Re: [R] string-to-number
Marc, Thanks very much for this. I hadn't really looked at Rprof in the past; now I have a new toy to play with! I have formulated an hypothesis that the reason parse/eval is quicker lies in the pattern-matching code: strsplit is using regular expressions, whereas perhaps parse is using some more clever (but possibly less general) matching algorithm. It will be interesting to inspect the source code to get to the bottom of it. Thanks again for your interest and efforts in this, and for pointing out Rprof! Regards, Mike Nielsen On 8/20/06, Marc Schwartz [EMAIL PROTECTED] wrote: On Sat, 2006-08-19 at 10:25 -0600, Mike Nielsen wrote: Wow. New respect for parse/eval. Do you think this is a special case of a more general principle? I suppose the cost is memory, but from time to time a speedup like this would be very beneficial. Any hints about how R programmers could recognize such cases would, I am sure, be of value to the list in general. Many thanks for your efforts, Marc! Mike, I think that one needs to consider where the time is being spent and then adjust accordingly. Once you understand that, you can develop some insight into what may be a more efficient approach. R provides good profiling tools that facilitate this process. In this case, almost all of the time in the first two examples using strsplit(), is in that function: repeated.measures.columns - paste(1:10, collapse = ,) library(utils) Rprof(tmp - tempfile()) res1 - as.numeric(unlist(strsplit(repeated.measures.columns, ,))) Rprof() summaryRprof(tmp) $by.self self.time self.pct total.time total.pct strsplit 23.68 99.7 23.68 99.7 as.double.default 0.06 0.3 0.06 0.3 as.numeric 0.00 0.0 23.74 100.0 unlist 0.00 0.0 23.68 99.7 $by.total total.time total.pct self.time self.pct as.numeric 23.74 100.0 0.00 0.0 strsplit 23.68 99.7 23.68 99.7 unlist 23.68 99.7 0.00 0.0 as.double.default 0.06 0.3 0.06 0.3 $sampling.time [1] 23.74 Contrast that with Prof. Ripley's approach: Rprof(tmp - tempfile()) res3 - eval(parse(text=paste(c(, repeated.measures.columns, Rprof() summaryRprof(tmp) $by.self self.time self.pct total.time total.pct parse 0.42 87.5 0.42 87.5 eval 0.06 12.5 0.48 100.0 $by.total total.time total.pct self.time self.pct eval0.48 100.0 0.06 12.5 parse 0.42 87.5 0.42 87.5 $sampling.time [1] 0.48 To some extent, one could argue that my initial timing examples are contrived, in that they specifically demonstrate a worst case scenario using strsplit(). Real world examples may or may not show such gains. For example with Charles' initial query, the initial vector was rather short: repeated.measures.columns [1] 3,6,10 So if this was a one-time conversion, we would not see such significant gains. However, what if we had a long list of shorter entries: repeated.measures.columns - paste(1:10, collapse = ,) repeated.measures.columns [1] 1,2,3,4,5,6,7,8,9,10 big.list - replicate(1, list(repeated.measures.columns)) head(big.list) [[1]] [1] 1,2,3,4,5,6,7,8,9,10 [[2]] [1] 1,2,3,4,5,6,7,8,9,10 [[3]] [1] 1,2,3,4,5,6,7,8,9,10 [[4]] [1] 1,2,3,4,5,6,7,8,9,10 [[5]] [1] 1,2,3,4,5,6,7,8,9,10 [[6]] [1] 1,2,3,4,5,6,7,8,9,10 system.time(res1 - t(sapply(big.list, function(x) as.numeric(unlist(strsplit(x, ,)) [1] 1.972 0.044 2.411 0.000 0.000 str(res1) num [1:1, 1:10] 1 1 1 1 1 1 1 1 1 1 ... head(res1) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [1,]12345678910 [2,]12345678910 [3,]12345678910 [4,]12345678910 [5,]12345678910 [6,]12345678910 Now use Prof. Ripley's approach: system.time(res3 - t(sapply(big.list, function(x) eval(parse(text=paste(c(, x, ))) [1] 1.676 0.012 1.877 0.000 0.000 str(res3) num [1:1, 1:10] 1 1 1 1 1 1 1 1 1 1 ... head(res3) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [1,]12345678910 [2,]12345678910 [3,]12345678910 [4,]12345678910 [5,]12345678910 [6,]12345678910 all(res1 == res3) [1] TRUE We do see a notable reduction in time with strsplit(), while a notable increase in time using
Re: [R] string-to-number
On Sat, 2006-08-19 at 10:25 -0600, Mike Nielsen wrote: Wow. New respect for parse/eval. Do you think this is a special case of a more general principle? I suppose the cost is memory, but from time to time a speedup like this would be very beneficial. Any hints about how R programmers could recognize such cases would, I am sure, be of value to the list in general. Many thanks for your efforts, Marc! Mike, I think that one needs to consider where the time is being spent and then adjust accordingly. Once you understand that, you can develop some insight into what may be a more efficient approach. R provides good profiling tools that facilitate this process. In this case, almost all of the time in the first two examples using strsplit(), is in that function: repeated.measures.columns - paste(1:10, collapse = ,) library(utils) Rprof(tmp - tempfile()) res1 - as.numeric(unlist(strsplit(repeated.measures.columns, ,))) Rprof() summaryRprof(tmp) $by.self self.time self.pct total.time total.pct strsplit 23.68 99.7 23.68 99.7 as.double.default 0.06 0.3 0.06 0.3 as.numeric 0.00 0.0 23.74 100.0 unlist 0.00 0.0 23.68 99.7 $by.total total.time total.pct self.time self.pct as.numeric 23.74 100.0 0.00 0.0 strsplit 23.68 99.7 23.68 99.7 unlist 23.68 99.7 0.00 0.0 as.double.default 0.06 0.3 0.06 0.3 $sampling.time [1] 23.74 Contrast that with Prof. Ripley's approach: Rprof(tmp - tempfile()) res3 - eval(parse(text=paste(c(, repeated.measures.columns, Rprof() summaryRprof(tmp) $by.self self.time self.pct total.time total.pct parse 0.42 87.5 0.42 87.5 eval 0.06 12.5 0.48 100.0 $by.total total.time total.pct self.time self.pct eval0.48 100.0 0.06 12.5 parse 0.42 87.5 0.42 87.5 $sampling.time [1] 0.48 To some extent, one could argue that my initial timing examples are contrived, in that they specifically demonstrate a worst case scenario using strsplit(). Real world examples may or may not show such gains. For example with Charles' initial query, the initial vector was rather short: repeated.measures.columns [1] 3,6,10 So if this was a one-time conversion, we would not see such significant gains. However, what if we had a long list of shorter entries: repeated.measures.columns - paste(1:10, collapse = ,) repeated.measures.columns [1] 1,2,3,4,5,6,7,8,9,10 big.list - replicate(1, list(repeated.measures.columns)) head(big.list) [[1]] [1] 1,2,3,4,5,6,7,8,9,10 [[2]] [1] 1,2,3,4,5,6,7,8,9,10 [[3]] [1] 1,2,3,4,5,6,7,8,9,10 [[4]] [1] 1,2,3,4,5,6,7,8,9,10 [[5]] [1] 1,2,3,4,5,6,7,8,9,10 [[6]] [1] 1,2,3,4,5,6,7,8,9,10 system.time(res1 - t(sapply(big.list, function(x) as.numeric(unlist(strsplit(x, ,)) [1] 1.972 0.044 2.411 0.000 0.000 str(res1) num [1:1, 1:10] 1 1 1 1 1 1 1 1 1 1 ... head(res1) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [1,]12345678910 [2,]12345678910 [3,]12345678910 [4,]12345678910 [5,]12345678910 [6,]12345678910 Now use Prof. Ripley's approach: system.time(res3 - t(sapply(big.list, function(x) eval(parse(text=paste(c(, x, ))) [1] 1.676 0.012 1.877 0.000 0.000 str(res3) num [1:1, 1:10] 1 1 1 1 1 1 1 1 1 1 ... head(res3) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [1,]12345678910 [2,]12345678910 [3,]12345678910 [4,]12345678910 [5,]12345678910 [6,]12345678910 all(res1 == res3) [1] TRUE We do see a notable reduction in time with strsplit(), while a notable increase in time using eval(parse)), even though we are converting the same net number of values (100,000). Much of the increase with eval(parse()) is of course due to the overhead of sapply() and navigating the list. Let's increase the size of the list components to 1000: repeated.measures.columns - paste(1:1000, collapse = ,) big.list - replicate(1, list(repeated.measures.columns)) system.time(res1 - sapply(big.list, function(x) as.numeric(unlist(strsplit(x, ,) [1] 33.270 0.744 37.163 0.000 0.000 system.time(res3 - t(sapply(big.list, function(x) eval(parse(text=paste(c(, x, ))) [1] 15.893 0.928 18.139 0.000 0.000 So we see here that as the size of the list components increases, there
Re: [R] string-to-number
On Sat, 19 Aug 2006, Charles Annis, P.E. wrote: Greetings, Amigos: I have been trying without success to convert a character string, repeated.measures.columns [1] 3,6,10 into c(3,6,10) for subsequent use. as.numeric(repeated.measures.columns) doesn't work (likely because of the commas) [1] NA Warning message: NAs introduced by coercion I've tried many things including strsplit(repeated.measures.columns, split = ,) which produces a list with only one element, viz: [[1]] [1] 3 6 10 as.numeric() doesn't like that either. repeated.measures.columns is a vector. Consider: repeated.measures.columns - c(3,6,10, 5,4,9) lst - strsplit(repeated.measures.columns, split = ,) lapply(lst, as.numeric) which is why strsplit() returns a list - one list component for each repeated.measures.columns element. Just pick off the one you want with [[]]: as.numeric(strsplit(repeated.measures.columns, split = ,)[[1]]) Clearly: 1) I cannot be the first person to attempt this, and 2) I've made this WAY harder than it is. Would some kind soul please instruct me (and perhaps subsequent searchers) how to convert the elements of a string into numbers? Thank you. Charles Annis, P.E. [EMAIL PROTECTED] phone: 561-352-9699 eFax: 614-455-3265 http://www.StatisticalEngineering.com __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. -- Roger Bivand Economic Geography Section, Department of Economics, Norwegian School of Economics and Business Administration, Helleveien 30, N-5045 Bergen, Norway. voice: +47 55 95 93 55; fax +47 55 95 95 43 e-mail: [EMAIL PROTECTED] __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] string-to-number
On Sat, 19 Aug 2006, Marc Schwartz wrote: On Sat, 2006-08-19 at 07:58 -0400, Charles Annis, P.E. wrote: Greetings, Amigos: I have been trying without success to convert a character string, repeated.measures.columns [1] 3,6,10 into c(3,6,10) for subsequent use. as.numeric(repeated.measures.columns) doesn't work (likely because of the commas) [1] NA Warning message: NAs introduced by coercion I've tried many things including strsplit(repeated.measures.columns, split = ,) which produces a list with only one element, viz: [[1]] [1] 3 6 10 as.numeric() doesn't like that either. Clearly: 1) I cannot be the first person to attempt this, and 2) I've made this WAY harder than it is. Would some kind soul please instruct me (and perhaps subsequent searchers) how to convert the elements of a string into numbers? Thank you. One more step: as.numeric(unlist(strsplit(repeated.measures.columns, ,))) [1] 3 6 10 Use unlist() to take the output of strsplit() and convert it to a vector, before coercing to numeric. Or, more simply, use [[1]] as in as.numeric(strsplit(repeated.measures.columns, ,)[[1]]) Also, eval(parse(text=paste(c(, repeated.measures.columns, looks competitive, and is quite a bit more general (e.g. allows spaces, works with complex numbers), or you can use scan() from an anonymous file or a textConnection. -- Brian D. Ripley, [EMAIL PROTECTED] Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UKFax: +44 1865 272595 __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] string-to-number
On Sat, 2006-08-19 at 13:30 +0100, Prof Brian Ripley wrote: On Sat, 19 Aug 2006, Marc Schwartz wrote: On Sat, 2006-08-19 at 07:58 -0400, Charles Annis, P.E. wrote: Greetings, Amigos: I have been trying without success to convert a character string, repeated.measures.columns [1] 3,6,10 into c(3,6,10) for subsequent use. as.numeric(repeated.measures.columns) doesn't work (likely because of the commas) [1] NA Warning message: NAs introduced by coercion I've tried many things including strsplit(repeated.measures.columns, split = ,) which produces a list with only one element, viz: [[1]] [1] 3 6 10 as.numeric() doesn't like that either. Clearly: 1) I cannot be the first person to attempt this, and 2) I've made this WAY harder than it is. Would some kind soul please instruct me (and perhaps subsequent searchers) how to convert the elements of a string into numbers? Thank you. One more step: as.numeric(unlist(strsplit(repeated.measures.columns, ,))) [1] 3 6 10 Use unlist() to take the output of strsplit() and convert it to a vector, before coercing to numeric. Or, more simply, use [[1]] as in as.numeric(strsplit(repeated.measures.columns, ,)[[1]]) Also, eval(parse(text=paste(c(, repeated.measures.columns, looks competitive, and is quite a bit more general (e.g. allows spaces, works with complex numbers), or you can use scan() from an anonymous file or a textConnection. I would say more than competitive: repeated.measures.columns - paste(1:10, collapse = ,) str(repeated.measures.columns) chr 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,4| __truncated__ system.time(res1 - as.numeric(unlist(strsplit(repeated.measures.columns, , [1] 24.238 0.192 26.200 0.000 0.000 system.time(res2 - as.numeric(strsplit(repeated.measures.columns, ,)[[1]])) [1] 24.313 0.196 26.471 0.000 0.000 system.time(res3 - eval(parse(text=paste(c(, repeated.measures.columns, ) [1] 0.328 0.004 0.395 0.000 0.000 str(res1) num [1:10] 1 2 3 4 5 6 7 8 9 10 ... str(res2) num [1:10] 1 2 3 4 5 6 7 8 9 10 ... str(res3) num [1:10] 1 2 3 4 5 6 7 8 9 10 ... all(res1 == res2) [1] TRUE all(res1 == res3) [1] TRUE Best regards, Marc __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] string-to-number SUMMARY
Much gratitude to Professor Ripley, Peter Dalgaard, Marc Schwartz, and Roger Bivand. __ Roger Bivand wrote that ... strsplit() returns a list - one list component for each repeated.measures.columns element. Just pick off the one you want with [[]]: as.numeric(strsplit(repeated.measures.columns, split = ,)[[1]]) which had stumped me, since that syntax fails without the [[1]] specification. __ Peter Dalgaard, who also suggested the [[1]] specification, pointed out that scan(textConnection(x), sep=,) will work, although that leaves you with a dangling open connection. __ Marc Schwartz advised to ... Use unlist() to take the output of strsplit() and convert it to a vector, before coercing to numeric. as.numeric(unlist(strsplit(repeated.measures.columns, ,))) Brian D. Ripley suggested that the following looks competitive, and is quite a bit more general (e.g. allows spaces, works with complex numbers) eval(parse(text=paste(c(, repeated.measures.columns, and Marc Schwartz showed that Professor Ripley's suggestion is much faster than the competition with some system.time trials. Many thanks to all. Charles Annis, P.E. [EMAIL PROTECTED] phone: 561-352-9699 eFax: 614-455-3265 http://www.StatisticalEngineering.com -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Charles Annis, P.E. Sent: Saturday, August 19, 2006 7:59 AM To: r-help@stat.math.ethz.ch Subject: [R] string-to-number Greetings, Amigos: I have been trying without success to convert a character string, repeated.measures.columns [1] 3,6,10 into c(3,6,10) for subsequent use. as.numeric(repeated.measures.columns) doesn't work (likely because of the commas) [1] NA Warning message: NAs introduced by coercion I've tried many things including strsplit(repeated.measures.columns, split = ,) which produces a list with only one element, viz: [[1]] [1] 3 6 10 as.numeric() doesn't like that either. Clearly: 1) I cannot be the first person to attempt this, and 2) I've made this WAY harder than it is. Would some kind soul please instruct me (and perhaps subsequent searchers) how to convert the elements of a string into numbers? Thank you. Charles Annis, P.E. [EMAIL PROTECTED] phone: 561-352-9699 eFax: 614-455-3265 http://www.StatisticalEngineering.com __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] string-to-number SUMMARY
On 8/19/06, Charles Annis, P.E. [EMAIL PROTECTED] wrote: Much gratitude to Professor Ripley, Peter Dalgaard, Marc Schwartz, and Roger Bivand. __ Roger Bivand wrote that ... strsplit() returns a list - one list component for each repeated.measures.columns element. Just pick off the one you want with [[]]: as.numeric(strsplit(repeated.measures.columns, split = ,)[[1]]) which had stumped me, since that syntax fails without the [[1]] specification. __ Peter Dalgaard, who also suggested the [[1]] specification, pointed out that scan(textConnection(x), sep=,) will work, although that leaves you with a dangling open connection. You do this: scan(textConnection(x), sep = ,) closeAllConnections() Now the following shows that none are open: showConnections() You could alternately explicitly close it: scan(con - textConnection(x), sep = ,) close(con) __ Marc Schwartz advised to ... Use unlist() to take the output of strsplit() and convert it to a vector, before coercing to numeric. as.numeric(unlist(strsplit(repeated.measures.columns, ,))) Brian D. Ripley suggested that the following looks competitive, and is quite a bit more general (e.g. allows spaces, works with complex numbers) eval(parse(text=paste(c(, repeated.measures.columns, and Marc Schwartz showed that Professor Ripley's suggestion is much faster than the competition with some system.time trials. Many thanks to all. Charles Annis, P.E. [EMAIL PROTECTED] phone: 561-352-9699 eFax: 614-455-3265 http://www.StatisticalEngineering.com -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Charles Annis, P.E. Sent: Saturday, August 19, 2006 7:59 AM To: r-help@stat.math.ethz.ch Subject: [R] string-to-number Greetings, Amigos: I have been trying without success to convert a character string, repeated.measures.columns [1] 3,6,10 into c(3,6,10) for subsequent use. as.numeric(repeated.measures.columns) doesn't work (likely because of the commas) [1] NA Warning message: NAs introduced by coercion I've tried many things including strsplit(repeated.measures.columns, split = ,) which produces a list with only one element, viz: [[1]] [1] 3 6 10 as.numeric() doesn't like that either. Clearly: 1) I cannot be the first person to attempt this, and 2) I've made this WAY harder than it is. Would some kind soul please instruct me (and perhaps subsequent searchers) how to convert the elements of a string into numbers? Thank you. Charles Annis, P.E. [EMAIL PROTECTED] phone: 561-352-9699 eFax: 614-455-3265 http://www.StatisticalEngineering.com __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] string-to-number
Wow. New respect for parse/eval. Do you think this is a special case of a more general principle? I suppose the cost is memory, but from time to time a speedup like this would be very beneficial. Any hints about how R programmers could recognize such cases would, I am sure, be of value to the list in general. Many thanks for your efforts, Marc! Regards, Mike On 8/19/06, Marc Schwartz [EMAIL PROTECTED] wrote: On Sat, 2006-08-19 at 13:30 +0100, Prof Brian Ripley wrote: On Sat, 19 Aug 2006, Marc Schwartz wrote: On Sat, 2006-08-19 at 07:58 -0400, Charles Annis, P.E. wrote: Greetings, Amigos: I have been trying without success to convert a character string, repeated.measures.columns [1] 3,6,10 into c(3,6,10) for subsequent use. as.numeric(repeated.measures.columns) doesn't work (likely because of the commas) [1] NA Warning message: NAs introduced by coercion I've tried many things including strsplit(repeated.measures.columns, split = ,) which produces a list with only one element, viz: [[1]] [1] 3 6 10 as.numeric() doesn't like that either. Clearly: 1) I cannot be the first person to attempt this, and 2) I've made this WAY harder than it is. Would some kind soul please instruct me (and perhaps subsequent searchers) how to convert the elements of a string into numbers? Thank you. One more step: as.numeric(unlist(strsplit(repeated.measures.columns, ,))) [1] 3 6 10 Use unlist() to take the output of strsplit() and convert it to a vector, before coercing to numeric. Or, more simply, use [[1]] as in as.numeric(strsplit(repeated.measures.columns, ,)[[1]]) Also, eval(parse(text=paste(c(, repeated.measures.columns, looks competitive, and is quite a bit more general (e.g. allows spaces, works with complex numbers), or you can use scan() from an anonymous file or a textConnection. I would say more than competitive: repeated.measures.columns - paste(1:10, collapse = ,) str(repeated.measures.columns) chr 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,4| __truncated__ system.time(res1 - as.numeric(unlist(strsplit(repeated.measures.columns, , [1] 24.238 0.192 26.200 0.000 0.000 system.time(res2 - as.numeric(strsplit(repeated.measures.columns, ,)[[1]])) [1] 24.313 0.196 26.471 0.000 0.000 system.time(res3 - eval(parse(text=paste(c(, repeated.measures.columns, ) [1] 0.328 0.004 0.395 0.000 0.000 str(res1) num [1:10] 1 2 3 4 5 6 7 8 9 10 ... str(res2) num [1:10] 1 2 3 4 5 6 7 8 9 10 ... str(res3) num [1:10] 1 2 3 4 5 6 7 8 9 10 ... all(res1 == res2) [1] TRUE all(res1 == res3) [1] TRUE Best regards, Marc __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. -- Regards, Mike Nielsen __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
