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|00000000| 5c 73 65 63 74 69 6f 6e | 7b 63 75 6d 73 75 6d 20 |\section|{cumsum |
|00000010| 2d 2d 2d 20 43 75 6d 75 | 6c 61 74 69 76 65 20 53 |--- Cumu|lative S|
|00000020| 75 6d 6d 61 74 69 6f 6e | 7d 0d 5c 6c 61 62 65 6c |ummation|}.\label|
|00000030| 7b 66 6e 3a 63 75 6d 73 | 75 6d 7d 0d 5c 69 6e 64 |{fn:cums|um}.\ind|
|00000040| 65 78 7b 63 75 6d 73 75 | 6d 28 29 7d 0d 5c 69 6e |ex{cumsu|m()}.\in|
|00000050| 64 65 78 7b 63 75 6d 75 | 6c 61 74 69 76 65 20 73 |dex{cumu|lative s|
|00000060| 75 6d 6d 61 74 69 6f 6e | 7d 0d 5c 62 65 67 69 6e |ummation|}.\begin|
|00000070| 7b 72 61 69 6c 7d 0d 43 | 75 6d 53 75 6d 20 3a 20 |{rail}.C|umSum : |
|00000080| 27 63 75 6d 73 75 6d 27 | 20 27 28 27 20 4d 61 74 |'cumsum'| '(' Mat|
|00000090| 72 69 78 20 27 29 27 20 | 3b 0d 5c 65 6e 64 7b 72 |rix ')' |;.\end{r|
|000000a0| 61 69 6c 7d 0d 0d 5c 76 | 65 72 62 2b 63 75 6d 73 |ail}..\v|erb+cums|
|000000b0| 75 6d 2b 20 74 61 6b 65 | 73 20 61 20 6d 61 74 72 |um+ take|s a matr|
|000000c0| 69 78 20 61 72 67 75 6d | 65 6e 74 2c 20 61 6e 64 |ix argum|ent, and|
|000000d0| 20 70 72 6f 64 75 63 65 | 73 20 61 6e 6f 74 68 65 | produce|s anothe|
|000000e0| 72 20 6d 61 74 72 69 78 | 0d 6f 66 20 74 68 65 20 |r matrix|.of the |
|000000f0| 73 61 6d 65 20 64 69 6d | 65 6e 73 69 6f 6e 73 2e |same dim|ensions.|
|00000100| 20 45 61 63 68 20 65 6c | 65 6d 65 6e 74 20 69 6e | Each el|ement in|
|00000110| 20 74 68 65 20 72 65 73 | 75 6c 74 61 6e 74 20 6d | the res|ultant m|
|00000120| 61 74 72 69 78 20 63 6f | 6e 73 69 73 74 73 20 0d |atrix co|nsists .|
|00000130| 6f 66 20 74 68 65 20 63 | 75 6d 75 6c 61 74 69 76 |of the c|umulativ|
|00000140| 65 20 73 75 6d 20 6f 66 | 20 74 68 65 20 74 68 61 |e sum of| the tha|
|00000150| 74 20 65 6c 65 6d 65 6e | 74 20 61 6e 64 20 61 6c |t elemen|t and al|
|00000160| 6c 20 70 72 65 76 69 6f | 75 73 20 65 6c 65 6d 65 |l previo|us eleme|
|00000170| 6e 74 73 0d 69 6e 20 74 | 68 61 74 20 63 6f 6c 75 |nts.in t|hat colu|
|00000180| 6d 6e 20 20 6f 66 20 74 | 68 65 20 61 72 67 75 6d |mn  of t|he argum|
|00000190| 65 6e 74 20 6d 61 74 72 | 69 78 2e 20 49 66 20 74 |ent matr|ix. If t|
|000001a0| 68 65 20 61 72 67 75 6d | 65 6e 74 20 69 73 20 65 |he argum|ent is e|
|000001b0| 69 74 68 65 72 20 61 20 | 72 6f 77 0d 6f 72 20 63 |ither a |row.or c|
|000001c0| 6f 6c 75 6d 6e 20 76 65 | 63 74 6f 72 2c 20 74 68 |olumn ve|ctor, th|
|000001d0| 65 20 63 75 6d 75 6c 61 | 74 69 76 65 20 73 75 6d |e cumula|tive sum|
|000001e0| 6d 61 74 69 6f 6e 20 69 | 73 20 70 65 72 66 6f 72 |mation i|s perfor|
|000001f0| 6d 65 64 20 6f 6e 20 74 | 68 61 74 20 72 6f 77 20 |med on t|hat row |
|00000200| 6f 72 0d 63 6f 6c 75 6d | 6e 2e 0d 0d 24 5c 4c 6f |or.colum|n...$\Lo|
|00000210| 6e 67 72 69 67 68 74 61 | 72 72 6f 77 24 20 54 68 |ngrighta|rrow$ Th|
|00000220| 69 73 20 69 73 20 6e 6f | 74 20 61 6e 20 5c 52 4c |is is no|t an \RL|
|00000230| 61 42 5c 20 62 75 69 6c | 74 2d 69 6e 20 66 75 6e |aB\ buil|t-in fun|
|00000240| 63 74 69 6f 6e 2e 20 20 | 54 68 69 73 20 66 75 6e |ction.  |This fun|
|00000250| 63 74 69 6f 6e 0d 69 73 | 20 6e 6f 72 6d 61 6c 6c |ction.is| normall|
|00000260| 79 20 6c 6f 61 64 65 64 | 20 6f 6e 20 73 74 61 72 |y loaded| on star|
|00000270| 74 2d 75 70 20 66 72 6f | 6d 20 74 68 65 20 5c 76 |t-up fro|m the \v|
|00000280| 65 72 62 2b 63 75 6d 73 | 75 6d 2e 72 2b 20 66 69 |erb+cums|um.r+ fi|
|00000290| 6c 65 20 69 6e 20 74 68 | 65 0d 73 74 61 6e 64 61 |le in th|e.standa|
|000002a0| 72 64 20 5c 76 65 72 62 | 2b 72 6c 69 62 2b 20 64 |rd \verb|+rlib+ d|
|000002b0| 69 72 65 63 74 6f 72 79 | 2e 20 55 73 65 20 6f 66 |irectory|. Use of|
|000002c0| 20 74 68 65 20 5c 76 65 | 72 62 2b 2d 72 2b 20 6f | the \ve|rb+-r+ o|
|000002d0| 70 74 69 6f 6e 2c 20 69 | 6e 63 6f 72 72 65 63 74 |ption, i|ncorrect|
|000002e0| 6c 79 20 0d 73 65 74 74 | 69 6e 67 20 74 68 65 20 |ly .sett|ing the |
|000002f0| 5c 76 65 72 62 2b 52 4c | 41 42 5f 4c 49 42 5f 44 |\verb+RL|AB_LIB_D|
|00000300| 49 52 2b 20 65 6e 76 69 | 72 6f 6e 6d 65 6e 74 61 |IR+ envi|ronmenta|
|00000310| 6c 20 76 61 72 69 61 62 | 6c 65 2c 20 6f 72 20 6d |l variab|le, or m|
|00000320| 6f 64 69 66 79 69 6e 67 | 0d 5c 76 65 72 62 2b 63 |odifying|.\verb+c|
|00000330| 75 6d 73 75 6d 2e 72 2b | 20 6d 61 79 20 6d 61 6b |umsum.r+| may mak|
|00000340| 65 20 74 68 69 73 20 66 | 75 6e 63 74 69 6f 6e 20 |e this f|unction |
|00000350| 75 6e 61 76 61 69 6c 61 | 62 6c 65 2e 0d 0d 0d 5c |unavaila|ble....\|
|00000360| 70 61 72 61 67 72 61 70 | 68 7b 45 78 61 6d 70 6c |paragrap|h{Exampl|
|00000370| 65 7d 0d 5c 69 6e 64 65 | 78 7b 65 78 61 6d 70 6c |e}.\inde|x{exampl|
|00000380| 65 20 6f 66 20 63 75 6d | 73 75 6d 28 29 7d 0d 5c |e of cum|sum()}.\|
|00000390| 69 6e 64 65 78 7b 63 75 | 6d 73 75 6d 28 29 21 65 |index{cu|msum()!e|
|000003a0| 78 61 6d 70 6c 65 7d 0d | 5c 62 65 67 69 6e 7b 76 |xample}.|\begin{v|
|000003b0| 65 72 62 61 74 69 6d 7d | 0d 3e 20 63 75 6d 73 75 |erbatim}|.> cumsu|
|000003c0| 6d 28 5b 31 2c 32 2c 33 | 2c 34 2c 35 5d 29 0d 20 |m([1,2,3|,4,5]). |
|000003d0| 20 20 20 20 20 20 20 31 | 20 20 20 20 20 20 20 20 |       1|        |
|000003e0| 20 20 33 20 20 20 20 20 | 20 20 20 20 20 36 20 20 |  3     |     6  |
|000003f0| 20 20 20 20 20 20 20 31 | 30 20 20 20 20 20 20 20 |       1|0       |
|00000400| 20 20 31 35 20 20 0d 3e | 20 63 75 6d 73 75 6d 28 |  15  .>| cumsum(|
|00000410| 5b 31 2c 32 2c 33 2c 34 | 5d 27 29 0d 20 20 20 20 |[1,2,3,4|]').    |
|00000420| 20 20 20 20 31 20 20 0d | 20 20 20 20 20 20 20 20 |    1  .|        |
|00000430| 33 20 20 0d 20 20 20 20 | 20 20 20 20 36 20 20 0d |3  .    |    6  .|
|00000440| 20 20 20 20 20 20 20 31 | 30 20 20 0d 3e 20 63 20 |       1|0  .> c |
|00000450| 3d 20 5b 31 2c 32 2c 33 | 3b 20 34 2c 35 2c 36 3b |= [1,2,3|; 4,5,6;|
|00000460| 20 37 2c 38 2c 39 3b 20 | 31 30 2c 20 2d 33 2e 34 | 7,8,9; |10, -3.4|
|00000470| 2c 20 32 2e 30 39 5d 0d | 20 63 20 3d 0d 20 20 20 |, 2.09].| c =.   |
|00000480| 20 20 20 20 20 31 20 20 | 20 20 20 20 20 20 20 20 |     1  |        |
|00000490| 32 20 20 20 20 20 20 20 | 20 20 20 33 20 20 0d 20 |2       |   3  . |
|000004a0| 20 20 20 20 20 20 20 34 | 20 20 20 20 20 20 20 20 |       4|        |
|000004b0| 20 20 35 20 20 20 20 20 | 20 20 20 20 20 36 20 20 |  5     |     6  |
|000004c0| 0d 20 20 20 20 20 20 20 | 20 37 20 20 20 20 20 20 |.       | 7      |
|000004d0| 20 20 20 20 38 20 20 20 | 20 20 20 20 20 20 20 39 |    8   |       9|
|000004e0| 20 20 0d 20 20 20 20 20 | 20 20 31 30 20 20 20 20 |  .     |  10    |
|000004f0| 20 20 20 2d 33 2e 34 20 | 20 20 20 20 20 20 32 2e |   -3.4 |      2.|
|00000500| 30 39 20 20 0d 3e 20 63 | 75 6d 73 75 6d 28 63 29 |09  .> c|umsum(c)|
|00000510| 0d 20 20 20 20 20 20 20 | 20 31 20 20 20 20 20 20 |.       | 1      |
|00000520| 20 20 20 20 32 20 20 20 | 20 20 20 20 20 20 20 33 |    2   |       3|
|00000530| 20 20 0d 20 20 20 20 20 | 20 20 20 35 20 20 20 20 |  .     |   5    |
|00000540| 20 20 20 20 20 20 37 20 | 20 20 20 20 20 20 20 20 |      7 |        |
|00000550| 20 39 20 20 0d 20 20 20 | 20 20 20 20 31 32 20 20 | 9  .   |    12  |
|00000560| 20 20 20 20 20 20 20 31 | 35 20 20 20 20 20 20 20 |       1|5       |
|00000570| 20 20 31 38 20 20 0d 20 | 20 20 20 20 20 20 32 32 |  18  . |      22|
|00000580| 20 20 20 20 20 20 20 31 | 31 2e 36 20 20 20 20 20 |       1|1.6     |
|00000590| 20 20 32 30 2e 31 0d 5c | 65 6e 64 7b 76 65 72 62 |  20.1.\|end{verb|
|000005a0| 61 74 69 6d 7d 0d 0d 53 | 65 65 20 61 6c 73 6f 3a |atim}..S|ee also:|
|000005b0| 20 50 61 67 65 7e 5c 70 | 61 67 65 72 65 66 7b 66 | Page~\p|ageref{f|
|000005c0| 6e 3a 63 75 6d 70 72 6f | 64 7d 20 5c 76 65 72 62 |n:cumpro|d} \verb|
|000005d0| 2b 63 75 6d 70 72 6f 64 | 28 29 2b 2e 0d 0d 5c 6e |+cumprod|()+...\n|
|000005e0| 65 77 70 61 67 65 0d 0d | 0d 0d 0d 0d 0d          |ewpage..|.....   |
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