[R] large factorials

Gabor Grothendieck ggrothendieck at gmail.com
Thu Apr 23 16:57:07 CEST 2009 

One more improvement.  Perhaps it would be best just to return a numeric
so sum1 inputs and outputs numerics:

library(rSymPy)

# define factorial to return a Sym object
factorial.Sym <- function(n) Sym("factorial(", n, ")")

sum1 <- function(l,u,t,i,n,w) {
 v <- 0
 for (m in 0 :w) {
        v1 <- ((u^(1/2))*(l^(1/2))*t)^(i-n+2*m)
        v2 <- (factorial.Sym(i-n+m))*(factorial.Sym(m))
        v3 <- v1/v2
        v <- v+v3
 }

 as.numeric(sympy(v)) # send it to SymPy, make result a Sym obj

}

s <- sum1(1,2,10,80,3,80)
s # numeric


On Thu, Apr 23, 2009 at 10:44 AM, Gabor Grothendieck
<ggrothendieck at gmail.com> wrote:
> The code in my prior post works (except one comment was wrong)
> but try this instead.  The only change is the last line of the sum1
> function.   This way it produces a Sym object rather than a character
> string.
>
> library(rSymPy)
>
> # define factorial to return a Sym object
> factorial.Sym <- function(n) Sym("factorial(", n, ")")
>
> sum1 <- function(l,u,t,i,n,w) {
>  v <- 0
>  for (m in 0 :w) {
>         v1 <- ((u^(1/2))*(l^(1/2))*t)^(i-n+2*m)
>         v2 <- (factorial.Sym(i-n+m))*(factorial.Sym(m))
>         v3 <- v1/v2
>         v <- v+v3
>  }
>  Sym(sympy(v)) # send it to SymPy, make result a Sym obj
> }
>
> s <- sum1(1,2,10,80,3,80)
> s # Sym
> as.numeric(s) # numeric
>
>
> On Thu, Apr 23, 2009 at 10:37 AM, Gabor Grothendieck
> <ggrothendieck at gmail.com> wrote:
>> sympy() returns a character string, not an R numeric -- it shouldn't
>> automatically return an R numeric since R can't represent all
>> the numbers that sympy can.
>>
>> The development version of rSymPy has a second class which
>> produces objects of class c("Sym", "character") and those
>> can be manipulated with +, -, *, / producing other Sym
>> objects so try this:
>>
>>
>> library(rSymPy)
>>
>> # next line pulls in code to handle Sym objects
>> source("http://rsympy.googlecode.com/svn/trunk/R/Sym.R")
>>
>> # define factorial to return a Sym object
>> factorial.Sym <- function(n) Sym("factorial(", n, ")")
>>
>> sum1 <- function(l,u,t,i,n,w) {
>>  v <- 0
>>  for (m in 0 :w) {
>>         v1 <- ((u^(1/2))*(l^(1/2))*t)^(i-n+2*m)
>>         v2 <- (factorial.Sym(i-n+m))*(factorial.Sym(m))
>>         v3 <- v1/v2
>>         v <- v+v3
>>  }
>>  sympy(v)
>> }
>>
>> s <- sum1(1,2,10,80,3,80)
>> s # Sym object
>> as.numeric(s) # numeric
>>
>>
>> On Thu, Apr 23, 2009 at 10:00 AM, molinar <sky2k2 at hotmail.com> wrote:
>>>
>>> Here is what I did:
>>> library(rSymPy)
>>> factorial.sympy <- function(n) sympy(paste("factorial(", n, ")"))
>>> factorial.sympy(171)
>>> [1]
>>> "1241018070217667823424840524103103992616605577501693185388951803611996075221691752992751978120487585576464959501670387052809889858690710767331242032218484364310473577889968548278290754541561964852153468318044293239598173696899657235903947616152278558180061176365108428800000000000000000000000000000000000000000"
>>>>
>>> Which work perfectly.
>>>
>>> Here is one of my summation functions:
>>>
>>> sum1 <- function(l,u,t,i,n,w) {
>>> + v <- 0
>>> + for (m in 0 :w) {
>>> + v1 <- ((u^(1/2))*(l^(1/2))*t)^(i-n+2*m)
>>> + v2 <- (factorial.sympy(i-n+m))*(factorial.sympy(m))
>>> + v3 <- v1/v2
>>> + v <- v+v3
>>> + }
>>> + return(v)
>>> + }
>>>
>>> sum1(1,2,10,80,3,80)
>>> Error in (factorial.sympy(i - n + m)) * (factorial.sympy(m)) :
>>>  non-numeric argument to binary operator
>>>
>>> I'm not sure why it works when I do the factorial normally but when I call
>>> my function it doesn't work?
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>> molinar wrote:
>>>>
>>>> Thank you everyone all of your posts were very helpful.  I tried each one
>>>> and I think I have about 10 new packages installed.  The formula I need to
>>>> calculate did not involve any logarithms but infinite summations of
>>>> factorials, I'm sorry for not specifying.  I read some things about using
>>>> logarithms but I thought in my case I would have to do an e to the log and
>>>> by doing that R still gave me the same problems with numbers over 170.
>>>>
>>>> But I was able to get it to work by using the last post about the rsympy
>>>> packages.
>>>>
>>>> I tried downloading bc but I didn't know how to connect it to R, so R said
>>>> "could not find function bc".
>>>>
>>>> Thanks again for all of your help.
>>>> Samantha
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> Gabor Grothendieck wrote:
>>>>>
>>>>> Also the R sympy package can handle this:
>>>>>
>>>>>> library(rSymPy)
>>>>> Loading required package: rJava
>>>>>
>>>>>> factorial.sympy <- function(n) sympy(paste("factorial(", n, ")"))
>>>>>
>>>>>> # note that first time sympy is called it loads java, jython and sympy
>>>>>> # but on subsequent calls its faster.  So make a dummy call first.
>>>>>> factorial.sympy(10)
>>>>> [1] "3628800"
>>>>>
>>>>>> # code from earlier post defining factorial.bc to be inserted here
>>>>>
>>>>>>    benchmark(replications=10, columns=c('test', 'elapsed'),
>>>>> +       bc=factorial.bc(500),
>>>>> +       sympy = factorial.sympy(500))
>>>>>    test elapsed
>>>>> 1    bc    2.17
>>>>> 2 sympy    0.09
>>>>>
>>>>> See the rSymPy, r-bc and rbenchmark home pages:
>>>>> http://rsympy.googlecode.com
>>>>> http://r-bc.googlecode.com
>>>>> http://rbenchmark.googlecode.com
>>>>>
>>>>> On Wed, Apr 22, 2009 at 3:21 PM, molinar <sky2k2 at hotmail.com> wrote:
>>>>>>
>>>>>> I am working on a project that requires me to do very large factorial
>>>>>> evaluations.  On R the built in factorial function and the one I created
>>>>>> both are not able to do factorials over 170.  The first gives an error
>>>>>> and
>>>>>> mine return Inf.
>>>>>>
>>>>>> Is there a way to have R do these larger calculations (the calculator in
>>>>>> accessories can do 10000 factorial and Maple can do even larger)
>>>>>> --
>>>>>> View this message in context:
>>>>>> http://www.nabble.com/large-factorials-tp23175816p23175816.html
>>>>>> Sent from the R help mailing list archive at Nabble.com.
>>>>>>
>>>>>> ______________________________________________
>>>>>> R-help at r-project.org 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 at r-project.org 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.
>>>>>
>>>>>
>>>>
>>>>
>>>
>>> --
>>> View this message in context: http://www.nabble.com/large-factorials-tp23175816p23197344.html
>>> Sent from the R help mailing list archive at Nabble.com.
>>>
>>> ______________________________________________
>>> R-help at r-project.org 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.
>>>
>>
>

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