Hello,
I would like to define an arbitrary function of an arbitrary number of
variables, for example, for 2 variables:
func2 <- function(time, temp) time + temp
I'd like to keep variable names that have a meaning in the problem (time and
temperature above).
If I have a vector of values for these variables, for example in the 2-d case,
c(10, 121), I'd like to apply my function (in this case func2) and obtain
the result. Conceptually, something like,
func2(c(10,121))
becomes
func2(10,121)
Is there a simple way to accomplish this, for an arbitrary number of variables?
I'd like something that would simply work from the definition of the
function. If that is possible.
Thanks,
Steve Kennedy
CONFIDENTIALITY NOTICE: This e-mail message, including a...{{dropped:11}}
Your architecture has a bad smell to me. For one thing you are mixing different units in the same vector but should be putting multiple instances of the same variable into one vector. Lists of vectors (data frames) are typically used when multiple variables need to be grouped. Another problem is that you are constraining the names of the variables you pass to the function to be named the same as they are inside the function. This really limits your use of those functions. There really is too much abstraction going on here. -- Sent from my phone. Please excuse my brevity. On September 9, 2016 12:44:52 PM PDT, Steve Kennedy <SKennedy at AnikaTherapeutics.com> wrote:>Hello, > >I would like to define an arbitrary function of an arbitrary number of >variables, for example, for 2 variables: > >func2 <- function(time, temp) time + temp > >I'd like to keep variable names that have a meaning in the problem >(time and temperature above). > >If I have a vector of values for these variables, for example in the >2-d case, c(10, 121), I'd like to apply my function (in this case >func2) and obtain the result. Conceptually, something like, > >func2(c(10,121)) > >becomes > >func2(10,121) > >Is there a simple way to accomplish this, for an arbitrary number of >variables? I'd like something that would simply work from the >definition of the function. If that is possible. > >Thanks, > >Steve Kennedy > >CONFIDENTIALITY NOTICE: This e-mail message, including >a...{{dropped:11}} > >______________________________________________ >R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see >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.
Not sure I understand what you really want, if you have found ways to
accomplish what you want but are not satisfied with them. That is one
reason why keeping the mailing list involved (by reply-all) is good for
you. From my end, I don't do one-on-one support online, and may not be
able to carry on a thread to the end if I get busy.
Your concept of a generalized outer function sounds to me like:
myfunc <- function( A, B, C ) {
A * B + C
}
gouter <- function( FUN, ... ) {
args <- list( ... )
DF <- do.call( expand.grid, args )
array( data = do.call( FUN, DF )
, dim = sapply( args, FUN=length )
, dimnames = args
)
}
gouter( myfunc, A = 1:3, B=2:6, C=3:4 )
# , , C = 3
#
# B
# A 2 3 4 5 6
# 1 5 6 7 8 9
# 2 7 9 11 13 15
# 3 9 12 15 18 21
#
# , , C = 4
#
# B
# A 2 3 4 5 6
# 1 6 7 8 9 10
# 2 8 10 12 14 16
# 3 10 13 16 19 22
I generally just tack on columns to the expand.grid result... I almost
never have a need for multidimensional arrays.
On Fri, 9 Sep 2016, Steve Kennedy wrote:
> Hello,
>
> Abstraction is what I want. I'm actually looking to do something more
> complicated. The functions do.call, and as.list get me most of the way
> there, but there is something I'm missing ...
>
> My eventual goal is to produce a multi-dimensional version of
'outer'.
> Like my.outer(func, a_vec, b_vec, c_vec, ..), where the function of the
> variables 'a', 'b', 'c', etc. would be applied to
the vectors from the
> outer product of the vectors of values for each variable.
>
> I wanted to use expand.grid (does require reshaping the output). Using
> temps = c(40,50,60) and times = c(1:5), this doesn't quite seem to
work:
>
> apply(expand.grid(temps,times), 1, function(a) do.call(func2,
as.list(a)))
>
> although this does work:
>
> do.call(func2, as.list(c(10, 121)))
>
> And, this also works:
>
> apply(expand.grid(temps,times), 1, function(a) do.call("+",
as.list(a)))
>
> There is some subtlety here I don't understand.
>
> Thanks,
>
> Steve
>
> -----Original Message-----
> From: Jeff Newmiller [mailto:jdnewmil at dcn.davis.ca.us]
> Sent: Friday, September 09, 2016 5:39 PM
> To: Steve Kennedy; r-help at r-project.org
> Subject: Re: [R] Apply a multi-variable function to a vector
>
> Your architecture has a bad smell to me. For one thing you are mixing
> different units in the same vector but should be putting multiple
> instances of the same variable into one vector. Lists of vectors (data
> frames) are typically used when multiple variables need to be grouped.
>
> Another problem is that you are constraining the names of the variables
> you pass to the function to be named the same as they are inside the
> function. This really limits your use of those functions.
>
> There really is too much abstraction going on here.
> --
> Sent from my phone. Please excuse my brevity.
>
> On September 9, 2016 12:44:52 PM PDT, Steve Kennedy <SKennedy at
AnikaTherapeutics.com> wrote:
>> Hello,
>>
>> I would like to define an arbitrary function of an arbitrary number of
>> variables, for example, for 2 variables:
>>
>> func2 <- function(time, temp) time + temp
>>
>> I'd like to keep variable names that have a meaning in the problem
>> (time and temperature above).
>>
>> If I have a vector of values for these variables, for example in the
>> 2-d case, c(10, 121), I'd like to apply my function (in this case
>> func2) and obtain the result. Conceptually, something like,
>>
>> func2(c(10,121))
>>
>> becomes
>>
>> func2(10,121)
>>
>> Is there a simple way to accomplish this, for an arbitrary number of
>> variables? I'd like something that would simply work from the
>> definition of the function. If that is possible.
>>
>> Thanks,
>>
>> Steve Kennedy
>>
>> CONFIDENTIALITY NOTICE: This e-mail message, including
>> a...{{dropped:11}}
>>
>> ______________________________________________
>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>> http://cp.mcafee.com/d/k-Kr6x0g6hASyMepov78FI6XCQXLK3AnCrFCQXLK3AnCnAPq
>> tTT1ObPdSjqaby8VMsUyYrEl-4fgb0HoiaXcDYtmZKsHkVsTI95tCj-eHuTelGsKrpYwCOw
>> evW_ccnpuKNRXBQQT1TfcFzCnTeEyCJtdmXP_axVZicHs3jq9JcTvANOoVcsCej76XCOsVH
>> kiPajSvvcCatoDwCHIcfBisEeRO9sDVWNIhgxVxmhUagJ3AdcOFRJVKxJBxdcS2_id41Fr1
>> pFtd40wIIumd46Cy1lI-syVDoOQwvVEwtrxqsGMd44WCy3jh0p-QWNdLECZzL1
>> PLEASE do read the posting guide
>> http://cp.mcafee.com/d/5fHCMUp418SyMepov78FI6XCQXLK3AnCrFCQXLK3AnCnAPqt
>> TT1ObPdSjqaby8VMsUyYrEl-4fgb0HoiaXcDYtmZKsHkVsTI95tCj-eHuTelGsKrpYwCOwe
>> vW_ccnpuKNRXBQQT1TfcFzCnTeEyCJtdmXP_axVZicHs3jqpJcTvANOoVcsCej76XCM0gbb
>> HhG8_qv00smHisE4iV5Ki7Y3zoyx3P2IzMkxq78qpBjHrPt3rb2qpI5-Aq83iS2PiWq811p
>> oYIq8dd42HpYV5PeNBF0_Ph0WT2QVlwq89Rd46Cy0PZFRyrvhd_2KV
>> and provide commented, minimal, self-contained, reproducible code.
>
> CONFIDENTIALITY NOTICE: This e-mail message, including any attachments,
contains information belonging to Anika Therapeutics, Inc. and is for the sole
use of the intended recipient(s) and may contain confidential, proprietary,
copyrighted and privileged information. Any unauthorized review, use,
disclosure, distribution or copying is strictly prohibited. If you are not the
intended recipient, please contact the sender by reply e-mail and destroy all
copies of the original message immediately.
>
---------------------------------------------------------------------------
Jeff Newmiller The ..... ..... Go Live...
DCN:<jdnewmil at dcn.davis.ca.us> Basics: ##.#. ##.#. Live
Go...
Live: OO#.. Dead: OO#.. Playing
Research Engineer (Solar/Batteries O.O#. #.O#. with
/Software/Embedded Controllers) .OO#. .OO#. rocks...1k
Thanks. I have gotten some replies. One problem was that I was not passing the names of the vectors to expand.grid. I didn't think I had to do that and that caused problems with do.call. I wanted to just define the vectors of variables values, the function, func, and then pass that to my.outer. I was using A <- c( ... ) Then, expand.grid(A, etc.) with do.call and as.list and without the names use in 'fund', there was an error. I didn't think it would matter what names I used in defining the function. Thanks very much. I think I have some good alternatives that all work. Steve On Sat, Sep 10, 2016 at 1:29 AM, Jeff Newmiller <jdnewmil at dcn.davis.ca.us> wrote:> Not sure I understand what you really want, if you have found ways to > accomplish what you want but are not satisfied with them. That is one > reason why keeping the mailing list involved (by reply-all) is good for > you. From my end, I don't do one-on-one support online, and may not be able > to carry on a thread to the end if I get busy. > > Your concept of a generalized outer function sounds to me like: > > myfunc <- function( A, B, C ) { > A * B + C > } > > gouter <- function( FUN, ... ) { > args <- list( ... ) > DF <- do.call( expand.grid, args ) > array( data = do.call( FUN, DF ) > , dim = sapply( args, FUN=length ) > , dimnames = args > ) > } > > gouter( myfunc, A = 1:3, B=2:6, C=3:4 ) > # , , C = 3 > # > # B > # A 2 3 4 5 6 > # 1 5 6 7 8 9 > # 2 7 9 11 13 15 > # 3 9 12 15 18 21 > # > # , , C = 4 > # > # B > # A 2 3 4 5 6 > # 1 6 7 8 9 10 > # 2 8 10 12 14 16 > # 3 10 13 16 19 22 > > I generally just tack on columns to the expand.grid result... I almost > never have a need for multidimensional arrays. > > On Fri, 9 Sep 2016, Steve Kennedy wrote: > > Hello, >> >> Abstraction is what I want. I'm actually looking to do something more >> complicated. The functions do.call, and as.list get me most of the way >> there, but there is something I'm missing ... >> >> My eventual goal is to produce a multi-dimensional version of 'outer'. >> Like my.outer(func, a_vec, b_vec, c_vec, ..), where the function of the >> variables 'a', 'b', 'c', etc. would be applied to the vectors from the >> outer product of the vectors of values for each variable. >> >> I wanted to use expand.grid (does require reshaping the output). Using >> temps = c(40,50,60) and times = c(1:5), this doesn't quite seem to work: >> >> apply(expand.grid(temps,times), 1, function(a) do.call(func2, >> as.list(a))) >> >> although this does work: >> >> do.call(func2, as.list(c(10, 121))) >> >> And, this also works: >> >> apply(expand.grid(temps,times), 1, function(a) do.call("+", as.list(a))) >> >> There is some subtlety here I don't understand. >> >> Thanks, >> >> Steve >> >> -----Original Message----- >> From: Jeff Newmiller [mailto:jdnewmil at dcn.davis.ca.us] >> Sent: Friday, September 09, 2016 5:39 PM >> To: Steve Kennedy; r-help at r-project.org >> Subject: Re: [R] Apply a multi-variable function to a vector >> >> Your architecture has a bad smell to me. For one thing you are mixing >> different units in the same vector but should be putting multiple instances >> of the same variable into one vector. Lists of vectors (data frames) are >> typically used when multiple variables need to be grouped. >> >> Another problem is that you are constraining the names of the variables >> you pass to the function to be named the same as they are inside the >> function. This really limits your use of those functions. >> >> There really is too much abstraction going on here. >> -- >> Sent from my phone. Please excuse my brevity. >> >> On September 9, 2016 12:44:52 PM PDT, Steve Kennedy >> <SKennedy at AnikaTherapeutics.com> wrote: >> >>> Hello, >>> >>> I would like to define an arbitrary function of an arbitrary number of >>> variables, for example, for 2 variables: >>> >>> func2 <- function(time, temp) time + temp >>> >>> I'd like to keep variable names that have a meaning in the problem >>> (time and temperature above). >>> >>> If I have a vector of values for these variables, for example in the >>> 2-d case, c(10, 121), I'd like to apply my function (in this case >>> func2) and obtain the result. Conceptually, something like, >>> >>> func2(c(10,121)) >>> >>> becomes >>> >>> func2(10,121) >>> >>> Is there a simple way to accomplish this, for an arbitrary number of >>> variables? I'd like something that would simply work from the >>> definition of the function. If that is possible. >>> >>> Thanks, >>> >>> Steve Kennedy >>> >>> CONFIDENTIALITY NOTICE: This e-mail message, including >>> a...{{dropped:11}} >>> >>> ______________________________________________ >>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see >>> http://cp.mcafee.com/d/k-Kr6x0g6hASyMepov78FI6XCQXLK3AnCrFCQXLK3AnCnAPq >>> tTT1ObPdSjqaby8VMsUyYrEl-4fgb0HoiaXcDYtmZKsHkVsTI95tCj-eHuTelGsKrpYwCOw >>> evW_ccnpuKNRXBQQT1TfcFzCnTeEyCJtdmXP_axVZicHs3jq9JcTvANOoVcsCej76XCOsVH >>> kiPajSvvcCatoDwCHIcfBisEeRO9sDVWNIhgxVxmhUagJ3AdcOFRJVKxJBxdcS2_id41Fr1 >>> pFtd40wIIumd46Cy1lI-syVDoOQwvVEwtrxqsGMd44WCy3jh0p-QWNdLECZzL1 >>> PLEASE do read the posting guide >>> http://cp.mcafee.com/d/5fHCMUp418SyMepov78FI6XCQXLK3AnCrFCQXLK3AnCnAPqt >>> TT1ObPdSjqaby8VMsUyYrEl-4fgb0HoiaXcDYtmZKsHkVsTI95tCj-eHuTelGsKrpYwCOwe >>> vW_ccnpuKNRXBQQT1TfcFzCnTeEyCJtdmXP_axVZicHs3jqpJcTvANOoVcsCej76XCM0gbb >>> HhG8_qv00smHisE4iV5Ki7Y3zoyx3P2IzMkxq78qpBjHrPt3rb2qpI5-Aq83iS2PiWq811p >>> oYIq8dd42HpYV5PeNBF0_Ph0WT2QVlwq89Rd46Cy0PZFRyrvhd_2KV >>> and provide commented, minimal, self-contained, reproducible code. >>> >> >> CONFIDENTIALITY NOTICE: This e-mail message, including any attachments, >> contains information belonging to Anika Therapeutics, Inc. and is for the >> sole use of the intended recipient(s) and may contain confidential, >> proprietary, copyrighted and privileged information. Any unauthorized >> review, use, disclosure, distribution or copying is strictly prohibited. If >> you are not the intended recipient, please contact the sender by reply >> e-mail and destroy all copies of the original message immediately. >> >> > ------------------------------------------------------------ > --------------- > Jeff Newmiller The ..... ..... Go Live... > DCN:<jdnewmil at dcn.davis.ca.us> Basics: ##.#. ##.#. Live > Go... > Live: OO#.. Dead: OO#.. Playing > Research Engineer (Solar/Batteries O.O#. #.O#. with > /Software/Embedded Controllers) .OO#. .OO#. rocks...1k > ------------------------------------------------------------ > --------------- >[[alternative HTML version deleted]]
Hello Jeff,
I kept fooling with this, and also looking around the web and I actually
found something on stackoverflow, which does what I had in mind. You
mentioned that you would rarely use someting like this, but the link is:
http://stackoverflow.com/questions/6192848/how-to-generalize-outer-to-n-dimensions
This may not be efficient, but what I like is that you can name the vectors
of variable values anything, as well as the names of the variables in the
arbitrary function. It is not sensitive to the 'names' of anything.
Here is the code. I used the function you defined for me, but for example
you can just pass in a vector of values (1:3, etc. below) and this produces
the output array. I would name the vector something that means something
to me (temperature_vals = c(), etc.), and then pass that to multi.outer,
and the function will be applied (independent of what you name the
variables in the function).
Thanks again for your help. The responses are like a tutorial for me ...
Best,
Steve
list_args <- Vectorize( function(a,b) c( as.list(a), as.list(b) ),
+ SIMPLIFY = FALSE)
make_args_mtx <- function( alist ) {
+ Reduce(function(x, y) outer(x, y, list_args), alist)
+ }
multi.outer <- function(f, ... ) {
+ args <- make_args_mtx(list(...))
+ apply(args, 1:length(dim(args)), function(a) do.call(f, a[[1]] ) )
+ }
multi.outer(myfunc, 1:3, 2:6, 3:4)
, , 1
[,1] [,2] [,3] [,4] [,5]
[1,] 5 6 7 8 9
[2,] 7 9 11 13 15
[3,] 9 12 15 18 21
, , 2
[,1] [,2] [,3] [,4] [,5]
[1,] 6 7 8 9 10
[2,] 8 10 12 14 16
[3,] 10 13 16 19 22
On Sat, Sep 10, 2016 at 1:29 AM, Jeff Newmiller <jdnewmil at
dcn.davis.ca.us>
wrote:
> Not sure I understand what you really want, if you have found ways to
> accomplish what you want but are not satisfied with them. That is one
> reason why keeping the mailing list involved (by reply-all) is good for
> you. From my end, I don't do one-on-one support online, and may not be
able
> to carry on a thread to the end if I get busy.
>
> Your concept of a generalized outer function sounds to me like:
>
> myfunc <- function( A, B, C ) {
> A * B + C
> }
>
> gouter <- function( FUN, ... ) {
> args <- list( ... )
> DF <- do.call( expand.grid, args )
> array( data = do.call( FUN, DF )
> , dim = sapply( args, FUN=length )
> , dimnames = args
> )
> }
>
> gouter( myfunc, A = 1:3, B=2:6, C=3:4 )
> # , , C = 3
> #
> # B
> # A 2 3 4 5 6
> # 1 5 6 7 8 9
> # 2 7 9 11 13 15
> # 3 9 12 15 18 21
> #
> # , , C = 4
> #
> # B
> # A 2 3 4 5 6
> # 1 6 7 8 9 10
> # 2 8 10 12 14 16
> # 3 10 13 16 19 22
>
> I generally just tack on columns to the expand.grid result... I almost
> never have a need for multidimensional arrays.
>
> On Fri, 9 Sep 2016, Steve Kennedy wrote:
>
> Hello,
>>
>> Abstraction is what I want. I'm actually looking to do something
more
>> complicated. The functions do.call, and as.list get me most of the way
>> there, but there is something I'm missing ...
>>
>> My eventual goal is to produce a multi-dimensional version of
'outer'.
>> Like my.outer(func, a_vec, b_vec, c_vec, ..), where the function of the
>> variables 'a', 'b', 'c', etc. would be applied
to the vectors from the
>> outer product of the vectors of values for each variable.
>>
>> I wanted to use expand.grid (does require reshaping the output). Using
>> temps = c(40,50,60) and times = c(1:5), this doesn't quite seem to
work:
>>
>> apply(expand.grid(temps,times), 1, function(a) do.call(func2,
>> as.list(a)))
>>
>> although this does work:
>>
>> do.call(func2, as.list(c(10, 121)))
>>
>> And, this also works:
>>
>> apply(expand.grid(temps,times), 1, function(a) do.call("+",
as.list(a)))
>>
>> There is some subtlety here I don't understand.
>>
>> Thanks,
>>
>> Steve
>>
>> -----Original Message-----
>> From: Jeff Newmiller [mailto:jdnewmil at dcn.davis.ca.us]
>> Sent: Friday, September 09, 2016 5:39 PM
>> To: Steve Kennedy; r-help at r-project.org
>> Subject: Re: [R] Apply a multi-variable function to a vector
>>
>> Your architecture has a bad smell to me. For one thing you are mixing
>> different units in the same vector but should be putting multiple
instances
>> of the same variable into one vector. Lists of vectors (data frames)
are
>> typically used when multiple variables need to be grouped.
>>
>> Another problem is that you are constraining the names of the variables
>> you pass to the function to be named the same as they are inside the
>> function. This really limits your use of those functions.
>>
>> There really is too much abstraction going on here.
>> --
>> Sent from my phone. Please excuse my brevity.
>>
>> On September 9, 2016 12:44:52 PM PDT, Steve Kennedy
>> <SKennedy at AnikaTherapeutics.com> wrote:
>>
>>> Hello,
>>>
>>> I would like to define an arbitrary function of an arbitrary number
of
>>> variables, for example, for 2 variables:
>>>
>>> func2 <- function(time, temp) time + temp
>>>
>>> I'd like to keep variable names that have a meaning in the
problem
>>> (time and temperature above).
>>>
>>> If I have a vector of values for these variables, for example in
the
>>> 2-d case, c(10, 121), I'd like to apply my function (in this
case
>>> func2) and obtain the result. Conceptually, something like,
>>>
>>> func2(c(10,121))
>>>
>>> becomes
>>>
>>> func2(10,121)
>>>
>>> Is there a simple way to accomplish this, for an arbitrary number
of
>>> variables? I'd like something that would simply work from the
>>> definition of the function. If that is possible.
>>>
>>> Thanks,
>>>
>>> Steve Kennedy
>>>
>>> CONFIDENTIALITY NOTICE: This e-mail message, including
>>> a...{{dropped:11}}
>>>
>>> ______________________________________________
>>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more,
see
>>>
http://cp.mcafee.com/d/k-Kr6x0g6hASyMepov78FI6XCQXLK3AnCrFCQXLK3AnCnAPq
>>>
tTT1ObPdSjqaby8VMsUyYrEl-4fgb0HoiaXcDYtmZKsHkVsTI95tCj-eHuTelGsKrpYwCOw
>>>
evW_ccnpuKNRXBQQT1TfcFzCnTeEyCJtdmXP_axVZicHs3jq9JcTvANOoVcsCej76XCOsVH
>>>
kiPajSvvcCatoDwCHIcfBisEeRO9sDVWNIhgxVxmhUagJ3AdcOFRJVKxJBxdcS2_id41Fr1
>>> pFtd40wIIumd46Cy1lI-syVDoOQwvVEwtrxqsGMd44WCy3jh0p-QWNdLECZzL1
>>> PLEASE do read the posting guide
>>>
http://cp.mcafee.com/d/5fHCMUp418SyMepov78FI6XCQXLK3AnCrFCQXLK3AnCnAPqt
>>>
TT1ObPdSjqaby8VMsUyYrEl-4fgb0HoiaXcDYtmZKsHkVsTI95tCj-eHuTelGsKrpYwCOwe
>>>
vW_ccnpuKNRXBQQT1TfcFzCnTeEyCJtdmXP_axVZicHs3jqpJcTvANOoVcsCej76XCM0gbb
>>>
HhG8_qv00smHisE4iV5Ki7Y3zoyx3P2IzMkxq78qpBjHrPt3rb2qpI5-Aq83iS2PiWq811p
>>> oYIq8dd42HpYV5PeNBF0_Ph0WT2QVlwq89Rd46Cy0PZFRyrvhd_2KV
>>> and provide commented, minimal, self-contained, reproducible code.
>>>
>>
>> CONFIDENTIALITY NOTICE: This e-mail message, including any attachments,
>> contains information belonging to Anika Therapeutics, Inc. and is for
the
>> sole use of the intended recipient(s) and may contain confidential,
>> proprietary, copyrighted and privileged information. Any unauthorized
>> review, use, disclosure, distribution or copying is strictly
prohibited. If
>> you are not the intended recipient, please contact the sender by reply
>> e-mail and destroy all copies of the original message immediately.
>>
>>
> ------------------------------------------------------------
> ---------------
> Jeff Newmiller The ..... ..... Go Live...
> DCN:<jdnewmil at dcn.davis.ca.us> Basics: ##.#. ##.#.
Live
> Go...
> Live: OO#.. Dead: OO#.. Playing
> Research Engineer (Solar/Batteries O.O#. #.O#. with
> /Software/Embedded Controllers) .OO#. .OO#. rocks...1k
> ------------------------------------------------------------
> ---------------
>
[[alternative HTML version deleted]]
> I would like to define an arbitrary function of an arbitrary number of variables, > for example, for 2 variables: > > func2 <- function(time, temp) time + temp > > I'd like to keep variable names that have a meaning in the problem (time and > temperature above).Not quite enough information here. If we called func2(30, 298, 23) which has an arbitrary third argument, what would you like to happen to the third argument? And a fourth, fifth and so on? Something consistent for all arguments, or something different for each depending on its (arbitrary) name? S Ellison ******************************************************************* This email and any attachments are confidential. Any use...{{dropped:8}}