home *** CD-ROM | disk | FTP | other *** search
/ Celestin Apprentice 4 / Apprentice-Release4.iso / Languages / RLaB 1.18c / manual / logspace.tex < prev    next >
LaTeX Document  |  1994-04-27  |  2.3 KB  |  [TEXT/ttxt]

open in: MacOS 8.1     |     Win98     |     DOS

view JSON data     |     view as text

This file was processed as: LaTeX Document (document/latex).

You can browse this item here: logspace.tex

ConfidenceProgramDetectionMatch TypeSupport
100% dexvert LaTeX Document (document/latex) magic Supported
1% dexvert Text File (text/txt) fallback Supported
100% file LaTeX document text default
99% file LaTeX document, ASCII text, with CR line terminators default
100% checkBytes Printable ASCII default
100% perlTextCheck Likely Text (Perl) default
100% siegfried fmt/281 LaTeX (Subdocument) default
100% detectItEasy Format: plain text[CR] default (weak)


id metadata
keyvalue
macFileType[TEXT]
macFileCreator[ttxt]



hex view
+--------+-------------------------+-------------------------+--------+--------+
|00000000| 5c 73 65 63 74 69 6f 6e | 7b 6c 6f 67 73 70 61 63 |\section|{logspac|
|00000010| 65 20 2d 2d 2d 20 4c 6f | 67 61 72 69 74 68 6d 69 |e --- Lo|garithmi|
|00000020| 63 61 6c 6c 79 20 73 70 | 61 63 65 64 20 76 65 63 |cally sp|aced vec|
|00000030| 74 6f 72 7d 0d 5c 6c 61 | 62 65 6c 7b 66 6e 3a 6c |tor}.\la|bel{fn:l|
|00000040| 6f 67 73 70 61 63 65 7d | 0d 5c 69 6e 64 65 78 7b |ogspace}|.\index{|
|00000050| 6c 6f 67 73 70 61 63 65 | 28 29 7d 0d 5c 69 6e 64 |logspace|()}.\ind|
|00000060| 65 78 7b 6c 6f 67 61 72 | 69 74 68 6d 69 63 61 6c |ex{logar|ithmical|
|00000070| 6c 79 20 73 70 61 63 65 | 64 20 76 65 63 74 6f 72 |ly space|d vector|
|00000080| 7d 0d 5c 69 6e 64 65 78 | 7b 76 65 63 74 6f 72 21 |}.\index|{vector!|
|00000090| 6c 6f 67 61 72 69 74 68 | 6d 69 63 7d 0d 5c 62 65 |logarith|mic}.\be|
|000000a0| 67 69 6e 7b 72 61 69 6c | 7d 0d 4c 6f 67 73 70 61 |gin{rail|}.Logspa|
|000000b0| 63 65 20 3a 20 27 6c 6f | 67 73 70 61 63 65 27 20 |ce : 'lo|gspace' |
|000000c0| 27 28 27 20 53 63 61 6c | 61 72 20 20 27 2c 27 20 |'(' Scal|ar ',' |
|000000d0| 53 63 61 6c 61 72 20 28 | 20 27 2c 27 20 53 63 61 |Scalar (| ',' Sca|
|000000e0| 6c 61 72 29 3f 20 27 29 | 27 20 3b 0d 5c 65 6e 64 |lar)? ')|' ;.\end|
|000000f0| 7b 72 61 69 6c 7d 0d 0d | 5c 76 65 72 62 2b 6c 6f |{rail}..|\verb+lo|
|00000100| 67 73 70 61 63 65 2b 20 | 63 72 65 61 74 65 73 20 |gspace+ |creates |
|00000110| 61 20 76 65 63 74 6f 72 | 20 6f 66 20 6c 6f 67 61 |a vector| of loga|
|00000120| 72 69 74 68 6d 69 63 61 | 6c 6c 79 20 73 70 61 63 |rithmica|lly spac|
|00000130| 65 64 20 70 6f 69 6e 74 | 73 2e 0d 49 66 20 74 68 |ed point|s..If th|
|00000140| 65 20 66 69 72 73 74 20 | 74 77 6f 20 61 72 67 75 |e first |two argu|
|00000150| 6d 65 6e 74 73 20 61 72 | 65 20 24 78 5f 7b 31 7d |ments ar|e $x_{1}|
|00000160| 24 20 61 6e 64 20 24 78 | 5f 7b 32 7d 24 2c 20 74 |$ and $x|_{2}$, t|
|00000170| 68 65 6e 20 74 68 65 20 | 70 6f 69 6e 74 73 20 61 |hen the |points a|
|00000180| 72 65 0d 67 65 6e 65 72 | 61 74 65 64 20 62 65 74 |re.gener|ated bet|
|00000190| 77 65 65 6e 20 24 31 30 | 5e 7b 78 5f 7b 31 7d 7d |ween $10|^{x_{1}}|
|000001a0| 24 20 61 6e 64 20 24 31 | 30 5e 7b 78 5f 7b 32 7d |$ and $1|0^{x_{2}|
|000001b0| 7d 24 2e 20 49 66 20 74 | 68 65 20 6f 70 74 69 6f |}$. If t|he optio|
|000001c0| 6e 61 6c 0d 74 68 69 72 | 64 20 61 72 67 75 6d 65 |nal.thir|d argume|
|000001d0| 6e 74 20 69 73 20 70 72 | 65 73 65 6e 74 2c 20 69 |nt is pr|esent, i|
|000001e0| 74 20 73 70 65 63 69 66 | 69 65 73 20 68 6f 77 20 |t specif|ies how |
|000001f0| 6d 61 6e 79 20 70 6f 69 | 6e 74 73 20 61 72 65 20 |many poi|nts are |
|00000200| 74 6f 20 62 65 0d 63 72 | 65 61 74 65 64 2e 20 20 |to be.cr|eated. |
|00000210| 49 66 20 74 68 65 20 74 | 68 69 72 64 20 61 72 67 |If the t|hird arg|
|00000220| 75 6d 65 6e 74 20 69 73 | 20 6d 69 73 73 69 6e 67 |ument is| missing|
|00000230| 2c 20 74 68 65 6e 20 35 | 30 20 70 6f 69 6e 74 73 |, then 5|0 points|
|00000240| 20 61 72 65 20 61 73 73 | 75 6d 65 64 2e 20 0d 0d | are ass|umed. ..|
|00000250| 41 73 20 61 20 73 70 65 | 63 69 61 6c 20 63 61 73 |As a spe|cial cas|
|00000260| 65 2c 20 69 66 20 74 68 | 65 20 73 65 63 6f 6e 64 |e, if th|e second|
|00000270| 20 61 72 67 75 6d 65 6e | 74 20 69 73 20 65 71 75 | argumen|t is equ|
|00000280| 61 6c 20 74 6f 20 24 5c | 70 69 24 2c 20 74 68 65 |al to $\|pi$, the|
|00000290| 6e 20 74 68 65 0d 70 6f | 69 6e 74 73 20 61 72 65 |n the.po|ints are|
|000002a0| 20 67 65 6e 65 72 61 74 | 65 64 20 62 65 74 77 65 | generat|ed betwe|
|000002b0| 65 6e 20 24 31 30 5e 7b | 78 5f 7b 31 7d 7d 24 20 |en $10^{|x_{1}}$ |
|000002c0| 61 6e 64 20 24 5c 70 69 | 24 2e 0d 0d 24 5c 4c 6f |and $\pi|$...$\Lo|
|000002d0| 6e 67 72 69 67 68 74 61 | 72 72 6f 77 24 20 54 68 |ngrighta|rrow$ Th|
|000002e0| 69 73 20 69 73 20 6e 6f | 74 20 61 6e 20 5c 52 4c |is is no|t an \RL|
|000002f0| 61 42 5c 20 62 75 69 6c | 74 2d 69 6e 20 66 75 6e |aB\ buil|t-in fun|
|00000300| 63 74 69 6f 6e 2e 20 20 | 54 68 69 73 20 66 75 6e |ction. |This fun|
|00000310| 63 74 69 6f 6e 0d 69 73 | 20 6e 6f 72 6d 61 6c 6c |ction.is| normall|
|00000320| 79 20 6c 6f 61 64 65 64 | 20 6f 6e 20 73 74 61 72 |y loaded| on star|
|00000330| 74 2d 75 70 20 66 72 6f | 6d 20 74 68 65 20 5c 76 |t-up fro|m the \v|
|00000340| 65 72 62 2b 6c 6f 67 73 | 70 61 63 65 2e 72 2b 20 |erb+logs|pace.r+ |
|00000350| 66 69 6c 65 20 69 6e 20 | 74 68 65 0d 73 74 61 6e |file in |the.stan|
|00000360| 64 61 72 64 20 5c 76 65 | 72 62 2b 72 6c 69 62 2b |dard \ve|rb+rlib+|
|00000370| 20 64 69 72 65 63 74 6f | 72 79 2e 20 55 73 65 20 | directo|ry. Use |
|00000380| 6f 66 20 74 68 65 20 5c | 76 65 72 62 2b 2d 72 2b |of the \|verb+-r+|
|00000390| 20 6f 70 74 69 6f 6e 2c | 20 69 6e 63 6f 72 72 65 | option,| incorre|
|000003a0| 63 74 6c 79 20 0d 73 65 | 74 74 69 6e 67 20 74 68 |ctly .se|tting th|
|000003b0| 65 20 5c 76 65 72 62 2b | 52 4c 41 42 5f 4c 49 42 |e \verb+|RLAB_LIB|
|000003c0| 5f 44 49 52 2b 20 65 6e | 76 69 72 6f 6e 6d 65 6e |_DIR+ en|vironmen|
|000003d0| 74 61 6c 20 76 61 72 69 | 61 62 6c 65 2c 20 6f 72 |tal vari|able, or|
|000003e0| 20 6d 6f 64 69 66 79 69 | 6e 67 0d 5c 76 65 72 62 | modifyi|ng.\verb|
|000003f0| 2b 6c 6f 67 73 70 61 63 | 65 2e 72 2b 20 6d 61 79 |+logspac|e.r+ may|
|00000400| 20 6d 61 6b 65 20 74 68 | 69 73 20 66 75 6e 63 74 | make th|is funct|
|00000410| 69 6f 6e 20 75 6e 61 76 | 61 69 6c 61 62 6c 65 2e |ion unav|ailable.|
|00000420| 0d 0d 5c 70 61 72 61 67 | 72 61 70 68 7b 45 78 61 |..\parag|raph{Exa|
|00000430| 6d 70 6c 65 7d 0d 5c 69 | 6e 64 65 78 7b 65 78 61 |mple}.\i|ndex{exa|
|00000440| 6d 70 6c 65 20 6f 66 20 | 6c 6f 67 73 70 61 63 65 |mple of |logspace|
|00000450| 28 29 7d 0d 5c 69 6e 64 | 65 78 7b 6c 6f 67 73 70 |()}.\ind|ex{logsp|
|00000460| 61 63 65 28 29 21 65 78 | 61 6d 70 6c 65 7d 0d 5c |ace()!ex|ample}.\|
|00000470| 62 65 67 69 6e 7b 76 65 | 72 62 61 74 69 6d 7d 0d |begin{ve|rbatim}.|
|00000480| 3e 20 6c 6f 67 73 70 61 | 63 65 28 30 2c 31 29 0d |> logspa|ce(0,1).|
|00000490| 20 6d 61 74 72 69 78 20 | 63 6f 6c 75 6d 6e 73 20 | matrix |columns |
|000004a0| 31 20 74 68 72 75 20 37 | 0d 20 20 20 20 20 20 20 |1 thru 7|. |
|000004b0| 20 31 20 20 20 20 20 20 | 20 31 2e 30 35 20 20 20 | 1 | 1.05 |
|000004c0| 20 20 20 20 20 31 2e 31 | 20 20 20 20 20 20 20 31 | 1.1| 1|
|000004d0| 2e 31 35 20 20 20 20 20 | 20 20 31 2e 32 31 20 20 |.15 | 1.21 |
|000004e0| 20 20 20 20 20 31 2e 32 | 36 20 20 20 20 20 20 20 | 1.2|6 |
|000004f0| 31 2e 33 33 20 20 0d 0d | 20 6d 61 74 72 69 78 20 |1.33 ..| matrix |
|00000500| 63 6f 6c 75 6d 6e 73 20 | 38 20 74 68 72 75 20 31 |columns |8 thru 1|
|00000510| 34 0d 20 20 20 20 20 31 | 2e 33 39 20 20 20 20 20 |4. 1|.39 |
|00000520| 20 20 31 2e 34 36 20 20 | 20 20 20 20 20 31 2e 35 | 1.46 | 1.5|
|00000530| 33 20 20 20 20 20 20 20 | 20 31 2e 36 20 20 20 20 |3 | 1.6 |
|00000540| 20 20 20 31 2e 36 38 20 | 20 20 20 20 20 20 31 2e | 1.68 | 1.|
|00000550| 37 36 20 20 20 20 20 20 | 20 31 2e 38 34 20 20 0d |76 | 1.84 .|
|00000560| 0d 20 6d 61 74 72 69 78 | 20 63 6f 6c 75 6d 6e 73 |. matrix| columns|
|00000570| 20 31 35 20 74 68 72 75 | 20 32 31 0d 20 20 20 20 | 15 thru| 21. |
|00000580| 20 31 2e 39 33 20 20 20 | 20 20 20 20 32 2e 30 32 | 1.93 | 2.02|
|00000590| 20 20 20 20 20 20 20 32 | 2e 31 32 20 20 20 20 20 | 2|.12 |
|000005a0| 20 20 32 2e 32 32 20 20 | 20 20 20 20 20 32 2e 33 | 2.22 | 2.3|
|000005b0| 33 20 20 20 20 20 20 20 | 32 2e 34 34 20 20 20 20 |3 |2.44 |
|000005c0| 20 20 20 32 2e 35 36 20 | 20 0d 0d 20 6d 61 74 72 | 2.56 | .. matr|
|000005d0| 69 78 20 63 6f 6c 75 6d | 6e 73 20 32 32 20 74 68 |ix colum|ns 22 th|
|000005e0| 72 75 20 32 38 0d 20 20 | 20 20 20 32 2e 36 38 20 |ru 28. | 2.68 |
|000005f0| 20 20 20 20 20 20 32 2e | 38 31 20 20 20 20 20 20 | 2.|81 |
|00000600| 20 32 2e 39 35 20 20 20 | 20 20 20 20 33 2e 30 39 | 2.95 | 3.09|
|00000610| 20 20 20 20 20 20 20 33 | 2e 32 34 20 20 20 20 20 | 3|.24 |
|00000620| 20 20 33 2e 33 39 20 20 | 20 20 20 20 20 33 2e 35 | 3.39 | 3.5|
|00000630| 36 20 20 0d 0d 20 6d 61 | 74 72 69 78 20 63 6f 6c |6 .. ma|trix col|
|00000640| 75 6d 6e 73 20 32 39 20 | 74 68 72 75 20 33 35 0d |umns 29 |thru 35.|
|00000650| 20 20 20 20 20 33 2e 37 | 33 20 20 20 20 20 20 20 | 3.7|3 |
|00000660| 33 2e 39 31 20 20 20 20 | 20 20 20 34 2e 30 39 20 |3.91 | 4.09 |
|00000670| 20 20 20 20 20 20 34 2e | 32 39 20 20 20 20 20 20 | 4.|29 |
|00000680| 20 20 34 2e 35 20 20 20 | 20 20 20 20 34 2e 37 31 | 4.5 | 4.71|
|00000690| 20 20 20 20 20 20 20 34 | 2e 39 34 20 20 0d 0d 20 | 4|.94 .. |
|000006a0| 6d 61 74 72 69 78 20 63 | 6f 6c 75 6d 6e 73 20 33 |matrix c|olumns 3|
|000006b0| 36 20 74 68 72 75 20 34 | 32 0d 20 20 20 20 20 35 |6 thru 4|2. 5|
|000006c0| 2e 31 38 20 20 20 20 20 | 20 20 35 2e 34 33 20 20 |.18 | 5.43 |
|000006d0| 20 20 20 20 20 35 2e 36 | 39 20 20 20 20 20 20 20 | 5.6|9 |
|000006e0| 35 2e 39 36 20 20 20 20 | 20 20 20 36 2e 32 35 20 |5.96 | 6.25 |
|000006f0| 20 20 20 20 20 20 36 2e | 35 35 20 20 20 20 20 20 | 6.|55 |
|00000700| 20 36 2e 38 37 20 20 0d | 0d 20 6d 61 74 72 69 78 | 6.87 .|. matrix|
|00000710| 20 63 6f 6c 75 6d 6e 73 | 20 34 33 20 74 68 72 75 | columns| 43 thru|
|00000720| 20 34 39 0d 20 20 20 20 | 20 20 37 2e 32 20 20 20 | 49. | 7.2 |
|00000730| 20 20 20 20 37 2e 35 34 | 20 20 20 20 20 20 20 37 | 7.54| 7|
|00000740| 2e 39 31 20 20 20 20 20 | 20 20 38 2e 32 39 20 20 |.91 | 8.29 |
|00000750| 20 20 20 20 20 38 2e 36 | 39 20 20 20 20 20 20 20 | 8.6|9 |
|00000760| 20 39 2e 31 20 20 20 20 | 20 20 20 39 2e 35 34 20 | 9.1 | 9.54 |
|00000770| 20 0d 0d 20 6d 61 74 72 | 69 78 20 63 6f 6c 75 6d | .. matr|ix colum|
|00000780| 6e 73 20 35 30 20 74 68 | 72 75 20 35 30 0d 20 20 |ns 50 th|ru 50. |
|00000790| 20 20 20 20 20 31 30 20 | 20 0d 3e 20 6c 6f 67 73 | 10 | .> logs|
|000007a0| 70 61 63 65 28 31 2c 33 | 2c 31 30 29 0d 20 6d 61 |pace(1,3|,10). ma|
|000007b0| 74 72 69 78 20 63 6f 6c | 75 6d 6e 73 20 31 20 74 |trix col|umns 1 t|
|000007c0| 68 72 75 20 37 0d 20 20 | 20 20 20 20 20 31 30 20 |hru 7. | 10 |
|000007d0| 20 20 20 20 20 20 31 36 | 2e 37 20 20 20 20 20 20 | 16|.7 |
|000007e0| 20 32 37 2e 38 20 20 20 | 20 20 20 20 34 36 2e 34 | 27.8 | 46.4|
|000007f0| 20 20 20 20 20 20 20 37 | 37 2e 34 20 20 20 20 20 | 7|7.4 |
|00000800| 20 20 20 31 32 39 20 20 | 20 20 20 20 20 20 32 31 | 129 | 21|
|00000810| 35 20 20 0d 0d 20 6d 61 | 74 72 69 78 20 63 6f 6c |5 .. ma|trix col|
|00000820| 75 6d 6e 73 20 38 20 74 | 68 72 75 20 31 30 0d 20 |umns 8 t|hru 10. |
|00000830| 20 20 20 20 20 33 35 39 | 20 20 20 20 20 20 20 20 | 359| |
|00000840| 35 39 39 20 20 20 20 20 | 20 31 65 2b 30 33 20 20 |599 | 1e+03 |
|00000850| 0d 3e 20 6c 6f 67 73 70 | 61 63 65 28 30 2c 70 69 |.> logsp|ace(0,pi|
|00000860| 2c 31 30 29 0d 20 6d 61 | 74 72 69 78 20 63 6f 6c |,10). ma|trix col|
|00000870| 75 6d 6e 73 20 31 20 74 | 68 72 75 20 37 0d 20 20 |umns 1 t|hru 7. |
|00000880| 20 20 20 20 20 20 31 20 | 20 20 20 20 20 20 31 2e | 1 | 1.|
|00000890| 31 34 20 20 20 20 20 20 | 20 31 2e 32 39 20 20 20 |14 | 1.29 |
|000008a0| 20 20 20 20 31 2e 34 36 | 20 20 20 20 20 20 20 31 | 1.46| 1|
|000008b0| 2e 36 36 20 20 20 20 20 | 20 20 31 2e 38 39 20 20 |.66 | 1.89 |
|000008c0| 20 20 20 20 20 32 2e 31 | 35 20 20 0d 0d 20 6d 61 | 2.1|5 .. ma|
|000008d0| 74 72 69 78 20 63 6f 6c | 75 6d 6e 73 20 38 20 74 |trix col|umns 8 t|
|000008e0| 68 72 75 20 31 30 0d 20 | 20 20 20 20 32 2e 34 34 |hru 10. | 2.44|
|000008f0| 20 20 20 20 20 20 20 32 | 2e 37 37 20 20 20 20 20 | 2|.77 |
|00000900| 20 20 33 2e 31 34 20 20 | 0d 5c 65 6e 64 7b 76 65 | 3.14 |.\end{ve|
|00000910| 72 62 61 74 69 6d 7d 0d | 0d 53 65 65 20 61 6c 73 |rbatim}.|.See als|
|00000920| 6f 3a 20 50 61 67 65 7e | 5c 70 61 67 65 72 65 66 |o: Page~|\pageref|
|00000930| 7b 66 6e 3a 6c 69 6e 73 | 70 61 63 65 7d 20 5c 76 |{fn:lins|pace} \v|
|00000940| 65 72 62 2b 6c 69 6e 73 | 70 61 63 65 28 29 2b 2e |erb+lins|pace()+.|
|00000950| 0d 0d 5c 6e 65 77 70 61 | 67 65 0d 0d 0d 0d 0d |..\newpa|ge..... |
+--------+-------------------------+-------------------------+--------+--------+