number of decimal places in a number?

15 messages
Open this post in threaded view
|
Report Content as Inappropriate

number of decimal places in a number?

 Dear R users, I need a function that gets a number and returns its number of actual decimal places. For example f(3.14) should return 2, f(3.142) should return 3, f(3.1400) should also return 2 and so on. Is such function already available in R? If not, could you give me a hint how to achieve that? Many thanks in advance. ----------------------------------------------------------------- Гражданска отговорност – Цените на компаниите http://www.sdi.bg/onlineInsurance/?utm_source=gbg&utm_medium=txtLink&utm_content=home______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
Open this post in threaded view
|
Report Content as Inappropriate

Re: number of decimal places in a number?

 On 07-Jul-2012 08:52:35 Martin Ivanov wrote: >  Dear R users, > > I need a function that gets a number and returns its number of > actual decimal places. > For example f(3.14) should return 2, f(3.142) should return 3, > f(3.1400) should also return 2 and so on. Is such function already > available in R? If not, could you give me a hint how to achieve that? > > Many thanks in advance. I'm not aware of such a function in R. In any case, it will be a tricky question to solve in full generality, since R stores numbers internally in a binary representation and the exact conversion of this representation to a decimal number may not match the exact value of the decimal representation of the original number. In particular, a number entered as a decimal representation from the keyboard, or read as such from a text file, may not be exactly matched by the internal representation in R. However, that said, the following function definition seems to do what you are asking for, for cases such as you list: f<-function(x) {min(which( x*10^(0:20)==floor(x*10^(0:20)) )) - 1}   f(3.14)   # [1] 2   f(3.142)   # [1] 3   f(3.1400)   # [1] 2 Note, however:   f(123456.123456789)   # [1] 9   f(123456789.123456789)   #[1] 7 (a consequence of the fact that R does not have enough binary digits in its binary representation to accommodate the precision in all the decimal digits of 123456789.123456789 -- not that it can do that exactly anyway in binary, no matter how many binary digits it had available). Similarly:   f(pi)   # [1] 15   f(sqrt(2))   # [1] 16 which is a consequence of the fact that 2 < pi < 4, while 1 < sqrt(2) < 2, so the binary representation of pi needs 1 more binary digit for its integer part than sqrt(2) does, which it therefore has to "steal" from the fractional part. Hoping this helps, Ted. ------------------------------------------------- E-Mail: (Ted Harding) <[hidden email]> Date: 07-Jul-2012  Time: 11:04:26 This message was sent by XFMail ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
Open this post in threaded view
|
Report Content as Inappropriate

Re: number of decimal places in a number?

 Hi Martin, Ted is spot on about the binary representation.  A very different approach from his would be to convert to character and use regular expressions: ## the example numbers in a vector x <- c(3.14, 3.142, 3.1400, 123456.123456789, 123456789.123456789, pi, sqrt(2)) nchar(gsub("(.*\\.)|([0]*\$)", "", as.character(x))) which for me returns: [1]  2  3  2  9  6 14 13 an advantage of this approach is that for numbers like 123456789.123456789, although R cannot represent it properly as a binary number, the character string is totally fine. nchar(gsub("(.*\\.)|([0]*\$)", "", "123456789.123456789")) returns 9 Essentially the expression looks for anything (the period) zero or more times (the *) followed by an actual period (the \\.) OR 0 repeated zero or more times at the end of the string, and replaces all of those with nothing (the "") and then returns the result, the number of characters of which is counted by nchar() See ?regex for details Cheers, Josh On Sat, Jul 7, 2012 at 3:04 AM, Ted Harding <[hidden email]> wrote: > On 07-Jul-2012 08:52:35 Martin Ivanov wrote: >>  Dear R users, >> >> I need a function that gets a number and returns its number of >> actual decimal places. >> For example f(3.14) should return 2, f(3.142) should return 3, >> f(3.1400) should also return 2 and so on. Is such function already >> available in R? If not, could you give me a hint how to achieve that? >> >> Many thanks in advance. > > I'm not aware of such a function in R. In any case, it will be > a tricky question to solve in full generality, since R stores > numbers internally in a binary representation and the exact > conversion of this representation to a decimal number may not > match the exact value of the decimal representation of the > original number. > > In particular, a number entered as a decimal representation > from the keyboard, or read as such from a text file, may not > be exactly matched by the internal representation in R. > > However, that said, the following function definition seems to > do what you are asking for, for cases such as you list: > > f<-function(x) {min(which( x*10^(0:20)==floor(x*10^(0:20)) )) - 1} > >   f(3.14) >   # [1] 2 >   f(3.142) >   # [1] 3 >   f(3.1400) >   # [1] 2 > > > > Note, however: > >   f(123456.123456789) >   # [1] 9 > >   f(123456789.123456789) >   #[1] 7 > > (a consequence of the fact that R does not have enough binary > digits in its binary representation to accommodate the precision > in all the decimal digits of 123456789.123456789 -- not that it > can do that exactly anyway in binary, no matter how many binary > digits it had available). > > Similarly: > >   f(pi) >   # [1] 15 >   f(sqrt(2)) >   # [1] 16 > > which is a consequence of the fact that 2 < pi < 4, while > 1 < sqrt(2) < 2, so the binary representation of pi needs > 1 more binary digit for its integer part than sqrt(2) does, > which it therefore has to "steal" from the fractional part. > > Hoping this helps, > Ted. > > ------------------------------------------------- > E-Mail: (Ted Harding) <[hidden email]> > Date: 07-Jul-2012  Time: 11:04:26 > This message was sent by XFMail > > ______________________________________________ > [hidden email] 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. -- Joshua Wiley Ph.D. Student, Health Psychology Programmer Analyst II, Statistical Consulting Group University of California, Los Angeles https://joshuawiley.com/______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
Open this post in threaded view
|
Report Content as Inappropriate

Re: number of decimal places in a number?

 I had thought of also (as well as my numerical routing) suggesting a "gsub()" type solution like Joshua's below, but held back because the result could depend on how the number arose (keyboard input, file input, or from computation within R). However, I now also realise that (again because of binary rounding errors), the "gsub()" method has interesting differences from my numerical method. Example: [A] (as from my original method):   f(123456789.123456789)   # [1] 7 [B] (the "gsub()" method)   nchar(gsub("(.*\\.)|([0]*\$)", "", as.character(123456789.123456789)))   # [1] 6 Now look at: [C] (what as.character() does to 123456789.123456789)   as.character(123456789.123456789)   # [1] "123456789.123457" [D] ("22" is the maximum number of decimal digits for print())   print(123456789.123456789,22)   # [1] 123456789.1234568 So as.character() has rounded it to 6 decimal places (agreeing with [B]), while using print() with the maximum of 22 digits (more than enough for the 18 digits in 123456789.123456789) rounds it to 7 decimal places (i.e. 16 digits in all), which is about the limit (depending on the magnitude of the number) that R can hold internally; this agrees with [A]. Note the difference between [D] ("22" is the maximum number of decimal digits for print())   print(123456789.123456789,22)   # [1] 123456789.1234568 [E] (similar, but with a different magnitude)   print(923456789.123456789,22)   # [1] 923456789.123457 (compare with [C]). So, clearly, there is potential uncertainty in the ouput from either method, but perhaps there is somewhat more uncertainty with the "gsub()" method. Also, another nasty little trap with "gsub()": [F] (my method)   f(0.0000012345)   # [1] 10 [G] ("gsub()" method)   nchar(gsub("(.*\\.)|([0]*\$)", "", as.character(0.0000012345)))   # [1] 8 which arises because:   as.character(0.0000012345)   # [1] "1.2345e-06" There would seem to be no clean general solution to this question. An important issue would be: What use do you want to put the result to? If there is something in the logic of your application which depends critically on the numbers of decimal places in its numerical input, then the final result could be completey wrong because of these uncertainties. In such a case, it might be best to force initial input to be of character format. For example, if reading numerical data into a dataframe from (say) a CSV file, then the option Data <- read.csv("datafile.csv",colClasses="character") (or similar) would convert all numerical data into the equivalent character formats. Then Joshua's "gsub()" method would always give exactly the right result when applied to these character strings. Then, having got that out of the way, you can convert the character strings into numeric (to within the precision that R will allow). However, if something in the logic depends critically on the numbers of "decimal places" in numbers computed internally by R, then I think the case is hopeless! Ted. On 07-Jul-2012 10:44:55 Joshua Wiley wrote: > Hi Martin, > > Ted is spot on about the binary representation.  A very different > approach from his would be to convert to character and use regular > expressions: > >## the example numbers in a vector > x <- c(3.14, 3.142, 3.1400, 123456.123456789, 123456789.123456789, pi, > sqrt(2)) > > nchar(gsub("(.*\\.)|([0]*\$)", "", as.character(x))) > > which for me returns: > [1]  2  3  2  9  6 14 13 > > an advantage of this approach is that for numbers like > 123456789.123456789, although R cannot represent it properly as a > binary number, the character string is totally fine. > > nchar(gsub("(.*\\.)|([0]*\$)", "", "123456789.123456789")) > > returns 9 > > Essentially the expression looks for anything (the period) zero or > more times (the *) followed by an actual period (the \\.) OR 0 > repeated zero or more times at the end of the string, and replaces all > of those with nothing (the "") and then returns the result, the number > of characters of which is counted by nchar() > > See ?regex for details > > Cheers, > > Josh > > On Sat, Jul 7, 2012 at 3:04 AM, Ted Harding <[hidden email]> wrote: >> On 07-Jul-2012 08:52:35 Martin Ivanov wrote: >>>  Dear R users, >>> >>> I need a function that gets a number and returns its number of >>> actual decimal places. >>> For example f(3.14) should return 2, f(3.142) should return 3, >>> f(3.1400) should also return 2 and so on. Is such function already >>> available in R? If not, could you give me a hint how to achieve that? >>> >>> Many thanks in advance. >> >> I'm not aware of such a function in R. In any case, it will be >> a tricky question to solve in full generality, since R stores >> numbers internally in a binary representation and the exact >> conversion of this representation to a decimal number may not >> match the exact value of the decimal representation of the >> original number. >> >> In particular, a number entered as a decimal representation >> from the keyboard, or read as such from a text file, may not >> be exactly matched by the internal representation in R. >> >> However, that said, the following function definition seems to >> do what you are asking for, for cases such as you list: >> >> f<-function(x) {min(which( x*10^(0:20)==floor(x*10^(0:20)) )) - 1} >> >>   f(3.14) >>   # [1] 2 >>   f(3.142) >>   # [1] 3 >>   f(3.1400) >>   # [1] 2 >> >> >> >> Note, however: >> >>   f(123456.123456789) >>   # [1] 9 >> >>   f(123456789.123456789) >>   #[1] 7 >> >> (a consequence of the fact that R does not have enough binary >> digits in its binary representation to accommodate the precision >> in all the decimal digits of 123456789.123456789 -- not that it >> can do that exactly anyway in binary, no matter how many binary >> digits it had available). >> >> Similarly: >> >>   f(pi) >>   # [1] 15 >>   f(sqrt(2)) >>   # [1] 16 >> >> which is a consequence of the fact that 2 < pi < 4, while >> 1 < sqrt(2) < 2, so the binary representation of pi needs >> 1 more binary digit for its integer part than sqrt(2) does, >> which it therefore has to "steal" from the fractional part. >> >> Hoping this helps, >> Ted. >> >> ------------------------------------------------- >> E-Mail: (Ted Harding) <[hidden email]> >> Date: 07-Jul-2012  Time: 11:04:26 >> This message was sent by XFMail >> >> ______________________________________________ >> [hidden email] 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. > > > > -- > Joshua Wiley > Ph.D. Student, Health Psychology > Programmer Analyst II, Statistical Consulting Group > University of California, Los Angeles > https://joshuawiley.com/------------------------------------------------- E-Mail: (Ted Harding) <[hidden email]> Date: 07-Jul-2012  Time: 13:12:31 This message was sent by XFMail ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
Open this post in threaded view
|
Report Content as Inappropriate

Re: number of decimal places in a number?

 In reply to this post by Martin Ivanov  Dear Mr Harding, Thank You very much for Your responsiveness.  >There would seem to be no clean general solution to this  >question. An important issue would be: What use do you  >want to put the result to?   I need this trick for the following task. I am writing a function which has to determine the bounding box for a spatial data set. The bounding box is a matrix(c(minLon minLat, maxLon, maxLat)). I have the longitudes (lon) and latitudes (lat), and I have a resolution (r), for example r = 0.004. The bounding box must have the same number of digits as resolution. So I first have to truncate min(lon) and min(lat) to 3 decimal places, then take the ceiling of max(lat)*10^3 and max(lon)*10^3 divided by 10^3. So I have the maximal interval with resolution r for each variable (lat or lon). Then I have to determine the number of cells in each direction, which I take as ceiling((maxLat-minLat)/r) and ceiling((maxLon-minLon)/r). Here is an example of my code:  # get the first n digits from a number truncf <- function(x, digits) {  # some control:  for(i in c("x", "digits")) if(!(is.numeric(get(i)) && length(get(i)) == 1)) stop(i, " in truncatef must be a  numeric scalar!");  ## make sure that digits is an integer:  if(as.integer(digits) - digits) stop("Please provide an integer digits to truncf!");  x <- trunc(x*10^digits)/10^digits;  x; }  for(i in 0:5) if(!(resolution*10^i - as.integer(resolution*10^i))) break;  lonMin <- truncf(x=min(lon), digits=i); lonMax <- ceiling(x=max(lon)*10^i)/10^i;  latMin <- truncf(min(lat), digits=i); latMax <- ceiling(x=max(lat)*10^i)/10^i;  cells.dim <- ceiling(c(lonMax - lonMin, latMax - latMin)/resolution);     I hope this sheds more light on my issue. Best regards, Martin ----------------------------------------------------------------- Гражданска отговорност – Цените на компаниите http://www.sdi.bg/onlineInsurance/?utm_source=gbg&utm_medium=txtLink&utm_content=home______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
Open this post in threaded view
|
Report Content as Inappropriate

Re: number of decimal places in a number?

 In reply to this post by ted.harding-3 Hi, I checked the count for the cases (A) and (F) with a variant of Josh's function: decimalnumcount<-function(x){stopifnot(class(x)=="character")  x<-gsub("(.*)(\\.)|([0]*\$)","",x)  nchar(x)  }  A) x<-"123456789.123456789"  decimalnumcount(x) #[1] 9 x<-"923456789.123456789" decimalnumcount(x) #[1] 9 B)  x<-"0.0000012345"  decimalnumcount(x) #[1] 10 c) x <- c("3.14", "3.142", "3.1400", "123456.123456789", "123456789.123456789",pi,sqrt(2))   decimalnumcount(x) #[1]  2  3  2  9  9 14 13 x [1] "3.14"                "3.142"               "3.1400"             [4] "123456.123456789"    "123456789.123456789" "3.14159265358979"   [7] "1.4142135623731"    D)  x <- c(3.14, 3.142, 3.1400, 123456.123456789, 123456789.123456789,pi,sqrt(2)) decimalnumcount(as.character(x) ) [1]  2  3  2  9  6 14 13 #as.character(x) #[1] "3.14"             "3.142"            "3.14"             "123456.123456789" #[5] "123456789.123457" "3.14159265358979" "1.4142135623731" E) print(pi,22) #[1] 3.141592653589793115998 print(sqrt(2),22) #[1] 1.414213562373095145475     x <- c("3.14", "3.142", "3.1400", "123456.123456789", "123456789.123456789","3.141592653589793115998","1.414213562373095145475")  decimalnumcount(x) #[1]  2  3  2  9  9 21 21 F) formatC(pi,format="f",digits=22) #[1] "3.1415926535897931159980"  formatC(sqrt(2),format="f",digits=22) #[1] "1.4142135623730951454746"  x <- c("3.14", "3.142", "3.1400", "123456.123456789", "123456789.123456789",formatC(pi,format="f",digits=22),formatC(sqrt(2),format="f",digits=22))  decimalnumcount(x) #[1]  2  3  2  9  9 21 22 G) #  formatC() didn't show the limitations of print()  print(sqrt(2),22) #[1] 1.414213562373095145475 print(sqrt(2),35) #Error in print.default(sqrt(2), 35) : invalid 'digits' argument formatC(sqrt(2),35) #[1] "1.4142135623730951454746218587388285" or, formatC(sqrt(2),format="f",digits=35) #[1] "1.41421356237309514547462185873882845" #using >22 x <- c("3.14", "3.142", "3.1400", "123456.123456789", "123456789.123456789",formatC(pi,format="f",digits=35),formatC(sqrt(2),format="f",digits=50))  decimalnumcount(x) #[1]  2  3  2  9  9 35 50 So, I guess it will be better to deal with character strings rather than using as.character. A.K. ----- Original Message ----- From: "[hidden email]" <[hidden email]> To: [hidden email] Cc: Martin Ivanov <[hidden email]> Sent: Saturday, July 7, 2012 8:12 AM Subject: Re: [R] number of decimal places in a number? I had thought of also (as well as my numerical routing) suggesting a "gsub()" type solution like Joshua's below, but held back because the result could depend on how the number arose (keyboard input, file input, or from computation within R). However, I now also realise that (again because of binary rounding errors), the "gsub()" method has interesting differences from my numerical method. Example: [A] (as from my original method):   f(123456789.123456789)   # [1] 7 [B] (the "gsub()" method)   nchar(gsub("(.*\\.)|([0]*\$)", "", as.character(123456789.123456789)))   # [1] 6 Now look at: [C] (what as.character() does to 123456789.123456789)   as.character(123456789.123456789)   # [1] "123456789.123457" [D] ("22" is the maximum number of decimal digits for print())   print(123456789.123456789,22)   # [1] 123456789.1234568 So as.character() has rounded it to 6 decimal places (agreeing with [B]), while using print() with the maximum of 22 digits (more than enough for the 18 digits in 123456789.123456789) rounds it to 7 decimal places (i.e. 16 digits in all), which is about the limit (depending on the magnitude of the number) that R can hold internally; this agrees with [A]. Note the difference between [D] ("22" is the maximum number of decimal digits for print())   print(123456789.123456789,22)   # [1] 123456789.1234568 [E] (similar, but with a different magnitude)   print(923456789.123456789,22)   # [1] 923456789.123457 (compare with [C]). So, clearly, there is potential uncertainty in the ouput from either method, but perhaps there is somewhat more uncertainty with the "gsub()" method. Also, another nasty little trap with "gsub()": [F] (my method)   f(0.0000012345)   # [1] 10 [G] ("gsub()" method)   nchar(gsub("(.*\\.)|([0]*\$)", "", as.character(0.0000012345)))   # [1] 8 which arises because:   as.character(0.0000012345)   # [1] "1.2345e-06" There would seem to be no clean general solution to this question. An important issue would be: What use do you want to put the result to? If there is something in the logic of your application which depends critically on the numbers of decimal places in its numerical input, then the final result could be completey wrong because of these uncertainties. In such a case, it might be best to force initial input to be of character format. For example, if reading numerical data into a dataframe from (say) a CSV file, then the option Data <- read.csv("datafile.csv",colClasses="character") (or similar) would convert all numerical data into the equivalent character formats. Then Joshua's "gsub()" method would always give exactly the right result when applied to these character strings. Then, having got that out of the way, you can convert the character strings into numeric (to within the precision that R will allow). However, if something in the logic depends critically on the numbers of "decimal places" in numbers computed internally by R, then I think the case is hopeless! Ted. On 07-Jul-2012 10:44:55 Joshua Wiley wrote: > Hi Martin, > > Ted is spot on about the binary representation.  A very different > approach from his would be to convert to character and use regular > expressions: > >## the example numbers in a vector > x <- c(3.14, 3.142, 3.1400, 123456.123456789, 123456789.123456789, pi, > sqrt(2)) > > nchar(gsub("(.*\\.)|([0]*\$)", "", as.character(x))) > > which for me returns: > [1]  2  3  2  9  6 14 13 > > an advantage of this approach is that for numbers like > 123456789.123456789, although R cannot represent it properly as a > binary number, the character string is totally fine. > > nchar(gsub("(.*\\.)|([0]*\$)", "", "123456789.123456789")) > > returns 9 > > Essentially the expression looks for anything (the period) zero or > more times (the *) followed by an actual period (the \\.) OR 0 > repeated zero or more times at the end of the string, and replaces all > of those with nothing (the "") and then returns the result, the number > of characters of which is counted by nchar() > > See ?regex for details > > Cheers, > > Josh > > On Sat, Jul 7, 2012 at 3:04 AM, Ted Harding <[hidden email]> wrote: >> On 07-Jul-2012 08:52:35 Martin Ivanov wrote: >>>  Dear R users, >>> >>> I need a function that gets a number and returns its number of >>> actual decimal places. >>> For example f(3.14) should return 2, f(3.142) should return 3, >>> f(3.1400) should also return 2 and so on. Is such function already >>> available in R? If not, could you give me a hint how to achieve that? >>> >>> Many thanks in advance. >> >> I'm not aware of such a function in R. In any case, it will be >> a tricky question to solve in full generality, since R stores >> numbers internally in a binary representation and the exact >> conversion of this representation to a decimal number may not >> match the exact value of the decimal representation of the >> original number. >> >> In particular, a number entered as a decimal representation >> from the keyboard, or read as such from a text file, may not >> be exactly matched by the internal representation in R. >> >> However, that said, the following function definition seems to >> do what you are asking for, for cases such as you list: >> >> f<-function(x) {min(which( x*10^(0:20)==floor(x*10^(0:20)) )) - 1} >> >>   f(3.14) >>   # [1] 2 >>   f(3.142) >>   # [1] 3 >>   f(3.1400) >>   # [1] 2 >> >> >> >> Note, however: >> >>   f(123456.123456789) >>   # [1] 9 >> >>   f(123456789.123456789) >>   #[1] 7 >> >> (a consequence of the fact that R does not have enough binary >> digits in its binary representation to accommodate the precision >> in all the decimal digits of 123456789.123456789 -- not that it >> can do that exactly anyway in binary, no matter how many binary >> digits it had available). >> >> Similarly: >> >>   f(pi) >>   # [1] 15 >>   f(sqrt(2)) >>   # [1] 16 >> >> which is a consequence of the fact that 2 < pi < 4, while >> 1 < sqrt(2) < 2, so the binary representation of pi needs >> 1 more binary digit for its integer part than sqrt(2) does, >> which it therefore has to "steal" from the fractional part. >> >> Hoping this helps, >> Ted. >> >> ------------------------------------------------- >> E-Mail: (Ted Harding) <[hidden email]> >> Date: 07-Jul-2012  Time: 11:04:26 >> This message was sent by XFMail >> >> ______________________________________________ >> [hidden email] 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. > > > > -- > Joshua Wiley > Ph.D. Student, Health Psychology > Programmer Analyst II, Statistical Consulting Group > University of California, Los Angeles > https://joshuawiley.com/------------------------------------------------- E-Mail: (Ted Harding) <[hidden email]> Date: 07-Jul-2012  Time: 13:12:31 This message was sent by XFMail ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code. ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
Open this post in threaded view
|
Report Content as Inappropriate

Re: number of decimal places in a number?

 In reply to this post by Martin Ivanov mod Ted's comments, I believe that for your situation (not too many digits to represent, decimal point always present) countDecDigits <- function(x)nchar(sapply(strsplit(as.character(x),"\\."),"[",2)) is simple and should work. No need for regular expressions here. -- Bert On Sat, Jul 7, 2012 at 6:52 AM, Martin Ivanov <[hidden email]> wrote: >  Dear Mr Harding, > > Thank You very much for Your responsiveness. > >  >There would seem to be no clean general solution to this >  >question. An important issue would be: What use do you >  >want to put the result to? > > I need this trick for the following task. > I am writing a function which has to determine the bounding box for a > spatial data set. The bounding box is a matrix(c(minLon minLat, maxLon, > maxLat)). > I have the longitudes (lon) and latitudes (lat), and I have a resolution > (r), for example > r = 0.004. The bounding box must have the same number of digits as > resolution. > So I first have to truncate min(lon) and min(lat) to 3 decimal places, > then take the ceiling of max(lat)*10^3 and max(lon)*10^3 divided by 10^3. > So I have the > maximal interval with resolution r for each variable (lat or lon). Then I > have to determine > the number of cells in each direction, which I take as > ceiling((maxLat-minLat)/r) and > ceiling((maxLon-minLon)/r). Here is an example of my code: > >  # get the first n digits from a number > truncf <- function(x, digits) { >  # some control: >  for(i in c("x", "digits")) if(!(is.numeric(get(i)) && length(get(i)) == > 1)) stop(i, " in truncatef must be a  numeric scalar!"); >  ## make sure that digits is an integer: >  if(as.integer(digits) - digits) stop("Please provide an integer digits to > truncf!"); > >  x <- trunc(x*10^digits)/10^digits; >  x; > } >  for(i in 0:5) if(!(resolution*10^i - as.integer(resolution*10^i))) break; >  lonMin <- truncf(x=min(lon), digits=i); lonMax <- > ceiling(x=max(lon)*10^i)/10^i; >  latMin <- truncf(min(lat), digits=i); latMax <- > ceiling(x=max(lat)*10^i)/10^i; >  cells.dim <- ceiling(c(lonMax - lonMin, latMax - latMin)/resolution); > > > I hope this sheds more light on my issue. > > Best regards, > Martin > > ----------------------------------------------------------------- > Ãðàæäàíñêà îòãîâîðíîñò  Öåíèòå íà êîìïàíèèòå > > http://www.sdi.bg/onlineInsurance/?utm_source=gbg&utm_medium=txtLink&utm_content=home> > ______________________________________________ > [hidden email] 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. > -- Bert Gunter Genentech Nonclinical Biostatistics Internal Contact Info: Phone: 467-7374 Website: http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm        [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
Open this post in threaded view
|
Report Content as Inappropriate

Re: number of decimal places in a number?

 In reply to this post by ted.harding-3 On Sat, Jul 07, 2012 at 01:12:34PM +0100, Ted Harding wrote: > I had thought of also (as well as my numerical routing) suggesting > a "gsub()" type solution like Joshua's below, but held back because > the result could depend on how the number arose (keyboard input, > file input, or from computation within R). > > However, I now also realise that (again because of binary rounding > errors), the "gsub()" method has interesting differences from my > numerical method. Example: > > [A] (as from my original method): >   f(123456789.123456789) >   # [1] 7 > > [B] (the "gsub()" method) >   nchar(gsub("(.*\\.)|([0]*\$)", "", as.character(123456789.123456789))) >   # [1] 6 > > Now look at: > > [C] (what as.character() does to 123456789.123456789) >   as.character(123456789.123456789) >   # [1] "123456789.123457" > > [D] ("22" is the maximum number of decimal digits for print()) >   print(123456789.123456789,22) >   # [1] 123456789.1234568 > > So as.character() has rounded it to 6 decimal places (agreeing > with [B]), while using print() with the maximum of 22 digits > (more than enough for the 18 digits in 123456789.123456789) > rounds it to 7 decimal places (i.e. 16 digits in all), which Hi. This difference is due to rounding to 15 digits in as.character(). This function rounds to 15 decimal digits, which is the maximum number of digits, which can always be converted to binary and back. Function print(, digits=22) prints the decimal equivalent of the represented number. So, it is more accurate, but its output may contain digits, which are purely the consequence of inaccuracy of the representation. The same output as from print(, digits=17) may be obtained using    sprintf("%20.17f", x) Of course, if the required number of digits is close to 17 or even more, the last digits are the last digits of the represented number, not of the intended result of the computation. Hope this helps. Petr Savicky. ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
Open this post in threaded view
|
Report Content as Inappropriate

Re: number of decimal places in a number?

 Hi Petr, I think sprintf and formatC are identical as it can round >22 decimal places as opposed to print and signif print(pi,digits=35) Error in print.default(pi, digits = 35) : invalid 'digits' argument  signif(pi,digits=22) [1] 3.141593 a<-sprintf("%.35f",pi) a [1] "3.14159265358979311599796346854418516" b<-formatC(pi,digits=36)  b [1] "3.14159265358979311599796346854418516"  identical(a,b) [1] TRUE identical(a,signif(pi,digits=35)) [1] FALSE A.K. ----- Original Message ----- From: Petr Savicky <[hidden email]> To: [hidden email] Cc: Sent: Sunday, July 8, 2012 2:21 PM Subject: Re: [R] number of decimal places in a number? On Sat, Jul 07, 2012 at 01:12:34PM +0100, Ted Harding wrote: > I had thought of also (as well as my numerical routing) suggesting > a "gsub()" type solution like Joshua's below, but held back because > the result could depend on how the number arose (keyboard input, > file input, or from computation within R). > > However, I now also realise that (again because of binary rounding > errors), the "gsub()" method has interesting differences from my > numerical method. Example: > > [A] (as from my original method): >   f(123456789.123456789) >   # [1] 7 > > [B] (the "gsub()" method) >   nchar(gsub("(.*\\.)|([0]*\$)", "", as.character(123456789.123456789))) >   # [1] 6 > > Now look at: > > [C] (what as.character() does to 123456789.123456789) >   as.character(123456789.123456789) >   # [1] "123456789.123457" > > [D] ("22" is the maximum number of decimal digits for print()) >   print(123456789.123456789,22) >   # [1] 123456789.1234568 > > So as.character() has rounded it to 6 decimal places (agreeing > with [B]), while using print() with the maximum of 22 digits > (more than enough for the 18 digits in 123456789.123456789) > rounds it to 7 decimal places (i.e. 16 digits in all), which Hi. This difference is due to rounding to 15 digits in as.character(). This function rounds to 15 decimal digits, which is the maximum number of digits, which can always be converted to binary and back. Function print(, digits=22) prints the decimal equivalent of the represented number. So, it is more accurate, but its output may contain digits, which are purely the consequence of inaccuracy of the representation. The same output as from print(, digits=17) may be obtained using    sprintf("%20.17f", x) Of course, if the required number of digits is close to 17 or even more, the last digits are the last digits of the represented number, not of the intended result of the computation. Hope this helps. Petr Savicky. ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code. ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
Open this post in threaded view
|
Report Content as Inappropriate

Re: number of decimal places in a number?

 On Sun, Jul 08, 2012 at 11:39:22AM -0700, arun wrote: > Hi Petr, > > I think sprintf and formatC are identical as it can round >22 decimal places as opposed to print and signif > print(pi,digits=35) Hi Arun: Thank you for pointing this out. Funtion formatC() is easier to use and uses the same C level function as sprintf(). Petr. ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
Open this post in threaded view
|
Report Content as Inappropriate

Re: number of decimal places in a number?

 In reply to this post by Martin Ivanov On Sat, Jul 07, 2012 at 11:52:35AM +0300, Martin Ivanov wrote: >  Dear R users, > > I need a function that gets a number and returns its number of actual decimal places. > For example f(3.14) should return 2, f(3.142) should return 3, f(3.1400) should also return 2 > and so on. Is such function already available in R? If not, could you give me a hint how to achieve that? Hi. Try the following.   getDigits <- function(x)   {       out <- format.info(x, digits=10)       stopifnot(out[3] == 0)       out[2]   } The function format.info() rounds the input number to "digits" significant digits and then outputs the width of the field for printing, the number of digits after the decimal dot and some information on the exponent (out[3] == 0, if exponent is not used). So, the required number of digits in the fractional part is out[2].   getDigits(3.123456)   [1] 6 Hope this helps. Petr Savicky. ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
Open this post in threaded view
|
Report Content as Inappropriate

Re: number of decimal places in a number?

 In reply to this post by Martin Ivanov   > -----Original Message----- > From:  Martin Ivanov > I have the longitudes (lon) and latitudes (lat), and I have a > resolution (r), for example r = 0.004. The bounding box must > have the same number of digits as resolution. Surely the issue is not the particular numeric resolution of the numbers but the idea that the bounding box limits should be integer multiples of the resolution? Is that not accomplished more straightforwardly by things like  min <- resol * floor( min(lat)/resol )  max <- resol * ceil( max(lat)/resol ) ? S Ellison******************************************************************* This email and any attachments are confidential. Any use...{{dropped:8}} ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
Open this post in threaded view
|
Report Content as Inappropriate

Re: number of decimal places in a number?

 In reply to this post by arun kirshna I don't know how significant this is, but WolframAlpha's value of pi disagrees with R's at about the 16th decimal:   Wpi->3.141592653589793238462643383279502884197169399375105 ......................^ Rpi->3.14159265358979311599796346854418516 Probably not of interest to anyone but astronomers, nanotechnologists, and us anal lurkers though. We went to the moon and back on two decimal places. Jim Plante On Jul 8, 2012, at 1:39 PM, arun wrote: > Hi Petr, > > I think sprintf and formatC are identical as it can round >22 decimal places as opposed to print and signif > print(pi,digits=35) > Error in print.default(pi, digits = 35) : invalid 'digits' argument >  signif(pi,digits=22) > [1] 3.141593 > a<-sprintf("%.35f",pi) > a > [1] "3.14159265358979311599796346854418516" > b<-formatC(pi,digits=36) >  b > [1] "3.14159265358979311599796346854418516" > >  identical(a,b) > [1] TRUE > > > identical(a,signif(pi,digits=35)) > [1] FALSE > > > A.K. > > > > ----- Original Message ----- > From: Petr Savicky <[hidden email]> > To: [hidden email] > Cc: > Sent: Sunday, July 8, 2012 2:21 PM > Subject: Re: [R] number of decimal places in a number? > > On Sat, Jul 07, 2012 at 01:12:34PM +0100, Ted Harding wrote: >> I had thought of also (as well as my numerical routing) suggesting >> a "gsub()" type solution like Joshua's below, but held back because >> the result could depend on how the number arose (keyboard input, >> file input, or from computation within R). >> >> However, I now also realise that (again because of binary rounding >> errors), the "gsub()" method has interesting differences from my >> numerical method. Example: >> >> [A] (as from my original method): >>    f(123456789.123456789) >>    # [1] 7 >> >> [B] (the "gsub()" method) >>    nchar(gsub("(.*\\.)|([0]*\$)", "", as.character(123456789.123456789))) >>    # [1] 6 >> >> Now look at: >> >> [C] (what as.character() does to 123456789.123456789) >>    as.character(123456789.123456789) >>    # [1] "123456789.123457" >> >> [D] ("22" is the maximum number of decimal digits for print()) >>    print(123456789.123456789,22) >>    # [1] 123456789.1234568 >> >> So as.character() has rounded it to 6 decimal places (agreeing >> with [B]), while using print() with the maximum of 22 digits >> (more than enough for the 18 digits in 123456789.123456789) >> rounds it to 7 decimal places (i.e. 16 digits in all), which > > Hi. > > This difference is due to rounding to 15 digits in as.character(). > This function rounds to 15 decimal digits, which is the maximum > number of digits, which can always be converted to binary > and back. Function print(, digits=22) prints the decimal > equivalent of the represented number. So, it is more accurate, but > its output may contain digits, which are purely the consequence > of inaccuracy of the representation. > > The same output as from print(, digits=17) may be obtained > using > >    sprintf("%20.17f", x) > > Of course, if the required number of digits is close to 17 or > even more, the last digits are the last digits of the represented > number, not of the intended result of the computation. > > Hope this helps. > > Petr Savicky. > > ______________________________________________ > [hidden email] 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. > > > ______________________________________________ > [hidden email] 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. ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
Open this post in threaded view
|
Report Content as Inappropriate

Re: number of decimal places in a number?

 On Mon, Jul 09, 2012 at 07:52:18AM -0500, Jim Plante wrote: > I don't know how significant this is, but WolframAlpha's value of pi disagrees with R's at about the 16th decimal: >   > Wpi->3.141592653589793238462643383279502884197169399375105 > ......................^ > Rpi->3.14159265358979311599796346854418516 > > Probably not of interest to anyone but astronomers, nanotechnologists, and us anal lurkers though. We went to the moon and back on two decimal places. Hi. This does not belong to this thread. The reason for the difference is explained in ?double   Double-precision values:      All R platforms are required to work with values conforming to the      IEC 60559 (also known as IEEE 754) standard.  This basically works      with a precision of 53 bits, and represents to that precision a      range of absolute values from about 2e-308 to 2e+308. Pi in binary is   (11.001001000011111101101010100010001000010110100011000)01000110100110001001100011001... and the brackets separate the first 53 significant bits. So, the double precision pi, which is represented by these bits, is slightly smaller than the exact value. The difference is not specific to R, but to the standard computer arithmetic implemented in the hardware, which uses 53 bits. Hope this helps. Petr Savicky. P.S. If you want to make further comments, please, open a new thread. ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.