 70 61 63 | and not| my.Xpac|
|00002800| 6b 61 67 65 20 61 6e 64 | 20 6d 61 79 20 6e 6f 74 |kage and| may not|
|00002810| 20 62 65 20 61 6e 20 65 | 72 72 6f 72 2e 20 54 68 | be an e|rror. Th|
|00002820| 65 20 70 72 65 76 69 6f | 75 73 20 76 65 72 73 69 |e previo|us versi|
|00002830| 6f 6e 20 6f 66 20 74 68 | 65 20 70 61 63 6b 61 67 |on of th|e packag|
|00002840| 65 20 64 69 64 0a 58 6e | 6f 74 20 77 6f 72 6b 20 |e did.Xn|ot work |
|00002850| 75 6e 64 65 72 20 47 6e | 75 20 31 2e 33 37 20 6f |under Gn|u 1.37 o|
|00002860| 72 20 31 2e 33 39 2e 0a | 58 0a 58 0a 58 2d 2d 2d |r 1.39..|X.X.X---|
|00002870| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00002880| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00002890| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000028a0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000028b0| 2d 2d 2d 2d 2d 2d 2d 2d | 0a 58 0a 58 45 78 61 6d |--------|.X.XExam|
|000028c0| 70 6c 65 0a 58 3d 3d 3d | 3d 3d 3d 3d 0a 58 0a 58 |ple.X===|====.X.X|
|000028d0| 41 6e 20 65 78 61 6d 70 | 6c 65 20 69 73 20 67 69 |An examp|le is gi|
|000028e0| 76 65 6e 20 69 6e 20 20 | 65 78 61 6d 70 6c 65 2e |ven in |example.|
|000028f0| 63 78 78 20 2e 20 20 54 | 68 69 73 20 67 69 76 65 |cxx . T|his give|
|00002900| 73 20 61 20 73 69 6d 70 | 6c 65 20 6c 69 6e 65 61 |s a simp|le linea|
|00002910| 72 0a 58 72 65 67 72 65 | 73 73 69 6f 6e 20 65 78 |r.Xregre|ssion ex|
|00002920| 61 6d 70 6c 65 20 75 73 | 69 6e 67 20 66 6f 75 72 |ample us|ing four|
|00002930| 20 64 69 66 66 65 72 65 | 6e 74 20 61 6c 67 6f 72 | differe|nt algor|
|00002940| 69 74 68 6d 73 2e 20 54 | 68 65 20 63 6f 72 72 65 |ithms. T|he corre|
|00002950| 63 74 20 6f 75 74 70 75 | 74 0a 58 69 73 20 67 69 |ct outpu|t.Xis gi|
|00002960| 76 65 6e 20 69 6e 20 65 | 78 61 6d 70 6c 65 2e 74 |ven in e|xample.t|
|00002970| 78 74 2e 20 54 68 65 20 | 70 72 6f 67 72 61 6d 20 |xt. The |program |
|00002980| 63 61 72 72 69 65 73 20 | 6f 75 74 20 61 20 63 68 |carries |out a ch|
|00002990| 65 63 6b 20 74 68 61 74 | 20 6e 6f 20 6d 65 6d 6f |eck that| no memo|
|000029a0| 72 79 0a 58 69 73 20 6c | 65 66 74 20 61 6c 6c 6f |ry.Xis l|eft allo|
|000029b0| 63 61 74 65 64 20 6f 6e | 20 74 68 65 20 68 65 61 |cated on| the hea|
|000029c0| 70 20 77 68 65 6e 20 69 | 74 20 74 65 72 6d 69 6e |p when i|t termin|
|000029d0| 61 74 65 73 2e 20 54 68 | 65 20 66 69 6c 65 20 20 |ates. Th|e file |
|000029e0| 65 78 61 6d 70 6c 65 2e | 64 65 70 0a 58 63 6f 6e |example.|dep.Xcon|
|000029f0| 74 61 69 6e 73 20 61 20 | 64 65 70 65 6e 64 65 6e |tains a |dependen|
|00002a00| 63 79 20 6c 69 73 74 20 | 66 6f 72 20 63 6f 6d 70 |cy list |for comp|
|00002a10| 69 6c 69 6e 67 20 20 65 | 78 61 6d 70 6c 65 2e 63 |iling e|xample.c|
|00002a20| 78 78 20 2e 20 59 6f 75 | 20 77 69 6c 6c 20 6e 65 |xx . You| will ne|
|00002a30| 65 64 20 74 6f 0a 58 61 | 64 64 20 74 68 65 20 63 |ed to.Xa|dd the c|
|00002a40| 6f 6d 70 69 6c 65 20 61 | 6e 64 20 6c 69 6e 6b 20 |ompile a|nd link |
|00002a50| 63 6f 6d 6d 61 6e 64 73 | 2e 20 65 78 61 6d 70 6c |commands|. exampl|
|00002a60| 65 2e 64 65 70 20 6c 69 | 73 74 73 20 61 6c 6c 20 |e.dep li|sts all |
|00002a70| 74 68 65 20 66 69 6c 65 | 73 20 69 6e 0a 58 74 68 |the file|s in.Xth|
|00002a80| 65 20 70 61 63 6b 61 67 | 65 20 73 6f 20 79 6f 75 |e packag|e so you|
|00002a90| 20 63 61 6e 20 61 64 61 | 70 74 20 66 6f 72 20 6f | can ada|pt for o|
|00002aa0| 74 68 65 72 20 70 72 6f | 6a 65 63 74 73 2e 20 44 |ther pro|jects. D|
|00002ab0| 6f 6e 27 74 20 66 6f 72 | 67 65 74 20 74 6f 20 72 |on't for|get to r|
|00002ac0| 65 6d 6f 76 65 0a 58 72 | 65 66 65 72 65 6e 63 65 |emove.Xr|eference|
|00002ad0| 73 20 74 6f 20 20 6e 65 | 77 6d 61 74 39 2e 63 78 |s to ne|wmat9.cx|
|00002ae0| 78 20 20 69 66 20 79 6f | 75 20 61 72 65 20 75 73 |x if yo|u are us|
|00002af0| 69 6e 67 20 61 20 63 6f | 6d 70 69 6c 65 72 20 74 |ing a co|mpiler t|
|00002b00| 68 61 74 20 64 6f 65 73 | 20 6e 6f 74 0a 58 73 75 |hat does| not.Xsu|
|00002b10| 70 70 6f 72 74 20 74 68 | 65 20 73 74 61 6e 64 61 |pport th|e standa|
|00002b20| 72 64 20 69 6f 20 6d 61 | 6e 69 70 75 6c 61 74 6f |rd io ma|nipulato|
|00002b30| 72 73 2e 0a 58 0a 58 0a | 58 2d 2d 2d 2d 2d 2d 2d |rs..X.X.|X-------|
|00002b40| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00002b50| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00002b60| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00002b70| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00002b80| 2d 2d 2d 2d 0a 58 0a 58 | 0a 58 44 65 74 61 69 6c |----.X.X|.XDetail|
|00002b90| 65 64 20 44 6f 63 75 6d | 65 6e 74 61 74 69 6f 6e |ed Docum|entation|
|00002ba0| 0a 58 3d 3d 3d 3d 3d 3d | 3d 3d 3d 3d 3d 3d 3d 3d |.X======|========|
|00002bb0| 3d 3d 3d 3d 3d 3d 3d 3d | 0a 58 0a 58 43 6f 70 79 |========|.X.XCopy|
|00002bc0| 72 69 67 68 74 20 28 43 | 29 20 31 39 38 39 2c 31 |right (C|) 1989,1|
|00002bd0| 39 39 30 2c 31 39 39 31 | 3a 20 52 20 42 20 44 61 |990,1991|: R B Da|
|00002be0| 76 69 65 73 20 61 6e 64 | 20 44 53 49 52 0a 58 0a |vies and| DSIR.X.|
|00002bf0| 58 50 65 72 6d 69 73 73 | 69 6f 6e 20 69 73 20 67 |XPermiss|ion is g|
|00002c00| 72 61 6e 74 65 64 20 74 | 6f 20 75 73 65 20 62 75 |ranted t|o use bu|
|00002c10| 74 20 6e 6f 74 20 74 6f | 20 73 65 6c 6c 2e 0a 58 |t not to| sell..X|
|00002c20| 0a 58 20 20 20 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |.X ---|--------|
|00002c30| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00002c40| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00002c50| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00002c60| 2d 2d 2d 0a 58 20 20 7c | 20 50 6c 65 61 73 65 20 |---.X || Please |
|00002c70| 75 6e 64 65 72 73 74 61 | 6e 64 20 74 68 61 74 20 |understa|nd that |
|00002c80| 74 68 69 73 20 69 73 20 | 61 20 74 65 73 74 20 76 |this is |a test v|
|00002c90| 65 72 73 69 6f 6e 3b 20 | 74 68 65 72 65 20 6d 61 |ersion; |there ma|
|00002ca0| 79 20 20 20 20 20 7c 0a | 58 20 20 7c 20 73 74 69 |y |.|X | sti|
|00002cb0| 6c 6c 20 62 65 20 62 75 | 67 73 20 61 6e 64 20 65 |ll be bu|gs and e|
|00002cc0| 72 72 6f 72 73 2e 20 55 | 73 65 20 61 74 20 79 6f |rrors. U|se at yo|
|00002cd0| 75 72 20 6f 77 6e 20 72 | 69 73 6b 2e 20 4e 65 69 |ur own r|isk. Nei|
|00002ce0| 74 68 65 72 20 49 20 20 | 20 20 7c 0a 58 20 20 7c |ther I | |.X ||
|00002cf0| 20 6e 6f 72 20 44 53 49 | 52 20 74 61 6b 65 20 61 | nor DSI|R take a|
|00002d00| 6e 79 20 72 65 73 70 6f | 6e 73 69 62 69 6c 69 74 |ny respo|nsibilit|
|00002d10| 79 20 66 6f 72 20 61 6e | 79 20 65 72 72 6f 72 73 |y for an|y errors|
|00002d20| 20 6f 72 20 6f 6d 69 73 | 73 69 6f 6e 73 20 7c 0a | or omis|sions |.|
|00002d30| 58 20 20 7c 20 69 6e 20 | 74 68 69 73 20 70 61 63 |X | in |this pac|
|00002d40| 6b 61 67 65 20 6f 72 20 | 66 6f 72 20 61 6e 79 20 |kage or |for any |
|00002d50| 6d 69 73 66 6f 72 74 75 | 6e 65 20 74 68 61 74 20 |misfortu|ne that |
|00002d60| 6d 61 79 20 62 65 66 61 | 6c 6c 20 79 6f 75 20 6f |may befa|ll you o|
|00002d70| 72 20 7c 0a 58 20 20 7c | 20 6f 74 68 65 72 73 20 |r |.X || others |
|00002d80| 61 73 20 61 20 72 65 73 | 75 6c 74 20 6f 66 20 69 |as a res|ult of i|
|00002d90| 74 73 20 75 73 65 2e 20 | 20 20 20 20 20 20 20 20 |ts use. | |
|00002da0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002db0| 20 20 20 20 20 20 7c 0a | 58 20 20 20 2d 2d 2d 2d | |.|X ----|
|00002dc0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00002dd0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00002de0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00002df0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 0a 58 0a 58 50 6c |--------|--.X.XPl|
|00002e00| 65 61 73 65 20 72 65 70 | 6f 72 74 20 62 75 67 73 |ease rep|ort bugs|
|00002e10| 20 74 6f 20 6d 65 20 61 | 74 0a 58 0a 58 20 20 20 | to me a|t.X.X |
|00002e20| 20 72 6f 62 65 72 74 40 | 61 6d 2e 64 73 69 72 2e | robert@|am.dsir.|
|00002e30| 67 6f 76 74 2e 6e 7a 0a | 58 0a 58 6f 72 0a 58 0a |govt.nz.|X.Xor.X.|
|00002e40| 58 20 20 20 20 43 6f 6d | 70 75 73 65 72 76 65 20 |X Com|puserve |
|00002e50| 37 32 37 37 37 2c 36 35 | 36 0a 58 0a 58 57 68 65 |72777,65|6.X.XWhe|
|00002e60| 6e 20 72 65 70 6f 72 74 | 69 6e 67 20 61 20 62 75 |n report|ing a bu|
|00002e70| 67 20 70 6c 65 61 73 65 | 20 74 65 6c 6c 20 6d 65 |g please| tell me|
|00002e80| 20 77 68 69 63 68 20 43 | 2b 2b 20 63 6f 6d 70 69 | which C|++ compi|
|00002e90| 6c 65 72 20 79 6f 75 20 | 61 72 65 20 75 73 69 6e |ler you |are usin|
|00002ea0| 67 20 28 69 66 0a 58 6b | 6e 6f 77 6e 29 2c 20 61 |g (if.Xk|nown), a|
|00002eb0| 6e 64 20 77 68 61 74 20 | 76 65 72 73 69 6f 6e 2e |nd what |version.|
|00002ec0| 20 41 6c 73 6f 20 67 69 | 76 65 20 6d 65 20 64 65 | Also gi|ve me de|
|00002ed0| 74 61 69 6c 73 20 6f 66 | 20 79 6f 75 72 20 63 6f |tails of| your co|
|00002ee0| 6d 70 75 74 65 72 20 28 | 69 66 0a 58 6b 6e 6f 77 |mputer (|if.Xknow|
|00002ef0| 6e 29 2e 20 54 65 6c 6c | 20 6d 65 20 77 68 65 72 |n). Tell| me wher|
|00002f00| 65 20 79 6f 75 20 64 6f | 77 6e 6c 6f 61 64 65 64 |e you do|wnloaded|
|00002f10| 20 79 6f 75 72 20 76 65 | 72 73 69 6f 6e 20 6f 66 | your ve|rsion of|
|00002f20| 20 6d 79 20 70 61 63 6b | 61 67 65 20 66 72 6f 6d | my pack|age from|
|00002f30| 20 61 6e 64 0a 58 69 74 | 73 20 76 65 72 73 69 6f | and.Xit|s versio|
|00002f40| 6e 20 6e 75 6d 62 65 72 | 20 28 65 67 20 6e 65 77 |n number| (eg new|
|00002f50| 6d 61 74 30 33 20 6f 72 | 20 6e 65 77 6d 61 74 30 |mat03 or| newmat0|
|00002f60| 34 29 2e 20 28 54 68 65 | 72 65 20 6d 61 79 20 62 |4). (The|re may b|
|00002f70| 65 20 76 65 72 79 20 6d | 69 6e 6f 72 0a 58 64 69 |e very m|inor.Xdi|
|00002f80| 66 66 65 72 65 6e 63 65 | 73 20 62 65 74 77 65 65 |fference|s betwee|
|00002f90| 6e 20 76 65 72 73 69 6f | 6e 73 20 61 74 20 64 69 |n versio|ns at di|
|00002fa0| 66 66 65 72 65 6e 74 20 | 73 69 74 65 73 29 2e 20 |fferent |sites). |
|00002fb0| 4e 6f 74 65 20 61 6e 79 | 20 63 68 61 6e 67 65 73 |Note any| changes|
|00002fc0| 20 79 6f 75 0a 58 68 61 | 76 65 20 6d 61 64 65 20 | you.Xha|ve made |
|00002fd0| 74 6f 20 6d 79 20 63 6f | 64 65 2e 20 49 66 20 61 |to my co|de. If a|
|00002fe0| 74 20 61 6c 6c 20 70 6f | 73 73 69 62 6c 65 20 67 |t all po|ssible g|
|00002ff0| 69 76 65 20 6d 65 20 61 | 20 70 69 65 63 65 20 6f |ive me a| piece o|
|00003000| 66 20 63 6f 64 65 0a 58 | 69 6c 6c 75 73 74 72 61 |f code.X|illustra|
|00003010| 74 69 6e 67 20 74 68 65 | 20 62 75 67 2e 0a 58 0a |ting the| bug..X.|
|00003020| 58 50 6c 65 61 73 65 20 | 64 6f 20 72 65 70 6f 72 |XPlease |do repor|
|00003030| 74 20 62 75 67 73 20 74 | 6f 20 6d 65 2e 0a 58 0a |t bugs t|o me..X.|
|00003040| 58 0a 58 54 68 65 20 6d | 61 74 72 69 78 20 69 6e |X.XThe m|atrix in|
|00003050| 76 65 72 73 65 20 72 6f | 75 74 69 6e 65 20 61 6e |verse ro|utine an|
|00003060| 64 20 74 68 65 20 73 6f | 72 74 20 72 6f 75 74 69 |d the so|rt routi|
|00003070| 6e 65 73 20 61 72 65 20 | 61 64 61 70 74 65 64 20 |nes are |adapted |
|00003080| 66 72 6f 6d 0a 58 22 4e | 75 6d 65 72 69 63 61 6c |from.X"N|umerical|
|00003090| 20 52 65 63 69 70 65 73 | 20 69 6e 20 43 22 20 62 | Recipes| in C" b|
|000030a0| 79 20 50 72 65 73 73 2c | 20 46 6c 61 6e 6e 65 72 |y Press,| Flanner|
|000030b0| 79 2c 20 54 65 75 6b 6f | 6c 73 6b 79 2c 20 56 65 |y, Teuko|lsky, Ve|
|000030c0| 74 74 65 72 6c 69 6e 67 | 2c 0a 58 70 75 62 6c 69 |tterling|,.Xpubli|
|000030d0| 73 68 65 64 20 62 79 20 | 74 68 65 20 43 61 6d 62 |shed by |the Camb|
|000030e0| 72 69 64 67 65 20 55 6e | 69 76 65 72 73 69 74 79 |ridge Un|iversity|
|000030f0| 20 50 72 65 73 73 2e 0a | 58 0a 58 4f 74 68 65 72 | Press..|X.XOther|
|00003100| 20 63 6f 64 65 20 69 73 | 20 61 64 61 70 74 65 64 | code is| adapted|
|00003110| 20 66 72 6f 6d 20 72 6f | 75 74 69 6e 65 73 20 69 | from ro|utines i|
|00003120| 6e 20 22 48 61 6e 64 62 | 6f 6f 6b 20 66 6f 72 20 |n "Handb|ook for |
|00003130| 41 75 74 6f 6d 61 74 69 | 63 0a 58 43 6f 6d 70 75 |Automati|c.XCompu|
|00003140| 74 61 74 69 6f 6e 2c 20 | 56 6f 6c 20 49 49 2c 20 |tation, |Vol II, |
|00003150| 4c 69 6e 65 61 72 20 41 | 6c 67 65 62 72 61 22 20 |Linear A|lgebra" |
|00003160| 62 79 20 57 69 6c 6b 69 | 6e 73 6f 6e 20 61 6e 64 |by Wilki|nson and|
|00003170| 20 52 65 69 6e 73 63 68 | 2c 20 70 75 62 6c 69 73 | Reinsch|, publis|
|00003180| 68 65 64 0a 58 62 79 20 | 53 70 72 69 6e 67 65 72 |hed.Xby |Springer|
|00003190| 20 56 65 72 6c 61 67 2e | 20 0a 58 0a 58 0a 58 43 | Verlag.| .X.X.XC|
|000031a0| 75 73 74 6f 6d 69 73 69 | 6e 67 0a 58 2d 2d 2d 2d |ustomisi|ng.X----|
|000031b0| 2d 2d 2d 2d 2d 2d 2d 0a | 58 0a 58 49 20 75 73 65 |-------.|X.XI use|
|000031c0| 20 2e 68 78 78 20 61 73 | 20 74 68 65 20 73 75 66 | .hxx as| the suf|
|000031d0| 66 69 78 20 6f 66 20 64 | 65 66 69 6e 69 74 69 6f |fix of d|efinitio|
|000031e0| 6e 20 66 69 6c 65 73 20 | 61 6e 64 20 2e 63 78 78 |n files |and .cxx|
|000031f0| 20 61 73 20 74 68 65 20 | 73 75 66 66 69 78 20 6f | as the |suffix o|
|00003200| 66 0a 58 43 2b 2b 20 73 | 6f 75 72 63 65 20 66 69 |f.XC++ s|ource fi|
|00003210| 6c 65 73 2e 20 54 68 69 | 73 20 64 6f 65 73 20 6e |les. Thi|s does n|
|00003220| 6f 74 20 63 61 75 73 65 | 20 61 6e 79 20 70 72 6f |ot cause| any pro|
|00003230| 62 6c 65 6d 73 20 77 69 | 74 68 20 74 68 65 20 63 |blems wi|th the c|
|00003240| 6f 6d 70 69 6c 65 72 73 | 20 49 0a 58 75 73 65 20 |ompilers| I.Xuse |
|00003250| 65 78 63 65 70 74 20 74 | 68 61 74 20 42 6f 72 6c |except t|hat Borl|
|00003260| 61 6e 64 20 61 6e 64 20 | 54 75 72 62 6f 20 6e 65 |and and |Turbo ne|
|00003270| 65 64 20 74 6f 20 62 65 | 20 74 6f 6c 64 20 74 6f |ed to be| told to|
|00003280| 20 61 63 63 65 70 74 20 | 61 6e 79 20 73 75 66 66 | accept |any suff|
|00003290| 69 78 0a 58 61 73 20 6d | 65 61 6e 69 6e 67 20 61 |ix.Xas m|eaning a|
|000032a0| 20 43 2b 2b 20 66 69 6c | 65 20 72 61 74 68 65 72 | C++ fil|e rather|
|000032b0| 20 74 68 61 6e 20 61 20 | 43 20 66 69 6c 65 2e 0a | than a |C file..|
|000032c0| 58 0a 58 55 73 65 20 74 | 68 65 20 6c 61 72 67 65 |X.XUse t|he large|
|000032d0| 20 6d 6f 64 65 6c 20 77 | 68 65 6e 20 79 6f 75 20 | model w|hen you |
|000032e0| 61 72 65 20 75 73 69 6e | 67 20 61 20 50 43 2e 20 |are usin|g a PC. |
|000032f0| 44 6f 20 6e 6f 74 20 22 | 6f 75 74 6c 69 6e 65 22 |Do not "|outline"|
|00003300| 20 69 6e 6c 69 6e 65 0a | 58 66 75 6e 63 74 69 6f | inline.|Xfunctio|
|00003310| 6e 73 2e 0a 58 0a 58 45 | 61 63 68 20 66 69 6c 65 |ns..X.XE|ach file|
|00003320| 20 61 63 63 65 73 73 69 | 6e 67 20 74 68 65 20 6d | accessi|ng the m|
|00003330| 61 74 72 69 78 20 70 61 | 63 6b 61 67 65 20 6e 65 |atrix pa|ckage ne|
|00003340| 65 64 73 20 74 6f 20 68 | 61 76 65 20 66 69 6c 65 |eds to h|ave file|
|00003350| 20 6e 65 77 6d 61 74 2e | 68 78 78 20 0a 58 23 69 | newmat.|hxx .X#i|
|00003360| 6e 63 6c 75 64 65 64 20 | 20 61 74 20 74 68 65 20 |ncluded | at the |
|00003370| 62 65 67 69 6e 6e 69 6e | 67 2e 20 46 69 6c 65 73 |beginnin|g. Files|
|00003380| 20 75 73 69 6e 67 20 6d | 61 74 72 69 78 20 61 70 | using m|atrix ap|
|00003390| 70 6c 69 63 61 74 69 6f | 6e 73 20 28 43 68 6f 6c |plicatio|ns (Chol|
|000033a0| 65 73 6b 79 0a 58 64 65 | 63 6f 6d 70 6f 73 69 74 |esky.Xde|composit|
|000033b0| 69 6f 6e 2c 20 48 6f 75 | 73 65 68 6f 6c 64 65 72 |ion, Hou|seholder|
|000033c0| 20 74 72 69 61 6e 67 75 | 6c 61 72 69 73 61 74 69 | triangu|larisati|
|000033d0| 6f 6e 29 20 6e 65 65 64 | 20 6e 65 77 6d 61 74 61 |on) need| newmata|
|000033e0| 70 2e 68 78 78 20 69 6e | 73 74 65 61 64 0a 58 28 |p.hxx in|stead.X(|
|000033f0| 6f 72 20 61 73 20 77 65 | 6c 6c 29 2e 20 49 66 20 |or as we|ll). If |
|00003400| 79 6f 75 20 6e 65 65 64 | 20 74 68 65 20 6f 75 74 |you need| the out|
|00003410| 70 75 74 20 66 75 6e 63 | 74 69 6f 6e 73 20 79 6f |put func|tions yo|
|00003420| 75 20 77 69 6c 6c 20 61 | 6c 73 6f 20 6e 65 65 64 |u will a|lso need|
|00003430| 0a 58 6e 65 77 6d 61 74 | 69 6f 2e 68 78 78 2e 20 |.Xnewmat|io.hxx. |
|00003440| 47 6c 6f 63 6b 65 6e 73 | 70 69 65 6c 20 61 6c 73 |Glockens|piel als|
|00003450| 6f 20 6e 65 65 64 73 20 | 74 6f 20 68 61 76 65 20 |o needs |to have |
|00003460| 69 6e 63 6c 75 64 65 2e | 68 78 78 20 23 69 6e 63 |include.|hxx #inc|
|00003470| 6c 75 64 65 64 20 62 65 | 66 6f 72 65 0a 58 6e 65 |luded be|fore.Xne|
|00003480| 77 6d 61 74 2e 68 78 78 | 2e 0a 58 0a 58 54 68 65 |wmat.hxx|..X.XThe|
|00003490| 20 66 69 6c 65 20 20 69 | 6e 63 6c 75 64 65 2e 68 | file i|nclude.h|
|000034a0| 78 78 20 20 73 65 74 73 | 20 74 68 65 20 6f 70 74 |xx sets| the opt|
|000034b0| 69 6f 6e 73 20 66 6f 72 | 20 74 68 65 20 63 6f 6d |ions for| the com|
|000034c0| 70 69 6c 65 72 2e 20 49 | 66 20 79 6f 75 20 61 72 |piler. I|f you ar|
|000034d0| 65 20 75 73 69 6e 67 0a | 58 61 20 63 6f 6d 70 69 |e using.|Xa compi|
|000034e0| 6c 65 72 20 64 69 66 66 | 65 72 65 6e 74 20 66 72 |ler diff|erent fr|
|000034f0| 6f 6d 20 6f 6e 65 20 49 | 20 68 61 76 65 20 77 6f |om one I| have wo|
|00003500| 72 6b 65 64 20 77 69 74 | 68 20 79 6f 75 20 6d 61 |rked wit|h you ma|
|00003510| 79 20 68 61 76 65 20 74 | 6f 20 73 65 74 20 75 70 |y have t|o set up|
|00003520| 0a 58 61 20 6e 65 77 20 | 73 65 63 74 69 6f 6e 20 |.Xa new |section |
|00003530| 69 6e 20 20 69 6e 63 6c | 75 64 65 2e 68 78 78 20 |in incl|ude.hxx |
|00003540| 20 61 70 70 72 6f 70 72 | 69 61 74 65 20 66 6f 72 | appropr|iate for|
|00003550| 20 79 6f 75 72 20 63 6f | 6d 70 69 6c 65 72 2e 0a | your co|mpiler..|
|00003560| 58 0a 58 42 6f 72 6c 61 | 6e 64 2c 20 54 75 72 62 |X.XBorla|nd, Turb|
|00003570| 6f 20 61 6e 64 20 5a 6f | 72 74 65 63 68 20 61 72 |o and Zo|rtech ar|
|00003580| 65 20 72 65 63 6f 67 6e | 69 73 65 64 20 61 75 74 |e recogn|ised aut|
|00003590| 6f 6d 61 74 69 63 61 6c | 6c 79 2e 20 49 66 20 79 |omatical|ly. If y|
|000035a0| 6f 75 20 75 73 69 6e 67 | 0a 58 47 6c 6f 63 6b 65 |ou using|.XGlocke|
|000035b0| 6e 73 70 69 65 6c 20 6f | 6e 20 61 20 50 43 2c 20 |nspiel o|n a PC, |
|000035c0| 41 54 26 54 2c 20 6f 72 | 20 47 6e 75 20 43 2b 2b |AT&T, or| Gnu C++|
|000035d0| 20 61 63 74 69 76 61 74 | 65 20 74 68 65 20 61 70 | activat|e the ap|
|000035e0| 70 72 6f 70 72 69 61 74 | 65 0a 58 73 74 61 74 65 |propriat|e.Xstate|
|000035f0| 6d 65 6e 74 20 61 74 20 | 74 68 65 20 62 65 67 69 |ment at |the begi|
|00003600| 6e 6e 69 6e 67 20 6f 66 | 20 69 6e 63 6c 75 64 65 |nning of| include|
|00003610| 2e 68 78 78 2e 0a 58 0a | 58 41 63 74 69 76 61 74 |.hxx..X.|XActivat|
|00003620| 65 20 74 68 65 20 61 70 | 70 72 6f 70 72 69 61 74 |e the ap|propriat|
|00003630| 65 20 73 74 61 74 65 6d | 65 6e 74 20 74 6f 20 6d |e statem|ent to m|
|00003640| 61 6b 65 20 74 68 65 20 | 65 6c 65 6d 65 6e 74 20 |ake the |element |
|00003650| 74 79 70 65 20 66 6c 6f | 61 74 20 6f 72 0a 58 64 |type flo|at or.Xd|
|00003660| 6f 75 62 6c 65 2e 0a 58 | 0a 58 54 68 65 20 66 69 |ouble..X|.XThe fi|
|00003670| 6c 65 20 28 6e 65 77 6d | 61 74 39 2e 63 78 78 29 |le (newm|at9.cxx)|
|00003680| 20 63 6f 6e 74 61 69 6e | 69 6e 67 20 74 68 65 20 | contain|ing the |
|00003690| 6f 75 74 70 75 74 20 72 | 6f 75 74 69 6e 65 73 20 |output r|outines |
|000036a0| 63 61 6e 20 62 65 20 75 | 73 65 64 20 6f 6e 6c 79 |can be u|sed only|
|000036b0| 0a 58 77 69 74 68 20 6c | 69 62 72 61 72 69 65 73 |.Xwith l|ibraries|
|000036c0| 20 74 68 61 74 20 73 75 | 70 70 6f 72 74 20 74 68 | that su|pport th|
|000036d0| 65 20 41 54 26 54 20 69 | 6e 70 75 74 2f 6f 75 74 |e AT&T i|nput/out|
|000036e0| 70 75 74 20 72 6f 75 74 | 69 6e 65 73 20 69 6e 63 |put rout|ines inc|
|000036f0| 6c 75 64 69 6e 67 0a 58 | 6d 61 6e 69 70 75 6c 61 |luding.X|manipula|
|00003700| 74 6f 72 73 2e 20 49 74 | 20 63 61 6e 6e 6f 74 20 |tors. It| cannot |
|00003710| 62 65 20 75 73 65 64 20 | 77 69 74 68 20 5a 6f 72 |be used |with Zor|
|00003720| 74 65 63 68 20 6f 72 20 | 47 6e 75 2e 0a 58 0a 58 |tech or |Gnu..X.X|
|00003730| 0a 58 43 6f 6e 73 74 72 | 75 63 74 6f 72 73 0a 58 |.XConstr|uctors.X|
|00003740| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 0a 58 0a 58 |--------|----.X.X|
|00003750| 54 6f 20 63 6f 6e 73 74 | 72 75 63 74 20 61 6e 20 |To const|ruct an |
|00003760| 6d 20 78 20 6e 20 6d 61 | 74 72 69 78 2c 20 41 2c |m x n ma|trix, A,|
|00003770| 20 28 6d 20 61 6e 64 20 | 6e 20 61 72 65 20 69 6e | (m and |n are in|
|00003780| 74 65 67 65 72 73 29 20 | 75 73 65 0a 58 0a 58 20 |tegers) |use.X.X |
|00003790| 20 20 20 4d 61 74 72 69 | 78 20 41 28 6d 2c 6e 29 | Matri|x A(m,n)|
|000037a0| 3b 0a 58 0a 58 54 68 65 | 20 55 70 70 65 72 54 72 |;.X.XThe| UpperTr|
|000037b0| 69 61 6e 67 75 6c 61 72 | 4d 61 74 72 69 78 2c 20 |iangular|Matrix, |
|000037c0| 4c 6f 77 65 72 54 72 69 | 61 6e 67 75 6c 61 72 4d |LowerTri|angularM|
|000037d0| 61 74 72 69 78 2c 20 53 | 79 6d 6d 65 74 72 69 63 |atrix, S|ymmetric|
|000037e0| 4d 61 74 72 69 78 20 61 | 6e 64 0a 58 44 69 61 67 |Matrix a|nd.XDiag|
|000037f0| 6f 6e 61 6c 4d 61 74 72 | 69 78 20 74 79 70 65 73 |onalMatr|ix types|
|00003800| 20 61 72 65 20 73 79 6d | 6d 65 74 72 69 63 2e 20 | are sym|metric. |
|00003810| 54 6f 20 63 6f 6e 73 74 | 72 75 63 74 20 61 6e 20 |To const|ruct an |
|00003820| 6e 20 78 20 6e 20 6d 61 | 74 72 69 78 20 75 73 65 |n x n ma|trix use|
|00003830| 2c 0a 58 66 6f 72 20 65 | 78 61 6d 70 6c 65 0a 58 |,.Xfor e|xample.X|
|00003840| 0a 58 20 20 20 20 55 70 | 70 65 72 54 72 69 61 6e |.X Up|perTrian|
|00003850| 67 75 6c 61 72 4d 61 74 | 72 69 78 20 55 28 6e 29 |gularMat|rix U(n)|
|00003860| 3b 0a 58 0a 58 4c 69 6b | 65 77 69 73 65 20 74 68 |;.X.XLik|ewise th|
|00003870| 65 20 52 6f 77 56 65 63 | 74 6f 72 20 61 6e 64 20 |e RowVec|tor and |
|00003880| 43 6f 6c 75 6d 6e 56 65 | 63 74 6f 72 20 74 79 70 |ColumnVe|ctor typ|
|00003890| 65 73 20 74 61 6b 65 20 | 6a 75 73 74 20 6f 6e 65 |es take |just one|
|000038a0| 20 61 72 67 75 6d 65 6e | 74 20 69 6e 0a 58 74 68 | argumen|t in.Xth|
|000038b0| 65 69 72 20 63 6f 6e 73 | 74 72 75 63 74 6f 72 73 |eir cons|tructors|
|000038c0| 3a 0a 58 0a 58 20 20 20 | 20 52 6f 77 56 65 63 74 |:.X.X | RowVect|
|000038d0| 6f 72 20 52 56 28 6e 29 | 3b 0a 58 0a 58 59 6f 75 |or RV(n)|;.X.XYou|
|000038e0| 20 63 61 6e 20 61 6c 73 | 6f 20 63 6f 6e 73 74 72 | can als|o constr|
|000038f0| 75 63 74 20 76 65 63 74 | 6f 72 73 20 61 6e 64 20 |uct vect|ors and |
|00003900| 6d 61 74 72 69 63 65 73 | 20 77 69 74 68 6f 75 74 |matrices| without|
|00003910| 20 73 70 65 63 69 66 79 | 69 6e 67 20 74 68 65 0a | specify|ing the.|
|00003920| 58 64 69 6d 65 6e 73 69 | 6f 6e 2e 20 46 6f 72 20 |Xdimensi|on. For |
|00003930| 65 78 61 6d 70 6c 65 0a | 58 0a 58 20 20 20 20 4d |example.|X.X M|
|00003940| 61 74 72 69 78 20 41 3b | 0a 58 0a 58 49 6e 20 74 |atrix A;|.X.XIn t|
|00003950| 68 69 73 20 63 61 73 65 | 20 74 68 65 20 64 69 6d |his case| the dim|
|00003960| 65 6e 73 69 6f 6e 20 6d | 75 73 74 20 62 65 20 73 |ension m|ust be s|
|00003970| 65 74 20 62 79 20 61 6e | 20 61 73 73 69 67 6e 6d |et by an| assignm|
|00003980| 65 6e 74 20 73 74 61 74 | 65 6d 65 6e 74 20 6f 72 |ent stat|ement or|
|00003990| 20 61 0a 58 72 65 2d 64 | 69 6d 65 6e 73 69 6f 6e | a.Xre-d|imension|
|000039a0| 20 73 74 61 74 65 6d 65 | 6e 74 2e 0a 58 0a 58 59 | stateme|nt..X.XY|
|000039b0| 6f 75 20 63 61 6e 20 61 | 6c 73 6f 20 75 73 65 20 |ou can a|lso use |
|000039c0| 61 20 63 6f 6e 73 74 72 | 75 63 74 6f 72 20 74 6f |a constr|uctor to|
|000039d0| 20 73 65 74 20 61 20 6d | 61 74 72 69 78 20 65 71 | set a m|atrix eq|
|000039e0| 75 61 6c 20 74 6f 20 61 | 6e 6f 74 68 65 72 20 6d |ual to a|nother m|
|000039f0| 61 74 72 69 78 0a 58 6f | 72 20 6d 61 74 72 69 78 |atrix.Xo|r matrix|
|00003a00| 20 65 78 70 72 65 73 73 | 69 6f 6e 2e 0a 58 0a 58 | express|ion..X.X|
|00003a10| 20 20 20 20 4d 61 74 72 | 69 78 20 41 20 3d 20 55 | Matr|ix A = U|
|00003a20| 3b 0a 58 0a 58 20 20 20 | 20 4d 61 74 72 69 78 20 |;.X.X | Matrix |
|00003a30| 41 20 3d 20 55 20 2a 20 | 4c 3b 0a 58 0a 58 4f 6e |A = U * |L;.X.XOn|
|00003a40| 6c 79 20 63 6f 6e 76 65 | 72 73 69 6f 6e 73 20 74 |ly conve|rsions t|
|00003a50| 68 61 74 20 64 6f 6e 27 | 74 20 6c 6f 73 65 20 69 |hat don'|t lose i|
|00003a60| 6e 66 6f 72 6d 61 74 69 | 6f 6e 20 61 72 65 20 73 |nformati|on are s|
|00003a70| 75 70 70 6f 72 74 65 64 | 20 2d 20 65 67 20 79 6f |upported| - eg yo|
|00003a80| 75 0a 58 63 61 6e 6e 6f | 74 20 63 6f 6e 76 65 72 |u.Xcanno|t conver|
|00003a90| 74 20 61 6e 20 75 70 70 | 65 72 20 74 72 69 61 6e |t an upp|er trian|
|00003aa0| 67 75 6c 61 72 20 6d 61 | 74 72 69 78 20 69 6e 74 |gular ma|trix int|
|00003ab0| 6f 20 61 20 64 69 61 67 | 6f 6e 61 6c 20 6d 61 74 |o a diag|onal mat|
|00003ac0| 72 69 78 20 75 73 69 6e | 67 20 3d 2e 0a 58 0a 58 |rix usin|g =..X.X|
|00003ad0| 0a 58 45 6c 65 6d 65 6e | 74 73 20 6f 66 20 6d 61 |.XElemen|ts of ma|
|00003ae0| 74 72 69 63 65 73 0a 58 | 2d 2d 2d 2d 2d 2d 2d 2d |trices.X|--------|
|00003af0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 0a 58 0a 58 |--------|----.X.X|
|00003b00| 45 6c 65 6d 65 6e 74 73 | 20 61 72 65 20 61 63 63 |Elements| are acc|
|00003b10| 65 73 73 65 64 20 62 79 | 20 65 78 70 72 65 73 73 |essed by| express|
|00003b20| 69 6f 6e 73 20 6f 66 20 | 74 68 65 20 66 6f 72 6d |ions of |the form|
|00003b30| 20 41 28 69 2c 6a 29 20 | 77 68 65 72 65 20 69 20 | A(i,j) |where i |
|00003b40| 61 6e 64 20 6a 0a 58 72 | 75 6e 20 66 72 6f 6d 20 |and j.Xr|un from |
|00003b50| 31 20 74 6f 20 74 68 65 | 20 61 70 70 72 6f 70 72 |1 to the| appropr|
|00003b60| 69 61 74 65 20 64 69 6d | 65 6e 73 69 6f 6e 2e 20 |iate dim|ension. |
|00003b70| 41 63 63 65 73 73 20 65 | 6c 65 6d 65 6e 74 73 20 |Access e|lements |
|00003b80| 6f 66 20 76 65 63 74 6f | 72 73 20 77 69 74 68 0a |of vecto|rs with.|
|00003b90| 58 6a 75 73 74 20 6f 6e | 65 20 61 72 67 75 6d 65 |Xjust on|e argume|
|00003ba0| 6e 74 2e 20 44 69 61 67 | 6f 6e 61 6c 20 6d 61 74 |nt. Diag|onal mat|
|00003bb0| 72 69 63 65 73 20 63 61 | 6e 20 61 63 63 65 70 74 |rices ca|n accept|
|00003bc0| 20 6f 6e 65 20 6f 72 20 | 74 77 6f 20 73 75 62 73 | one or |two subs|
|00003bd0| 63 72 69 70 74 73 2e 0a | 58 0a 58 54 68 69 73 20 |cripts..|X.XThis |
|00003be0| 69 73 20 64 69 66 66 65 | 72 65 6e 74 20 66 72 6f |is diffe|rent fro|
|00003bf0| 6d 20 74 68 65 20 65 61 | 72 6c 69 65 72 20 76 65 |m the ea|rlier ve|
|00003c00| 72 73 69 6f 6e 20 6f 66 | 20 74 68 65 20 70 61 63 |rsion of| the pac|
|00003c10| 6b 61 67 65 20 69 6e 20 | 77 68 69 63 68 20 74 68 |kage in |which th|
|00003c20| 65 0a 58 73 75 62 73 63 | 72 69 70 74 73 20 72 61 |e.Xsubsc|ripts ra|
|00003c30| 6e 20 66 72 6f 6d 20 30 | 20 74 6f 20 6f 6e 65 20 |n from 0| to one |
|00003c40| 6c 65 73 73 20 74 68 61 | 6e 20 74 68 65 20 61 70 |less tha|n the ap|
|00003c50| 70 72 6f 70 72 69 61 74 | 65 20 64 69 6d 65 6e 73 |propriat|e dimens|
|00003c60| 69 6f 6e 2e 20 55 73 65 | 0a 58 41 2e 65 6c 65 6d |ion. Use|.XA.elem|
|00003c70| 65 6e 74 28 69 2c 6a 29 | 20 69 66 20 79 6f 75 20 |ent(i,j)| if you |
|00003c80| 77 61 6e 74 20 74 68 69 | 73 20 65 61 72 6c 69 65 |want thi|s earlie|
|00003c90| 72 20 63 6f 6e 76 65 6e | 74 69 6f 6e 2e 0a 58 0a |r conven|tion..X.|
|00003ca0| 58 0a 58 4d 61 74 72 69 | 78 20 63 6f 70 79 0a 58 |X.XMatri|x copy.X|
|00003cb0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 0a 58 0a 58 54 |--------|---.X.XT|
|00003cc0| 68 65 20 6f 70 65 72 61 | 74 6f 72 20 3d 20 69 73 |he opera|tor = is|
|00003cd0| 20 75 73 65 64 20 66 6f | 72 20 63 6f 70 79 69 6e | used fo|r copyin|
|00003ce0| 67 20 6d 61 74 72 69 63 | 65 73 2c 20 63 6f 6e 76 |g matric|es, conv|
|00003cf0| 65 72 74 69 6e 67 20 6d | 61 74 72 69 63 65 73 2c |erting m|atrices,|
|00003d00| 20 6f 72 0a 58 65 76 61 | 6c 75 61 74 69 6e 67 20 | or.Xeva|luating |
|00003d10| 65 78 70 72 65 73 73 69 | 6f 6e 73 2e 20 46 6f 72 |expressi|ons. For|
|00003d20| 20 65 78 61 6d 70 6c 65 | 0a 58 0a 58 20 20 20 20 | example|.X.X |
|00003d30| 41 20 3d 20 42 3b 20 20 | 41 20 3d 20 4c 3b 20 20 |A = B; |A = L; |
|00003d40| 41 20 3d 20 4c 20 2a 20 | 55 3b 0a 58 0a 58 4f 6e |A = L * |U;.X.XOn|
|00003d50| 6c 79 20 63 6f 6e 76 65 | 72 73 69 6f 6e 73 20 74 |ly conve|rsions t|
|00003d60| 68 61 74 20 64 6f 6e 27 | 74 20 6c 6f 73 65 20 69 |hat don'|t lose i|
|00003d70| 6e 66 6f 72 6d 61 74 69 | 6f 6e 20 61 72 65 20 73 |nformati|on are s|
|00003d80| 75 70 70 6f 72 74 65 64 | 2e 20 54 68 65 0a 58 64 |upported|. The.Xd|
|00003d90| 69 6d 65 6e 73 69 6f 6e | 73 20 6f 66 20 74 68 65 |imension|s of the|
|00003da0| 20 6d 61 74 72 69 78 20 | 6f 6e 20 74 68 65 20 6c | matrix |on the l|
|00003db0| 65 66 74 20 68 61 6e 64 | 20 73 69 64 65 20 61 72 |eft hand| side ar|
|00003dc0| 65 20 61 64 6a 75 73 74 | 65 64 20 74 6f 20 74 68 |e adjust|ed to th|
|00003dd0| 6f 73 65 20 6f 66 0a 58 | 74 68 65 20 6d 61 74 72 |ose of.X|the matr|
|00003de0| 69 78 20 6f 72 20 65 78 | 70 72 65 73 73 69 6f 6e |ix or ex|pression|
|00003df0| 20 6f 6e 20 74 68 65 20 | 72 69 67 68 74 20 68 61 | on the |right ha|
|00003e00| 6e 64 20 73 69 64 65 2e | 20 45 6c 65 6d 65 6e 74 |nd side.| Element|
|00003e10| 73 20 6f 6e 20 74 68 65 | 20 72 69 67 68 74 0a 58 |s on the| right.X|
|00003e20| 68 61 6e 64 20 73 69 64 | 65 20 77 68 69 63 68 20 |hand sid|e which |
|00003e30| 61 72 65 20 6e 6f 74 20 | 70 72 65 73 65 6e 74 20 |are not |present |
|00003e40| 6f 6e 20 74 68 65 20 6c | 65 66 74 20 68 61 6e 64 |on the l|eft hand|
|00003e50| 20 73 69 64 65 20 61 72 | 65 20 73 65 74 20 74 6f | side ar|e set to|
|00003e60| 20 7a 65 72 6f 2e 0a 58 | 0a 58 54 68 65 20 6f 70 | zero..X|.XThe op|
|00003e70| 65 72 61 74 6f 72 20 3c | 3c 20 63 61 6e 20 62 65 |erator <|< can be|
|00003e80| 20 75 73 65 64 20 69 6e | 20 70 6c 61 63 65 20 6f | used in| place o|
|00003e90| 66 20 3d 20 77 68 65 72 | 65 20 69 74 20 69 73 20 |f = wher|e it is |
|00003ea0| 70 65 72 6d 69 73 73 69 | 62 6c 65 20 66 6f 72 0a |permissi|ble for.|
|00003eb0| 58 69 6e 66 6f 72 6d 61 | 74 69 6f 6e 20 74 6f 20 |Xinforma|tion to |
|00003ec0| 62 65 20 6c 6f 73 74 2e | 0a 58 0a 58 46 6f 72 20 |be lost.|.X.XFor |
|00003ed0| 65 78 61 6d 70 6c 65 0a | 58 0a 58 20 20 20 20 53 |example.|X.X S|
|00003ee0| 79 6d 6d 65 74 72 69 63 | 4d 61 74 72 69 78 20 53 |ymmetric|Matrix S|
|00003ef0| 3b 20 4d 61 74 72 69 78 | 20 41 3b 0a 58 20 20 20 |; Matrix| A;.X |
|00003f00| 20 2e 2e 2e 2e 2e 2e 0a | 58 20 20 20 20 53 20 3c | .......|X S <|
|00003f10| 3c 20 41 2e 74 28 29 20 | 2a 20 41 3b 0a 58 0a 58 |< A.t() |* A;.X.X|
|00003f20| 69 73 20 61 63 63 65 70 | 74 61 62 6c 65 20 77 68 |is accep|table wh|
|00003f30| 65 72 65 61 73 0a 58 0a | 58 20 20 20 20 53 20 3d |ereas.X.|X S =|
|00003f40| 20 41 2e 74 28 29 20 2a | 20 41 3b 20 20 20 20 20 | A.t() *| A; |
|00003f50| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00003f60| 20 20 20 20 20 20 20 2f | 2f 20 65 72 72 6f 72 0a | /|/ error.|
|00003f70| 58 0a 58 77 69 6c 6c 20 | 63 61 75 73 65 20 61 20 |X.Xwill |cause a |
|00003f80| 72 75 6e 74 69 6d 65 20 | 65 72 72 6f 72 20 73 69 |runtime |error si|
|00003f90| 6e 63 65 20 74 68 65 20 | 70 61 63 6b 61 67 65 20 |nce the |package |
|00003fa0| 64 6f 65 73 20 6e 6f 74 | 20 28 79 65 74 29 20 72 |does not| (yet) r|
|00003fb0| 65 63 6f 67 6e 69 73 65 | 0a 58 41 2e 74 28 29 2a |ecognise|.XA.t()*|
|00003fc0| 41 20 61 73 20 73 79 6d | 6d 65 74 72 69 63 2e 0a |A as sym|metric..|
|00003fd0| 58 0a 58 4e 6f 74 65 20 | 74 68 61 74 20 79 6f 75 |X.XNote |that you|
|00003fe0| 20 63 61 6e 20 6e 6f 74 | 20 75 73 65 20 3c 3c 20 | can not| use << |
|00003ff0| 77 69 74 68 20 63 6f 6e | 73 74 72 75 63 74 6f 72 |with con|structor|
|00004000| 73 2e 20 46 6f 72 20 65 | 78 61 6d 70 6c 65 0a 58 |s. For e|xample.X|
|00004010| 0a 58 20 20 20 20 53 79 | 6d 6d 65 74 72 69 63 4d |.X Sy|mmetricM|
|00004020| 61 74 72 69 78 20 53 20 | 3c 3c 20 41 2e 74 28 29 |atrix S |<< A.t()|
|00004030| 20 2a 20 41 3b 20 20 20 | 20 20 20 20 20 20 20 20 | * A; | |
|00004040| 2f 2f 20 65 72 72 6f 72 | 0a 58 0a 58 64 6f 65 73 |// error|.X.Xdoes|
|00004050| 20 6e 6f 74 20 77 6f 72 | 6b 2e 0a 58 0a 58 41 20 | not wor|k..X.XA |
|00004060| 74 68 69 72 64 20 63 6f | 70 79 20 72 6f 75 74 69 |third co|py routi|
|00004070| 6e 65 20 69 73 20 75 73 | 65 64 20 69 6e 20 61 20 |ne is us|ed in a |
|00004080| 73 69 6d 69 6c 61 72 20 | 72 6f 6c 65 20 74 6f 20 |similar |role to |
|00004090| 3d 2e 20 55 73 65 0a 58 | 0a 58 20 20 20 20 41 2e |=. Use.X|.X A.|
|000040a0| 49 6e 6a 65 63 74 28 44 | 29 3b 0a 58 0a 58 74 6f |Inject(D|);.X.Xto|
|000040b0| 20 63 6f 70 79 20 74 68 | 65 20 65 6c 65 6d 65 6e | copy th|e elemen|
|000040c0| 74 73 20 6f 66 20 44 20 | 74 6f 20 74 68 65 20 63 |ts of D |to the c|
|000040d0| 6f 72 72 65 73 70 6f 6e | 64 69 6e 67 20 65 6c 65 |orrespon|ding ele|
|000040e0| 6d 65 6e 74 73 20 6f 66 | 20 41 20 62 75 74 20 6c |ments of| A but l|
|000040f0| 65 61 76 65 0a 58 74 68 | 65 20 65 6c 65 6d 65 6e |eave.Xth|e elemen|
|00004100| 74 73 20 6f 66 20 41 20 | 75 6e 63 68 61 6e 67 65 |ts of A |unchange|
|00004110| 64 20 69 66 20 74 68 65 | 72 65 20 69 73 20 6e 6f |d if the|re is no|
|00004120| 20 63 6f 72 72 65 73 70 | 6f 6e 64 69 6e 67 20 65 | corresp|onding e|
|00004130| 6c 65 6d 65 6e 74 20 6f | 66 20 44 0a 58 28 74 68 |lement o|f D.X(th|
|00004140| 65 20 3d 20 6f 70 65 72 | 61 74 6f 72 20 77 6f 75 |e = oper|ator wou|
|00004150| 6c 64 20 73 65 74 20 74 | 68 65 6d 20 74 6f 20 30 |ld set t|hem to 0|
|00004160| 29 2e 20 54 68 69 73 20 | 69 73 20 75 73 65 66 75 |). This |is usefu|
|00004170| 6c 2c 20 66 6f 72 20 65 | 78 61 6d 70 6c 65 2c 20 |l, for e|xample, |
|00004180| 66 6f 72 0a 58 73 65 74 | 74 69 6e 67 20 74 68 65 |for.Xset|ting the|
|00004190| 20 64 69 61 67 6f 6e 61 | 6c 20 65 6c 65 6d 65 6e | diagona|l elemen|
|000041a0| 74 73 20 6f 66 20 61 20 | 6d 61 74 72 69 78 20 77 |ts of a |matrix w|
|000041b0| 69 74 68 6f 75 74 20 64 | 69 73 74 75 72 62 69 6e |ithout d|isturbin|
|000041c0| 67 20 74 68 65 20 72 65 | 73 74 20 6f 66 0a 58 74 |g the re|st of.Xt|
|000041d0| 68 65 20 6d 61 74 72 69 | 78 2e 20 55 6e 6c 69 6b |he matri|x. Unlik|
|000041e0| 65 20 3d 20 61 6e 64 20 | 3c 3c 2c 20 49 6e 6a 65 |e = and |<<, Inje|
|000041f0| 63 74 20 64 6f 65 73 20 | 6e 6f 74 20 72 65 73 65 |ct does |not rese|
|00004200| 74 20 74 68 65 20 64 69 | 6d 65 6e 73 69 6f 6e 73 |t the di|mensions|
|00004210| 20 6f 66 20 41 2c 20 77 | 68 69 63 68 0a 58 6d 75 | of A, w|hich.Xmu|
|00004220| 73 74 20 6d 61 74 63 68 | 20 74 68 6f 73 65 20 6f |st match| those o|
|00004230| 66 20 44 2e 0a 58 0a 58 | 42 6f 74 68 20 3c 3c 20 |f D..X.X|Both << |
|00004240| 61 6e 64 20 49 6e 6a 65 | 63 74 20 63 61 6e 20 62 |and Inje|ct can b|
|00004250| 65 20 75 73 65 64 20 77 | 69 74 68 20 73 75 62 6d |e used w|ith subm|
|00004260| 61 74 72 69 78 20 65 78 | 70 72 65 73 73 69 6f 6e |atrix ex|pression|
|00004270| 73 20 6f 6e 20 74 68 65 | 20 6c 65 66 74 0a 58 68 |s on the| left.Xh|
|00004280| 61 6e 64 20 73 69 64 65 | 2e 20 53 65 65 20 74 68 |and side|. See th|
|00004290| 65 20 73 65 63 74 69 6f | 6e 20 6f 6e 20 73 75 62 |e sectio|n on sub|
|000042a0| 6d 61 74 72 69 63 65 73 | 2e 0a 58 0a 58 54 6f 20 |matrices|..X.XTo |
|000042b0| 73 65 74 20 74 68 65 20 | 65 6c 65 6d 65 6e 74 73 |set the |elements|
|000042c0| 20 6f 66 20 61 20 6d 61 | 74 72 69 78 20 74 6f 20 | of a ma|trix to |
|000042d0| 61 20 73 63 61 6c 61 72 | 20 75 73 65 20 6f 70 65 |a scalar| use ope|
|000042e0| 72 61 74 6f 72 20 3d 0a | 58 0a 58 20 20 20 20 72 |rator =.|X.X r|
|000042f0| 65 61 6c 20 72 3b 20 4d | 61 74 72 69 78 20 41 28 |eal r; M|atrix A(|
|00004300| 6d 2c 6e 29 3b 0a 58 20 | 20 20 20 2e 2e 2e 2e 2e |m,n);.X | .....|
|00004310| 2e 0a 58 20 20 20 20 4d | 61 74 72 69 78 20 41 28 |..X M|atrix A(|
|00004320| 6d 2c 6e 29 3b 20 41 20 | 3d 20 72 3b 0a 58 0a 58 |m,n); A |= r;.X.X|
|00004330| 59 6f 75 20 63 61 6e 20 | 6c 6f 61 64 20 74 68 65 |You can |load the|
|00004340| 20 65 6c 65 6d 65 6e 74 | 73 20 6f 66 20 61 20 6d | element|s of a m|
|00004350| 61 74 72 69 78 20 66 72 | 6f 6d 20 61 6e 20 61 72 |atrix fr|om an ar|
|00004360| 72 61 79 3a 0a 58 0a 58 | 20 20 20 20 4d 61 74 72 |ray:.X.X| Matr|
|00004370| 69 78 20 41 28 33 2c 32 | 29 3b 0a 58 20 20 20 20 |ix A(3,2|);.X |
|00004380| 72 65 61 6c 20 61 5b 5d | 20 3d 20 7b 20 31 31 2c |real a[]| = { 11,|
|00004390| 31 32 2c 32 31 2c 32 32 | 2c 33 31 2c 33 33 20 7d |12,21,22|,31,33 }|
|000043a0| 3b 0a 58 20 20 20 20 41 | 20 3c 3c 20 61 3b 0a 58 |;.X A| << a;.X|
|000043b0| 0a 58 54 68 69 73 20 63 | 6f 6e 73 74 72 75 63 74 |.XThis c|onstruct|
|000043c0| 69 6f 6e 20 63 61 6e 6e | 6f 74 20 63 68 65 63 6b |ion cann|ot check|
|000043d0| 20 74 68 61 74 20 74 68 | 65 20 6e 75 6d 62 65 72 | that th|e number|
|000043e0| 73 20 6f 66 20 65 6c 65 | 6d 65 6e 74 73 20 6d 61 |s of ele|ments ma|
|000043f0| 74 63 68 0a 58 63 6f 72 | 72 65 63 74 6c 79 2e 20 |tch.Xcor|rectly. |
|00004400| 54 68 69 73 20 76 65 72 | 73 69 6f 6e 20 6f 66 20 |This ver|sion of |
|00004410| 3c 3c 20 63 61 6e 20 62 | 65 20 75 73 65 64 20 77 |<< can b|e used w|
|00004420| 69 74 68 20 73 75 62 6d | 61 74 72 69 63 65 73 20 |ith subm|atrices |
|00004430| 6f 6e 20 74 68 65 20 6c | 65 66 74 0a 58 68 61 6e |on the l|eft.Xhan|
|00004440| 64 20 73 69 64 65 2e 0a | 58 0a 58 0a 58 55 6e 61 |d side..|X.X.XUna|
|00004450| 72 79 20 6f 70 65 72 61 | 74 6f 72 73 0a 58 2d 2d |ry opera|tors.X--|
|00004460| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 0a 58 0a |--------|-----.X.|
|00004470| 58 54 68 65 20 70 61 63 | 6b 61 67 65 20 73 75 70 |XThe pac|kage sup|
|00004480| 70 6f 72 74 73 20 75 6e | 61 72 79 20 6f 70 65 72 |ports un|ary oper|
|00004490| 61 74 69 6f 6e 73 0a 58 | 0a 58 20 20 20 20 63 68 |ations.X|.X ch|
|000044a0| 61 6e 67 65 20 73 69 67 | 6e 20 6f 66 20 65 6c 65 |ange sig|n of ele|
|000044b0| 6d 65 6e 74 73 20 20 20 | 20 20 20 20 20 20 20 20 |ments | |
|000044c0| 20 2d 41 0a 58 20 20 20 | 20 74 72 61 6e 73 70 6f | -A.X | transpo|
|000044d0| 73 65 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |se | |
|000044e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 41 2e 74 28 | | A.t(|
|000044f0| 29 0a 58 20 20 20 20 69 | 6e 76 65 72 73 65 20 28 |).X i|nverse (|
|00004500| 6f 66 20 73 71 75 61 72 | 65 20 6d 61 74 72 69 78 |of squar|e matrix|
|00004510| 20 41 29 20 20 20 20 20 | 20 20 41 2e 69 28 29 0a | A) | A.i().|
|00004520| 58 0a 58 0a 58 42 69 6e | 61 72 79 20 6f 70 65 72 |X.X.XBin|ary oper|
|00004530| 61 74 69 6f 6e 73 0a 58 | 2d 2d 2d 2d 2d 2d 2d 2d |ations.X|--------|
|00004540| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 0a 58 0a 58 54 68 65 |--------|-.X.XThe|
|00004550| 20 70 61 63 6b 61 67 65 | 20 73 75 70 70 6f 72 74 | package| support|
|00004560| 73 20 62 69 6e 61 72 79 | 20 6f 70 65 72 61 74 69 |s binary| operati|
|00004570| 6f 6e 73 0a 58 0a 58 20 | 20 20 20 6d 61 74 72 69 |ons.X.X | matri|
|00004580| 78 20 61 64 64 69 74 69 | 6f 6e 20 20 20 20 20 20 |x additi|on |
|00004590| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 41 2b | | A+|
|000045a0| 42 0a 58 20 20 20 20 6d | 61 74 72 69 78 20 73 75 |B.X m|atrix su|
|000045b0| 62 74 72 61 63 74 69 6f | 6e 20 20 20 20 20 20 20 |btractio|n |
|000045c0| 20 20 20 20 20 20 20 20 | 20 20 41 2d 42 0a 58 20 | | A-B.X |
|000045d0| 20 20 20 6d 61 74 72 69 | 78 20 6d 75 6c 74 69 70 | matri|x multip|
|000045e0| 6c 69 63 61 74 69 6f 6e | 20 20 20 20 20 20 20 20 |lication| |
|000045f0| 20 20 20 20 20 20 41 2a | 42 0a 58 20 20 20 20 65 | A*|B.X e|
|00004600| 71 75 61 74 69 6f 6e 20 | 73 6f 6c 76 65 20 28 73 |quation |solve (s|
|00004610| 71 75 61 72 65 20 6d 61 | 74 72 69 78 20 41 29 20 |quare ma|trix A) |
|00004620| 20 20 41 2e 69 28 29 2a | 42 0a 58 0a 58 49 6e 20 | A.i()*|B.X.XIn |
|00004630| 74 68 65 20 6c 61 73 74 | 20 63 61 73 65 20 74 68 |the last| case th|
|00004640| 65 20 69 6e 76 65 72 73 | 65 20 69 73 20 6e 6f 74 |e invers|e is not|
|00004650| 20 63 61 6c 63 75 6c 61 | 74 65 64 2e 0a 58 0a 58 | calcula|ted..X.X|
|00004660| 4e 6f 74 65 73 3a 0a 58 | 0a 58 49 66 20 79 6f 75 |Notes:.X|.XIf you|
|00004670| 20 61 72 65 20 64 6f 69 | 6e 67 20 72 65 70 65 61 | are doi|ng repea|
|00004680| 74 65 64 20 6d 75 6c 74 | 69 70 6c 69 63 61 74 69 |ted mult|iplicati|
|00004690| 6f 6e 2e 20 46 6f 72 20 | 65 78 61 6d 70 6c 65 20 |on. For |example |
|000046a0| 41 2a 42 2a 43 2c 20 75 | 73 65 0a 58 62 72 61 63 |A*B*C, u|se.Xbrac|
|000046b0| 6b 65 74 73 20 74 6f 20 | 66 6f 72 63 65 20 74 68 |kets to |force th|
|000046c0| 65 20 6f 72 64 65 72 20 | 74 6f 20 6d 69 6e 69 6d |e order |to minim|
|000046d0| 69 7a 65 20 74 68 65 20 | 6e 75 6d 62 65 72 20 6f |ize the |number o|
|000046e0| 66 20 6f 70 65 72 61 74 | 69 6f 6e 73 2e 20 49 66 |f operat|ions. If|
|000046f0| 20 43 0a 58 69 73 20 61 | 20 63 6f 6c 75 6d 6e 20 | C.Xis a| column |
|00004700| 76 65 63 74 6f 72 20 61 | 6e 64 20 41 20 69 73 20 |vector a|nd A is |
|00004710| 6e 6f 74 20 61 20 76 65 | 63 74 6f 72 2c 20 74 68 |not a ve|ctor, th|
|00004720| 65 6e 20 69 74 20 77 69 | 6c 6c 20 75 73 75 61 6c |en it wi|ll usual|
|00004730| 6c 79 20 72 65 64 75 63 | 65 0a 58 74 68 65 20 6e |ly reduc|e.Xthe n|
|00004740| 75 6d 62 65 72 20 6f 66 | 20 6f 70 65 72 61 74 69 |umber of| operati|
|00004750| 6f 6e 73 20 74 6f 20 75 | 73 65 20 41 2a 28 42 2a |ons to u|se A*(B*|
|00004760| 43 29 20 2e 0a 58 0a 58 | 54 68 65 20 70 61 63 6b |C) ..X.X|The pack|
|00004770| 61 67 65 20 64 6f 65 73 | 20 6e 6f 74 20 72 65 63 |age does| not rec|
|00004780| 6f 67 6e 69 73 65 20 42 | 2a 41 2e 69 28 29 20 61 |ognise B|*A.i() a|
|00004790| 73 20 61 6e 20 65 71 75 | 61 74 69 6f 6e 20 73 6f |s an equ|ation so|
|000047a0| 6c 76 65 2e 20 49 74 20 | 69 73 0a 58 70 72 6f 62 |lve. It |is.Xprob|
|000047b0| 61 62 6c 79 20 62 65 74 | 74 65 72 20 74 6f 20 75 |ably bet|ter to u|
|000047c0| 73 65 20 28 41 2e 74 28 | 29 2e 69 28 29 2a 42 2e |se (A.t(|).i()*B.|
|000047d0| 74 28 29 29 2e 74 28 29 | 20 2e 0a 58 0a 58 0a 58 |t()).t()| ..X.X.X|
|000047e0| 43 6f 6d 62 69 6e 61 74 | 69 6f 6e 20 6f 66 20 61 |Combinat|ion of a|
|000047f0| 20 6d 61 74 72 69 78 20 | 61 6e 64 20 73 63 61 6c | matrix |and scal|
|00004800| 61 72 0a 58 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |ar.X----|--------|
|00004810| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00004820| 2d 2d 2d 2d 2d 2d 0a 58 | 0a 58 54 68 65 20 66 6f |------.X|.XThe fo|
|00004830| 6c 6c 6f 77 69 6e 67 20 | 65 78 70 72 65 73 73 69 |llowing |expressi|
|00004840| 6f 6e 20 6d 75 6c 74 69 | 70 6c 69 65 73 20 74 68 |on multi|plies th|
|00004850| 65 20 65 6c 65 6d 65 6e | 74 73 20 6f 66 20 61 20 |e elemen|ts of a |
|00004860| 6d 61 74 72 69 78 20 41 | 20 62 79 20 61 0a 58 73 |matrix A| by a.Xs|
|00004870| 63 61 6c 61 72 20 66 3a | 20 20 41 20 2a 20 66 3b |calar f:| A * f;|
|00004880| 20 4c 69 6b 65 77 69 73 | 65 20 6f 6e 65 20 63 61 | Likewis|e one ca|
|00004890| 6e 20 64 69 76 69 64 65 | 20 74 68 65 20 65 6c 65 |n divide| the ele|
|000048a0| 6d 65 6e 74 73 20 6f 66 | 20 61 20 6d 61 74 72 69 |ments of| a matri|
|000048b0| 78 20 41 20 62 79 0a 58 | 61 20 73 63 61 6c 61 72 |x A by.X|a scalar|
|000048c0| 20 66 3a 20 20 41 20 2f | 20 66 3b 0a 58 0a 58 54 | f: A /| f;.X.XT|
|000048d0| 68 65 20 65 78 70 72 65 | 73 73 69 6f 6e 73 20 20 |he expre|ssions |
|000048e0| 41 20 2b 20 66 20 61 6e | 64 20 41 20 2d 20 66 20 |A + f an|d A - f |
|000048f0| 61 64 64 20 6f 72 20 73 | 75 62 74 72 61 63 74 20 |add or s|ubtract |
|00004900| 61 20 72 65 63 74 61 6e | 67 75 6c 61 72 20 6d 61 |a rectan|gular ma|
|00004910| 74 72 69 78 20 6f 66 0a | 58 74 68 65 20 73 61 6d |trix of.|Xthe sam|
|00004920| 65 20 64 69 6d 65 6e 73 | 69 6f 6e 20 61 73 20 41 |e dimens|ion as A|
|00004930| 20 77 69 74 68 20 65 6c | 65 6d 65 6e 74 73 20 65 | with el|ements e|
|00004940| 71 75 61 6c 20 74 6f 20 | 66 20 74 6f 20 6f 72 20 |qual to |f to or |
|00004950| 66 72 6f 6d 20 74 68 65 | 20 6d 61 74 72 69 78 0a |from the| matrix.|
|00004960| 58 41 2e 0a 58 0a 58 49 | 6e 20 65 61 63 68 20 63 |XA..X.XI|n each c|
|00004970| 61 73 65 20 74 68 65 20 | 6d 61 74 72 69 78 20 6d |ase the |matrix m|
|00004980| 75 73 74 20 62 65 20 74 | 68 65 20 66 69 72 73 74 |ust be t|he first|
|00004990| 20 74 65 72 6d 20 69 6e | 20 74 68 65 20 65 78 70 | term in| the exp|
|000049a0| 72 65 73 73 69 6f 6e 2e | 0a 58 45 78 70 72 65 73 |ression.|.XExpres|
|000049b0| 73 69 6f 6e 73 20 73 75 | 63 68 20 20 66 20 2b 20 |sions su|ch f + |
|000049c0| 41 20 20 6f 72 20 20 66 | 20 2a 20 41 20 20 61 72 |A or f| * A ar|
|000049d0| 65 20 6e 6f 74 20 72 65 | 63 6f 67 6e 69 73 65 64 |e not re|cognised|
|000049e0| 2e 0a 58 0a 58 0a 58 53 | 63 61 6c 61 72 20 66 75 |..X.X.XS|calar fu|
|000049f0| 6e 63 74 69 6f 6e 73 20 | 6f 66 20 6d 61 74 72 69 |nctions |of matri|
|00004a00| 63 65 73 0a 58 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |ces.X---|--------|
|00004a10| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00004a20| 2d 0a 58 20 20 20 20 20 | 20 20 20 20 20 20 20 0a |-.X | .|
|00004a30| 58 20 20 20 20 69 6e 74 | 20 6d 20 3d 20 41 2e 4e |X int| m = A.N|
|00004a40| 72 6f 77 73 28 29 3b 20 | 20 20 20 20 20 20 20 20 |rows(); | |
|00004a50| 20 20 20 20 20 20 20 20 | 20 20 20 2f 2f 20 6e 75 | | // nu|
|00004a60| 6d 62 65 72 20 6f 66 20 | 72 6f 77 73 0a 58 20 20 |mber of |rows.X |
|00004a70| 20 20 69 6e 74 20 6e 20 | 3d 20 41 2e 4e 63 6f 6c | int n |= A.Ncol|
|00004a80| 73 28 29 3b 20 20 20 20 | 20 20 20 20 20 20 20 20 |s(); | |
|00004a90| 20 20 20 20 20 20 20 20 | 2f 2f 20 6e 75 6d 62 65 | |// numbe|
|00004aa0| 72 20 6f 66 20 63 6f 6c | 75 6d 6e 73 0a 58 20 20 |r of col|umns.X |
|00004ab0| 20 20 72 65 61 6c 20 73 | 73 71 20 3d 20 41 2e 53 | real s|sq = A.S|
|00004ac0| 75 6d 53 71 75 61 72 65 | 28 29 3b 20 20 20 20 20 |umSquare|(); |
|00004ad0| 20 20 20 20 20 20 20 20 | 2f 2f 20 73 75 6d 20 6f | |// sum o|
|00004ae0| 66 20 73 71 75 61 72 65 | 73 20 6f 66 20 65 6c 65 |f square|s of ele|
|00004af0| 6d 65 6e 74 73 0a 58 20 | 20 20 20 72 65 61 6c 20 |ments.X | real |
|00004b00| 73 61 76 20 3d 20 41 2e | 53 75 6d 41 62 73 6f 6c |sav = A.|SumAbsol|
|00004b10| 75 74 65 56 61 6c 75 65 | 28 29 3b 20 20 20 20 20 |uteValue|(); |
|00004b20| 20 2f 2f 20 73 75 6d 20 | 6f 66 20 61 62 73 6f 6c | // sum |of absol|
|00004b30| 75 74 65 20 76 61 6c 75 | 65 73 0a 58 20 20 20 20 |ute valu|es.X |
|00004b40| 72 65 61 6c 20 6d 61 76 | 20 3d 20 41 2e 4d 61 78 |real mav| = A.Max|
|00004b50| 69 6d 75 6d 41 62 73 6f | 6c 75 74 65 56 61 6c 75 |imumAbso|luteValu|
|00004b60| 65 28 29 3b 20 20 2f 2f | 20 6d 61 78 69 6d 75 6d |e(); //| maximum|
|00004b70| 20 6f 66 20 61 62 73 6f | 6c 75 74 65 20 76 61 6c | of abso|lute val|
|00004b80| 75 65 73 0a 58 20 20 20 | 20 72 65 61 6c 20 6e 6f |ues.X | real no|
|00004b90| 72 6d 20 3d 20 41 2e 4e | 6f 72 6d 31 28 29 3b 20 |rm = A.N|orm1(); |
|00004ba0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 2f | | /|
|00004bb0| 2f 20 6d 61 78 69 6d 75 | 6d 20 6f 66 20 73 75 6d |/ maximu|m of sum|
|00004bc0| 20 6f 66 20 61 62 73 6f | 6c 75 74 65 0a 58 20 20 | of abso|lute.X |
|00004bd0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00004be0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00004bf0| 20 20 20 20 20 20 20 20 | 20 20 20 76 61 6c 75 65 | | value|
|00004c00| 73 20 6f 66 20 65 6c 65 | 6d 65 6e 74 73 20 6f 66 |s of ele|ments of|
|00004c10| 20 61 20 63 6f 6c 75 6d | 6e 0a 58 20 20 20 20 72 | a colum|n.X r|
|00004c20| 65 61 6c 20 6e 6f 72 6d | 20 3d 20 41 2e 4e 6f 72 |eal norm| = A.Nor|
|00004c30| 6d 49 6e 66 69 6e 69 74 | 79 28 29 3b 20 20 20 20 |mInfinit|y(); |
|00004c40| 20 20 20 20 20 2f 2f 20 | 6d 61 78 69 6d 75 6d 20 | // |maximum |
|00004c50| 6f 66 20 73 75 6d 20 6f | 66 20 61 62 73 6f 6c 75 |of sum o|f absolu|
|00004c60| 74 65 0a 58 20 20 20 20 | 20 20 20 20 20 20 20 20 |te.X | |
|00004c70| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00004c80| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00004c90| 20 76 61 6c 75 65 73 20 | 6f 66 20 65 6c 65 6d 65 | values |of eleme|
|00004ca0| 6e 74 73 20 6f 66 20 61 | 20 72 6f 77 0a 58 20 20 |nts of a| row.X |
|00004cb0| 20 20 72 65 61 6c 20 74 | 20 3d 20 41 2e 54 72 61 | real t| = A.Tra|
|00004cc0| 63 65 28 29 3b 20 20 20 | 20 20 20 20 20 20 20 20 |ce(); | |
|00004cd0| 20 20 20 20 20 20 20 20 | 2f 2f 20 74 72 61 63 65 | |// trace|
|00004ce0| 0a 58 20 20 20 20 4c 6f | 67 61 6e 64 53 69 67 6e |.X Lo|gandSign|
|00004cf0| 20 6c 64 20 3d 20 41 2e | 4c 6f 67 44 65 74 65 72 | ld = A.|LogDeter|
|00004d00| 6d 69 6e 61 6e 74 28 29 | 3b 20 20 20 2f 2f 20 6c |minant()|; // l|
|00004d10| 6f 67 20 6f 66 20 64 65 | 74 65 72 6d 69 6e 61 6e |og of de|terminan|
|00004d20| 74 0a 58 20 20 20 20 42 | 4f 4f 4c 20 7a 20 3d 20 |t.X B|OOL z = |
|00004d30| 41 2e 49 73 5a 65 72 6f | 28 29 3b 20 20 20 20 20 |A.IsZero|(); |
|00004d40| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 2f 2f 20 | | // |
|00004d50| 74 65 73 74 20 61 6c 6c | 20 65 6c 65 6d 65 6e 74 |test all| element|
|00004d60| 73 20 7a 65 72 6f 0a 58 | 20 20 20 20 4d 61 74 72 |s zero.X| Matr|
|00004d70| 69 78 54 79 70 65 20 6d | 74 20 3d 20 41 2e 54 79 |ixType m|t = A.Ty|
|00004d80| 70 65 28 29 3b 20 20 20 | 20 20 20 20 20 20 20 20 |pe(); | |
|00004d90| 20 20 2f 2f 20 74 79 70 | 65 20 6f 66 20 6d 61 74 | // typ|e of mat|
|00004da0| 72 69 78 0a 58 20 20 20 | 20 72 65 61 6c 2a 20 73 |rix.X | real* s|
|00004db0| 20 3d 20 53 74 6f 72 65 | 28 29 3b 20 20 20 20 20 | = Store|(); |
|00004dc0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 2f | | /|
|00004dd0| 2f 20 70 6f 69 6e 74 65 | 72 20 74 6f 20 61 72 72 |/ pointe|r to arr|
|00004de0| 61 79 20 6f 66 20 65 6c | 65 6d 65 6e 74 73 0a 58 |ay of el|ements.X|
|00004df0| 20 20 20 20 69 6e 74 20 | 6c 20 3d 20 53 74 6f 72 | int |l = Stor|
|00004e00| 61 67 65 28 29 3b 20 20 | 20 20 20 20 20 20 20 20 |age(); | |
|00004e10| 20 20 20 20 20 20 20 20 | 20 20 2f 2f 20 6c 65 6e | | // len|
|00004e20| 67 74 68 20 6f 66 20 61 | 72 72 61 79 20 6f 66 20 |gth of a|rray of |
|00004e30| 65 6c 65 6d 65 6e 74 73 | 0a 58 0a 58 41 2e 4c 6f |elements|.X.XA.Lo|
|00004e40| 67 44 65 74 65 72 6d 69 | 6e 61 6e 74 28 29 20 72 |gDetermi|nant() r|
|00004e50| 65 74 75 72 6e 73 20 61 | 20 76 61 6c 75 65 20 6f |eturns a| value o|
|00004e60| 66 20 74 79 70 65 20 4c | 6f 67 61 6e 64 53 69 67 |f type L|ogandSig|
|00004e70| 6e 2e 20 49 66 20 6c 64 | 20 69 73 20 6f 66 20 74 |n. If ld| is of t|
|00004e80| 79 70 65 20 0a 58 4c 6f | 67 41 6e 64 53 69 67 6e |ype .XLo|gAndSign|
|00004e90| 20 20 75 73 65 0a 58 0a | 58 20 20 20 20 6c 64 2e | use.X.|X ld.|
|00004ea0| 56 61 6c 75 65 28 29 20 | 20 20 20 74 6f 20 67 65 |Value() | to ge|
|00004eb0| 74 20 74 68 65 20 76 61 | 6c 75 65 20 6f 66 20 74 |t the va|lue of t|
|00004ec0| 68 65 20 64 65 74 65 72 | 6d 69 6e 61 6e 74 0a 58 |he deter|minant.X|
|00004ed0| 20 20 20 20 6c 64 2e 53 | 69 67 6e 28 29 20 20 20 | ld.S|ign() |
|00004ee0| 20 20 74 6f 20 67 65 74 | 20 74 68 65 20 73 69 67 | to get| the sig|
|00004ef0| 6e 20 6f 66 20 74 68 65 | 20 64 65 74 65 72 6d 69 |n of the| determi|
|00004f00| 6e 61 6e 74 20 28 76 61 | 6c 75 65 73 20 31 2c 20 |nant (va|lues 1, |
|00004f10| 30 2c 20 2d 31 29 0a 58 | 20 20 20 20 6c 64 2e 4c |0, -1).X| ld.L|
|00004f20| 6f 67 56 61 6c 75 65 28 | 29 20 74 6f 20 67 65 74 |ogValue(|) to get|
|00004f30| 20 74 68 65 20 6c 6f 67 | 20 6f 66 20 74 68 65 20 | the log| of the |
|00004f40| 61 62 73 6f 6c 75 74 65 | 20 76 61 6c 75 65 2e 0a |absolute| value..|
|00004f50| 58 0a 58 41 2e 49 73 5a | 65 72 6f 28 29 20 72 65 |X.XA.IsZ|ero() re|
|00004f60| 74 75 72 6e 73 20 42 4f | 4f 4c 20 76 61 6c 75 65 |turns BO|OL value|
|00004f70| 20 54 52 55 45 20 69 66 | 20 74 68 65 20 6d 61 74 | TRUE if| the mat|
|00004f80| 72 69 78 20 41 20 68 61 | 73 20 61 6c 6c 20 65 6c |rix A ha|s all el|
|00004f90| 65 6d 65 6e 74 73 0a 58 | 65 71 75 61 6c 20 74 6f |ements.X|equal to|
|00004fa0| 20 30 2e 30 2e 0a 58 0a | 58 4d 61 74 72 69 78 54 | 0.0..X.|XMatrixT|
|00004fb0| 79 70 65 20 6d 74 20 3d | 20 41 2e 54 79 70 65 28 |ype mt =| A.Type(|
|00004fc0| 29 20 72 65 74 75 72 6e | 73 20 74 68 65 20 74 79 |) return|s the ty|
|00004fd0| 70 65 20 6f 66 20 61 20 | 6d 61 74 72 69 78 2e 20 |pe of a |matrix. |
|00004fe0| 55 73 65 20 28 63 68 61 | 72 2a 29 6d 74 20 74 6f |Use (cha|r*)mt to|
|00004ff0| 0a 58 67 65 74 20 61 20 | 73 74 72 69 6e 67 20 20 |.Xget a |string |
|00005000| 28 55 54 2c 20 4c 54 2c | 20 52 65 63 74 2c 20 53 |(UT, LT,| Rect, S|
|00005010| 79 6d 2c 20 44 69 61 67 | 2c 20 52 6f 77 56 2c 20 |ym, Diag|, RowV, |
|00005020| 43 6f 6c 56 2c 20 43 72 | 6f 75 74 29 20 73 68 6f |ColV, Cr|out) sho|
|00005030| 77 69 6e 67 20 74 68 65 | 0a 58 74 79 70 65 2e 0a |wing the|.Xtype..|
|00005040| 58 0a 58 53 75 6d 53 71 | 75 61 72 65 28 41 29 2c |X.XSumSq|uare(A),|
|00005050| 20 53 75 6d 41 62 73 6f | 6c 75 74 65 56 61 6c 75 | SumAbso|luteValu|
|00005060| 65 28 41 29 2c 20 4d 61 | 78 69 6d 75 6d 41 62 73 |e(A), Ma|ximumAbs|
|00005070| 6f 6c 75 74 65 56 61 6c | 75 65 28 41 29 2c 20 54 |oluteVal|ue(A), T|
|00005080| 72 61 63 65 28 41 29 2c | 0a 58 4c 6f 67 44 65 74 |race(A),|.XLogDet|
|00005090| 65 72 6d 69 6e 61 6e 74 | 28 41 29 2c 20 4e 6f 72 |erminant|(A), Nor|
|000050a0| 6d 31 28 41 29 2c 20 4e | 6f 72 6d 49 6e 66 69 6e |m1(A), N|ormInfin|
|000050b0| 69 74 79 28 41 29 20 20 | 63 61 6e 20 62 65 20 75 |ity(A) |can be u|
|000050c0| 73 65 64 20 69 6e 20 70 | 6c 61 63 65 20 6f 66 0a |sed in p|lace of.|
|000050d0| 58 41 2e 53 75 6d 53 71 | 75 61 72 65 28 29 2c 20 |XA.SumSq|uare(), |
|000050e0| 41 2e 53 75 6d 41 62 73 | 6f 6c 75 74 65 56 61 6c |A.SumAbs|oluteVal|
|000050f0| 75 65 28 29 2c 20 41 2e | 4d 61 78 69 6d 75 6d 41 |ue(), A.|MaximumA|
|00005100| 62 73 6f 6c 75 74 65 56 | 61 6c 75 65 28 29 2c 0a |bsoluteV|alue(),.|
|00005110| 58 41 2e 54 72 61 63 65 | 28 29 2c 20 41 2e 4c 6f |XA.Trace|(), A.Lo|
|00005120| 67 44 65 74 65 72 6d 69 | 6e 61 6e 74 28 29 2c 20 |gDetermi|nant(), |
|00005130| 41 2e 4e 6f 72 6d 31 28 | 29 2c 20 41 2c 4e 6f 72 |A.Norm1(|), A,Nor|
|00005140| 6d 49 6e 66 69 6e 69 74 | 79 28 29 2e 0a 58 0a 58 |mInfinit|y()..X.X|
|00005150| 0a 58 53 75 62 6d 61 74 | 72 69 78 20 6f 70 65 72 |.XSubmat|rix oper|
|00005160| 61 74 69 6f 6e 73 0a 58 | 2d 2d 2d 2d 2d 2d 2d 2d |ations.X|--------|
|00005170| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 0a 58 0a 58 |--------|----.X.X|
|00005180| 41 2e 53 75 62 4d 61 74 | 72 69 78 28 66 72 2c 6c |A.SubMat|rix(fr,l|
|00005190| 72 2c 66 63 2c 6c 63 29 | 0a 58 0a 58 54 68 69 73 |r,fc,lc)|.X.XThis|
|000051a0| 20 73 65 6c 65 63 74 73 | 20 61 20 73 75 62 6d 61 | selects| a subma|
|000051b0| 74 72 69 78 20 66 72 6f | 6d 20 41 2e 20 74 68 65 |trix fro|m A. the|
|000051c0| 20 61 72 67 75 6d 65 6e | 74 73 20 20 66 72 2c 6c | argumen|ts fr,l|
|000051d0| 72 2c 66 63 2c 6c 63 20 | 20 61 72 65 20 74 68 65 |r,fc,lc | are the|
|000051e0| 0a 58 66 69 72 73 74 20 | 72 6f 77 2c 20 6c 61 73 |.Xfirst |row, las|
|000051f0| 74 20 72 6f 77 2c 20 66 | 69 72 73 74 20 63 6f 6c |t row, f|irst col|
|00005200| 75 6d 6e 2c 20 6c 61 73 | 74 20 63 6f 6c 75 6d 6e |umn, las|t column|
|00005210| 20 6f 66 20 74 68 65 20 | 73 75 62 6d 61 74 72 69 | of the |submatri|
|00005220| 78 20 77 69 74 68 20 74 | 68 65 0a 58 6e 75 6d 62 |x with t|he.Xnumb|
|00005230| 65 72 69 6e 67 20 62 65 | 67 69 6e 6e 69 6e 67 20 |ering be|ginning |
|00005240| 61 74 20 31 2e 20 54 68 | 69 73 20 6d 61 79 20 62 |at 1. Th|is may b|
|00005250| 65 20 75 73 65 64 20 69 | 6e 20 61 6e 79 20 6d 61 |e used i|n any ma|
|00005260| 74 72 69 78 20 65 78 70 | 72 65 73 73 69 6f 6e 20 |trix exp|ression |
|00005270| 6f 72 0a 58 6f 6e 20 74 | 68 65 20 6c 65 66 74 20 |or.Xon t|he left |
|00005280| 68 61 6e 64 20 73 69 64 | 65 20 6f 66 20 3c 3c 20 |hand sid|e of << |
|00005290| 6f 72 20 49 6e 6a 65 63 | 74 2e 20 49 6e 6a 65 63 |or Injec|t. Injec|
|000052a0| 74 20 64 6f 65 73 20 6e | 6f 74 20 63 68 65 63 6b |t does n|ot check|
|000052b0| 20 6e 6f 0a 58 69 6e 66 | 6f 72 6d 61 74 69 6f 6e | no.Xinf|ormation|
|000052c0| 20 6c 6f 73 73 20 69 6e | 20 74 68 69 73 20 63 61 | loss in| this ca|
|000052d0| 73 65 2e 20 59 6f 75 20 | 63 61 6e 20 61 6c 73 6f |se. You |can also|
|000052e0| 20 75 73 65 20 74 68 65 | 20 63 6f 6e 73 74 72 75 | use the| constru|
|000052f0| 63 74 69 6f 6e 0a 58 0a | 58 20 20 20 20 72 65 61 |ction.X.|X rea|
|00005300| 6c 20 63 3b 20 2e 2e 2e | 2e 20 41 2e 53 75 62 4d |l c; ...|. A.SubM|
|00005310| 61 74 72 69 78 28 66 72 | 2c 6c 72 2c 66 63 2c 6c |atrix(fr|,lr,fc,l|
|00005320| 63 29 20 3c 3c 20 63 3b | 0a 58 0a 58 74 6f 20 73 |c) << c;|.X.Xto s|
|00005330| 65 74 20 61 20 73 75 62 | 6d 61 74 72 69 78 20 65 |et a sub|matrix e|
|00005340| 71 75 61 6c 20 74 6f 20 | 61 20 63 6f 6e 73 74 61 |qual to |a consta|
|00005350| 6e 74 2e 0a 58 0a 58 54 | 68 65 20 66 6f 6c 6c 77 |nt..X.XT|he follw|
|00005360| 69 6e 67 20 61 72 65 20 | 76 61 72 69 61 6e 74 73 |ing are |variants|
|00005370| 20 6f 66 20 53 75 62 4d | 61 74 72 69 78 3a 0a 58 | of SubM|atrix:.X|
|00005380| 0a 58 20 20 20 20 41 2e | 53 79 6d 53 75 62 4d 61 |.X A.|SymSubMa|
|00005390| 74 72 69 78 28 66 2c 6c | 29 20 20 20 20 20 20 20 |trix(f,l|) |
|000053a0| 20 20 20 20 20 20 2f 2f | 20 20 20 54 68 69 73 20 | //| This |
|000053b0| 61 73 73 75 6d 65 73 20 | 66 72 3d 66 63 20 61 6e |assumes |fr=fc an|
|000053c0| 64 20 6c 72 3d 6c 63 2e | 0a 58 20 20 20 20 41 2e |d lr=lc.|.X A.|
|000053d0| 52 6f 77 73 28 66 2c 6c | 29 20 20 20 20 20 20 20 |Rows(f,l|) |
|000053e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 2f 2f | | //|
|000053f0| 20 20 20 73 65 6c 65 63 | 74 20 72 6f 77 73 0a 58 | selec|t rows.X|
|00005400| 20 20 20 20 41 2e 52 6f | 77 28 66 29 20 20 20 20 | A.Ro|w(f) |
|00005410| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00005420| 20 20 20 20 2f 2f 20 20 | 20 73 65 6c 65 63 74 20 | // | select |
|00005430| 73 69 6e 67 6c 65 20 72 | 6f 77 0a 58 20 20 20 20 |single r|ow.X |
|00005440| 41 2e 43 6f 6c 75 6d 6e | 73 28 66 2c 6c 29 20 20 |A.Column|s(f,l) |
|00005450| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00005460| 2f 2f 20 20 20 73 65 6c | 65 63 74 20 63 6f 6c 75 |// sel|ect colu|
|00005470| 6d 6e 73 0a 58 20 20 20 | 20 41 2e 43 6f 6c 75 6d |mns.X | A.Colum|
|00005480| 6e 28 66 29 20 20 20 20 | 20 20 20 20 20 20 20 20 |n(f) | |
|00005490| 20 20 20 20 20 20 20 20 | 20 2f 2f 20 20 20 73 65 | | // se|
|000054a0| 6c 65 63 74 20 73 69 6e | 67 6c 65 20 63 6f 6c 75 |lect sin|gle colu|
|000054b0| 6d 6e 0a 58 0a 58 49 6e | 20 65 61 63 68 20 63 61 |mn.X.XIn| each ca|
|000054c0| 73 65 20 66 20 61 6e 64 | 20 6c 20 6d 65 61 6e 20 |se f and| l mean |
|000054d0| 74 68 65 20 66 69 72 73 | 74 20 61 6e 64 20 6c 61 |the firs|t and la|
|000054e0| 73 74 20 72 6f 77 20 6f | 72 20 63 6f 6c 75 6d 6e |st row o|r column|
|000054f0| 20 74 6f 20 62 65 0a 58 | 73 65 6c 65 63 74 65 64 | to be.X|selected|
|00005500| 20 28 73 74 61 72 74 69 | 6e 67 20 61 74 20 31 29 | (starti|ng at 1)|
|00005510| 2e 0a 58 0a 58 49 66 20 | 53 75 62 4d 61 74 72 69 |..X.XIf |SubMatri|
|00005520| 78 20 6f 72 20 69 74 73 | 20 76 61 72 69 61 6e 74 |x or its| variant|
|00005530| 20 6f 63 63 75 72 73 20 | 6f 6e 20 74 68 65 20 72 | occurs |on the r|
|00005540| 69 67 68 74 20 68 61 6e | 64 20 73 69 64 65 20 6f |ight han|d side o|
|00005550| 66 20 61 6e 20 3d 20 6f | 72 20 3c 3c 0a 58 6f 72 |f an = o|r <<.Xor|
|00005560| 20 77 69 74 68 69 6e 20 | 61 6e 20 65 78 70 72 65 | within |an expre|
|00005570| 73 73 69 6f 6e 20 69 74 | 73 20 74 79 70 65 20 69 |ssion it|s type i|
|00005580| 73 20 61 73 20 66 6f 6c | 6c 6f 77 73 0a 58 0a 58 |s as fol|lows.X.X|
|00005590| 20 20 20 20 41 2e 53 75 | 62 6d 61 74 72 69 78 28 | A.Su|bmatrix(|
|000055a0| 66 72 2c 6c 72 2c 66 63 | 2c 6c 63 29 3a 20 20 20 |fr,lr,fc|,lc): |
|000055b0| 20 20 20 20 20 20 20 20 | 49 66 20 41 20 69 73 20 | |If A is |
|000055c0| 52 6f 77 56 65 63 74 6f | 72 20 6f 72 0a 58 20 20 |RowVecto|r or.X |
|000055d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000055e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000055f0| 20 20 20 20 20 20 43 6f | 6c 75 6d 6e 56 65 63 74 | Co|lumnVect|
|00005600| 6f 72 20 74 68 65 6e 20 | 73 61 6d 65 20 74 79 70 |or then |same typ|
|00005610| 65 0a 58 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |e.X | |
|00005620| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00005630| 20 20 20 20 20 20 20 20 | 20 20 20 6f 74 68 65 72 | | other|
|00005640| 77 69 73 65 20 74 79 70 | 65 20 4d 61 74 72 69 78 |wise typ|e Matrix|
|00005650| 0a 58 20 20 20 20 41 2e | 53 79 6d 53 75 62 4d 61 |.X A.|SymSubMa|
|00005660| 74 72 69 78 28 66 2c 6c | 29 3a 20 20 20 20 20 20 |trix(f,l|): |
|00005670| 20 20 20 20 20 20 20 20 | 20 20 53 61 6d 65 20 74 | | Same t|
|00005680| 79 70 65 20 61 73 20 41 | 0a 58 20 20 20 20 41 2e |ype as A|.X A.|
|00005690| 52 6f 77 73 28 66 2c 6c | 29 3a 20 20 20 20 20 20 |Rows(f,l|): |
|000056a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000056b0| 20 20 54 79 70 65 20 4d | 61 74 72 69 78 0a 58 20 | Type M|atrix.X |
|000056c0| 20 20 20 41 2e 52 6f 77 | 28 66 29 3a 20 20 20 20 | A.Row|(f): |
|000056d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000056e0| 20 20 20 20 20 20 20 54 | 79 70 65 20 52 6f 77 56 | T|ype RowV|
|000056f0| 65 63 74 6f 72 0a 58 20 | 20 20 20 41 2e 43 6f 6c |ector.X | A.Col|
|00005700| 75 6d 6e 73 28 66 2c 6c | 29 3a 20 20 20 20 20 20 |umns(f,l|): |
|00005710| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 54 | | T|
|00005720| 79 70 65 20 4d 61 74 72 | 69 78 0a 58 20 20 20 20 |ype Matr|ix.X |
|00005730| 41 2e 43 6f 6c 75 6d 6e | 28 66 29 3a 20 20 20 20 |A.Column|(f): |
|00005740| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00005750| 20 20 20 20 54 79 70 65 | 20 43 6f 6c 75 6d 6e 56 | Type| ColumnV|
|00005760| 65 63 74 6f 72 0a 58 0a | 58 0a 58 49 66 20 53 75 |ector.X.|X.XIf Su|
|00005770| 62 4d 61 74 72 69 78 20 | 6f 72 20 69 74 73 20 76 |bMatrix |or its v|
|00005780| 61 72 69 61 6e 74 20 61 | 70 70 65 61 72 73 20 6f |ariant a|ppears o|
|00005790| 6e 20 74 68 65 20 6c 65 | 66 74 20 68 61 6e 64 20 |n the le|ft hand |
|000057a0| 73 69 64 65 20 6f 66 20 | 20 3c 3c 20 2c 20 74 68 |side of | << , th|
|000057b0| 69 6e 6b 0a 58 6f 66 20 | 69 74 73 20 74 79 70 65 |ink.Xof |its type|
|000057c0| 20 62 65 69 6e 67 20 4d | 61 74 72 69 78 2e 20 54 | being M|atrix. T|
|000057d0| 68 75 73 20 4c 2e 52 6f | 77 28 31 29 20 77 68 65 |hus L.Ro|w(1) whe|
|000057e0| 72 65 20 4c 20 69 73 20 | 4c 6f 77 65 72 54 72 69 |re L is |LowerTri|
|000057f0| 61 6e 67 75 6c 61 72 4d | 61 74 72 69 78 0a 58 65 |angularM|atrix.Xe|
|00005800| 78 70 65 63 74 73 20 20 | 4c 2e 4e 63 6f 6c 73 28 |xpects |L.Ncols(|
|00005810| 29 20 20 65 6c 65 6d 65 | 6e 74 73 20 65 76 65 6e |) eleme|nts even|
|00005820| 20 74 68 6f 75 67 68 20 | 69 74 20 77 69 6c 6c 20 | though |it will |
|00005830| 75 73 65 20 6f 6e 6c 79 | 20 6f 6e 65 20 6f 66 20 |use only| one of |
|00005840| 74 68 65 6d 2e 0a 58 0a | 58 0a 58 43 68 61 6e 67 |them..X.|X.XChang|
|00005850| 65 20 64 69 6d 65 6e 73 | 69 6f 6e 73 0a 58 2d 2d |e dimens|ions.X--|
|00005860| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 0a |--------|-------.|
|00005870| 58 0a 58 54 68 65 20 66 | 6f 6c 6c 6f 77 69 6e 67 |X.XThe f|ollowing|
|00005880| 20 6f 70 65 72 61 74 69 | 6f 6e 73 20 63 68 61 6e | operati|ons chan|
|00005890| 67 65 20 74 68 65 20 64 | 69 6d 65 6e 73 69 6f 6e |ge the d|imension|
|000058a0| 73 20 6f 66 20 61 20 6d | 61 74 72 69 78 2e 20 54 |s of a m|atrix. T|
|000058b0| 68 65 20 76 61 6c 75 65 | 73 0a 58 6f 66 20 74 68 |he value|s.Xof th|
|000058c0| 65 20 65 6c 65 6d 65 6e | 74 73 20 61 72 65 20 6c |e elemen|ts are l|
|000058d0| 6f 73 74 2e 0a 58 0a 58 | 20 20 20 20 41 2e 52 65 |ost..X.X| A.Re|
|000058e0| 44 69 6d 65 6e 73 69 6f | 6e 28 6e 72 6f 77 73 2c |Dimensio|n(nrows,|
|000058f0| 6e 63 6f 6c 73 29 3b 20 | 20 20 20 20 2f 2f 20 66 |ncols); | // f|
|00005900| 6f 72 20 74 79 70 65 20 | 4d 61 74 72 69 78 20 6f |or type |Matrix o|
|00005910| 72 20 6e 72 69 63 4d 61 | 74 72 69 78 0a 58 20 20 |r nricMa|trix.X |
|00005920| 20 20 41 2e 52 65 44 69 | 6d 65 6e 73 69 6f 6e 28 | A.ReDi|mension(|
|00005930| 6e 29 3b 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |n); | |
|00005940| 20 20 2f 2f 20 66 6f 72 | 20 61 6c 6c 20 6f 74 68 | // for| all oth|
|00005950| 65 72 20 74 79 70 65 73 | 0a 58 0a 58 0a 58 43 68 |er types|.X.X.XCh|
|00005960| 61 6e 67 65 20 74 79 70 | 65 0a 58 2d 2d 2d 2d 2d |ange typ|e.X-----|
|00005970| 2d 2d 2d 2d 2d 2d 0a 58 | 0a 58 54 68 65 20 66 6f |------.X|.XThe fo|
|00005980| 6c 6c 6f 77 69 6e 67 20 | 66 75 6e 63 74 69 6f 6e |llowing |function|
|00005990| 73 20 69 6e 74 65 72 70 | 72 65 74 20 74 68 65 20 |s interp|ret the |
|000059a0| 65 6c 65 6d 65 6e 74 73 | 20 6f 66 20 61 20 6d 61 |elements| of a ma|
|000059b0| 74 72 69 78 0a 58 28 73 | 74 6f 72 65 64 20 72 6f |trix.X(s|tored ro|
|000059c0| 77 20 62 79 20 72 6f 77 | 29 20 74 6f 20 62 65 20 |w by row|) to be |
|000059d0| 61 20 76 65 63 74 6f 72 | 20 6f 72 20 6d 61 74 72 |a vector| or matr|
|000059e0| 69 78 20 6f 66 20 61 20 | 64 69 66 66 65 72 65 6e |ix of a |differen|
|000059f0| 74 20 74 79 70 65 2e 20 | 41 63 74 75 61 6c 0a 58 |t type. |Actual.X|
|00005a00| 63 6f 70 79 69 6e 67 20 | 69 73 20 75 73 75 61 6c |copying |is usual|
|00005a10| 6c 79 20 61 76 6f 69 64 | 65 64 20 77 68 65 72 65 |ly avoid|ed where|
|00005a20| 20 74 68 65 73 65 20 6f | 63 63 75 72 20 61 73 20 | these o|ccur as |
|00005a30| 70 61 72 74 20 6f 66 20 | 61 20 6d 6f 72 65 0a 58 |part of |a more.X|
|00005a40| 63 6f 6d 70 6c 69 63 61 | 74 65 64 20 65 78 70 72 |complica|ted expr|
|00005a50| 65 73 73 69 6f 6e 2e 0a | 58 0a 58 20 20 20 20 41 |ession..|X.X A|
|00005a60| 2e 43 6f 70 79 54 6f 52 | 6f 77 28 29 0a 58 20 20 |.CopyToR|ow().X |
|00005a70| 20 20 41 2e 43 6f 70 79 | 54 6f 43 6f 6c 75 6d 6e | A.Copy|ToColumn|
|00005a80| 28 29 0a 58 20 20 20 20 | 41 2e 43 6f 70 79 54 6f |().X |A.CopyTo|
|00005a90| 44 69 61 67 6f 6e 61 6c | 28 29 0a 58 20 20 20 20 |Diagonal|().X |
|00005aa0| 41 2e 43 6f 70 79 54 6f | 4d 61 74 72 69 78 28 6e |A.CopyTo|Matrix(n|
|00005ab0| 72 6f 77 73 2c 6e 63 6f | 6c 73 29 0a 58 20 20 20 |rows,nco|ls).X |
|00005ac0| 20 41 2e 63 28 29 0a 58 | 20 20 20 20 72 65 61 6c | A.c().X| real|
|00005ad0| 28 41 29 0a 58 0a 58 54 | 68 65 20 66 6f 72 6d 20 |(A).X.XT|he form |
|00005ae0| 2e 63 28 29 20 69 73 20 | 75 73 65 64 20 69 6e 20 |.c() is |used in |
|00005af0| 6d 61 74 72 69 78 20 65 | 78 70 72 65 73 73 69 6f |matrix e|xpressio|
|00005b00| 6e 73 20 77 68 65 6e 20 | 41 20 69 73 20 6f 66 20 |ns when |A is of |
|00005b10| 61 20 63 6f 6e 73 74 0a | 58 74 79 70 65 2e 20 54 |a const.|Xtype. T|
|00005b20| 68 65 20 65 78 70 72 65 | 73 73 69 6f 6e 20 72 65 |he expre|ssion re|
|00005b30| 61 6c 28 41 29 20 69 73 | 20 75 73 65 64 20 74 6f |al(A) is| used to|
|00005b40| 20 63 6f 6e 76 65 72 74 | 20 61 20 31 20 78 20 31 | convert| a 1 x 1|
|00005b50| 20 6d 61 74 72 69 78 20 | 74 6f 20 61 0a 58 73 63 | matrix |to a.Xsc|
|00005b60| 61 6c 61 72 2e 0a 58 0a | 58 0a 58 4d 75 6c 74 69 |alar..X.|X.XMulti|
|00005b70| 70 6c 65 20 6d 61 74 72 | 69 78 20 73 6f 6c 76 65 |ple matr|ix solve|
|00005b80| 0a 58 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |.X------|--------|
|00005b90| 2d 2d 2d 2d 2d 2d 2d 0a | 58 0a 58 49 66 20 41 20 |-------.|X.XIf A |
|00005ba0| 69 73 20 61 20 73 71 75 | 61 72 65 20 6f 72 20 73 |is a squ|are or s|
|00005bb0| 79 6d 6d 65 74 72 69 63 | 20 6d 61 74 72 69 78 20 |ymmetric| matrix |
|00005bc0| 75 73 65 0a 58 0a 58 20 | 20 20 20 43 72 6f 75 74 |use.X.X | Crout|
|00005bd0| 4d 61 74 72 69 78 20 58 | 20 3d 20 41 3b 20 20 20 |Matrix X| = A; |
|00005be0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 2f 2f 20 | | // |
|00005bf0| 63 61 72 72 69 65 73 20 | 6f 75 74 20 4c 55 20 64 |carries |out LU d|
|00005c00| 65 63 6f 6d 70 6f 73 69 | 74 69 6f 6e 0a 58 20 20 |ecomposi|tion.X |
|00005c10| 20 20 4d 61 74 72 69 78 | 20 41 50 20 3d 20 58 2e | Matrix| AP = X.|
|00005c20| 69 28 29 2a 50 3b 20 4d | 61 74 72 69 78 20 41 51 |i()*P; M|atrix AQ|
|00005c30| 20 3d 20 58 2e 69 28 29 | 2a 51 3b 0a 58 20 20 20 | = X.i()|*Q;.X |
|00005c40| 20 4c 6f 67 41 6e 64 53 | 69 67 6e 20 6c 64 20 3d | LogAndS|ign ld =|
|00005c50| 20 58 2e 4c 6f 67 44 65 | 74 65 72 6d 69 6e 61 6e | X.LogDe|terminan|
|00005c60| 74 28 29 3b 0a 58 0a 58 | 72 61 74 68 65 72 20 74 |t();.X.X|rather t|
|00005c70| 68 61 6e 0a 58 0a 58 20 | 20 20 20 4d 61 74 72 69 |han.X.X | Matri|
|00005c80| 78 20 41 50 20 3d 20 41 | 2e 69 28 29 2a 50 3b 20 |x AP = A|.i()*P; |
|00005c90| 4d 61 74 72 69 78 20 41 | 51 20 3d 20 41 2e 69 28 |Matrix A|Q = A.i(|
|00005ca0| 29 2a 51 3b 0a 58 20 20 | 20 20 4c 6f 67 41 6e 64 |)*Q;.X | LogAnd|
|00005cb0| 53 69 67 6e 20 6c 64 20 | 3d 20 41 2e 4c 6f 67 44 |Sign ld |= A.LogD|
|00005cc0| 65 74 65 72 6d 69 6e 61 | 6e 74 28 29 3b 0a 58 0a |etermina|nt();.X.|
|00005cd0| 58 73 69 6e 63 65 20 65 | 61 63 68 20 6f 70 65 72 |Xsince e|ach oper|
|00005ce0| 61 74 69 6f 6e 20 77 69 | 6c 6c 20 72 65 70 65 61 |ation wi|ll repea|
|00005cf0| 74 20 74 68 65 20 4c 55 | 20 64 65 63 6f 6d 70 6f |t the LU| decompo|
|00005d00| 73 74 69 6f 6e 2e 0a 58 | 0a 58 0a 58 4d 65 6d 6f |stion..X|.X.XMemo|
|00005d10| 72 79 20 6d 61 6e 61 67 | 65 6d 65 6e 74 0a 58 2d |ry manag|ement.X-|
|00005d20| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00005d30| 0a 58 0a 58 54 68 65 20 | 70 61 63 6b 61 67 65 20 |.X.XThe |package |
|00005d40| 64 6f 65 73 20 6e 6f 74 | 20 73 75 70 70 6f 72 74 |does not| support|
|00005d50| 20 64 65 6c 61 79 65 64 | 20 63 6f 70 79 2e 20 53 | delayed| copy. S|
|00005d60| 65 76 65 72 61 6c 20 73 | 74 72 61 74 65 67 69 65 |everal s|trategie|
|00005d70| 73 20 61 72 65 0a 58 72 | 65 71 75 69 72 65 64 20 |s are.Xr|equired |
|00005d80| 74 6f 20 70 72 65 76 65 | 6e 74 20 75 6e 6e 65 63 |to preve|nt unnec|
|00005d90| 65 73 73 61 72 79 20 6d | 61 74 72 69 78 20 63 6f |essary m|atrix co|
|00005da0| 70 69 65 73 2e 0a 58 0a | 58 57 68 65 72 65 20 61 |pies..X.|XWhere a|
|00005db0| 20 6d 61 74 72 69 78 20 | 69 73 20 63 61 6c 6c 65 | matrix |is calle|
|00005dc0| 64 20 61 73 20 61 20 66 | 75 6e 63 74 69 6f 6e 20 |d as a f|unction |
|00005dd0| 61 72 67 75 6d 65 6e 74 | 20 75 73 65 20 61 20 63 |argument| use a c|
|00005de0| 6f 6e 73 74 61 6e 74 0a | 58 72 65 66 65 72 65 6e |onstant.|Xreferen|
|00005df0| 63 65 2e 20 46 6f 72 20 | 65 78 61 6d 70 6c 65 0a |ce. For |example.|
|00005e00| 58 0a 58 20 20 20 20 59 | 6f 75 72 46 75 6e 63 74 |X.X Y|ourFunct|
|00005e10| 69 6f 6e 28 63 6f 6e 73 | 74 20 4d 61 74 72 69 78 |ion(cons|t Matrix|
|00005e20| 26 20 41 29 0a 58 0a 58 | 72 61 74 68 65 72 20 74 |& A).X.X|rather t|
|00005e30| 68 61 6e 0a 58 0a 58 20 | 20 20 20 59 6f 75 72 46 |han.X.X | YourF|
|00005e40| 75 6e 63 74 69 6f 6e 28 | 4d 61 74 72 69 78 20 41 |unction(|Matrix A|
|00005e50| 29 0a 58 0a 58 43 6f 6e | 73 74 61 6e 74 20 6d 61 |).X.XCon|stant ma|
|00005e60| 74 72 69 63 65 73 20 63 | 61 6e 6e 6f 74 20 62 65 |trices c|annot be|
|00005e70| 20 75 73 65 64 20 69 6e | 20 6d 61 74 72 69 78 20 | used in| matrix |
|00005e80| 65 78 70 72 65 73 73 69 | 6f 6e 73 20 73 6f 20 69 |expressi|ons so i|
|00005e90| 66 20 79 6f 75 20 77 69 | 73 68 20 74 6f 0a 58 75 |f you wi|sh to.Xu|
|00005ea0| 73 65 20 41 20 69 6e 20 | 61 6e 20 65 78 70 72 65 |se A in |an expre|
|00005eb0| 73 73 69 6f 6e 20 77 69 | 74 68 69 6e 20 74 68 69 |ssion wi|thin thi|
|00005ec0| 73 20 66 75 6e 63 74 69 | 6f 6e 20 75 73 65 20 41 |s functi|on use A|
|00005ed0| 2e 63 28 29 20 72 61 74 | 68 65 72 20 74 68 61 6e |.c() rat|her than|
|00005ee0| 20 41 2e 0a 58 0a 58 53 | 6b 69 70 20 74 68 65 20 | A..X.XS|kip the |
|00005ef0| 72 65 73 74 20 6f 66 20 | 74 68 69 73 20 73 65 63 |rest of |this sec|
|00005f00| 74 69 6f 6e 20 6f 6e 20 | 79 6f 75 72 20 66 69 72 |tion on |your fir|
|00005f10| 73 74 20 72 65 61 64 69 | 6e 67 2e 0a 58 0a 58 41 |st readi|ng..X.XA|
|00005f20| 20 73 65 63 6f 6e 64 20 | 70 6c 61 63 65 20 77 68 | second |place wh|
|00005f30| 65 72 65 20 69 74 20 69 | 73 20 64 65 73 69 72 61 |ere it i|s desira|
|00005f40| 62 6c 65 20 74 6f 20 61 | 76 6f 69 64 20 75 6e 6e |ble to a|void unn|
|00005f50| 65 63 65 73 73 61 72 79 | 20 63 6f 70 69 65 73 20 |ecessary| copies |
|00005f60| 69 73 20 77 68 65 6e 0a | 58 61 20 66 75 6e 63 74 |is when.|Xa funct|
|00005f70| 69 6f 6e 20 69 73 20 72 | 65 74 75 72 6e 69 6e 67 |ion is r|eturning|
|00005f80| 20 61 20 6d 61 74 72 69 | 78 2e 20 4d 61 74 72 69 | a matri|x. Matri|
|00005f90| 63 65 73 20 63 61 6e 20 | 62 65 20 72 65 74 75 72 |ces can |be retur|
|00005fa0| 6e 65 64 20 66 72 6f 6d | 20 61 0a 58 66 75 6e 63 |ned from| a.Xfunc|
|00005fb0| 74 69 6f 6e 20 77 69 74 | 68 20 74 68 65 20 72 65 |tion wit|h the re|
|00005fc0| 74 75 72 6e 20 63 6f 6d | 6d 61 6e 64 20 61 73 20 |turn com|mand as |
|00005fd0| 79 6f 75 20 77 6f 75 6c | 64 20 65 78 70 65 63 74 |you woul|d expect|
|00005fe0| 2e 20 48 6f 77 65 76 65 | 72 20 74 68 65 73 65 20 |. Howeve|r these |
|00005ff0| 6d 61 79 0a 58 69 6e 63 | 75 72 20 6f 6e 65 20 61 |may.Xinc|ur one a|
|00006000| 6e 64 20 70 6f 73 73 69 | 62 6c 79 20 74 77 6f 20 |nd possi|bly two |
|00006010| 63 6f 70 79 69 6e 67 73 | 20 6f 66 20 74 68 65 20 |copyings| of the |
|00006020| 6d 61 74 72 69 78 2e 20 | 54 6f 20 61 76 6f 69 64 |matrix. |To avoid|
|00006030| 20 74 68 69 73 20 75 73 | 65 20 74 68 65 0a 58 66 | this us|e the.Xf|
|00006040| 6f 6c 6c 6f 77 69 6e 67 | 20 69 6e 73 74 72 75 63 |ollowing| instruc|
|00006050| 74 69 6f 6e 73 2e 0a 58 | 0a 58 4d 61 6b 65 20 79 |tions..X|.XMake y|
|00006060| 6f 75 72 20 66 75 6e 63 | 74 69 6f 6e 20 6f 66 20 |our func|tion of |
|00006070| 74 79 70 65 20 20 52 65 | 74 75 72 6e 4d 61 74 72 |type Re|turnMatr|
|00006080| 69 78 20 2e 20 54 68 65 | 6e 20 70 72 65 63 65 64 |ix . The|n preced|
|00006090| 65 20 74 68 65 20 72 65 | 74 75 72 6e 0a 58 73 74 |e the re|turn.Xst|
|000060a0| 61 74 65 6d 65 6e 74 20 | 77 69 74 68 20 61 20 52 |atement |with a R|
|000060b0| 65 6c 65 61 73 65 20 73 | 74 61 74 65 6d 65 6e 74 |elease s|tatement|
|000060c0| 20 28 6f 72 20 61 20 52 | 65 6c 65 61 73 65 41 6e | (or a R|eleaseAn|
|000060d0| 64 44 65 6c 65 74 65 20 | 73 74 61 74 65 6d 65 6e |dDelete |statemen|
|000060e0| 74 20 69 66 0a 58 74 68 | 65 20 6d 61 74 72 69 78 |t if.Xth|e matrix|
|000060f0| 20 77 61 73 20 63 72 65 | 61 74 65 64 20 77 69 74 | was cre|ated wit|
|00006100| 68 20 6e 65 77 29 2e 20 | 46 6f 72 20 65 78 61 6d |h new). |For exam|
|00006110| 70 6c 65 0a 58 0a 58 0a | 58 20 20 20 20 52 65 74 |ple.X.X.|X Ret|
|00006120| 75 72 6e 4d 61 74 72 69 | 78 20 4d 61 6b 65 41 4d |urnMatri|x MakeAM|
|00006130| 61 74 72 69 78 28 29 0a | 58 20 20 20 20 7b 0a 58 |atrix().|X {.X|
|00006140| 20 20 20 20 20 20 20 4d | 61 74 72 69 78 20 41 3b | M|atrix A;|
|00006150| 0a 58 20 20 20 20 20 20 | 20 2e 2e 2e 2e 2e 2e 0a |.X | .......|
|00006160| 58 20 20 20 20 20 20 20 | 41 2e 52 65 6c 65 61 73 |X |A.Releas|
|00006170| 65 28 29 3b 20 72 65 74 | 75 72 6e 20 41 3b 0a 58 |e(); ret|urn A;.X|
|00006180| 20 20 20 20 7d 0a 58 0a | 58 6f 72 0a 58 0a 58 20 | }.X.|Xor.X.X |
|00006190| 20 20 20 52 65 74 75 72 | 6e 4d 61 74 72 69 78 20 | Retur|nMatrix |
|000061a0| 4d 61 6b 65 41 4d 61 74 | 72 69 78 28 29 0a 58 20 |MakeAMat|rix().X |
|000061b0| 20 20 20 7b 0a 58 20 20 | 20 20 20 20 20 4d 61 74 | {.X | Mat|
|000061c0| 72 69 78 2a 20 6d 20 3d | 20 6e 65 77 20 4d 61 74 |rix* m =| new Mat|
|000061d0| 72 69 78 3b 0a 58 20 20 | 20 20 20 20 20 2e 2e 2e |rix;.X | ...|
|000061e0| 2e 2e 2e 0a 58 20 20 20 | 20 20 20 20 6d 2d 3e 52 |....X | m->R|
|000061f0| 65 6c 65 61 73 65 41 6e | 64 44 65 6c 65 74 65 28 |eleaseAn|dDelete(|
|00006200| 29 3b 20 72 65 74 75 72 | 6e 20 2a 6d 3b 0a 58 20 |); retur|n *m;.X |
|00006210| 20 20 20 7d 0a 58 0a 58 | 4e 6f 74 65 20 74 68 61 | }.X.X|Note tha|
|00006220| 74 20 2e 63 28 29 20 63 | 61 6e 6e 6f 74 20 62 65 |t .c() c|annot be|
|00006230| 20 61 70 70 6c 69 65 64 | 20 74 6f 20 61 20 6d 61 | applied| to a ma|
|00006240| 74 72 69 78 20 66 6f 6c | 6c 6f 77 69 6e 67 20 61 |trix fol|lowing a|
|00006250| 70 70 6c 69 63 61 74 69 | 6f 6e 20 6f 66 0a 58 2e |pplicati|on of.X.|
|00006260| 52 65 6c 65 61 73 65 28 | 29 20 6f 72 20 2d 3e 52 |Release(|) or ->R|
|00006270| 65 6c 65 61 73 65 41 6e | 64 44 65 6c 65 74 65 28 |eleaseAn|dDelete(|
|00006280| 29 20 2e 0a 58 0a 58 20 | 2d 2d 2d 2d 2d 2d 2d 2d |) ..X.X |--------|
|00006290| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000062a0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000062b0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000062c0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 20 0a 58 |--------|----- .X|
|000062d0| 7c 20 44 6f 20 6e 6f 74 | 20 66 6f 72 67 65 74 20 || Do not| forget |
|000062e0| 74 6f 20 6d 61 6b 65 20 | 74 68 65 20 66 75 6e 63 |to make |the func|
|000062f0| 74 69 6f 6e 20 6f 66 20 | 74 79 70 65 20 52 65 74 |tion of |type Ret|
|00006300| 75 72 6e 4d 61 74 72 69 | 78 3b 20 6f 74 68 65 72 |urnMatri|x; other|
|00006310| 77 69 73 65 20 20 7c 0a | 58 7c 20 69 6e 63 6f 6d |wise |.|X| incom|
|00006320| 70 72 65 68 65 6e 73 69 | 62 6c 65 20 72 75 6e 2d |prehensi|ble run-|
|00006330| 74 69 6d 65 20 65 72 72 | 6f 72 73 20 77 69 6c 6c |time err|ors will|
|00006340| 20 6f 63 63 75 72 20 77 | 69 74 68 20 73 6f 6d 65 | occur w|ith some|
|00006350| 20 63 6f 6d 70 69 6c 65 | 72 73 2e 20 20 20 20 7c | compile|rs. ||
|00006360| 0a 58 20 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |.X -----|--------|
|00006370| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00006380| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00006390| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000063a0| 2d 2d 2d 2d 2d 2d 2d 2d | 20 0a 58 0a 58 59 6f 75 |--------| .X.XYou|
|000063b0| 20 63 61 6e 20 61 6c 73 | 6f 20 75 73 65 20 2e 52 | can als|o use .R|
|000063c0| 65 6c 65 61 73 65 28 29 | 20 6f 72 20 2d 3e 52 65 |elease()| or ->Re|
|000063d0| 6c 65 61 73 65 41 6e 64 | 44 65 6c 65 74 65 28 29 |leaseAnd|Delete()|
|000063e0| 20 74 6f 20 61 6c 6c 6f | 77 20 61 20 6d 61 74 72 | to allo|w a matr|
|000063f0| 69 78 0a 58 65 78 70 72 | 65 73 73 69 6f 6e 20 74 |ix.Xexpr|ession t|
+--------+-------------------------+-------------------------+--------+--------+
Only 25.0 KB of data is shown above.
