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|00000000| 0d 00 0a 11 f4 20 3e 4d | 61 74 72 69 78 5f 49 6e |..... >M|atrix_In|
|00000010| 76 0d 00 14 05 3a 0d 00 | 1e 2d 2a 2a 2a 2a 2a 2a |v....:..|.-******|
|00000020| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00000030| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00000040| 2a 2a 2a 0d 00 28 2b f4 | 20 2a 2a 2a 20 49 6e 76 |***..(+.| *** Inv|
|00000050| 65 72 74 69 6e 67 20 61 | 6e 20 61 72 62 69 74 72 |erting a|n arbitr|
|00000060| 61 72 79 20 6d 61 74 72 | 69 78 20 2a 2a 2a 0d 00 |ary matr|ix ***..|
|00000070| 32 2b f4 20 2a 2a 2a 20 | 20 45 2e 44 2e 20 45 6e |2+. *** | E.D. En|
|00000080| 67 65 6c 68 61 72 64 74 | 2c 20 4d 61 72 63 68 20 |gelhardt|, March |
|00000090| 31 39 38 39 20 20 2a 2a | 2a 0d 00 3c 2d 2a 2a 2a |1989  **|*..<-***|
|000000a0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|000000b0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|000000c0| 2a 2a 2a 2a 2a 2a 0d 00 | 46 05 3a 0d 00 50 3e f4 |******..|F.:..P>.|
|000000d0| 20 2a 2a 2a 20 47 65 6e | 65 72 61 74 65 20 72 61 | *** Gen|erate ra|
|000000e0| 6e 64 6f 6d 20 6d 61 74 | 72 69 78 20 4d 2c 20 63 |ndom mat|rix M, c|
|000000f0| 6f 6c 25 20 63 6f 6c 75 | 6d 6e 73 20 61 6e 64 20 |ol% colu|mns and |
|00000100| 72 6f 77 25 20 72 6f 77 | 73 0d 00 5a 05 db 0d 00 |row% row|s..Z....|
|00000110| 64 27 f1 27 22 20 49 6e | 76 65 72 74 69 6e 67 20 |d'.'" In|verting |
|00000120| 61 6e 20 61 72 62 69 74 | 72 61 72 79 20 6d 61 74 |an arbit|rary mat|
|00000130| 72 69 78 22 27 0d 00 6e | 29 f5 3a e8 22 20 52 6f |rix"'..n|).:." Ro|
|00000140| 77 73 20 20 20 20 20 20 | 20 20 20 20 20 20 3a 20 |ws      |      : |
|00000150| 22 72 6f 77 25 3a fd 20 | 72 6f 77 25 3e 30 0d 00 |"row%:. |row%>0..|
|00000160| 78 36 f5 3a e8 22 20 43 | 6f 6c 75 6d 6e 73 20 3c |x6.:." C|olumns <|
|00000170| 3d 20 72 6f 77 73 20 3a | 20 22 63 6f 6c 25 3a fd |= rows :| "col%:.|
|00000180| 20 63 6f 6c 25 3c 3d 72 | 6f 77 25 20 80 20 63 6f | col%<=r|ow% . co|
|00000190| 6c 25 3e 30 0d 00 82 2d | db 3a f1 27 22 20 52 6f |l%>0...-|.:.'" Ro|
|000001a0| 77 73 20 20 20 20 3a 20 | 22 c3 72 6f 77 25 27 22 |ws    : |".row%'"|
|000001b0| 20 43 6f 6c 75 6d 6e 73 | 20 3a 20 22 c3 63 6f 6c | Columns| : ".col|
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|000001d0| 25 2d 3d 31 0d 00 96 12 | de 20 4d 28 72 6f 77 25 |%-=1....|. M(row%|
|000001e0| 2c 63 6f 6c 25 29 0d 00 | a0 39 e3 20 72 25 3d 30 |,col%)..|.9. r%=0|
|000001f0| b8 72 6f 77 25 3a e3 20 | 63 25 3d 30 b8 63 6f 6c |.row%:. |c%=0.col|
|00000200| 25 3a 4d 28 72 25 2c 63 | 25 29 3d b3 28 31 29 2a |%:M(r%,c|%)=.(1)*|
|00000210| b4 28 30 2e 35 2d b3 28 | 31 29 29 3a ed 3a ed 0d |.(0.5-.(|1)):.:..|
|00000220| 00 aa 05 3a 0d 00 b4 0c | 73 74 61 72 74 25 3d 91 |...:....|start%=.|
|00000230| 0d 00 be 05 3a 0d 00 c8 | 91 f4 20 2a 2a 2a 20 44 |....:...|.. *** D|
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|00000270| 75 6c 74 20 3a 20 4d 69 | 2e 4d 20 69 73 20 20 20 |ult : Mi|.M is   |
|00000280| 20 20 20 20 20 20 20 20 | 20 65 71 75 61 6c 20 74 |        | equal t|
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|000002a0| 61 74 72 69 78 20 45 2e | 20 49 66 20 72 6f 77 73 |atrix E.| If rows|
|000002b0| 20 3d 20 63 6f 6c 73 20 | 61 6c 73 6f 20 4d 2e 4d | = cols |also M.M|
|000002c0| 69 20 3d 20 45 2e 0d 00 | d2 05 3a 0d 00 dc 29 de |i = E...|..:...).|
|000002d0| 20 4d 69 28 63 6f 6c 25 | 2c 72 6f 77 25 29 3a f2 | Mi(col%|,row%):.|
|000002e0| 6c 73 74 5f 73 71 5f 69 | 6e 76 28 4d 28 29 2c 4d |lst_sq_i|nv(M(),M|
|000002f0| 69 28 29 29 0d 00 e6 0a | 65 6e 64 25 3d 91 0d 00 |i())....|end%=...|
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|00000320| 28 65 6e 64 25 2d 73 74 | 61 72 74 25 29 27 27 0d |(end%-st|art%)''.|
|00000330| 01 04 05 3a 0d 01 0e 0a | f2 70 72 69 6e 74 0d 01 |...:....|.print..|
|00000340| 18 05 e0 0d 01 22 4e 2d | 2d 2d 2d 2d 2d 2d 2d 2d |....."N-|--------|
|00000350| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000360| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000370| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000380| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000390| 2d 0d 01 2c 1a dd f2 6c | 73 74 5f 73 71 5f 69 6e |-..,...l|st_sq_in|
|000003a0| 76 28 52 28 29 2c 52 69 | 28 29 29 0d 01 36 7c 20 |v(R(),Ri|())..6| |
|000003b0| 20 f4 20 2a 2a 2a 20 52 | 69 20 69 73 20 27 6c 65 | . *** R|i is 'le|
|000003c0| 61 73 74 20 73 71 75 61 | 72 65 27 20 69 6e 76 65 |ast squa|re' inve|
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|000003e0| 69 2e 52 20 3d 20 45 20 | 28 69 64 65 6e 74 69 74 |i.R = E |(identit|
|000003f0| 79 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |y       |        |
|00000400| 20 6d 61 74 72 69 78 29 | 2e 20 49 66 20 72 6f 77 | matrix)|. If row|
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|00000420| 52 69 20 3d 20 45 2e 0d | 01 40 46 20 20 f4 20 2a |Ri = E..|.@F  . *|
|00000430| 2a 2a 20 44 69 6d 65 6e | 73 69 6f 6e 73 20 52 28 |** Dimen|sions R(|
|00000440| 76 25 2c 68 25 29 2c 52 | 69 28 68 25 2c 76 25 29 |v%,h%),R|i(h%,v%)|
|00000450| 20 3d 3d 3e 20 76 25 20 | 3a 20 72 6f 77 73 20 2c | ==> v% |: rows ,|
|00000460| 20 68 25 20 3a 20 63 6f | 6c 75 6d 6e 73 0d 01 4a | h% : co|lumns..J|
|00000470| 46 20 20 f4 20 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |F  . ***|********|
|00000480| 2a 2a 2a 2a 2a 20 20 45 | 2e 44 2e 20 45 6e 67 65 |*****  E|.D. Enge|
|00000490| 6c 68 61 72 64 74 2c 20 | 4d 61 72 63 68 20 31 39 |lhardt, |March 19|
|000004a0| 38 39 20 20 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |89  ****|********|
|000004b0| 2a 2a 2a 0d 01 54 07 20 | 20 3a 0d 01 5e 24 20 20 |***..T. | :..^$  |
|000004c0| ea 20 52 74 52 28 29 2c | 4c 28 29 2c 49 28 29 2c |. RtR(),|L(),I(),|
|000004d0| 76 25 2c 68 25 2c 63 25 | 2c 72 25 2c 74 25 0d 01 |v%,h%,c%|,r%,t%..|
|000004e0| 68 1d 20 20 76 25 3d de | 28 52 28 29 2c 31 29 3a |h.  v%=.|(R(),1):|
|000004f0| 68 25 3d de 28 52 28 29 | 2c 32 29 0d 01 72 24 20 |h%=.(R()|,2)..r$ |
|00000500| 20 de 20 52 74 52 28 68 | 25 2c 68 25 29 2c 4c 28 | . RtR(h|%,h%),L(|
|00000510| 68 25 2c 68 25 29 2c 49 | 28 68 25 2c 68 25 29 0d |h%,h%),I|(h%,h%).|
|00000520| 01 7c 07 20 20 3a 0d 01 | 86 24 20 20 f4 20 2a 2a |.|.  :..|.$  . **|
|00000530| 2a 20 44 65 74 65 72 6d | 69 6e 65 20 74 72 61 6e |* Determ|ine tran|
|00000540| 73 70 6f 73 65 20 6f 66 | 20 52 0d 01 90 34 20 20 |spose of| R...4  |
|00000550| e3 20 72 25 3d 30 20 b8 | 20 76 25 3a e3 20 63 25 |. r%=0 .| v%:. c%|
|00000560| 3d 30 20 b8 20 68 25 3a | 52 69 28 63 25 2c 72 25 |=0 . h%:|Ri(c%,r%|
|00000570| 29 3d 52 28 72 25 2c 63 | 25 29 3a ed 3a ed 0d 01 |)=R(r%,c|%):.:...|
|00000580| 9a 07 20 20 3a 0d 01 a4 | 32 20 20 f4 20 2a 2a 2a |..  :...|2  . ***|
|00000590| 20 43 61 6c 63 75 6c 61 | 74 65 20 73 71 75 61 72 | Calcula|te squar|
|000005a0| 65 20 6d 61 74 72 69 78 | 20 74 6f 20 62 65 20 69 |e matrix| to be i|
|000005b0| 6e 76 65 72 74 65 64 0d | 01 ae 14 20 20 52 74 52 |nverted.|...  RtR|
|000005c0| 28 29 3d 52 69 28 29 2e | 52 28 29 0d 01 b8 07 20 |()=Ri().|R().... |
|000005d0| 20 3a 0d 01 c2 2d 20 20 | f4 20 2a 2a 2a 20 43 61 | :...-  |. *** Ca|
|000005e0| 6c 63 75 6c 61 74 65 20 | 6c 6f 77 65 72 20 74 72 |lculate |lower tr|
|000005f0| 69 61 6e 67 6c 65 20 4c | 20 6f 66 20 52 74 52 0d |iangle L| of RtR.|
|00000600| 01 cc 1e 20 20 e3 20 63 | 25 3d 30 20 b8 20 68 25 |...  . c|%=0 . h%|
|00000610| 3a e3 20 72 25 3d 63 25 | 20 b8 20 68 25 0d 01 d6 |:. r%=c%| . h%...|
|00000620| 23 20 20 20 20 4c 28 72 | 25 2c 63 25 29 3d 52 74 |#    L(r|%,c%)=Rt|
|00000630| 52 28 72 25 2c 63 25 29 | 3a 74 25 3d 63 25 2d 31 |R(r%,c%)|:t%=c%-1|
|00000640| 0d 01 e0 42 20 20 20 20 | e7 20 74 25 3e 3d 30 20 |...B    |. t%>=0 |
|00000650| e3 20 74 25 3d 74 25 b8 | 30 88 2d 31 3a 4c 28 72 |. t%=t%.|0.-1:L(r|
|00000660| 25 2c 63 25 29 3d 4c 28 | 72 25 2c 63 25 29 2d 4c |%,c%)=L(|r%,c%)-L|
|00000670| 28 72 25 2c 74 25 29 2a | 4c 28 63 25 2c 74 25 29 |(r%,t%)*|L(c%,t%)|
|00000680| 3a ed 0d 01 ea 42 20 20 | 20 20 e7 20 72 25 3e 63 |:....B  |  . r%>c|
|00000690| 25 20 8c 20 4c 28 72 25 | 2c 63 25 29 3d 4c 28 72 |% . L(r%|,c%)=L(r|
|000006a0| 25 2c 63 25 29 2f 4c 28 | 63 25 2c 63 25 29 20 8b |%,c%)/L(|c%,c%) .|
|000006b0| 20 4c 28 72 25 2c 63 25 | 29 3d b6 20 4c 28 72 25 | L(r%,c%|)=. L(r%|
|000006c0| 2c 63 25 29 0d 01 f4 09 | 20 20 ed 3a ed 0d 01 fe |,c%)....|  .:....|
|000006d0| 07 20 20 3a 0d 02 08 c4 | 20 20 f4 20 2a 2a 2a 20 |.  :....|  . *** |
|000006e0| 49 66 20 52 20 69 73 20 | 73 71 75 61 72 65 20 28 |If R is |square (|
|000006f0| 72 6f 77 73 20 3d 20 63 | 6f 6c 73 29 20 69 74 73 |rows = c|ols) its|
|00000700| 20 64 65 74 65 72 6d 69 | 6e 61 6e 74 20 65 71 75 | determi|nant equ|
|00000710| 61 6c 73 20 74 68 65 20 | 70 72 6f 64 75 63 74 20 |als the |product |
|00000720| 20 20 20 20 20 20 20 20 | 20 20 20 6f 66 20 74 68 |        |   of th|
|00000730| 65 20 64 69 61 67 6f 6e | 61 6c 20 65 6c 65 6d 65 |e diagon|al eleme|
|00000740| 6e 74 73 20 6f 66 20 4c | 2e 20 54 68 65 20 64 65 |nts of L|. The de|
|00000750| 74 65 72 6d 69 6e 61 6e | 74 20 6f 66 20 52 74 52 |terminan|t of RtR|
|00000760| 20 65 71 75 61 6c 73 20 | 20 20 20 20 20 20 20 20 | equals |        |
|00000770| 20 20 20 20 20 74 68 65 | 20 73 71 75 61 72 65 20 |     the| square |
|00000780| 6f 66 20 74 68 65 20 64 | 65 74 65 72 6d 69 6e 61 |of the d|etermina|
|00000790| 6e 74 20 6f 66 20 4c 2e | 0d 02 12 07 20 20 3a 0d |nt of L.|....  :.|
|000007a0| 02 1c 2b 20 20 f4 20 2a | 2a 2a 20 49 6e 76 65 72 |..+  . *|** Inver|
|000007b0| 74 20 74 72 69 61 6e 67 | 75 6c 61 72 20 6d 61 74 |t triang|ular mat|
|000007c0| 72 69 78 20 4c 20 74 6f | 20 49 0d 02 26 1e 20 20 |rix L to| I..&.  |
|000007d0| e3 20 63 25 3d 30 20 b8 | 20 68 25 3a e3 20 72 25 |. c%=0 .| h%:. r%|
|000007e0| 3d 63 25 20 b8 20 68 25 | 0d 02 30 3c 20 20 20 20 |=c% . h%|..0<    |
|000007f0| e3 20 74 25 3d 63 25 20 | b8 20 72 25 2d 31 3a 49 |. t%=c% |. r%-1:I|
|00000800| 28 72 25 2c 63 25 29 3d | 49 28 72 25 2c 63 25 29 |(r%,c%)=|I(r%,c%)|
|00000810| 2d 4c 28 72 25 2c 74 25 | 29 2a 49 28 74 25 2c 63 |-L(r%,t%|)*I(t%,c|
|00000820| 25 29 3a ed 0d 02 3a 42 | 20 20 20 20 e7 20 72 25 |%):...:B|    . r%|
|00000830| 3e 63 25 20 8c 20 49 28 | 72 25 2c 63 25 29 3d 49 |>c% . I(|r%,c%)=I|
|00000840| 28 72 25 2c 63 25 29 2f | 4c 28 72 25 2c 72 25 29 |(r%,c%)/|L(r%,r%)|
|00000850| 20 8b 20 49 28 72 25 2c | 63 25 29 3d 31 2f 4c 28 | . I(r%,|c%)=1/L(|
|00000860| 72 25 2c 72 25 29 0d 02 | 44 09 20 20 ed 3a ed 0d |r%,r%)..|D.  .:..|
|00000870| 02 4e 07 20 20 3a 0d 02 | 58 37 20 20 f4 20 2a 2a |.N.  :..|X7  . **|
|00000880| 2a 20 44 65 74 65 72 6d | 69 6e 65 20 74 72 61 6e |* Determ|ine tran|
|00000890| 73 70 6f 73 65 20 4c 20 | 6f 66 20 69 6e 76 65 72 |spose L |of inver|
|000008a0| 73 65 20 74 72 69 61 6e | 67 6c 65 20 49 0d 02 62 |se trian|gle I..b|
|000008b0| 33 20 20 e3 20 72 25 3d | 30 20 b8 20 68 25 3a e3 |3  . r%=|0 . h%:.|
|000008c0| 20 63 25 3d 30 20 b8 20 | 68 25 3a 4c 28 63 25 2c | c%=0 . |h%:L(c%,|
|000008d0| 72 25 29 3d 49 28 72 25 | 2c 63 25 29 3a ed 3a ed |r%)=I(r%|,c%):.:.|
|000008e0| 0d 02 6c 07 20 20 3a 0d | 02 76 25 20 20 f4 20 2a |..l.  :.|.v%  . *|
|000008f0| 2a 2a 20 49 6e 76 65 72 | 73 65 20 6d 61 74 72 69 |** Inver|se matri|
|00000900| 78 20 6f 66 20 52 20 69 | 73 20 52 69 0d 02 80 23 |x of R i|s Ri...#|
|00000910| 20 20 52 74 52 28 29 3d | 4c 28 29 2e 49 28 29 3a |  RtR()=|L().I():|
|00000920| 52 69 28 29 3d 52 74 52 | 28 29 2e 52 69 28 29 0d |Ri()=RtR|().Ri().|
|00000930| 02 8a 07 20 20 3a 0d 02 | 94 05 e1 0d 02 9e 4e 2d |...  :..|......N-|
|00000940| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000950| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000960| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000970| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000980| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 0d 02 a8 0b dd f2 70 |--------|-......p|
|00000990| 72 69 6e 74 0d 02 b2 0a | 20 20 ef 20 31 34 0d 02 |rint....|  . 14..|
|000009a0| bc 23 20 20 f1 22 20 2a | 2a 2a 2a 2a 2a 2a 2a 20 |.#  ." *|******* |
|000009b0| 45 6c 65 6d 65 6e 74 73 | 20 4d 61 74 72 69 78 22 |Elements| Matrix"|
|000009c0| 27 0d 02 c6 33 20 20 e3 | 20 72 25 3d 30 20 b8 20 |'...3  .| r%=0 . |
|000009d0| 72 6f 77 25 3a e3 20 63 | 25 3d 30 20 b8 20 63 6f |row%:. c|%=0 . co|
|000009e0| 6c 25 3a f1 20 4d 28 72 | 25 2c 63 25 29 3a ed 3a |l%:. M(r|%,c%):.:|
|000009f0| f1 20 3a ed 0d 02 d0 2b | 20 20 f1 22 20 2a 2a 2a |. :....+|  ." ***|
|00000a00| 2a 2a 2a 2a 2a 20 45 6c | 65 6d 65 6e 74 73 20 69 |***** El|ements i|
|00000a10| 6e 76 65 72 73 65 20 4d | 61 74 72 69 78 22 27 0d |nverse M|atrix"'.|
|00000a20| 02 da 34 20 20 e3 20 72 | 25 3d 30 20 b8 20 63 6f |..4  . r|%=0 . co|
|00000a30| 6c 25 3a e3 20 63 25 3d | 30 20 b8 20 72 6f 77 25 |l%:. c%=|0 . row%|
|00000a40| 3a f1 20 4d 69 28 72 25 | 2c 63 25 29 3a ed 3a f1 |:. Mi(r%|,c%):.:.|
|00000a50| 20 3a ed 0d 02 e4 14 20 | 20 de 20 45 28 63 6f 6c | :..... | . E(col|
|00000a60| 25 2c 63 6f 6c 25 29 0d | 02 ee 12 20 20 45 28 29 |%,col%).|...  E()|
|00000a70| 3d 4d 69 28 29 2e 4d 28 | 29 0d 02 f8 35 20 20 f1 |=Mi().M(|)...5  .|
|00000a80| 22 20 2a 2a 2a 2a 2a 2a | 2a 2a 20 45 6c 65 6d 65 |" ******|** Eleme|
|00000a90| 6e 74 73 20 6f 66 20 49 | 6e 76 65 72 73 65 5f 4d |nts of I|nverse_M|
|00000aa0| 61 74 72 69 78 2e 4d 61 | 74 72 69 78 22 27 0d 03 |atrix.Ma|trix"'..|
|00000ab0| 02 33 20 20 e3 20 72 25 | 3d 30 20 b8 20 63 6f 6c |.3  . r%|=0 . col|
|00000ac0| 25 3a e3 20 63 25 3d 30 | 20 b8 20 63 6f 6c 25 3a |%:. c%=0| . col%:|
|00000ad0| f1 20 45 28 72 25 2c 63 | 25 29 3a ed 3a f1 20 3a |. E(r%,c|%):.:. :|
|00000ae0| ed 0d 03 0c 0a 20 20 ef | 20 31 35 0d 03 16 05 e1 |.....  .| 15.....|
|00000af0| 0d 03 20 4e 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |.. N----|--------|
|00000b00| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000b10| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000b20| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000b30| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 0d ff |--------|------..|
+--------+-------------------------+-------------------------+--------+--------+