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|00000000| 5c 73 65 63 74 69 6f 6e | 7b 64 69 66 66 20 2d 2d |\section|{diff --|
|00000010| 2d 20 44 69 66 66 65 72 | 65 6e 63 65 20 62 65 74 |- Differ|ence bet|
|00000020| 77 65 65 6e 20 6d 61 74 | 72 69 78 20 65 6c 65 6d |ween mat|rix elem|
|00000030| 65 6e 74 73 7d 0d 5c 6c | 61 62 65 6c 7b 66 6e 3a |ents}.\l|abel{fn:|
|00000040| 64 69 66 66 7d 0d 5c 69 | 6e 64 65 78 7b 64 69 66 |diff}.\i|ndex{dif|
|00000050| 66 28 29 7d 0d 5c 69 6e | 64 65 78 7b 64 69 66 66 |f()}.\in|dex{diff|
|00000060| 65 72 65 6e 63 65 20 62 | 65 74 77 65 65 6e 20 6d |erence b|etween m|
|00000070| 61 74 72 69 78 20 65 6c | 65 6d 65 6e 74 73 7d 0d |atrix el|ements}.|
|00000080| 5c 69 6e 64 65 78 7b 6d | 61 74 72 69 78 21 64 69 |\index{m|atrix!di|
|00000090| 66 66 65 72 65 6e 63 65 | 20 62 65 74 77 65 65 6e |fference| between|
|000000a0| 20 65 6c 65 6d 65 6e 74 | 73 7d 0d 5c 62 65 67 69 | element|s}.\begi|
|000000b0| 6e 7b 72 61 69 6c 7d 0d | 44 69 66 66 65 72 65 6e |n{rail}.|Differen|
|000000c0| 63 65 20 3a 20 27 64 69 | 66 66 27 20 27 28 27 20 |ce : 'di|ff' '(' |
|000000d0| 4d 61 74 72 69 78 20 28 | 20 27 2c 27 20 53 63 61 |Matrix (| ',' Sca|
|000000e0| 6c 61 72 20 29 20 3f 20 | 27 29 27 20 3b 0d 5c 65 |lar ) ? |')' ;.\e|
|000000f0| 6e 64 7b 72 61 69 6c 7d | 0d 0d 5c 76 65 72 62 2b |nd{rail}|..\verb+|
|00000100| 64 69 66 66 2b 20 63 61 | 6c 63 75 6c 61 74 65 73 |diff+ ca|lculates|
|00000110| 20 74 68 65 20 64 69 66 | 66 65 72 65 6e 63 65 20 | the dif|ference |
|00000120| 62 65 74 77 65 65 6e 20 | 65 6c 65 6d 65 6e 74 73 |between |elements|
|00000130| 20 6f 66 20 74 68 65 20 | 6d 61 74 72 69 78 0d 61 | of the |matrix.a|
|00000140| 72 67 75 6d 65 6e 74 2e | 20 20 49 66 20 74 68 65 |rgument.|  If the|
|00000150| 20 6d 61 74 72 69 78 20 | 69 73 20 61 20 76 65 63 | matrix |is a vec|
|00000160| 74 6f 72 2c 20 74 68 65 | 6e 20 5c 76 65 72 62 2b |tor, the|n \verb+|
|00000170| 64 69 66 66 2b 20 72 65 | 74 75 72 6e 73 20 61 20 |diff+ re|turns a |
|00000180| 76 65 63 74 6f 72 0d 6f | 66 20 74 68 65 20 64 69 |vector.o|f the di|
|00000190| 66 66 65 72 65 6e 63 65 | 73 20 62 65 74 77 65 65 |fference|s betwee|
|000001a0| 6e 20 61 64 6a 61 63 65 | 6e 74 20 65 6c 65 6d 65 |n adjace|nt eleme|
|000001b0| 6e 74 73 2e 20 54 68 65 | 20 72 65 74 75 72 6e 20 |nts. The| return |
|000001c0| 76 65 63 74 6f 72 20 68 | 61 73 20 6f 6e 65 0d 6c |vector h|as one.l|
|000001d0| 65 73 73 20 65 6c 65 6d | 65 6e 74 20 74 68 61 6e |ess elem|ent than|
|000001e0| 20 74 68 65 20 61 72 67 | 75 6d 65 6e 74 2e 20 49 | the arg|ument. I|
|000001f0| 66 20 74 68 65 20 61 72 | 67 75 6d 65 6e 74 20 69 |f the ar|gument i|
|00000200| 73 20 6e 6f 74 20 61 20 | 76 65 63 74 6f 72 2c 20 |s not a |vector, |
|00000210| 74 68 65 6e 0d 64 69 66 | 66 65 72 65 6e 63 65 73 |then.dif|ferences|
|00000220| 20 61 72 65 20 63 61 6c | 75 6c 61 74 65 64 20 64 | are cal|ulated d|
|00000230| 6f 77 6e 20 65 61 63 68 | 20 63 6f 6c 75 6d 6e 2c |own each| column,|
|00000240| 20 72 65 74 75 72 6e 69 | 6e 67 20 61 20 6d 61 74 | returni|ng a mat|
|00000250| 72 69 78 20 77 69 74 68 | 20 6f 6e 65 0d 6c 65 73 |rix with| one.les|
|00000260| 73 20 72 6f 77 20 74 68 | 61 6e 20 74 68 65 20 61 |s row th|an the a|
|00000270| 72 67 75 6d 65 6e 74 2e | 20 20 0d 0d 49 66 20 74 |rgument.|  ..If t|
|00000280| 68 65 20 6f 70 74 69 6f | 6e 61 6c 20 73 63 61 6c |he optio|nal scal|
|00000290| 61 72 20 61 72 67 75 6d | 65 6e 74 20 69 73 20 70 |ar argum|ent is p|
|000002a0| 72 65 73 65 6e 74 2c 20 | 69 74 20 73 70 65 63 69 |resent, |it speci|
|000002b0| 66 69 65 73 20 74 68 65 | 20 6e 75 6d 62 65 72 0d |fies the| number.|
|000002c0| 6f 66 20 74 69 6d 65 73 | 20 64 69 66 66 65 72 65 |of times| differe|
|000002d0| 6e 63 65 73 20 61 72 65 | 20 74 61 6b 65 6e 2e 20 |nces are| taken. |
|000002e0| 46 6f 72 20 65 78 61 6d | 70 6c 65 2c 20 69 66 20 |For exam|ple, if |
|000002f0| 69 74 20 69 73 20 24 32 | 24 2c 20 74 68 65 6e 20 |it is $2|$, then |
|00000300| 74 68 65 0d 64 69 66 66 | 65 72 65 6e 63 65 73 20 |the.diff|erences |
|00000310| 62 65 74 77 65 65 6e 20 | 74 68 65 20 64 69 66 66 |between |the diff|
|00000320| 65 72 65 6e 63 65 73 20 | 61 72 65 20 72 65 74 75 |erences |are retu|
|00000330| 72 6e 65 64 2e 0d 0d 24 | 5c 4c 6f 6e 67 72 69 67 |rned...$|\Longrig|
|00000340| 68 74 61 72 72 6f 77 24 | 20 54 68 69 73 20 69 73 |htarrow$| This is|
|00000350| 20 6e 6f 74 20 61 6e 20 | 5c 52 4c 61 42 5c 20 62 | not an |\RLaB\ b|
|00000360| 75 69 6c 74 2d 69 6e 20 | 66 75 6e 63 74 69 6f 6e |uilt-in |function|
|00000370| 2e 20 20 54 68 69 73 20 | 66 75 6e 63 74 69 6f 6e |.  This |function|
|00000380| 0d 69 73 20 6e 6f 72 6d | 61 6c 6c 79 20 6c 6f 61 |.is norm|ally loa|
|00000390| 64 65 64 20 6f 6e 20 73 | 74 61 72 74 2d 75 70 20 |ded on s|tart-up |
|000003a0| 66 72 6f 6d 20 74 68 65 | 20 5c 76 65 72 62 2b 64 |from the| \verb+d|
|000003b0| 69 66 66 2e 72 2b 20 66 | 69 6c 65 20 69 6e 20 74 |iff.r+ f|ile in t|
|000003c0| 68 65 0d 73 74 61 6e 64 | 61 72 64 20 5c 76 65 72 |he.stand|ard \ver|
|000003d0| 62 2b 72 6c 69 62 2b 20 | 64 69 72 65 63 74 6f 72 |b+rlib+ |director|
|000003e0| 79 2e 20 55 73 65 20 6f | 66 20 74 68 65 20 5c 76 |y. Use o|f the \v|
|000003f0| 65 72 62 2b 2d 72 2b 20 | 6f 70 74 69 6f 6e 2c 20 |erb+-r+ |option, |
|00000400| 69 6e 63 6f 72 72 65 63 | 74 6c 79 20 0d 73 65 74 |incorrec|tly .set|
|00000410| 74 69 6e 67 20 74 68 65 | 20 5c 76 65 72 62 2b 52 |ting the| \verb+R|
|00000420| 4c 41 42 5f 4c 49 42 5f | 44 49 52 2b 20 65 6e 76 |LAB_LIB_|DIR+ env|
|00000430| 69 72 6f 6e 6d 65 6e 74 | 61 6c 20 76 61 72 69 61 |ironment|al varia|
|00000440| 62 6c 65 2c 20 6f 72 20 | 6d 6f 64 69 66 79 69 6e |ble, or |modifyin|
|00000450| 67 0d 5c 76 65 72 62 2b | 64 69 66 66 2e 72 2b 20 |g.\verb+|diff.r+ |
|00000460| 6d 61 79 20 6d 61 6b 65 | 20 74 68 69 73 20 66 75 |may make| this fu|
|00000470| 6e 63 74 69 6f 6e 20 75 | 6e 61 76 61 69 6c 61 62 |nction u|navailab|
|00000480| 6c 65 2e 0d 0d 5c 70 61 | 72 61 67 72 61 70 68 7b |le...\pa|ragraph{|
|00000490| 45 78 61 6d 70 6c 65 7d | 0d 5c 69 6e 64 65 78 7b |Example}|.\index{|
|000004a0| 65 78 61 6d 70 6c 65 20 | 6f 66 20 64 69 66 66 28 |example |of diff(|
|000004b0| 29 7d 0d 5c 69 6e 64 65 | 78 7b 64 69 66 66 28 29 |)}.\inde|x{diff()|
|000004c0| 21 65 78 61 6d 70 6c 65 | 7d 0d 5c 62 65 67 69 6e |!example|}.\begin|
|000004d0| 7b 76 65 72 62 61 74 69 | 6d 7d 0d 3e 20 61 20 3d |{verbati|m}.> a =|
|000004e0| 20 5b 31 2c 32 2c 33 2c | 34 2c 35 5d 0d 20 61 20 | [1,2,3,|4,5]. a |
|000004f0| 3d 0d 20 20 20 20 20 20 | 20 20 31 20 20 20 20 20 |=.      |  1     |
|00000500| 20 20 20 20 20 32 20 20 | 20 20 20 20 20 20 20 20 |     2  |        |
|00000510| 33 20 20 20 20 20 20 20 | 20 20 20 34 20 20 20 20 |3       |   4    |
|00000520| 20 20 20 20 20 20 35 20 | 20 0d 3e 20 64 69 66 66 |      5 | .> diff|
|00000530| 28 61 29 0d 20 20 20 20 | 20 20 20 20 31 20 20 20 |(a).    |    1   |
|00000540| 20 20 20 20 20 20 20 31 | 20 20 20 20 20 20 20 20 |       1|        |
|00000550| 20 20 31 20 20 20 20 20 | 20 20 20 20 20 31 20 20 |  1     |     1  |
|00000560| 0d 3e 20 62 20 3d 20 5b | 31 2c 32 2c 34 2c 37 2c |.> b = [|1,2,4,7,|
|00000570| 31 31 5d 0d 20 62 20 3d | 0d 20 20 20 20 20 20 20 |11]. b =|.       |
|00000580| 20 31 20 20 20 20 20 20 | 20 20 20 20 32 20 20 20 | 1      |    2   |
|00000590| 20 20 20 20 20 20 20 34 | 20 20 20 20 20 20 20 20 |       4|        |
|000005a0| 20 20 37 20 20 20 20 20 | 20 20 20 20 31 31 20 20 |  7     |    11  |
|000005b0| 0d 3e 20 64 69 66 66 28 | 62 29 0d 20 20 20 20 20 |.> diff(|b).     |
|000005c0| 20 20 20 31 20 20 20 20 | 20 20 20 20 20 20 32 20 |   1    |      2 |
|000005d0| 20 20 20 20 20 20 20 20 | 20 33 20 20 20 20 20 20 |        | 3      |
|000005e0| 20 20 20 20 34 20 20 0d | 3e 20 64 69 66 66 28 64 |    4  .|> diff(d|
|000005f0| 69 66 66 28 62 29 29 0d | 20 20 20 20 20 20 20 20 |iff(b)).|        |
|00000600| 31 20 20 20 20 20 20 20 | 20 20 20 31 20 20 20 20 |1       |   1    |
|00000610| 20 20 20 20 20 20 31 20 | 20 0d 3e 20 64 69 66 66 |      1 | .> diff|
|00000620| 28 62 2c 32 29 0d 20 20 | 20 20 20 20 20 20 31 20 |(b,2).  |      1 |
|00000630| 20 20 20 20 20 20 20 20 | 20 31 20 20 20 20 20 20 |        | 1      |
|00000640| 20 20 20 20 31 20 20 0d | 3e 20 64 69 66 66 28 62 |    1  .|> diff(b|
|00000650| 2c 33 29 0d 20 20 20 20 | 20 20 20 20 30 20 20 20 |,3).    |    0   |
|00000660| 20 20 20 20 20 20 20 30 | 20 20 0d 3e 20 63 20 3d |       0|  .> c =|
|00000670| 20 5b 31 2c 31 2c 31 3b | 0d 3e 20 20 20 20 20 20 | [1,1,1;|.>      |
|00000680| 32 2c 32 2c 32 3b 0d 3e | 20 20 20 20 20 20 33 2c |2,2,2;.>|      3,|
|00000690| 34 2c 35 3b 0d 3e 20 20 | 20 20 20 20 34 2c 37 2c |4,5;.>  |    4,7,|
|000006a0| 31 31 5d 0d 20 63 20 3d | 0d 20 20 20 20 20 20 20 |11]. c =|.       |
|000006b0| 20 31 20 20 20 20 20 20 | 20 20 20 20 31 20 20 20 | 1      |    1   |
|000006c0| 20 20 20 20 20 20 20 31 | 20 20 0d 20 20 20 20 20 |       1|  .     |
|000006d0| 20 20 20 32 20 20 20 20 | 20 20 20 20 20 20 32 20 |   2    |      2 |
|000006e0| 20 20 20 20 20 20 20 20 | 20 32 20 20 0d 20 20 20 |        | 2  .   |
|000006f0| 20 20 20 20 20 33 20 20 | 20 20 20 20 20 20 20 20 |     3  |        |
|00000700| 34 20 20 20 20 20 20 20 | 20 20 20 35 20 20 0d 20 |4       |   5  . |
|00000710| 20 20 20 20 20 20 20 34 | 20 20 20 20 20 20 20 20 |       4|        |
|00000720| 20 20 37 20 20 20 20 20 | 20 20 20 20 31 31 20 20 |  7     |    11  |
|00000730| 0d 3e 20 64 69 66 66 28 | 63 29 0d 20 20 20 20 20 |.> diff(|c).     |
|00000740| 20 20 20 31 20 20 20 20 | 20 20 20 20 20 20 31 20 |   1    |      1 |
|00000750| 20 20 20 20 20 20 20 20 | 20 31 20 20 0d 20 20 20 |        | 1  .   |
|00000760| 20 20 20 20 20 31 20 20 | 20 20 20 20 20 20 20 20 |     1  |        |
|00000770| 32 20 20 20 20 20 20 20 | 20 20 20 33 20 20 0d 20 |2       |   3  . |
|00000780| 20 20 20 20 20 20 20 31 | 20 20 20 20 20 20 20 20 |       1|        |
|00000790| 20 20 33 20 20 20 20 20 | 20 20 20 20 20 36 20 20 |  3     |     6  |
|000007a0| 0d 3e 20 64 69 66 66 28 | 63 2c 32 29 0d 20 20 20 |.> diff(|c,2).   |
|000007b0| 20 20 20 20 20 30 20 20 | 20 20 20 20 20 20 20 20 |     0  |        |
|000007c0| 31 20 20 20 20 20 20 20 | 20 20 20 32 20 20 0d 20 |1       |   2  . |
|000007d0| 20 20 20 20 20 20 20 30 | 20 20 20 20 20 20 20 20 |       0|        |
|000007e0| 20 20 31 20 20 20 20 20 | 20 20 20 20 20 33 20 20 |  1     |     3  |
|000007f0| 0d 3e 20 64 69 66 66 28 | 63 2c 33 29 0d 20 20 20 |.> diff(|c,3).   |
|00000800| 20 20 20 20 20 30 20 20 | 20 20 20 20 20 20 20 20 |     0  |        |
|00000810| 30 20 20 20 20 20 20 20 | 20 20 20 31 0d 5c 65 6e |0       |   1.\en|
|00000820| 64 7b 76 65 72 62 61 74 | 69 6d 7d 0d 0d 5c 6e 65 |d{verbat|im}..\ne|
|00000830| 77 70 61 67 65 0d 0d 0d | 0d 0d 0d                |wpage...|...     |
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