R : Copyright 2005, The R Foundation for Statistical Computing Version 2.1.1 (2005-06-20), ISBN 3-900051-07-0 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for a HTML browser interface to help. Type 'q()' to quit R. > ### *
> ### > attach(NULL, name = "CheckExEnv") > assign(".CheckExEnv", as.environment(2), pos = length(search())) # base > ## add some hooks to label plot pages for base and grid graphics > setHook("plot.new", ".newplot.hook") > setHook("persp", ".newplot.hook") > setHook("grid.newpage", ".gridplot.hook") > > assign("cleanEx", + function(env = .GlobalEnv) { + rm(list = ls(envir = env, all.names = TRUE), envir = env) + RNGkind("default", "default") + set.seed(1) + options(warn = 1) + delayedAssign("T", stop("T used instead of TRUE"), + assign.env = .CheckExEnv) + delayedAssign("F", stop("F used instead of FALSE"), + assign.env = .CheckExEnv) + sch <- search() + newitems <- sch[! sch %in% .oldSearch] + for(item in rev(newitems)) + eval(substitute(detach(item), list(item=item))) + missitems <- .oldSearch[! .oldSearch %in% sch] + if(length(missitems)) + warning("items ", paste(missitems, collapse=", "), + " have been removed from the search path") + }, + env = .CheckExEnv) > assign("..nameEx", "__{must remake R-ex/*.R}__", env = .CheckExEnv) # for now > assign("ptime", proc.time(), env = .CheckExEnv) > grDevices::postscript("NISTnls-Examples.ps") > assign("par.postscript", graphics::par(no.readonly = TRUE), env = .CheckExEnv) > options(contrasts = c(unordered = "contr.treatment", ordered = "contr.poly")) > options(warn = 1) > library('NISTnls') > > assign(".oldSearch", search(), env = .CheckExEnv) > assign(".oldNS", loadedNamespaces(), env = .CheckExEnv) > cleanEx(); ..nameEx <- "Bennett5" > > ### * Bennett5 > > flush(stderr()); flush(stdout()) > > ### Name: Bennett5 > ### Title: Magentization modelling > ### Aliases: Bennett5 > ### Keywords: datasets > > ### ** Examples > > data(Bennett5) > plot(y ~ x, data = Bennett5) > ## Not run: > ##D fm1 <- nls(y ~ b1*(b2+x)**(-1/b3), data = Bennett5, > ##D start = c(b1 = -2000, b2 = 50, b3 = 0.8), trace = TRUE) > ## End(Not run) > fm2 <- nls(y ~ b1*(b2+x)**(-1/b3), data = Bennett5, + start = c(b1 = -1500, b2 = 45, b3 = 0.85), trace = TRUE) 57261.1 : -1500.00 45.00 0.85 18191.49 : -1914.654709 46.493945 1.070183 4.647613 : -2117.559108 45.893463 0.966549 4.52855 : -2208.9266606 46.1001106 0.9577604 3.581903 : -2281.6765159 46.2571248 0.9512485 2.631036 : -2395.8024999 46.4947524 0.9415769 0.5031881 : -2519.9742669 46.7357979 0.9321035 0.0005241039 : -2523.4159095 46.7361895 0.9321911 0.0005240474 : -2523.4502120 46.7363318 0.9321886 > fm3 <- nls(y ~ (b2+x)**(-1/b3), data = Bennett5, alg = "plinear", + start = c( b2 = 50, b3 = 0.8), trace = TRUE) 0.5338162 : 50.000 0.800 -5550.004 0.01664294 : 46.2295866 0.9240461 -2597.4015615 0.0005268717 : 46.7023832 0.9325218 -2517.9443282 0.0005240474 : 46.7364533 0.9321864 -2523.4821951 0.0005240474 : 46.7365446 0.9321852 -2523.5010213 > fm4 <- nls(y ~ (b2+x)**(-1/b3), data = Bennett5, alg = "plinear", + start = c( b2 = 45, b3 = 0.8), trace = TRUE) 2.075439 : 45.000 0.800 -4989.565 0.04921469 : 44.4445272 0.9418989 -2311.5374878 0.0005971025 : 46.5182393 0.9346327 -2484.8325186 0.000524054 : 46.7349625 0.9322004 -2523.2480337 0.0005240474 : 46.736555 0.932185 -2523.503581 > > > > cleanEx(); ..nameEx <- "Chwirut1" > > ### * Chwirut1 > > flush(stderr()); flush(stdout()) > > ### Name: Chwirut1 > ### Title: Ultrasonic calibration study 1 > ### Aliases: Chwirut1 > ### Keywords: datasets > > ### ** Examples > > data(Chwirut1) > plot(y ~ x, data = Chwirut1) > fm1 <- nls(y ~ exp(-b1*x)/(b2+b3*x), data = Chwirut1, trace = TRUE, + start = c(b1 = 0.1, b2 = 0.01, b3 = 0.02)) 50068.65 : 0.10 0.01 0.02 4258.757 : 0.15755894 0.00656069 0.01212201 2416.907 : 0.188633920 0.006055854 0.010471022 2384.48 : 0.190182703 0.006129919 0.010532848 2384.477 : 0.190274343 0.006131376 0.010531006 2384.477 : 0.190277967 0.006131398 0.010530915 > fm2 <- nls(y ~ exp(-b1*x)/(b2+b3*x), data = Chwirut1, trace = TRUE, + start = c(b1 = 0.15, b2 = 0.008, b3 = 0.010)) 4575.709 : 0.150 0.008 0.010 2431.842 : 0.16786093 0.00560620 0.01143976 2384.679 : 0.189567761 0.006141611 0.010523876 2384.477 : 0.190155392 0.006129649 0.010535289 2384.477 : 0.190275831 0.006131414 0.010530932 2384.477 : 0.190277923 0.006131397 0.010530917 > fm3 <- nls(y ~ exp(-b1*x)/(1+p3*x), data = Chwirut1, trace = TRUE, + start = c(b1 = 0.1, p3 = 0.02/0.01), algorithm = "plinear") 3144.225 : 0.100 2.000 163.305 2395.405 : 0.1703262 1.8778966 168.5821864 2384.695 : 0.1890125 1.7177558 162.9130082 2384.478 : 0.1901318 1.7188860 163.1455698 2384.477 : 0.1902745 1.7175465 163.0948218 2384.477 : 0.1902779 1.7175400 163.0949786 > fm4 <- nls(y ~ exp(-b1*x)/(1+p3*x), data = Chwirut1, trace = TRUE, + start = c(b1 = 0.15, p3 = 0.01/0.008), algorithm = "plinear") 3769.524 : 0.1500 1.2500 131.6984 2434.583 : 0.1668770 1.7734832 162.4791461 2384.697 : 0.1872659 1.7424999 163.9832264 2384.478 : 0.1901634 1.7179372 163.0989854 2384.477 : 0.1902689 1.7176165 163.0977513 2384.477 : 0.1902779 1.7175385 163.0949033 2384.477 : 0.1902782 1.7175374 163.0948827 > > > > cleanEx(); ..nameEx <- "Chwirut2" > > ### * Chwirut2 > > flush(stderr()); flush(stdout()) > > ### Name: Chwirut2 > ### Title: Ultrasonic calibration data 2 > ### Aliases: Chwirut2 > ### Keywords: datasets > > ### ** Examples > > data(Chwirut2) > plot(y ~ x, data = Chwirut2) > fm1 <- nls(y ~ exp(-b1*x)/(b2+b3*x), data = Chwirut2, trace = TRUE, + start = c(b1 = 0.1 , b2 = 0.01, b3 = 0.02) ) 14794.79 : 0.10 0.01 0.02 1127.464 : 0.139981133 0.005210818 0.014326137 524.0564 : 0.166842526 0.005181954 0.011911595 513.0496 : 0.166542923 0.005165775 0.012147521 513.048 : 0.166574405 0.005165294 0.012150094 > fm2 <- nls(y ~ exp(-b1*x)/(b2+b3*x), data = Chwirut2, trace = TRUE, + start = c(b1 = 0.15 , b2 = 0.008, b3 = 0.01) ) 1486.959 : 0.150 0.008 0.010 534.4129 : 0.141831871 0.004586793 0.013138455 513.091 : 0.164508990 0.005143257 0.012210244 513.0481 : 0.166473989 0.005163946 0.012153654 513.048 : 0.166571971 0.005165264 0.012150178 513.048 : 0.166576461 0.005165326 0.012150014 > fm3 <- nls(y ~ exp(-b1*x)/(1+p3*x), data = Chwirut2, trace = TRUE, + start = c(b1 = 0.1, p3 = 2.), alg = "plinear" ) 852.0762 : 0.1000 2.0000 165.1199 518.4111 : 0.1482451 2.4711552 196.6031152 513.0639 : 0.1652067 2.3665482 194.1067262 513.0481 : 0.166510 2.353067 193.630766 513.048 : 0.1665736 2.3522638 193.6000828 513.048 : 0.1665765 2.3522251 193.5985790 > fm4 <- nls(y ~ exp(-b1*x)/(1+p3*x), data = Chwirut2, trace = TRUE, + start = c(b1 = 0.15, p3 = 0.01/0.008), alg = "plinear" ) 1098.890 : 0.1500 1.2500 133.8166 574.2242 : 0.1424199 2.1089886 177.3429804 513.3576 : 0.1623870 2.3749935 194.0763848 513.0484 : 0.1663405 2.3552654 193.7154918 513.048 : 0.1665658 2.3523655 193.6040140 513.048 : 0.1665762 2.3522300 193.5987686 > > > > cleanEx(); ..nameEx <- "DanielWood" > > ### * DanielWood > > flush(stderr()); flush(stdout()) > > ### Name: DanielWood > ### Title: Radiated energy > ### Aliases: DanielWood > ### Keywords: datasets > > ### ** Examples > > data(DanielWood) > plot(y ~ x, data = DanielWood) > fm1 <- nls(y ~ b1*x**b2, data = DanielWood, trace = TRUE, + start = c(b1 = 1, b2 = 5)) 149.7192 : 1 5 4.610878 : 0.7061691 4.4567375 0.03168417 : 0.7499191 3.9483634 0.004320594 : 0.7685973 3.8607752 0.004317308 : 0.7688633 3.8604026 0.004317308 : 0.7688623 3.8604056 > fm2 <- nls(y ~ b1*x**b2, data = DanielWood, trace = TRUE, + start = c(b1 = 0.7, b2 = 4)) 0.1037647 : 0.7 4.0 0.005930406 : 0.7679852 3.8542844 0.004317316 : 0.7688429 3.8604767 0.004317308 : 0.7688625 3.8604050 > fm3 <- nls(y ~ x**b2, data = DanielWood, trace = TRUE, + start = c(b2 = 5), algorithm = "plinear") 0.4910019 : 5.0000000 0.4543013 0.005361624 : 3.8098133 0.7867722 0.004317347 : 3.860712 0.768755 0.004317308 : 3.8604032 0.7688631 0.004317308 : 3.8604056 0.7688623 > fm4 <- nls(y ~ x**b2, data = DanielWood, trace = TRUE, + start = c(b2 = 4), algorithm = "plinear") 0.01216267 : 4.0000000 0.7214201 0.004318602 : 3.8586217 0.7694872 0.004317308 : 3.8604195 0.7688574 0.004317308 : 3.8604055 0.7688623 > > > > cleanEx(); ..nameEx <- "ENSO" > > ### * ENSO > > flush(stderr()); flush(stdout()) > > ### Name: ENSO > ### Title: Atmospheric pressure differences > ### Aliases: ENSO > ### Keywords: datasets > > ### ** Examples > > data(ENSO) > plot(y ~ x, data = ENSO) > plot(y ~ x, data = ENSO, type = "l") # to see the pattern more clearly > fm1 <- nls(y ~ b1 + b2*cos( 2*pi*x/12 ) + b3*sin( 2*pi*x/12 ) + + b5*cos( 2*pi*x/b4 ) + b6*sin( 2*pi*x/b4 ) + + b8*cos( 2*pi*x/b7 ) + b9*sin( 2*pi*x/b7 ), + data = ENSO, trace = TRUE, + start = c(b1 = 11.0, b2 = 3.0, b3 = 0.5, b4 = 40.0, b5 = -0.7, + b6 = -1.3, b7 = 25.0, b8 = -0.3, b9 = 1.4)) 1153.944 : 11.0 3.0 0.5 40.0 -0.7 -1.3 25.0 -0.3 1.4 998.5415 : 10.5931007 3.0858358 0.4762940 41.7286733 -1.1084222 -1.0644073 26.0250919 0.3129043 0.3016584 971.5736 : 10.5834357 3.0674679 0.5368181 42.1528248 -1.4561794 -0.7653524 27.5160512 -0.3986077 0.8030687 897.1261 : 10.5678221 3.0494562 0.5656704 43.5160092 -1.6980095 -0.1396041 25.9080741 -0.0679817 0.7299873 819.5494 : 10.54471809 3.06076641 0.55446652 43.64542554 -1.71360746 0.05498981 27.16746249 0.28406965 0.95081055 814.0157 : 10.517371271 3.076977052 0.539415322 43.835891431 -1.702051515 0.260949107 26.380768516 -0.008790843 1.559054756 792.1721 : 10.5146765 3.0702959 0.5376599 44.3829574 -1.6472279 0.5249176 27.1648000 0.5286278 1.4040347 790.471 : 10.5080901 3.0786189 0.5355129 44.1378163 -1.6541043 0.4628975 26.7240213 0.0888912 1.5655475 789.0062 : 10.5120976 3.0745581 0.5322500 44.3822376 -1.6176267 0.5402076 26.9836452 0.3105849 1.4885690 788.7322 : 10.5099754 3.0770581 0.5336662 44.2510928 -1.6316162 0.5080732 26.8287399 0.1605430 1.5089577 788.6136 : 10.5111901 3.0756619 0.5324458 44.3426744 -1.6196497 0.5330798 26.9246976 0.2462200 1.4929832 788.5708 : 10.5104554 3.0765502 0.5331192 44.2883938 -1.6261353 0.5193059 26.8636885 0.1909976 1.5003843 788.5524 : 10.5109338 3.0759910 0.5326335 44.3245625 -1.6215302 0.5289554 26.9029098 0.2261012 1.4948736 788.545 : 10.5106283 3.0763531 0.5329250 44.3019976 -1.6243079 0.5231102 26.8777410 0.2034990 1.4980800 788.542 : 10.5108263 3.0761216 0.5327282 44.3167536 -1.6224460 0.5270106 26.8939541 0.2180140 1.4958849 788.5407 : 10.5106992 3.0762711 0.5328512 44.3073684 -1.6236133 0.5245600 26.8835273 0.2086649 1.4972422 788.5402 : 10.5107813 3.0761751 0.5327704 44.3134511 -1.6228492 0.5261611 26.8902425 0.2146793 1.4963459 788.54 : 10.5107285 3.0762370 0.5328218 44.3095539 -1.6233358 0.5251405 26.8859211 0.2108063 1.4969134 788.5399 : 10.5107625 3.0761972 0.5327885 44.3120707 -1.6230203 0.5258020 26.8887039 0.2132993 1.4965441 788.5398 : 10.5107406 3.0762229 0.5328098 44.3104539 -1.6232225 0.5253780 26.8869129 0.2116946 1.4967802 788.5398 : 10.5107547 3.0762064 0.5327960 44.3114956 -1.6230920 0.5256515 26.8880653 0.2127266 1.4966276 788.5398 : 10.5107457 3.0762170 0.5328048 44.3108251 -1.6231759 0.5254755 26.8873232 0.2120616 1.4967257 788.5398 : 10.5107515 3.0762101 0.5327992 44.3112574 -1.6231218 0.5255891 26.8878018 0.2124909 1.4966623 788.5398 : 10.5107477 3.0762145 0.5328028 44.3109792 -1.6231566 0.5255161 26.8874933 0.2122141 1.4967031 788.5398 : 10.5107501 3.0762117 0.5328004 44.3111589 -1.6231341 0.5255634 26.8876924 0.2123928 1.4966768 788.5398 : 10.5107486 3.0762135 0.5328020 44.3110429 -1.6231486 0.5255328 26.8875639 0.2122774 1.4966937 788.5398 : 10.5107496 3.0762123 0.5328010 44.3111173 -1.6231393 0.5255523 26.8876463 0.2123512 1.4966829 788.5398 : 10.5107490 3.0762131 0.5328016 44.3110693 -1.6231453 0.5255397 26.8875934 0.2123039 1.4966899 > fm2 <- nls(y ~ b1 + b2*cos( 2*pi*x/12 ) + b3*sin( 2*pi*x/12 ) + + b5*cos( 2*pi*x/b4 ) + b6*sin( 2*pi*x/b4 ) + + b8*cos( 2*pi*x/b7 ) + b9*sin( 2*pi*x/b7 ), + data = ENSO, trace = TRUE, + start = c(b1 = 10.0, b2 = 3.0, b3 = 0.5, b4 = 44.0, b5 = -1.5, + b6 = 0.5, b7 = 26.0, b8 = -0.1, b9 = 1.5)) 914.9755 : 10.0 3.0 0.5 44.0 -1.5 0.5 26.0 -0.1 1.5 796.8067 : 10.4980674 3.0730275 0.5444843 44.6107622 -1.6088111 0.6512932 27.2298080 0.6983651 1.1959011 792.75 : 10.5051494 3.0799807 0.5317388 44.2092956 -1.6444403 0.5143363 26.7243176 0.1723749 1.6126653 789.1126 : 10.5115258 3.0741734 0.5321720 44.4322120 -1.6072406 0.5670616 27.0002131 0.3394931 1.4691476 788.7848 : 10.5093760 3.0772449 0.5335966 44.2590872 -1.6300496 0.5162053 26.8242055 0.1602607 1.5120060 788.6304 : 10.5110495 3.0756223 0.5323902 44.3521545 -1.6180141 0.5376759 26.9292646 0.2510145 1.4921890 788.578 : 10.5103493 3.0765979 0.5331473 44.2879693 -1.6260771 0.5200255 26.8612583 0.1889986 1.5008172 788.5552 : 10.5109260 3.0759706 0.5326140 44.3268327 -1.6211964 0.5298418 26.9046232 0.2276992 1.4946703 788.5463 : 10.5106050 3.0763697 0.5329378 44.3012938 -1.6243802 0.5230358 26.8766931 0.2025818 1.4982335 788.5424 : 10.5108308 3.0761122 0.5327201 44.3174752 -1.6223498 0.5272394 26.8946483 0.2186448 1.4957986 788.5409 : 10.5106924 3.0762776 0.5328566 44.3070038 -1.6236569 0.5244790 26.8830878 0.2082744 1.4973029 788.5402 : 10.5107842 3.0761711 0.5327670 44.3137219 -1.6228147 0.5262376 26.8905282 0.2149366 1.4963092 788.54 : 10.5107261 3.0762396 0.5328240 44.3093934 -1.6233556 0.5251004 26.8857385 0.2106433 1.4969380 788.5399 : 10.5107639 3.0761955 0.5327870 44.3121787 -1.6230067 0.5258310 26.8888216 0.2134048 1.4965288 788.5398 : 10.5107397 3.0762239 0.5328107 44.3103854 -1.6232310 0.5253601 26.8868366 0.2116260 1.4967904 788.5398 : 10.5107553 3.0762056 0.5327954 44.3115401 -1.6230864 0.5256632 26.8881147 0.2127712 1.4966211 788.5398 : 10.5107453 3.0762174 0.5328052 44.3107971 -1.6231794 0.5254683 26.8872921 0.2120341 1.4967297 788.5398 : 10.5107517 3.0762098 0.5327989 44.3112758 -1.6231195 0.5255940 26.8878218 0.2125087 1.4966597 788.5398 : 10.5107476 3.0762147 0.5328029 44.3109673 -1.6231581 0.5255129 26.8874809 0.2122034 1.4967047 788.5398 : 10.5107503 3.0762116 0.5328004 44.3111648 -1.6231334 0.5255645 26.8876995 0.2123987 1.4966759 788.5398 : 10.5107485 3.0762136 0.5328021 44.3110383 -1.6231492 0.5255316 26.8875588 0.2122727 1.4966944 788.5398 : 10.5107496 3.0762123 0.5328010 44.3111202 -1.6231389 0.5255530 26.8876498 0.2123545 1.4966824 788.5398 : 10.5107489 3.0762131 0.5328016 44.3110672 -1.6231456 0.5255391 26.8875913 0.2123021 1.4966901 > fm3 <- nls(y ~ cbind(1, cos( 2*pi*x/12 ), sin( 2*pi*x/12 ), cos( 2*pi*x/b4 ), + sin( 2*pi*x/b4 ), cos( 2*pi*x/b7 ), sin( 2*pi*x/b7 )), + data = ENSO, trace = TRUE, + start = c(b4 = 40.0, b7 = 25.0), algorithm = "plinear") 937.3633 : 40.00000000 25.00000000 10.66929930 3.05663587 0.48313089 -0.32019690 -1.43188100 -0.90951484 0.01722343 851.8496 : 40.6712409 25.9513841 10.6279006 3.0661308 0.5138108 -0.7806003 -1.3267443 -0.8195038 1.0715794 810.844 : 42.0975882 26.9075045 10.5937574 3.0665279 0.5159976 -1.4214220 -0.7018279 0.2132808 1.4538698 794.092 : 43.204776885 26.718084130 10.545615159 3.073204374 0.532113521 -1.675544888 -0.091877948 0.001872401 1.510573593 789.3571 : 43.9372608 26.9125174 10.5243632 3.0745059 0.5305445 -1.6670289 0.3241656 0.2413878 1.4932154 788.626 : 44.1828776 26.8594141 10.5140970 3.0760124 0.5332202 -1.6425751 0.4585255 0.1781650 1.5023239 788.5493 : 44.2816053 26.8954700 10.5119739 3.0760254 0.5324595 -1.6275510 0.5100004 0.2217780 1.4954781 788.541 : 44.2997487 26.8827803 10.5109634 3.0762193 0.5329132 -1.6250391 0.5197282 0.2064884 1.4976413 788.54 : 44.3093644 26.8893971 10.5108636 3.0761887 0.5327406 -1.6233768 0.5246126 0.2144720 1.4963799 788.5398 : 44.3099860 26.8867197 10.5107561 3.0762177 0.5328254 -1.6233377 0.5249881 0.2112436 1.4968570 788.5398 : 44.3110635 26.8879841 10.5107620 3.0762090 0.5327899 -1.6231387 0.5255247 0.2127686 1.4966208 788.5398 : 44.3109573 26.8874420 10.5107479 3.0762140 0.5328063 -1.6231675 0.5254799 0.2121150 1.4967192 788.5398 : 44.3111073 26.8876887 10.5107510 3.0762121 0.5327991 -1.6231383 0.5255532 0.2124124 1.4966735 788.5398 : 44.3110689 26.8875805 10.5107487 3.0762131 0.5328024 -1.6231468 0.5255353 0.2122820 1.4966933 788.5398 : 44.3110937 26.8876291 10.5107495 3.0762127 0.5328009 -1.6231417 0.5255473 0.2123405 1.4966844 788.5398 : 44.3110848 26.8876076 10.5107491 3.0762129 0.5328016 -1.6231436 0.5255431 0.2123146 1.4966883 > fm4 <- nls(y ~ cbind(1, cos( 2*pi*x/12 ), sin( 2*pi*x/12 ), cos( 2*pi*x/b4 ), + sin( 2*pi*x/b4 ), cos( 2*pi*x/b7 ), sin( 2*pi*x/b7 )), + data = ENSO, trace = TRUE, + start = c(b4 = 44.0, b7 = 26.0), algorithm = "plinear") 825.2069 : 44.0000000 26.0000000 10.5129896 3.0786579 0.5445966 -1.6281691 0.3729593 -0.7496152 1.1454319 789.0144 : 44.1849498 26.9672897 10.5176941 3.0749089 0.5298093 -1.6388185 0.4575942 0.3074457 1.4786978 788.6197 : 44.2462667 26.8454839 10.5115463 3.0763855 0.5338651 -1.6339296 0.4923938 0.1613522 1.5036992 788.5543 : 44.3056159 26.9045015 10.5114841 3.0760228 0.5322579 -1.6236090 0.5223669 0.2326580 1.4935073 788.5426 : 44.3038119 26.8795734 10.5107269 3.0762660 0.5330252 -1.6244686 0.5219093 0.2026183 1.4981543 788.5403 : 44.3116294 26.8910443 10.5108434 3.0761805 0.5326970 -1.6229804 0.5257600 0.2164582 1.4960584 788.5399 : 44.3100993 26.8860482 10.5107306 3.0762248 0.5328465 -1.6233344 0.5250601 0.2104336 1.4969756 788.5398 : 44.3113211 26.8882994 10.5107639 3.0762068 0.5327810 -1.6230908 0.5256527 0.2131490 1.4965616 788.5398 : 44.3109274 26.8873064 10.5107444 3.0762153 0.5328104 -1.6231753 0.5254669 0.2119514 1.4967437 788.5398 : 44.3111438 26.8877503 10.5107518 3.0762117 0.5327974 -1.6231311 0.5255710 0.2124867 1.4966621 788.5398 : 44.3110590 26.8875535 10.5107482 3.0762133 0.5328032 -1.6231489 0.5255307 0.2122494 1.4966982 788.5398 : 44.3110999 26.8876412 10.5107497 3.0762126 0.5328006 -1.6231405 0.5255502 0.2123551 1.4966821 788.5398 : 44.3110826 26.8876022 10.5107490 3.0762129 0.5328017 -1.6231441 0.5255420 0.2123082 1.4966893 788.5398 : 44.3110905 26.8876196 10.5107493 3.0762128 0.5328012 -1.6231425 0.5255458 0.2123291 1.4966861 > > > > cleanEx(); ..nameEx <- "Eckerle4" > > ### * Eckerle4 > > flush(stderr()); flush(stdout()) > > ### Name: Eckerle4 > ### Title: Circular interference data > ### Aliases: Eckerle4 > ### Keywords: datasets > > ### ** Examples > > data(Eckerle4) > plot(y ~ x, data = Eckerle4) > ## Not run: > ##D ## should fail - ridiculous starting value for b3 > ##D fm1 <- nls(y ~ (b1/b2) * exp(-0.5*((x-b3)/b2)**2), data = Eckerle4, trace = TRUE, > ##D start = c(b1 = 1, b2 = 10, b3 = 500)) > ## End(Not run) > fm2 <- nls(y ~ (b1/b2) * exp(-0.5*((x-b3)/b2)**2), data = Eckerle4, trace = TRUE, + start = c(b1 = 1.5, b2 = 5, b3 = 450)) 0.05668291 : 1.5 5.0 450.0 0.00722609 : 1.563149 4.374689 451.974368 0.001525831 : 1.551040 4.091636 451.488425 0.001463731 : 1.554819 4.091467 451.541251 0.001463589 : 1.554395 4.088899 451.541108 0.001463589 : 1.554384 4.088839 451.541216 0.001463589 : 1.554383 4.088832 451.541218 > ## Not run: > ##D ## should fail - ridiculous starting value for b3 > ##D fm3 <- nls(y ~ (1/b2) * exp(-0.5*((x-b3)/b2)**2), data = Eckerle4, trace = TRUE, > ##D start = c(b2 = 10, b3 = 500), algorithm = "plinear") > ## End(Not run) > fm4 <- nls(y ~ (1/b2) * exp(-0.5*((x-b3)/b2)**2), data = Eckerle4, trace = TRUE, + start = c(b2 = 5, b3 = 450), algorithm = "plinear") 0.05086068 : 5.00000 450.00000 1.65696 0.004539377 : 4.471095 451.669974 1.621837 0.001478679 : 4.085508 451.514686 1.553734 0.001463615 : 4.089948 451.541333 1.554595 0.001463589 : 4.088856 451.541172 1.554387 0.001463589 : 4.088835 451.541217 1.554383 0.001463589 : 4.088832 451.541218 1.554383 > > > > cleanEx(); ..nameEx <- "Gauss1" > > ### * Gauss1 > > flush(stderr()); flush(stdout()) > > ### Name: Gauss1 > ### Title: Generated data > ### Aliases: Gauss1 > ### Keywords: datasets > > ### ** Examples > > data(Gauss1) > plot(y ~ x, data = Gauss1) > fm1 <- nls(y ~ b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 ) + + b6*exp( -(x-b7)**2 / b8**2 ), data = Gauss1, trace = TRUE, + start = c(b1 = 97.0, b2 = 0.009, b3 = 100.0, b4 = 65.0, b5 = 20.0, + b6 = 70.0, b7 = 178., b8 = 16.5)) 7371.72 : 97.000 0.009 100.000 65.000 20.000 70.000 178.000 16.500 1474.666 : 98.38039826 0.01014456 97.87166358 67.22240890 23.10017915 71.06846489 178.97831313 18.26854431 1315.939 : 98.78120128 0.01049248 100.47438144 67.48904145 23.12959344 72.00330946 178.99854205 18.39519485 1315.822 : 98.77831456 0.01049737 100.48996573 67.48112487 23.12990265 71.99464961 178.99806458 18.38948556 1315.822 : 98.77820846 0.01049728 100.48990425 67.48111151 23.12977250 71.99450045 178.99805064 18.38938817 > fm2 <- nls(y ~ b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 ) + + b6*exp( -(x-b7)**2 / b8**2 ), data = Gauss1, trace = TRUE, + start = c(b1 = 94.0, b2 = 0.0105, b3 = 99.0, b4 = 63.0, b5 = 25.0, + b6 = 71.0, b7 = 180.0, b8 = 20.0)) 12081.69 : 94.0000 0.0105 99.0000 63.0000 25.0000 71.0000 180.0000 20.0000 1649.684 : 99.82100496 0.01063119 96.76681082 67.70835782 23.92351986 71.72448340 178.95117943 18.50994776 1316.570 : 98.78934913 0.01048733 100.40554939 67.47081150 23.09002064 71.97349927 178.99994046 18.37887995 1315.822 : 98.77837716 0.01049736 100.48994587 67.48098155 23.12985270 71.99464264 178.99800642 18.38947167 1315.822 : 98.77820975 0.01049727 100.48990510 67.48111134 23.12977101 71.99450054 178.99805064 18.38938733 > fm3 <- nls(y ~ cbind(exp(-b2*x), exp(-(x-b4)**2/b5**2), exp(-(x-b7)**2/b8**2)), + data = Gauss1, trace = TRUE, + start = c( b2 = 0.009, b4 = 65.0, b5 = 20.0, b7 = 178., b8 = 16.5), + algorithm = "plinear") 7331.545 : 0.00900 65.00000 20.00000 178.00000 16.50000 97.32273 100.88909 69.49958 1416.421 : 0.01012354 67.14584817 22.99350422 178.97647740 18.25478577 97.51631496 99.98543746 71.07720870 1315.843 : 0.01049367 67.48230246 23.13028926 178.99865875 18.39472736 98.76449091 100.48221276 71.97328954 1315.822 : 0.01049734 67.48112560 23.12981342 178.99806577 18.38944920 98.77834360 100.48999552 71.99458453 1315.822 : 0.01049728 67.48111125 23.12977300 178.99805048 18.38938854 98.77820888 100.48990488 71.99450131 > fm4 <- nls(y ~ cbind(exp(-b2*x), exp(-(x-b4)**2/b5**2), exp(-(x-b7)**2/b8**2)), + data = Gauss1, trace = TRUE, + start = c( b2 = 0.0105, b4 = 63.0, b5 = 25.0, b7 = 180., b8 = 20.0), + algorithm = "plinear") 12020.87 : 0.01050 63.00000 25.00000 180.00000 20.00000 93.21599 98.99091 70.03257 1436.447 : 0.01052232 67.44436697 23.93008250 178.95559231 18.42924199 97.61960458 99.69787336 72.26330923 1315.900 : 0.01049287 67.48627175 23.11107436 178.99889825 18.38299692 98.79726296 100.49717661 71.98604498 1315.822 : 0.01049734 67.48105232 23.12991049 178.99802066 18.38945789 98.77816387 100.48994530 71.99463514 1315.822 : 0.01049728 67.48111161 23.12977176 178.99805055 18.38938781 98.77821004 100.48990514 71.99450113 > > > > cleanEx(); ..nameEx <- "Gauss2" > > ### * Gauss2 > > flush(stderr()); flush(stdout()) > > ### Name: Gauss2 > ### Title: Generated data > ### Aliases: Gauss2 > ### Keywords: datasets > > ### ** Examples > > data(Gauss2) > plot(y ~ x, data = Gauss2) > fm1 <- nls(y ~ b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 ) + + b6*exp( -(x-b7)**2 / b8**2 ), data = Gauss2, trace = TRUE, + start = c(b1 = 96, b2 = 0.009, b3 = 103, b4 = 106, b5 = 18, + b6 = 72, b7 = 151, b8 = 18)) 9158.14 : 96.000 0.009 103.000 106.000 18.000 72.000 151.000 18.000 1613.56 : 98.45253280 0.01051603 99.38850229 106.48525660 22.32370980 72.41003489 152.15181890 20.45197551 1248.662 : 98.99126955 0.01097356 101.86556794 107.03941892 23.57426328 72.01257294 153.26301971 19.56177337 1247.528 : 99.01805804 0.01099481 101.88020184 107.03103141 23.57853653 72.04581717 153.27000687 19.52559244 1247.528 : 99.01833207 0.01099495 101.88022792 107.03095328 23.57858242 72.04558539 153.27010170 19.52597963 > fm2 <- nls(y ~ b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 ) + + b6*exp( -(x-b7)**2 / b8**2 ), data = Gauss2, trace = TRUE, + start = c(b1 = 98, b2 = 0.0105, b3 = 103, b4 = 105, b5 = 20, + b6 = 73, b7 = 150, b8 = 20)) 4683.131 : 98.0000 0.0105 103.0000 105.0000 20.0000 73.0000 150.0000 20.0000 1381.816 : 99.06960234 0.01095555 100.60411638 106.47040277 22.97605594 71.93900304 152.51045630 20.55444025 1247.944 : 99.01184316 0.01099244 101.92671701 107.06144403 23.60363849 71.96538485 153.30523084 19.50014812 1247.528 : 99.01836275 0.01099502 101.87990857 107.03121551 23.57917927 72.04543632 153.27053359 19.52563079 1247.528 : 99.01832879 0.01099495 101.88021964 107.03095945 23.57859459 72.04558763 153.27010975 19.52596578 > fm3 <- nls(y ~ cbind(exp(-b2*x), exp(-(x-b4)**2/b5**2), exp(-(x-b7)**2/b8**2)), + data = Gauss2, trace = TRUE, + start = c(b2 = 0.009, b4 = 106, b5 = 18, b7 = 151, b8 = 18), + algorithm = "plinear") 8866.014 : 0.00900 106.00000 18.00000 151.00000 18.00000 95.96598 105.75578 74.22943 1530.342 : 0.01049287 106.44248073 22.07937985 152.06773601 20.39981995 97.99785791 101.80779903 71.49880586 1248.210 : 0.01097101 107.00572248 23.51555256 153.24897146 19.57794034 98.96295873 101.87954364 71.99181084 1247.528 : 0.01099465 107.03066675 23.57755987 153.26937112 19.52603325 99.01791651 101.88068858 72.04622122 1247.528 : 0.01099494 107.03094632 23.57856542 153.27008950 19.52599140 99.01833201 101.88023739 72.04558782 1247.528 : 0.01099495 107.03095508 23.57858372 153.27010169 19.52597272 99.01832833 101.88022541 72.04558961 > fm4 <- nls(y ~ cbind(exp(-b2*x), exp(-(x-b4)**2/b5**2), exp(-(x-b7)**2/b8**2)), + data = Gauss2, trace = TRUE, + start = c(b2 = 0.0105, b4 = 105, b5 = 20, b7 = 150, b8 = 20), + algorithm = "plinear") 4284.417 : 0.01050 105.00000 20.00000 150.00000 20.00000 98.93239 104.69502 75.76338 1364.820 : 0.01094259 106.42733492 22.89080469 152.39077575 20.54810931 98.91377303 101.74111247 71.71053368 1247.775 : 0.01099405 107.05255932 23.59552897 153.30814069 19.50747579 99.01575776 101.88267666 72.02700682 1247.528 : 0.01099498 107.03121621 23.57908192 153.27051044 19.52553428 99.01827563 101.87995093 72.04552690 1247.528 : 0.01099495 107.03095858 23.57859303 153.27010901 19.52596820 99.01832968 101.88022109 72.04558683 > > > > cleanEx(); ..nameEx <- "Gauss3" > > ### * Gauss3 > > flush(stderr()); flush(stdout()) > > ### Name: Gauss3 > ### Title: Generated data > ### Aliases: Gauss3 > ### Keywords: datasets > > ### ** Examples > > data(Gauss3) > plot(y ~ x, data = Gauss3) > fm1 <- nls(y ~ b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 ) + + b6*exp( -(x-b7)**2 / b8**2 ), data = Gauss3, trace = TRUE, + start = c(b1 = 94.9, b2 = 0.009, b3 = 90.1, b4 = 113, b5 = 20, + b6 = 73.8, b7 = 140, b8 = 20)) 18905.14 : 94.900 0.009 90.100 113.000 20.000 73.800 140.000 20.000 4278.048 : 98.26013914 0.01058424 101.56686171 112.76311939 24.44357476 57.19870278 148.32532930 22.26622300 1476.732 : 98.80020749 0.01087053 99.16634787 111.01241904 22.79573900 75.64307038 146.69563212 19.40599964 1245.232 : 98.93146895 0.01094038 100.49315776 111.57306617 23.25446148 73.75802603 147.65801985 19.76105371 1244.485 : 98.94032709 0.01094585 100.69926979 111.63726228 23.30098365 73.70164634 147.76307215 19.66735888 1244.485 : 98.94037024 0.01094588 100.69551887 111.63618821 23.30049591 73.70504609 147.76163542 19.66822825 > fm2 <- nls(y ~ b1*exp( -b2*x ) + b3*exp( -(x-b4)**2 / b5**2 ) + + b6*exp( -(x-b7)**2 / b8**2 ), data = Gauss3, trace = TRUE, + start = c(b1 = 96, b2 = 0.0096, b3 = 80, b4 = 110, b5 = 25, + b6 = 74, b7 = 139, b8 = 25)) 13998.92 : 96.0000 0.0096 80.0000 110.0000 25.0000 74.0000 139.0000 25.0000 12816.13 : 9.663748e+01 9.907893e-03 1.066542e+02 1.148710e+02 2.620337e+01 5.280029e+01 1.465226e+02 2.167340e+01 3299.464 : 97.68451402 0.01037581 102.84256632 112.87638843 24.48220230 66.14743100 147.38975385 20.07997755 1256.755 : 98.88960985 0.01092412 100.32567869 111.51512095 23.22555635 74.56842832 147.73184087 19.63287096 1244.485 : 98.94024689 0.01094575 100.69166769 111.63510689 23.29947910 73.71204690 147.75982691 19.66847263 1244.485 : 98.94036704 0.01094588 100.69553588 111.63619307 23.30049155 73.70505017 147.76163885 19.66821907 > fm3 <- nls(y ~ cbind(exp(-b2*x), exp(-(x-b4)**2/b5**2), exp(-(x-b7)**2/b8**2)), + data = Gauss3, trace = TRUE, + start = c(b2 = 0.009, b4 = 113, b5 = 20, b7 = 140, b8 = 20), + algorithm = "plinear") 18150.38 : 0.00900 113.00000 20.00000 140.00000 20.00000 96.80710 86.46263 70.41532 2535.188 : 0.01047125 108.52047072 21.84682428 143.11015378 25.34195144 97.08905390 85.35505522 75.84619494 2335.399 : 0.01084746 113.01111215 23.57364619 150.51535581 17.72835704 98.85420440 105.93636022 71.87235441 1274.647 : 0.01096894 112.27025268 23.81507122 148.52801622 19.34430779 98.96932818 101.57409712 71.59327278 1244.528 : 0.01094799 111.63573932 23.30772296 147.75706804 19.68482867 98.94363131 100.66488062 73.67369734 1244.485 : 0.01094590 111.63636724 23.30072461 147.76186935 19.66808509 98.94037109 100.69575848 73.70441210 1244.485 : 0.01094588 111.63619624 23.30050314 147.76164470 19.66822012 98.94036913 100.69553179 73.70502390 > fm4 <- nls(y ~ cbind(exp(-b2*x), exp(-(x-b4)**2/b5**2), exp(-(x-b7)**2/b8**2)), + data = Gauss3, trace = TRUE, + start = c(b2 = 0.0096, b4 = 110, b5 = 25, b7 = 139, b8 = 25), + algorithm = "plinear") 10005.53 : 0.00960 110.00000 25.00000 139.00000 25.00000 94.83527 72.83722 69.01910 5874.61 : 0.01088802 108.18091596 19.01247375 146.68288371 22.38743341 99.30495338 101.58629504 83.34995753 1388.657 : 0.01085105 109.94884377 21.79227248 145.98924336 20.79137803 98.76225831 98.30049323 78.66896047 1244.824 : 0.0109456 111.5504048 23.2367156 147.6781118 19.7364150 98.9375603 100.5728758 73.9375120 1244.485 : 0.01094581 111.63622219 23.30019076 147.76167369 19.66818340 98.94030289 100.69591703 73.70540037 1244.485 : 0.01094588 111.63618855 23.30049165 147.76163504 19.66822623 98.94036914 100.69552410 73.70505356 > > > > cleanEx(); ..nameEx <- "Hahn1" > > ### * Hahn1 > > flush(stderr()); flush(stdout()) > > ### Name: Hahn1 > ### Title: Thermal expansion data > ### Aliases: Hahn1 > ### Keywords: datasets > > ### ** Examples > > data(Hahn1) > plot(y ~ x, data = Hahn1) > fm1 <- nls(y ~ (b1+b2*x+b3*x**2+b4*x**3) / (1+b5*x+b6*x**2+b7*x**3), + data = Hahn1, trace = TRUE, + start = c(b1 = 10, b2 = -1, b3 = 0.05, + b4 = -0.00001, b5 = -0.05, b6 = 0.001, b7 = -0.000001)) 3097557 : 1e+01 -1e+00 5e-02 -1e-05 -5e-02 1e-03 -1e-06 82100.1 : 1.516193e+01 -1.385384e+00 2.737919e-02 -1.823072e-05 -5.668482e-02 1.181933e-03 -1.182258e-06 8813.72 : 1.780129e+01 -1.545853e+00 3.075675e-02 -2.524824e-05 -5.748976e-02 1.587225e-03 -1.591735e-06 1142.501 : 2.149589e+01 -1.944711e+00 4.079217e-02 -3.618207e-05 -4.174500e-02 2.113272e-03 -2.119925e-06 25.20987 : 1.790480e+01 -1.694785e+00 3.850249e-02 -3.559869e-05 5.473611e-03 1.870805e-03 -1.870175e-06 10.48793 : 7.762050e+00 -7.396711e-01 1.747105e-02 -1.511747e-05 -5.093395e-04 8.664325e-04 -8.134771e-07 1.903758 : 1.519565e+00 -1.624315e-01 4.884663e-03 -2.669651e-06 -5.376338e-03 2.743214e-04 -1.813177e-07 1.534960 : 1.087567e+00 -1.234188e-01 4.104808e-03 -1.481746e-06 -5.752892e-03 2.412560e-04 -1.257536e-07 1.532439 : 1.078396e+00 -1.227539e-01 4.087652e-03 -1.428535e-06 -5.760203e-03 2.405899e-04 -1.232497e-07 1.532438 : 1.077662e+00 -1.226950e-01 4.086416e-03 -1.426326e-06 -5.760978e-03 2.405391e-04 -1.231473e-07 1.532438 : 1.077635e+00 -1.226930e-01 4.086375e-03 -1.426266e-06 -5.760993e-03 2.405373e-04 -1.231445e-07 > fm2 <- nls(y ~ (b1+b2*x+b3*x**2+b4*x**3) / (1+b5*x+b6*x**2+b7*x**3), + data = Hahn1, trace = TRUE, + start = c(b1 = 1, b2 = -0.1, b3 = 0.005, b4 = -0.000001, + b5 = -0.005, b6 = 0.0001, b7 = -0.0000001)) 2093448 : 1e+00 -1e-01 5e-03 -1e-06 -5e-03 1e-04 -1e-07 97253.17 : 3.488710e-01 -6.759932e-02 3.165752e-03 -2.070266e-06 -4.014998e-03 1.223686e-04 -1.242884e-07 13548.68 : 9.410618e-01 -1.149654e-01 4.111473e-03 -3.396129e-06 -2.859847e-03 1.863526e-04 -1.915439e-07 1764.704 : 1.850149e+00 -1.884738e-01 5.607535e-03 -5.023080e-06 -2.961574e-03 2.768395e-04 -2.823372e-07 100.4438 : 2.013377e+00 -2.025054e-01 5.876705e-03 -5.263042e-06 -4.123592e-03 3.097146e-04 -3.033087e-07 9.938802 : 1.706670e+00 -1.764456e-01 5.296685e-03 -4.168360e-06 -4.742721e-03 2.879676e-04 -2.507642e-07 2.325091 : 1.354622e+00 -1.462216e-01 4.615850e-03 -2.684929e-06 -5.314360e-03 2.609100e-04 -1.813507e-07 1.558291 : 1.133364e+00 -1.273636e-01 4.190637e-03 -1.684908e-06 -5.679118e-03 2.445285e-04 -1.351268e-07 1.532503 : 1.082155e+00 -1.230595e-01 4.094232e-03 -1.442818e-06 -5.755889e-03 2.408517e-04 -1.239136e-07 1.532438 : 1.077832e+00 -1.227083e-01 4.086685e-03 -1.426743e-06 -5.760852e-03 2.405506e-04 -1.231668e-07 1.532438 : 1.077641e+00 -1.226934e-01 4.086384e-03 -1.426279e-06 -5.760991e-03 2.405378e-04 -1.231451e-07 > fm3 <- nls(y ~ cbind(1, x, x^2, x^3)/(1+x*(b5+x*(b6+x*b7))), + data = Hahn1, trace = TRUE, algorithm = "plinear", + start = c(b5 = -0.05, b6 = 0.001, b7 = -0.000001)) 614.0119 : -5.000000e-02 1.000000e-03 -1.000000e-06 1.660175e+01 -1.075155e+00 1.711235e-02 -1.618302e-05 141.1693 : -3.611099e-02 1.058983e-03 -9.727388e-07 1.608819e+01 -1.117473e+00 1.926855e-02 -1.621306e-05 15.24395 : -1.245886e-02 8.978578e-04 -7.346500e-07 1.114455e+01 -8.634183e-01 1.735952e-02 -1.277403e-05 3.516468 : -2.039067e-03 1.917047e-04 -9.769112e-08 -5.806348e-01 -3.910381e-02 3.266684e-03 -1.146078e-06 1.533897 : -5.755183e-03 2.442506e-04 -1.256090e-07 1.125896e+00 -1.265620e-01 4.161848e-03 -1.470320e-06 1.532438 : -5.761623e-03 2.405497e-04 -1.231720e-07 1.078049e+00 -1.227151e-01 4.086650e-03 -1.426838e-06 1.532438 : -5.760988e-03 2.405381e-04 -1.231456e-07 1.077646e+00 -1.226938e-01 4.086391e-03 -1.426288e-06 1.532438 : -5.760994e-03 2.405373e-04 -1.231445e-07 1.077635e+00 -1.226929e-01 4.086374e-03 -1.426265e-06 > fm4 <- nls(y ~ cbind(1, x, x^2, x^3)/(1+x*(b5+x*(b6+x*b7))), + data = Hahn1, trace = TRUE, algorithm = "plinear", + start = c(b5 = -0.005, b6 = 0.0001, b7 = -0.0000001)) 52.37535 : -5.000000e-03 1.000000e-04 -1.000000e-07 4.246432e-01 -1.384956e-02 1.638663e-03 -1.641111e-06 13.16452 : -2.685126e-03 1.672625e-04 -1.668996e-07 1.020464e-01 -5.126586e-02 3.075557e-03 -2.952519e-06 4.465369 : -3.413849e-03 2.848764e-04 -2.660818e-07 1.728468e+00 -1.787342e-01 5.446743e-03 -4.762388e-06 1.927021 : -4.799327e-03 2.848452e-04 -2.105583e-07 1.697481e+00 -1.737163e-01 5.192300e-03 -3.353824e-06 1.537299 : -5.717978e-03 2.437645e-04 -1.312889e-07 1.135972e+00 -1.269224e-01 4.170145e-03 -1.606480e-06 1.532444 : -5.758511e-03 2.407192e-04 -1.234895e-07 1.080395e+00 -1.229078e-01 4.090781e-03 -1.433753e-06 1.532438 : -5.760947e-03 2.405432e-04 -1.231536e-07 1.077724e+00 -1.226998e-01 4.086510e-03 -1.426460e-06 1.532438 : -5.760993e-03 2.405375e-04 -1.231447e-07 1.077637e+00 -1.226931e-01 4.086378e-03 -1.426271e-06 > > > > cleanEx(); ..nameEx <- "Kirby2" > > ### * Kirby2 > > flush(stderr()); flush(stdout()) > > ### Name: Kirby2 > ### Title: Microscope line width standards > ### Aliases: Kirby2 > ### Keywords: datasets > > ### ** Examples > > data(Kirby2) > plot(y ~ x, data = Kirby2) > fm1 <- nls(y ~ (b1 + b2*x + b3*x**2) / (1 + b4*x + b5*x**2), + data = Kirby2, trace = TRUE, + start = c(b1 = 2, b2 = -0.1, b3 = 0.003, b4 = -0.001, b5 = 0.00001)) 373285.4 : 2e+00 -1e-01 3e-03 -1e-03 1e-05 31570.51 : 2.008123e+00 -1.652584e-01 3.059637e-03 -1.235277e-04 1.446730e-05 640.0477 : 1.959603e+00 -1.613072e-01 2.914916e-03 -6.856353e-04 2.027708e-05 7.2142 : 1.643053e+00 -1.376103e-01 2.579465e-03 -1.759931e-03 2.171312e-05 3.90511 : 1.675932e+00 -1.393485e-01 2.596838e-03 -1.723469e-03 2.166880e-05 3.905074 : 1.674411e+00 -1.392683e-01 2.596057e-03 -1.724264e-03 2.166453e-05 3.905074 : 1.674515e+00 -1.392745e-01 2.596123e-03 -1.724174e-03 2.166483e-05 3.905074 : 1.6745054726 -0.1392739313 0.0025961176 -0.0017241818 0.0000216648 > fm2 <- nls(y ~ (b1 + b2*x + b3*x**2) / (1 + b4*x + b5*x**2), + data = Kirby2, trace = TRUE, + start = c(b1 = 1.5, b2 = -0.15, b3 = 0.0025, b4 = -0.0015, + b5 = 0.00002)) 987.721 : 1.50000 -0.15000 0.00250 -0.00150 0.00002 4.659112 : 1.693651e+00 -1.406735e-01 2.616882e-03 -1.664550e-03 2.170547e-05 3.905248 : 1.670347e+00 -1.390355e-01 2.593595e-03 -1.727595e-03 2.165338e-05 3.905075 : 1.674855e+00 -1.392944e-01 2.596335e-03 -1.723896e-03 2.166579e-05 3.905074 : 1.674477e+00 -1.392722e-01 2.596100e-03 -1.724206e-03 2.166472e-05 3.905074 : 1.674509e+00 -1.392741e-01 2.596120e-03 -1.724179e-03 2.166481e-05 > fm3 <- nls(y ~ cbind(1, x, x**2)/(1 + x*(b4 + b5*x)), + data = Kirby2, trace = TRUE, algorithm = "plinear", + start = c(b4 = -0.001, b5 = 0.00001)) 379.4387 : -0.001000000 0.000010000 -4.166484812 0.084556948 0.001174962 18.13233 : -1.144903e-03 2.030319e-05 9.623247e-01 -1.190046e-01 2.580174e-03 3.911828 : -1.743674e-03 2.166404e-05 1.679054e+00 -1.391026e-01 2.590334e-03 3.905081 : -1.723497e-03 2.166786e-05 1.675638e+00 -1.393356e-01 2.596732e-03 3.905074 : -1.724250e-03 2.166457e-05 1.674426e+00 -1.392692e-01 2.596067e-03 3.905074 : -1.724175e-03 2.166482e-05 1.674513e+00 -1.392744e-01 2.596122e-03 3.905074 : -0.0017241817 0.0000216648 1.6745057046 -0.1392739433 0.0025961177 > fm4 <- nls(y ~ cbind(1, x, x**2)/(1 + x*(b4 + b5*x)), + data = Kirby2, trace = TRUE, algorithm = "plinear", + start = c(b4 = -0.0015, b5 = 0.00002)) 12.13407 : -0.001500000 0.000020000 0.901842821 -0.110309312 0.002434939 3.913795 : -1.693842e-03 2.171309e-05 1.687523e+00 -1.404051e-01 2.611507e-03 3.905112 : -1.726146e-03 2.165789e-05 1.672055e+00 -1.391314e-01 2.594608e-03 3.905074 : -1.724012e-03 2.166538e-05 1.674712e+00 -1.392860e-01 2.596246e-03 3.905074 : -1.724196e-03 2.166475e-05 1.674489e+00 -1.392730e-01 2.596107e-03 3.905074 : -1.724180e-03 2.166481e-05 1.674508e+00 -1.392741e-01 2.596119e-03 3.905074 : -1.724181e-03 2.166480e-05 1.674506e+00 -1.392740e-01 2.596118e-03 > > > > cleanEx(); ..nameEx <- "Lanczos1" > > ### * Lanczos1 > > flush(stderr()); flush(stdout()) > > ### Name: Lanczos1 > ### Title: Generated data > ### Aliases: Lanczos1 > ### Keywords: datasets > > ### ** Examples > > data(Lanczos1) > plot(y ~ x, data = Lanczos1) > ## plot on log scaleto see the apparent number of exponential terms > plot(y ~ x, data = Lanczos1, log = "y") > ## Not run: > ##D ## data are an exact fit so the convergence criterion fails > ##D fm1 <- nls(y ~ b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x), > ##D data = Lanczos1, trace = TRUE, > ##D start = c(b1 = 1.2, b2 = 0.3, b3 = 5.6, b4 = 5.5, > ##D b5 = 6.5, b6 = 7.6)) > ## End(Not run) > ## Not run: > ##D ## data are an exact fit so the convergence criterion fails > ##D fm2 <- nls(y ~ b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x), > ##D data = Lanczos1, trace = TRUE, > ##D start = c(b1 = 0.5, b2 = 0.7, b3 = 3.6, b4 = 4.2, > ##D b5 = 4, b6 = 6.3)) > ## End(Not run) > ## Not run: > ##D ## data are an exact fit so the convergence criterion fails > ##D fm3 <- nls(y ~ exp(outer(x,-c(b2, b4, b6))), > ##D data = Lanczos1, trace = TRUE, algorithm = "plinear", > ##D start = c(b2 = 0.3, b4 = 5.5, b6 = 7.6)) > ## End(Not run) > ## Not run: > ##D ## data are an exact fit so the convergence criterion fails > ##D fm4 <- nls(y ~ exp(outer(x,-c(b2, b4, b6))), > ##D data = Lanczos1, trace = TRUE, algorithm = "plinear", > ##D start = c(b2 = 0.7, b4 = 4.2, b6 = 6.3)) > ## End(Not run) > > > > cleanEx(); ..nameEx <- "Lanczos2" > > ### * Lanczos2 > > flush(stderr()); flush(stdout()) > > ### Name: Lanczos2 > ### Title: Generated data > ### Aliases: Lanczos2 > ### Keywords: datasets > > ### ** Examples > > data(Lanczos2) > plot(y ~ x, data = Lanczos2) > ## plot log response to see the number of exponential terms > plot(y ~ x, data = Lanczos2, log = "y") > ## Not run: > ##D ## Numerical derivatives do not produce sufficient accuracy to converge > ##D fm1 <- nls(y ~ b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x), > ##D data = Lanczos2, trace = TRUE, > ##D start = c(b1 = 1.2, b2 = 0.3, b3 = 5.6, b4 = 5.5, > ##D b5 = 6.5, b6 = 7.6)) > ## End(Not run) > ## Not run: > ##D ## Numerical derivatives do not produce sufficient accuracy to converge > ##D fm2 <- nls(y ~ b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x), > ##D data = Lanczos2, trace = TRUE, > ##D start = c(b1 = 0.5, b2 = 0.7, b3 = 3.6, b4 = 4.2, > ##D b5 = 4, b6 = 6.3)) > ## End(Not run) > ## Not run: > ##D ## Numerical derivatives do not produce sufficient accuracy to converge > ##D fm3 <- nls(y ~ exp(outer(x,-c(b2, b4, b6))), > ##D data = Lanczos2, trace = TRUE, algorithm = "plinear", > ##D start = c(b2 = 0.3, b4 = 5.5, b6 = 7.6)) > ## End(Not run) > ## Not run: > ##D ## Numerical derivatives do not produce sufficient accuracy to converge > ##D fm4 <- nls(y ~ exp(outer(x,-c(b2, b4, b6))), > ##D data = Lanczos2, trace = TRUE, algorithm = "plinear", > ##D start = c(b2 = 0.7, b4 = 4.2, b6 = 6.3)) > ## End(Not run) > ## Use analytic derivatives > Lanczos <- deriv(~ b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x), + paste("b", 1:6, sep = ""), + function(x, b1, b2, b3, b4, b5, b6){}) > fm5 <- nls(y ~ Lanczos(x, b1, b2, b3, b4, b5, b6), + data = Lanczos2, trace = TRUE, + start = c(b1 = 1.2, b2 = 0.3, b3 = 5.6, b4 = 5.5, + b5 = 6.5, b6 = 7.6)) 269.7505 : 1.2 0.3 5.6 5.5 6.5 7.6 12.09280 : 0.1557453 0.3657420 -4.2717953 3.6362013 6.6293511 6.6558640 0.01606244 : 0.09636195 0.60836746 1.59522065 3.66888806 0.82179905 6.54394417 3.990272e-05 : 0.1187057 1.0189608 1.5699093 3.5935011 0.8247720 5.7094073 3.587714e-05 : 0.1203315 1.0348048 1.5128146 3.5660724 0.8802421 5.6210947 3.151298e-05 : 0.1213522 1.0470432 1.4554407 3.5361375 0.9365965 5.5418934 2.862798e-05 : 0.1222946 1.0652194 1.3422753 3.4723737 1.0488216 5.4009800 1.876486e-05 : 0.1202570 1.0797310 1.1315671 3.3340383 1.2615708 5.1848399 3.035081e-06 : 0.1131083 1.0646100 0.9876828 3.2002763 1.4126060 5.0804777 3.027316e-06 : 0.1062076 1.0434056 0.9191288 3.1097286 1.4880618 5.0371943 1.870014e-06 : 0.0970268 1.0107621 0.8599810 3.0095278 1.5563917 5.0005393 2.867012e-11 : 0.09624648 1.00572780 0.86425315 3.00781252 1.55289998 5.00287785 2.229943e-11 : 0.09625103 1.00573328 0.86424689 3.00782838 1.55290169 5.00287981 > fm6 <- nls(y ~ Lanczos(x, b1, b2, b3, b4, b5, b6), + data = Lanczos2, trace = TRUE, + start = c(b1 = 0.5, b2 = 0.7, b3 = 3.6, b4 = 4.2, + b5 = 4, b6 = 6.3)) 78.78867 : 0.5 0.7 3.6 4.2 4.0 6.3 0.1065354 : 0.1375743 0.7888927 1.0193084 3.7834947 1.3565043 6.0485875 0.003836550 : 0.1284274 1.0311586 1.2688219 3.2657285 1.1161437 5.5365848 0.0004866829 : 0.1180555 1.0883470 1.0576426 3.2392443 1.3376998 5.0969078 8.95785e-05 : 0.1002228 1.0283597 0.8438680 3.0314885 1.5693086 4.9854309 5.768697e-08 : 0.0962241 1.0059872 0.8643395 3.0070917 1.5528360 5.0028743 2.230792e-11 : 0.09625103 1.00573310 0.86424651 3.00782776 1.55290207 5.00287963 2.229943e-11 : 0.09625103 1.00573328 0.86424689 3.00782839 1.55290169 5.00287981 > > > > cleanEx(); ..nameEx <- "Lanczos3" > > ### * Lanczos3 > > flush(stderr()); flush(stdout()) > > ### Name: Lanczos3 > ### Title: Generated data > ### Aliases: Lanczos3 > ### Keywords: datasets > > ### ** Examples > > data(Lanczos3) > plot(y ~ x, data = Lanczos3) > ## plot log response to see the number of exponential terms > plot(y ~ x, data = Lanczos3, log = "y") > ## Not run: > ##D ## Numerical derivatives do not produce sufficient accuracy to converge > ##D fm1 <- nls(y ~ b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x), > ##D data = Lanczos3, trace = TRUE, > ##D start = c(b1 = 1.2, b2 = 0.3, b3 = 5.6, b4 = 5.5, > ##D b5 = 6.5, b6 = 7.6)) > ##D fm2 <- nls(y ~ b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x), > ##D data = Lanczos3, trace = TRUE, > ##D start = c(b1 = 0.5, b2 = 0.7, b3 = 3.6, b4 = 4.2, > ##D b5 = 4, b6 = 6.3)) > ##D fm3 <- nls(y ~ exp(outer(x,-c(b2, b4, b6))), > ##D data = Lanczos3, trace = TRUE, algorithm = "plinear", > ##D start = c(b2 = 0.3, b4 = 5.5, b6 = 7.6)) > ##D fm4 <- nls(y ~ exp(outer(x,-c(b2, b4, b6))), > ##D data = Lanczos3, trace = TRUE, algorithm = "plinear", > ##D start = c(b2 = 0.7, b4 = 4.2, b6 = 6.3)) > ## End(Not run) > ## Use analytic derivatives > Lanczos <- deriv(~ b1*exp(-b2*x) + b3*exp(-b4*x) + b5*exp(-b6*x), + paste("b", 1:6, sep = ""), + function(x, b1, b2, b3, b4, b5, b6){}) > fm5 <- nls(y ~ Lanczos(x, b1, b2, b3, b4, b5, b6), + data = Lanczos3, trace = TRUE, + start = c(b1 = 1.2, b2 = 0.3, b3 = 5.6, b4 = 5.5, + b5 = 6.5, b6 = 7.6)) 269.7515 : 1.2 0.3 5.6 5.5 6.5 7.6 12.13413 : 0.1556676 0.3656974 -4.2796666 3.6346410 6.6372962 6.6546364 0.0169783 : 0.09565568 0.60549640 1.59048836 3.66900854 0.82723213 6.54177302 4.930732e-05 : 0.1174347 1.0125932 1.5635976 3.5845447 0.8323493 5.7020119 4.383216e-05 : 0.1187507 1.0271209 1.5049596 3.5553820 0.8896724 5.6122453 4.279985e-05 : 0.1201302 1.0488138 1.3869549 3.4916210 1.0062999 5.4512696 3.828135e-05 : 0.1182464 1.0661656 1.1578113 3.3463392 1.2373308 5.2003100 4.712822e-06 : 0.1096975 1.0461312 0.9881753 3.1923894 1.4155179 5.0757685 3.212511e-06 : 0.1052330 1.0310531 0.9473295 3.1370014 1.4608287 5.0505053 3.006268e-06 : 0.09754817 1.00310782 0.89002887 3.04973236 1.52581509 5.01535110 1.559400e-06 : 0.08775013 0.96215946 0.84117765 2.95461901 1.58446515 4.98517001 1.612743e-08 : 0.08683104 0.95509296 0.84406259 2.95170466 1.58249916 4.98639749 1.611719e-08 : 0.08681706 0.95498467 0.84400932 2.95159925 1.58256640 4.98635779 1.611719e-08 : 0.08681644 0.95498114 0.84400783 2.95159532 1.58256851 4.98635655 > fm6 <- nls(y ~ Lanczos(x, b1, b2, b3, b4, b5, b6), + data = Lanczos3, trace = TRUE, + start = c(b1 = 0.5, b2 = 0.7, b3 = 3.6, b4 = 4.2, + b5 = 4, b6 = 6.3)) 78.78922 : 0.5 0.7 3.6 4.2 4.0 6.3 0.1101315 : 0.1368786 0.7879843 1.0059287 3.7786448 1.3705746 6.0451175 0.00429529 : 0.1267675 1.0246865 1.2568025 3.2416223 1.1298175 5.5294136 0.0005102519 : 0.1123390 1.0644162 1.0422924 3.2076973 1.3587605 5.0830676 0.0001280764 : 0.0920163 0.9886907 0.8221886 2.9819894 1.5991881 4.9690194 9.247752e-08 : 0.08683358 0.95589715 0.84424832 2.95095457 1.58231093 4.98649152 1.611721e-08 : 0.08681746 0.95498632 0.84401027 2.95160157 1.58256505 4.98635859 1.611719e-08 : 0.08681645 0.95498121 0.84400786 2.95159540 1.58256848 4.98635658 > > > > cleanEx(); ..nameEx <- "MGH09" > > ### * MGH09 > > flush(stderr()); flush(stdout()) > > ### Name: MGH09 > ### Title: More, Gabrow and Hillstrom example 9 > ### Aliases: MGH09 > ### Keywords: datasets > > ### ** Examples > > data(MGH09) > plot(y ~ x, data = MGH09) > ## Not run: > ##D ## starting values for this attempt are ridiculous > ##D fm1 <- nls(y ~ b1*(x**2+x*b2) / (x**2+x*b3+b4), > ##D data = MGH09, trace = TRUE, > ##D start = c(b1 = 25, b2 = 39, b3 = 41.5, b4 = 39)) > ## End(Not run) > fm2 <- nls(y ~ b1*(x**2+x*b2) / (x**2+x*b3+b4), + data = MGH09, trace = TRUE, + start = c(b1 = 0.25, b2 = 0.39, b3 = 0.415, b4 = 0.39)) 0.005313172 : 0.250 0.390 0.415 0.390 0.005232621 : 0.23293276 0.07667716 0.30016639 0.02789148 0.00159573 : 0.1914055 1.1136252 1.0487320 0.3685326 0.001058537 : 0.1946773 0.4037020 0.4518702 0.1693378 0.0006907685 : 0.1946687 0.2841167 0.3111557 0.1404410 0.0003927936 : 0.1938013 0.2276876 0.2037691 0.1359273 0.0003076325 : 0.1929903 0.1905980 0.1223155 0.1360138 0.0003075056 : 0.1928001 0.1913543 0.1230296 0.1361014 0.0003075056 : 0.1928091 0.1912299 0.1230443 0.1360384 0.0003075056 : 0.1928055 0.1913149 0.1230625 0.1360774 0.0003075056 : 0.1928079 0.1912618 0.1230527 0.1360528 0.0003075056 : 0.1928064 0.1912954 0.1230590 0.1360684 0.0003075056 : 0.1928073 0.1912743 0.1230550 0.1360586 0.0003075056 : 0.1928067 0.1912876 0.1230575 0.1360648 0.0003075056 : 0.1928071 0.1912792 0.1230559 0.1360609 > fm3 <- nls(y ~ cbind(x, x**2) / (x**2+x*b3+b4), + data = MGH09, trace = TRUE, algorithm = "plinear", + start = c(b3 = 41.5, b4 = 39)) 0.001399012 : 41.50000 39.00000 16.41478 -1.50723 0.001324137 : 19.4522256 17.9821631 7.6329810 -0.5945577 0.001185518 : 8.4698950 7.6082848 3.2776241 -0.1432744 0.0009479963 : 3.0621523 2.6514368 1.1623022 0.0742248 0.0005390333 : 0.5468154 0.5180272 0.2096956 0.1717668 0.000379211 : 0.25170300 0.26236719 0.09299445 0.18543503 0.0003107126 : 0.11268994 0.11878684 0.02979573 0.19419818 0.0003081432 : 0.12499560 0.14467166 0.04020154 0.19186364 0.0003078148 : 0.12044201 0.13028304 0.03456313 0.19334190 0.0003076060 : 0.12430481 0.13947443 0.03822936 0.19246830 0.0003075495 : 0.12211243 0.13385126 0.03599755 0.19301608 0.0003075217 : 0.12358897 0.13742050 0.03741982 0.19267482 0.0003075122 : 0.12269773 0.13519811 0.03653609 0.19288948 0.0003075082 : 0.12327243 0.13660059 0.03709460 0.19275495 0.0003075066 : 0.12291715 0.13572248 0.03674521 0.19283953 0.000307506 : 0.12314257 0.13627511 0.03696522 0.19278644 0.0003075058 : 0.12300182 0.13592837 0.03682723 0.19281980 0.0003075057 : 0.12309062 0.13614638 0.03691401 0.19279885 0.0003075056 : 0.12303500 0.13600952 0.03685954 0.19281201 0.0003075056 : 0.12307001 0.13609550 0.03689376 0.19280375 0.0003075056 : 0.12304806 0.13604148 0.03687226 0.19280894 0.0003075056 : 0.12306182 0.13607543 0.03688577 0.19280567 0.0003075056 : 0.12305316 0.13605410 0.03687728 0.19280773 0.0003075056 : 0.12305860 0.13606751 0.03688262 0.19280644 0.0003075056 : 0.12305514 0.13605902 0.03687924 0.19280725 0.0003075056 : 0.1230574 0.1360644 0.0368814 0.1928067 0.0003075056 : 0.12305592 0.13606095 0.03688001 0.19280707 0.0003075056 : 0.1230569 0.1360632 0.0368809 0.1928069 > fm4 <- nls(y ~ cbind(x, x**2) / (x**2+x*b3+b4), + data = MGH09, trace = TRUE, algorithm = "plinear", + start = c(b3 = 0.415, b4 = 0.39)) 0.0004712242 : 0.4150000 0.3900000 0.1527902 0.1793574 0.0003551739 : 0.22370908 0.22363445 0.07659772 0.18850348 0.0003085353 : 0.12717817 0.12788146 0.03410752 0.19415723 0.0003077064 : 0.1255028 0.1408924 0.0388353 0.1923776 0.0003075976 : 0.12169551 0.13287291 0.03560691 0.19310860 0.0003075383 : 0.12380518 0.13800109 0.03764959 0.19261747 0.0003075193 : 0.12253743 0.13482207 0.03638594 0.19292507 0.0003075108 : 0.12336328 0.13683185 0.03718644 0.19273247 0.0003075077 : 0.12285607 0.13557535 0.03668657 0.19285358 0.0003075064 : 0.12317935 0.13636673 0.03700166 0.19277759 0.0003075059 : 0.1229781 0.1358706 0.0368042 0.1928253 0.0003075057 : 0.12310524 0.13618254 0.03692839 0.19279536 0.0003075057 : 0.12302569 0.13598675 0.03685047 0.19281420 0.0003075056 : 0.12307581 0.13610981 0.03689946 0.19280237 0.0003075056 : 0.12304436 0.13603248 0.03686868 0.19280980 0.0003075056 : 0.12306412 0.13608106 0.03688801 0.19280513 0.0003075056 : 0.12305172 0.13605056 0.03687587 0.19280807 0.0003075056 : 0.12305952 0.13606970 0.03688349 0.19280623 0.0003075056 : 0.12305462 0.13605769 0.03687871 0.19280738 0.0003075056 : 0.12305771 0.13606529 0.03688174 0.19280665 0.0003075056 : 0.12305578 0.13606051 0.03687984 0.19280711 0.0003075056 : 0.12305699 0.13606346 0.03688101 0.19280683 0.0003075056 : 0.12305622 0.13606162 0.03688028 0.19280700 > > > > cleanEx(); ..nameEx <- "MGH10" > > ### * MGH10 > > flush(stderr()); flush(stdout()) > > ### Name: MGH10 > ### Title: More, Gabrow and Hillstrom example 10 > ### Aliases: MGH10 > ### Keywords: datasets > > ### ** Examples > > data(MGH10) > plot(y ~ x, data = MGH10) > ## check plot on log scale for shape > plot(y ~ x, data = MGH10, log = "y") > ## Not run: > ##D ## starting values for this run are ridiculous > ##D fm1 <- nls(y ~ b1 * exp(b2/(x+b3)), data = MGH10, trace = TRUE, > ##D start = c(b1 = 2, b2 = 400000, b3 = 25000)) > ## End(Not run) > fm2 <- nls(y ~ b1 * exp(b2/(x+b3)), data = MGH10, trace = TRUE, + start = c(b1 = 0.02, b2 = 4000, b3 = 250)) 1693607809 : 0.02 4000.00 250.00 1217987754 : 1.179854e-02 4.836962e+03 2.933311e+02 962447395 : 6.668679e-03 5.447175e+03 3.184696e+02 260922999 : 0.0046522 6105.9408884 343.2605391 3907274 : 5.580519e-03 6.205901e+03 3.458634e+02 763.1143 : 5.606709e-03 6.181984e+03 3.452405e+02 87.94589 : 5.609632e-03 6.181347e+03 3.452237e+02 87.94586 : 5.609637e-03 6.181346e+03 3.452236e+02 > ## Not run: > ##D fm3 <- nls(y ~ exp(b2/(x+b3)), data = MGH10, trace = TRUE, > ##D start = c(b2 = 400000, b3 = 25000), > ##D algorithm = "plinear") > ## End(Not run) > fm4 <- nls(y ~ exp(b2/(x+b3)), data = MGH10, trace = TRUE, + start = c(b2 = 4000, b3 = 250), + algorithm = "plinear") 6977343 : 4.00000e+03 2.50000e+02 5.86502e-02 23094.19 : 5.139586e+03 3.089984e+02 2.108902e-02 13515.30 : 5.593555e+03 3.255459e+02 1.181886e-02 4941.606 : 6.139264e+03 3.442822e+02 6.007058e-03 88.21933 : 6.180663e+03 3.452042e+02 5.614985e-03 87.94586 : 6.181346e+03 3.452236e+02 5.609638e-03 87.94586 : 6.181346e+03 3.452236e+02 5.609638e-03 > > > > cleanEx(); ..nameEx <- "MGH17" > > ### * MGH17 > > flush(stderr()); flush(stdout()) > > ### Name: MGH17 > ### Title: More, Gabrow and Hillstrom example 17 > ### Aliases: MGH17 > ### Keywords: datasets > > ### ** Examples > > data(MGH17) > plot(y ~ x, data = MGH17) > ## Not run: > ##D ## Starting values here are ridiculous > ##D fm1 <- nls(y ~ b1 + b2*exp(-x*b4) + b3*exp(-x*b5), > ##D data = MGH17, trace = TRUE, > ##D start = c(b1 = 50, b2 = 150, b3 = -100, b4 = 1, b5 = 2)) > ## End(Not run) > fm2 <- nls(y ~ b1 + b2*exp(-x*b4) + b3*exp(-x*b5), + data = MGH17, trace = TRUE, + start = c(b1 = 0.5, b2 = 1.5, b3 = -1, b4 = 0.01, b5 = 0.02)) 0.8790263 : 0.50 1.50 -1.00 0.01 0.02 0.001898686 : 0.37834626 1.36701462 -0.89868590 0.01151197 0.02543841 0.001703870 : 0.37673358 1.53907815 -1.06920589 0.01205174 0.02384126 0.001016144 : 0.37603259 1.68714320 -1.21660082 0.01241257 0.02300198 0.0003689203 : 0.37537686 1.89806587 -1.42688741 0.01283722 0.02213953 5.467062e-05 : 0.37541223 1.93594894 -1.46479108 0.01286830 0.02212172 5.464895e-05 : 0.37541007 1.93584978 -1.46469001 0.01286754 0.02212269 > ## Not run: > ##D fm3 <- nls(y ~ cbind(1, exp(-x*b4), exp(-x*b5)), > ##D data = MGH17, trace = TRUE, algorithm = "plinear", > ##D start = c(b4 = 1, b5 = 2)) > ## End(Not run) > fm4 <- nls(y ~ cbind(1, exp(-x*b4), exp(-x*b5)), + data = MGH17, trace = TRUE, algorithm = "plinear", + start = c(b4 = 0.01, b5 = 0.02)) 0.004917861 : 0.0100000 0.0200000 0.3266639 1.5213649 -0.9729747 5.92985e-05 : 0.01242288 0.02321911 0.37387415 1.72618159 -1.25459633 5.482366e-05 : 0.01280806 0.02219877 0.37500425 1.91198417 -1.44031644 5.464896e-05 : 0.01286669 0.02212404 0.37540530 1.93547318 -1.46430824 5.464895e-05 : 0.01286752 0.02212273 0.37541000 1.93584038 -1.46468057 5.464895e-05 : 0.01286753 0.02212270 0.37541005 1.93584684 -1.46468706 > > > > cleanEx(); ..nameEx <- "Misra1a" > > ### * Misra1a > > flush(stderr()); flush(stdout()) > > ### Name: Misra1a > ### Title: Monomolecular Absorption Data > ### Aliases: Misra1a > ### Keywords: datasets > > ### ** Examples > > data(Misra1a) > plot(y ~ x, data = Misra1a) > fm1 <- nls(y ~ b1*(1-exp(-b2*x)), data = Misra1a, trace = TRUE, + start = c(b1 = 500, b2 = 0.0001) ) 10780.19 : 5e+02 1e-04 10697.62 : 4.666633e+02 1.079252e-04 10640.08 : 4.112467e+02 1.234257e-04 10497.53 : 3.716416e+02 1.383456e-04 10374.66 : 3.127815e+02 1.669194e-04 10230.61 : 2.430935e+02 2.198045e-04 9280.13 : 1.868551e+02 3.105042e-04 5770.42 : 1.705528e+02 4.354660e-04 1242.317 : 1.979720e+02 5.328954e-04 1.13784 : 238.75381622 0.00055422 0.1245559 : 2.389272e+02 5.501891e-04 0.1245514 : 2.389421e+02 5.501565e-04 > fm2 <- nls(y ~ b1*(1-exp(-b2*x)), data = Misra1a, trace = TRUE, + start = c(b1 = 250, b2 = 0.0005) ) 44.77128 : 2.5e+02 5.0e-04 1.178132 : 2.370130e+02 5.517301e-04 0.1245658 : 2.389389e+02 5.501518e-04 0.1245514 : 2.389421e+02 5.501564e-04 > fm3 <- nls(y ~ 1-exp(-b2*x), data = Misra1a, trace = TRUE, + start = c(b2 = 0.0001), algorithm = "plinear" ) 42.32939 : 0.0001 1163.5481 0.1675215 : 5.353648e-04 2.445981e+02 0.1245520 : 5.500990e-04 2.389635e+02 0.1245514 : 5.501563e-04 2.389422e+02 0.1245514 : 5.501564e-04 2.389421e+02 > fm4 <- nls(y ~ 1-exp(-b2*x), data = Misra1a, trace = TRUE, + start = c(b2 = 0.0005), algorithm = "plinear" ) 0.6210665 : 0.0005 259.4827 0.1245712 : 5.498389e-04 2.390603e+02 0.1245514 : 5.501555e-04 2.389425e+02 0.1245514 : 5.501564e-04 2.389421e+02 > ## Using a self-starting model > fm5 <- nls(y ~ SSasympOrig(x, Asym, lrc), data = Misra1a) > > > > cleanEx(); ..nameEx <- "Misra1b" > > ### * Misra1b > > flush(stderr()); flush(stdout()) > > ### Name: Misra1b > ### Title: Monomolecular Absorption Data > ### Aliases: Misra1b > ### Keywords: datasets > > ### ** Examples > > data(Misra1b) > plot(y ~ x, data = Misra1b) > fm1 <- nls(y ~ b1 * (1-(1+b2*x/2)**(-2)), data = Misra1b, trace = TRUE, + start = c(b1 = 500, b2 = 0.0001) ) 10994.32 : 5e+02 1e-04 10785.33 : 4.258762e+02 1.198812e-04 10479.91 : 3.369894e+02 1.566407e-04 9334.4 : 2.641880e+02 2.195925e-04 5755.487 : 2.430607e+02 3.067722e-04 1241.285 : 2.808682e+02 3.769135e-04 1.260361 : 3.376896e+02 3.935314e-04 0.07547095 : 3.379743e+02 3.904160e-04 0.07546468 : 3.379974e+02 3.903910e-04 > fm2 <- nls(y ~ b1 * (1-(1+b2*x/2)**(-2)), data = Misra1b, trace = TRUE, + start = c(b1 = 300, b2 = 0.0002) ) 8654.692 : 3e+02 2e-04 5652.014 : 2.003644e+02 3.855841e-04 1.830186 : 3.379666e+02 3.937477e-04 0.07546767 : 3.379715e+02 3.904218e-04 0.07546468 : 3.379974e+02 3.903910e-04 > fm3 <- nls(y ~ 1-(1+b2*x/2)**(-2), data = Misra1b, trace = TRUE, + start = c(b2 = 0.0001), algorithm = "plinear" ) 33.67935 : 0.0001 1179.4953 0.2293415 : 3.694179e-04 3.544625e+02 0.07547355 : 3.902309e-04 3.381164e+02 0.07546468 : 3.903905e-04 3.379978e+02 0.07546468 : 3.903909e-04 3.379975e+02 > fm4 <- nls(y ~ 1-(1+b2*x/2)**(-2), data = Misra1b, trace = TRUE, + start = c(b2 = 0.0005), algorithm = "plinear" ) 4.033906 : 0.0005 274.3971 0.07752716 : 3.879523e-04 3.398205e+02 0.0754647 : 3.903828e-04 3.380035e+02 0.07546468 : 3.903909e-04 3.379975e+02 > > > > cleanEx(); ..nameEx <- "Misra1c" > > ### * Misra1c > > flush(stderr()); flush(stdout()) > > ### Name: Misra1c > ### Title: Monomolecular Absorption data > ### Aliases: Misra1c > ### Keywords: datasets > > ### ** Examples > > data(Misra1c) > plot(y ~ x, data = Misra1c) > fm1 <- nls(y ~ b1*(1-(1+2*b2*x)**(-.5)), data = Misra1c, trace = TRUE, + start = c(b1 = 500, b2 = 0.0001) ) 11603.02 : 5e+02 1e-04 8452.255 : 2.973034e+02 2.223794e-04 138.0323 : 6.344276e+02 1.933621e-04 0.0596407 : 6.337917e+02 2.089646e-04 0.04097522 : 6.364150e+02 2.081371e-04 0.04096684 : 6.364273e+02 2.081363e-04 > fm2 <- nls(y ~ b1*(1-(1+2*b2*x)**(-.5)), data = Misra1c, trace = TRUE, + start = c(b1 = 600, b2 = 0.0002) ) 262.4566 : 6e+02 2e-04 0.1559867 : 6.357031e+02 2.088635e-04 0.0409676 : 6.364173e+02 2.081389e-04 0.04096684 : 6.364272e+02 2.081363e-04 > fm3 <- nls(y ~ 1-(1+2*b2*x)**(-.5), data = Misra1c, trace = TRUE, + start = c(b2 = 0.0001), algorithm = "plinear" ) 14.79260 : 0.0001 1226.0429 0.1176382 : 1.997722e-04 6.593247e+02 0.04097147 : 2.080709e-04 6.365991e+02 0.04096684 : 2.081361e-04 6.364277e+02 0.04096684 : 2.081363e-04 6.364273e+02 > fm4 <- nls(y ~ 1-(1+2*b2*x)**(-.5), data = Misra1c, trace = TRUE, + start = c(b2 = 0.0002), algorithm = "plinear" ) 0.1134958 : 0.0002 658.6757 0.04097105 : 2.080739e-04 6.365911e+02 0.04096684 : 2.081361e-04 6.364276e+02 0.04096684 : 2.081363e-04 6.364273e+02 > > > > cleanEx(); ..nameEx <- "Misra1d" > > ### * Misra1d > > flush(stderr()); flush(stdout()) > > ### Name: Misra1d > ### Title: Monomolecular Absorption data > ### Aliases: Misra1d > ### Keywords: datasets > > ### ** Examples > > data(Misra1d) > plot(y ~ x, data = Misra1d) > fm1 <- nls(y ~ b1*b2*x*((1+b2*x)**(-1)), data = Misra1d, trace = TRUE, + start = c(b1 = 500, b2 = 0.0001) ) 11202.66 : 5e+02 1e-04 10602.92 : 4.121070e+02 1.277358e-04 9104.287 : 3.386065e+02 1.744376e-04 5482.165 : 3.192118e+02 2.381496e-04 1189.908 : 3.664470e+02 2.907604e-04 1.356636 : 4.368891e+02 3.048701e-04 0.05642816 : 4.373375e+02 3.022935e-04 0.0564193 : 4.373696e+02 3.022733e-04 > fm2 <- nls(y ~ b1*b2*x*((1+b2*x)**(-1)), data = Misra1d, trace = TRUE, + start = c(b1 = 450, b2 = 0.0003) ) 16.39022 : 4.5e+02 3.0e-04 0.05759993 : 4.373580e+02 3.022162e-04 0.0564193 : 4.373699e+02 3.022731e-04 0.0564193 : 4.373697e+02 3.022732e-04 > fm3 <- nls(y ~ b2*x*((1+b2*x)**(-1)), data = Misra1d, trace = TRUE, + start = c(b2 = 0.0001), algorithm = "plinear" ) 26.28574 : 0.0001 1195.2189 0.2117572 : 2.854982e-04 4.594355e+02 0.05643158 : 3.021231e-04 4.375563e+02 0.0564193 : 3.022729e-04 4.373702e+02 0.0564193 : 3.022732e-04 4.373697e+02 > fm4 <- nls(y ~ b2*x*((1+b2*x)**(-1)), data = Misra1d, trace = TRUE, + start = c(b2 = 0.0005), algorithm = "plinear" ) 18.51470 : 0.0005 288.5110 0.1600211 : 2.885575e-04 4.552206e+02 0.0564255 : 3.021665e-04 4.375023e+02 0.0564193 : 3.022730e-04 4.373701e+02 0.0564193 : 3.022732e-04 4.373697e+02 > > > > cleanEx(); ..nameEx <- "Nelson" > > ### * Nelson > > flush(stderr()); flush(stdout()) > > ### Name: Nelson > ### Title: Dialectric breakdown data > ### Aliases: Nelson > ### Keywords: datasets > > ### ** Examples > > data(Nelson) > plot(y ~ x1, data = Nelson, log = "y") > plot(y ~ x2, data = Nelson, log = "y") > coplot(y ~ x1 | x2, data = Nelson) > coplot(y ~ x2 | x1, data = Nelson) > ## Not run: > ##D fm1 <- nls(log(y) ~ b1 - b2*x1 * exp(-b3*x2), data = Nelson, > ##D start = c(b1 = 2, b2 = 0.0001, b3 = -0.01), trace = TRUE) > ## End(Not run) > fm2 <- nls(log(y) ~ b1 - b2*x1 * exp(-b3*x2), data = Nelson, + start = c(b1 = 2.5, b2 = 0.000000005, b3 = -0.05), trace = TRUE) 48.48993 : 2.5e+00 5.0e-09 -5.0e-02 45.65385 : 2.505640e+00 2.160872e-09 -5.395902e-02 31.19039 : 2.516271e+00 1.975843e-09 -5.712235e-02 17.92667 : 2.534881e+00 2.874560e-09 -5.758984e-02 7.114593 : 2.562785e+00 4.247015e-09 -5.769908e-02 3.797685 : 2.590684e+00 5.617843e-09 -5.770158e-02 3.797683 : 2.590684e+00 5.617745e-09 -5.770103e-02 > ## Not run: > ##D fm3 <- nls(log(y) ~ cbind(1, -x1 * exp(-b3*x2)), data = Nelson, > ##D start = c(b3 = -0.01), trace = TRUE, algorithm = "plinear") > ## End(Not run) > fm4 <- nls(log(y) ~ cbind(1, -x1 * exp(-b3*x2)), data = Nelson, + start = c(b3 = -0.05), trace = TRUE, algorithm = "plinear") 3.938286 : -5.000000e-02 2.608949e+00 4.654491e-08 3.799312 : -5.678605e-02 2.592665e+00 7.224035e-09 3.797685 : -5.766917e-02 2.590752e+00 5.667156e-09 3.797683 : -5.770026e-02 2.590685e+00 5.618935e-09 3.797683 : -5.770100e-02 2.590684e+00 5.617799e-09 > > > > cleanEx(); ..nameEx <- "Ratkowsky2" > > ### * Ratkowsky2 > > flush(stderr()); flush(stdout()) > > ### Name: Ratkowsky2 > ### Title: Pasture yield data > ### Aliases: Ratkowsky2 > ### Keywords: datasets > > ### ** Examples > > data(Ratkowsky2) > plot(y ~ x, data = Ratkowsky2) > ## Not run: > ##D fm1 <- nls(y ~ b1 / (1+exp(b2-b3*x)), data = Ratkowsky2, trace = TRUE, > ##D start = c(b1 = 100, b2 = 1, b3 = 0.1)) > ## End(Not run) > fm2 <- nls(y ~ b1 / (1+exp(b2-b3*x)), data = Ratkowsky2, trace = TRUE, + start = c(b1 = 75, b2 = 2.5, b3 = 0.07)) 152.762 : 75.00 2.50 0.07 8.306839 : 72.4716052 2.5866659 0.0665379 8.05665 : 72.45057008 2.61781502 0.06736813 8.056523 : 72.46286654 2.61805288 0.06735785 8.056523 : 72.46219756 2.61807783 0.06735928 8.056523 : 72.4622402 2.6180768 0.0673592 > fm3 <- nls(y ~ 1 / (1+exp(b2-b3*x)), data = Ratkowsky2, trace = TRUE, + start = c(b2 = 1, b3 = 0.1), alg = "plinear") 2129.617 : 1.00000 0.10000 48.75038 1987.222 : 0.89330030 0.01460026 95.91189057 1896.183 : 0.36680118 0.02765868 61.80917362 476.5503 : 1.44492787 0.03769399 77.74372978 47.98725 : 2.27125156 0.06321649 70.41981238 8.234656 : 2.58822545 0.06618433 72.89429797 8.057043 : 2.61812348 0.06739851 72.43467697 8.056525 : 2.61802018 0.06735567 72.46397874 8.056523 : 2.61807969 0.06735941 72.46212737 8.056523 : 2.61807665 0.06735919 72.46224460 > fm4 <- nls(y ~ 1 / (1+exp(b2-b3*x)), data = Ratkowsky2, trace = TRUE, + start = c(b2 = 2.5, b3 = 0.07), alg = "plinear") 25.06979 : 2.50000 0.07000 69.20315 8.203936 : 2.59383643 0.06625146 72.92597425 8.057053 : 2.61828889 0.06740379 72.43321658 8.056525 : 2.61801909 0.06735551 72.46407280 8.056523 : 2.61807987 0.06735942 72.46212149 8.056523 : 2.61807664 0.06735919 72.46224497 > ## Using a self-starting model > fm5 <- nls(y ~ SSlogis(x, Asym, xmid, scal), data = Ratkowsky2) > summary(fm5) Formula: y ~ SSlogis(x, Asym, xmid, scal) Parameters: Estimate Std. Error t value Pr(>|t|) Asym 72.4622 1.7340 41.79 1.26e-08 *** xmid 38.8674 1.1794 32.95 5.19e-08 *** scal 14.8458 0.7596 19.54 1.16e-06 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 1.159 on 6 degrees of freedom Correlation of Parameter Estimates: Asym xmid xmid 0.9082 scal 0.8389 0.7733 > > > > cleanEx(); ..nameEx <- "Ratkowsky3" > > ### * Ratkowsky3 > > flush(stderr()); flush(stdout()) > > ### Name: Ratkowsky3 > ### Title: Onion growth data > ### Aliases: Ratkowsky3 > ### Keywords: datasets > > ### ** Examples > > data(Ratkowsky3) > plot(y ~ x, data = Ratkowsky3) > ## Not run: > ##D ## causes NA/NaN/Inf error > ##D fm1 <- nls(y ~ b1 / ((1+exp(b2-b3*x))**(1/b4)), data = Ratkowsky3, > ##D start = c(b1 = 100, b2 = 10, b3 = 1, b4 = 1), > ##D trace = TRUE) > ## End(Not run) > fm2 <- nls(y ~ b1 / ((1+exp(b2-b3*x))**(1/b4)), data = Ratkowsky3, + start = c(b1 = 700, b2 = 5, b3 = 0.75, b4 = 1.3), + trace = TRUE) 14655.21 : 700.00 5.00 0.75 1.30 8838.785 : 700.8256863 4.9358701 0.7258174 1.1731207 8788.805 : 699.1175021 5.3117935 0.7632701 1.2867861 8786.424 : 699.6857291 5.2735985 0.7591746 1.2785566 8786.406 : 699.631044 5.278726 0.759792 1.279715 8786.405 : 699.6436141 5.2769215 0.7596058 1.2791976 8786.405 : 699.6410703 5.2771864 0.7596358 1.2792657 8786.405 : 699.6415961 5.2771170 0.7596284 1.2792463 > fm3 <- nls(y ~ 1 / ((1+exp(b2-b3*x))**(1/b4)), data = Ratkowsky3, + start = c(b2 = 10, b3 = 1, b4 = 1), algorithm = "plinear", + trace = TRUE) 703222.7 : 10.0000 1.0000 1.0000 824.0297 684916.2 : 29.682630 2.282841 6.836056 897.834108 182343.7 : 14.895933 1.160926 6.560735 836.920452 131167.5 : 5.8722621 0.5078587 2.3614708 880.2650623 106283.7 : 3.974112 0.395267 1.458177 893.578838 75081.19 : 2.4731112 0.3410042 0.7682193 878.6168899 27092.55 : 2.2976657 0.4132804 0.6167367 775.4632412 13979.91 : 5.0201258 0.6907089 1.2225363 722.8498539 8855.048 : 5.6368066 0.7878332 1.4018450 700.2622667 8788.181 : 5.3438426 0.7648127 1.3029683 699.6854380 8786.447 : 5.2890740 0.7605899 1.2834732 699.6345180 8786.406 : 5.2787715 0.7597562 1.2798512 699.6417684 8786.405 : 5.2774182 0.7596533 1.2793518 699.6411893 8786.405 : 5.277160 0.759632 1.279261 699.641540 > fm4 <- nls(y ~ 1 / ((1+exp(b2-b3*x))**(1/b4)), data = Ratkowsky3, + start = c(b2 = 5, b3 = 0.75, b4 = 1.3), algorithm = "plinear", + trace = TRUE) 13101.93 : 5.0000 0.7500 1.3000 686.0396 8834.483 : 4.9346408 0.7253536 1.1706873 702.5500175 8787.802 : 5.3180554 0.7637925 1.2886604 699.5374259 8786.426 : 5.2745580 0.7592463 1.2789187 699.6883686 8786.406 : 5.278918 0.759808 1.279782 699.630804 8786.405 : 5.2769398 0.7596071 1.2792048 699.6436631 8786.405 : 5.2771930 0.7596363 1.2792679 699.6410511 > > > > cleanEx(); ..nameEx <- "Roszman1" > > ### * Roszman1 > > flush(stderr()); flush(stdout()) > > ### Name: Roszman1 > ### Title: Quantum defects in iodine > ### Aliases: Roszman1 > ### Keywords: datasets > > ### ** Examples > > data(Roszman1) > plot(y ~ x, data = Roszman1) > fm1 <- nls(y ~ b1 - b2*x - atan(b3/(x-b4))/pi, data = Roszman1, + start = c(b1 = 0.1, b2 = -0.00001, b3 = 1000, b4 = -100), + trace = TRUE) 0.5108107 : 1e-01 -1e-05 1e+03 -1e+02 0.000652679 : 2.057271e-01 -6.797293e-06 1.197851e+03 -1.498035e+02 0.0004948839 : 2.018532e-01 -6.180855e-06 1.205227e+03 -1.816680e+02 0.0004948485 : 2.019636e-01 -6.194578e-06 1.204477e+03 -1.813535e+02 0.0004948485 : 2.019685e-01 -6.195328e-06 1.204456e+03 -1.813430e+02 > fm2 <- nls(y ~ b1 - b2*x - atan(b3/(x-b4))/pi, data = Roszman1, + start = c(b1 = 0.2, b2 = -0.0000015, b3 = 1200, b4 = -150), + trace = TRUE) 0.002608273 : 2.0e-01 -1.5e-06 1.2e+03 -1.5e+02 0.0004948902 : 2.018432e-01 -6.178783e-06 1.205202e+03 -1.817592e+02 0.0004948485 : 2.019638e-01 -6.194622e-06 1.204476e+03 -1.813527e+02 0.0004948485 : 2.019685e-01 -6.195334e-06 1.204456e+03 -1.813429e+02 > > > > cleanEx(); ..nameEx <- "Thurber" > > ### * Thurber > > flush(stderr()); flush(stdout()) > > ### Name: Thurber > ### Title: Electron mobility data > ### Aliases: Thurber > ### Keywords: datasets > > ### ** Examples > > data(Thurber) > plot(y ~ x, data = Thurber) > fm1 <- nls(y ~ (b1+x*(b2+x*(b3+b4*x))) / (1+x*(b5+x*(b6+x*b7))), + data = Thurber, trace = TRUE, + start = c(b1 = 1000, b2 = 1000, b3 = 400, b4 = 40, + b5 = 0.7, b6 = 0.3, b7 = 0.03)) 4528125 : 1e+03 1e+03 4e+02 4e+01 7e-01 3e-01 3e-02 2917906 : 1.017774e+03 1.154287e+03 5.125921e+02 7.798057e+01 8.450532e-01 3.683700e-01 6.079624e-02 2211529 : 1.051789e+03 1.190913e+03 5.099164e+02 7.455358e+01 8.587354e-01 3.623121e-01 5.733568e-02 1224790 : 1.111307e+03 1.269700e+03 5.209949e+02 7.197847e+01 8.947460e-01 3.641980e-01 5.364407e-02 382267.3 : 1.200294e+03 1.401285e+03 5.607404e+02 7.378506e+01 9.539194e-01 3.860523e-01 5.196946e-02 44571.86 : 1.288335e+03 1.490593e+03 5.806581e+02 7.350717e+01 9.668231e-01 3.970005e-01 4.801429e-02 7238.203 : 1.288056e+03 1.501822e+03 5.920960e+02 7.746724e+01 9.742648e-01 4.027497e-01 5.168976e-02 5672.84 : 1288.1119913 1489.2204407 582.2917384 75.2869325 0.9653677 0.3978018 0.0492034 5644.678 : 1.288113e+03 1.493502e+03 5.849138e+02 7.573835e+01 9.679718e-01 3.987011e-01 5.018907e-02 5643.374 : 1288.1452328 1489.6639551 582.2539613 75.2237774 0.9653565 0.3975439 0.0494343 5643.05 : 1.288133e+03 1.492129e+03 5.839723e+02 7.556004e+01 9.670082e-01 3.982978e-01 4.993477e-02 5642.85 : 1.288143e+03 1.490417e+03 5.827772e+02 7.532647e+01 9.658517e-01 3.977707e-01 4.959273e-02 5642.776 : 1288.1369373 1491.5445869 583.5634412 75.4801741 0.9666099 0.3981164 0.0498201 5642.738 : 1.288141e+03 1.490775e+03 5.830261e+02 7.537513e+01 9.660904e-01 3.978795e-01 4.966582e-02 5642.722 : 1.288138e+03 1.491288e+03 5.833843e+02 7.544516e+01 9.664361e-01 3.980372e-01 4.976914e-02 5642.714 : 1.288140e+03 1.490940e+03 5.831414e+02 7.539770e+01 9.662015e-01 3.979302e-01 4.969932e-02 5642.711 : 1.288139e+03 1.491174e+03 5.833042e+02 7.542952e+01 9.663587e-01 3.980019e-01 4.974623e-02 5642.71 : 1.288140e+03 1.491016e+03 5.831942e+02 7.540802e+01 9.662524e-01 3.979534e-01 4.971458e-02 5642.709 : 1.288139e+03 1.491122e+03 5.832682e+02 7.542247e+01 9.663238e-01 3.979860e-01 4.973587e-02 5642.709 : 1.288140e+03 1.491051e+03 5.832183e+02 7.541272e+01 9.662757e-01 3.979640e-01 4.972152e-02 5642.708 : 1.288140e+03 1.491099e+03 5.832518e+02 7.541928e+01 9.663080e-01 3.979788e-01 4.973118e-02 5642.708 : 1.288140e+03 1.491066e+03 5.832293e+02 7.541486e+01 9.662862e-01 3.979688e-01 4.972468e-02 5642.708 : 1.288140e+03 1.491088e+03 5.832445e+02 7.541784e+01 9.663009e-01 3.979755e-01 4.972906e-02 5642.708 : 1288.1397119 1491.0732941 583.2342091 75.4158312 0.9662910 0.3979710 0.0497261 5642.708 : 1288.1396589 1491.0832342 583.2411453 75.4171871 0.9662977 0.3979741 0.0497281 5642.708 : 1.288140e+03 1.491077e+03 5.832365e+02 7.541628e+01 9.662932e-01 3.979720e-01 4.972676e-02 5642.708 : 1.288140e+03 1.491081e+03 5.832396e+02 7.541688e+01 9.662962e-01 3.979734e-01 4.972765e-02 5642.708 : 1.288140e+03 1.491078e+03 5.832376e+02 7.541649e+01 9.662942e-01 3.979725e-01 4.972706e-02 5642.708 : 1.288140e+03 1.491080e+03 5.832389e+02 7.541675e+01 9.662956e-01 3.979731e-01 4.972746e-02 > fm2 <- nls(y ~ (b1+x*(b2+x*(b3+b4*x))) / (1+x*(b5+x*(b6+x*b7))), + data = Thurber, trace = TRUE, + start = c(b1 = 1300, b2 = 1500, b3 = 500, b4 = 75, + b5 = 1, b6 = 0.4, b7 = 0.05)) 85873750 : 1300.00 1500.00 500.00 75.00 1.00 0.40 0.05 733524.4 : 1.287773e+03 1.492396e+03 5.702054e+02 7.381027e+01 9.696534e-01 3.865921e-01 4.799485e-02 37931.59 : 1.288146e+03 1.477903e+03 5.721139e+02 7.390069e+01 9.568291e-01 3.915220e-01 4.815011e-02 5751.822 : 1.288190e+03 1.492522e+03 5.840795e+02 7.552000e+01 9.670472e-01 3.982726e-01 5.007821e-02 5643.339 : 1.288150e+03 1.489790e+03 5.823224e+02 7.523432e+01 9.654079e-01 3.975591e-01 4.947535e-02 5642.946 : 1288.1349894 1491.9463562 583.8446795 75.5353032 0.9668808 0.3982410 0.0499007 5642.808 : 1.288142e+03 1.490521e+03 5.828494e+02 7.534059e+01 9.659205e-01 3.978021e-01 4.961424e-02 5642.756 : 1.288137e+03 1.491468e+03 5.835100e+02 7.546973e+01 9.665580e-01 3.980927e-01 4.980496e-02 5642.729 : 1288.1410158 1490.8235134 583.0600175 75.3817754 0.9661231 0.3978944 0.0496757 5642.718 : 1.288139e+03 1.491254e+03 5.833606e+02 7.544053e+01 9.664132e-01 3.980267e-01 4.976236e-02 5642.713 : 1.288140e+03 1.490963e+03 5.831570e+02 7.540073e+01 9.662165e-01 3.979370e-01 4.970382e-02 5642.71 : 1.288139e+03 1.491158e+03 5.832936e+02 7.542744e+01 9.663484e-01 3.979972e-01 4.974317e-02 5642.709 : 1.288140e+03 1.491026e+03 5.832013e+02 7.540940e+01 9.662592e-01 3.979565e-01 4.971663e-02 5642.709 : 1.288139e+03 1.491115e+03 5.832635e+02 7.542155e+01 9.663193e-01 3.979839e-01 4.973451e-02 5642.708 : 1.288140e+03 1.491055e+03 5.832216e+02 7.541336e+01 9.662788e-01 3.979655e-01 4.972245e-02 5642.708 : 1.288140e+03 1.491096e+03 5.832497e+02 7.541886e+01 9.663060e-01 3.979779e-01 4.973056e-02 5642.708 : 1.288140e+03 1.491068e+03 5.832307e+02 7.541514e+01 9.662876e-01 3.979695e-01 4.972509e-02 5642.708 : 1.288140e+03 1.491087e+03 5.832435e+02 7.541765e+01 9.663000e-01 3.979751e-01 4.972878e-02 5642.708 : 1.288140e+03 1.491074e+03 5.832348e+02 7.541596e+01 9.662916e-01 3.979713e-01 4.972629e-02 5642.708 : 1.288140e+03 1.491083e+03 5.832407e+02 7.541711e+01 9.662973e-01 3.979739e-01 4.972798e-02 5642.708 : 1.288140e+03 1.491077e+03 5.832368e+02 7.541634e+01 9.662935e-01 3.979722e-01 4.972684e-02 5642.708 : 1288.1396712 1491.0807360 583.2394025 75.4168464 0.9662960 0.3979733 0.0497276 5642.708 : 1.288140e+03 1.491078e+03 5.832376e+02 7.541650e+01 9.662943e-01 3.979725e-01 4.972709e-02 5642.708 : 1.288140e+03 1.491080e+03 5.832388e+02 7.541674e+01 9.662955e-01 3.979731e-01 4.972743e-02 > fm3 <- nls(y ~ outer(x, 0:3, "^")/(1+x*(b5+x*(b6+x*b7))), + data = Thurber, trace = TRUE, + start = c(b5 = 0.7, b6 = 0.3, b7 = 0.03), alg = "plinear") 15342.21 : 0.7000 0.3000 0.0300 1302.6450 1202.1374 380.3813 39.0765 9418.713 : 9.957833e-01 4.056820e-01 5.789391e-02 1.284409e+03 1.532009e+03 6.107927e+02 8.064974e+01 6130.941 : 9.837839e-01 4.062383e-01 5.564791e-02 1.288437e+03 1.518224e+03 6.017817e+02 7.903103e+01 5647.933 : 9.706971e-01 4.000814e-01 5.002773e-02 1.288043e+03 1.495842e+03 5.868597e+02 7.610432e+01 5642.843 : 9.664310e-01 3.980114e-01 4.963913e-02 1.288110e+03 1.491050e+03 5.832480e+02 7.541495e+01 5642.741 : 9.665613e-01 3.980917e-01 4.979155e-02 1.288134e+03 1.491447e+03 5.834987e+02 7.546712e+01 5642.722 : 9.661598e-01 3.979109e-01 4.968505e-02 1.288140e+03 1.490875e+03 5.830964e+02 7.538884e+01 5642.715 : 9.663924e-01 3.980172e-01 4.975602e-02 1.288139e+03 1.491223e+03 5.833389e+02 7.543629e+01 5642.711 : 9.662306e-01 3.979435e-01 4.970803e-02 1.288140e+03 1.490984e+03 5.831716e+02 7.540359e+01 5642.71 : 9.663388e-01 3.979928e-01 4.974031e-02 1.288139e+03 1.491144e+03 5.832836e+02 7.542549e+01 5642.709 : 9.662657e-01 3.979595e-01 4.971856e-02 1.288140e+03 1.491036e+03 5.832080e+02 7.541072e+01 5642.709 : 9.663148e-01 3.979819e-01 4.973318e-02 1.288140e+03 1.491109e+03 5.832588e+02 7.542064e+01 5642.708 : 9.662817e-01 3.979668e-01 4.972333e-02 1.288140e+03 1.491059e+03 5.832246e+02 7.541395e+01 5642.708 : 9.663041e-01 3.979770e-01 4.972999e-02 1.288140e+03 1.491093e+03 5.832477e+02 7.541847e+01 5642.708 : 0.9662890 0.3979701 0.0497255 1288.1397292 1491.0703307 583.2321438 75.4154274 5642.708 : 0.9662991 0.3979747 0.0497285 1288.1396463 1491.0852324 583.2425402 75.4174597 5642.708 : 9.662924e-01 3.979717e-01 4.972652e-02 1.288140e+03 1.491075e+03 5.832357e+02 7.541612e+01 5642.708 : 9.662968e-01 3.979737e-01 4.972782e-02 1.288140e+03 1.491082e+03 5.832402e+02 7.541700e+01 5642.708 : 0.9662937 0.3979722 0.0497269 1288.1396875 1491.0772377 583.2369575 75.4163684 5642.708 : 9.662959e-01 3.979732e-01 4.972755e-02 1.288140e+03 1.491081e+03 5.832392e+02 7.541681e+01 5642.708 : 9.662945e-01 3.979726e-01 4.972713e-02 1.288140e+03 1.491078e+03 5.832378e+02 7.541653e+01 5642.708 : 9.662954e-01 3.979730e-01 4.972742e-02 1.288140e+03 1.491080e+03 5.832388e+02 7.541673e+01 5642.708 : 9.662948e-01 3.979728e-01 4.972724e-02 1.288140e+03 1.491079e+03 5.832382e+02 7.541660e+01 > fm4 <- nls(y ~ outer(x, 0:3, "^")/(1+x*(b5+x*(b6+x*b7))), + data = Thurber, trace = TRUE, + start = c(b5 = 1, b6 = 0.4, b7 = 0.05), alg = "plinear") 7762.272 : 1.00000 0.40000 0.05000 1277.99118 1521.58858 605.60816 79.36523 5658.355 : 9.704452e-01 3.987413e-01 4.942063e-02 1.287280e+03 1.494322e+03 5.856819e+02 7.582895e+01 5642.843 : 9.670238e-01 3.982925e-01 4.976933e-02 1.288106e+03 1.491849e+03 5.838208e+02 7.552616e+01 5642.713 : 9.663069e-01 3.979745e-01 4.970999e-02 1.288135e+03 1.491059e+03 5.832294e+02 7.541431e+01 5642.71 : 9.663447e-01 3.979951e-01 4.973966e-02 1.288139e+03 1.491149e+03 5.832873e+02 7.542614e+01 5642.709 : 9.662684e-01 3.979607e-01 4.971907e-02 1.288140e+03 1.491039e+03 5.832105e+02 7.541119e+01 5642.708 : 9.663137e-01 3.979814e-01 4.973284e-02 1.288140e+03 1.491107e+03 5.832577e+02 7.542042e+01 5642.708 : 9.662825e-01 3.979671e-01 4.972356e-02 1.288140e+03 1.491061e+03 5.832254e+02 7.541411e+01 5642.708 : 9.663035e-01 3.979767e-01 4.972982e-02 1.288140e+03 1.491092e+03 5.832471e+02 7.541835e+01 5642.708 : 9.662892e-01 3.979702e-01 4.972557e-02 1.288140e+03 1.491071e+03 5.832324e+02 7.541547e+01 5642.708 : 9.662989e-01 3.979746e-01 4.972846e-02 1.288140e+03 1.491085e+03 5.832424e+02 7.541743e+01 5642.708 : 9.662925e-01 3.979717e-01 4.972654e-02 1.288140e+03 1.491075e+03 5.832357e+02 7.541613e+01 5642.708 : 0.9662967 0.3979736 0.0497278 1288.1396655 1491.0817433 583.2401049 75.4169837 5642.708 : 9.662939e-01 3.979723e-01 4.972696e-02 1.288140e+03 1.491078e+03 5.832372e+02 7.541641e+01 5642.708 : 9.662958e-01 3.979732e-01 4.972752e-02 1.288140e+03 1.491080e+03 5.832391e+02 7.541679e+01 5642.708 : 9.662945e-01 3.979726e-01 4.972713e-02 1.288140e+03 1.491078e+03 5.832378e+02 7.541653e+01 5642.708 : 9.662954e-01 3.979730e-01 4.972741e-02 1.288140e+03 1.491080e+03 5.832387e+02 7.541672e+01 5642.708 : 0.9662947 0.3979727 0.0497272 1288.1396812 1491.0787506 583.2380149 75.4165752 > fm4 Nonlinear regression model model: y ~ outer(x, 0:3, "^")/(1 + x * (b5 + x * (b6 + x * b7))) data: Thurber b5 b6 b7 .lin1 .lin2 .lin3 0.9662947 0.3979727 0.0497272 1288.1396812 1491.0787506 583.2380149 .lin4 75.4165752 residual sum-of-squares: 5642.708 > > > > ### *