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| dexvert
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| id metadata |
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| key | value |
|---|
| macFileType | [TEXT] |
| macFileCreator | [ttxt] |
hex view+--------+-------------------------+-------------------------+--------+--------+
|00000000| 5c 73 65 63 74 69 6f 6e | 7b 6c 75 20 2d 2d 2d 20 |\section|{lu --- |
|00000010| 4c 55 20 64 65 63 6f 6d | 70 6f 73 69 74 69 6f 6e |LU decom|position|
|00000020| 7d 0d 5c 6c 61 62 65 6c | 7b 66 6e 3a 6c 75 7d 0d |}.\label|{fn:lu}.|
|00000030| 5c 69 6e 64 65 78 7b 6c | 75 28 29 7d 0d 5c 69 6e |\index{l|u()}.\in|
|00000040| 64 65 78 7b 4c 55 20 64 | 65 63 6f 6d 70 6f 73 69 |dex{LU d|ecomposi|
|00000050| 74 69 6f 6e 7d 0d 5c 62 | 65 67 69 6e 7b 72 61 69 |tion}.\b|egin{rai|
|00000060| 6c 7d 0d 4c 55 20 3a 20 | 27 6c 75 27 20 27 28 27 |l}.LU : |'lu' '('|
|00000070| 20 4d 61 74 72 69 78 20 | 27 29 27 20 3b 0d 5c 65 | Matrix |')' ;.\e|
|00000080| 6e 64 7b 72 61 69 6c 7d | 0d 0d 5c 76 65 72 62 2b |nd{rail}|..\verb+|
|00000090| 6c 75 2b 20 70 65 72 66 | 6f 72 6d 73 20 61 6e 20 |lu+ perf|orms an |
|000000a0| 4c 55 20 64 65 63 6f 6d | 70 6f 73 69 74 69 6f 6e |LU decom|position|
|000000b0| 20 6f 66 20 74 68 65 20 | 6d 61 74 72 69 78 20 61 | of the |matrix a|
|000000c0| 72 67 75 6d 65 6e 74 2e | 20 54 68 65 20 0d 69 6e |rgument.| The .in|
|000000d0| 70 75 74 20 6d 61 74 72 | 69 78 20 6d 75 73 74 20 |put matr|ix must |
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|000000f0| 6e 2d 73 69 6e 67 75 6c | 61 72 2e 20 5c 76 65 72 |n-singul|ar. \ver|
|00000100| 62 2b 6c 75 2b 20 72 65 | 74 75 72 6e 73 20 0d 74 |b+lu+ re|turns .t|
|00000110| 68 65 20 6c 6f 77 65 72 | 2c 20 75 70 70 65 72 20 |he lower|, upper |
|00000120| 61 6e 64 20 70 69 76 6f | 74 20 6d 61 74 72 69 63 |and pivo|t matric|
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|00000170| 20 49 66 20 74 68 65 20 | 61 72 67 75 6d 65 6e 74 | If the |argument|
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|00000190| 74 68 65 6e 0d 74 68 65 | 20 64 65 63 6f 6d 70 6f |then.the| decompo|
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|000001c0| 20 6c 20 75 20 5c 5d 20 | 0d 0d 24 5c 4c 6f 6e 67 | l u \] |..$\Long|
|000001d0| 72 69 67 68 74 61 72 72 | 6f 77 24 20 54 68 69 73 |rightarr|ow$ This|
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|00000220| 6c 6f 61 64 65 64 20 6f | 6e 20 73 74 61 72 74 2d |loaded o|n start-|
|00000230| 75 70 20 66 72 6f 6d 20 | 74 68 65 20 5c 76 65 72 |up from |the \ver|
|00000240| 62 2b 6c 75 2e 72 2b 20 | 66 69 6c 65 20 69 6e 20 |b+lu.r+ |file in |
|00000250| 74 68 65 0d 73 74 61 6e | 64 61 72 64 20 5c 76 65 |the.stan|dard \ve|
|00000260| 72 62 2b 72 6c 69 62 2b | 20 64 69 72 65 63 74 6f |rb+rlib+| directo|
|00000270| 72 79 2e 20 55 73 65 20 | 6f 66 20 74 68 65 20 5c |ry. Use |of the \|
|00000280| 76 65 72 62 2b 2d 72 2b | 20 6f 70 74 69 6f 6e 2c |verb+-r+| option,|
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|000002f0| 61 79 20 6d 61 6b 65 20 | 74 68 69 73 20 66 75 6e |ay make |this fun|
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|00000320| 45 78 61 6d 70 6c 65 7d | 0d 5c 69 6e 64 65 78 7b |Example}|.\index{|
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|00000360| 62 61 74 69 6d 7d 0d 3e | 20 61 20 3d 20 72 61 6e |batim}.>| a = ran|
|00000370| 64 28 34 2c 34 29 0d 20 | 61 20 3d 0d 20 20 20 20 |d(4,4). |a =. |
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|00000430| 3e 20 62 20 3d 20 6c 75 | 28 61 29 0d 20 20 20 6c |> b = lu|(a). l|
|00000440| 20 20 20 20 20 20 20 20 | 20 20 20 20 70 76 74 20 | | pvt |
|00000450| 20 20 20 20 20 20 20 20 | 20 75 20 20 20 20 20 20 | | u |
|00000460| 20 20 20 0d 3e 20 62 2e | 6c 0d 20 6c 20 3d 0d 20 | .> b.|l. l =. |
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|00000520| 20 20 0d 3e 20 62 2e 75 | 0d 20 75 20 3d 0d 20 20 | .> b.u|. u =. |
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|00000540| 36 37 20 20 20 20 20 20 | 30 2e 36 34 31 20 20 20 |67 |0.641 |
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|00000580| 30 2e 32 36 35 20 20 0d | 20 20 20 20 20 20 20 20 |0.265 .| |
|00000590| 30 20 20 20 20 20 20 20 | 20 20 20 30 20 20 20 20 |0 | 0 |
|000005a0| 20 2d 30 2e 37 35 38 20 | 20 20 20 20 20 30 2e 35 | -0.758 | 0.5|
|000005b0| 33 37 20 20 0d 20 20 20 | 20 20 20 20 20 30 20 20 |37 . | 0 |
|000005c0| 20 20 20 20 20 20 20 20 | 30 20 20 20 20 20 20 20 | |0 |
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|000005e0| 20 0d 3e 20 62 2e 70 76 | 74 0d 20 70 76 74 20 3d | .> b.pv|t. pvt =|
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|00000610| 20 20 20 20 20 20 20 20 | 20 20 30 20 20 0d 20 20 | | 0 . |
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|00000670| 20 20 20 20 31 20 20 0d | 20 20 20 20 20 20 20 20 | 1 .| |
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|00000690| 20 20 20 20 20 20 30 20 | 20 20 20 20 20 20 20 20 | 0 | |
|000006a0| 20 30 20 20 0d 3e 20 62 | 2e 70 76 74 2a 62 2e 6c | 0 .> b|.pvt*b.l|
|000006b0| 2a 62 2e 75 0d 20 20 20 | 20 30 2e 39 35 37 20 20 |*b.u. | 0.957 |
|000006c0| 20 20 20 20 30 2e 33 36 | 37 20 20 20 20 20 20 30 | 0.36|7 0|
|000006d0| 2e 36 34 31 20 20 20 20 | 20 20 30 2e 32 35 32 20 |.641 | 0.252 |
|000006e0| 20 0d 20 20 20 20 20 30 | 2e 38 39 20 20 20 20 20 | . 0|.89 |
|000006f0| 20 30 2e 36 33 38 20 20 | 20 20 20 20 30 2e 32 34 | 0.638 | 0.24|
|00000700| 35 20 20 20 20 20 20 30 | 2e 39 35 35 20 20 0d 20 |5 0|.955 . |
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|00000720| 2e 31 38 20 20 20 20 20 | 20 30 2e 32 38 34 20 20 |.18 | 0.284 |
|00000730| 20 20 20 20 30 2e 39 32 | 31 20 20 0d 20 20 20 20 | 0.92|1 . |
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|00000750| 20 20 20 20 20 20 30 2e | 38 36 39 20 20 20 20 20 | 0.|869 |
|00000760| 20 30 2e 33 37 36 20 0d | 5c 65 6e 64 7b 76 65 72 | 0.376 .|\end{ver|
|00000770| 62 61 74 69 6d 7d 0d 0d | 53 65 65 20 61 6c 73 6f |batim}..|See also|
|00000780| 3a 20 50 61 67 65 20 5c | 70 61 67 65 72 65 66 7b |: Page \|pageref{|
|00000790| 66 6e 3a 62 61 63 6b 73 | 75 62 7d 20 5c 76 65 72 |fn:backs|ub} \ver|
|000007a0| 62 2b 62 61 63 6b 73 75 | 62 28 29 2b 2c 0d 20 50 |b+backsu|b()+,. P|
|000007b0| 61 67 65 20 5c 70 61 67 | 65 72 65 66 7b 66 6e 3a |age \pag|eref{fn:|
|000007c0| 66 61 63 74 6f 72 7d 20 | 5c 76 65 72 62 2b 66 61 |factor} |\verb+fa|
|000007d0| 63 74 6f 72 28 29 2b 2c | 0d 20 50 61 67 65 20 5c |ctor()+,|. Page \|
|000007e0| 70 61 67 65 72 65 66 7b | 66 6e 3a 69 6e 76 7d 20 |pageref{|fn:inv} |
|000007f0| 5c 76 65 72 62 2b 69 6e | 76 28 29 2b 2c 0d 20 50 |\verb+in|v()+,. P|
|00000800| 61 67 65 20 5c 70 61 67 | 65 72 65 66 7b 66 6e 3a |age \pag|eref{fn:|
|00000810| 73 6f 6c 76 65 7d 20 5c | 76 65 72 62 2b 73 6f 6c |solve} \|verb+sol|
|00000820| 76 65 28 29 2b 2e 0d 0d | 5c 6e 65 77 70 61 67 65 |ve()+...|\newpage|
|00000830| 0d 0d 0d 0d 0d 0d 0d | |....... | |
+--------+-------------------------+-------------------------+--------+--------+
