john.gavin@ubs.com
2006-Feb-27 19:33 UTC
[R] elements in each row of a matrix to the left.
Hi, Given a matrix like (z <- matrix(c( 1, 1, NA, NA, NA, NA, 1, NA, 1, NA, 1, NA, NA, 1, 1, 1, NA, NA), ncol = 3)) [,1] [,2] [,3] [1,] 1 1 NA [2,] 1 NA 1 [3,] NA 1 1 [4,] NA NA 1 [5,] NA 1 NA [6,] NA NA NA is there a vectorised way to produce the output like [,1] [,2] [,3] [1,] 1 1 NA [2,] 1 NA 1 [3,] 1 1 NA [4,] 1 NA NA [5,] 1 NA NA [6,] NA NA NA That is, given an n by m matrix, and going row by row, if the first non-NA element is in column k I want to move elements in columns from k to m to columns 1 to m-k+1 with NAs filling in from m-k+2 to m.> version_ platform i386-pc-mingw32 arch i386 os mingw32 system i386, mingw32 status major 2 minor 2.1 year 2005 month 12 day 20 svn rev 36812 language R Regards, John. John Gavin <john.gavin at ubs.com>, Quantitative Risk Control, UBS Investment Bank, 6th floor, 100 Liverpool St., London EC2M 2RH, UK. Phone +44 (0) 207 567 4289 Fax +44 (0) 207 568 5352 Visit our website at http://www.ubs.com This message contains confidential information and is intend...{{dropped}}
John, Does t(apply(z, 1, sort, na.last=TRUE)) do what you want? Patrick Burns patrick at burns-stat.com +44 (0)20 8525 0696 http://www.burns-stat.com (home of S Poetry and "A Guide for the Unwilling S User") john.gavin at ubs.com wrote:>Hi, > >Given a matrix like > >(z <- matrix(c( >1, 1, NA, NA, NA, NA, >1, NA, 1, NA, 1, NA, >NA, 1, 1, 1, NA, NA), ncol = 3)) > > [,1] [,2] [,3] >[1,] 1 1 NA >[2,] 1 NA 1 >[3,] NA 1 1 >[4,] NA NA 1 >[5,] NA 1 NA >[6,] NA NA NA > >is there a vectorised way to produce the output like > > [,1] [,2] [,3] >[1,] 1 1 NA >[2,] 1 NA 1 >[3,] 1 1 NA >[4,] 1 NA NA >[5,] 1 NA NA >[6,] NA NA NA > >That is, given an n by m matrix, and going row by row, >if the first non-NA element is in column k >I want to move elements in columns from k to m >to columns 1 to m-k+1 with NAs filling in from >m-k+2 to m. > > > >>version >> >> > _ >platform i386-pc-mingw32 >arch i386 >os mingw32 >system i386, mingw32 >status >major 2 >minor 2.1 >year 2005 >month 12 >day 20 >svn rev 36812 >language R > >Regards, > >John. > >John Gavin <john.gavin at ubs.com>, >Quantitative Risk Control, >UBS Investment Bank, 6th floor, >100 Liverpool St., London EC2M 2RH, UK. >Phone +44 (0) 207 567 4289 >Fax +44 (0) 207 568 5352 > >Visit our website at http://www.ubs.com > >This message contains confidential information and is intend...{{dropped}} > >______________________________________________ >R-help at 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 > > > > >
john.gavin@ubs.com
2006-Feb-28 09:31 UTC
[R] elements in each row of a matrix to the left.
Hi Patrick/Jeff,> Does > > t(apply(z, 1, sort, na.last=TRUE)) > > do what you want?Not quite. t(apply(z, 1, sort, na.last=TRUE)) [,1] [,2] [,3] [1,] 1 1 NA [2,] 1 1 NA [3,] 1 1 NA [4,] 1 NA NA [5,] 1 NA NA [6,] NA NA NA Row 2 is the problem. I dont want to move all NAs to the end of each row. I just want to move all of the NAs before the first non-NA element, if any, to the end of each row. So in my example, rows 1 and 2 should remain unchanged. What I have got at the moment is ugly shiftLeft <- function(z) { x <- as.data.frame(t(z)) # work with cols not rows. ans <- lapply(x, function(xx) { # get indices of first and last non-NA element ind <- which(!is.na(xx)) ind <- ind[c(1, length(ind))] # if all NAs or if first element is non-NA do no work if (any(is.na(ind)) || ind[1] == 1) xx else { temp <- numeric(length(xx)) ; temp[] <- NA # move elements in posns ind[1] to ind[2] to the start temp[1:(ind[2]-ind[1]+1)] <- xx[ind[1]:ind[2]] temp } # if }) # lapply ans <- as.matrix(data.frame(ans)) dimnames(ans) <- dimnames(z) t(ans) }> z ; shiftLeft(z)[,1] [,2] [,3] [1,] 1 1 NA [2,] 1 NA 1 [3,] NA 1 1 [4,] NA NA 1 [5,] NA 1 NA [6,] NA NA NA [,1] [,2] [,3] [1,] 1 1 NA [2,] 1 NA 1 [3,] 1 1 NA [4,] 1 NA NA [5,] 1 NA NA [6,] NA NA NA I feel that there is probably a shorter vectorised way to do this. In general, I have matrices (z) with several thousand rows and and few hundred columns so vectorisation would help. Regards, John.> -----Original Message----- > From: Patrick Burns [mailto:pburns at pburns.seanet.com] > Sent: 27 February 2006 19:55 > To: Gavin, John > Cc: r-help at stat.math.ethz.ch > Subject: Re: [R] elements in each row of a matrix to the left. > > John, > > Does > > t(apply(z, 1, sort, na.last=TRUE)) > > do what you want? > > > Patrick Burns > patrick at burns-stat.com > +44 (0)20 8525 0696 > http://www.burns-stat.com > (home of S Poetry and "A Guide for the Unwilling S User") > > john.gavin at ubs.com wrote: > > >Hi, > > > >Given a matrix like > > > >(z <- matrix(c( > >1, 1, NA, NA, NA, NA, > >1, NA, 1, NA, 1, NA, > >NA, 1, 1, 1, NA, NA), ncol = 3)) > > > > [,1] [,2] [,3] > >[1,] 1 1 NA > >[2,] 1 NA 1 > >[3,] NA 1 1 > >[4,] NA NA 1 > >[5,] NA 1 NA > >[6,] NA NA NA > > > >is there a vectorised way to produce the output like > > > > [,1] [,2] [,3] > >[1,] 1 1 NA > >[2,] 1 NA 1 > >[3,] 1 1 NA > >[4,] 1 NA NA > >[5,] 1 NA NA > >[6,] NA NA NA > > > >That is, given an n by m matrix, and going row by row, > >if the first non-NA element is in column k > >I want to move elements in columns from k to m > >to columns 1 to m-k+1 with NAs filling in from > >m-k+2 to m. > > > > > > > >>version > >> > >> > > _ > >platform i386-pc-mingw32 > >arch i386 > >os mingw32 > >system i386, mingw32 > >status > >major 2 > >minor 2.1 > >year 2005 > >month 12 > >day 20 > >svn rev 36812 > >language R > > > >Regards, > > > >John. > > > >John Gavin <john.gavin at ubs.com>, > >Quantitative Risk Control, > >UBS Investment Bank, 6th floor, > >100 Liverpool St., London EC2M 2RH, UK. > >Phone +44 (0) 207 567 4289 > >Fax +44 (0) 207 568 5352 > > > >Visit our website at http://www.ubs.com > > > >This message contains confidential information and is > intend...{{dropped}} > > > >______________________________________________ > >R-help at 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> > > > >Visit our website at http://www.ubs.com This message contains confidential information and is intend...{{dropped}}
Hi not a complete solution but z.f<-matrix(z%in%1, ncol=3) gives you a matrix of logicals and apply(apply(z.f*1, 1,cumsum),2,function(x) sum(x==0)) [1] 0 0 1 2 1 3 shall give you number of values to drop from each row. Then you maybe could use it to manipulate your z matrix. HTH Petr On 28 Feb 2006 at 9:31, john.gavin at ubs.com wrote: Date sent: Tue, 28 Feb 2006 09:31:51 -0000 From: <john.gavin at ubs.com> To: <pburns at pburns.seanet.com>, <Jeff.Laake at noaa.gov> Copies to: r-help at stat.math.ethz.ch Subject: Re: [R] elements in each row of a matrix to the left.> Hi Patrick/Jeff, > > > Does > > > > t(apply(z, 1, sort, na.last=TRUE)) > > > > do what you want? > > Not quite. > > t(apply(z, 1, sort, na.last=TRUE)) > > [,1] [,2] [,3] > [1,] 1 1 NA > [2,] 1 1 NA > [3,] 1 1 NA > [4,] 1 NA NA > [5,] 1 NA NA > [6,] NA NA NA > > Row 2 is the problem. > > I dont want to move all NAs to the end of each row. > I just want to move all of the NAs before the first non-NA element, if > any, to the end of each row. So in my example, rows 1 and 2 should > remain unchanged. > > What I have got at the moment is ugly > > shiftLeft <- function(z) > { x <- as.data.frame(t(z)) # work with cols not rows. > ans <- lapply(x, function(xx) > { # get indices of first and last non-NA element > ind <- which(!is.na(xx)) > ind <- ind[c(1, length(ind))] > # if all NAs or if first element is non-NA do no work > if (any(is.na(ind)) || ind[1] == 1) xx else > { temp <- numeric(length(xx)) ; temp[] <- NA > # move elements in posns ind[1] to ind[2] to the start > temp[1:(ind[2]-ind[1]+1)] <- xx[ind[1]:ind[2]] > temp > } # if > }) # lapply > ans <- as.matrix(data.frame(ans)) > dimnames(ans) <- dimnames(z) > t(ans) > } > > > z ; shiftLeft(z) > [,1] [,2] [,3] > [1,] 1 1 NA > [2,] 1 NA 1 > [3,] NA 1 1 > [4,] NA NA 1 > [5,] NA 1 NA > [6,] NA NA NA > [,1] [,2] [,3] > [1,] 1 1 NA > [2,] 1 NA 1 > [3,] 1 1 NA > [4,] 1 NA NA > [5,] 1 NA NA > [6,] NA NA NA > > I feel that there is probably a shorter vectorised way to do this. In > general, I have matrices (z) with several thousand rows and and few > hundred columns so vectorisation would help. > > Regards, > > John. > > > > -----Original Message----- > > From: Patrick Burns [mailto:pburns at pburns.seanet.com] > > Sent: 27 February 2006 19:55 > > To: Gavin, John > > Cc: r-help at stat.math.ethz.ch > > Subject: Re: [R] elements in each row of a matrix to the left. > > > > John, > > > > Does > > > > t(apply(z, 1, sort, na.last=TRUE)) > > > > do what you want? > > > > > > Patrick Burns > > patrick at burns-stat.com > > +44 (0)20 8525 0696 > > http://www.burns-stat.com > > (home of S Poetry and "A Guide for the Unwilling S User") > > > > john.gavin at ubs.com wrote: > > > > >Hi, > > > > > >Given a matrix like > > > > > >(z <- matrix(c( > > >1, 1, NA, NA, NA, NA, > > >1, NA, 1, NA, 1, NA, > > >NA, 1, 1, 1, NA, NA), ncol = 3)) > > > > > > [,1] [,2] [,3] > > >[1,] 1 1 NA > > >[2,] 1 NA 1 > > >[3,] NA 1 1 > > >[4,] NA NA 1 > > >[5,] NA 1 NA > > >[6,] NA NA NA > > > > > >is there a vectorised way to produce the output like > > > > > > [,1] [,2] [,3] > > >[1,] 1 1 NA > > >[2,] 1 NA 1 > > >[3,] 1 1 NA > > >[4,] 1 NA NA > > >[5,] 1 NA NA > > >[6,] NA NA NA > > > > > >That is, given an n by m matrix, and going row by row, > > >if the first non-NA element is in column k > > >I want to move elements in columns from k to m > > >to columns 1 to m-k+1 with NAs filling in from > > >m-k+2 to m. > > > > > > > > > > > >>version > > >> > > >> > > > _ > > >platform i386-pc-mingw32 > > >arch i386 > > >os mingw32 > > >system i386, mingw32 > > >status > > >major 2 > > >minor 2.1 > > >year 2005 > > >month 12 > > >day 20 > > >svn rev 36812 > > >language R > > > > > >Regards, > > > > > >John. > > > > > >John Gavin <john.gavin at ubs.com>, > > >Quantitative Risk Control, > > >UBS Investment Bank, 6th floor, > > >100 Liverpool St., London EC2M 2RH, UK. > > >Phone +44 (0) 207 567 4289 > > >Fax +44 (0) 207 568 5352 > > > > > >Visit our website at http://www.ubs.com > > > > > >This message contains confidential information and is > > intend...{{dropped}} > > > > > >______________________________________________ > > >R-help at 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 > > > > > > > > > > > > > Visit our website at http://www.ubs.com > > This message contains confidential information and is\ > i...{{dropped}}
Okay, I think this does the requested operation: > single.shift function (x) { r <- rle(is.na(x)) if(!r$values[1]) return(x) num <- r$length[1] c(x[-1:-num], rep(NA, num)) } > t(apply(z, 1, single.shift)) john.gavin at ubs.com wrote:>Hi Patrick/Jeff, > > > >>Does >> >>t(apply(z, 1, sort, na.last=TRUE)) >> >>do what you want? >> >> > >Not quite. > >t(apply(z, 1, sort, na.last=TRUE)) > > [,1] [,2] [,3] >[1,] 1 1 NA >[2,] 1 1 NA >[3,] 1 1 NA >[4,] 1 NA NA >[5,] 1 NA NA >[6,] NA NA NA > >Row 2 is the problem. > >I dont want to move all NAs to the end of each row. >I just want to move all of the NAs before the first non-NA element, >if any, to the end of each row. >So in my example, rows 1 and 2 should remain unchanged. > >What I have got at the moment is ugly > >shiftLeft <- function(z) >{ x <- as.data.frame(t(z)) # work with cols not rows. > ans <- lapply(x, function(xx) > { # get indices of first and last non-NA element > ind <- which(!is.na(xx)) > ind <- ind[c(1, length(ind))] > # if all NAs or if first element is non-NA do no work > if (any(is.na(ind)) || ind[1] == 1) xx else > { temp <- numeric(length(xx)) ; temp[] <- NA > # move elements in posns ind[1] to ind[2] to the start > temp[1:(ind[2]-ind[1]+1)] <- xx[ind[1]:ind[2]] > temp > } # if > }) # lapply > ans <- as.matrix(data.frame(ans)) > dimnames(ans) <- dimnames(z) > t(ans) >} > > > >>z ; shiftLeft(z) >> >> > [,1] [,2] [,3] >[1,] 1 1 NA >[2,] 1 NA 1 >[3,] NA 1 1 >[4,] NA NA 1 >[5,] NA 1 NA >[6,] NA NA NA > [,1] [,2] [,3] >[1,] 1 1 NA >[2,] 1 NA 1 >[3,] 1 1 NA >[4,] 1 NA NA >[5,] 1 NA NA >[6,] NA NA NA > >I feel that there is probably a shorter vectorised way to do this. >In general, I have matrices (z) with several thousand rows and >and few hundred columns so vectorisation would help. > >Regards, > >John. > > > > >>-----Original Message----- >>From: Patrick Burns [mailto:pburns at pburns.seanet.com] >>Sent: 27 February 2006 19:55 >>To: Gavin, John >>Cc: r-help at stat.math.ethz.ch >>Subject: Re: [R] elements in each row of a matrix to the left. >> >>John, >> >>Does >> >>t(apply(z, 1, sort, na.last=TRUE)) >> >>do what you want? >> >> >>Patrick Burns >>patrick at burns-stat.com >>+44 (0)20 8525 0696 >>http://www.burns-stat.com >>(home of S Poetry and "A Guide for the Unwilling S User") >> >>john.gavin at ubs.com wrote: >> >> >> >>>Hi, >>> >>>Given a matrix like >>> >>>(z <- matrix(c( >>>1, 1, NA, NA, NA, NA, >>>1, NA, 1, NA, 1, NA, >>>NA, 1, 1, 1, NA, NA), ncol = 3)) >>> >>> [,1] [,2] [,3] >>>[1,] 1 1 NA >>>[2,] 1 NA 1 >>>[3,] NA 1 1 >>>[4,] NA NA 1 >>>[5,] NA 1 NA >>>[6,] NA NA NA >>> >>>is there a vectorised way to produce the output like >>> >>> [,1] [,2] [,3] >>>[1,] 1 1 NA >>>[2,] 1 NA 1 >>>[3,] 1 1 NA >>>[4,] 1 NA NA >>>[5,] 1 NA NA >>>[6,] NA NA NA >>> >>>That is, given an n by m matrix, and going row by row, >>>if the first non-NA element is in column k >>>I want to move elements in columns from k to m >>>to columns 1 to m-k+1 with NAs filling in from >>>m-k+2 to m. >>> >>> >>> >>> >>> >>>>version >>>> >>>> >>>> >>>> >>> _ >>>platform i386-pc-mingw32 >>>arch i386 >>>os mingw32 >>>system i386, mingw32 >>>status >>>major 2 >>>minor 2.1 >>>year 2005 >>>month 12 >>>day 20 >>>svn rev 36812 >>>language R >>> >>>Regards, >>> >>>John. >>> >>>John Gavin <john.gavin at ubs.com>, >>>Quantitative Risk Control, >>>UBS Investment Bank, 6th floor, >>>100 Liverpool St., London EC2M 2RH, UK. >>>Phone +44 (0) 207 567 4289 >>>Fax +44 (0) 207 568 5352 >>> >>>Visit our website at http://www.ubs.com >>> >>>This message contains confidential information and is >>> >>> >>intend...{{dropped}} >> >> >>>______________________________________________ >>>R-help at 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 > > >> >> >> >> >> > > >Visit our website at http://www.ubs.com > >This message contains confidential information and is intended only >for the individual named. If you are not the named addressee you >should not disseminate, distribute or copy this e-mail. Please >notify the sender immediately by e-mail if you have received this >e-mail by mistake and delete this e-mail from your system. > >E-mail transmission cannot be guaranteed to be secure or error-free >as information could be intercepted, corrupted, lost, destroyed, >arrive late or incomplete, or contain viruses. The sender therefore >does not accept liability for any errors or omissions in the contents >of this message which arise as a result of e-mail transmission. If >verification is required please request a hard-copy version. This >message is provided for informational purposes and should not be >construed as a solicitation or offer to buy or sell any securities or >related financial instruments. > > > > > >
john.gavin@ubs.com
2006-Feb-28 11:10 UTC
[R] elements in each row of a matrix to the left.
Hi Patrick, Yes, that works. Thanks for your time. Regards, John.> -----Original Message----- > From: Patrick Burns [mailto:pburns at pburns.seanet.com] > Sent: 28 February 2006 10:28 > To: Gavin, John > Cc: Jeff.Laake at noaa.gov; r-help at stat.math.ethz.ch > Subject: Re: [R] elements in each row of a matrix to the left. > > > Okay, I think this does the requested operation: > > > single.shift > function (x) > { > r <- rle(is.na(x)) > if(!r$values[1]) return(x) > num <- r$length[1] > c(x[-1:-num], rep(NA, num)) > } > > t(apply(z, 1, single.shift)) > > > john.gavin at ubs.com wrote: > > >Hi Patrick/Jeff, > > > > > > > >>Does > >> > >>t(apply(z, 1, sort, na.last=TRUE)) > >> > >>do what you want? > >> > >> > > > >Not quite. > > > >t(apply(z, 1, sort, na.last=TRUE)) > > > > [,1] [,2] [,3] > >[1,] 1 1 NA > >[2,] 1 1 NA > >[3,] 1 1 NA > >[4,] 1 NA NA > >[5,] 1 NA NA > >[6,] NA NA NA > > > >Row 2 is the problem. > > > >I dont want to move all NAs to the end of each row. > >I just want to move all of the NAs before the first non-NA element, > >if any, to the end of each row. > >So in my example, rows 1 and 2 should remain unchanged. > > > >What I have got at the moment is ugly > > > >shiftLeft <- function(z) > >{ x <- as.data.frame(t(z)) # work with cols not rows. > > ans <- lapply(x, function(xx) > > { # get indices of first and last non-NA element > > ind <- which(!is.na(xx)) > > ind <- ind[c(1, length(ind))] > > # if all NAs or if first element is non-NA do no work > > if (any(is.na(ind)) || ind[1] == 1) xx else > > { temp <- numeric(length(xx)) ; temp[] <- NA > > # move elements in posns ind[1] to ind[2] to the start > > temp[1:(ind[2]-ind[1]+1)] <- xx[ind[1]:ind[2]] > > temp > > } # if > > }) # lapply > > ans <- as.matrix(data.frame(ans)) > > dimnames(ans) <- dimnames(z) > > t(ans) > >} > > > > > > > >>z ; shiftLeft(z) > >> > >> > > [,1] [,2] [,3] > >[1,] 1 1 NA > >[2,] 1 NA 1 > >[3,] NA 1 1 > >[4,] NA NA 1 > >[5,] NA 1 NA > >[6,] NA NA NA > > [,1] [,2] [,3] > >[1,] 1 1 NA > >[2,] 1 NA 1 > >[3,] 1 1 NA > >[4,] 1 NA NA > >[5,] 1 NA NA > >[6,] NA NA NA > > > >I feel that there is probably a shorter vectorised way to do this. > >In general, I have matrices (z) with several thousand rows and > >and few hundred columns so vectorisation would help. > > > >Regards, > > > >John. > > > > > > > > > >>-----Original Message----- > >>From: Patrick Burns [mailto:pburns at pburns.seanet.com] > >>Sent: 27 February 2006 19:55 > >>To: Gavin, John > >>Cc: r-help at stat.math.ethz.ch > >>Subject: Re: [R] elements in each row of a matrix to the left. > >> > >>John, > >> > >>Does > >> > >>t(apply(z, 1, sort, na.last=TRUE)) > >> > >>do what you want? > >> > >> > >>Patrick Burns > >>patrick at burns-stat.com > >>+44 (0)20 8525 0696 > >>http://www.burns-stat.com > >>(home of S Poetry and "A Guide for the Unwilling S User") > >> > >>john.gavin at ubs.com wrote: > >> > >> > >> > >>>Hi, > >>> > >>>Given a matrix like > >>> > >>>(z <- matrix(c( > >>>1, 1, NA, NA, NA, NA, > >>>1, NA, 1, NA, 1, NA, > >>>NA, 1, 1, 1, NA, NA), ncol = 3)) > >>> > >>> [,1] [,2] [,3] > >>>[1,] 1 1 NA > >>>[2,] 1 NA 1 > >>>[3,] NA 1 1 > >>>[4,] NA NA 1 > >>>[5,] NA 1 NA > >>>[6,] NA NA NA > >>> > >>>is there a vectorised way to produce the output like > >>> > >>> [,1] [,2] [,3] > >>>[1,] 1 1 NA > >>>[2,] 1 NA 1 > >>>[3,] 1 1 NA > >>>[4,] 1 NA NA > >>>[5,] 1 NA NA > >>>[6,] NA NA NA > >>> > >>>That is, given an n by m matrix, and going row by row, > >>>if the first non-NA element is in column k > >>>I want to move elements in columns from k to m > >>>to columns 1 to m-k+1 with NAs filling in from > >>>m-k+2 to m. > >>> > >>> > >>> > >>> > >>> > >>>>version > >>>> > >>>> > >>>> > >>>> > >>> _ > >>>platform i386-pc-mingw32 > >>>arch i386 > >>>os mingw32 > >>>system i386, mingw32 > >>>status > >>>major 2 > >>>minor 2.1 > >>>year 2005 > >>>month 12 > >>>day 20 > >>>svn rev 36812 > >>>language R > >>> > >>>Regards, > >>> > >>>John. > >>> > >>>John Gavin <john.gavin at ubs.com>, > >>>Quantitative Risk Control, > >>>UBS Investment Bank, 6th floor, > >>>100 Liverpool St., London EC2M 2RH, UK. > >>>Phone +44 (0) 207 567 4289 > >>>Fax +44 (0) 207 568 5352 > >>> > >>>Visit our website at http://www.ubs.com > >>> > >>>This message contains confidential information and is > >>> > >>> > >>intend...{{dropped}} > >> > >> > >>>______________________________________________ > >>>R-help at 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 > > > > > >> > >> > >> > >> > >> > > > > > >Visit our website at http://www.ubs.com > > > >This message contains confidential information and is intended only > >for the individual named. If you are not the named addressee you > >should not disseminate, distribute or copy this e-mail. Please > >notify the sender immediately by e-mail if you have received this > >e-mail by mistake and delete this e-mail from your system. > > > >E-mail transmission cannot be guaranteed to be secure or error-free > >as information could be intercepted, corrupted, lost, destroyed, > >arrive late or incomplete, or contain viruses. The sender therefore > >does not accept liability for any errors or omissions in the > contents > >of this message which arise as a result of e-mail transmission. If > >verification is required please request a hard-copy version. This > >message is provided for informational purposes and should not be > >construed as a solicitation or offer to buy or sell any > securities or > >related financial instruments. > > > > > > > > > > > > > >Visit our website at http://www.ubs.com This message contains confidential information and is intend...{{dropped}}